Non-linear flow law of rockglacier creep determined from geomorphological observations: A case study from the Murtèl rockglacier (Engadin, SE Switzerland)

NASA Astrophysics Data System (ADS)

Frehner, Marcel; Amschwand, Dominik; Gärtner-Roer, Isabelle

2016-04-01

Rockglaciers consist of unconsolidated rock fragments (silt/sand-rock boulders) with interstitial ice; hence their creep behavior (i.e., rheology) may deviate from the simple and well-known flow-laws for pure ice. Here we constrain the non-linear viscous flow law that governs rockglacier creep based on geomorphological observations. We use the Murtèl rockglacier (upper Engadin valley, SE Switzerland) as a case study, for which high-resolution digital elevation models (DEM), time-lapse borehole deformation data, and geophysical soundings exist that reveal the exterior and interior architecture and dynamics of the landform. Rockglaciers often feature a prominent furrow-and-ridge topography. For the Murtèl rockglacier, Frehner et al. (2015) reproduced the wavelength, amplitude, and distribution of the furrow-and-ridge morphology using a linear viscous (Newtonian) flow model. Arenson et al. (2002) presented borehole deformation data, which highlight the basal shear zone at about 30 m depth and a curved deformation profile above the shear zone. Similarly, the furrow-and-ridge morphology also exhibits a curved geometry in map view. Hence, the surface morphology and the borehole deformation data together describe a curved 3D geometry, which is close to, but not quite parabolic. We use a high-resolution DEM to quantify the curved geometry of the Murtèl furrow-and-ridge morphology. We then calculate theoretical 3D flow geometries using different non-linear viscous flow laws. By comparing them to the measured curved 3D geometry (i.e., both surface morphology and borehole deformation data), we can determine the most adequate flow-law that fits the natural data best. Linear viscous models result in perfectly parabolic flow geometries; non-linear creep leads to localized deformation at the sides and bottom of the rockglacier while the deformation in the interior and top are less intense. In other words, non-linear creep results in non-parabolic flow geometries. Both the linear (power-law exponent, n=1) and strongly non-linear models (n=10) do not match the measured data well. However, the moderately non-linear models (n=2-3) match the data quite well indicating that the creep of the Murtèl rockglacier is governed by a moderately non-linear viscous flow law with a power-law exponent close to the one of pure ice. Our results are crucial for improving existing numerical models of rockglacier flow that currently use simplified (i.e., linear viscous) flow-laws. References: Arenson L., Hoelzle M., and Springman S., 2002: Borehole deformation measurements and internal structure of some rock glaciers in Switzerland, Permafrost and Periglacial Processes 13, 117-135. Frehner M., Ling A.H.M., and Gärtner-Roer I., 2015: Furrow-and-ridge morphology on rockglaciers explained by gravity-driven buckle folding: A case study from the Murtèl rockglacier (Switzerland), Permafrost and Periglacial Processes 26, 57-66.

Development of a multiple-parameter nonlinear perturbation procedure for transonic turbomachinery flows: Preliminary application to design/optimization problems

NASA Technical Reports Server (NTRS)

Stahara, S. S.; Elliott, J. P.; Spreiter, J. R.

1983-01-01

An investigation was conducted to continue the development of perturbation procedures and associated computational codes for rapidly determining approximations to nonlinear flow solutions, with the purpose of establishing a method for minimizing computational requirements associated with parametric design studies of transonic flows in turbomachines. The results reported here concern the extension of the previously developed successful method for single parameter perturbations to simultaneous multiple-parameter perturbations, and the preliminary application of the multiple-parameter procedure in combination with an optimization method to blade design/optimization problem. In order to provide as severe a test as possible of the method, attention is focused in particular on transonic flows which are highly supercritical. Flows past both isolated blades and compressor cascades, involving simultaneous changes in both flow and geometric parameters, are considered. Comparisons with the corresponding exact nonlinear solutions display remarkable accuracy and range of validity, in direct correspondence with previous results for single-parameter perturbations.

Nonlinear evolution of the Kelvin-Helmholtz instability in the double current sheet configuration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mao, Aohua; Li, Jiquan, E-mail: lijq@energy.kyoto-u.ac.jp; Kishimoto, Yasuaki

2016-03-15

The nonlinear evolution of the Kelvin-Helmholtz (KH) instability driven by a radially antisymmetric shear flow in the double current sheet configuration is numerically investigated based on a reduced magnetohydrodynamic model. Simulations reveal different nonlinear fate of the KH instability depending on the amplitude of the shear flow, which restricts the strength of the KH instability. For strong shear flows far above the KH instability threshold, the linear electrostatic-type KH instability saturates and achieves a vortex flow dominated quasi-steady state of the electromagnetic (EM) KH turbulence with large-amplitude zonal flows as well as zonal fields. The magnetic surfaces are twisted significantlymore » due to strong vortices but without the formation of magnetic islands. However, for the shear flow just over the KH instability threshold, a weak EM-type KH instability is saturated and remarkably damped by zonal flows through modifying the equilibrium shear flow. Interestingly, a secondary double tearing mode (DTM) is excited subsequently in highly damped KH turbulence, behaving as a pure DTM in a flowing plasma as described in Mao et al. [Phys. Plasmas 21, 052304 (2014)]. However, the explosive growth phenomenon is replaced by a gradually growing oscillation due to the extremely twisted islands. As a result, the release of the magnetic energy becomes slow and the global magnetic reconnection tends to be gentle. A complex nonlinear interaction between the EM KH turbulence and the DTMs occurs for the medium shear flows above the KH instability threshold, turbulent EM fluctuations experience oscillatory nonlinear growth of the DTMs, finally achieves a quasi-steady state with the interplay of the fluctuations between the DTMs and the EM KH instability.« less

Non-Linear Interactions between Consumers and Flow Determine the Probability of Plant Community Dominance on Maine Rocky Shores

PubMed Central

Silliman, Brian R.; McCoy, Michael W.; Trussell, Geoffrey C.; Crain, Caitlin M.; Ewanchuk, Patrick J.; Bertness, Mark D.

2013-01-01

Although consumers can strongly influence community recovery from disturbance, few studies have explored the effects of consumer identity and density and how they may vary across abiotic gradients. On rocky shores in Maine, recent experiments suggest that recovery of plant- or animal- dominated community states is governed by rates of water movement and consumer pressure. To further elucidate the mechanisms of consumer control, we examined the species-specific and density-dependent effects of rocky shore consumers (crabs and snails) on community recovery under both high (mussel dominated) and low flow (plant dominated) conditions. By partitioning the direct impacts of predators (crabs) and grazers (snails) on community recovery across a flow gradient, we found that grazers, but not predators, are likely the primary agent of consumer control and that their impact is highly non-linear. Manipulating snail densities revealed that herbivorous and bull-dozing snails (Littorina littorea) alone can control recovery of high and low flow communities. After ∼1.5 years of recovery, snail density explained a significant amount of the variation in macroalgal coverage at low flow sites and also mussel recovery at high flow sites. These density-dependent grazer effects were were both non-linear and flow-dependent, with low abundance thresholds needed to suppress plant community recovery, and much higher levels needed to control mussel bed development. Our study suggests that consumer density and identity are key in regulating both plant and animal community recovery and that physical conditions can determine the functional forms of these consumer effects. PMID:23940510

Nonlinear interaction of near-planar TS waves and longitudinal vortices in boundary-layer transition

NASA Technical Reports Server (NTRS)

Smith, F. T.

1988-01-01

The nonlinear interactions that evolve between a planar or nearly planar Tollmien-Schlichting (TS) wave and the associated longitudinal vortices are considered theoretically for a boundary layer at high Reynolds number. The vortex flow is either induced by the TS nonlinear forcing or is input upstream, and similarly for the nonlinear wave development. Three major kinds of nonlinear spatial evolution, Types 1-3, are found. Each can start from secondary instability and then become nonlinear, Type 1 proving to be relatively benign but able to act as a pre-cursor to the Types 2, 3 which turn out to be very powerful nonlinear interactions. Type 2 involves faster stream-wise dependence and leads to a finite-distance blow-up in the amplitudes, which then triggers the full nonlinear 3-D triple-deck response, thus entirely altering the mean-flow profile locally. In contrast, Type 3 involves slower streamwise dependence but a faster spanwise response, with a small TS amplitude thereby causing an enhanced vortex effect which, again, is substantial enough to entirely alter the meanflow profile, on a more global scale. Streak-like formations in which there is localized concentration of streamwise vorticity and/or wave amplitude can appear, and certain of the nonlinear features also suggest by-pass processes for transition and significant changes in the flow structure downstream. The powerful nonlinear 3-D interactions 2, 3 are potentially very relevant to experimental findings in transition.

Near-planar TS waves and longitudinal vortices in channel flow: Nonlinear interaction and focusing

NASA Technical Reports Server (NTRS)

Hall, P.; Smith, F. T.

1989-01-01

The nonlinear interaction between planar or near-planar Tollmien-Schlichting waves and longitudinal vortices, induced or input, is considered theoretically for channel flows at high Reynolds numbers. Several kinds of nonlinear interaction, dependent on the input amplitudes and wavenumbers or on previously occurring interactions, are found and inter-related. The first, Type 1, is studied the most here and it usually produces spanwise focusing of both the wave and the vortex motion, within a finite scaled time, along with enhancement of both their amplitudes. This then points to the nonlinear interaction Type 2 where new interactive effects come into force to drive the wave and the vortex nonlinearly. Types 3, 4 correspond to still higher amplitudes, with 3 being related to 2, while 4 is connected with a larger-scale interaction 5 studied in an allied paper. Both 3, 4 are subsets of the full three-dimensional triple-deck-lie interaction, 6. The strongest nonlinear interactions are those of 4, 5, 6 since they alter the mean-flow profile substantially, i.e., by an 0(1) relative amount. All the types of nonlinear interaction however can result in the formation of focussed responses in the sense of spanwise concentrations and/or amplifications of vorticity and wave amplitude.

Coronal Jet Collimation by Nonlinear Induced Flows

NASA Astrophysics Data System (ADS)

Vasheghani Farahani, S.; Hejazi, S. M.

2017-08-01

Our objective is to study the collimation of solar jets by nonlinear forces corresponding to torsional Alfvén waves together with external forces. We consider a straight, initially non-rotating, untwisted magnetic cylinder embedded in a plasma with a straight magnetic field, where a shear between the internal and external flows exists. By implementing magnetohydrodynamic theory and taking into account the second-order thin flux tube approximation, the balance between the internal nonlinear forces is visualized. The nonlinear differential equation containing the ponderomotive, magnetic tension, and centrifugal forces in the presence of the shear flow is obtained. The solution presents the scale of influence of the propagating torsional Alfvén wave on compressive perturbations. Explicit expressions for the compressive perturbations caused by the forces connected to the torsional Alfvén wave show that, in the presence of a shear flow, the magnetic tension and centrifugal forces do not cancel each other’s effects as they did in its absence. This shear flow plays in favor of the magnetic tension force, resulting in a more efficient collimation. Regarding the ponderomotive force, the shear flow has no effect. The phase relations highlight the interplay of the shear flow and the plasma-β. As the shear flow and plasma-β increase, compressive perturbation amplitudes emerge. We conclude that the jet collimation due to the torsional Alfvén wave highly depends on the location of the jet. The shear flow tightens the collimation as the jet elevates up to the solar corona.

On the secondary instability of the most dangerous Goertler vortex

NASA Technical Reports Server (NTRS)

Otto, S. R.; Denier, James P.

1993-01-01

Recent studies have demonstrated the most unstable Goertler vortex mode is found in flows, both two and three-dimensional, with regions of (moderately) large body curvature and these modes reside within a thin layer situated at the base of the conventional boundary layer. Further work concerning the nonlinear development of the most dangerous mode demonstrates that the flow results in a self induced flow reversal. However, prior to the point at which flow reversal is encountered, the total streamwise velocity profile is found to be highly inflectional in nature. Previous work then suggests that the nonlinear vortex state will become unstable to secondary, inviscid, Rayleigh wave instabilities prior to the point of flow reversal. Our concern is with the secondary instability of the nonlinear vortex states, which result from the streamwise evolution of the most unstable Goertler vortex mode, with the aim of determining whether such modes can induce a transition to a fully turbulent state before separation is encountered.

A finite difference solution for the propagation of sound in near sonic flows

NASA Technical Reports Server (NTRS)

Hariharan, S. I.; Lester, H. C.

1983-01-01

An explicit time/space finite difference procedure is used to model the propagation of sound in a quasi one-dimensional duct containing high Mach number subsonic flow. Nonlinear acoustic equations are derived by perturbing the time-dependent Euler equations about a steady, compressible mean flow. The governing difference relations are based on a fourth-order, two-step (predictor-corrector) MacCormack scheme. The solution algorithm functions by switching on a time harmonic source and allowing the difference equations to iterate to a steady state. The principal effect of the non-linearities was to shift acoustical energy to higher harmonics. With increased source strengths, wave steepening was observed. This phenomenon suggests that the acoustical response may approach a shock behavior at at higher sound pressure level as the throat Mach number aproaches unity. On a peak level basis, good agreement between the nonlinear finite difference and linear finite element solutions was observed, even through a peak sound pressure level of about 150 dB occurred in the throat region. Nonlinear steady state waveform solutions are shown to be in excellent agreement with a nonlinear asymptotic theory.

Hybrid Upwinding for Two-Phase Flow in Heterogeneous Porous Media with Buoyancy and Capillarity

NASA Astrophysics Data System (ADS)

Hamon, F. P.; Mallison, B.; Tchelepi, H.

2016-12-01

In subsurface flow simulation, efficient discretization schemes for the partial differential equations governing multiphase flow and transport are critical. For highly heterogeneous porous media, the temporal discretization of choice is often the unconditionally stable fully implicit (backward-Euler) method. In this scheme, the simultaneous update of all the degrees of freedom requires solving large algebraic nonlinear systems at each time step using Newton's method. This is computationally expensive, especially in the presence of strong capillary effects driven by abrupt changes in porosity and permeability between different rock types. Therefore, discretization schemes that reduce the simulation cost by improving the nonlinear convergence rate are highly desirable. To speed up nonlinear convergence, we present an efficient fully implicit finite-volume scheme for immiscible two-phase flow in the presence of strong capillary forces. In this scheme, the discrete viscous, buoyancy, and capillary spatial terms are evaluated separately based on physical considerations. We build on previous work on Implicit Hybrid Upwinding (IHU) by using the upstream saturations with respect to the total velocity to compute the relative permeabilities in the viscous term, and by determining the directionality of the buoyancy term based on the phase density differences. The capillary numerical flux is decomposed into a rock- and geometry-dependent transmissibility factor, a nonlinear capillary diffusion coefficient, and an approximation of the saturation gradient. Combining the viscous, buoyancy, and capillary terms, we obtain a numerical flux that is consistent, bounded, differentiable, and monotone for homogeneous one-dimensional flow. The proposed scheme also accounts for spatially discontinuous capillary pressure functions. Specifically, at the interface between two rock types, the numerical scheme accurately honors the entry pressure condition by solving a local nonlinear problem to compute the numerical flux. Heterogeneous numerical tests demonstrate that this extended IHU scheme is non-oscillatory and convergent upon refinement. They also illustrate the superior accuracy and nonlinear convergence rate of the IHU scheme compared with the standard phase-based upstream weighting approach.

Algebraic disturbances and their consequences in rotating channel flow transition

NASA Astrophysics Data System (ADS)

Jose, Sharath; Kuzhimparampil, Vishnu; Pier, Benoît.; Govindarajan, Rama

2017-08-01

It is now established that subcritical mechanisms play a crucial role in the transition to turbulence of nonrotating plane shear flows. The role of these mechanisms in rotating channel flow is examined here in the linear and nonlinear stages. Distinct patterns of behavior are found: the transient growth leading to nonlinearity at low rotation rates R o , a highly chaotic intermediate R o regime, a localized weak chaos at higher R o , and complete stabilization of transient disturbances at very high R o . At very low R o , the transient growth amplitudes are close to those for nonrotating flow, but Coriolis forces assert themselves by producing distinct asymmetry about the channel centreline. Nonlinear processes are then triggered, in a streak-breakdown mode of transition. The high R o regimes do not show these signatures; here the leading eigenmode emerges as dominant in the early stages. Elongated structures plastered close to one wall are seen at higher rotation rates. Rotation is shown to reduce nonnormality in the linear operator, in an indirect manifestation of Taylor-Proudman effects. Although the critical Reynolds for exponential growth of instabilities is known to vary a lot with rotation rate, we show that the energy critical Reynolds number is insensitive to rotation rate. It is hoped that these findings will motivate experimental verification and examination of other rotating flows in this light.

Numerical optimization of Ignition and Growth reactive flow modeling for PAX2A

NASA Astrophysics Data System (ADS)

Baker, E. L.; Schimel, B.; Grantham, W. J.

1996-05-01

Variable metric nonlinear optimization has been successfully applied to the parameterization of unreacted and reacted products thermodynamic equations of state and reactive flow modeling of the HMX based high explosive PAX2A. The NLQPEB nonlinear optimization program has been recently coupled to the LLNL developed two-dimensional high rate continuum modeling programs DYNA2D and CALE. The resulting program has the ability to optimize initial modeling parameters. This new optimization capability was used to optimally parameterize the Ignition and Growth reactive flow model to experimental manganin gauge records. The optimization varied the Ignition and Growth reaction rate model parameters in order to minimize the difference between the calculated pressure histories and the experimental pressure histories.

Designing Adaptive Low Dissipative High Order Schemes

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjoegreen, B.; Parks, John W. (Technical Monitor)

2002-01-01

Proper control of the numerical dissipation/filter to accurately resolve all relevant multiscales of complex flow problems while still maintaining nonlinear stability and efficiency for long-time numerical integrations poses a great challenge to the design of numerical methods. The required type and amount of numerical dissipation/filter are not only physical problem dependent, but also vary from one flow region to another. This is particularly true for unsteady high-speed shock/shear/boundary-layer/turbulence/acoustics interactions and/or combustion problems since the dynamics of the nonlinear effect of these flows are not well-understood. Even with extensive grid refinement, it is of paramount importance to have proper control on the type and amount of numerical dissipation/filter in regions where it is needed.

A Nonlinear Dynamic Subscale Model for Partially Resolved Numerical Simulation (PRNS)/Very Large Eddy Simulation (VLES) of Internal Non-Reacting Flows

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Liu, nan-Suey

2010-01-01

A brief introduction of the temporal filter based partially resolved numerical simulation/very large eddy simulation approach (PRNS/VLES) and its distinct features are presented. A nonlinear dynamic subscale model and its advantages over the linear subscale eddy viscosity model are described. In addition, a guideline for conducting a PRNS/VLES simulation is provided. Results are presented for three turbulent internal flows. The first one is the turbulent pipe flow at low and high Reynolds numbers to illustrate the basic features of PRNS/VLES; the second one is the swirling turbulent flow in a LM6000 single injector to further demonstrate the differences in the calculated flow fields resulting from the nonlinear model versus the pure eddy viscosity model; the third one is a more complex turbulent flow generated in a single-element lean direct injection (LDI) combustor, the calculated result has demonstrated that the current PRNS/VLES approach is capable of capturing the dynamically important, unsteady turbulent structures while using a relatively coarse grid.

Rheologic effects of crystal preferred orientation in upper mantle flow near plate boundaries

NASA Astrophysics Data System (ADS)

Blackman, Donna; Castelnau, Olivier; Dawson, Paul; Boyce, Donald

2016-04-01

Observations of anisotropy provide insight into upper mantle processes. Flow-induced mineral alignment provides a link between mantle deformation patterns and seismic anisotropy. Our study focuses on the rheologic effects of crystal preferred orientation (CPO), which develops during mantle flow, in order to assess whether corresponding anisotropic viscosity could significantly impact the pattern of flow. We employ a coupled nonlinear numerical method to link CPO and the flow model via a local viscosity tensor field that quantifies the stress/strain-rate response of a textured mineral aggregate. For a given flow field, the CPO is computed along streamlines using a self-consistent texture model and is then used to update the viscosity tensor field. The new viscosity tensor field defines the local properties for the next flow computation. This iteration produces a coupled nonlinear model for which seismic signatures can be predicted. Results thus far confirm that CPO can impact flow pattern by altering rheology in directionally-dependent ways, particularly in regions of high flow gradient. Multiple iterations run for an initial, linear stress/strain-rate case (power law exponent n=1) converge to a flow field and CPO distribution that are modestly different from the reference, scalar viscosity case. Upwelling rates directly below the spreading axis are slightly reduced and flow is focused somewhat toward the axis. Predicted seismic anisotropy differences are modest. P-wave anisotropy is a few percent greater in the flow 'corner', near the spreading axis, below the lithosphere and extending 40-100 km off axis. Predicted S-wave splitting differences would be below seafloor measurement limits. Calculations with non-linear stress/strain-rate relation, which is more realistic for olivine, indicate that effects are stronger than for the linear case. For n=2-3, the distribution and strength of CPO for the first iteration are greater than for n=1, although the fast seismic axis directions are similar. The greatest difference in CPO for the nonlinear cases develop at the flow 'corner' at depths of 10-30 km and 20-100 km off-axis. J index values up to 10% greater than the linear case are predicted near the lithosphere base in that region. Viscosity tensor components are notably altered in the nonlinear cases. Iterations between the texture and flow calculations for the non-linear cases are underway this winter; results will be reported in the presentation.

Stabilization Approaches for Linear and Nonlinear Reduced Order Models

NASA Astrophysics Data System (ADS)

Rezaian, Elnaz; Wei, Mingjun

2017-11-01

It has been a major concern to establish reduced order models (ROMs) as reliable representatives of the dynamics inherent in high fidelity simulations, while fast computation is achieved. In practice it comes to stability and accuracy of ROMs. Given the inviscid nature of Euler equations it becomes more challenging to achieve stability, especially where moving discontinuities exist. Originally unstable linear and nonlinear ROMs are stabilized here by two approaches. First, a hybrid method is developed by integrating two different stabilization algorithms. At the same time, symmetry inner product is introduced in the generation of ROMs for its known robust behavior for compressible flows. Results have shown a notable improvement in computational efficiency and robustness compared to similar approaches. Second, a new stabilization algorithm is developed specifically for nonlinear ROMs. This method adopts Particle Swarm Optimization to enforce a bounded ROM response for minimum discrepancy between the high fidelity simulation and the ROM outputs. Promising results are obtained in its application on the nonlinear ROM of an inviscid fluid flow with discontinuities. Supported by ARL.

A note on a nonlinear equation arising in discussions of the steady fall of a resistive, viscous, isothermal fluid across a magnetic field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tautz, R. C., E-mail: robert.c.tautz@gmail.com; Lerche, I., E-mail: lercheian@yahoo.com

2015-11-15

This note considers the evolution of steady isothermal flow across a uniform magnetic field from an analytic standpoint. This problem is of concern in developments of magnetic fields in the solar corona and for prominence dynamics. Limiting behaviors are obtained to the nonlinear equation describing the flow depending on the value of a single parameter. For the situation where the viscous drag is a small correction to the inviscid flow limiting structures are also outlined. The purpose of the note is to show how one can evaluate some of the analytic properties of the highly nonlinear equation that are ofmore » use in considering the numerical evolution as done in Low and Egan [Phys. Plasmas 21, 062105 (2014)].« less

Nonlinear radiative peristaltic flow of hydromagnetic fluid through porous medium

NASA Astrophysics Data System (ADS)

Hussain, Q.; Latif, T.; Alvi, N.; Asghar, S.

2018-06-01

The radiative heat and mass transfer in wall induced flow of hydromagnetic fluid through porous medium in an asymmetric channel is analyzed. The fluid viscosity is considered temperature dependent. In the theory of peristalsis, the radiation effects are either ignored or taken as linear approximation of radiative heat flux. Such approximation is only possible when there is sufficiently small temperature differences in the flow field; however, nonlinear radiation effects are valid for large temperature differences as well (the new feature added in the present study). Mathematical modeling of the problems include the complicated system of highly nonlinear differential equations. Semi-analytical solutions are established in the wave reference frame. Results are displayed graphically and discussed in detail for the variation of various physical parameters with the special attention to viscosity, radiation, and temperature ratio parameters.

Coronal Jet Collimation by Nonlinear Induced Flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vasheghani Farahani, S.; Hejazi, S. M.

2017-08-01

Our objective is to study the collimation of solar jets by nonlinear forces corresponding to torsional Alfvén waves together with external forces. We consider a straight, initially non-rotating, untwisted magnetic cylinder embedded in a plasma with a straight magnetic field, where a shear between the internal and external flows exists. By implementing magnetohydrodynamic theory and taking into account the second-order thin flux tube approximation, the balance between the internal nonlinear forces is visualized. The nonlinear differential equation containing the ponderomotive, magnetic tension, and centrifugal forces in the presence of the shear flow is obtained. The solution presents the scale ofmore » influence of the propagating torsional Alfvén wave on compressive perturbations. Explicit expressions for the compressive perturbations caused by the forces connected to the torsional Alfvén wave show that, in the presence of a shear flow, the magnetic tension and centrifugal forces do not cancel each other’s effects as they did in its absence. This shear flow plays in favor of the magnetic tension force, resulting in a more efficient collimation. Regarding the ponderomotive force, the shear flow has no effect. The phase relations highlight the interplay of the shear flow and the plasma- β . As the shear flow and plasma- β increase, compressive perturbation amplitudes emerge. We conclude that the jet collimation due to the torsional Alfvén wave highly depends on the location of the jet. The shear flow tightens the collimation as the jet elevates up to the solar corona.« less

A data-driven approach for modeling post-fire debris-flow volumes and their uncertainty

USGS Publications Warehouse

Friedel, Michael J.

2011-01-01

This study demonstrates the novel application of genetic programming to evolve nonlinear post-fire debris-flow volume equations from variables associated with a data-driven conceptual model of the western United States. The search space is constrained using a multi-component objective function that simultaneously minimizes root-mean squared and unit errors for the evolution of fittest equations. An optimization technique is then used to estimate the limits of nonlinear prediction uncertainty associated with the debris-flow equations. In contrast to a published multiple linear regression three-variable equation, linking basin area with slopes greater or equal to 30 percent, burn severity characterized as area burned moderate plus high, and total storm rainfall, the data-driven approach discovers many nonlinear and several dimensionally consistent equations that are unbiased and have less prediction uncertainty. Of the nonlinear equations, the best performance (lowest prediction uncertainty) is achieved when using three variables: average basin slope, total burned area, and total storm rainfall. Further reduction in uncertainty is possible for the nonlinear equations when dimensional consistency is not a priority and by subsequently applying a gradient solver to the fittest solutions. The data-driven modeling approach can be applied to nonlinear multivariate problems in all fields of study.

Dynamic pressure probe response tests for robust measurements in periodic flows close to probe resonating frequency

NASA Astrophysics Data System (ADS)

Ceyhun Şahin, Fatma; Schiffmann, Jürg

2018-02-01

A single-hole probe was designed to measure steady and periodic flows with high fluctuation amplitudes and with minimal flow intrusion. Because of its high aspect ratio, estimations showed that the probe resonates at a frequency two orders of magnitude lower than the fast response sensor cut-off frequencies. The high fluctuation amplitudes cause a non-linear behavior of the probe and available models are neither adequate for a quantitative estimation of the resonating frequencies nor for predicting the system damping. Instead, a non-linear data correction procedure based on individual transfer functions defined for each harmonic contribution is introduced for pneumatic probes that allows to extend their operating range beyond the resonating frequencies and linear dynamics. This data correction procedure was assessed on a miniature single-hole probe of 0.35 mm inner diameter which was designed to measure flow speed and direction. For the reliable use of such a probe in periodic flows, its frequency response was reproduced with a siren disk, which allows exciting the probe up to 10 kHz with peak-to-peak amplitudes ranging between 20%-170% of the absolute mean pressure. The effect of the probe interior design on the phase lag and amplitude distortion in periodic flow measurements was investigated on probes with similar inner diameters and different lengths or similar aspect ratios (L/D) and different total interior volumes. The results suggest that while the tube length consistently sets the resonance frequency, the internal total volume affects the non-linear dynamic response in terms of varying gain functions. A detailed analysis of the introduced calibration methodology shows that the goodness of the reconstructed data compared to the reference data is above 75% for fundamental frequencies up to twice the probe resonance frequency. The results clearly suggest that the introduced procedure is adequate to capture non-linear pneumatic probe dynamics and to reproduce time-resolved data far above probe resonant frequency.

Nonlinear flow affects hydrodynamic forces and neutrophil adhesion rates in cone-plate viscometers.

PubMed Central

Shankaran, H; Neelamegham, S

2001-01-01

We present a theoretical and experimental analysis of the effects of nonlinear flow in a cone-plate viscometer. The analysis predicts that flow in the viscometer is a function of two parameters, the Reynolds number and the cone angle. Nonlinear flow occurs at high shear rates and causes spatial variations in wall shear stress, collision frequency, interparticle forces and attachment times within the viscometer. We examined the effect of these features on cellular adhesion kinetics. Based on recent data (Taylor, A. D., S. Neelamegham, J. D. Hellums, et al. 1996. Biophys. J. 71:3488-3500), we modeled neutrophil homotypic aggregation as a process that is integrin-limited at low shear and selectin-limited at high shear. Our calculations suggest that selectin and integrin on-rates lie in the order of 10(-2)-10(-4)/s. They also indicate that secondary flow causes positional variations in adhesion efficiency in the viscometer, and that the overall efficiency is dependent not only on the shear rate, but also the sample volume and the cone angle. Experiments performed with isolated neutrophils confirmed these predictions. In these experiments, enhancing secondary flow by increasing the sample volume from 100 to 1000 microl at 1500/s for a 2 degrees cone caused up to an approximately 45% drop in adhesion efficiency. Our results suggest that secondary flow may significantly influence cellular aggregation, platelet activation, and endothelial cell mechanotransduction measurements made in the viscometer over the range of conditions applied in typical biological studies. PMID:11371440

Identification of aerodynamic models for maneuvering aircraft

NASA Technical Reports Server (NTRS)

Chin, Suei; Lan, C. Edward

1990-01-01

Due to the requirement of increased performance and maneuverability, the flight envelope of a modern fighter is frequently extended to the high angle-of-attack regime. Vehicles maneuvering in this regime are subjected to nonlinear aerodynamic loads. The nonlinearities are due mainly to three-dimensional separated flow and concentrated vortex flow that occur at large angles of attack. Accurate prediction of these nonlinear airloads is of great importance in the analysis of a vehicle's flight motion and in the design of its flight control system. A satisfactory evaluation of the performance envelope of the aircraft may require a large number of coupled computations, one for each change in initial conditions. To avoid the disadvantage of solving the coupled flow-field equations and aircraft's motion equations, an alternate approach is to use a mathematical modeling to describe the steady and unsteady aerodynamics for the aircraft equations of motion. Aerodynamic forces and moments acting on a rapidly maneuvering aircraft are, in general, nonlinear functions of motion variables, their time rate of change, and the history of maneuvering. A numerical method was developed to analyze the nonlinear and time-dependent aerodynamic response to establish the generalized indicial function in terms of motion variables and their time rates of change.

Position Corrections for Airspeed and Flow Angle Measurements on Fixed-Wing Aircraft

NASA Technical Reports Server (NTRS)

Grauer, Jared A.

2017-01-01

This report addresses position corrections made to airspeed and aerodynamic flow angle measurements on fixed-wing aircraft. These corrections remove the effects of angular rates, which contribute to the measurements when the sensors are installed away from the aircraft center of mass. Simplified corrections, which are routinely used in practice and assume small flow angles and angular rates, are reviewed. The exact, nonlinear corrections are then derived. The simplified corrections are sufficient in most situations; however, accuracy diminishes for smaller aircraft that incur higher angular rates, and for flight at high air flow angles. This is demonstrated using both flight test data and a nonlinear flight dynamics simulation of a subscale transport aircraft in a variety of low-speed, subsonic flight conditions.

Nonlinear dynamics in flow through unsaturated fractured-porous media: Status and perspectives

DOE Office of Scientific and Technical Information (OSTI.GOV)

Faybishenko, Boris

2002-11-27

The need has long been recognized to improve predictions of flow and transport in partially saturated heterogeneous soils and fractured rock of the vadose zone for many practical applications, such as remediation of contaminated sites, nuclear waste disposal in geological formations, and climate predictions. Until recently, flow and transport processes in heterogeneous subsurface media with oscillating irregularities were assumed to be random and were not analyzed using methods of nonlinear dynamics. The goals of this paper are to review the theoretical concepts, present the results, and provide perspectives on investigations of flow and transport in unsaturated heterogeneous soils and fracturedmore » rock, using the methods of nonlinear dynamics and deterministic chaos. The results of laboratory and field investigations indicate that the nonlinear dynamics of flow and transport processes in unsaturated soils and fractured rocks arise from the dynamic feedback and competition between various nonlinear physical processes along with complex geometry of flow paths. Although direct measurements of variables characterizing the individual flow processes are not technically feasible, their cumulative effect can be characterized by analyzing time series data using the models and methods of nonlinear dynamics and chaos. Identifying flow through soil or rock as a nonlinear dynamical system is important for developing appropriate short- and long-time predictive models, evaluating prediction uncertainty, assessing the spatial distribution of flow characteristics from time series data, and improving chemical transport simulations. Inferring the nature of flow processes through the methods of nonlinear dynamics could become widely used in different areas of the earth sciences.« less

Rotating Flow of Magnetite-Water Nanofluid over a Stretching Surface Inspired by Non-Linear Thermal Radiation.

PubMed

Mustafa, M; Mushtaq, A; Hayat, T; Alsaedi, A

2016-01-01

Present study explores the MHD three-dimensional rotating flow and heat transfer of ferrofluid induced by a radiative surface. The base fluid is considered as water with magnetite-Fe3O4 nanoparticles. Novel concept of non-linear radiative heat flux is considered which produces a non-linear energy equation in temperature field. Conventional transformations are employed to obtain the self-similar form of the governing differential system. The arising system involves an interesting temperature ratio parameter which is an indicator of small/large temperature differences in the flow. Numerical simulations with high precision are determined by well-known shooting approach. Both uniform stretching and rotation have significant impact on the solutions. The variation in velocity components with the nanoparticle volume fraction is non-monotonic. Local Nusselt number in Fe3O4-water ferrofluid is larger in comparison to the pure fluid even at low particle concentration.

Use of Picard and Newton iteration for solving nonlinear ground water flow equations

USGS Publications Warehouse

Mehl, S.

2006-01-01

This study examines the use of Picard and Newton iteration to solve the nonlinear, saturated ground water flow equation. Here, a simple three-node problem is used to demonstrate the convergence difficulties that can arise when solving the nonlinear, saturated ground water flow equation in both homogeneous and heterogeneous systems with and without nonlinear boundary conditions. For these cases, the characteristic types of convergence patterns are examined. Viewing these convergence patterns as orbits of an attractor in a dynamical system provides further insight. It is shown that the nonlinearity that arises from nonlinear head-dependent boundary conditions can cause more convergence difficulties than the nonlinearity that arises from flow in an unconfined aquifer. Furthermore, the effects of damping on both convergence and convergence rate are investigated. It is shown that no single strategy is effective for all problems and how understanding pitfalls and merits of several methods can be helpful in overcoming convergence difficulties. Results show that Picard iterations can be a simple and effective method for the solution of nonlinear, saturated ground water flow problems.

Nonlinear Instability of Hypersonic Flow past a Wedge

NASA Technical Reports Server (NTRS)

Seddougui, Sharon O.; Bassom, Andrew P.

1991-01-01

The nonlinear stability of a compressible flow past a wedge is investigated in the hypersonic limit. The analysis follows the ideas of a weakly nonlinear approach. Interest is focussed on Tollmien-Schlichting waves governed by a triple deck structure and it is found that the attached shock can profoundly affect the stability characteristics of the flow. In particular, it is shown that nonlinearity tends to have a stabilizing influence. The nonlinear evolution of the Tollmien-Schlichting mode is described in a number of asymptotic limits.

A three-dimensional dynamical model for channeled lava flow with nonlinear rheology

NASA Astrophysics Data System (ADS)

Filippucci, Marilena; Tallarico, Andrea; Dragoni, Michele

2010-05-01

Recent laboratory studies on the rheology of lava samples from different volcanic areas have highlighted that the apparent viscosity depends on a power of the strain rate. Several authors agree in attributing this dependence to the crystal content of the sample and to temperature. Starting from these results, in this paper we studied the effect of a power law rheology on a gravity-driven lava flow. The equation of motion is nonlinear in the diffusion term, and an analytical solution does not seem to be possible. The finite-volume method has been applied to solve numerically the equation governing the fully developed laminar flow of a power law non-Newtonian fluid in an inclined rectangular channel. The convergence, the stability, and the order of approximation were tested for the Newtonian rheology case, comparing the numerical solution with the available analytical solution. Results indicate that the assumption on the rheology, whether linear or nonlinear, strongly affects the velocity and/or the thickness of the lava channel both for channels with fixed geometry and for channels with constant flow rate. Results on channels with fixed geometry are confirmed by some simulations for real lava channels. Finally, the study of the Reynolds number indicates that gravity-driven lava channel flows are always in laminar regime, except for strongly nonlinear pseudoplastic fluids with low fluid consistency and at high slopes.

A new approach to determining symmetry groups of filtration properties of porous media in nonlinear filtration laws

NASA Astrophysics Data System (ADS)

Maksimov, V. M.; Dmitriev, N. M.; Dmitriev, M. N.

2017-04-01

Theoretical analysis of filtration properties of porous media for orthotropic and monoclinic symmetry groups has been carried out. It is shown how it is possible to establish a type of symmetry with the help of special laboratory investigations and to distinguish groups with orthotropic and monoclinic symmetry. It is established that the criterion for solving this problem is the use of nonlinear Darcy law at high flow velocities, where the effects of asymmetry of filtration properties manifest themselves upon a change in the flow direction.

Transonic Flow Computations Using Nonlinear Potential Methods

NASA Technical Reports Server (NTRS)

Holst, Terry L.; Kwak, Dochan (Technical Monitor)

2000-01-01

This presentation describes the state of transonic flow simulation using nonlinear potential methods for external aerodynamic applications. The presentation begins with a review of the various potential equation forms (with emphasis on the full potential equation) and includes a discussion of pertinent mathematical characteristics and all derivation assumptions. Impact of the derivation assumptions on simulation accuracy, especially with respect to shock wave capture, is discussed. Key characteristics of all numerical algorithm types used for solving nonlinear potential equations, including steady, unsteady, space marching, and design methods, are described. Both spatial discretization and iteration scheme characteristics are examined. Numerical results for various aerodynamic applications are included throughout the presentation to highlight key discussion points. The presentation ends with concluding remarks and recommendations for future work. Overall. nonlinear potential solvers are efficient, highly developed and routinely used in the aerodynamic design environment for cruise conditions. Published by Elsevier Science Ltd. All rights reserved.

Impact of E × B shear flow on low-n MHD instabilities.

PubMed

Chen, J G; Xu, X Q; Ma, C H; Xi, P W; Kong, D F; Lei, Y A

2017-05-01

Recently, the stationary high confinement operations with improved pedestal conditions have been achieved in DIII-D [K. H. Burrell et al. , Phys. Plasmas 23 , 056103 (2016)], accompanying the spontaneous transition from the coherent edge harmonic oscillation (EHO) to the broadband MHD turbulence state by reducing the neutral beam injection torque to zero. It is highly significant for the burning plasma devices such as ITER. Simulations about the effects of E  ×  B shear flow on the quiescent H-mode (QH-mode) are carried out using the three-field two-fluid model in the field-aligned coordinate under the BOUT++ framework. Using the shifted circular cross-section equilibriums including bootstrap current, the results demonstrate that the E  ×  B shear flow strongly destabilizes low-n peeling modes, which are mainly driven by the gradient of parallel current in peeling-dominant cases and are sensitive to the E r shear. Adopting the much more general shape of E  ×  B shear ([Formula: see text]) profiles, the linear and nonlinear BOUT++ simulations show qualitative consistence with the experiments. The stronger shear flow shifts the most unstable mode to lower-n and narrows the mode spectrum. At the meantime, the nonlinear simulations of the QH-mode indicate that the shear flow in both co- and counter directions of diamagnetic flow has some similar effects. The nonlinear mode interaction is enhanced during the mode amplitude saturation phase. These results reveal that the fundamental physics mechanism of the QH-mode may be shear flow and are significant for understanding the mechanism of EHO and QH-mode.

Impact of E × B shear flow on low-n MHD instabilities

NASA Astrophysics Data System (ADS)

Chen, J. G.; Xu, X. Q.; Ma, C. H.; Xi, P. W.; Kong, D. F.; Lei, Y. A.

2017-05-01

Recently, the stationary high confinement operations with improved pedestal conditions have been achieved in DIII-D [K. H. Burrell et al., Phys. Plasmas 23, 056103 (2016)], accompanying the spontaneous transition from the coherent edge harmonic oscillation (EHO) to the broadband MHD turbulence state by reducing the neutral beam injection torque to zero. It is highly significant for the burning plasma devices such as ITER. Simulations about the effects of E × B shear flow on the quiescent H-mode (QH-mode) are carried out using the three-field two-fluid model in the field-aligned coordinate under the BOUT++ framework. Using the shifted circular cross-section equilibriums including bootstrap current, the results demonstrate that the E × B shear flow strongly destabilizes low-n peeling modes, which are mainly driven by the gradient of parallel current in peeling-dominant cases and are sensitive to the Er shear. Adopting the much more general shape of E × B shear ( ω E = E r / R B θ ) profiles, the linear and nonlinear BOUT++ simulations show qualitative consistence with the experiments. The stronger shear flow shifts the most unstable mode to lower-n and narrows the mode spectrum. At the meantime, the nonlinear simulations of the QH-mode indicate that the shear flow in both co- and counter directions of diamagnetic flow has some similar effects. The nonlinear mode interaction is enhanced during the mode amplitude saturation phase. These results reveal that the fundamental physics mechanism of the QH-mode may be shear flow and are significant for understanding the mechanism of EHO and QH-mode.

Impact of E × B shear flow on low-n MHD instabilities

PubMed Central

Chen, J. G.; Ma, C. H.; Xi, P. W.; Lei, Y. A.

2017-01-01

Recently, the stationary high confinement operations with improved pedestal conditions have been achieved in DIII-D [K. H. Burrell et al., Phys. Plasmas 23, 056103 (2016)], accompanying the spontaneous transition from the coherent edge harmonic oscillation (EHO) to the broadband MHD turbulence state by reducing the neutral beam injection torque to zero. It is highly significant for the burning plasma devices such as ITER. Simulations about the effects of E × B shear flow on the quiescent H-mode (QH-mode) are carried out using the three-field two-fluid model in the field-aligned coordinate under the BOUT++ framework. Using the shifted circular cross-section equilibriums including bootstrap current, the results demonstrate that the E × B shear flow strongly destabilizes low-n peeling modes, which are mainly driven by the gradient of parallel current in peeling-dominant cases and are sensitive to the Er shear. Adopting the much more general shape of E × B shear (ωE=Er/RBθ) profiles, the linear and nonlinear BOUT++ simulations show qualitative consistence with the experiments. The stronger shear flow shifts the most unstable mode to lower-n and narrows the mode spectrum. At the meantime, the nonlinear simulations of the QH-mode indicate that the shear flow in both co- and counter directions of diamagnetic flow has some similar effects. The nonlinear mode interaction is enhanced during the mode amplitude saturation phase. These results reveal that the fundamental physics mechanism of the QH-mode may be shear flow and are significant for understanding the mechanism of EHO and QH-mode. PMID:28579732

Euler flow predictions for an oscillating cascade using a high resolution wave-split scheme

NASA Technical Reports Server (NTRS)

Huff, Dennis L.; Swafford, Timothy W.; Reddy, T. S. R.

1991-01-01

A compressible flow code that can predict the nonlinear unsteady aerodynamics associated with transonic flows over oscillating cascades is developed and validated. The code solves the two dimensional, unsteady Euler equations using a time-marching, flux-difference splitting scheme. The unsteady pressures and forces can be determined for arbitrary input motions, although only harmonic pitching and plunging motions are addressed. The code solves the flow equations on a H-grid which is allowed to deform with the airfoil motion. Predictions are presented for both flat plate cascades and loaded airfoil cascades. Results are compared to flat plate theory and experimental data. Predictions are also presented for several oscillating cascades with strong normal shocks where the pitching amplitudes, cascade geometry and interblade phase angles are varied to investigate nonlinear behavior.

Performance of thermal deposition and mass flux condition on bioconvection nanoparticles containing gyrotactic microorganisms

NASA Astrophysics Data System (ADS)

Iqbal, Z.; Ahmad, Bilal

2017-11-01

This is an attempt to investigate the influence of thermal radiation on the movement of motile gyrotactic microorganisms submerged in a water-based nanofluid flow over a nonlinear stretching sheet. The mathematical modeling of this physical problem leads to a system of nonlinear coupled partial differential equations. The problem is tackled by converting nonlinear partial differential equations into the system of highly nonlinear ordinary differential equations. The resulting nonlinear equations of momentum, energy, concentration of nanoparticles and motile gyrotactic microorganisms along with the mass flux condition are solved numerically by means of a shooting algorithm. The effects of the involved physical parameters of interest are discussed graphically. The values of the skin friction coefficient, Nusselt number, Sherwood number and local density number of motile microorganisms are tabulated for detailed analysis on the flow pattern at the stretching surface. It is concluded that the nanofluid temperature is an increasing function of the thermal radiation and the Biot number parameter. An opposite trend is observed for the local Nusselt number. The association with the preceding results in limiting sense is shown as well. A tremendous agreement of the current study in a restrictive manner is achieved as well. In addition, flow configurations through stream functions are presented and deliberated significantly.

Nonlinear model-order reduction for compressible flow solvers using the Discrete Empirical Interpolation Method

NASA Astrophysics Data System (ADS)

Fosas de Pando, Miguel; Schmid, Peter J.; Sipp, Denis

2016-11-01

Nonlinear model reduction for large-scale flows is an essential component in many fluid applications such as flow control, optimization, parameter space exploration and statistical analysis. In this article, we generalize the POD-DEIM method, introduced by Chaturantabut & Sorensen [1], to address nonlocal nonlinearities in the equations without loss of performance or efficiency. The nonlinear terms are represented by nested DEIM-approximations using multiple expansion bases based on the Proper Orthogonal Decomposition. These extensions are imperative, for example, for applications of the POD-DEIM method to large-scale compressible flows. The efficient implementation of the presented model-reduction technique follows our earlier work [2] on linearized and adjoint analyses and takes advantage of the modular structure of our compressible flow solver. The efficacy of the nonlinear model-reduction technique is demonstrated to the flow around an airfoil and its acoustic footprint. We could obtain an accurate and robust low-dimensional model that captures the main features of the full flow.

Nonlinear storage models of unconfined flow through a shallow aquifer on an inclined base and their quasi-steady flow application

NASA Astrophysics Data System (ADS)

Varvaris, Ioannis; Gravanis, Elias; Koussis, Antonis; Akylas, Evangelos

2013-04-01

Hillslope processes involving flow through an inclined shallow aquifer range from subsurface stormflow to stream base flow (drought flow, or groundwater recession flow). In the case of recharge, the infiltrating water moves vertically as unsaturated flow until it reaches the saturated groundwater, where the flow is approximately parallel to the base of the aquifer. Boussinesq used the Dupuit-Forchheimer (D-F) hydraulic theory to formulate unconfined groundwater flow through a soil layer resting on an impervious inclined bed, deriving a nonlinear equation for the flow rate that consists of a linear gravity-driven component and a quadratic pressure-gradient component. Inserting that flow rate equation into the differential storage balance equation (volume conservation) Boussinesq obtained a nonlinear second-order partial differential equation for the depth. So far however, only few special solutions have been advanced for that governing equation. The nonlinearity of the equation of Boussinesq is the major obstacle to deriving a general analytical solution for the depth profile of unconfined flow on a sloping base with recharge (from which the discharges could be then determined). Henderson and Wooding (1964) were able to obtain an exact analytical solution for steady unconfined flow on a sloping base, with recharge, and their work deserves special note in the realm of solutions of the nonlinear equation of Boussinesq. However, the absence of a general solution for the transient case, which is of practical interest to hydrologists, has been the motivation for developing approximate solutions of the non-linear equation of Boussinesq. In this work, we derive the aquifer storage function by integrating analytically over the aquifer base the depth profiles resulting from the complete nonlinear Boussinesq equation for steady flow. This storage function consists of a linear and a nonlinear outflow-dependent term. Then, we use this physics-based storage function in the transient storage balance over the hillslope, obtaining analytical solutions of the outflow and the storage, for recharge and drainage, via a quasi-steady flow calculation. The hydraulically derived storage model is thus embedded in a quasi-steady approximation of transient unconfined flow in sloping aquifers. We generalise this hydrologic model of groundwater flow by modifying the storage function to be the weighted sum of the linear and the nonlinear storage terms, determining the weighting factor objectively from a known integral quantity of the flow (either an initial volume of water stored in the aquifer or a drained water volume). We demonstrate the validity of this model through comparisons with experimental data and simulation results.

Macroscopic modeling of freeway traffic using an artificial neural network

DOT National Transportation Integrated Search

1997-01-01

Traffic flow on freeways is a complex process that often is described by a set of highly nonlinear, dynamic equations in the form of a macroscopic traffic flow model. However, some of the existing macroscopic models have been found to exhibit instabi...

Bio-convection on the nonlinear radiative flow of a Carreau fluid over a moving wedge with suction or injection

NASA Astrophysics Data System (ADS)

Raju, C. S. K.; Ibrahim, S. M.; Anuradha, S.; Priyadharshini, P.

2016-11-01

In modern days, the mass transfer rate is challenging to the scientists due to its noticeable significance for industrial as well as engineering applications; owing to this we attempt to study the cross-diffusion effects on the magnetohydrodynamic nonlinear radiative Carreau fluid over a wedge filled with gyro tactic microorganisms. Numerical results are presented graphically as well as in tabular form with the aid of the Runge-Kutta and Newton methods. The effects of pertinent parameters on velocity, temperature, concentration and density of motile organism distributions are presented and discussed for two cases (suction and injection flows). For real-life application we also calculated the local Nusselt and Sherwood numbers. It is observed that thermal and concentration profiles are not uniform in the suction and injection flow cases. It is found that the heat and mass transport phenomenon is high in the injection case, while heat and mass transfer rates are high in the suction flow case.

Progress in the Development of a Class of Efficient Low Dissipative High Order Shock-capturing Methods

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjogreen, B.; Sandham, N. D.; Hadjadj, A.; Kwak, Dochan (Technical Monitor)

2000-01-01

In a series of papers, Olsson (1994, 1995), Olsson & Oliger (1994), Strand (1994), Gerritsen Olsson (1996), Yee et al. (1999a,b, 2000) and Sandham & Yee (2000), the issue of nonlinear stability of the compressible Euler and Navier-Stokes Equations, including physical boundaries, and the corresponding development of the discrete analogue of nonlinear stable high order schemes, including boundary schemes, were developed, extended and evaluated for various fluid flows. High order here refers to spatial schemes that are essentially fourth-order or higher away from shock and shear regions. The objective of this paper is to give an overview of the progress of the low dissipative high order shock-capturing schemes proposed by Yee et al. (1999a,b, 2000). This class of schemes consists of simple non-dissipative high order compact or non-compact central spatial differencings and adaptive nonlinear numerical dissipation operators to minimize the use of numerical dissipation. The amount of numerical dissipation is further minimized by applying the scheme to the entropy splitting form of the inviscid flux derivatives, and by rewriting the viscous terms to minimize odd-even decoupling before the application of the central scheme (Sandham & Yee). The efficiency and accuracy of these scheme are compared with spectral, TVD and fifth- order WENO schemes. A new approach of Sjogreen & Yee (2000) utilizing non-orthogonal multi-resolution wavelet basis functions as sensors to dynamically determine the appropriate amount of numerical dissipation to be added to the non-dissipative high order spatial scheme at each grid point will be discussed. Numerical experiments of long time integration of smooth flows, shock-turbulence interactions, direct numerical simulations of a 3-D compressible turbulent plane channel flow, and various mixing layer problems indicate that these schemes are especially suitable for practical complex problems in nonlinear aeroacoustics, rotorcraft dynamics, direct numerical simulation or large eddy simulation of compressible turbulent flows at various speeds including high-speed shock-turbulence interactions, and general long time wave propagation problems. These schemes, including entropy splitting, have also been extended to freestream preserving schemes on curvilinear moving grids for a thermally perfect gas (Vinokur & Yee 2000).

Pre-Darcy flow in tight and shale formations

NASA Astrophysics Data System (ADS)

Dejam, Morteza; Hassanzadeh, Hassan; Chen, Zhangxin

2017-11-01

There are evidences that the fluid flow in tight and shale formations does not follow Darcy law, which is identified as pre-Darcy flow. Here, the unsteady linear flow of a slightly compressible fluid under the action of pre-Darcy flow is modeled and a generalized Boltzmann transformation technique is used to solve the corresponding highly nonlinear diffusivity equation analytically. The effect of pre-Darcy flow on the pressure diffusion in a homogenous formation is studied in terms of the nonlinear exponent, m, and the threshold pressure gradient, G1. In addition, the pressure gradient, flux, and cumulative production per unit area for different m and G1 are compared with the classical solution of the diffusivity equation based on Darcy flow. Department of Petroleum Engineering in College of Engineering and Applied Science at University of Wyoming and NSERC/AI-EES(AERI)/Foundation CMG and AITF (iCORE) Chairs in Department of Chemical and Petroleum Engineering at University of Calgary.

Technique for Very High Order Nonlinear Simulation and Validation

NASA Technical Reports Server (NTRS)

Dyson, Rodger W.

2001-01-01

Finding the sources of sound in large nonlinear fields via direct simulation currently requires excessive computational cost. This paper describes a simple technique for efficiently solving the multidimensional nonlinear Euler equations that significantly reduces this cost and demonstrates a useful approach for validating high order nonlinear methods. Up to 15th order accuracy in space and time methods were compared and it is shown that an algorithm with a fixed design accuracy approaches its maximal utility and then its usefulness exponentially decays unless higher accuracy is used. It is concluded that at least a 7th order method is required to efficiently propagate a harmonic wave using the nonlinear Euler equations to a distance of 5 wavelengths while maintaining an overall error tolerance that is low enough to capture both the mean flow and the acoustics.

Boundary layer streaming in viscoelastic fluids

NASA Astrophysics Data System (ADS)

Bahrani, Seyed Amir; Costalanga, Maxime; Royon, Laurent; Brunet, Philippe; DSHE Team; Energy Team

2017-11-01

Oscillations of bodies immersed in fluids are known to generate secondary steady flows (streaming). These flows have strong similarities with acoustic streaming induced by sound and ultrasound waves. A typical situation, investigated here, is that of a cylinder oscillating perpendicular to its axis, generating two pairs of counter-rotating steady vortices due to the transfer of vorticity from an inner boundary layer. While most studies so far investigated the situation of newtonian fluids, here, we consider the situation of a viscoelastic fluid. By using Particle Image Velocimetry, we carry out an experimental study of the flow structure and magnitude over a range of amplitude (A up to 2.5 mm, nearly half the cylinder diameter) and frequency (f between 5 and 100 Hz). We observe unprecedented behaviors at higher frequency (f >50 Hz) : at high enough amplitude, the usual flow with 2 pairs of vortices is replaced by a more complex flow where 4 pairs of vortices are observed. At smaller frequency, we observe reversal large scale vortices that replace the usual inner and outer ones in Newtonian fluids. The main intention of this work is to understand the influence of the complex and nonlinear rheology on the mechanism of streaming flow. In this way, another source of purely rheological nonlinearity is expected, competing with hydrodynamic nonlinearity. We evidence the effect of elasticity in streaming.

A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods

NASA Technical Reports Server (NTRS)

Yee, H. C.

1994-01-01

The development of shock-capturing finite difference methods for hyperbolic conservation laws has been a rapidly growing area for the last decade. Many of the fundamental concepts, state-of-the-art developments and applications to fluid dynamics problems can only be found in meeting proceedings, scientific journals and internal reports. This paper attempts to give a unified and generalized formulation of a class of high-resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock waves, perfect gases, equilibrium real gases and nonequilibrium flow computations. These numerical methods are formulated for the purpose of ease and efficient implementation into a practical computer code. The various constructions of high-resolution shock-capturing methods fall nicely into the present framework and a computer code can be implemented with the various methods as separate modules. Included is a systematic overview of the basic design principle of the various related numerical methods. Special emphasis will be on the construction of the basic nonlinear, spatially second and third-order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and flux-vector splitting approaches. Generalization of these methods to efficiently include real gases and large systems of nonequilibrium flows will be discussed. Some perbolic conservation laws to problems containing stiff source terms and terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for one-, two- and three-dimensional gas-dynamics problems. The use of the Lax-Friedrichs numerical flux to obtain high-resolution shock-capturing schemes is generalized. This method can be extended to nonlinear systems of equations without the use of Riemann solvers or flux-vector splitting approaches and thus provides a large savings for multidimensional, equilibrium real gases and nonequilibrium flow computations.

Nonlinear oscillatory rarefied gas flow inside a rectangular cavity

NASA Astrophysics Data System (ADS)

Wang, Peng; Zhu, Lianhua; Su, Wei; Wu, Lei; Zhang, Yonghao

2018-04-01

The nonlinear oscillation of rarefied gas flow inside a two-dimensional rectangular cavity is investigated on the basis of the Shakhov kinetic equation. The gas dynamics, heat transfer, and damping force are studied numerically via the discrete unified gas-kinetic scheme for a wide range of parameters, including gas rarefaction, cavity aspect ratio, and oscillation frequency. Contrary to the linear oscillation where the velocity, temperature, and heat flux are symmetrical and oscillate with the same frequency as the oscillating lid, flow properties in nonlinear oscillatory cases turn out to be asymmetrical, and second-harmonic oscillation of the temperature field is observed. As a consequence, the amplitude of the shear stress near the top-right corner of the cavity could be several times larger than that at the top-left corner, while the temperature at the top-right corner could be significantly higher than the wall temperature in nearly the whole oscillation period. For the linear oscillation with the frequency over a critical value, and for the nonlinear oscillation, the heat transfer from the hot to cold region dominates inside the cavity, which is contrary to the anti-Fourier heat transfer in a low-speed rarefied lid-driven cavity flow. The damping force exerted on the oscillating lid is studied in detail, and the scaling laws are developed to describe the dependency of the resonance and antiresonance frequencies (corresponding to the damping force at a local maximum and minimum, respectively) on the reciprocal aspect ratio from the near hydrodynamic to highly rarefied regimes. These findings could be useful in the design of the micro-electro-mechanical devices operating in the nonlinear-flow regime.

Validation of a RANS transition model using a high-order weighted compact nonlinear scheme

NASA Astrophysics Data System (ADS)

Tu, GuoHua; Deng, XiaoGang; Mao, MeiLiang

2013-04-01

A modified transition model is given based on the shear stress transport (SST) turbulence model and an intermittency transport equation. The energy gradient term in the original model is replaced by flow strain rate to saving computational costs. The model employs local variables only, and then it can be conveniently implemented in modern computational fluid dynamics codes. The fifth-order weighted compact nonlinear scheme and the fourth-order staggered scheme are applied to discrete the governing equations for the purpose of minimizing discretization errors, so as to mitigate the confusion between numerical errors and transition model errors. The high-order package is compared with a second-order TVD method on simulating the transitional flow of a flat plate. Numerical results indicate that the high-order package give better grid convergence property than that of the second-order method. Validation of the transition model is performed for transitional flows ranging from low speed to hypersonic speed.

Fundamental Studies and Device Development in Beta Silicon Carbide.

DTIC Science & Technology

1987-08-31

2 and Cr exhibited nonlinear I - V characteristics; however, the resistivity to current flow in either voltage direction was small, as seen in the...this material. The nonlinear I - V characteristics previously noted and shown in Fig. 1 for the as-deposited TaSi 2, became linear upon annealing at 1123K...for these three materials. Even after heating at 1473K for 1800 s, the Au-Ta-Al alloy contact showed nonlinear I - V characteristics and possessed a high

Channel geometry change of a first-order stream after a small debris flow in Ashio Mountains of central Japan

NASA Astrophysics Data System (ADS)

Hattanji, T.; Wasklewicz, T.

2006-12-01

We examined geometry change of a steep first-order channel with a laserscanner before and after a small debris flow. The study site is located in chert area, Ashio Mountains, Japan. On August 12, 2005, a 20-year storm event with maximum 1-hour rainfall of 75.4 mm/h triggered a small landslide at a steep channel head. The sliding material moved as a debris flow along the first-order channel (C3) to the mouth. We successfully measured high-resolution channel topography with the Leica Geosystems High-Definition Surveying Laser Scanner before (April 30) and after the debris-flow event (October 9-11). Width, depth and other related parameters were measured for 30 selected cross sections. Bankfull stage of this first-order channel after the debris-flow event is much higher than two-year flood stage. The magnitude of channel geometry change varies non-linearly in downstream direction. The non-linear variability is attributed to differences in stream bed and bank characteristics. Bedrock-channel reach is less impacted by the debris flow. The largest magnitude changes in the channel geometry parameters occur along colluvially confined channel reaches.

Parametric Study of Flow Patterns behind the Standing Accretion Shock Wave for Core-Collapse Supernovae

NASA Astrophysics Data System (ADS)

Iwakami, Wakana; Nagakura, Hiroki; Yamada, Shoichi

2014-05-01

In this study, we conduct three-dimensional hydrodynamic simulations systematically to investigate the flow patterns behind the accretion shock waves that are commonly formed in the post-bounce phase of core-collapse supernovae. Adding small perturbations to spherically symmetric, steady, shocked accretion flows, we compute the subsequent evolutions to find what flow pattern emerges as a consequence of hydrodynamical instabilities such as convection and standing accretion shock instability for different neutrino luminosities and mass accretion rates. Depending on these two controlling parameters, various flow patterns are indeed realized. We classify them into three basic patterns and two intermediate ones; the former includes sloshing motion (SL), spiral motion (SP), and multiple buoyant bubble formation (BB); the latter consists of spiral motion with buoyant-bubble formation (SPB) and spiral motion with pulsationally changing rotational velocities (SPP). Although the post-shock flow is highly chaotic, there is a clear trend in the pattern realization. The sloshing and spiral motions tend to be dominant for high accretion rates and low neutrino luminosities, and multiple buoyant bubbles prevail for low accretion rates and high neutrino luminosities. It is interesting that the dominant pattern is not always identical between the semi-nonlinear and nonlinear phases near the critical luminosity; the intermediate cases are realized in the latter case. Running several simulations with different random perturbations, we confirm that the realization of flow pattern is robust in most cases.

Nonlinear effects on sound propagation through high subsonic Mach number flows in variable area ducts

NASA Technical Reports Server (NTRS)

Callegari, A. J.

1979-01-01

A nonlinear theory for sound propagation in variable area ducts carrying a nearly sonic flow is presented. Linear acoustic theory is shown to be singular and the detailed nature of the singularity is used to develop the correct nonlinear theory. The theory is based on a quasi-one dimensional model. It is derived by the method of matched asymptotic expansions. In a nearly chocked flow, the theory indicates the following processes to be acting: a transonic trapping of upstream propagating sound causing an intensification of this sound in the throat region of the duct; generation of superharmonics and an acoustic streaming effect; development of shocks in the acoustic quantities near the throat. Several specific problems are solved analytically and numerical parameter studies are carried out. Results indicate that appreciable acoustic power is shifted to higher harmonics as shocked conditions are approached. The effect of the throat Mach number on the attenuation of upstream propagating sound excited by a fixed source is also determined.

Study of non-linear deformation of vocal folds in simulations of human phonation

NASA Astrophysics Data System (ADS)

Saurabh, Shakti; Bodony, Daniel

2014-11-01

Direct numerical simulation is performed on a two-dimensional compressible, viscous fluid interacting with a non-linear, viscoelastic solid as a model for the generation of the human voice. The vocal fold (VF) tissues are modeled as multi-layered with varying stiffness in each layer and using a finite-strain Standard Linear Solid (SLS) constitutive model implemented in a quadratic finite element code and coupled to a high-order compressible Navier-Stokes solver through a boundary-fitted fluid-solid interface. The large non-linear mesh deformation is handled using an elliptic/poisson smoothening technique. Supra-glottal flow shows asymmetry in the flow, which in turn has a coupling effect on the motion of the VF. The fully compressible simulations gives direct insight into the sound produced as pressure distributions and the vocal fold deformation helps study the unsteady vortical flow resulting from the fluid-structure interaction along the full phonation cycle. Supported by the National Science Foundation (CAREER Award Number 1150439).

A Modified Double Multiple Nonlinear Regression Constitutive Equation for Modeling and Prediction of High Temperature Flow Behavior of BFe10-1-2 Alloy

NASA Astrophysics Data System (ADS)

Cai, Jun; Wang, Kuaishe; Shi, Jiamin; Wang, Wen; Liu, Yingying

2018-01-01

Constitutive analysis for hot working of BFe10-1-2 alloy was carried out by using experimental stress-strain data from isothermal hot compression tests, in a wide range of temperature of 1,023 1,273 K, and strain rate range of 0.001 10 s-1. A constitutive equation based on modified double multiple nonlinear regression was proposed considering the independent effects of strain, strain rate, temperature and their interrelation. The predicted flow stress data calculated from the developed equation was compared with the experimental data. Correlation coefficient (R), average absolute relative error (AARE) and relative errors were introduced to verify the validity of the developed constitutive equation. Subsequently, a comparative study was made on the capability of strain-compensated Arrhenius-type constitutive model. The results showed that the developed constitutive equation based on modified double multiple nonlinear regression could predict flow stress of BFe10-1-2 alloy with good correlation and generalization.

Buoyancy effects on the radiative magneto Micropolar nanofluid flow with double stratification, activation energy and binary chemical reaction.

PubMed

Ramzan, M; Ullah, Naeem; Chung, Jae Dong; Lu, Dianchen; Farooq, Umer

2017-10-10

A mathematical model has been developed to examine the magneto hydrodynamic micropolar nanofluid flow with buoyancy effects. Flow analysis is carried out in the presence of nonlinear thermal radiation and dual stratification. The impact of binary chemical reaction with Arrhenius activation energy is also considered. Apposite transformations are engaged to transform nonlinear partial differential equations to differential equations with high nonlinearity. Resulting nonlinear system of differential equations is solved by differential solver method in Maple software which uses Runge-Kutta fourth and fifth order technique (RK45). To authenticate the obtained results, a comparison with the preceding article is also made. The evaluations are executed graphically for numerous prominent parameters versus velocity, micro rotation component, temperature, and concentration distributions. Tabulated numerical calculations of Nusselt and Sherwood numbers with respective well-argued discussions are also presented. Our findings illustrate that the angular velocity component declines for opposing buoyancy forces and enhances for aiding buoyancy forces by changing the micropolar parameter. It is also found that concentration profile increases for higher values of chemical reaction parameter, whereas it diminishes for growing values of solutal stratification parameter.

Solution of a few nonlinear problems in aerodynamics by the finite elements and functional least squares methods. Ph.D. Thesis - Paris Univ.; [mathematical models of transonic flow using nonlinear equations

NASA Technical Reports Server (NTRS)

Periaux, J.

1979-01-01

The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.

Nonlinear interactions in mixing layers and compressible heated round jets. Ph.D. Thesis Final Report

NASA Technical Reports Server (NTRS)

Jarrah, Yousef Mohd

1989-01-01

The nonlinear interactions between a fundamental instability mode and both its harmonics and the changing mean flow are studied using the weakly nonlinear stability theory of Stuart and Watson, and numerical solutions of coupled nonlinear partial differential equations. The first part focuses on incompressible cold (or isothermal; constant temperature throughout) mixing layers, and for these, the first and second Landau constants are calculated as functions of wavenumber and Reynolds number. It is found that the dominant contribution to the Landau constants arises from the mean flow changes and not from the higher harmonics. In order to establish the range of validity of the weakly nonlinear theory, the weakly nonlinear and numerical solutions are compared and the limitation of each is discussed. At small amplitudes and at low-to-moderate Reynolds numbers, the two results compare well in describing the saturation of the fundamental, the distortion of the mean flow, and the initial stages of vorticity roll-up. At larger amplitudes, the interaction between the fundamental, second harmonic, and the mean flow is strongly nonlinear and the numerical solution predicts flow oscillations, whereas the weakly nonlinear theory yields saturation. In the second part, the weakly nonlinear theory is extended to heated (or nonisothermal; mean temperature distribution) subsonic round jets where quadratic and cubic nonlinear interactions are present, and the Landau constants also depend on jet temperature ratio, Mach number and azimuthal mode number. Under exponential growth and nonlinear saturation, it is found that heating and compressibility suppress the growth of instability waves, that the first azimuthal mode is the dominant instability mode, and that the weakly nonlinear solution describes the early stages of the roll-up of an axisymmetric shear layer. The receptivity of a typical jet flow to pulse type input disturbance is also studied by solving the initial value problem and then examining the behavior of the long-time solution.

On the interaction of small-scale linear waves with nonlinear solitary waves

NASA Astrophysics Data System (ADS)

Xu, Chengzhu; Stastna, Marek

2017-04-01

In the study of environmental and geophysical fluid flows, linear wave theory is well developed and its application has been considered for phenomena of various length and time scales. However, due to the nonlinear nature of fluid flows, in many cases results predicted by linear theory do not agree with observations. One of such cases is internal wave dynamics. While small-amplitude wave motion may be approximated by linear theory, large amplitude waves tend to be solitary-like. In some cases, when the wave is highly nonlinear, even weakly nonlinear theories fail to predict the wave properties correctly. We study the interaction of small-scale linear waves with nonlinear solitary waves using highly accurate pseudo spectral simulations that begin with a fully nonlinear solitary wave and a train of small-amplitude waves initialized from linear waves. The solitary wave then interacts with the linear waves through either an overtaking collision or a head-on collision. During the collision, there is a net energy transfer from the linear wave train to the solitary wave, resulting in an increase in the kinetic energy carried by the solitary wave and a phase shift of the solitary wave with respect to a freely propagating solitary wave. At the same time the linear waves are greatly reduced in amplitude. The percentage of energy transferred depends primarily on the wavelength of the linear waves. We found that after one full collision cycle, the longest waves may retain as much as 90% of the kinetic energy they had initially, while the shortest waves lose almost all of their initial energy. We also found that a head-on collision is more efficient in destroying the linear waves than an overtaking collision. On the other hand, the initial amplitude of the linear waves has very little impact on the percentage of energy that can be transferred to the solitary wave. Because of the nonlinearity of the solitary wave, these results provide us some insight into wave-mean flow interaction in a fully nonlinear framework.

Toroidal equilibrium states with reversed magnetic shear and parallel flow in connection with the formation of Internal Transport Barriers

NASA Astrophysics Data System (ADS)

Kuiroukidis, Ap.; Throumoulopoulos, G. N.

2015-08-01

We construct nonlinear toroidal equilibria of fixed diverted boundary shaping with reversed magnetic shear and flows parallel to the magnetic field. The equilibria have hole-like current density and the reversed magnetic shear increases as the equilibrium nonlinearity becomes stronger. Also, application of a sufficient condition for linear stability implies that the stability is improved as the equilibrium nonlinearity correlated to the reversed magnetic shear gets stronger with a weaker stabilizing contribution from the flow. These results indicate synergetic stabilizing effects of reversed magnetic shear, equilibrium nonlinearity and flow in the establishment of Internal Transport Barriers (ITBs).

Nonlinear problems in flight dynamics

NASA Technical Reports Server (NTRS)

Chapman, G. T.; Tobak, M.

1984-01-01

A comprehensive framework is proposed for the description and analysis of nonlinear problems in flight dynamics. Emphasis is placed on the aerodynamic component as the major source of nonlinearities in the flight dynamic system. Four aerodynamic flows are examined to illustrate the richness and regularity of the flow structures and the nature of the flow structures and the nature of the resulting nonlinear aerodynamic forces and moments. A framework to facilitate the study of the aerodynamic system is proposed having parallel observational and mathematical components. The observational component, structure is described in the language of topology. Changes in flow structure are described via bifurcation theory. Chaos or turbulence is related to the analogous chaotic behavior of nonlinear dynamical systems characterized by the existence of strange attractors having fractal dimensionality. Scales of the flow are considered in the light of ideas from group theory. Several one and two degree of freedom dynamical systems with various mathematical models of the nonlinear aerodynamic forces and moments are examined to illustrate the resulting types of dynamical behavior. The mathematical ideas that proved useful in the description of fluid flows are shown to be similarly useful in the description of flight dynamic behavior.

Experiment on a feedback control of nonlinear thermocapillary convection in a half-zone liquid bridge

NASA Astrophysics Data System (ADS)

Kudo, M.; Ueno, I.; Shiomi, J.; Amberg, G.; Kawamura, H.

Under microgravity condition, themocapillarity dominates in material processing. In a half-zone method, two co-axial cylindrical rods hold a liquid bridge by the surface tension. By adding a temperature difference Δ T between the rods, thermocapillary flow is induced in the bridge. The convection changes from two-dimensional steady flow to three-dimensional oscillatory one at a critical Δ T in the case of medium to high Prandtl number (Pr) fluid. In our latest study (Shiomi et al., JFM, 2003), complete damping of the temperature oscillation was not achieved at highly nonlinear regions by a simple cancellation scheme. The excitation of unexpected other azimuthal wave numbers prevented the suppression of the oscillation. The present study aimed to develop a new control scheme with taking into account of spatio-temporal azimuthal temperature distribution. The target geometry was a liquid bridge of 5 mm in diameter and of a unit aspect ratio, Γ g(g= H/R=1, where H and R are the height and the radius of the bridge, respectively). At this aspect ratio, a dominant azimuthal mode was wave number of 2 when the control was absent. Silicone oil of 5 cSt (Pr = 68 at 25C) was employed as a test fluid. The flow field was visualized by suspending polystyrene sphere particles (D =17μ m). The present experiments were performed with 4 sensors located at different azimuthal positions for the evaluation of the azimuthal surface temperature distribution as well as with 2 heaters to suppress its non-uniform distribution. All sensors and heaters were located at the mid-height of the bridge. The present algorithm involved two main features; the first one was the time-dependent estimation of the azimuthal surface temperature distribution at the height of the sensors and heaters. Evaluation of the azimuthal temperature distribution enabled us to cancel the temperature oscillation by local heating effectively. The second one was the time-dependent evaluation of a frequency of the dominant mode number. This scheme enabled us to predict the azimuthal temperature distribution properly. The control was applied to a highly nonlinear flow that exhibited a traveling-wave type oscillatory flow (traveling flow) in the absence of the control. Under the control, the amplitude of temperature measured by each sensor attenuated significantly. The flow visualization exhibited a gradual change of the flow structure from the traveling down to the standing flow with less nonlinearity. We realized the reduction of the amplitude less than half of the initial value without amplifying other azimuthal-wave-number oscillations.

An Investigation of High-Order Shock-Capturing Methods for Computational Aeroacoustics

NASA Technical Reports Server (NTRS)

Casper, Jay; Baysal, Oktay

1997-01-01

Topics covered include: Low-dispersion scheme for nonlinear acoustic waves in nonuniform flow; Computation of acoustic scattering by a low-dispersion scheme; Algorithmic extension of low-dispersion scheme and modeling effects for acoustic wave simulation; The accuracy of shock capturing in two spatial dimensions; Using high-order methods on lower-order geometries; and Computational considerations for the simulation of discontinuous flows.

Tracer-aided modelling to explore non-linearities in flow paths, hydrological connectivity and faecal contamination risk

NASA Astrophysics Data System (ADS)

Neill, A. J.; Tetzlaff, D.; Strachan, N.; Soulsby, C.

2016-12-01

The non-linearities of runoff generation processes are strongly influenced by the connectivity of hillslopes and channel networks, particularly where overland flow is an important runoff mechanism. Despite major advances in understanding hydrological connectivity and runoff generation, the role of connectivity in the contamination of potable water supplies by faecal pathogens from grazing animals remains unclear. This is a water quality issue with serious implications for public health. Here, we sought to understand the dynamics of hydrological connectivity, flow paths and linked faecal pathogen transport in a montane catchment in Scotland with high deer populations. We firstly calibrated, within an uncertainty framework, a parsimonious tracer-aided hydrological model to daily discharge and stream isotope data. The model, developed on the basis of past empirical and tracer studies, conceptualises the catchment as three interacting hydrological source areas (dynamic saturation zone, dynamic hillslope, and groundwater) for which water fluxes, water ages and storage-based connectivity can be simulated. We next coupled several faecal indicator organism (FIO; a common indicator of faecal pathogen contamination) behaviour and transport schemes to the robust hydrological models. A further calibration was then undertaken based on the ability of each coupled model to simulate daily FIO concentrations. This gave us a final set of coupled behavioural models from which we explored how in-stream FIO dynamics could be related to the changing connectivity between the three hydrological source areas, flow paths, water ages and consequent dominant runoff generation processes. We found that high levels of FIOs were transient and episodic, and strongly correlated with periods of high connectivity through overland flow. This non-linearity in connectivity and FIO flux was successfully captured within our dynamic, tracer-aided hydrological model.

Pre-Darcy Flow in Porous Media

NASA Astrophysics Data System (ADS)

Dejam, Morteza; Hassanzadeh, Hassan; Chen, Zhangxin

2017-10-01

Fluid flow in porous media is very important in a wide range of science and engineering applications. The entire establishment of fluid flow application in porous media is based on the use of an experimental law proposed by Darcy (1856). There are evidences in the literature that the flow of a fluid in consolidated and unconsolidated porous media does not follow Darcy law at very low fluxes, which is called pre-Darcy flow. In this paper, the unsteady flow regimes of a slightly compressible fluid under the linear and radial pre-Darcy flow conditions are modeled and the corresponding highly nonlinear diffusivity equations are solved analytically by aid of a generalized Boltzmann transformation technique. The influence of pre-Darcy flow on the pressure diffusion for homogeneous porous media is studied in terms of the nonlinear exponent and the threshold pressure gradient. In addition, the pressure gradient, flux, and cumulative production per unit area are compared with the classical solution of the diffusivity equation based on Darcy flow. The presented results advance our understanding of fluid flow in low-permeability media such as shale and tight formations, where pre-Darcy is the dominant flow regime.

Linear and nonlinear instability in vertical counter-current laminar gas-liquid flows

NASA Astrophysics Data System (ADS)

Schmidt, Patrick; Ó Náraigh, Lennon; Lucquiaud, Mathieu; Valluri, Prashant

2016-04-01

We consider the genesis and dynamics of interfacial instability in vertical gas-liquid flows, using as a model the two-dimensional channel flow of a thin falling film sheared by counter-current gas. The methodology is linear stability theory (Orr-Sommerfeld analysis) together with direct numerical simulation of the two-phase flow in the case of nonlinear disturbances. We investigate the influence of two main flow parameters on the interfacial dynamics, namely the film thickness and pressure drop applied to drive the gas stream. To make contact with existing studies in the literature, the effect of various density contrasts is also examined. Energy budget analyses based on the Orr-Sommerfeld theory reveal various coexisting unstable modes (interfacial, shear, internal) in the case of high density contrasts, which results in mode coalescence and mode competition, but only one dynamically relevant unstable interfacial mode for low density contrast. A study of absolute and convective instability for low density contrast shows that the system is absolutely unstable for all but two narrow regions of the investigated parameter space. Direct numerical simulations of the same system (low density contrast) show that linear theory holds up remarkably well upon the onset of large-amplitude waves as well as the existence of weakly nonlinear waves. For high density contrasts, corresponding more closely to an air-water-type system, linear stability theory is also successful at determining the most-dominant features in the interfacial wave dynamics at early-to-intermediate times. Nevertheless, the short waves selected by the linear theory undergo secondary instability and the wave train is no longer regular but rather exhibits chaotic motion. The same linear stability theory predicts when the direction of travel of the waves changes — from downwards to upwards. We outline the practical implications of this change in terms of loading and flooding. The change in direction of the wave propagation is represented graphically in terms of a flow map based on the liquid and gas flow rates and the prediction carries over to the nonlinear regime with only a small deviation.

Linear and nonlinear instability in vertical counter-current laminar gas-liquid flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schmidt, Patrick; Lucquiaud, Mathieu; Valluri, Prashant, E-mail: prashant.valluri@ed.ac.uk

We consider the genesis and dynamics of interfacial instability in vertical gas-liquid flows, using as a model the two-dimensional channel flow of a thin falling film sheared by counter-current gas. The methodology is linear stability theory (Orr-Sommerfeld analysis) together with direct numerical simulation of the two-phase flow in the case of nonlinear disturbances. We investigate the influence of two main flow parameters on the interfacial dynamics, namely the film thickness and pressure drop applied to drive the gas stream. To make contact with existing studies in the literature, the effect of various density contrasts is also examined. Energy budget analysesmore » based on the Orr-Sommerfeld theory reveal various coexisting unstable modes (interfacial, shear, internal) in the case of high density contrasts, which results in mode coalescence and mode competition, but only one dynamically relevant unstable interfacial mode for low density contrast. A study of absolute and convective instability for low density contrast shows that the system is absolutely unstable for all but two narrow regions of the investigated parameter space. Direct numerical simulations of the same system (low density contrast) show that linear theory holds up remarkably well upon the onset of large-amplitude waves as well as the existence of weakly nonlinear waves. For high density contrasts, corresponding more closely to an air-water-type system, linear stability theory is also successful at determining the most-dominant features in the interfacial wave dynamics at early-to-intermediate times. Nevertheless, the short waves selected by the linear theory undergo secondary instability and the wave train is no longer regular but rather exhibits chaotic motion. The same linear stability theory predicts when the direction of travel of the waves changes — from downwards to upwards. We outline the practical implications of this change in terms of loading and flooding. The change in direction of the wave propagation is represented graphically in terms of a flow map based on the liquid and gas flow rates and the prediction carries over to the nonlinear regime with only a small deviation.« less

Non-Linear Harmonic flow simulations of a High-Head Francis Turbine test case

NASA Astrophysics Data System (ADS)

Lestriez, R.; Amet, E.; Tartinville, B.; Hirsch, C.

2016-11-01

This work investigates the use of the non-linear harmonic (NLH) method for a high- head Francis turbine, the Francis99 workshop test case. The NLH method relies on a Fourier decomposition of the unsteady flow components in harmonics of Blade Passing Frequencies (BPF), which are the fundamentals of the periodic disturbances generated by the adjacent blade rows. The unsteady flow solution is obtained by marching in pseudo-time to a steady-state solution of the transport equations associated with the time-mean, the BPFs and their harmonics. Thanks to this transposition into frequency domain, meshing only one blade channel is sufficient, like for a steady flow simulation. Notable benefits in terms of computing costs and engineering time can therefore be obtained compared to classical time marching approach using sliding grid techniques. The method has been applied for three operating points of the Francis99 workshop high-head Francis turbine. Steady and NLH flow simulations have been carried out for these configurations. Impact of the grid size and near-wall refinement is analysed on all operating points for steady simulations and for Best Efficiency Point (BEP) for NLH simulations. Then, NLH results for a selected grid size are compared for the three different operating points, reproducing the tendencies observed in the experiment.

Bayesian Nonlinear Assimilation of Eulerian and Lagrangian Coastal Flow Data

DTIC Science & Technology

2015-09-30

Lagrangian Coastal Flow Data Dr. Pierre F.J. Lermusiaux Department of Mechanical Engineering Center for Ocean Science and Engineering Massachusetts...Develop and apply theory, schemes and computational systems for rigorous Bayesian nonlinear assimilation of Eulerian and Lagrangian coastal flow data...coastal ocean fields, both in Eulerian and Lagrangian forms. - Further develop and implement our GMM-DO schemes for robust Bayesian nonlinear estimation

Physical vapor transport of mercurous chloride under a nonlinear thermal profile

NASA Technical Reports Server (NTRS)

Mennetrier, Christophe; Duval, Walter M. B.; Singh, Narsingh B.

1992-01-01

Our study investigates numerically the flow field characteristics during the growth of mercurous chloride (Hg2Cl2) crystals in a rectangular ampoule under terrestrial and microgravity conditions for a nonlinear thermal gradient. With a residual gas lighter than the nutrient, the solutal Grashof number is dominant. We observe that in tilted configurations, when solutal convection is dominant, the maximum transport rate occurs at approximately 40 percent. For the vertical configurations, we were able to obtain solutions only for the cases either below the critical Rayleigh numbers or the stabilized configurations. The total mass flux decreases exponentially with an increase of pressure of residual gas, but it increases following a power law with the temperature difference driving the transport. The nonlinear thermal gradient appears to destabilize the flow field when thermal convection is dominant for both vertical top-heated and bottom-heated configurations. However, when the solutal Grashof number is dominant, the density gradient resulting from the solutal gradient appears to stabilize the flow for the bottom-heated configuration. The flow field for the top-heated configuration is destabilized for high Grashof numbers. The microgravity environment provides a means for lowering convection. For gravity levels of 10(exp -3) g(0) or less, the Stefan wind drives the flow, and no recirculating cell is predicted.

A Mass Tracking Formulation for Bubbles in Incompressible Flow

DTIC Science & Technology

2012-10-14

incompressible flow to fully nonlinear compressible flow including the effects of shocks and rarefactions , and then subsequently making a number of...using the ideas from [19] to couple together incompressible flow with fully nonlinear compressible flow including shocks and rarefactions . The results...compressible flow including the effects of shocks and rarefactions , and then subsequently making a number of simplifying assumptions on the air flow

Subcritical transition scenarios via linear and nonlinear localized optimal perturbations in plane Poiseuille flow

NASA Astrophysics Data System (ADS)

Farano, Mirko; Cherubini, Stefania; Robinet, Jean-Christophe; De Palma, Pietro

2016-12-01

Subcritical transition in plane Poiseuille flow is investigated by means of a Lagrange-multiplier direct-adjoint optimization procedure with the aim of finding localized three-dimensional perturbations optimally growing in a given time interval (target time). Space localization of these optimal perturbations (OPs) is achieved by choosing as objective function either a p-norm (with p\\gg 1) of the perturbation energy density in a linear framework; or the classical (1-norm) perturbation energy, including nonlinear effects. This work aims at analyzing the structure of linear and nonlinear localized OPs for Poiseuille flow, and comparing their transition thresholds and scenarios. The nonlinear optimization approach provides three types of solutions: a weakly nonlinear, a hairpin-like and a highly nonlinear optimal perturbation, depending on the value of the initial energy and the target time. The former shows localization only in the wall-normal direction, whereas the latter appears much more localized and breaks the spanwise symmetry found at lower target times. Both solutions show spanwise inclined vortices and large values of the streamwise component of velocity already at the initial time. On the other hand, p-norm optimal perturbations, although being strongly localized in space, keep a shape similar to linear 1-norm optimal perturbations, showing streamwise-aligned vortices characterized by low values of the streamwise velocity component. When used for initializing direct numerical simulations, in most of the cases nonlinear OPs provide the most efficient route to transition in terms of time to transition and initial energy, even when they are less localized in space than the p-norm OP. The p-norm OP follows a transition path similar to the oblique transition scenario, with slightly oscillating streaks which saturate and eventually experience secondary instability. On the other hand, the nonlinear OP rapidly forms large-amplitude bent streaks and skips the phases of streak saturation, providing a contemporary growth of all of the velocity components due to strong nonlinear coupling.

On a solution of the nonlinear differential equation for transonic flow past a wave-shaped wall

NASA Technical Reports Server (NTRS)

Kaplan, Carl

1952-01-01

The Prandtl-Busemann small-perturbation method is utilized to obtain the flow of a compressible fluid past an infinitely long wave-shaped wall. When the essential assumption for transonic flow (that all Mach numbers in the region of flow are nearly unity) is introduced, the expression for the velocity potential takes the form of a power series in the transonic similarity parameter. On the basis of this form of the solution, an attempt is made to solve the nonlinear differential equation for transonic flow past the wavy wall. The analysis utilized exhibits clearly the difficulties inherent in nonlinear-flow problems.

Darcy-Forchheimer Three-Dimensional Flow of Williamson Nanofluid over a Convectively Heated Nonlinear Stretching Surface

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Alsaedi, Ahmed

2017-09-01

The present study elaborates three-dimensional flow of Williamson nanoliquid over a nonlinear stretchable surface. Fluid flow obeys Darcy-Forchheimer porous medium. A bidirectional nonlinear stretching surface generates the flow. Convective surface condition of heat transfer is taken into consideration. Further the zero nanoparticles mass flux condition is imposed at the boundary. Effects of thermophoresis and Brownian diffusion are considered. Assumption of boundary layer has been employed in the problem formulation. Convergent series solutions for the nonlinear governing system are established through the optimal homotopy analysis method (OHAM). Graphs have been sketched in order to analyze that how the velocity, temperature and concentration distributions are affected by distinct emerging flow parameters. Skin friction coefficients and local Nusselt number are also computed and discussed.

Nonlinear saturation of the slab ITG instability and zonal flow generation with fully kinetic ions

NASA Astrophysics Data System (ADS)

Miecnikowski, Matthew T.; Sturdevant, Benjamin J.; Chen, Yang; Parker, Scott E.

2018-05-01

Fully kinetic turbulence models are of interest for their potential to validate or replace gyrokinetic models in plasma regimes where the gyrokinetic expansion parameters are marginal. Here, we demonstrate fully kinetic ion capability by simulating the growth and nonlinear saturation of the ion-temperature-gradient instability in shearless slab geometry assuming adiabatic electrons and including zonal flow dynamics. The ion trajectories are integrated using the Lorentz force, and the cyclotron motion is fully resolved. Linear growth and nonlinear saturation characteristics show excellent agreement with analogous gyrokinetic simulations across a wide range of parameters. The fully kinetic simulation accurately reproduces the nonlinearly generated zonal flow. This work demonstrates nonlinear capability, resolution of weak gradient drive, and zonal flow physics, which are critical aspects of modeling plasma turbulence with full ion dynamics.

Low-Dispersion Scheme for Nonlinear Acoustic Waves in Nonuniform Flow

NASA Technical Reports Server (NTRS)

Baysal, Oktay; Kaushik, Dinesh K.; Idres, Moumen

1997-01-01

The linear dispersion-relation-preserving scheme and its boundary conditions have been extended to the nonlinear Euler equations. This allowed computing, a nonuniform flowfield and a nonlinear acoustic wave propagation in such a medium, by the same scheme. By casting all the equations, boundary conditions, and the solution scheme in generalized curvilinear coordinates, the solutions were made possible for non-Cartesian domains and, for the better deployment of the grid points, nonuniform grid step sizes could be used. It has been tested for a number of simple initial-value and periodic-source problems. A simple demonstration of the difference between a linear and nonlinear propagation was conducted. The wall boundary condition, derived from the momentum equations and implemented through a pressure at a ghost point, and the radiation boundary condition, derived from the asymptotic solution to the Euler equations, have proven to be effective for the nonlinear equations and nonuniform flows. The nonreflective characteristic boundary conditions also have shown success but limited to the nonlinear waves in no mean flow, and failed for nonlinear waves in nonuniform flow.

Efficient C1-continuous phase-potential upwind (C1-PPU) schemes for coupled multiphase flow and transport with gravity

NASA Astrophysics Data System (ADS)

Jiang, Jiamin; Younis, Rami M.

2017-10-01

In the presence of counter-current flow, nonlinear convergence problems may arise in implicit time-stepping when the popular phase-potential upwinding (PPU) scheme is used. The PPU numerical flux is non-differentiable across the co-current/counter-current flow regimes. This may lead to cycles or divergence in the Newton iterations. Recently proposed methods address improved smoothness of the numerical flux. The objective of this work is to devise and analyze an alternative numerical flux scheme called C1-PPU that, in addition to improving smoothness with respect to saturations and phase potentials, also improves the level of scalar nonlinearity and accuracy. C1-PPU involves a novel use of the flux limiter concept from the context of high-resolution methods, and allows a smooth variation between the co-current/counter-current flow regimes. The scheme is general and applies to fully coupled flow and transport formulations with an arbitrary number of phases. We analyze the consistency property of the C1-PPU scheme, and derive saturation and pressure estimates, which are used to prove the solution existence. Several numerical examples for two- and three-phase flows in heterogeneous and multi-dimensional reservoirs are presented. The proposed scheme is compared to the conventional PPU and the recently proposed Hybrid Upwinding schemes. We investigate three properties of these numerical fluxes: smoothness, nonlinearity, and accuracy. The results indicate that in addition to smoothness, nonlinearity may also be critical for convergence behavior and thus needs to be considered in the design of an efficient numerical flux scheme. Moreover, the numerical examples show that the C1-PPU scheme exhibits superior convergence properties for large time steps compared to the other alternatives.

A statistical state dynamics approach to wall turbulence.

PubMed

Farrell, B F; Gayme, D F; Ioannou, P J

2017-03-13

This paper reviews results obtained using statistical state dynamics (SSD) that demonstrate the benefits of adopting this perspective for understanding turbulence in wall-bounded shear flows. The SSD approach used in this work employs a second-order closure that retains only the interaction between the streamwise mean flow and the streamwise mean perturbation covariance. This closure restricts nonlinearity in the SSD to that explicitly retained in the streamwise constant mean flow together with nonlinear interactions between the mean flow and the perturbation covariance. This dynamical restriction, in which explicit perturbation-perturbation nonlinearity is removed from the perturbation equation, results in a simplified dynamics referred to as the restricted nonlinear (RNL) dynamics. RNL systems, in which a finite ensemble of realizations of the perturbation equation share the same mean flow, provide tractable approximations to the SSD, which is equivalent to an infinite ensemble RNL system. This infinite ensemble system, referred to as the stochastic structural stability theory system, introduces new analysis tools for studying turbulence. RNL systems provide computationally efficient means to approximate the SSD and produce self-sustaining turbulence exhibiting qualitative features similar to those observed in direct numerical simulations despite greatly simplified dynamics. The results presented show that RNL turbulence can be supported by as few as a single streamwise varying component interacting with the streamwise constant mean flow and that judicious selection of this truncated support or 'band-limiting' can be used to improve quantitative accuracy of RNL turbulence. These results suggest that the SSD approach provides new analytical and computational tools that allow new insights into wall turbulence.This article is part of the themed issue 'Toward the development of high-fidelity models of wall turbulence at large Reynolds number'. © 2017 The Author(s).

A statistical state dynamics approach to wall turbulence

PubMed Central

Gayme, D. F.; Ioannou, P. J.

2017-01-01

This paper reviews results obtained using statistical state dynamics (SSD) that demonstrate the benefits of adopting this perspective for understanding turbulence in wall-bounded shear flows. The SSD approach used in this work employs a second-order closure that retains only the interaction between the streamwise mean flow and the streamwise mean perturbation covariance. This closure restricts nonlinearity in the SSD to that explicitly retained in the streamwise constant mean flow together with nonlinear interactions between the mean flow and the perturbation covariance. This dynamical restriction, in which explicit perturbation–perturbation nonlinearity is removed from the perturbation equation, results in a simplified dynamics referred to as the restricted nonlinear (RNL) dynamics. RNL systems, in which a finite ensemble of realizations of the perturbation equation share the same mean flow, provide tractable approximations to the SSD, which is equivalent to an infinite ensemble RNL system. This infinite ensemble system, referred to as the stochastic structural stability theory system, introduces new analysis tools for studying turbulence. RNL systems provide computationally efficient means to approximate the SSD and produce self-sustaining turbulence exhibiting qualitative features similar to those observed in direct numerical simulations despite greatly simplified dynamics. The results presented show that RNL turbulence can be supported by as few as a single streamwise varying component interacting with the streamwise constant mean flow and that judicious selection of this truncated support or ‘band-limiting’ can be used to improve quantitative accuracy of RNL turbulence. These results suggest that the SSD approach provides new analytical and computational tools that allow new insights into wall turbulence. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’. PMID:28167577

Non-linear optical flow cytometry using a scanned, Bessel beam light-sheet.

PubMed

Collier, Bradley B; Awasthi, Samir; Lieu, Deborah K; Chan, James W

2015-05-29

Modern flow cytometry instruments have become vital tools for high-throughput analysis of single cells. However, as issues with the cellular labeling techniques often used in flow cytometry have become more of a concern, the development of label-free modalities for cellular analysis is increasingly desired. Non-linear optical phenomena (NLO) are of growing interest for label-free analysis because of the ability to measure the intrinsic optical response of biomolecules found in cells. We demonstrate that a light-sheet consisting of a scanned Bessel beam is an optimal excitation geometry for efficiently generating NLO signals in a microfluidic environment. The balance of photon density and cross-sectional area provided by the light-sheet allowed significantly larger two-photon fluorescence intensities to be measured in a model polystyrene microparticle system compared to measurements made using other excitation focal geometries, including a relaxed Gaussian excitation beam often used in conventional flow cytometers.

Nonlinear MHD study on the influence of E×B flow in QH-mode plasma of DIII-D

NASA Astrophysics Data System (ADS)

Liu, Feng; Huijsmans, Guido; Loarte, Alberto; Garofalo, Andrea; Solomon, Wayne; Nkonga, Boniface; Hoelzl, Matthias

2017-10-01

In QH-mode experiments with zero-net NBI torque show that there remains a finite E×B rotation in the pedestal region implying that a minimum E×B flow or flow shear is required for the plasma to develop the Edge Harmonic Oscillation (EHO), which is a saturated KPM (kink-peeling mode) characteristic of the QH-mode. To understand the roles of E×B flow and its shear in the saturation of KPMs, non-linear MHD simulations of DIII-D QH-mode plasmas including toroidal mode numbers n = 0 to 10 with different E×B rotation speed have been performed. These simulation show that ExB rotation strongly stabilizes high-n modes but destabilizes low-n modes (particularly the n =2 mode) in the linear growth phase, which is consistent experimental observations and previous linear MHD modelling. US DOE under DE-FC02-04ER54698.

Prediction of High-Lift Flows using Turbulent Closure Models

NASA Technical Reports Server (NTRS)

Rumsey, Christopher L.; Gatski, Thomas B.; Ying, Susan X.; Bertelrud, Arild

1997-01-01

The flow over two different multi-element airfoil configurations is computed using linear eddy viscosity turbulence models and a nonlinear explicit algebraic stress model. A subset of recently-measured transition locations using hot film on a McDonnell Douglas configuration is presented, and the effect of transition location on the computed solutions is explored. Deficiencies in wake profile computations are found to be attributable in large part to poor boundary layer prediction on the generating element, and not necessarily inadequate turbulence modeling in the wake. Using measured transition locations for the main element improves the prediction of its boundary layer thickness, skin friction, and wake profile shape. However, using measured transition locations on the slat still yields poor slat wake predictions. The computation of the slat flow field represents a key roadblock to successful predictions of multi-element flows. In general, the nonlinear explicit algebraic stress turbulence model gives very similar results to the linear eddy viscosity models.

Reduced-order modeling of the flow around a high-lift configuration with unsteady Coanda blowing

NASA Astrophysics Data System (ADS)

Semaan, Richard; Cordier, Laurent; Noack, Bernd; Kumar, Pradeep; Burnazzi, Marco; Tissot, Gilles

2015-11-01

We propose a low-dimensional POD model for the transient and post-transient flow around a high-lift airfoil with unsteady Coanda blowing over the trailing edge. This model comprises the effect of high-frequency modulated blowing which mitigates vortex shedding and increases lift. The structure of the dynamical system is derived from the Navier-Stokes equations with a Galerkin projection and from subsequent dynamic simplifications. The system parameters are determined with a data assimilation (4D-Var) method. The boundary actuation is incorporated into the model with actuation modes following Graham et al. (1999); Kasnakoğlu et al. (2008). As novel enabler, we show that the performance of the POD model significantly benefits from employing additional actuation modes for different frequency components associated with the same actuation input. In addition, linear, weakly nonlinear and fully nonlinear models are considered. The current study suggests that separate actuation modes for different actuation frequencies improve Galerkin model performance, in particular with respect to the important base-flow changes. We acknowledge (1) the Collaborative Research Centre (CRC 880) ``Fundamentals of High Lift of Future Civil Aircraft,'' and 2) the Senior Chair of Excellence ``Closed-loop control of turbulent shear flows using reduced-order models'' (TUCOROM).

On controlling nonlinear dissipation in high order filter methods for ideal and non-ideal MHD

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjogreen, B.

2004-01-01

The newly developed adaptive numerical dissipation control in spatially high order filter schemes for the compressible Euler and Navier-Stokes equations has been recently extended to the ideal and non-ideal magnetohydrodynamics (MHD) equations. These filter schemes are applicable to complex unsteady MHD high-speed shock/shear/turbulence problems. They also provide a natural and efficient way for the minimization of Div(B) numerical error. The adaptive numerical dissipation mechanism consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and leave the rest of the region free from numerical dissipation contamination. The numerical dissipation considered consists of high order linear dissipation for the suppression of high frequency oscillation and the nonlinear dissipative portion of high-resolution shock-capturing methods for discontinuity capturing. The applicable nonlinear dissipative portion of high-resolution shock-capturing methods is very general. The objective of this paper is to investigate the performance of three commonly used types of nonlinear numerical dissipation for both the ideal and non-ideal MHD.

A simple model describing the nonlinear dynamics of the dusk/dawn asymmetry in the high-latitude thermospheric flow

NASA Technical Reports Server (NTRS)

Gundlach, J. P.; Larsen, M. F.; Mikkelsen, I. S.

1988-01-01

A simple nonlinear, axisymmetric, shallow-water numerical model has been used to study the asymmetry in the neutral flow between the dusk and dawn sides of the auroral oval. The results indicate that the Coriolis force and the curvature terms are nearly in balance on the evening side and require only a small pressure gradient to effect adjustment. The result is smaller neutral velocities near dawn and larger velocities near dusk than would be the case for a linearized treatment. A consequence is that more gravity wave energy is produced on the morning side than on the evening side.

Parametric study of flow patterns behind the standing accretion shock wave for core-collapse supernovae

DOE Office of Scientific and Technical Information (OSTI.GOV)

Iwakami, Wakana; Nagakura, Hiroki; Yamada, Shoichi, E-mail: wakana@heap.phys.waseda.ac.jp

2014-05-10

In this study, we conduct three-dimensional hydrodynamic simulations systematically to investigate the flow patterns behind the accretion shock waves that are commonly formed in the post-bounce phase of core-collapse supernovae. Adding small perturbations to spherically symmetric, steady, shocked accretion flows, we compute the subsequent evolutions to find what flow pattern emerges as a consequence of hydrodynamical instabilities such as convection and standing accretion shock instability for different neutrino luminosities and mass accretion rates. Depending on these two controlling parameters, various flow patterns are indeed realized. We classify them into three basic patterns and two intermediate ones; the former includes sloshingmore » motion (SL), spiral motion (SP), and multiple buoyant bubble formation (BB); the latter consists of spiral motion with buoyant-bubble formation (SPB) and spiral motion with pulsationally changing rotational velocities (SPP). Although the post-shock flow is highly chaotic, there is a clear trend in the pattern realization. The sloshing and spiral motions tend to be dominant for high accretion rates and low neutrino luminosities, and multiple buoyant bubbles prevail for low accretion rates and high neutrino luminosities. It is interesting that the dominant pattern is not always identical between the semi-nonlinear and nonlinear phases near the critical luminosity; the intermediate cases are realized in the latter case. Running several simulations with different random perturbations, we confirm that the realization of flow pattern is robust in most cases.« less

Evolution of finite-amplitude localized vortices in planar homogeneous shear flows

NASA Astrophysics Data System (ADS)

Karp, Michael; Shukhman, Ilia G.; Cohen, Jacob

2017-02-01

An analytical-based method is utilized to follow the evolution of localized initially Gaussian disturbances in flows with homogeneous shear, in which the base velocity components are at most linear functions of the coordinates, including hyperbolic, elliptic, and simple shear. Coherent structures, including counterrotating vortex pairs (CVPs) and hairpin vortices, are formed for the cases where the streamlines of the base flow are open (hyperbolic and simple shear). For hyperbolic base flows, the dominance of shear over rotation leads to elongation of the localized disturbance along the outlet asymptote and formation of CVPs. For simple shear CVPs are formed from linear and nonlinear disturbances, whereas hairpins are observed only for highly nonlinear disturbances. For elliptic base flows CVPs, hairpins and vortex loops form initially, however they do not last and break into various vortical structures that spread in the spanwise direction. The effect of the disturbance's initial amplitude and orientation is examined and the optimal orientation achieving maximal growth is identified.

Polarization curve measurements combined with potential probe sensing for determining current density distribution in vanadium redox-flow batteries

NASA Astrophysics Data System (ADS)

Becker, Maik; Bredemeyer, Niels; Tenhumberg, Nils; Turek, Thomas

2016-03-01

Potential probes are applied to vanadium redox-flow batteries for determination of effective felt resistance and current density distribution. During the measurement of polarization curves in 100 cm2 cells with different carbon felt compression rates, alternating potential steps at cell voltages between 0.6 V and 2.0 V are applied. Polarization curves are recorded at different flow rates and states of charge of the battery. Increasing compression rates lead to lower effective felt resistances and a more uniform resistance distribution. Low flow rates at high or low state of charge result in non-linear current density distribution with high gradients, while high flow rates give rise to a nearly linear behavior.

Large-eddy simulations of the restricted nonlinear system

NASA Astrophysics Data System (ADS)

Bretheim, Joel; Gayme, Dennice; Meneveau, Charles

2014-11-01

Wall-bounded shear flows often exhibit elongated flow structures with streamwise coherence (e.g. rolls/streaks), prompting the exploration of a streamwise-constant modeling framework to investigate wall-turbulence. Simulations of a streamwise-constant (2D/3C) model have been shown to produce the roll/streak structures and accurately reproduce the blunted turbulent mean velocity profile in plane Couette flow. The related restricted nonlinear (RNL) model captures these same features but also exhibits self-sustaining turbulent behavior. Direct numerical simulation (DNS) of the RNL system results in similar statistics for a number of flow quantities and a flow field that is consistent with DNS of the Navier-Stokes equations. Aiming to develop reduced-order models of wall-bounded turbulence at very high Reynolds numbers in which viscous near-wall dynamics cannot be resolved, this work presents the development of an RNL formulation of the filtered Navier-Stokes equations solved for in large-eddy simulations (LES). The proposed LES-RNL system is a computationally affordable reduced-order modeling tool that is of interest for studying the underlying dynamics of high-Reynolds wall-turbulence and for engineering applications where the flow field is dominated by streamwise-coherent motions. This work is supported by NSF (IGERT, SEP-1230788 and IIA-1243482).

Rheological Variations in Lahars Expected to Flow Along the Sides of Sakurajima and Ontake Volcanoes, Japan

NASA Astrophysics Data System (ADS)

Kurokawa, A. K.; Ishibashi, H.

2016-12-01

Volcanic ash is known to accumulate on the ground surface around volcano after eruptions. Once the ash gains weight and mixes with water to a critical point, the mixture of volcanic ash and water runs down a side of volcano causing severe damage to the ambient environment. The flow is referred to as lahar that is widely observed all over the world and it occasionally generates seismic signals [Walsh et al., 2016; Ogiso and Yomogida, 2015]. Sometimes it happens just after an eruption [Nakayama and Kuroda, 2003] whereas a large debris flow, which occurred about 30 years after the latest eruption due to heavy rainfall is also reported [Ogiso and Yomogida, 2015]. Thus when the lahar starts flowing is a key. In order to understand flow characteristics of lahar, it is important to focus on the rheology. However, little is known about the rheological property although the experimental condition can be controlled at atmospheric pressure and ambient temperature. This is an advantage when compared with magma and rock, which need to reach high-pressure and/or high-temperature conditions to be measured. Based on the background, we have performed basic rheological measurements using mixtures of water and volcanic ashes collected at Sakurajima and Ontake volcanoes in Japan. The first important point of our findings is that the two types of mixtures show non-linear characteristics differently. For instance, the viscosity variation strongly depends on the water content in the case of Sakurajima sample while the viscosity fluctuates within a certain definite range of shear rate using Ontake sample. Since these non-linear characteristics are related to structural changes in the flow, our results indicate that the flow of lahar is time-variable and complicated. In this presentation, we report the non-linear rheology in detail and go into the relation to temporal changes in the flow.

Phase relations in a forced turbulent boundary layer: implications for modelling of high Reynolds number wall turbulence

PubMed Central

2017-01-01

Phase relations between specific scales in a turbulent boundary layer are studied here by highlighting the associated nonlinear scale interactions in the flow. This is achieved through an experimental technique that allows for targeted forcing of the flow through the use of a dynamic wall perturbation. Two distinct large-scale modes with well-defined spatial and temporal wavenumbers were simultaneously forced in the boundary layer, and the resulting nonlinear response from their direct interactions was isolated from the turbulence signal for the study. This approach advances the traditional studies of large- and small-scale interactions in wall turbulence by focusing on the direct interactions between scales with triadic wavenumber consistency. The results are discussed in the context of modelling high Reynolds number wall turbulence. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’. PMID:28167576

Direct numerical simulation of a compressible boundary-layer flow past an isolated three-dimensional hump in a high-speed subsonic regime

NASA Astrophysics Data System (ADS)

De Grazia, D.; Moxey, D.; Sherwin, S. J.; Kravtsova, M. A.; Ruban, A. I.

2018-02-01

In this paper we study the boundary-layer separation produced in a high-speed subsonic boundary layer by a small wall roughness. Specifically, we present a direct numerical simulation (DNS) of a two-dimensional boundary-layer flow over a flat plate encountering a three-dimensional Gaussian-shaped hump. This work was motivated by the lack of DNS data of boundary-layer flows past roughness elements in a similar regime which is typical of civil aviation. The Mach and Reynolds numbers are chosen to be relevant for aeronautical applications when considering small imperfections at the leading edge of wings. We analyze different heights of the hump: The smaller heights result in a weakly nonlinear regime, while the larger result in a fully nonlinear regime with an increasing laminar separation bubble arising downstream of the roughness element and the formation of a pair of streamwise counterrotating vortices which appear to support themselves.

A high order accurate finite element algorithm for high Reynolds number flow prediction

NASA Technical Reports Server (NTRS)

Baker, A. J.

1978-01-01

A Galerkin-weighted residuals formulation is employed to establish an implicit finite element solution algorithm for generally nonlinear initial-boundary value problems. Solution accuracy, and convergence rate with discretization refinement, are quantized in several error norms, by a systematic study of numerical solutions to several nonlinear parabolic and a hyperbolic partial differential equation characteristic of the equations governing fluid flows. Solutions are generated using selective linear, quadratic and cubic basis functions. Richardson extrapolation is employed to generate a higher-order accurate solution to facilitate isolation of truncation error in all norms. Extension of the mathematical theory underlying accuracy and convergence concepts for linear elliptic equations is predicted for equations characteristic of laminar and turbulent fluid flows at nonmodest Reynolds number. The nondiagonal initial-value matrix structure introduced by the finite element theory is determined intrinsic to improved solution accuracy and convergence. A factored Jacobian iteration algorithm is derived and evaluated to yield a consequential reduction in both computer storage and execution CPU requirements while retaining solution accuracy.

Non-linear models for the detection of impaired cerebral blood flow autoregulation.

PubMed

Chacón, Max; Jara, José Luis; Miranda, Rodrigo; Katsogridakis, Emmanuel; Panerai, Ronney B

2018-01-01

The ability to discriminate between normal and impaired dynamic cerebral autoregulation (CA), based on measurements of spontaneous fluctuations in arterial blood pressure (BP) and cerebral blood flow (CBF), has considerable clinical relevance. We studied 45 normal subjects at rest and under hypercapnia induced by breathing a mixture of carbon dioxide and air. Non-linear models with BP as input and CBF velocity (CBFV) as output, were implemented with support vector machines (SVM) using separate recordings for learning and validation. Dynamic SVM implementations used either moving average or autoregressive structures. The efficiency of dynamic CA was estimated from the model's derived CBFV response to a step change in BP as an autoregulation index for both linear and non-linear models. Non-linear models with recurrences (autoregressive) showed the best results, with CA indexes of 5.9 ± 1.5 in normocapnia, and 2.5 ± 1.2 for hypercapnia with an area under the receiver-operator curve of 0.955. The high performance achieved by non-linear SVM models to detect deterioration of dynamic CA should encourage further assessment of its applicability to clinical conditions where CA might be impaired.

Non-linear models for the detection of impaired cerebral blood flow autoregulation

PubMed Central

Miranda, Rodrigo; Katsogridakis, Emmanuel

2018-01-01

The ability to discriminate between normal and impaired dynamic cerebral autoregulation (CA), based on measurements of spontaneous fluctuations in arterial blood pressure (BP) and cerebral blood flow (CBF), has considerable clinical relevance. We studied 45 normal subjects at rest and under hypercapnia induced by breathing a mixture of carbon dioxide and air. Non-linear models with BP as input and CBF velocity (CBFV) as output, were implemented with support vector machines (SVM) using separate recordings for learning and validation. Dynamic SVM implementations used either moving average or autoregressive structures. The efficiency of dynamic CA was estimated from the model’s derived CBFV response to a step change in BP as an autoregulation index for both linear and non-linear models. Non-linear models with recurrences (autoregressive) showed the best results, with CA indexes of 5.9 ± 1.5 in normocapnia, and 2.5 ± 1.2 for hypercapnia with an area under the receiver-operator curve of 0.955. The high performance achieved by non-linear SVM models to detect deterioration of dynamic CA should encourage further assessment of its applicability to clinical conditions where CA might be impaired. PMID:29381724

On the nonlinear forced response of the North Atlantic atmosphere to meridional shifts of the Gulf Stream path

NASA Astrophysics Data System (ADS)

Seo, H.; Kwon, Y. O.; Joyce, T. M.; Ummenhofer, C.

2016-12-01

This study examines the North Atlantic atmospheric circulation response to the meridional shift of Gulf Stream path using a large-ensemble, high-resolution, and hemispheric-scale WRF simulations. The model is forced with wintertime SST anomalies derived from a wide range of Gulf Stream shift scenarios. The key result of the model experiments, supported in part by an independent analysis of a reanalysis data set, is that the large-scale, quasi-steady North Atlantic circulation response is unambiguously nonlinear about the sign and amplitude of chosen SST anomalies. This nonlinear response prevails over the weak linear response and resembles the negative North Atlantic Oscillation, the leading intrinsic mode of variability in the model and the observations. Further analysis of the associated dynamics reveals that the nonlinear responses are accompanied by the anomalous southward shift of the North Atlantic eddy-driven jet stream, which is reinforced nearly equally by the high-frequency transient eddy feedback and the low-frequency high-latitude wave breaking events. The result highlights the importance of the intrinsically nonlinear transient eddy dynamics and eddy-mean flow interactions in generating the nonlinear forced response to the meridional shift in the Gulf Stream.

A predication model for combustion modes of the scramjet-powered aerospace vehicle based on the nonlinear features of the isolator flow field

NASA Astrophysics Data System (ADS)

Yang, Qingchun; Wang, Hongxin; Chetehouna, Khaled; Gascoin, Nicolas

2017-01-01

The supersonic combustion ramjet (scramjet) engine remains the most promising airbreathing engine cycle for hypersonic flight, particularly the high-performance dual-mode scramjet in the range of flight Mach number from 4 to 7, because it can operates under different combustion modes. Isolator is a very key component of the dual-mode scramjet engine. In this paper, nonlinear characteristics of combustion mode transition is theoretically analyzed. The discontinuous sudden changes of static pressure and Mach number are obtained as the mode transition occurs, which emphasizing the importance of predication and control of combustion modes. In this paper, a predication model of different combustion modes is developed based on these these nonlinear features in the isolator flow field. it can provide a valuable reference for control system design of the scramjet-powered aerospace vehicle.

Sliding Mode Thermal Control System for Space Station Furnace Facility

NASA Technical Reports Server (NTRS)

Jackson Mark E.; Shtessel, Yuri B.

1998-01-01

The decoupled control of the nonlinear, multiinput-multioutput, and highly coupled space station furnace facility (SSFF) thermal control system is addressed. Sliding mode control theory, a subset of variable-structure control theory, is employed to increase the performance, robustness, and reliability of the SSFF's currently designed control system. This paper presents the nonlinear thermal control system description and develops the sliding mode controllers that cause the interconnected subsystems to operate in their local sliding modes, resulting in control system invariance to plant uncertainties and external and interaction disturbances. The desired decoupled flow-rate tracking is achieved by optimization of the local linear sliding mode equations. The controllers are implemented digitally and extensive simulation results are presented to show the flow-rate tracking robustness and invariance to plant uncertainties, nonlinearities, external disturbances, and variations of the system pressure supplied to the controlled subsystems.

A study of nonlinear dynamics of single- and two-phase flow oscillations

NASA Astrophysics Data System (ADS)

Mawasha, Phetolo Ruby

The dynamics of single- and two-phase flows in channels can be contingent on nonlinearities which are not clearly understood. These nonlinearities could be interfacial forces between the flowing fluid and its walls, variations in fluid properties, growth of voids, etc. The understanding of nonlinear dynamics of fluid flow is critical in physical systems which can undergo undesirable system operating scenarios such an oscillatory behavior which may lead to component failure. A nonlinear lumped mathematical model of a surge tank with a constant inlet flow into the tank and an outlet flow through a channel is derived from first principles. The model is used to demonstrate that surge tanks with inlet and outlet flows contribute to oscillatory behavior in laminar, turbulent, single-phase, and two-phase flow systems. Some oscillations are underdamped while others are self-sustaining. The mechanisms that are active in single-phase oscillations with no heating are presented using specific cases of simplified models. Also, it is demonstrated how an external mechanism such as boiling contributes to the oscillations observed in two-phase flow and gives rise to sustained oscillations (or pressure drop oscillations). A description of the pressure drop oscillation mechanism is presented using the steady state pressure drop versus mass flow rate characteristic curve of the heated channel, available steady state pressure drop versus mass flow rate from the surge tank, and the transient pressure drop versus mass flow rate limit cycle. Parametric studies are used to verify the theoretical pressure drop oscillations model using experimental data by Yuncu's (1990). The following contributions are unique: (1) comparisons of nonlinear pressure drop oscillation models with and without the effect of the wall thermal heat capacity and (2) comparisons of linearized pressure drop oscillation models with and without the effect of the wall thermal heat capacity to identify stability boundaries.

Numerical Simulations of Multidimensional Flows in Presence of either Strong Shocks or Strong Gravitational Fields

NASA Astrophysics Data System (ADS)

Font, J. A.; Ibanez, J. M.; Marti, J. M.

1993-04-01

Some numerical solutions via local characteristic approach have been obtained describing multidimensional flows. These solutions have been used as tests of a two- dimensional code which extends some high-resolution shock-captunng methods, designed recently to solve nonlinear hyperbolic systems of conservation laws. K words: HYDRODYNAMICS - BLACK HOLE - RELATIVITY - SHOCK WAVES

The mechanism by which nonlinearity sustains turbulence in plane Couette flow

NASA Astrophysics Data System (ADS)

Nikolaidis, M.-A.; Farrell, B. F.; Ioannou, P. J.

2018-04-01

Turbulence in wall-bounded shear flow results from a synergistic interaction between linear non-normality and nonlinearity in which non-normal growth of a subset of perturbations configured to transfer energy from the externally forced component of the turbulent state to the perturbation component maintains the perturbation energy, while the subset of energy-transferring perturbations is replenished by nonlinearity. Although it is accepted that both linear non-normality mediated energy transfer from the forced component of the mean flow and nonlinear interactions among perturbations are required to maintain the turbulent state, the detailed physical mechanism by which these processes interact in maintaining turbulence has not been determined. In this work a statistical state dynamics based analysis is performed on turbulent Couette flow at R = 600 and a comparison to DNS is used to demonstrate that the perturbation component in Couette flow turbulence is replenished by a non-normality mediated parametric growth process in which the fluctuating streamwise mean flow has been adjusted to marginal Lyapunov stability. It is further shown that the alternative mechanism in which the subspace of non-normally growing perturbations is maintained directly by perturbation-perturbation nonlinearity does not contribute to maintaining the turbulent state. This work identifies parametric interaction between the fluctuating streamwise mean flow and the streamwise varying perturbations to be the mechanism of the nonlinear interaction maintaining the perturbation component of the turbulent state, and identifies the associated Lyapunov vectors with positive energetics as the structures of the perturbation subspace supporting the turbulence.

High Level Impulse Sounds and Human Hearing: Standards, Physiology, Quantification

DTIC Science & Technology

2012-05-01

a result of this change the piston-like movements of the stapes are replaced by a tilting action, which is much less effective in pushing cochlear ...Above this threshold, high noise levels result in a turbulent flow of air through the nonlinear element of the protector, effectively dissipating the...electrical diagrams of earplug and earmuff models (Kalb, 2011). In the model shown, the energy flow through the HPD propagates along three parallel

Correlating non-linear properties with spectral states of RXTE data: possible observational evidences for four different accretion modes around compact objects

NASA Astrophysics Data System (ADS)

Adegoke, Oluwashina; Dhang, Prasun; Mukhopadhyay, Banibrata; Ramadevi, M. C.; Bhattacharya, Debbijoy

2018-05-01

By analysing the time series of RXTE/PCA data, the non-linear variabilities of compact sources have been repeatedly established. Depending on the variation in temporal classes, compact sources exhibit different non-linear features. Sometimes they show low correlation/fractal dimension, but in other classes or intervals of time they exhibit stochastic nature. This could be because the accretion flow around a compact object is a non-linear general relativistic system involving magnetohydrodynamics. However, the more conventional way of addressing a compact source is the analysis of its spectral state. Therefore, the question arises: What is the connection of non-linearity to the underlying spectral properties of the flow when the non-linear properties are related to the associated transport mechanisms describing the geometry of the flow? This work is aimed at addressing this question. Based on the connection between observed spectral and non-linear (time series) properties of two X-ray binaries: GRS 1915+105 and Sco X-1, we attempt to diagnose the underlying accretion modes of the sources in terms of known accretion classes, namely, Keplerian disc, slim disc, advection dominated accretion flow and general advective accretion flow. We explore the possible transition of the sources from one accretion mode to others with time. We further argue that the accretion rate must play an important role in transition between these modes.

High order entropy conservative central schemes for wide ranges of compressible gas dynamics and MHD flows

NASA Astrophysics Data System (ADS)

Sjögreen, Björn; Yee, H. C.

2018-07-01

The Sjogreen and Yee [31] high order entropy conservative numerical method for compressible gas dynamics is extended to include discontinuities and also extended to equations of ideal magnetohydrodynamics (MHD). The basic idea is based on Tadmor's [40] original work for inviscid perfect gas flows. For the MHD four formulations of the MHD are considered: (a) the conservative MHD, (b) the Godunov [14] non-conservative form, (c) the Janhunen [19] - MHD with magnetic field source terms, and (d) a MHD with source terms by Brackbill and Barnes [5]. Three forms of the high order entropy numerical fluxes for the MHD in the finite difference framework are constructed. They are based on the extension of the low order form of Chandrashekar and Klingenberg [9], and two forms with modifications of the Winters and Gassner [49] numerical fluxes. For flows containing discontinuities and multiscale turbulence fluctuations the high order entropy conservative numerical fluxes as the new base scheme under the Yee and Sjogreen [31] and Kotov et al. [21,22] high order nonlinear filter approach is developed. The added nonlinear filter step on the high order centered entropy conservative spatial base scheme is only utilized at isolated computational regions, while maintaining high accuracy almost everywhere for long time integration of unsteady flows and DNS and LES of turbulence computations. Representative test cases for both smooth flows and problems containing discontinuities for the gas dynamics and the ideal MHD are included. The results illustrate the improved stability by using the high order entropy conservative numerical flux as the base scheme instead of the pure high order central scheme.

Self-organization of large-scale ULF electromagnetic wave structures in their interaction with nonuniform zonal winds in the ionospheric E region

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aburjania, G. D.; Chargazia, Kh. Z.

A study is made of the generation and subsequent linear and nonlinear evolution of ultralow-frequency planetary electromagnetic waves in the E region of a dissipative ionosphere in the presence of a nonuniform zonal wind (a sheared flow). Hall currents flowing in the E region and such permanent global factors as the spatial nonuniformity of the geomagnetic field and of the normal component of the Earth's angular velocity give rise to fast and slow planetary-scale electromagnetic waves. The efficiency of the linear amplification of planetary electromagnetic waves in their interaction with a nonuniform zonal wind is analyzed. When there are shearedmore » flows, the operators of linear problems are non-self-conjugate and the corresponding eigenfunctions are nonorthogonal, so the canonical modal approach is poorly suited for studying such motions and it is necessary to utilize the so-called nonmodal mathematical analysis. It is shown that, in the linear evolutionary stage, planetary electromagnetic waves efficiently extract energy from the sheared flow, thereby substantially increasing their amplitude and, accordingly, energy. The criterion for instability of a sheared flow in an ionospheric medium is derived. As the shear instability develops and the perturbation amplitude grows, a nonlinear self-localization mechanism comes into play and the process ends with the self-organization of nonlinear, highly localized, solitary vortex structures. The system thus acquires a new degree of freedom, thereby providing a new way for the perturbation to evolve in a medium with a sheared flow. Depending on the shape of the sheared flow velocity profile, nonlinear structures can be either purely monopole vortices or vortex streets against the background of the zonal wind. The accumulation of such vortices can lead to a strongly turbulent state in an ionospheric medium.« less

An artificial nonlinear diffusivity method for supersonic reacting flows with shocks

NASA Astrophysics Data System (ADS)

Fiorina, B.; Lele, S. K.

2007-03-01

A computational approach for modeling interactions between shocks waves, contact discontinuities and reactions zones with a high-order compact scheme is investigated. To prevent the formation of spurious oscillations around shocks, artificial nonlinear viscosity [A.W. Cook, W.H. Cabot, A high-wavenumber viscosity for high resolution numerical method, J. Comput. Phys. 195 (2004) 594-601] based on high-order derivative of the strain rate tensor is used. To capture temperature and species discontinuities a nonlinear diffusivity based on the entropy gradient is added. It is shown that the damping of 'wiggles' is controlled by the model constants and is largely independent of the mesh size and the shock strength. The same holds for the numerical shock thickness and allows a determination of the L2 error. In the shock tube problem, with fluids of different initial entropy separated by the diaphragm, an artificial diffusivity is required to accurately capture the contact surface. Finally, the method is applied to a shock wave propagating into a medium with non-uniform density/entropy and to a CJ detonation wave. Multi-dimensional formulation of the model is presented and is illustrated by a 2D oblique wave reflection from an inviscid wall, by a 2D supersonic blunt body flow and by a Mach reflection problem.

Cluster-based control of a separating flow over a smoothly contoured ramp

NASA Astrophysics Data System (ADS)

Kaiser, Eurika; Noack, Bernd R.; Spohn, Andreas; Cattafesta, Louis N.; Morzyński, Marek

2017-12-01

The ability to manipulate and control fluid flows is of great importance in many scientific and engineering applications. The proposed closed-loop control framework addresses a key issue of model-based control: The actuation effect often results from slow dynamics of strongly nonlinear interactions which the flow reveals at timescales much longer than the prediction horizon of any model. Hence, we employ a probabilistic approach based on a cluster-based discretization of the Liouville equation for the evolution of the probability distribution. The proposed methodology frames high-dimensional, nonlinear dynamics into low-dimensional, probabilistic, linear dynamics which considerably simplifies the optimal control problem while preserving nonlinear actuation mechanisms. The data-driven approach builds upon a state space discretization using a clustering algorithm which groups kinematically similar flow states into a low number of clusters. The temporal evolution of the probability distribution on this set of clusters is then described by a control-dependent Markov model. This Markov model can be used as predictor for the ergodic probability distribution for a particular control law. This probability distribution approximates the long-term behavior of the original system on which basis the optimal control law is determined. We examine how the approach can be used to improve the open-loop actuation in a separating flow dominated by Kelvin-Helmholtz shedding. For this purpose, the feature space, in which the model is learned, and the admissible control inputs are tailored to strongly oscillatory flows.

Lagrangian flows within reflecting internal waves at a horizontal free-slip surface

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Qi, E-mail: q.zhou@damtp.cam.ac.uk; Diamessis, Peter J.

In this paper sequel to Zhou and Diamessis [“Reflection of an internal gravity wave beam off a horizontal free-slip surface,” Phys. Fluids 25, 036601 (2013)], we consider Lagrangian flows within nonlinear internal waves (IWs) reflecting off a horizontal free-slip rigid lid, the latter being a model of the ocean surface. The problem is approached both analytically using small-amplitude approximations and numerically by tracking Lagrangian fluid particles in direct numerical simulation (DNS) datasets of the Eulerian flow. Inviscid small-amplitude analyses for both plane IWs and IW beams (IWBs) show that Eulerian mean flow due to wave-wave interaction and wave-induced Stokes driftmore » cancels each other out completely at the second order in wave steepness A, i.e., O(A{sup 2}), implying zero Lagrangian mean flow up to that order. However, high-accuracy particle tracking in finite-Reynolds-number fully nonlinear DNS datasets from the work of Zhou and Diamessis suggests that the Euler-Stokes cancelation on O(A{sup 2}) is not complete. This partial cancelation significantly weakens the mean Lagrangian flows but does not entirely eliminate them. As a result, reflecting nonlinear IWBs produce mean Lagrangian drifts on O(A{sup 2}) and thus particle dispersion on O(A{sup 4}). The above findings can be relevant to predicting IW-driven mass transport in the oceanic surface and subsurface region which bears important observational and environmental implications, under circumstances where the effect of Earth rotation can be ignored.« less

Darcy-Forchheimer flow of Maxwell nanofluid flow with nonlinear thermal radiation and activation energy

NASA Astrophysics Data System (ADS)

Sajid, T.; Sagheer, M.; Hussain, S.; Bilal, M.

2018-03-01

The present article is about the study of Darcy-Forchheimer flow of Maxwell nanofluid over a linear stretching surface. Effects like variable thermal conductivity, activation energy, nonlinear thermal radiation is also incorporated for the analysis of heat and mass transfer. The governing nonlinear partial differential equations (PDEs) with convective boundary conditions are first converted into the nonlinear ordinary differential equations (ODEs) with the help of similarity transformation, and then the resulting nonlinear ODEs are solved with the help of shooting method and MATLAB built-in bvp4c solver. The impact of different physical parameters like Brownian motion, thermophoresis parameter, Reynolds number, magnetic parameter, nonlinear radiative heat flux, Prandtl number, Lewis number, reaction rate constant, activation energy and Biot number on Nusselt number, velocity, temperature and concentration profile has been discussed. It is viewed that both thermophoresis parameter and activation energy parameter has ascending effect on the concentration profile.

Nonlinear analysis of aortic flow in living dogs.

NASA Technical Reports Server (NTRS)

Ling, S. C.; Atabek, H. B.; Letzing, W. G.; Patel, D. J.

1973-01-01

A nonlinear theory which considered the convective accelerations of blood and the nonlinear elastic behavior and taper angle of the vascular wall was used to study the nature of blood flow in the descending thoracic aorta of living dogs under a wide range of pressures and flows. Velocity profiles, wall friction, and discharge waves were predicted from locally measured input data about the pressure-gradient wave and arterial distention. The results indicated that a major part of the mean pressure gradient was balanced by convective accelerations; the theory, which took this factor into account, predicted the correct velocity distributions and flow waves.

Non-linear effects in finite amplitude wave propagation through ducts and nozzles

NASA Technical Reports Server (NTRS)

Salikuddin, M.; Brown, W. H.

1986-01-01

In this paper an extensive study of non-linear effects in finite amplitude wave propagation through ducts and nozzles is summarized. Some results from earlier studies are included to illustrate the non-linear effects on the transmission characteristics of duct and nozzle terminations. Investigaiations, both experimental and analytical, were carried out to determine the magnitudes of the effects for high intensity pulse propagation. The results derived from these investigations are presented in this paper. They include the effect of the sound intensity on the acoustic characteristics of duct and nozzle terminations, the extent of the non-linearities in the propagation of high intensity impulsive sound inside the duct and out into free field, the acoustic energy dissipation mechanism at a termination as shown by flow visualizations, and quantitative evaluations by experimental and analytical means of the influence of the intensity of a sound pulse on the dissipation of its acoustic power.

Nonlinear coupling of flow harmonics: Hexagonal flow and beyond

NASA Astrophysics Data System (ADS)

Giacalone, Giuliano; Yan, Li; Ollitrault, Jean-Yves

2018-05-01

Higher Fourier harmonics of anisotropic flow (v4 and beyond) get large contributions induced by elliptic and triangular flow through nonlinear response. We present a general framework of nonlinear hydrodynamic response which encompasses the existing one and allows us to take into account the mutual correlation between the nonlinear couplings affecting Fourier harmonics of any order. Using Large Hadron Collider data on Pb+Pb collisions at s =2.76 TeV, we perform an application of our formalism to hexagonal flow, v6, a coefficient affected by several nonlinear contributions which are of the same order of magnitude. We obtain the first experimental measure of the coefficient χ624, which couples v6 to v2 and v4. This is achieved by putting together the information from several analyses: event-plane correlations, symmetric cumulants, and higher order moments recently analyzed by the ALICE Collaboration. The value of χ624 extracted from data is in fair agreement with hydrodynamic calculations, although with large error bars, which would be dramatically reduced by a dedicated analysis. We argue that within our formalism the nonlinear structure of a given higher order harmonic can be determined more accurately than the harmonic itself, and we emphasize potential applications to future measurements of v7 and v8.

A variational approach to probing extreme events in turbulent dynamical systems

PubMed Central

Farazmand, Mohammad; Sapsis, Themistoklis P.

2017-01-01

Extreme events are ubiquitous in a wide range of dynamical systems, including turbulent fluid flows, nonlinear waves, large-scale networks, and biological systems. We propose a variational framework for probing conditions that trigger intermittent extreme events in high-dimensional nonlinear dynamical systems. We seek the triggers as the probabilistically feasible solutions of an appropriately constrained optimization problem, where the function to be maximized is a system observable exhibiting intermittent extreme bursts. The constraints are imposed to ensure the physical admissibility of the optimal solutions, that is, significant probability for their occurrence under the natural flow of the dynamical system. We apply the method to a body-forced incompressible Navier-Stokes equation, known as the Kolmogorov flow. We find that the intermittent bursts of the energy dissipation are independent of the external forcing and are instead caused by the spontaneous transfer of energy from large scales to the mean flow via nonlinear triad interactions. The global maximizer of the corresponding variational problem identifies the responsible triad, hence providing a precursor for the occurrence of extreme dissipation events. Specifically, monitoring the energy transfers within this triad allows us to develop a data-driven short-term predictor for the intermittent bursts of energy dissipation. We assess the performance of this predictor through direct numerical simulations. PMID:28948226

A Nonlinear Modal Aeroelastic Solver for FUN3D

NASA Technical Reports Server (NTRS)

Goldman, Benjamin D.; Bartels, Robert E.; Biedron, Robert T.; Scott, Robert C.

2016-01-01

A nonlinear structural solver has been implemented internally within the NASA FUN3D computational fluid dynamics code, allowing for some new aeroelastic capabilities. Using a modal representation of the structure, a set of differential or differential-algebraic equations are derived for general thin structures with geometric nonlinearities. ODEPACK and LAPACK routines are linked with FUN3D, and the nonlinear equations are solved at each CFD time step. The existing predictor-corrector method is retained, whereby the structural solution is updated after mesh deformation. The nonlinear solver is validated using a test case for a flexible aeroshell at transonic, supersonic, and hypersonic flow conditions. Agreement with linear theory is seen for the static aeroelastic solutions at relatively low dynamic pressures, but structural nonlinearities limit deformation amplitudes at high dynamic pressures. No flutter was found at any of the tested trajectory points, though LCO may be possible in the transonic regime.

Exact Recovery of Chaotic Systems from Highly Corrupted Data

DTIC Science & Technology

2016-08-01

dimension to reconstruct a state space which preserves the topological properties of the original system. In [CM87, RS92], the authors use the singular...in high dimensional nonlinear functional spaces [Spr94, SL00, LCC04]. In this work, we bring together connections between compressed sensing, splitting... compact , connected attractor Λ and the flow admits a unique so-called “physical" measure µ with supp(µ) = Λ. An invariant probability measure µ for a flow

Characterising Dynamic Instability in High Water-Cut Oil-Water Flows Using High-Resolution Microwave Sensor Signals

NASA Astrophysics Data System (ADS)

Liu, Weixin; Jin, Ningde; Han, Yunfeng; Ma, Jing

2018-06-01

In the present study, multi-scale entropy algorithm was used to characterise the complex flow phenomena of turbulent droplets in high water-cut oil-water two-phase flow. First, we compared multi-scale weighted permutation entropy (MWPE), multi-scale approximate entropy (MAE), multi-scale sample entropy (MSE) and multi-scale complexity measure (MCM) for typical nonlinear systems. The results show that MWPE presents satisfied variability with scale and anti-noise ability. Accordingly, we conducted an experiment of vertical upward oil-water two-phase flow with high water-cut and collected the signals of a high-resolution microwave resonant sensor, based on which two indexes, the entropy rate and mean value of MWPE, were extracted. Besides, the effects of total flow rate and water-cut on these two indexes were analysed. Our researches show that MWPE is an effective method to uncover the dynamic instability of oil-water two-phase flow with high water-cut.

The Effect of Acoustic Forcing on Instabilities and Breakdown in Swept-Wing Flow over a Backward-Facing Step

NASA Technical Reports Server (NTRS)

Eppink, Jenna L.; Shishkov, Olga; Wlezien, Richard W.; King, Rudolph A.; Choudhari, Meelan

2016-01-01

Instability interaction and breakdown were experimentally investigated in the flow over a swept backward-facing step. Acoustic forcing was used to excite the Tollmien-Schlichting (TS) instability and to acquire phase-locked results. The phase-averaged results illustrate the complex nature of the interaction between the TS and stationary cross flow instabilities. The weak stationary cross flow disturbance causes a distortion of the TS wavefront. The breakdown process is characterized by large positive and negative spikes in velocity. The positive spikes occur near the same time and location as the positive part of the TS wave. Higher-order spectral analysis was used to further investigate the nonlinear interactions between the TS instability and the traveling cross flow disturbances. The results reveal that a likely cause for the generation of the spikes corresponds to nonlinear interactions between the TS, traveling cross flow, and stationary cross flow disturbances. The spikes begin at low amplitudes of the unsteady and steady disturbances (2-4% U (sub e) (i.e. boundary layer edge velocity)) but can achieve very large amplitudes (20-30 percent U (sub e) (i.e. boundary layer edge velocity)) that initiate an early, though highly intermittent, breakdown to turbulence.

Uncertainty in simulated groundwater-quality trends in transient flow

USGS Publications Warehouse

Starn, J. Jeffrey; Bagtzoglou, Amvrossios; Robbins, Gary A.

2013-01-01

In numerical modeling of groundwater flow, the result of a given solution method is affected by the way in which transient flow conditions and geologic heterogeneity are simulated. An algorithm is demonstrated that simulates breakthrough curves at a pumping well by convolution-based particle tracking in a transient flow field for several synthetic basin-scale aquifers. In comparison to grid-based (Eulerian) methods, the particle (Lagrangian) method is better able to capture multimodal breakthrough caused by changes in pumping at the well, although the particle method may be apparently nonlinear because of the discrete nature of particle arrival times. Trial-and-error choice of number of particles and release times can perhaps overcome the apparent nonlinearity. Heterogeneous aquifer properties tend to smooth the effects of transient pumping, making it difficult to separate their effects in parameter estimation. Porosity, a new parameter added for advective transport, can be accurately estimated using both grid-based and particle-based methods, but predictions can be highly uncertain, even in the simple, nonreactive case.

Nonlinear flow model of multiple fractured horizontal wells with stimulated reservoir volume including the quadratic gradient term

NASA Astrophysics Data System (ADS)

Ren, Junjie; Guo, Ping

2017-11-01

The real fluid flow in porous media is consistent with the mass conservation which can be described by the nonlinear governing equation including the quadratic gradient term (QGT). However, most of the flow models have been established by ignoring the QGT and little work has been conducted to incorporate the QGT into the flow model of the multiple fractured horizontal (MFH) well with stimulated reservoir volume (SRV). This paper first establishes a semi-analytical model of an MFH well with SRV including the QGT. Introducing the transformed pressure and flow-rate function, the nonlinear model of a point source in a composite system including the QGT is linearized. Then the Laplace transform, principle of superposition, numerical discrete method, Gaussian elimination method and Stehfest numerical inversion are employed to establish and solve the seepage model of the MFH well with SRV. Type curves are plotted and the effects of relevant parameters are analyzed. It is found that the nonlinear effect caused by the QGT can increase the flow capacity of fluid flow and influence the transient pressure positively. The relevant parameters not only have an effect on the type curve but also affect the error in the pressure calculated by the conventional linear model. The proposed model, which is consistent with the mass conservation, reflects the nonlinear process of the real fluid flow, and thus it can be used to obtain more accurate transient pressure of an MFH well with SRV.

The Dynamics of Small-Scale Turbulence Driven Flows

NASA Astrophysics Data System (ADS)

Beer, M. A.; Hammett, G. W.

1997-11-01

The dynamics of small-scale fluctuation driven flows are of great interest for micro-instability driven turbulence, since nonlinear toroidal simulations have shown that these flows play an important role in the regulation of the turbulence and transport levels. The gyrofluid treatment of these flows was shown to be accurate for times shorter than a bounce time.(Beer, M. A., Ph. D. thesis, Princeton University (1995).) Since the decorrelation times of the turbulence are generally shorter than a bounce time, our original hypothesis was that this description was adequate. Recent work(Hinton, F. L., Rosenbluth, M. N., and Waltz, R. E., International Sherwood Fusion Theory Conference (1997).) pointed out possible problems with this hypothesis, emphasizing the existence of a linearly undamped component of the flow which could build up in time and lower the final turbulence level. While our original gyrofluid model reproduces some aspects of the linear flow, there are differences between the long time gyrofluid and kinetic linear results in some cases. On the other hand, if the long time behavior of these flows is dominated by nonlinear damping (which seems reasonable), then the existing nonlinear gyrofluid simulations may be sufficiently accurate. We test these possibilities by modifying the gyrofluid description of these flows and diagnosing the flow evolution in nonlinear simulations.

The Langley Stability and Transition Analysis Code (LASTRAC) : LST, Linear and Nonlinear PSE for 2-D, Axisymmetric, and Infinite Swept Wing Boundary Layers

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan

2003-01-01

During the past two decades, our understanding of laminar-turbulent transition flow physics has advanced significantly owing to, in a large part, the NASA program support such as the National Aerospace Plane (NASP), High-speed Civil Transport (HSCT), and Advanced Subsonic Technology (AST). Experimental, theoretical, as well as computational efforts on various issues such as receptivity and linear and nonlinear evolution of instability waves take part in broadening our knowledge base for this intricate flow phenomenon. Despite all these advances, transition prediction remains a nontrivial task for engineers due to the lack of a widely available, robust, and efficient prediction tool. The design and development of the LASTRAC code is aimed at providing one such engineering tool that is easy to use and yet capable of dealing with a broad range of transition related issues. LASTRAC was written from scratch based on the state-of-the-art numerical methods for stability analysis and modem software technologies. At low fidelity, it allows users to perform linear stability analysis and N-factor transition correlation for a broad range of flow regimes and configurations by using either the linear stability theory (LST) or linear parabolized stability equations (LPSE) method. At high fidelity, users may use nonlinear PSE to track finite-amplitude disturbances until the skin friction rise. Coupled with the built-in receptivity model that is currently under development, the nonlinear PSE method offers a synergistic approach to predict transition onset for a given disturbance environment based on first principles. This paper describes the governing equations, numerical methods, code development, and case studies for the current release of LASTRAC. Practical applications of LASTRAC are demonstrated for linear stability calculations, N-factor transition correlation, non-linear breakdown simulations, and controls of stationary crossflow instability in supersonic swept wing boundary layers.

A novel investigation of a micropolar fluid characterized by nonlinear constitutive diffusion model in boundary layer flow and heat transfer.

PubMed

Sui, Jize; Zhao, Peng; Cheng, Zhengdong; Zheng, Liancun; Zhang, Xinxin

2017-02-01

The rheological and heat-conduction constitutive models of micropolar fluids (MFs), which are important non-Newtonian fluids, have been, until now, characterized by simple linear expressions, and as a consequence, the non-Newtonian performance of such fluids could not be effectively captured. Here, we establish the novel nonlinear constitutive models of a micropolar fluid and apply them to boundary layer flow and heat transfer problems. The nonlinear power law function of angular velocity is represented in the new models by employing generalized " n -diffusion theory," which has successfully described the characteristics of non-Newtonian fluids, such as shear-thinning and shear-thickening fluids. These novel models may offer a new approach to the theoretical understanding of shear-thinning behavior and anomalous heat transfer caused by the collective micro-rotation effects in a MF with shear flow according to recent experiments. The nonlinear similarity equations with a power law form are derived and the approximate analytical solutions are obtained by the homotopy analysis method, which is in good agreement with the numerical solutions. The results indicate that non-Newtonian behaviors involving a MF depend substantially on the power exponent n and the modified material parameter [Formula: see text] introduced by us. Furthermore, the relations of the engineering interest parameters, including local boundary layer thickness, local skin friction, and Nusselt number are found to be fitted by a quadratic polynomial to n with high precision, which enables the extraction of the rapid predictions from a complex nonlinear boundary-layer transport system.

A novel investigation of a micropolar fluid characterized by nonlinear constitutive diffusion model in boundary layer flow and heat transfer

PubMed Central

Zhao, Peng; Cheng, Zhengdong; Zheng, Liancun; Zhang, Xinxin

2017-01-01

The rheological and heat-conduction constitutive models of micropolar fluids (MFs), which are important non-Newtonian fluids, have been, until now, characterized by simple linear expressions, and as a consequence, the non-Newtonian performance of such fluids could not be effectively captured. Here, we establish the novel nonlinear constitutive models of a micropolar fluid and apply them to boundary layer flow and heat transfer problems. The nonlinear power law function of angular velocity is represented in the new models by employing generalized “n-diffusion theory,” which has successfully described the characteristics of non-Newtonian fluids, such as shear-thinning and shear-thickening fluids. These novel models may offer a new approach to the theoretical understanding of shear-thinning behavior and anomalous heat transfer caused by the collective micro-rotation effects in a MF with shear flow according to recent experiments. The nonlinear similarity equations with a power law form are derived and the approximate analytical solutions are obtained by the homotopy analysis method, which is in good agreement with the numerical solutions. The results indicate that non-Newtonian behaviors involving a MF depend substantially on the power exponent n and the modified material parameter K0 introduced by us. Furthermore, the relations of the engineering interest parameters, including local boundary layer thickness, local skin friction, and Nusselt number are found to be fitted by a quadratic polynomial to n with high precision, which enables the extraction of the rapid predictions from a complex nonlinear boundary-layer transport system. PMID:28344433

Nonlinear pressure-flow relationships for passive microfluidic valves.

PubMed

Seker, Erkin; Leslie, Daniel C; Haj-Hariri, Hossein; Landers, James P; Utz, Marcel; Begley, Matthew R

2009-09-21

An analytical solution is presented for the nonlinear pressure-flow relationship of deformable passive valves, which are formed by bonding a deformable film over etched channels separated by a weir. A fluidic pathway connecting the channels is opened when the upstream pressure creates a tunnel along a predefined narrow strip where the film is not bonded to the weir. When the width of the strip is comparable to the inlet channel width, the predicted closed-form pressure-flow rate relationship is in excellent agreement with experiments, which determine pressures by measuring film deflections for prescribed flow rates. The validated closed-form models involve no fitting parameters, and provide the foundation to design passive diodes with specific nonlinear pressure-flow characteristics.

Waveguide structures in anisotropic nonlinear crystals

NASA Astrophysics Data System (ADS)

Li, Da; Hong, Pengda; Meissner, Helmuth E.

2017-02-01

We report on the design and manufacturing parameters of waveguiding structures of anisotropic nonlinear crystals that are employed for harmonic conversions, using Adhesive-Free Bonding (AFB®). This technology enables a full range of predetermined refractive index differences that are essential for the design of single mode or low-mode propagation with high efficiency in anisotropic nonlinear crystals which in turn results in compact frequency conversion systems. Examples of nonlinear optical waveguides include periodically bonded walk-off corrected nonlinear optical waveguides and periodically poled waveguide components, such as lithium triborate (LBO), beta barium borate (β-BBO), lithium niobate (LN), potassium titanyl phosphate (KTP), zinc germanium phosphide (ZGP) and silver selenogallate (AGSE). Simulation of planar LN waveguide shows that when the electric field vector E lies in the k-c plane, the power flow is directed precisely along the propagation direction, demonstrating waveguiding effect in the planar waveguide. Employment of anisotropic nonlinear optical waveguides, for example in combination with AFB® crystalline fiber waveguides (CFW), provides access to the design of a number of novel high power and high efficiency light sources spanning the range of wavelengths from deep ultraviolet (as short as 200 nm) to mid-infrared (as long as about 18 μm). To our knowledge, the technique is the only generally applicable one because most often there are no compatible cladding crystals available to nonlinear optical cores, especially not with an engineer-able refractive index difference and large mode area.

A baker's dozen of new particle flows for nonlinear filters, Bayesian decisions and transport

NASA Astrophysics Data System (ADS)

Daum, Fred; Huang, Jim

2015-05-01

We describe a baker's dozen of new particle flows to compute Bayes' rule for nonlinear filters, Bayesian decisions and learning as well as transport. Several of these new flows were inspired by transport theory, but others were inspired by physics or statistics or Markov chain Monte Carlo methods.

Influence of chemical reactions on the nonlinear dynamics of dissipative flows

NASA Astrophysics Data System (ADS)

Karimov, A. R.; Korshunov, A. M.; Beklemishev, V. V.

2015-08-01

The nonlinear dynamics of resistive flow with a chemical reaction is studied. Proceeding from the Lagrangian description, the influence of a chemical reaction on the development of fluid singularities is considered.

Nonlinear effects in the bounded dust-vortex flow in plasma

NASA Astrophysics Data System (ADS)

Laishram, Modhuchandra; Sharma, Devendra; Chattopdhyay, Prabal K.; Kaw, Predhiman K.

2017-03-01

The vortex structures in a cloud of electrically suspended dust in a streaming plasma constitutes a driven system with a rich nonlinear flow regime. Experimentally recovered toroidal formations of this system have motivated study of its volumetrically driven-dissipative vortex flow dynamics using two-dimensional hydrodynamics in the incompressible Navier-Stokes regime. Nonlinear equilibrium solutions are obtained for this system where a nonuniformly driven two-dimensional dust flow exhibits distinct regions of localized accelerations and strong friction caused by stationary fluids at the confining boundaries resisting the dust flow. In agreement with observations in experiments, it is demonstrated that the nonlinear effects appear in the limit of small viscosity, where the primary vortices form scaling with the most dominant spatial scales of the domain topology and develop separated virtual boundaries along their periphery. This separation is triggered beyond a critical dust viscosity that signifies a structural bifurcation. Emergence of uniform vorticity core and secondary vortices with a newer level of identical dynamics highlights the applicability of the studied dynamics to gigantic vortex flows, such as the Jovian great red spot, to microscopic biophysical intracellular activity.

An immersed boundary method for direct and large eddy simulation of stratified flows in complex geometry

NASA Astrophysics Data System (ADS)

Rapaka, Narsimha R.; Sarkar, Sutanu

2016-10-01

A sharp-interface Immersed Boundary Method (IBM) is developed to simulate density-stratified turbulent flows in complex geometry using a Cartesian grid. The basic numerical scheme corresponds to a central second-order finite difference method, third-order Runge-Kutta integration in time for the advective terms and an alternating direction implicit (ADI) scheme for the viscous and diffusive terms. The solver developed here allows for both direct numerical simulation (DNS) and large eddy simulation (LES) approaches. Methods to enhance the mass conservation and numerical stability of the solver to simulate high Reynolds number flows are discussed. Convergence with second-order accuracy is demonstrated in flow past a cylinder. The solver is validated against past laboratory and numerical results in flow past a sphere, and in channel flow with and without stratification. Since topographically generated internal waves are believed to result in a substantial fraction of turbulent mixing in the ocean, we are motivated to examine oscillating tidal flow over a triangular obstacle to assess the ability of this computational model to represent nonlinear internal waves and turbulence. Results in laboratory-scale (order of few meters) simulations show that the wave energy flux, mean flow properties and turbulent kinetic energy agree well with our previous results obtained using a body-fitted grid (BFG). The deviation of IBM results from BFG results is found to increase with increasing nonlinearity in the wave field that is associated with either increasing steepness of the topography relative to the internal wave propagation angle or with the amplitude of the oscillatory forcing. LES is performed on a large scale ridge, of the order of few kilometers in length, that has the same geometrical shape and same non-dimensional values for the governing flow and environmental parameters as the laboratory-scale topography, but significantly larger Reynolds number. A non-linear drag law is utilized in the large-scale application to parameterize turbulent losses due to bottom friction at high Reynolds number. The large scale problem exhibits qualitatively similar behavior to the laboratory scale problem with some differences: slightly larger intensification of the boundary flow and somewhat higher non-dimensional values for the energy fluxed away by the internal wave field. The phasing of wave breaking and turbulence exhibits little difference between small-scale and large-scale obstacles as long as the important non-dimensional parameters are kept the same. We conclude that IBM is a viable approach to the simulation of internal waves and turbulence in high Reynolds number stratified flows over topography.

Supersonic, nonlinear, attached-flow wing design for high lift with experimental validation

NASA Technical Reports Server (NTRS)

Pittman, J. L.; Miller, D. S.; Mason, W. H.

1984-01-01

Results of the experimental validation are presented for the three dimensional cambered wing which was designed to achieve attached supercritical cross flow for lifting conditions typical of supersonic maneuver. The design point was a lift coefficient of 0.4 at Mach 1.62 and 12 deg angle of attack. Results from the nonlinear full potential method are presented to show the validity of the design process along with results from linear theory codes. Longitudinal force and moment data and static pressure data were obtained in the Langley Unitary Plan Wind Tunnel at Mach numbers of 1.58, 1.62, 1.66, 1.70, and 2.00 over an angle of attack range of 0 to 14 deg at a Reynolds number of 2.0 x 10 to the 6th power per foot. Oil flow photographs of the upper surface were obtained at M = 1.62 for alpha approx. = 8, 10, 12, and 14 deg.

Application of nonlinear-regression methods to a ground-water flow model of the Albuquerque Basin, New Mexico

USGS Publications Warehouse

Tiedeman, C.R.; Kernodle, J.M.; McAda, D.P.

1998-01-01

This report documents the application of nonlinear-regression methods to a numerical model of ground-water flow in the Albuquerque Basin, New Mexico. In the Albuquerque Basin, ground water is the primary source for most water uses. Ground-water withdrawal has steadily increased since the 1940's, resulting in large declines in water levels in the Albuquerque area. A ground-water flow model was developed in 1994 and revised and updated in 1995 for the purpose of managing basin ground- water resources. In the work presented here, nonlinear-regression methods were applied to a modified version of the previous flow model. Goals of this work were to use regression methods to calibrate the model with each of six different configurations of the basin subsurface and to assess and compare optimal parameter estimates, model fit, and model error among the resulting calibrations. The Albuquerque Basin is one in a series of north trending structural basins within the Rio Grande Rift, a region of Cenozoic crustal extension. Mountains, uplifts, and fault zones bound the basin, and rock units within the basin include pre-Santa Fe Group deposits, Tertiary Santa Fe Group basin fill, and post-Santa Fe Group volcanics and sediments. The Santa Fe Group is greater than 14,000 feet (ft) thick in the central part of the basin. During deposition of the Santa Fe Group, crustal extension resulted in development of north trending normal faults with vertical displacements of as much as 30,000 ft. Ground-water flow in the Albuquerque Basin occurs primarily in the Santa Fe Group and post-Santa Fe Group deposits. Water flows between the ground-water system and surface-water bodies in the inner valley of the basin, where the Rio Grande, a network of interconnected canals and drains, and Cochiti Reservoir are located. Recharge to the ground-water flow system occurs as infiltration of precipitation along mountain fronts and infiltration of stream water along tributaries to the Rio Grande; subsurface flow from adjacent regions; irrigation and septic field seepage; and leakage through the Rio Grande, canal, and Cochiti Reservoir beds. Ground water is discharged from the basin by withdrawal; evapotranspiration; subsurface flow; and flow to the Rio Grande, canals, and drains. The transient, three-dimensional numerical model of ground-water flow to which nonlinear-regression methods were applied simulates flow in the Albuquerque Basin from 1900 to March 1995. Six different basin subsurface configurations are considered in the model. These configurations are designed to test the effects of (1) varying the simulated basin thickness, (2) including a hypothesized hydrogeologic unit with large hydraulic conductivity in the western part of the basin (the west basin high-K zone), and (3) substantially lowering the simulated hydraulic conductivity of a fault in the western part of the basin (the low-K fault zone). The model with each of the subsurface configurations was calibrated using a nonlinear least- squares regression technique. The calibration data set includes 802 hydraulic-head measurements that provide broad spatial and temporal coverage of basin conditions, and one measurement of net flow from the Rio Grande and drains to the ground-water system in the Albuquerque area. Data are weighted on the basis of estimates of the standard deviations of measurement errors. The 10 to 12 parameters to which the calibration data as a whole are generally most sensitive were estimated by nonlinear regression, whereas the remaining model parameter values were specified. Results of model calibration indicate that the optimal parameter estimates as a whole are most reasonable in calibrations of the model with with configurations 3 (which contains 1,600-ft-thick basin deposits and the west basin high-K zone), 4 (which contains 5,000-ft-thick basin de

Insight into the effect of screw dislocations and oxygen vacancy defects on the optical nonlinear refraction response in chemically grown ZnO/Al2O3 films

NASA Astrophysics Data System (ADS)

Agrawal, Arpana; Saroj, Rajendra K.; Dar, Tanveer A.; Baraskar, Priyanka; Sen, Pratima; Dhar, Subhabrata

2017-11-01

We report the effect of screw dislocations and oxygen vacancy defects on the optical nonlinear refraction response of ZnO films grown on a sapphire substrate at various oxygen flow rates using the chemical vapor deposition technique. The nonlinear refraction response was investigated in the off-resonant regime using a CW He-Ne laser source to examine the role of the intermediate bandgap states. It has been observed that the structural defects strongly influence the optical nonlinearity in the off-resonant regime. Nonlinearity has been found to improve as the oxygen flow rate is lowered from 2 sccm to 0.3 sccm. From photoluminescence studies, we observe that the enhanced defect density of the electronic defect levels due to the increased concentration of structural defects (with the decrease in the oxygen flow rate) is responsible for this improved optical nonlinearity along with the thermal effect. This suggests that defect engineering is an effective way to tailor the nonlinearity of ZnO films and their utility for optoelectronic device applications.

Model Development and Model-Based Control Design for High Performance Nonlinear Smart Systems

DTIC Science & Technology

2007-11-20

potentially impact a broad range of flow control problems of interest to the Air Force and Boeing. Point of contact: James Mabe , Boeing Phantom Works...rotorcraft blades. In both cases, models and control designs will be validated using data from Boeing experiments and flight tests. Point of contact: James ... Mabe , Boeing Phantom Works, Seattle, WA, 206-655-0091. 3. PZT Unimorphs – Boeing: Nonlinear structural models developed through AFOSR support are being

A nonlinear relaxation/quasi-Newton algorithm for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Edwards, Jack R.; Mcrae, D. S.

1992-01-01

A highly efficient implicit method for the computation of steady, two-dimensional compressible Navier-Stokes flowfields is presented. The discretization of the governing equations is hybrid in nature, with flux-vector splitting utilized in the streamwise direction and central differences with flux-limited artificial dissipation used for the transverse fluxes. Line Jacobi relaxation is used to provide a suitable initial guess for a new nonlinear iteration strategy based on line Gauss-Seidel sweeps. The applicability of quasi-Newton methods as convergence accelerators for this and other line relaxation algorithms is discussed, and efficient implementations of such techniques are presented. Convergence histories and comparisons with experimental data are presented for supersonic flow over a flat plate and for several high-speed compression corner interactions. Results indicate a marked improvement in computational efficiency over more conventional upwind relaxation strategies, particularly for flowfields containing large pockets of streamwise subsonic flow.

Nonlinear MHD simulations of QH-mode DIII-D plasmas and implications for ITER high Q scenarios

NASA Astrophysics Data System (ADS)

Liu, F.; Huijsmans, G. T. A.; Loarte, A.; Garofalo, A. M.; Solomon, W. M.; Hoelzl, M.; Nkonga, B.; Pamela, S.; Becoulet, M.; Orain, F.; Van Vugt, D.

2018-01-01

In nonlinear MHD simulations of DIII-D QH-mode plasmas it has been found that low n kink/peeling modes (KPMs) are unstable and grow to a saturated kink-peeling mode. The features of the dominant saturated KPMs, which are localised toroidally by nonlinear coupling of harmonics, such as mode frequencies, density fluctuations and their effect on pedestal particle and energy transport, are in good agreement with the observations of the edge harmonic oscillation typically present in DIII-D QH-mode experiments. The nonlinear evolution of MHD modes including both kink-peeling modes and ballooning modes, is investigated through MHD simulations by varying the pedestal current and pressure relative to the initial conditions of DIII-D QH-mode plasma. The edge current and pressure at the pedestal are key parameters for the plasma either saturating to a QH-mode regime or a ballooning mode dominant regime. The influence of E × B flow and its shear on the QH-mode plasma has been investigated. E × B flow shear has a strong stabilisation effect on the medium to high-n modes but is destabilising for the n = 2 mode. The QH-mode extrapolation results of an ITER Q = 10 plasma show that the pedestal currents are large enough to destabilise n = 1-5 KPMs, leading to a stationary saturated kink-peeling mode.

Transonic Flutter Suppression Control Law Design, Analysis and Wind-Tunnel Results

NASA Technical Reports Server (NTRS)

Mukhopadhyay, Vivek

1999-01-01

The benchmark active controls technology and wind tunnel test program at NASA Langley Research Center was started with the objective to investigate the nonlinear, unsteady aerodynamics and active flutter suppression of wings in transonic flow. The paper will present the flutter suppression control law design process, numerical nonlinear simulation and wind tunnel test results for the NACA 0012 benchmark active control wing model. The flutter suppression control law design processes using classical, and minimax techniques are described. A unified general formulation and solution for the minimax approach, based on the steady state differential game theory is presented. Design considerations for improving the control law robustness and digital implementation are outlined. It was shown that simple control laws when properly designed based on physical principles, can suppress flutter with limited control power even in the presence of transonic shocks and flow separation. In wind tunnel tests in air and heavy gas medium, the closed-loop flutter dynamic pressure was increased to the tunnel upper limit of 200 psf. The control law robustness and performance predictions were verified in highly nonlinear flow conditions, gain and phase perturbations, and spoiler deployment. A non-design plunge instability condition was also successfully suppressed.

A recurrence network approach for the analysis of skin blood flow dynamics in response to loading pressure.

PubMed

Liao, Fuyuan; Jan, Yih-Kuen

2012-06-01

This paper presents a recurrence network approach for the analysis of skin blood flow dynamics in response to loading pressure. Recurrence is a fundamental property of many dynamical systems, which can be explored in phase spaces constructed from observational time series. A visualization tool of recurrence analysis called recurrence plot (RP) has been proved to be highly effective to detect transitions in the dynamics of the system. However, it was found that delay embedding can produce spurious structures in RPs. Network-based concepts have been applied for the analysis of nonlinear time series recently. We demonstrate that time series with different types of dynamics exhibit distinct global clustering coefficients and distributions of local clustering coefficients and that the global clustering coefficient is robust to the embedding parameters. We applied the approach to study skin blood flow oscillations (BFO) response to loading pressure. The results showed that global clustering coefficients of BFO significantly decreased in response to loading pressure (p<0.01). Moreover, surrogate tests indicated that such a decrease was associated with a loss of nonlinearity of BFO. Our results suggest that the recurrence network approach can practically quantify the nonlinear dynamics of BFO.

Magnetohydrodynamic Flow by a Stretching Cylinder with Newtonian Heating and Homogeneous-Heterogeneous Reactions

PubMed Central

Hayat, T.; Hussain, Zakir; Alsaedi, A.; Farooq, M.

2016-01-01

This article examines the effects of homogeneous-heterogeneous reactions and Newtonian heating in magnetohydrodynamic (MHD) flow of Powell-Eyring fluid by a stretching cylinder. The nonlinear partial differential equations of momentum, energy and concentration are reduced to the nonlinear ordinary differential equations. Convergent solutions of momentum, energy and reaction equations are developed by using homotopy analysis method (HAM). This method is very efficient for development of series solutions of highly nonlinear differential equations. It does not depend on any small or large parameter like the other methods i. e., perturbation method, δ—perturbation expansion method etc. We get more accurate result as we increase the order of approximations. Effects of different parameters on the velocity, temperature and concentration distributions are sketched and discussed. Comparison of present study with the previous published work is also made in the limiting sense. Numerical values of skin friction coefficient and Nusselt number are also computed and analyzed. It is noticed that the flow accelerates for large values of Powell-Eyring fluid parameter. Further temperature profile decreases and concentration profile increases when Powell-Eyring fluid parameter enhances. Concentration distribution is decreasing function of homogeneous reaction parameter while opposite influence of heterogeneous reaction parameter appears. PMID:27280883

Magnetohydrodynamic Flow by a Stretching Cylinder with Newtonian Heating and Homogeneous-Heterogeneous Reactions.

PubMed

Hayat, T; Hussain, Zakir; Alsaedi, A; Farooq, M

2016-01-01

This article examines the effects of homogeneous-heterogeneous reactions and Newtonian heating in magnetohydrodynamic (MHD) flow of Powell-Eyring fluid by a stretching cylinder. The nonlinear partial differential equations of momentum, energy and concentration are reduced to the nonlinear ordinary differential equations. Convergent solutions of momentum, energy and reaction equations are developed by using homotopy analysis method (HAM). This method is very efficient for development of series solutions of highly nonlinear differential equations. It does not depend on any small or large parameter like the other methods i. e., perturbation method, δ-perturbation expansion method etc. We get more accurate result as we increase the order of approximations. Effects of different parameters on the velocity, temperature and concentration distributions are sketched and discussed. Comparison of present study with the previous published work is also made in the limiting sense. Numerical values of skin friction coefficient and Nusselt number are also computed and analyzed. It is noticed that the flow accelerates for large values of Powell-Eyring fluid parameter. Further temperature profile decreases and concentration profile increases when Powell-Eyring fluid parameter enhances. Concentration distribution is decreasing function of homogeneous reaction parameter while opposite influence of heterogeneous reaction parameter appears.

Nonlinear flow response of soft hair beds

NASA Astrophysics Data System (ADS)

Alvarado, José; Comtet, Jean; de Langre, Emmanuel; Hosoi, A. E.

2017-10-01

We are `hairy' on the inside: beds of passive fibres anchored to a surface and immersed in fluids are prevalent in many biological systems, including intestines, tongues, and blood vessels. These hairs are soft enough to deform in response to stresses from fluid flows. Yet fluid stresses are in turn affected by hair deformation, leading to a coupled elastoviscous problem that is poorly understood. Here we investigate a biomimetic model system of elastomer hair beds subject to shear-driven Stokes flows. We characterize this system with a theoretical model that accounts for the large-deformation flow response of hair beds. Hair bending results in a drag-reducing nonlinearity because the hair tip lowers towards the base, widening the gap through which fluid flows. When hairs are cantilevered at an angle subnormal to the surface, flow against the grain bends hairs away from the base, narrowing the gap. The flow response of angled hair beds is axially asymmetric and amounts to a rectification nonlinearity. We identify an elastoviscous parameter that controls nonlinear behaviour. Our study raises the hypothesis that biological hairy surfaces function to reduce fluid drag. Furthermore, angled hairs may be incorporated in the design of integrated microfluidic components, such as diodes and pumps.

Vapor Flow Patterns During a Start-Up Transient in Heat Pipes

NASA Technical Reports Server (NTRS)

Issacci, F.; Ghoniem, N, M.; Catton, I.

1996-01-01

The vapor flow patterns in heat pipes are examined during the start-up transient phase. The vapor core is modelled as a channel flow using a two dimensional compressible flow model. A nonlinear filtering technique is used as a post process to eliminate the non-physical oscillations of the flow variables. For high-input heat flux, multiple shock reflections are observed in the evaporation region. The reflections cause a reverse flow in the evaporation and circulations in the adiabatic region. Furthermore, each shock reflection causes a significant increase in the local pressure and a large pressure drop along the heat pipe.

Nonlinear hydrodynamic stability and transition; Proceedings of the IUTAM Symposium, Nice, France, Sept. 3-7, 1990

NASA Astrophysics Data System (ADS)

Theoretical and experimental research on nonlinear hydrodynamic stability and transition is presented. Bifurcations, amplitude equations, pattern in experiments, and shear flows are considered. Particular attention is given to bifurcations of plane viscous fluid flow and transition to turbulence, chaotic traveling wave covection, chaotic behavior of parametrically excited surface waves in square geometry, amplitude analysis of the Swift-Hohenberg equation, traveling wave convection in finite containers, focus instability in axisymmetric Rayleigh-Benard convection, scaling and pattern formation in flowing sand, dynamical behavior of instabilities in spherical gap flows, and nonlinear short-wavelength Taylor vortices. Also discussed are stability of a flow past a two-dimensional grid, inertia wave breakdown in a precessing fluid, flow-induced instabilities in directional solidification, structure and dynamical properties of convection in binary fluid mixtures, and instability competition for convecting superfluid mixtures.

Nonlinear vocal fold dynamics resulting from asymmetric fluid loading on a two-mass model of speech

NASA Astrophysics Data System (ADS)

Erath, Byron D.; Zañartu, Matías; Peterson, Sean D.; Plesniak, Michael W.

2011-09-01

Nonlinear vocal fold dynamics arising from asymmetric flow formations within the glottis are investigated using a two-mass model of speech with asymmetric vocal fold tensioning, representative of unilateral vocal fold paralysis. A refined theoretical boundary-layer flow solver is implemented to compute the intraglottal pressures, providing a more realistic description of the flow than the standard one-dimensional, inviscid Bernoulli flow solution. Vocal fold dynamics are investigated for subglottal pressures of 0.6 < ps < 1.5 kPa and tension asymmetries of 0.5 < Q < 0.8. As tension asymmetries become pronounced the asymmetric flow incites nonlinear behavior in the vocal fold dynamics at subglottal pressures that are associated with normal speech, behavior that is not captured with standard Bernoulli flow solvers. Regions of bifurcation, coexistence of solutions, and chaos are identified.

Phase relations in a forced turbulent boundary layer: implications for modelling of high Reynolds number wall turbulence.

PubMed

Duvvuri, Subrahmanyam; McKeon, Beverley

2017-03-13

Phase relations between specific scales in a turbulent boundary layer are studied here by highlighting the associated nonlinear scale interactions in the flow. This is achieved through an experimental technique that allows for targeted forcing of the flow through the use of a dynamic wall perturbation. Two distinct large-scale modes with well-defined spatial and temporal wavenumbers were simultaneously forced in the boundary layer, and the resulting nonlinear response from their direct interactions was isolated from the turbulence signal for the study. This approach advances the traditional studies of large- and small-scale interactions in wall turbulence by focusing on the direct interactions between scales with triadic wavenumber consistency. The results are discussed in the context of modelling high Reynolds number wall turbulence.This article is part of the themed issue 'Toward the development of high-fidelity models of wall turbulence at large Reynolds number'. © 2017 The Author(s).

Information flow to assess cardiorespiratory interactions in patients on weaning trials.

PubMed

Vallverdú, M; Tibaduisa, O; Clariá, F; Hoyer, D; Giraldo, B; Benito, S; Caminal, P

2006-01-01

Nonlinear processes of the autonomic nervous system (ANS) can produce breath-to-breath variability in the pattern of breathing. In order to provide assess to these nonlinear processes, nonlinear statistical dependencies between heart rate variability and respiratory pattern variability are analyzed. In this way, auto-mutual information and cross-mutual information concepts are applied. This information flow analysis is presented as a short-term non linear analysis method to investigate the information flow interactions in patients on weaning trials. 78 patients from mechanical ventilation were studied: Group A of 28 patients that failed to maintain spontaneous breathing and were reconnected; Group B of 50 patients with successful trials. The results show lower complexity with an increase of information flow in group A than in group B. Furthermore, a more (weakly) coupled nonlinear oscillator behavior is observed in the series of group A than in B.

Numerical Study of Pressure Field in Laterally Closed Industrial Buildings with Curved Metallic Roofs due to the Wind Effect by FEM and European Rule Comparison

NASA Astrophysics Data System (ADS)

Nieto, P. J. García; del Coz Díaz, J. J.; Vilán, J. A. Vilán; Placer, C. Casqueiro

2009-08-01

In this paper, an evaluation of distribution of the air pressure is determined throughout the laterally closed industrial buildings with curved metallic roofs due to the wind effect by the finite element method (FEM). The non-linearity is due to Reynolds-averaged Navier-Stokes (RANS) equations that govern the turbulent flow. The Navier-Stokes equations are non-linear partial differential equations and this non-linearity makes most problems difficult to solve and is part of the cause of turbulence. The RANS equations are time-averaged equations of motion for fluid flow. They are primarily used while dealing with turbulent flows. Turbulence is a highly complex physical phenomenon that is pervasive in flow problems of scientific and engineering concern like this one. In order to solve the RANS equations a two-equation model is used: the standard k-ɛ model. The calculation has been carried out keeping in mind the following assumptions: turbulent flow, an exponential-like wind speed profile with a maximum velocity of 40 m/s at 10 m reference height, and different heights of the building ranging from 6 to 10 meters. Finally, the forces and moments are determined on the cover, as well as the distribution of pressures on the same one, comparing the numerical results obtained with the Spanish CTE DB SE-AE, Spanish NBE AE-88 and European standard rules, giving place to the conclusions that are exposed in the study.

Rarefied gas flow simulations using high-order gas-kinetic unified algorithms for Boltzmann model equations

NASA Astrophysics Data System (ADS)

Li, Zhi-Hui; Peng, Ao-Ping; Zhang, Han-Xin; Yang, Jaw-Yen

2015-04-01

This article reviews rarefied gas flow computations based on nonlinear model Boltzmann equations using deterministic high-order gas-kinetic unified algorithms (GKUA) in phase space. The nonlinear Boltzmann model equations considered include the BGK model, the Shakhov model, the Ellipsoidal Statistical model and the Morse model. Several high-order gas-kinetic unified algorithms, which combine the discrete velocity ordinate method in velocity space and the compact high-order finite-difference schemes in physical space, are developed. The parallel strategies implemented with the accompanying algorithms are of equal importance. Accurate computations of rarefied gas flow problems using various kinetic models over wide ranges of Mach numbers 1.2-20 and Knudsen numbers 0.0001-5 are reported. The effects of different high resolution schemes on the flow resolution under the same discrete velocity ordinate method are studied. A conservative discrete velocity ordinate method to ensure the kinetic compatibility condition is also implemented. The present algorithms are tested for the one-dimensional unsteady shock-tube problems with various Knudsen numbers, the steady normal shock wave structures for different Mach numbers, the two-dimensional flows past a circular cylinder and a NACA 0012 airfoil to verify the present methodology and to simulate gas transport phenomena covering various flow regimes. Illustrations of large scale parallel computations of three-dimensional hypersonic rarefied flows over the reusable sphere-cone satellite and the re-entry spacecraft using almost the largest computer systems available in China are also reported. The present computed results are compared with the theoretical prediction from gas dynamics, related DSMC results, slip N-S solutions and experimental data, and good agreement can be found. The numerical experience indicates that although the direct model Boltzmann equation solver in phase space can be computationally expensive, nevertheless, the present GKUAs for kinetic model Boltzmann equations in conjunction with current available high-performance parallel computer power can provide a vital engineering tool for analyzing rarefied gas flows covering the whole range of flow regimes in aerospace engineering applications.

An efficient and stable hydrodynamic model with novel source term discretization schemes for overland flow and flood simulations

NASA Astrophysics Data System (ADS)

Xia, Xilin; Liang, Qiuhua; Ming, Xiaodong; Hou, Jingming

2017-05-01

Numerical models solving the full 2-D shallow water equations (SWEs) have been increasingly used to simulate overland flows and better understand the transient flow dynamics of flash floods in a catchment. However, there still exist key challenges that have not yet been resolved for the development of fully dynamic overland flow models, related to (1) the difficulty of maintaining numerical stability and accuracy in the limit of disappearing water depth and (2) inaccurate estimation of velocities and discharges on slopes as a result of strong nonlinearity of friction terms. This paper aims to tackle these key research challenges and present a new numerical scheme for accurately and efficiently modeling large-scale transient overland flows over complex terrains. The proposed scheme features a novel surface reconstruction method (SRM) to correctly compute slope source terms and maintain numerical stability at small water depth, and a new implicit discretization method to handle the highly nonlinear friction terms. The resulting shallow water overland flow model is first validated against analytical and experimental test cases and then applied to simulate a hypothetic rainfall event in the 42 km2 Haltwhistle Burn, UK.

Least Median of Squares Filtering of Locally Optimal Point Matches for Compressible Flow Image Registration

PubMed Central

Castillo, Edward; Castillo, Richard; White, Benjamin; Rojo, Javier; Guerrero, Thomas

2012-01-01

Compressible flow based image registration operates under the assumption that the mass of the imaged material is conserved from one image to the next. Depending on how the mass conservation assumption is modeled, the performance of existing compressible flow methods is limited by factors such as image quality, noise, large magnitude voxel displacements, and computational requirements. The Least Median of Squares Filtered Compressible Flow (LFC) method introduced here is based on a localized, nonlinear least squares, compressible flow model that describes the displacement of a single voxel that lends itself to a simple grid search (block matching) optimization strategy. Spatially inaccurate grid search point matches, corresponding to erroneous local minimizers of the nonlinear compressible flow model, are removed by a novel filtering approach based on least median of squares fitting and the forward search outlier detection method. The spatial accuracy of the method is measured using ten thoracic CT image sets and large samples of expert determined landmarks (available at www.dir-lab.com). The LFC method produces an average error within the intra-observer error on eight of the ten cases, indicating that the method is capable of achieving a high spatial accuracy for thoracic CT registration. PMID:22797602

An approximately factored incremental strategy for calculating consistent discrete aerodynamic sensitivity derivatives

NASA Technical Reports Server (NTRS)

Korivi, V. M.; Taylor, A. C., III; Newman, P. A.; Hou, G. J.-W.; Jones, H. E.

1992-01-01

An incremental strategy is presented for iteratively solving very large systems of linear equations, which are associated with aerodynamic sensitivity derivatives for advanced CFD codes. It is shown that the left-hand side matrix operator and the well-known factorization algorithm used to solve the nonlinear flow equations can also be used to efficiently solve the linear sensitivity equations. Two airfoil problems are considered as an example: subsonic low Reynolds number laminar flow and transonic high Reynolds number turbulent flow.

Unsteady Boundary-Layer Flow over Jerked Plate Moving in a Free Stream of Viscoelastic Fluid

PubMed Central

Mehmood, Ahmer; Ali, Asif; Saleem, Najma

2014-01-01

This study aims to investigate the unsteady boundary-layer flow of a viscoelastic non-Newtonian fluid over a flat surface. The plate is suddenly jerked to move with uniform velocity in a uniform stream of non-Newtonian fluid. Purely analytic solution to governing nonlinear equation is obtained. The solution is highly accurate and valid for all values of the dimensionless time 0 ≤ τ < ∞. Flow properties of the viscoelastic fluid are discussed through graphs. PMID:24892060

Level-Dependent Nonlinear Hearing Protector Model in the Auditory Hazard Assessment Algorithm for Humans

DTIC Science & Technology

2015-04-01

9 Fig. 8 Resistance of orifice flow plotted vs. flow velocity. Acoustic ohm units are dynes∙s∙cm5; the changing resistance demonstrates the...process of nonlinear flow through the orifice. (The blue single-orifice fit and the red total resistance for a dual orifice configuration were added...piston hearing protection model with level- dependent extensions in cushion visco-elastic elements and leakage flow impedance

A numerical study of linear and nonlinear kinematic models in fish swimming with the DSD/SST method

NASA Astrophysics Data System (ADS)

Tian, Fang-Bao

2015-03-01

Flow over two fish (modeled by two flexible plates) in tandem arrangement is investigated by solving the incompressible Navier-Stokes equations numerically with the DSD/SST method to understand the differences between the geometrically linear and nonlinear models. In the simulation, the motions of the plates are reconstructed from a vertically flowing soap film tunnel experiment with linear and nonlinear kinematic models. Based on the simulations, the drag, lift, power consumption, vorticity and pressure fields are discussed in detail. It is found that the linear and nonlinear models are able to reasonably predict the forces and power consumption of a single plate in flow. Moreover, if multiple plates are considered, these two models yield totally different results, which implies that the nonlinear model should be used. The results presented in this work provide a guideline for future studies in fish swimming.

Current flow instability and nonlinear structures in dissipative two-fluid plasmas

NASA Astrophysics Data System (ADS)

Koshkarov, O.; Smolyakov, A. I.; Romadanov, I. V.; Chapurin, O.; Umansky, M. V.; Raitses, Y.; Kaganovich, I. D.

2018-01-01

The current flow in two-fluid plasma is inherently unstable if plasma components (e.g., electrons and ions) are in different collisionality regimes. A typical example is a partially magnetized E ×B plasma discharge supported by the energy released from the dissipation of the current in the direction of the applied electric field (perpendicular to the magnetic field). Ions are not magnetized so they respond to the fluctuations of the electric field ballistically on the inertial time scale. In contrast, the electron current in the direction of the applied electric field is dissipatively supported either by classical collisions or anomalous processes. The instability occurs due to a positive feedback between the electron and ion current coupled by the quasi-neutrality condition. The theory of this instability is further developed taking into account the electron inertia, finite Larmor radius and nonlinear effects. It is shown that this instability results in highly nonlinear quasi-coherent structures resembling breathing mode oscillations in Hall thrusters.

Multiple secondary islands formation in nonlinear evolution of double tearing mode simulations

NASA Astrophysics Data System (ADS)

Guo, W.; Ma, J.; Yu, Z.

2017-03-01

A new numerical code solving the conservative perturbed resistive magnetohydrodynamic (MHD) model is developed. Numerical tests of the ideal Kelvin-Helmholtz instability and the resistive double tearing mode (DTM) show its capability in solving linear and nonlinear MHD instabilities. The nonlinear DTM evolution in 2D geometry is numerically investigated with low guiding field B z 0 , short half-distance y 0 between the equilibrium current sheets, and small resistivity η. The interaction of islands on the two initial current sheets may generate an unstable flow driven current sheet with a high length-to-thickness aspect ratio (α), and multiple secondary islands can form. In general, the length-to-thickness aspect ratio α and the number of secondary islands increase with decreasing guide field B z 0 , decreasing half-distance y 0 , and increasing Lundquist number of the flow driven current sheet S L although the dependence may be non-monotonic. The reconnection rate dependence on S L , B z 0 , and y 0 is also investigated.

A Computational and Experimental Study of Nonlinear Aspects of Induced Drag

NASA Technical Reports Server (NTRS)

Smith, Stephen C.

1996-01-01

Despite the 80-year history of classical wing theory, considerable research has recently been directed toward planform and wake effects on induced drag. Nonlinear interactions between the trailing wake and the wing offer the possibility of reducing drag. The nonlinear effect of compressibility on induced drag characteristics may also influence wing design. This thesis deals with the prediction of these nonlinear aspects of induced drag and ways to exploit them. A potential benefit of only a few percent of the drag represents a large fuel savings for the world's commercial transport fleet. Computational methods must be applied carefully to obtain accurate induced drag predictions. Trefftz-plane drag integration is far more reliable than surface pressure integration, but is very sensitive to the accuracy of the force-free wake model. The practical use of Trefftz plane drag integration was extended to transonic flow with the Tranair full-potential code. The induced drag characteristics of a typical transport wing were studied with Tranair, a full-potential method, and A502, a high-order linear panel method to investigate changes in lift distribution and span efficiency due to compressibility. Modeling the force-free wake is a nonlinear problem, even when the flow governing equation is linear. A novel method was developed for computing the force-free wake shape. This hybrid wake-relaxation scheme couples the well-behaved nature of the discrete vortex wake with viscous-core modeling and the high-accuracy velocity prediction of the high-order panel method. The hybrid scheme produced converged wake shapes that allowed accurate Trefftz-plane integration. An unusual split-tip wing concept was studied for exploiting nonlinear wake interaction to reduced induced drag. This design exhibits significant nonlinear interactions between the wing and wake that produced a 12% reduction in induced drag compared to an equivalent elliptical wing at a lift coefficient of 0.7. The performance of the split-tip wing was also investigated by wing tunnel experiments. Induced drag was determined from force measurements by subtracting the estimated viscous drag, and from an analytical drag-decomposition method using a wake survey. The experimental results confirm the computational prediction.

An enstrophy-based linear and nonlinear receptivity theory

NASA Astrophysics Data System (ADS)

Sengupta, Aditi; Suman, V. K.; Sengupta, Tapan K.; Bhaumik, Swagata

2018-05-01

In the present research, a new theory of instability based on enstrophy is presented for incompressible flows. Explaining instability through enstrophy is counter-intuitive, as it has been usually associated with dissipation for the Navier-Stokes equation (NSE). This developed theory is valid for both linear and nonlinear stages of disturbance growth. A previously developed nonlinear theory of incompressible flow instability based on total mechanical energy described in the work of Sengupta et al. ["Vortex-induced instability of an incompressible wall-bounded shear layer," J. Fluid Mech. 493, 277-286 (2003)] is used to compare with the present enstrophy based theory. The developed equations for disturbance enstrophy and disturbance mechanical energy are derived from NSE without any simplifying assumptions, as compared to other classical linear/nonlinear theories. The theory is tested for bypass transition caused by free stream convecting vortex over a zero pressure gradient boundary layer. We explain the creation of smaller scales in the flow by a cascade of enstrophy, which creates rotationality, in general inhomogeneous flows. Linear and nonlinear versions of the theory help explain the vortex-induced instability problem under consideration.

Active control of panel vibrations induced by a boundary layer flow

NASA Technical Reports Server (NTRS)

Chow, Pao-Liu

1995-01-01

The problems of active and passive control of sound and vibration has been investigated by many researchers for a number of years. However, few of the articles are concerned with the sound and vibration with flow-structure interaction. Experimental and numerical studies on the coupling between panel vibration and acoustic radiation due to flow excitation have been done by Maestrello and his associates at NASA/Langley Research Center. Since the coupled system of nonlinear partial differential equations is formidable, an analytical solution to the full problem seems impossible. For this reason, we have to simplify the problem to that of the nonlinear panel vibration induced by a uniform flow or a boundary-layer flow with a given wall pressure distribution. Based on this simplified model, we have been able to consider the control and stabilization of the nonlinear panel vibration, which have not been treated satisfactorily by other authors. Although the sound radiation has not been included, the vibration suppression will clearly reduce the sound radiation power from the panel. The major research findings are presented in three sections. In section two we describe results on the boundary control of nonlinear panel vibration, with or without flow excitation. Sections three and four are concerned with some analytical and numerical results in the optimal control of the linear and nonlinear panel vibrations, respectively, excited by the flow pressure fluctuations. Finally, in section five, we draw some conclusions from research findings.

Hemodynamics of physiological blood flow in the aorta with nonlinear anisotropic heart valve

NASA Astrophysics Data System (ADS)

Sotiropoulos, Fotis; Gilmanov, Anvar; Stolarski, Henryk

2016-11-01

The hemodynamic blood flow in cardiovascular system is one of the most important factor, which causing several vascular diseases. We developed a new Curvilinear Immersed Boundary - Finite Element - Fluid Structure Interaction (CURVIB-FE-FSI) method to analyze hemodynamic of pulsatile blood flow in a real aorta with nonlinear anisotropic aortic valve at physiological conditions. Hyperelastic material model, which is more realistic for describing heart valve have been incorporated in the CURVIB-FE-FSI code to simulate interaction of aortic heart valve with pulsatile blood flow. Comparative studies of hemodynamics for linear and nonlinear models of heart valve show drastic differences in blood flow patterns and hence differences of stresses causing impact at leaflets and aortic wall. This work is supported by the Lillehei Heart Institute at the University of Minnesota.

Nonlinear Generation of shear flows and large scale magnetic fields by small scale

NASA Astrophysics Data System (ADS)

Aburjania, G.

2009-04-01

EGU2009-233 Nonlinear Generation of shear flows and large scale magnetic fields by small scale turbulence in the ionosphere by G. Aburjania Contact: George Aburjania, g.aburjania@gmail.com,aburj@mymail.ge

Two-dimensional supersonic nonlinear Schrödinger flow past an extended obstacle

NASA Astrophysics Data System (ADS)

El, G. A.; Kamchatnov, A. M.; Khodorovskii, V. V.; Annibale, E. S.; Gammal, A.

2009-10-01

Supersonic flow of a superfluid past a slender impenetrable macroscopic obstacle is studied in the framework of the two-dimensional (2D) defocusing nonlinear Schrödinger (NLS) equation. This problem is of fundamental importance as a dispersive analog of the corresponding classical gas-dynamics problem. Assuming the oncoming flow speed is sufficiently high, we asymptotically reduce the original boundary-value problem for a steady flow past a slender body to the one-dimensional dispersive piston problem described by the nonstationary NLS equation, in which the role of time is played by the stretched x coordinate and the piston motion curve is defined by the spatial body profile. Two steady oblique spatial dispersive shock waves (DSWs) spreading from the pointed ends of the body are generated in both half planes. These are described analytically by constructing appropriate exact solutions of the Whitham modulation equations for the front DSW and by using a generalized Bohr-Sommerfeld quantization rule for the oblique dark soliton fan in the rear DSW. We propose an extension of the traditional modulation description of DSWs to include the linear “ship-wave” pattern forming outside the nonlinear modulation region of the front DSW. Our analytic results are supported by direct 2D unsteady numerical simulations and are relevant to recent experiments on Bose-Einstein condensates freely expanding past obstacles.

Non-linear isotope and fast ions effects: routes for low turbulence in DT plasmas

NASA Astrophysics Data System (ADS)

Garcia, Jeronimo

2017-10-01

The isotope effect, i.e. the fact that heat and particle fluxes do not follow the expected Gyro-Bohm estimate for turbulent transport when the plasma mass is changed, is one of the main challenges in plasma theory. Of particular interest is the isotope exchange between the fusion of deuterium (DD) and deuterium-tritium (DT) nuclei as there are no clear indications of what kind of transport difference can be expected in burning plasmas. The GENE code is therefore used for computing DD vs DT linear and nonlinear microturbulence characteristics in the core plasma region of a previously ITER hybrid scenario at high beta obtained in the framework of simplified integrated modelling. Scans on common turbulence related quantitates as external ExB flow shear, Parallel Velocity Gradient (PVG), plasma beta, colisionality or the number of ion species have been performed. Additionally, the role of energetic particles, known to reduce Ion Temperature Gradient (ITG) turbulence has been also addressed. It is obtained that the ITER operational point will be close to threshold and in these conditions turbulence is dominated by ITG modes. A purely weak non-linear isotope effect, absent in linear scans, can be found when separately adding moderate ExB flow shear or electromagnetic effects, whereas collisionality just modulates the intensity. The isotope effect, on the other hand, becomes very strong in conditions with simultaneously moderate ExB flow shear, beta and low q profile with significant reductions of ion heat transport from DD to DT. By analyzing the radial structure of the two point electrostatic potential correlation function it has been found that the inherent Gyro-Bohm scaling for plasma microturbulence, which increases the radial correlation length at short scales form DD to DT, is counteracted by the concomitant appearance of a complex nonlinear multiscale space interaction involving external ExB flow shear, zonal flow activity, magnetic geometry and electromagnetic effects. The number of ion species and the fast ion population is also found to play a role in this non-linear process whereas a symmetry breaking between D and T, with systematic reduced heat and particle transport for T, is always obtained.

Renormalizability of the gradient flow in the 2D O(N) non-linear sigma model

NASA Astrophysics Data System (ADS)

Makino, Hiroki; Suzuki, Hiroshi

2015-03-01

It is known that the gauge field and its composite operators evolved by the Yang-Mills gradient flow are ultraviolet (UV) finite without any multiplicative wave function renormalization. In this paper, we prove that the gradient flow in the 2D O(N) non-linear sigma model possesses a similar property: The flowed N-vector field and its composite operators are UV finite without multiplicative wave function renormalization. Our proof in all orders of perturbation theory uses a (2+1)-dimensional field theoretical representation of the gradient flow, which possesses local gauge invariance without gauge field. As an application of the UV finiteness of the gradient flow, we construct the energy-momentum tensor in the lattice formulation of the O(N) non-linear sigma model that automatically restores the correct normalization and the conservation law in the continuum limit.

Nonlinear stability of non-stationary cross-flow vortices in compressible boundary layers

NASA Technical Reports Server (NTRS)

Gajjar, J. S. B.

1995-01-01

The nonlinear evolution of long wavelength non-stationary cross-flow vortices in a compressible boundary layer is investigated and the work extends that of Gajjar (1994) to flows involving multiple critical layers. The basic flow profile considered in this paper is that appropriate for a fully three-dimensional boundary layer with O(1) Mach number and with wall heating or cooling. The governing equations for the evolution of the cross-flow vortex are obtained and some special cases are discussed. One special case includes linear theory where exact analytic expressions for the growth rate of the vortices are obtained. Another special case is a generalization of the Bassom & Gajjar (1988) results for neutral waves to compressible flows. The viscous correction to the growth rate is derived and it is shown how the unsteady nonlinear critical layer structure merges with that for a Haberman type of viscous critical layer.

Nonlinear Reynolds stress model for turbulent shear flows

NASA Technical Reports Server (NTRS)

Barton, J. Michael; Rubinstein, R.; Kirtley, K. R.

1991-01-01

A nonlinear algebraic Reynolds stress model, derived using the renormalization group, is applied to equilibrium homogeneous shear flow and fully developed flow in a square duct. The model, which is quadratically nonlinear in the velocity gradients, successfully captures the large-scale inhomogeneity and anisotropy of the flows studied. The ratios of normal stresses, as well as the actual magnitudes of the stresses are correctly predicted for equilibrium homogeneous shear flow. Reynolds normal stress anisotropy and attendant turbulence driven secondary flow are predicted for a square duct. Profiles of mean velocity and normal stresses are in good agreement with measurements. Very close to walls, agreement with measurements diminishes. The model has the benefit of containing no arbitrary constants; all values are determined directly from the theory. It seems that near wall behavior is influenced by more than the large scale anisotropy accommodated in the current model. More accurate near wall calculations may well require a model for anisotropic dissipation.

HIFU procedures at moderate intensities--effect of large blood vessels.

PubMed

Hariharan, P; Myers, M R; Banerjee, R K

2007-06-21

A three-dimensional computational model is presented for studying the efficacy of high-intensity focused ultrasound (HIFU) procedures targeted near large blood vessels. The analysis applies to procedures performed at intensities below the threshold for cavitation, boiling and highly nonlinear propagation, but high enough to increase tissue temperature a few degrees per second. The model is based upon the linearized KZK equation and the bioheat equation in tissue. In the blood vessel the momentum and energy equations are satisfied. The model is first validated in a tissue phantom, to verify the absence of bubble formation and nonlinear effects. Temperature rise and lesion-volume calculations are then shown for different beam locations and orientations relative to a large vessel. Both single and multiple ablations are considered. Results show that when the vessel is located within about a beam width (few mm) of the ultrasound beam, significant reduction in lesion volume is observed due to blood flow. However, for gaps larger than a beam width, blood flow has no major effect on the lesion formation. Under the clinically representative conditions considered, the lesion volume is reduced about 40% (relative to the no-flow case) when the beam is parallel to the blood vessel, compared to about 20% for a perpendicular orientation. Procedures involving multiple ablation sites are affected less by blood flow than single ablations. The model also suggests that optimally focused transducers can generate lesions that are significantly larger (>2 times) than the ones produced by highly focused beams.

HIFU procedures at moderate intensities—effect of large blood vessels

NASA Astrophysics Data System (ADS)

Hariharan, P.; Myers, M. R.; Banerjee, R. K.

2007-07-01

A three-dimensional computational model is presented for studying the efficacy of high-intensity focused ultrasound (HIFU) procedures targeted near large blood vessels. The analysis applies to procedures performed at intensities below the threshold for cavitation, boiling and highly nonlinear propagation, but high enough to increase tissue temperature a few degrees per second. The model is based upon the linearized KZK equation and the bioheat equation in tissue. In the blood vessel the momentum and energy equations are satisfied. The model is first validated in a tissue phantom, to verify the absence of bubble formation and nonlinear effects. Temperature rise and lesion-volume calculations are then shown for different beam locations and orientations relative to a large vessel. Both single and multiple ablations are considered. Results show that when the vessel is located within about a beam width (few mm) of the ultrasound beam, significant reduction in lesion volume is observed due to blood flow. However, for gaps larger than a beam width, blood flow has no major effect on the lesion formation. Under the clinically representative conditions considered, the lesion volume is reduced about 40% (relative to the no-flow case) when the beam is parallel to the blood vessel, compared to about 20% for a perpendicular orientation. Procedures involving multiple ablation sites are affected less by blood flow than single ablations. The model also suggests that optimally focused transducers can generate lesions that are significantly larger (>2 times) than the ones produced by highly focused beams.

Limits of localized control in extended nonlinear systems

NASA Astrophysics Data System (ADS)

Handel, Andreas

We investigate the limits of localized linear control in spatially extended, nonlinear systems. Spatially extended, nonlinear systems can be found in virtually every field of engineering and science. An important category of such systems are fluid flows. Fluid flows play an important role in many commercial applications, for instance in the chemical, pharmaceutical and food-processing industries. Other important fluid flows include air- or water flows around cars, planes or ships. In all these systems, it is highly desirable to control the flow of the respective fluid. For instance control of the air flow around an airplane or car leads to better fuel-economy and reduced noise production. Usually, it is impossible to apply control everywhere. Consider an airplane: It would not be feasibly to cover the whole body of the plane with control units. Instead, one can place the control units at localized regions, such as points along the edge of the wings, spaced as far apart from each other as possible. These considerations lead to an important question: For a given system, what is the minimum number of localized controllers that still ensures successful control? Too few controllers will not achieve control, while using too many leads to unnecessary expenses and wastes resources. To answer this question, we study localized control in a class of model equations. These model equations are good representations of many real fluid flows. Using these equations, we show how one can design localized control that renders the system stable. We study the properties of the control and derive several expressions that allow us to determine the limits of successful control. We show how the number of controllers that are needed for successful control depends on the size and type of the system, as well as the way control is implemented. We find that especially the nonlinearities and the amount of noise present in the system play a crucial role. This analysis allows us to determine under which circumstances a given number of controllers can successfully stabilize a given system.

Nonlinear growth of zonal flows by secondary instability in general magnetic geometry

DOE PAGES

Plunk, G. G.; Navarro, A. Banon

2017-02-23

Here we present a theory of the nonlinear growth of zonal flows in magnetized plasma turbulence, by the mechanism of secondary instability. The theory is derived for general magnetic geometry, and is thus applicable to both tokamaks and stellarators. The predicted growth rate is shown to compare favorably with nonlinear gyrokinetic simulations, with the error scaling as expected with the small parameter of the theory.

A three-dimensional autonomous nonlinear dynamical system modelling equatorial ocean flows

NASA Astrophysics Data System (ADS)

Ionescu-Kruse, Delia

2018-04-01

We investigate a nonlinear three-dimensional model for equatorial flows, finding exact solutions that capture the most relevant geophysical features: depth-dependent currents, poleward or equatorial surface drift and a vertical mixture of upward and downward motions.

High speed flow past wings

NASA Technical Reports Server (NTRS)

Norstrud, H.

1973-01-01

The analytical solution to the transonic small perturbation equation which describes steady compressible flow past finite wings at subsonic speeds can be expressed as a nonlinear integral equation with the perturbation velocity potential as the unknown function. This known formulation is substituted by a system of nonlinear algebraic equations to which various methods are applicable for its solution. Due to the presence of mathematical discontinuities in the flow solutions, however, a main computational difficulty was to ensure uniqueness of the solutions when local velocities on the wing exceeded the speed of sound. For continuous solutions this was achieved by embedding the algebraic system in an one-parameter operator homotopy in order to apply the method of parametric differentiation. The solution to the initial system of equations appears then as a solution to a Cauchy problem where the initial condition is related to the accompanying incompressible flow solution. In using this technique, however, a continuous dependence of the solution development on the initial data is lost when the solution reaches the minimum bifurcation point. A steepest descent iteration technique was therefore, added to the computational scheme for the calculation of discontinuous flow solutions. Results for purely subsonic flows and supersonic flows with and without compression shocks are given and compared with other available theoretical solutions.

Weighted Non-linear Compact Schemes for the Direct Numerical Simulation of Compressible, Turbulent Flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, Debojyoti; Baeder, James D.

2014-01-21

A new class of compact-reconstruction weighted essentially non-oscillatory (CRWENO) schemes were introduced (Ghosh and Baeder in SIAM J Sci Comput 34(3): A1678–A1706, 2012) with high spectral resolution and essentially non-oscillatory behavior across discontinuities. The CRWENO schemes use solution-dependent weights to combine lower-order compact interpolation schemes and yield a high-order compact scheme for smooth solutions and a non-oscillatory compact scheme near discontinuities. The new schemes result in lower absolute errors, and improved resolution of discontinuities and smaller length scales, compared to the weighted essentially non-oscillatory (WENO) scheme of the same order of convergence. Several improvements to the smoothness-dependent weights, proposed inmore » the literature in the context of the WENO schemes, address the drawbacks of the original formulation. This paper explores these improvements in the context of the CRWENO schemes and compares the different formulations of the non-linear weights for flow problems with small length scales as well as discontinuities. Simplified one- and two-dimensional inviscid flow problems are solved to demonstrate the numerical properties of the CRWENO schemes and its different formulations. Canonical turbulent flow problems—the decay of isotropic turbulence and the shock-turbulence interaction—are solved to assess the performance of the schemes for the direct numerical simulation of compressible, turbulent flows« less

Study of the Transition from MRI to Magnetic Turbulence via Parasitic Instability by a High-order MHD Simulation Code

NASA Astrophysics Data System (ADS)

Hirai, Kenichiro; Katoh, Yuto; Terada, Naoki; Kawai, Soshi

2018-02-01

Magnetic turbulence in accretion disks under ideal magnetohydrodynamic (MHD) conditions is expected to be driven by the magneto-rotational instability (MRI) followed by secondary parasitic instabilities. We develop a three-dimensional ideal MHD code that can accurately resolve turbulent structures, and carry out simulations with a net vertical magnetic field in a local shearing box disk model to investigate the role of parasitic instabilities in the formation process of magnetic turbulence. Our simulations reveal that a highly anisotropic Kelvin–Helmholtz (K–H) mode parasitic instability evolves just before the first peak in turbulent stress and then breaks large-scale shear flows created by MRI. The wavenumber of the enhanced parasitic instability is larger than the theoretical estimate, because the shear flow layers sometimes become thinner than those assumed in the linear analysis. We also find that interaction between antiparallel vortices caused by the K–H mode parasitic instability induces small-scale waves that break the shear flows. On the other hand, at repeated peaks in the nonlinear phase, anisotropic wavenumber spectra are observed only in the small wavenumber region and isotropic waves dominate at large wavenumbers unlike for the first peak. Restructured channel flows due to MRI at the peaks in nonlinear phase seem to be collapsed by the advection of small-scale shear structures into the restructured flow and resultant mixing.

Linear and nonlinear dynamo properties of time-dependent ABC flows

NASA Astrophysics Data System (ADS)

Brummell, N. H.; Cattaneo, F.; Tobias, S. M.

2001-04-01

The linear and nonlinear dynamo properties of a class of periodically forced flows is considered. The forcing functions are chosen to drive, in the absence of magnetic effects (kinematic regime), a time-dependent version of the ABC flow with A= B= C=1. The time-dependence consists of a harmonic displacement of the origin along the line x= y= z=1 with amplitude ɛ and frequency Ω. The finite-time Lyapunov exponents are computed for several values of ɛ and Ω. It is found that for values of these parameters near unity chaotic streamlines occupy most of the volume. In this parameter range, and for moderate kinetic and magnetic Reynolds numbers, the basic flow is both hydrodynamically and hydromagnetically unstable. However, the dynamo instability has a higher growth rate than the hydrodynamic one, so that the nonlinear regime can be reached with negligible departures from the basic ABC flow. In the nonlinear regime, two distinct classes of behaviour are observed. In one, the exponential growth of the magnetic field saturates and the dynamo settles to a stationary state whereby the magnetic energy is maintained indefinitely. In the other the velocity field evolves to a nondynamo state and the magnetic field, following an initial amplification, decays to zero. The transition from the dynamo to the nondynamo state can be mediated by the hydrodynamic instability or by magnetic perturbations. The properties of the ensuing nonlinear dynamo states are investigated for different parameter values. The implications for a general theory of nonlinear dynamos are discussed.

A class of high resolution explicit and implicit shock-capturing methods

NASA Technical Reports Server (NTRS)

Yee, H. C.

1989-01-01

An attempt is made to give a unified and generalized formulation of a class of high resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock wave computations. Included is a systematic review of the basic design principle of the various related numerical methods. Special emphasis is on the construction of the basis nonlinear, spatially second and third order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and the flux vector splitting approaches. Generalization of these methods to efficiently include equilibrium real gases and large systems of nonequilibrium flows are discussed. Some issues concerning the applicability of these methods that were designed for homogeneous hyperbolic conservation laws to problems containing stiff source terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for 1-, 2- and 3-dimensional gas dynamics problems.

Static Flow Characteristics of a Mass Flow Injecting Valve

NASA Technical Reports Server (NTRS)

Mattern, Duane; Paxson, Dan

1995-01-01

A sleeve valve is under development for ground-based forced response testing of air compression systems. This valve will be used to inject air and to impart momentum to the flow inside the first stage of a multi-stage compressor. The valve was designed to deliver a maximum mass flow of 0.22 lbm/s (0.1 kg/s) with a maximum valve throat area of 0.12 sq. in (80 sq. mm), a 100 psid (689 KPA) pressure difference across the valve and a 68 F, (20 C) air supply. It was assumed that the valve mass flow rate would be proportional to the valve orifice area. A static flow calibration revealed a nonlinear valve orifice area to mass flow relationship which limits the maximum flow rate that the valve can deliver. This nonlinearity was found to be caused by multiple choking points in the flow path. A simple model was used to explain this nonlinearity and the model was compared to the static flow calibration data. Only steady flow data is presented here. In this report, the static flow characteristics of a proportionally controlled sleeve valve are modelled and validated against experimental data.

Combination of automated high throughput platforms, flow cytometry, and hierarchical clustering to detect cell state.

PubMed

Kitsos, Christine M; Bhamidipati, Phani; Melnikova, Irena; Cash, Ethan P; McNulty, Chris; Furman, Julia; Cima, Michael J; Levinson, Douglas

2007-01-01

This study examined whether hierarchical clustering could be used to detect cell states induced by treatment combinations that were generated through automation and high-throughput (HT) technology. Data-mining techniques were used to analyze the large experimental data sets to determine whether nonlinear, non-obvious responses could be extracted from the data. Unary, binary, and ternary combinations of pharmacological factors (examples of stimuli) were used to induce differentiation of HL-60 cells using a HT automated approach. Cell profiles were analyzed by incorporating hierarchical clustering methods on data collected by flow cytometry. Data-mining techniques were used to explore the combinatorial space for nonlinear, unexpected events. Additional small-scale, follow-up experiments were performed on cellular profiles of interest. Multiple, distinct cellular profiles were detected using hierarchical clustering of expressed cell-surface antigens. Data-mining of this large, complex data set retrieved cases of both factor dominance and cooperativity, as well as atypical cellular profiles. Follow-up experiments found that treatment combinations producing "atypical cell types" made those cells more susceptible to apoptosis. CONCLUSIONS Hierarchical clustering and other data-mining techniques were applied to analyze large data sets from HT flow cytometry. From each sample, the data set was filtered and used to define discrete, usable states that were then related back to their original formulations. Analysis of resultant cell populations induced by a multitude of treatments identified unexpected phenotypes and nonlinear response profiles.

Method for transition prediction in high-speed boundary layers, phase 2

NASA Astrophysics Data System (ADS)

Herbert, T.; Stuckert, G. K.; Lin, N.

1993-09-01

The parabolized stability equations (PSE) are a new and more reliable approach to analyzing the stability of streamwise varying flows such as boundary layers. This approach has been previously validated for idealized incompressible flows. Here, the PSE are formulated for highly compressible flows in general curvilinear coordinates to permit the analysis of high-speed boundary-layer flows over fairly general bodies. Vigorous numerical studies are carried out to study convergence and accuracy of the linear-stability code LSH and the linear/nonlinear PSE code PSH. Physical interfaces are set up to analyze the M = 8 boundary layer over a blunt cone calculated by using a thin-layer Navier Stokes (TNLS) code and the flow over a sharp cone at angle of attack calculated using the AFWAL parabolized Navier-Stokes (PNS) code. While stability and transition studies at high speeds are far from routine, the method developed here is the best tool available to research the physical processes in high-speed boundary layers.

Parabolic equation for nonlinear acoustic wave propagation in inhomogeneous moving media

NASA Astrophysics Data System (ADS)

Aver'yanov, M. V.; Khokhlova, V. A.; Sapozhnikov, O. A.; Blanc-Benon, Ph.; Cleveland, R. O.

2006-12-01

A new parabolic equation is derived to describe the propagation of nonlinear sound waves in inhomogeneous moving media. The equation accounts for diffraction, nonlinearity, absorption, scalar inhomogeneities (density and sound speed), and vectorial inhomogeneities (flow). A numerical algorithm employed earlier to solve the KZK equation is adapted to this more general case. A two-dimensional version of the algorithm is used to investigate the propagation of nonlinear periodic waves in media with random inhomogeneities. For the case of scalar inhomogeneities, including the case of a flow parallel to the wave propagation direction, a complex acoustic field structure with multiple caustics is obtained. Inclusion of the transverse component of vectorial random inhomogeneities has little effect on the acoustic field. However, when a uniform transverse flow is present, the field structure is shifted without changing its morphology. The impact of nonlinearity is twofold: it produces strong shock waves in focal regions, while, outside the caustics, it produces higher harmonics without any shocks. When the intensity is averaged across the beam propagating through a random medium, it evolves similarly to the intensity of a plane nonlinear wave, indicating that the transverse redistribution of acoustic energy gives no considerable contribution to nonlinear absorption.

Estimating Ω from Galaxy Redshifts: Linear Flow Distortions and Nonlinear Clustering

NASA Astrophysics Data System (ADS)

Bromley, B. C.; Warren, M. S.; Zurek, W. H.

1997-02-01

We propose a method to determine the cosmic mass density Ω from redshift-space distortions induced by large-scale flows in the presence of nonlinear clustering. Nonlinear structures in redshift space, such as fingers of God, can contaminate distortions from linear flows on scales as large as several times the small-scale pairwise velocity dispersion σv. Following Peacock & Dodds, we work in the Fourier domain and propose a model to describe the anisotropy in the redshift-space power spectrum; tests with high-resolution numerical data demonstrate that the model is robust for both mass and biased galaxy halos on translinear scales and above. On the basis of this model, we propose an estimator of the linear growth parameter β = Ω0.6/b, where b measures bias, derived from sampling functions that are tuned to eliminate distortions from nonlinear clustering. The measure is tested on the numerical data and found to recover the true value of β to within ~10%. An analysis of IRAS 1.2 Jy galaxies yields β=0.8+0.4-0.3 at a scale of 1000 km s-1, which is close to optimal given the shot noise and finite size of the survey. This measurement is consistent with dynamical estimates of β derived from both real-space and redshift-space information. The importance of the method presented here is that nonlinear clustering effects are removed to enable linear correlation anisotropy measurements on scales approaching the translinear regime. We discuss implications for analyses of forthcoming optical redshift surveys in which the dispersion is more than a factor of 2 greater than in the IRAS data.

Ice-sheet modelling accelerated by graphics cards

NASA Astrophysics Data System (ADS)

Brædstrup, Christian Fredborg; Damsgaard, Anders; Egholm, David Lundbek

2014-11-01

Studies of glaciers and ice sheets have increased the demand for high performance numerical ice flow models over the past decades. When exploring the highly non-linear dynamics of fast flowing glaciers and ice streams, or when coupling multiple flow processes for ice, water, and sediment, researchers are often forced to use super-computing clusters. As an alternative to conventional high-performance computing hardware, the Graphical Processing Unit (GPU) is capable of massively parallel computing while retaining a compact design and low cost. In this study, we present a strategy for accelerating a higher-order ice flow model using a GPU. By applying the newest GPU hardware, we achieve up to 180× speedup compared to a similar but serial CPU implementation. Our results suggest that GPU acceleration is a competitive option for ice-flow modelling when compared to CPU-optimised algorithms parallelised by the OpenMP or Message Passing Interface (MPI) protocols.

Estuarine Response to River Flow and Sea-Level Rise under Future Climate Change and Human Development

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Zhaoqing; Wang, Taiping; Voisin, Nathalie

Understanding the response of river flow and estuarine hydrodynamics to climate change, land-use/land-cover change (LULC), and sea-level rise is essential to managing water resources and stress on living organisms under these changing conditions. This paper presents a modeling study using a watershed hydrology model and an estuarine hydrodynamic model, in a one-way coupling, to investigate the estuarine hydrodynamic response to sea-level rise and change in river flow due to the effect of future climate and LULC changes in the Snohomish River estuary, Washington, USA. A set of hydrodynamic variables, including salinity intrusion points, average water depth, and salinity of themore » inundated area, were used to quantify the estuarine response to river flow and sea-level rise. Model results suggest that salinity intrusion points in the Snohomish River estuary and the average salinity of the inundated areas are a nonlinear function of river flow, although the average water depth in the inundated area is approximately linear with river flow. Future climate changes will shift salinity intrusion points further upstream under low flow conditions and further downstream under high flow conditions. In contrast, under the future LULC change scenario, the salinity intrusion point will shift downstream under both low and high flow conditions, compared to present conditions. The model results also suggest that the average water depth in the inundated areas increases linearly with sea-level rise but at a slower rate, and the average salinity in the inundated areas increases linearly with sea-level rise; however, the response of salinity intrusion points in the river to sea-level rise is strongly nonlinear.« less

Adaptive Harmonic Balance Method for Unsteady, Nonlinear, One-Dimensional Periodic Flows

DTIC Science & Technology

2002-09-01

Design and Implemen- tation. May 1999. REF-2 23. Toro , Eleuterio F . Fiemann Solvers and Numerical Methods for Fluid Dynamics, chapter 15. New York...prominent for high-frequency unsteady-flows. Experimental Analysis of Splitting-induced Error To assess the actual effect of splitting error on a...VITA-1 vi List of Figures Figure Page 1.1. Experimental Pressure Data on Inlet Guide Vane Upstream of Transonic Rotating

Development of an Unmanned Air Research Vehicle for Supermaneuverability Studies

DTIC Science & Technology

1990-03-29

VORTEX CONTROL Another emerging concept involves strake- generated vortex interactions, which improves maneuverability using non-linear lift generated by...undisturbed flow and is capable of prcJucing powerful vortex flow fields at high angles of attack. Asymmetrical vort ,;x control is feasible with actuated...control configuration, serves as an initial test vehicle for supermaneuverability analysis . Due to the relatively small scale of the UAV and the use of

Nonlinear flow response of soft hair beds

NASA Astrophysics Data System (ADS)

Alvarado, José

2017-11-01

We are hairy inside: beds of passive fibers anchored to a surface and immersed in fluids are prevalent in many biological systems, including intestines, tongues, and blood vessels. Such hairs are soft enough to deform in response to stresses from fluid flows. Fluid stresses are in turn affected by hair deformation, leading to a coupled elastoviscous problem which is poorly understood. Here we investigate a biomimetic model system of elastomer hair beds subject to shear- driven Stokes flows. We characterize this system with a theoretical model which accounts for the large-deformation flow response of hair beds. Hair bending results in a drag-reducing nonlinearity because the hair tip lowers toward the base, widening the gap through which fluid flows. When hairs are cantilevered at an angle subnormal to the surface, flow against the grain bends hairs away from the base, narrowing the gap. The flow response of angled hair beds is axially asymmetric and amounts to a rectification nonlinearity. We identify an elastoviscous parameter which controls nonlinear behavior. Our study raises the hypothesis that biological hairy surfaces function to reduce fluid drag. Furthermore, angled hairs may be incorporated in the design of integrated microfluidic components, such as diodes and pumps. J.A. acknowledges support the U. S. Army Research Office under Grant Number W911NF-14-1-0396.

Nonlinear Evolution of Short-wavelength Torsional Alfvén Waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shestov, S. V.; Nakariakov, V. M.; Ulyanov, A. S.

2017-05-10

We analyze nonlinear evolution of torsional Alfvén waves in a straight magnetic flux tube filled in with a low- β plasma, and surrounded with a plasma of lower density. Such magnetic tubes model, in particular, a segment of a coronal loop or a polar plume. The wavelength is taken comparable to the tube radius. We perform a numerical simulation of the wave propagation using ideal magnetohydrodynamics. We find that a torsional wave nonlinearly induces three kinds of compressive flows: the parallel flow at the Alfvén speed, which constitutes a bulk plasma motion along the magnetic field, the tube wave, andmore » also transverse flows in the radial direction, associated with sausage fast magnetoacoustic modes. In addition, the nonlinear torsional wave steepens and its propagation speed increases. The latter effect leads to the progressive distortion of the torsional wave front, i.e., nonlinear phase mixing. Because of the intrinsic non-uniformity of the torsional wave amplitude across the tube radius, the nonlinear effects are more pronounced in regions with higher wave amplitudes. They are always absent at the axes of the flux tube. In the case of a linear radial profile of the wave amplitude, the nonlinear effects are localized in an annulus region near the tube boundary. Thus, the parallel compressive flows driven by torsional Alfvén waves in the solar and stellar coronae, are essentially non-uniform in the perpendicular direction. The presence of additional sinks for the wave energy reduces the efficiency of the nonlinear parallel cascade in torsional Alfvén waves.« less

Nonlinear Evolution of Short-wavelength Torsional Alfvén Waves

NASA Astrophysics Data System (ADS)

Shestov, S. V.; Nakariakov, V. M.; Ulyanov, A. S.; Reva, A. A.; Kuzin, S. V.

2017-05-01

We analyze nonlinear evolution of torsional Alfvén waves in a straight magnetic flux tube filled in with a low-β plasma, and surrounded with a plasma of lower density. Such magnetic tubes model, in particular, a segment of a coronal loop or a polar plume. The wavelength is taken comparable to the tube radius. We perform a numerical simulation of the wave propagation using ideal magnetohydrodynamics. We find that a torsional wave nonlinearly induces three kinds of compressive flows: the parallel flow at the Alfvén speed, which constitutes a bulk plasma motion along the magnetic field, the tube wave, and also transverse flows in the radial direction, associated with sausage fast magnetoacoustic modes. In addition, the nonlinear torsional wave steepens and its propagation speed increases. The latter effect leads to the progressive distortion of the torsional wave front, I.e., nonlinear phase mixing. Because of the intrinsic non-uniformity of the torsional wave amplitude across the tube radius, the nonlinear effects are more pronounced in regions with higher wave amplitudes. They are always absent at the axes of the flux tube. In the case of a linear radial profile of the wave amplitude, the nonlinear effects are localized in an annulus region near the tube boundary. Thus, the parallel compressive flows driven by torsional Alfvén waves in the solar and stellar coronae, are essentially non-uniform in the perpendicular direction. The presence of additional sinks for the wave energy reduces the efficiency of the nonlinear parallel cascade in torsional Alfvén waves.

On the nonlinear interfacial instability of rotating core-annular flow

NASA Technical Reports Server (NTRS)

Coward, Aidrian V.; Hall, Philip

1993-01-01

The interfacial stability of rotating core-annular flows is investigated. The linear and nonlinear effects are considered for the case when the annular region is very thin. Both asymptotic and numerical methods are used to solve the flow in the core and film regions which are coupled by a difference in viscosity and density. The long-term behavior of the fluid-fluid interface is determined by deriving its nonlinear evolution in the form of a modified Kuramoto-Sivashinsky equation. We obtain a generalization of this equation to three dimensions. The flows considered are applicable to a wide array of physical problems where liquid films are used to lubricate higher or lower viscosity core fluids, for which a concentric arrangement is desired. Linearized solutions show that the effects of density and viscosity stratification are crucial to the stability of the interface. Rotation generally destabilizes non-axisymmetric disturbances to the interface, whereas the centripetal forces tend to stabilize flows in which the film contains the heavier fluid. Nonlinear affects allow finite amplitude helically travelling waves to exist when the fluids have different viscosities.

Simulating nonlinear steady-state traveling waves on the falling liquid film entrained by a gas flow

NASA Astrophysics Data System (ADS)

Tsvelodub, O. Yu; Bocharov, A. A.

2017-09-01

The article is devoted to the simulation of nonlinear waves on a liquid film flowing under gravity in the known stress field at the interface. The paper studies nonlinear waves on a liquid film, flowing under the action of gravity in a known stress field at the interface. In the case of small Reynolds numbers the problem is reduced to the consideration of solutions of the nonlinear integral-differential equation for film thickness deviation from the undisturbed level. The periodic and soliton steady-state traveling solutions of this equation have been numerically found. The analysis of branching of new families of steady-state traveling solutions has been performed. In particular, it is shown that this model equation has solutions in the form of solitons-humps.

Microfluidic flow rate detection based on integrated optical fiber cantilever.

PubMed

Lien, Victor; Vollmer, Frank

2007-10-01

We demonstrate an integrated microfluidic flow sensor with ultra-wide dynamic range, suitable for high throughput applications such as flow cytometry and particle sorting/counting. A fiber-tip cantilever transduces flow rates to optical signal readout, and we demonstrate a dynamic range from 0 to 1500 microL min(-1) for operation in water. Fiber-optic sensor alignment is guided by preformed microfluidic channels, and the dynamic range can be adjusted in a one-step chemical etch. An overall non-linear response is attributed to the far-field angular distribution of single-mode fiber output.

Coherent motion in excited free shear flows

NASA Technical Reports Server (NTRS)

Wygnanski, Israel J.; Petersen, Robert A.

1987-01-01

The application of the inviscid instability approach to externally excited turbulent free shear flows at high Reynolds numbers is explored. Attention is given to the cases of a small-deficit plane turbulent wake, a plane turbulent jet, an axisymmetric jet, the nonlinear evolution of instabilities in free shear flows, the concept of the 'preferred mode', vortex pairing in turbulent mixing layers, and experimental results for the control of free turbulent shear layers. The special features often attributed to pairing or to the preferred mode are found to be difficult to comprehend; the concept of feedback requires further substantiation in the case of incompressible flow.

Experimental investigations on airfoils with different geometries in the domain of high angles of attack-flow separation

NASA Technical Reports Server (NTRS)

Keil, J.

1985-01-01

Wind tunnel tests were conducted on airfoil models in order to study the flow separation phenomena occurring for high angles of attack. Pressure distribution on wings of different geometries were measured. Results show that for three-dimensional airfoils layout and span lift play a role. Separation effects on airfoils with moderate extension are three-dimensional. The flow domains separated from the air foil must be treated three-dimensionally. The rolling-up of separated vortex layers increases with angle in intensity and induction effect and shows strong nonlinearities. Boundary layer material moves perpendicularly to the flow direction due to the pressure gradients at the airfoil; this has a stabilizing effect. The separation starts earlier with increasing pointed profiles.

Growth of thin films of dicyanovinylanisole on quartz and teflon-coated quartz by physical vapor transport

NASA Technical Reports Server (NTRS)

Pearson, Earl F.

1994-01-01

Organic compounds offer the possibility of molecular engineering in order to optimize the nonlinearity and minimize damage due to the high-power lasers used in nonlinear optical devices. Recently dicyanovinylanisole (DIVA), ((2-methoxyphenyl) methylenepropanedinitrile) has been shown to have a second order nonlinearity 40 times that of alpha-quartz. Debe et. al. have shown that a high degree of orientational order exists for thin films of phthalocyanine grown by physical vapor transport in microgravity. The microgravity environment eliminates convective flow and was critical to the formation of highly ordered dense continuous films in these samples. This work seeks to discover the parameters necessary for the production of thin continuous films of high optical quality in Earth gravity. These parameters must be known before the experiment can be planned for growing DIVA in a microgravity environment. The microgravity grown films are expected to be denser and of better optical quality than the unit gravity films as was observed in the phthalocyanine films.

Mixed convection flow of viscoelastic fluid by a stretching cylinder with heat transfer.

PubMed

Hayat, Tasawar; Anwar, Muhammad Shoaib; Farooq, Muhammad; Alsaedi, Ahmad

2015-01-01

Flow of viscoelastic fluid due to an impermeable stretching cylinder is discussed. Effects of mixed convection and variable thermal conductivity are present. Thermal conductivity is taken temperature dependent. Nonlinear partial differential system is reduced into the nonlinear ordinary differential system. Resulting nonlinear system is computed for the convergent series solutions. Numerical values of skin friction coefficient and Nusselt number are computed and discussed. The results obtained with the current method are in agreement with previous studies using other methods as well as theoretical ideas. Physical interpretation reflecting the contribution of influential parameters in the present flow is presented. It is hoped that present study serves as a stimulus for modeling further stretching flows especially in polymeric and paper production processes.

Exact Solutions to Several Nonlinear Cases of Generalized Grad-Shafranov Equation for Ideal Magnetohydrodynamic Flows in Axisymmetric Domain

NASA Astrophysics Data System (ADS)

Adem, Abdullahi Rashid; Moawad, Salah M.

2018-05-01

In this paper, the steady-state equations of ideal magnetohydrodynamic incompressible flows in axisymmetric domains are investigated. These flows are governed by a second-order elliptic partial differential equation as a type of generalized Grad-Shafranov equation. The problem of finding exact equilibria to the full governing equations in the presence of incompressible mass flows is considered. Two different types of constraints on position variables are presented to construct exact solution classes for several nonlinear cases of the governing equations. Some of the obtained results are checked for their applications to magnetic confinement plasma. Besides, they cover many previous configurations and include new considerations about the nonlinearity of magnetic flux stream variables.

Mixed Convection Flow of Viscoelastic Fluid by a Stretching Cylinder with Heat Transfer

PubMed Central

Hayat, Tasawar; Anwar, Muhammad Shoaib; Farooq, Muhammad; Alsaedi, Ahmad

2015-01-01

Flow of viscoelastic fluid due to an impermeable stretching cylinder is discussed. Effects of mixed convection and variable thermal conductivity are present. Thermal conductivity is taken temperature dependent. Nonlinear partial differential system is reduced into the nonlinear ordinary differential system. Resulting nonlinear system is computed for the convergent series solutions. Numerical values of skin friction coefficient and Nusselt number are computed and discussed. The results obtained with the current method are in agreement with previous studies using other methods as well as theoretical ideas. Physical interpretation reflecting the contribution of influential parameters in the present flow is presented. It is hoped that present study serves as a stimulus for modeling further stretching flows especially in polymeric and paper production processes. PMID:25775032

A numerical study of nonlinear waves in a transcritical flow of stratified fluid past an obstacle

NASA Astrophysics Data System (ADS)

Hanazaki, Hideshi

1992-10-01

A numerical study of the flow of stratified fluid past an obstacle in a horizontal channel is described. Upstream advancing of waves near critically (resonance) appears in the case of ordinary two-layer flow, in which case the flow is described well by the solution of the forced extended Korteweg-de Vries (KdV) equation which has a cubic nonlinear term. It is shown theoretically that the upstream waves in the general two-layer flow cannot be well described by the forced KdV equation except when the wave amplitude is very small. The critical-level flow is also governed by the forced extended KdV equation. However, because of the smallness of the coefficient of the quadratic nonlinear term, the bore cannot propagate upstream at exact resonance. The results for the linearly stratified Boussinesq flow show good agreement with the solution of the Grimshaw and Yi (1991) equation, at least for exact resonance.

Nonlinear Large Scale Flow in a Precessing Cylinder and Its Ability To Drive Dynamo Action

NASA Astrophysics Data System (ADS)

Giesecke, André; Vogt, Tobias; Gundrum, Thomas; Stefani, Frank

2018-01-01

We have conducted experimental measurements and numerical simulations of a precession-driven flow in a cylindrical cavity. The study is dedicated to the precession dynamo experiment currently under construction at Helmholtz-Zentrum Dresden-Rossendorf and aims at the evaluation of the hydrodynamic flow with respect to its ability to drive a dynamo. We focus on the strongly nonlinear regime in which the flow is essentially composed of the directly forced primary Kelvin mode and higher modes in terms of standing inertial waves arising from nonlinear self-interactions. We obtain an excellent agreement between experiment and simulation with regard to both flow amplitudes and flow geometry. A peculiarity is the resonance-like emergence of an axisymmetric mode that represents a double roll structure in the meridional plane. Kinematic simulations of the magnetic field evolution induced by the time-averaged flow yield dynamo action at critical magnetic Reynolds numbers around Rmc≈430 , which is well within the range of the planned liquid sodium experiment.

Nonlinear Large Scale Flow in a Precessing Cylinder and Its Ability To Drive Dynamo Action.

PubMed

Giesecke, André; Vogt, Tobias; Gundrum, Thomas; Stefani, Frank

2018-01-12

We have conducted experimental measurements and numerical simulations of a precession-driven flow in a cylindrical cavity. The study is dedicated to the precession dynamo experiment currently under construction at Helmholtz-Zentrum Dresden-Rossendorf and aims at the evaluation of the hydrodynamic flow with respect to its ability to drive a dynamo. We focus on the strongly nonlinear regime in which the flow is essentially composed of the directly forced primary Kelvin mode and higher modes in terms of standing inertial waves arising from nonlinear self-interactions. We obtain an excellent agreement between experiment and simulation with regard to both flow amplitudes and flow geometry. A peculiarity is the resonance-like emergence of an axisymmetric mode that represents a double roll structure in the meridional plane. Kinematic simulations of the magnetic field evolution induced by the time-averaged flow yield dynamo action at critical magnetic Reynolds numbers around Rm^{c}≈430, which is well within the range of the planned liquid sodium experiment.

Nonlinear Dynamics of Non-uniform Current-Vortex Sheets in Magnetohydrodynamic Flows

NASA Astrophysics Data System (ADS)

Matsuoka, C.; Nishihara, K.; Sano, T.

2017-04-01

A theoretical model is proposed to describe fully nonlinear dynamics of interfaces in two-dimensional MHD flows based on an idea of non-uniform current-vortex sheet. Application of vortex sheet model to MHD flows has a crucial difficulty because of non-conservative nature of magnetic tension. However, it is shown that when a magnetic field is initially parallel to an interface, the concept of vortex sheet can be extended to MHD flows (current-vortex sheet). Two-dimensional MHD flows are then described only by a one-dimensional Lagrange parameter on the sheet. It is also shown that bulk magnetic field and velocity can be calculated from their values on the sheet. The model is tested by MHD Richtmyer-Meshkov instability with sinusoidal vortex sheet strength. Two-dimensional ideal MHD simulations show that the nonlinear dynamics of a shocked interface with density stratification agrees fairly well with that for its corresponding potential flow. Numerical solutions of the model reproduce properly the results of the ideal MHD simulations, such as the roll-up of spike, exponential growth of magnetic field, and its saturation and oscillation. Nonlinear evolution of the interface is found to be determined by the Alfvén and Atwood numbers. Some of their dependence on the sheet dynamics and magnetic field amplification are discussed. It is shown by the model that the magnetic field amplification occurs locally associated with the nonlinear dynamics of the current-vortex sheet. We expect that our model can be applicable to a wide variety of MHD shear flows.

Experimental Comparison of Speed : Fuel-flow and Speed-area Controls on a Turbojet Engine for Small Step Disturbances

NASA Technical Reports Server (NTRS)

Wenzel, L M; Hart, C E; Craig, R T

1957-01-01

Optimum proportional-plus-integral control settings for speed - fuel-flow control, determined by minimization of integral criteria, correlated well with analytically predicted optimum settings. Engine response data are given for a range of control settings around the optimum. An inherent nonlinearity in the speed-area loop necessitated the use of nonlinear controls. Response data for two such nonlinear control schemes are presented.

Soil thaw effects on river discharge recessions of a subarctic catchment

NASA Astrophysics Data System (ADS)

Ploum, Stefan; Lyon, Steve; Teuling, Ryan; van der Velde, Ype

2017-04-01

Thawing permafrost in circumpolar regions is likely to change subsurface hydrology. In high latitude areas continuous permafrost is expected to partially thaw leading to sporadic permafrost with deeper groundwater flow paths. Moreover, freeze-thaw cycles of the shallow subsurface are likely to increase. River discharge recession analysis can be particularly useful to understand the hydrological effects of a thawing Arctic. Here we examine river discharge recessions of the Abiskojokka, a 560 km2 watershed with sporadic permafrost, using a river discharge record of 30 years (1985 - 2015). Snow observation records were used to separate river recessions in snowmelt and snowfree periods. We found significant differences between recessions during the snowmelt and snowfree seasons. During the snowmelt, recessions were close to linear (b=1.11), while during the snowfree period, recessions were more non-linear (b=1.54). Typically, non-linearity has been found to increase with discharge magnitude, while we observed the opposite (snowfree periods tend to have lower discharges than the snowmelt periods). We explain these contrasting results by hypothesizing that increased connectivity (increasing magnitude and number of water flow paths) between groundwater and stream leads to higher non-linearity. In temperate catchments without frozen soils, connectivity tends to increase with increasing discharge. In contrast, in Arctic systems, where soils are frozen, connectivity between groundwater and stream is limited. Therefore, thawing of frozen soils is expected to increase connectivity and thus non-linearity of river discharges. We tested this hypothesis with a detailed analysis of all spring flood recessions. Years with cold soil temperatures (b=1.08) and years with a below median snowpack depth were found to have progressively linear slopes (b=1.08 and 1.01 respectively). On the other hand, years with warm soil conditions show increasingly non-linear recessions (b=1.67). Although limited in spatial extent, these results further support our connectivity hypothesis, which predicts increasing non-linearity of river discharges (higher discharge peaks and lower low flows under the same precipitation regime) as permafrost thaws.

An empirical method for estimating travel times for wet volcanic mass flows

USGS Publications Warehouse

Pierson, Thomas C.

1998-01-01

Travel times for wet volcanic mass flows (debris avalanches and lahars) can be forecast as a function of distance from source when the approximate flow rate (peak discharge near the source) can be estimated beforehand. The near-source flow rate is primarily a function of initial flow volume, which should be possible to estimate to an order of magnitude on the basis of geologic, geomorphic, and hydrologic factors at a particular volcano. Least-squares best fits to plots of flow-front travel time as a function of distance from source provide predictive second-degree polynomial equations with high coefficients of determination for four broad size classes of flow based on near-source flow rate: extremely large flows (>1 000 000 m3/s), very large flows (10 000–1 000 000 m3/s), large flows (1000–10 000 m3/s), and moderate flows (100–1000 m3/s). A strong nonlinear correlation that exists between initial total flow volume and flow rate for "instantaneously" generated debris flows can be used to estimate near-source flow rates in advance. Differences in geomorphic controlling factors among different flows in the data sets have relatively little effect on the strong nonlinear correlations between travel time and distance from source. Differences in flow type may be important, especially for extremely large flows, but this could not be evaluated here. At a given distance away from a volcano, travel times can vary by approximately an order of magnitude depending on flow rate. The method can provide emergency-management officials a means for estimating time windows for evacuation of communities located in hazard zones downstream from potentially hazardous volcanoes.

Three dimensional radiative flow of magnetite-nanofluid with homogeneous-heterogeneous reactions

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Rashid, Madiha; Alsaedi, Ahmed

2018-03-01

Present communication deals with the effects of homogeneous-heterogeneous reactions in flow of nanofluid by non-linear stretching sheet. Water based nanofluid containing magnetite nanoparticles is considered. Non-linear radiation and non-uniform heat sink/source effects are examined. Non-linear differential systems are computed by Optimal homotopy analysis method (OHAM). Convergent solutions of nonlinear systems are established. The optimal data of auxiliary variables is obtained. Impact of several non-dimensional parameters for velocity components, temperature and concentration fields are examined. Graphs are plotted for analysis of surface drag force and heat transfer rate.

Active and passive controls of Jeffrey nanofluid flow over a nonlinear stretching surface

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Alsaedi, Ahmed

This communication explores magnetohydrodynamic (MHD) boundary-layer flow of Jeffrey nanofluid over a nonlinear stretching surface with active and passive controls of nanoparticles. A nonlinear stretching surface generates the flow. Effects of thermophoresis and Brownian diffusion are considered. Jeffrey fluid is electrically conducted subject to non-uniform magnetic field. Low magnetic Reynolds number and boundary-layer approximations have been considered in mathematical modelling. The phenomena of impulsing the particles away from the surface in combination with non-zero mass flux condition is known as the condition of zero mass flux. Convergent series solutions for the nonlinear governing system are established through optimal homotopy analysis method (OHAM). Graphs have been sketched in order to analyze that how the temperature and concentration distributions are affected by distinct physical flow parameters. Skin friction coefficient and local Nusselt and Sherwood numbers are also computed and analyzed. Our findings show that the temperature and concentration distributions are increasing functions of Hartman number and thermophoresis parameter.

Periodic magnetorotational dynamo action as a prototype of nonlinear magnetic-field generation in shear flows.

PubMed

Herault, J; Rincon, F; Cossu, C; Lesur, G; Ogilvie, G I; Longaretti, P-Y

2011-09-01

The nature of dynamo action in shear flows prone to magnetohydrodynamc instabilities is investigated using the magnetorotational dynamo in Keplerian shear flow as a prototype problem. Using direct numerical simulations and Newton's method, we compute an exact time-periodic magnetorotational dynamo solution to three-dimensional dissipative incompressible magnetohydrodynamic equations with rotation and shear. We discuss the physical mechanism behind the cycle and show that it results from a combination of linear and nonlinear interactions between a large-scale axisymmetric toroidal magnetic field and nonaxisymmetric perturbations amplified by the magnetorotational instability. We demonstrate that this large-scale dynamo mechanism is overall intrinsically nonlinear and not reducible to the standard mean-field dynamo formalism. Our results therefore provide clear evidence for a generic nonlinear generation mechanism of time-dependent coherent large-scale magnetic fields in shear flows and call for new theoretical dynamo models. These findings may offer important clues to understanding the transitional and statistical properties of subcritical magnetorotational turbulence.

A weakly nonlinear theory for wave-vortex interactions in curved channel flow

NASA Technical Reports Server (NTRS)

Singer, Bart A.; Erlebacher, Gordon; Zang, Thomas A.

1992-01-01

A weakly nonlinear theory is developed to study the interaction of Tollmien-Schlichting (TS) waves and Dean vortices in curved channel flow. The predictions obtained from the theory agree well with results obtained from direct numerical simulations of curved channel flow, especially for low amplitude disturbances. Some discrepancies in the results of a previous theory with direct numerical simulations are resolved.

Statistical State Dynamics Based Study of the Role of Nonlinearity in the Maintenance of Turbulence in Couette Flow

NASA Astrophysics Data System (ADS)

Farrell, Brian; Ioannou, Petros; Nikolaidis, Marios-Andreas

2017-11-01

While linear non-normality underlies the mechanism of energy transfer from the externally driven flow to the perturbation field, nonlinearity is also known to play an essential role in sustaining turbulence. We report a study based on the statistical state dynamics of Couette flow turbulence with the goal of better understanding the role of nonlinearity in sustaining turbulence. The statistical state dynamics implementations used are ensemble closures at second order in a cumulant expansion of the Navier-Stokes equations in which the averaging operator is the streamwise mean. Two fundamentally non-normal mechanisms potentially contributing to maintaining the second cumulant are identified. These are essentially parametric perturbation growth arising from interaction of the perturbations with the fluctuating mean flow and transient growth of perturbations arising from nonlinear interaction between components of the perturbation field. By the method of selectively including these mechanisms parametric growth is found to maintain the perturbation field in the turbulent state while the more commonly invoked mechanism associated with transient growth of perturbations arising from scattering by nonlinear interaction is found to suppress perturbation variance. Funded by ERC Coturb Madrid Summer Program and NSF AGS-1246929.

Nonlinear Monte Carlo model of superdiffusive shock acceleration with magnetic field amplification

NASA Astrophysics Data System (ADS)

Bykov, Andrei M.; Ellison, Donald C.; Osipov, Sergei M.

2017-03-01

Fast collisionless shocks in cosmic plasmas convert their kinetic energy flow into the hot downstream thermal plasma with a substantial fraction of energy going into a broad spectrum of superthermal charged particles and magnetic fluctuations. The superthermal particles can penetrate into the shock upstream region producing an extended shock precursor. The cold upstream plasma flow is decelerated by the force provided by the superthermal particle pressure gradient. In high Mach number collisionless shocks, efficient particle acceleration is likely coupled with turbulent magnetic field amplification (MFA) generated by the anisotropic distribution of accelerated particles. This anisotropy is determined by fast particle transport, making the problem strongly nonlinear and multiscale. Here, we present a nonlinear Monte Carlo model of collisionless shock structure with superdiffusive propagation of high-energy Fermi accelerated particles coupled to particle acceleration and MFA, which affords a consistent description of strong shocks. A distinctive feature of the Monte Carlo technique is that it includes the full angular anisotropy of the particle distribution at all precursor positions. The model reveals that the superdiffusive transport of energetic particles (i.e., Lévy-walk propagation) generates a strong quadruple anisotropy in the precursor particle distribution. The resultant pressure anisotropy of the high-energy particles produces a nonresonant mirror-type instability that amplifies compressible wave modes with wavelengths longer than the gyroradii of the highest-energy protons produced by the shock.

Three-dimensional instabilities of natural convection between two differentially heated vertical plates: Linear and nonlinear complementary approaches

NASA Astrophysics Data System (ADS)

Gao, Zhenlan; Podvin, Berengere; Sergent, Anne; Xin, Shihe; Chergui, Jalel

2018-05-01

The transition to the chaos of the air flow between two vertical plates maintained at different temperatures is studied in the Boussinesq approximation. After the first bifurcation at critical Rayleigh number Rac, the flow consists of two-dimensional (2D) corotating rolls. The stability of the 2D rolls is examined, confronting linear predictions with nonlinear integration. In all cases the 2D rolls are destabilized in the spanwise direction. Efficient linear stability analysis based on an Arnoldi method shows competition between two eigenmodes, corresponding to different spanwise wavelengths and different types of roll distortion. Nonlinear integration shows that the lower-wave-number mode is always dominant. A partial route to chaos is established through the nonlinear simulations. The flow becomes temporally chaotic for Ra =1.05 Rac , but remains characterized by the spatial patterns identified by linear stability analysis. This highlights the complementary role of linear stability analysis and nonlinear simulation.

Modern aspects of nonlinear convection and magnetic field in flow of thixotropic nanofluid over a nonlinear stretching sheet with variable thickness

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Qayyum, Sajid; Alsaedi, Ahmed; Ahmad, Bashir

2018-05-01

Main objective of present analysis is to study the magnetohydrodynamic (MHD) nonlinear convective flow of thixotropic nanofluid. Flow is due to nonlinear stretching surface with variable thickness. Nonlinear thermal radiation and heat generation/absorption are utilized in the energy expression. Convective conditions and zero mass flux at sheet are considered. Intention in present analysis is to develop a model for nanomaterial comprising Brownian motion and thermophoresis phenomena. Appropriate transformations are implemented for the conversion of partial differential systems into a sets of ordinary differential equations. The transformed expressions have been scrutinized through homotopic algorithm. Behavior of various sundry variables on velocity, temperature, nanoparticle concentration, skin friction coefficient and local Nusselt number are displayed through graphs. It is concluded that qualitative behaviors of temperature and thermal layer thickness are similar for radiation and temperature ratio variables. Moreover an enhancement in heat generation/absorption show rise to thermal field.

Transition Theory and Experimental Comparisons on (I) Amplification into Streets and (II) a Strongly Nonlinear Break-up Criterion

NASA Astrophysics Data System (ADS)

Smith, F. T.; Bowles, R. I.

1992-10-01

The two stages I, II are studied by using recent nonlinear theory and then compared with the experiments of Nishioka et al. (1979) on the transition of plane Poiseuille flow. The first stage I starts at low amplitude from warped input, which is deformed through weakly nonlinear interaction into a blow-up in amplitude and phase accompanied by spanwise focusing into streets. This leads into the strongly nonlinear stage II. It holds for a broad range of interactive boundary layers and related flows, to all of which the nonlinear break-up criterion applies. The experimental comparisons on I, II for channel flow overall show encouraging quantitative agreement, supporting recent comparisons (in the boundary-layer setting) of the description of stage I in Stewart & Smith (1992) with the experiments of Klebanoff & Tidstrom (1959) and of the break-up criterion of Smith (1988a) with the computations of Peridier et al. (1991 a, b).

Transonic Flutter Suppression Control Law Design, Analysis and Wind Tunnel Results

NASA Technical Reports Server (NTRS)

Mukhopadhyay, Vivek

1999-01-01

The benchmark active controls technology and wind tunnel test program at NASA Langley Research Center was started with the objective to investigate the nonlinear, unsteady aerodynamics and active flutter suppression of wings in transonic flow. The paper will present the flutter suppression control law design process, numerical nonlinear simulation and wind tunnel test results for the NACA 0012 benchmark active control wing model. The flutter suppression control law design processes using (1) classical, (2) linear quadratic Gaussian (LQG), and (3) minimax techniques are described. A unified general formulation and solution for the LQG and minimax approaches, based on the steady state differential game theory is presented. Design considerations for improving the control law robustness and digital implementation are outlined. It was shown that simple control laws when properly designed based on physical principles, can suppress flutter with limited control power even in the presence of transonic shocks and flow separation. In wind tunnel tests in air and heavy gas medium, the closed-loop flutter dynamic pressure was increased to the tunnel upper limit of 200 psf The control law robustness and performance predictions were verified in highly nonlinear flow conditions, gain and phase perturbations, and spoiler deployment. A non-design plunge instability condition was also successfully suppressed.

Transonic Flutter Suppression Control Law Design, Analysis and Wind-Tunnel Results

NASA Technical Reports Server (NTRS)

Mukhopadhyay, Vivek

1999-01-01

The benchmark active controls technology and wind tunnel test program at NASA Langley Research Center was started with the objective to investigate the nonlinear, unsteady aerodynamics and active flutter suppression of wings in transonic flow. The paper will present the flutter suppression control law design process, numerical nonlinear simulation and wind tunnel test results for the NACA 0012 benchmark active control wing model. The flutter suppression control law design processes using (1) classical, (2) linear quadratic Gaussian (LQG), and (3) minimax techniques are described. A unified general formulation and solution for the LQG and minimax approaches, based on the steady state differential game theory is presented. Design considerations for improving the control law robustness and digital implementation are outlined. It was shown that simple control laws when properly designed based on physical principles, can suppress flutter with limited control power even in the presence of transonic shocks and flow separation. In wind tunnel tests in air and heavy gas medium, the closed-loop flutter dynamic pressure was increased to the tunnel upper limit of 200 psf. The control law robustness and performance predictions were verified in highly nonlinear flow conditions, gain and phase perturbations, and spoiler deployment. A non-design plunge instability condition was also successfully suppressed.

Transonic Flutter Suppression Control Law Design Using Classical and Optimal Techniques with Wind-Tunnel Results

NASA Technical Reports Server (NTRS)

Mukhopadhyay, Vivek

1999-01-01

The benchmark active controls technology and wind tunnel test program at NASA Langley Research Center was started with the objective to investigate the nonlinear, unsteady aerodynamics and active flutter suppression of wings in transonic flow. The paper will present the flutter suppression control law design process, numerical nonlinear simulation and wind tunnel test results for the NACA 0012 benchmark active control wing model. The flutter suppression control law design processes using (1) classical, (2) linear quadratic Gaussian (LQG), and (3) minimax techniques are described. A unified general formulation and solution for the LQG and minimax approaches, based on the steady state differential game theory is presented. Design considerations for improving the control law robustness and digital implementation are outlined. It was shown that simple control laws when properly designed based on physical principles, can suppress flutter with limited control power even in the presence of transonic shocks and flow separation. In wind tunnel tests in air and heavy gas medium, the closed-loop flutter dynamic pressure was increased to the tunnel upper limit of 200 psf. The control law robustness and performance predictions were verified in highly nonlinear flow conditions, gain and phase perturbations, and spoiler deployment. A non-design plunge instability condition was also successfully suppressed.

Excitation and propagation of nonlinear waves in a rotating fluid

NASA Astrophysics Data System (ADS)

Hanazaki, Hideshi

1993-09-01

A numerical study of the nonlinear waves excited in an axisymmetric rotating flow through a circular tube is described. The waves are excited by either an undulation of the tube wall or an obstacle on the axis of the tube. The results are compared with the weakly nonlinear theory (forced KdV equation). The computations are done when the upstream swirling velocity is that of Burgers' vortex type. The flow behaves like the solution of the forced KdV equation, and the upstream advancing of the waves appear even when the flow is critical or slightly supercritical to the fastest inertial wave mode.

The Numerical Studies Program for the Atmospheric General Circulation Experiment (AGCE) for Spacelab Flights

NASA Technical Reports Server (NTRS)

Fowlis, W. W. (Editor); Davis, M. H. (Editor)

1981-01-01

The atmospheric general circulation experiment (AGCE) numerical design for Spacelab flights was studied. A spherical baroclinic flow experiment which models the large scale circulations of the Earth's atmosphere was proposed. Gravity is simulated by a radial dielectric body force. The major objective of the AGCE is to study nonlinear baroclinic wave flows in spherical geometry. Numerical models must be developed which accurately predict the basic axisymmetric states and the stability of nonlinear baroclinic wave flows. A three dimensional, fully nonlinear, numerical model and the AGCE based on the complete set of equations is required. Progress in the AGCE numerical design studies program is reported.

Development of a nonlinear unsteady transonic flow theory

NASA Technical Reports Server (NTRS)

Stahara, S. S.; Spreiter, J. R.

1973-01-01

A nonlinear, unsteady, small-disturbance theory capable of predicting inviscid transonic flows about aerodynamic configurations undergoing both rigid body and elastic oscillations was developed. The theory is based on the concept of dividing the flow into steady and unsteady components and then solving, by method of local linearization, the coupled differential equation for unsteady surface pressure distribution. The equations, valid at all frequencies, were derived for two-dimensional flows, numerical results, were obtained for two classses of airfoils and two types of oscillatory motions.

Nonlinear dynamics near the stability margin in rotating pipe flow

NASA Technical Reports Server (NTRS)

Yang, Z.; Leibovich, S.

1991-01-01

The nonlinear evolution of marginally unstable wave packets in rotating pipe flow is studied. These flows depend on two control parameters, which may be taken to be the axial Reynolds number R and a Rossby number, q. Marginal stability is realized on a curve in the (R, q)-plane, and the entire marginal stability boundary is explored. As the flow passes through any point on the marginal stability curve, it undergoes a supercritical Hopf bifurcation and the steady base flow is replaced by a traveling wave. The envelope of the wave system is governed by a complex Ginzburg-Landau equation. The Ginzburg-Landau equation admits Stokes waves, which correspond to standing modulations of the linear traveling wavetrain, as well as traveling wave modulations of the linear wavetrain. Bands of wavenumbers are identified in which the nonlinear modulated waves are subject to a sideband instability.

The effect of gas and fluid flows on nonlinear lateral vibrations of rotating drill strings

NASA Astrophysics Data System (ADS)

Khajiyeva, Lelya; Kudaibergenov, Askar; Kudaibergenov, Askat

2018-06-01

In this work we develop nonlinear mathematical models describing coupled lateral vibrations of a rotating drill string under the effect of external supersonic gas and internal fluid flows. An axial compressive load and a torque also affect the drill string. The mathematical models are derived by the use of Novozhilov's nonlinear theory of elasticity with implementation of Hamilton's variation principle. Expressions for the gas flow pressure are determined according to the piston theory. The fluid flow is considered as added mass inside the curved tube of the drill string. Using an algorithm developed in the Mathematica computation program on the basis of the Galerkin approach and the stiffness switching method the numerical solution of the obtained approximate differential equations is found. Influences of the external loads, drill string angular speed of rotation, parameters of the gas and fluid flows on the drill string vibrations are shown.

Fuzzy Temporal Logic Based Railway Passenger Flow Forecast Model

PubMed Central

Dou, Fei; Jia, Limin; Wang, Li; Xu, Jie; Huang, Yakun

2014-01-01

Passenger flow forecast is of essential importance to the organization of railway transportation and is one of the most important basics for the decision-making on transportation pattern and train operation planning. Passenger flow of high-speed railway features the quasi-periodic variations in a short time and complex nonlinear fluctuation because of existence of many influencing factors. In this study, a fuzzy temporal logic based passenger flow forecast model (FTLPFFM) is presented based on fuzzy logic relationship recognition techniques that predicts the short-term passenger flow for high-speed railway, and the forecast accuracy is also significantly improved. An applied case that uses the real-world data illustrates the precision and accuracy of FTLPFFM. For this applied case, the proposed model performs better than the k-nearest neighbor (KNN) and autoregressive integrated moving average (ARIMA) models. PMID:25431586

Investigation of contact acoustic nonlinearities on metal and composite airframe structures via intensity based health monitoring.

PubMed

Romano, P Q; Conlon, S C; Smith, E C

2013-01-01

Nonlinear structural intensity (NSI) and nonlinear structural surface intensity (NSSI) based damage detection techniques were improved and extended to metal and composite airframe structures. In this study, the measurement of NSI maps at sub-harmonic frequencies was completed to provide enhanced understanding of the energy flow characteristics associated with the damage induced contact acoustic nonlinearity mechanism. Important results include NSI source localization visualization at ultra-subharmonic (nf/2) frequencies, and damage detection results utilizing structural surface intensity in the nonlinear domain. A detection metric relying on modulated wave spectroscopy was developed and implemented using the NSSI feature. The data fusion of the intensity formulation provided a distinct advantage, as both the single interrogation frequency NSSI and its modulated wave extension (NSSI-MW) exhibited considerably higher sensitivities to damage than using single-sensor (strain or acceleration) nonlinear detection metrics. The active intensity based techniques were also extended to composite materials, and results show both NSSI and NSSI-MW can be used to detect damage in the bond line of an integrally stiffened composite plate structure with high sensitivity. Initial damage detection measurements made on an OH-58 tailboom (Penn State Applied Research Laboratory, State College, PA) indicate the techniques can be transitioned to complex airframe structures achieving high detection sensitivities with minimal sensors and actuators.

Bayesian Inference of High-Dimensional Dynamical Ocean Models

NASA Astrophysics Data System (ADS)

Lin, J.; Lermusiaux, P. F. J.; Lolla, S. V. T.; Gupta, A.; Haley, P. J., Jr.

2015-12-01

This presentation addresses a holistic set of challenges in high-dimension ocean Bayesian nonlinear estimation: i) predict the probability distribution functions (pdfs) of large nonlinear dynamical systems using stochastic partial differential equations (PDEs); ii) assimilate data using Bayes' law with these pdfs; iii) predict the future data that optimally reduce uncertainties; and (iv) rank the known and learn the new model formulations themselves. Overall, we allow the joint inference of the state, equations, geometry, boundary conditions and initial conditions of dynamical models. Examples are provided for time-dependent fluid and ocean flows, including cavity, double-gyre and Strait flows with jets and eddies. The Bayesian model inference, based on limited observations, is illustrated first by the estimation of obstacle shapes and positions in fluid flows. Next, the Bayesian inference of biogeochemical reaction equations and of their states and parameters is presented, illustrating how PDE-based machine learning can rigorously guide the selection and discovery of complex ecosystem models. Finally, the inference of multiscale bottom gravity current dynamics is illustrated, motivated in part by classic overflows and dense water formation sites and their relevance to climate monitoring and dynamics. This is joint work with our MSEAS group at MIT.

Perturbation method for the second-order nonlinear effect of focused acoustic field around a scatterer in an ideal fluid.

PubMed

Liu, Gang; Jayathilake, Pahala Gedara; Khoo, Boo Cheong

2014-02-01

Two nonlinear models are proposed to investigate the focused acoustic waves that the nonlinear effects will be important inside the liquid around the scatterer. Firstly, the one dimensional solutions for the widely used Westervelt equation with different coordinates are obtained based on the perturbation method with the second order nonlinear terms. Then, by introducing the small parameter (Mach number), a dimensionless formulation and asymptotic perturbation expansion via the compressible potential flow theory is applied. This model permits the decoupling between the velocity potential and enthalpy to second order, with the first potential solutions satisfying the linear wave equation (Helmholtz equation), whereas the second order solutions are associated with the linear non-homogeneous equation. Based on the model, the local nonlinear effects of focused acoustic waves on certain volume are studied in which the findings may have important implications for bubble cavitation/initiation via focused ultrasound called HIFU (High Intensity Focused Ultrasound). The calculated results show that for the domain encompassing less than ten times the radius away from the center of the scatterer, the non-linear effect exerts a significant influence on the focused high intensity acoustic wave. Moreover, at the comparatively higher frequencies, for the model of spherical wave, a lower Mach number may result in stronger nonlinear effects. Copyright © 2013 Elsevier B.V. All rights reserved.

Nonlinear Evolution of Azimuthally Compact Crossflow-Vortex Packet over a Yawed Cone

NASA Astrophysics Data System (ADS)

Choudhari, Meelan; Li, Fei; Paredes, Pedro; Duan, Lian; NASA Langley Research Center Team; Missouri Univ of Sci; Tech Team

2017-11-01

Hypersonic boundary-layer flows over a circular cone at moderate incidence angle can support strong crossflow instability and, therefore, a likely scenario for laminar-turbulent transition in such flows corresponds to rapid amplification of high-frequency secondary instabilities sustained by finite amplitude stationary crossflow vortices. Direct numerical simulations (DNS) are used to investigate the nonlinear evolution of azimuthally compact crossflow vortex packets over a 7-degree half-angle, yawed circular cone in a Mach 6 free stream. Simulation results indicate that the azimuthal distribution of forcing has a strong influence on the stationary crossflow amplitudes; however, the vortex trajectories are nearly the same for both periodic and localized roughness height distributions. The frequency range, mode shapes, and amplification characteristics of strongly amplified secondary instabilities in the DNS are found to overlap with the predictions of secondary instability theory. The DNS computations also provide valuable insights toward the application of planar, partial-differential-equation based eigenvalue analysis to spanwise inhomogeneous, fully three-dimensional, crossflow-dominated flow configurations.

Stagnation point flow on bioconvection nanofluid over a stretching/shrinking surface with velocity and thermal slip effects

NASA Astrophysics Data System (ADS)

Chan, Sze Qi; Aman, Fazlina; Mansur, Syahira

2017-09-01

Nanofluid containing nanometer sized particles has become an ideal thermal conductivity medium for the flow and heat transfer in many industrial and engineering applications due to their high rate of heat transfer. However, swimming microorganisms are imposed into the nanofluid to overcome the instability of nanoparticles due to a bioconvection phenomenon. This paper investigates the stagnation point flow on bioconvection heat transfer of a nanofluid over a stretching/shrinking surface containing gyrotactic microorganisms. Velocity and thermal slip effects are the two conditions incorporated into the model. Similarity transformation is applied to reduce the governing nonlinear partial differential equations into the nonlinear ordinary differential equations. The transformed equations are then solved numerically. The results are displayed in the form of graphs and tables. The effects of these governing parameters on the skin friction coefficient, local Nusselt number, local Sherwood number and the local density of the motile microorganisms are analysed and discussed in details.

On the nonlinear aerodynamic and stability characteristics of a generic chine-forebody slender-wing fighter configuration

NASA Technical Reports Server (NTRS)

Erickson, Gary E.; Brandon, Jay M.

1987-01-01

An exploratory investigation was conducted of the nonlinear aerodynamic and stability characteristics of a tailless generic fighter configuration featuring a chine-shaped forebody coupled to a slender cropped delta wing in the NASA Langley Research Center's 12-Foot Low-Speed Wind Tunnel. Forebody and wing vortex flow mechanisms were identified through off-body flow visualizations to explain the trends in the longitudinal and lateral-directional characteristics at extreme attitudes (angles of attack and sideslip). The interactions of the vortical motions with centerline and wing-mounted vertical tail surfaces were studied and the flow phenomena were correlated with the configuration forces and moments. Single degree of freedom, free-to-roll tests were used to study the wing rock susceptibility of the generic fighter model. Modifications to the nose region of the chine forebody were examined and fluid mechanisms were established to account for their ineffectiveness in modulating the highly interactive forebody and wing vortex systems.

Double stratified radiative Jeffery magneto nanofluid flow along an inclined stretched cylinder with chemical reaction and slip condition

NASA Astrophysics Data System (ADS)

Ramzan, M.; Gul, Hina; Dong Chung, Jae

2017-11-01

A mathematical model is designed to deliberate the flow of an MHD Jeffery nanofluid past a vertically inclined stretched cylinder near a stagnation point. The flow analysis is performed in attendance of thermal radiation, mixed convection and chemical reaction. Influence of thermal and solutal stratification with slip boundary condition is also considered. Apposite transformations are engaged to convert the nonlinear partial differential equations to differential equations with high nonlinearity. Convergent series solutions of the problem are established via the renowned Homotopy Analysis Method (HAM). Graphical illustrations are plotted to depict the effects of prominent arising parameters against all involved distributions. Numerically erected tables of important physical parameters like Skin friction, Nusselt and Sherwood numbers are also give. Comparative studies (with a previously examined work) are also included to endorse our results. It is noticed that the thermal stratification parameter has diminishing effect on temperature distribution. Moreover, the velocity field is a snowballing and declining function of curvature and slip parameters respectively.

Active Fail-Safe Micro-Array Flow Control for Advanced Embedded Propulsion Systems

NASA Technical Reports Server (NTRS)

Anderson, Bernhard H.; Mace, James L.; Mani, Mori

2009-01-01

The primary objective of this research effort was to develop and analytically demonstrate enhanced first generation active "fail-safe" hybrid flow-control techniques to simultaneously manage the boundary layer on the vehicle fore-body and to control the secondary flow generated within modern serpentine or embedded inlet S-duct configurations. The enhanced first-generation technique focused on both micro-vanes and micro-ramps highly-integrated with micro -jets to provide nonlinear augmentation for the "strength' or effectiveness of highly-integrated flow control systems. The study focused on the micro -jet mass flow ratio (Wjet/Waip) range from 0.10 to 0.30 percent and jet total pressure ratios (Pjet/Po) from 1.0 to 3.0. The engine bleed airflow range under study represents about a 10 fold decrease in micro -jet airflow than previously required. Therefore, by pre-conditioning, or injecting a very small amount of high-pressure jet flow into the vortex generated by the micro-vane and/or micro-ramp, active flow control is achieved and substantial augmentation of the controlling flow is realized.

Nonlinearity in cytoplasm viscosity can generate an essential symmetry breaking in cellular behaviors.

PubMed

Tachikawa, Masashi; Mochizuki, Atsushi

2015-01-07

The cytoplasms of ameboid cells are nonlinearly viscous. The cell controls this viscosity by modulating the amount, localization and interactions of bio-polymers. Here we investigated how the nonlinearity infers the cellular behaviors and whether nonlinearity-specific behaviors exist. We modeled the developed plasmodium of the slime mold Physarum polycephalum as a network of branching tubes and examined the linear and nonlinear viscous cytoplasm flows in the tubes. We found that the nonlinearity in the cytoplasm׳s viscosity induces a novel type of symmetry breaking in the protoplasmic flow. We also show that symmetry breaking can play an important role in adaptive behaviors, namely, connection of behavioral modes implemented on different time scales and transportation of molecular signals from the front to the rear of the cell during cellular locomotion. Copyright © 2014 Elsevier Ltd. All rights reserved.

Nonlinear dynamics and anisotropic structure of rotating sheared turbulence.

PubMed

Salhi, A; Jacobitz, F G; Schneider, K; Cambon, C

2014-01-01

Homogeneous turbulence in rotating shear flows is studied by means of pseudospectral direct numerical simulation and analytical spectral linear theory (SLT). The ratio of the Coriolis parameter to shear rate is varied over a wide range by changing the rotation strength, while a constant moderate shear rate is used to enable significant contributions to the nonlinear interscale energy transfer and to the nonlinear intercomponental redistribution terms. In the destabilized and neutral cases, in the sense of kinetic energy evolution, nonlinearity cannot saturate the growth of the largest scales. It permits the smallest scale to stabilize by a scale-by-scale quasibalance between the nonlinear energy transfer and the dissipation spectrum. In the stabilized cases, the role of rotation is mainly nonlinear, and interacting inertial waves can affect almost all scales as in purely rotating flows. In order to isolate the nonlinear effect of rotation, the two-dimensional manifold with vanishing spanwise wave number is revisited and both two-component spectra and single-point two-dimensional energy components exhibit an important effect of rotation, whereas the SLT as well as the purely two-dimensional nonlinear analysis are unaffected by rotation as stated by the Proudman theorem. The other two-dimensional manifold with vanishing streamwise wave number is analyzed with similar tools because it is essential for any shear flow. Finally, the spectral approach is used to disentangle, in an analytical way, the linear and nonlinear terms in the dynamical equations.

The role of nonlinear critical layers in boundary layer transition

NASA Technical Reports Server (NTRS)

Goldstein, M.E.

1995-01-01

Asymptotic methods are used to describe the nonlinear self-interaction between pairs of oblique instability modes that eventually develops when initially linear spatially growing instability waves evolve downstream in nominally two-dimensional laminar boundary layers. The first nonlinear reaction takes place locally within a so-called 'critical layer', with the flow outside this layer consisting of a locally parallel mean flow plus a pair of oblique instability waves - which may or may not be accompanied by an associated plane wave. The amplitudes of these waves, which are completely determined by nonlinear effects within the critical layer, satisfy either a single integro-differential equation or a pair of integro-differential equations with quadratic to quartic-type nonlinearities. The physical implications of these equations are discussed.

Fully Nonlinear Edge Gyrokinetic Simulations of Kinetic Geodesic-Acoustic Modes and Boundary Flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, X Q; Belli, E; Bodi, K

We present edge gyrokinetic neoclassical simulations of tokamak plasmas using the fully nonlinear (full-f) continuum code TEMPEST. A nonlinear Boltzmann model is used for the electrons. The electric field is obtained by solving the 2D gyrokinetic Poisson Equation. We demonstrate the following: (1) High harmonic resonances (n > 2) significantly enhance geodesic-acoustic mode (GAM) damping at high-q (tokamak safety factor), and are necessary to explain both the damping observed in our TEMPEST q-scans and experimental measurements of the scaling of the GAM amplitude with edge q{sub 95} in the absence of obvious evidence that there is a strong q dependencemore » of the turbulent drive and damping of the GAM. (2) The kinetic GAM exists in the edge for steep density and temperature gradients in the form of outgoing waves, its radial scale is set by the ion temperature profile, and ion temperature inhomogeneity is necessary for GAM radial propagation. (3) The development of the neoclassical electric field evolves through different phases of relaxation, including GAMs, their radial propagation, and their long-time collisional decay. (4) Natural consequences of orbits in the pedestal and scrape-off layer region in divertor geometry are substantial non-Maxwellian ion distributions and flow characteristics qualitatively like those observed in experiments.« less

The role of flow field structure in determining the aerodynamic response of a delta wing

NASA Astrophysics Data System (ADS)

Addington, Gregory Alan

Delta wings have long been known to exhibit nonlinear aerodynamic responses as a result of the presence of helical leading-edge vortices. This nonlinearity, found under both steady-state and unsteady conditions, is particularly profound in the presence of vortex burst. Modeling such aerodynamic responses with the Nonlinear Indicial Response (NIR) methodology provides a means of simulating these nonlinearities through its inclusion of motion history in addition to superposition. The NIR model also includes provisions for a finite number of discrete locations where the aerodynamic response is discontinuous with response to a state variable. These critical states also separate regions of states where the unsteady aerodynamic responses are potentially of highly-disparate characters. Although these critical states have been found in the past, their relationship with flow field bifurcation is uncertain. The purpose of this dissertation is to explore the relationship between nonlinear aerodynamic responses, critical states and flow field bifurcations from an experimental approach. This task has been accomplished by comparing a comprehensive database of skin-friction line topologies with static and unsteady aerodynamic responses. These data were collected using a 65sp° delta wing which rolled about an inclined longitudinal body axis. In this study, compelling, but not conclusive, evidence was found to suggest that a bifurcation in the skin-friction line topology was a necessary condition for the presence of a critical state. Although the presence of critical states was well predicted through careful observation and analysis of highly-resolved static loading data alone, their precise placement as a function of the independent variable was aided through the consideration of the locations of skin-friction line bifurcations. Furthermore, these static data were found to contain indications of the basic lagged or unlagged behavior of the unsteady aerodynamic response. This indication was found by comparing the relative rate of change seen in the estimated vortical- and potential-rolling-moment components. Through the review of these data in light of current theories on the mechanisms of leading-edge vortex breakdown, the formulation of a hypothesis regarding the relationship between both the static and unsteady aerodynamic response and vorticity dynamics was possible.

Influence of Lorentz force, Cattaneo-Christov heat flux and viscous dissipation on the flow of micropolar fluid past a nonlinear convective stretching vertical surface

NASA Astrophysics Data System (ADS)

Gnaneswara Reddy, Machireddy

2017-12-01

The problem of micropolar fluid flow over a nonlinear stretching convective vertical surface in the presence of Lorentz force and viscous dissipation is investigated. Due to the nature of heat transfer in the flow past vertical surface, Cattaneo-Christov heat flux model effect is properly accommodated in the energy equation. The governing partial differential equations for the flow and heat transfer are converted into a set of ordinary differential equations by employing the acceptable similarity transformations. Runge-Kutta and Newton's methods are utilized to resolve the altered governing nonlinear equations. Obtained numerical results are compared with the available literature and found to be an excellent agreement. The impacts of dimensionless governing flow pertinent parameters on velocity, micropolar velocity and temperature profiles are presented graphically for two cases (linear and nonlinear) and analyzed in detail. Further, the variations of skin friction coefficient and local Nusselt number are reported with the aid of plots for the sundry flow parameters. The temperature and the related boundary enhances enhances with the boosting values of M. It is found that fluid temperature declines for larger thermal relaxation parameter. Also, it is revealed that the Nusselt number declines for the hike values of Bi.

Mechanism of nonlinear flow pattern selection in moderately non-Boussinesq mixed convection.

PubMed

Suslov, Sergey A

2010-02-01

Nonlinear (non-Boussinesq) variations in fluid's density, viscosity, and thermal conductivity caused by a large temperature gradient in a flow domain lead to a wide variety of instability phenomena in mixed convection channel flow of a simple gas such as air. It is known that in strongly nonisothermal flows, the instabilities and the resulting flow patterns are caused by competing buoyancy and shear effects [see S. A. Suslov and S. Paolucci, J. Fluid Mech. 302, 91 (1995)]. However, as is the case in the Boussinesq limit of small temperature gradients, in moderately non-Boussinesq regimes, only a shear instability mechanism is active. Yet in contrast to Boussinesq flows, multiple instability modes are still detected. By reducing the system of full governing Navier-Stokes equations to a dynamical system of coupled Landau-type disturbance amplitude equations we compute a comprehensive parametric map of various shear-driven instabilities observed in a representative moderately non-Boussinesq regime. Subsequently, we analyze nonlinear interaction of unstable modes and reveal physical reasons for their appearance.

Weakly Nonlinear Description of Parametric Instabilities in Vibrating Flows

NASA Technical Reports Server (NTRS)

Knobloch, E.; Vega, J. M.

1999-01-01

This project focuses on the effects of weak dissipation on vibrational flows in microgravity and in particular on (a) the generation of mean flows through viscous effects and their reaction on the flows themselves, and (b) the effects of finite group velocity and dispersion on the resulting dynamics in large domains. The basic mechanism responsible for the generation of such flows is nonlinear and was identified by Schlichting [21] and Longuet-Higgins. However, only recently has it become possible to describe such flows self-consistently in terms of amplitude equations for the parametrically excited waves coupled to a mean flow equation. The derivation of these equations is nontrivial because the limit of zero viscosity is singular. This project focuses on various aspects of this singular problem (i.e., the limit C equivalent to (nu)((g)(h(exp 3)))exp -1/2 << 1,where nu is the kinematic viscosity and h is the liquid depth) in the weakly nonlinear regime. A number of distinct cases is identified depending on the values of the Bond number, the size of the nonlinear terms, distance above threshold and the length scales of interest. The theory provides a quantitative explanation of a number of experiments on the vibration modes of liquid bridges and related experiments on parametric excitation of capillary waves in containers of both small and large aspect ratio. The following is a summary of results obtained thus far.

Streamflow Forecasting Using Nuero-Fuzzy Inference System

NASA Astrophysics Data System (ADS)

Nanduri, U. V.; Swain, P. C.

2005-12-01

The prediction of flow into a reservoir is fundamental in water resources planning and management. The need for timely and accurate streamflow forecasting is widely recognized and emphasized by many in water resources fraternity. Real-time forecasts of natural inflows to reservoirs are of particular interest for operation and scheduling. The physical system of the river basin that takes the rainfall as an input and produces the runoff is highly nonlinear, complicated and very difficult to fully comprehend. The system is influenced by large number of factors and variables. The large spatial extent of the systems forces the uncertainty into the hydrologic information. A variety of methods have been proposed for forecasting reservoir inflows including conceptual (physical) and empirical (statistical) models (WMO 1994), but none of them can be considered as unique superior model (Shamseldin 1997). Owing to difficulties of formulating reasonable non-linear watershed models, recent attempts have resorted to Neural Network (NN) approach for complex hydrologic modeling. In recent years the use of soft computing in the field of hydrological forecasting is gaining ground. The relatively new soft computing technique of Adaptive Neuro-Fuzzy Inference System (ANFIS), developed by Jang (1993) is able to take care of the non-linearity, uncertainty, and vagueness embedded in the system. It is a judicious combination of the Neural Networks and fuzzy systems. It can learn and generalize highly nonlinear and uncertain phenomena due to the embedded neural network (NN). NN is efficient in learning and generalization, and the fuzzy system mimics the cognitive capability of human brain. Hence, ANFIS can learn the complicated processes involved in the basin and correlate the precipitation to the corresponding discharge. In the present study, one step ahead forecasts are made for ten-daily flows, which are mostly required for short term operational planning of multipurpose reservoirs. A Neuro-Fuzzy model is developed to forecast ten-daily flows into the Hirakud reservoir on River Mahanadi in the state of Orissa in India. Correlation analysis is carried out to find out the most influential variables on the ten daily flow at Hirakud. Based on this analysis, four variables, namely, flow during the previous time period, ql1, rainfall during the previous two time periods, rl1 and rl2, and flow during the same period in previous year, qpy, are identified as the most influential variables to forecast the ten daily flow. Performance measures such as Root Mean Square Error (RMSE), Correlation Coefficient (CORR) and coefficient of efficiency R2 are computed for training and testing phases of the model to evaluate its performance. The results indicate that the ten-daily forecasting model is efficient in predicting the high and medium flows with reasonable accuracy. The forecast of low flows is associated with less efficiency. REFERENCES Jang, J.S.R. (1993). "ANFIS: Adaptive - network- based fuzzy inference system." IEEE Trans. on Systems, Man and Cybernetics, 23 (3), 665-685. Shamseldin, A.Y. (1997). "Application of a neural network technique to rainfall-runoff modeling." Journal of Hydrology, 199, 272-294. World Meteorological Organization (1975). Intercomparison of conceptual models used in operational hydrological forecasting. World Meteorological Organization, Technical Report No.429, Geneva, Switzerland.

A numerical approach for assessing effects of shear on equivalent permeability and nonlinear flow characteristics of 2-D fracture networks

NASA Astrophysics Data System (ADS)

Liu, Richeng; Li, Bo; Jiang, Yujing; Yu, Liyuan

2018-01-01

Hydro-mechanical properties of rock fractures are core issues for many geoscience and geo-engineering practices. Previous experimental and numerical studies have revealed that shear processes could greatly enhance the permeability of single rock fractures, yet the shear effects on hydraulic properties of fractured rock masses have received little attention. In most previous fracture network models, single fractures are typically presumed to be formed by parallel plates and flow is presumed to obey the cubic law. However, related studies have suggested that the parallel plate model cannot realistically represent the surface characters of natural rock fractures, and the relationship between flow rate and pressure drop will no longer be linear at sufficiently large Reynolds numbers. In the present study, a numerical approach was established to assess the effects of shear on the hydraulic properties of 2-D discrete fracture networks (DFNs) in both linear and nonlinear regimes. DFNs considering fracture surface roughness and variation of aperture in space were generated using an originally developed code DFNGEN. Numerical simulations by solving Navier-Stokes equations were performed to simulate the fluid flow through these DFNs. A fracture that cuts through each model was sheared and by varying the shear and normal displacements, effects of shear on equivalent permeability and nonlinear flow characteristics of DFNs were estimated. The results show that the critical condition of quantifying the transition from a linear flow regime to a nonlinear flow regime is: 10-4 〈 J < 10-3, where J is the hydraulic gradient. When the fluid flow is in a linear regime (i.e., J < 10-4), the relative deviation of equivalent permeability induced by shear, δ2, is linearly correlated with J with small variations, while for fluid flow in the nonlinear regime (J 〉 10-3), δ2 is nonlinearly correlated with J. A shear process would reduce the equivalent permeability significantly in the orientation perpendicular to the sheared fracture as much as 53.86% when J = 1, shear displacement Ds = 7 mm, and normal displacement Dn = 1 mm. By fitting the calculated results, the mathematical expression for δ2 is established to help choose proper governing equations when solving fluid flow problems in fracture networks.

The nonlinear Galerkin method: A multi-scale method applied to the simulation of homogeneous turbulent flows

NASA Technical Reports Server (NTRS)

Debussche, A.; Dubois, T.; Temam, R.

1993-01-01

Using results of Direct Numerical Simulation (DNS) in the case of two-dimensional homogeneous isotropic flows, the behavior of the small and large scales of Kolmogorov like flows at moderate Reynolds numbers are first analyzed in detail. Several estimates on the time variations of the small eddies and the nonlinear interaction terms were derived; those terms play the role of the Reynolds stress tensor in the case of LES. Since the time step of a numerical scheme is determined as a function of the energy-containing eddies of the flow, the variations of the small scales and of the nonlinear interaction terms over one iteration can become negligible by comparison with the accuracy of the computation. Based on this remark, a multilevel scheme which treats differently the small and the large eddies was proposed. Using mathematical developments, estimates of all the parameters involved in the algorithm, which then becomes a completely self-adaptive procedure were derived. Finally, realistic simulations of (Kolmorov like) flows over several eddy-turnover times were performed. The results are analyzed in detail and a parametric study of the nonlinear Galerkin method is performed.

Comparison of Rolling Moment Characteristics During Roll Oscillations for a Low and a High Aspect Ratio Configuration

NASA Technical Reports Server (NTRS)

Brandon, Jay M.; Foster, John V.; Shah, Gautam H.; Gato, William; Wilborn, James E.

2004-01-01

Improvements in testing and modeling of nonlinear and unsteady aerodynamic effects for flight dynamics predictions of vehicle performance is critical to enable the design and implementation of new, innovative vehicle concepts. Any configuration which exhibits significant flow separation, nonlinear aerodynamics, control interactions or attempts maneuvering through one or more conditions such as these is, at present, a challenge to test, model or predict flight dynamic responses prior to flight. Even in flight test experiments, adequate models are not available to study and characterize the complex nonlinear and time-dependent flow effects occurring during portions of the maneuvering envelope. Traditionally, airplane designs have been conducted to avoid these areas of the flight envelope. Better understanding and characterization of these flight regimes may not only reduce risk and cost of flight test development programs, but also may pave the way for exploitation of those characteristics that increase airplane capabilities. One of the hurdles is that the nonlinear/unsteady effects appear to be configuration dependent. This paper compares some of the dynamic aerodynamic stability characteristics of two very different configurations - representative of a fighter and a transport airplane - during dynamic body-axis roll wind tunnel tests. The fighter model shows significant effects of oscillation frequency which are not as apparent for the transport configuration.

Inertial Effects on Flow and Transport in Heterogeneous Porous Media.

PubMed

Nissan, Alon; Berkowitz, Brian

2018-02-02

We investigate the effects of high fluid velocities on flow and tracer transport in heterogeneous porous media. We simulate fluid flow and advective transport through two-dimensional pore-scale matrices with varying structural complexity. As the Reynolds number increases, the flow regime transitions from linear to nonlinear; this behavior is controlled by the medium structure, where higher complexity amplifies inertial effects. The result is, nonintuitively, increased homogenization of the flow field, which leads in the context of conservative chemical transport to less anomalous behavior. We quantify the transport patterns via a continuous time random walk, using the spatial distribution of the kinetic energy within the fluid as a characteristic measure.

Solitons and Vortices of Shear-Flow-Modified Dust Acoustic Wave

NASA Astrophysics Data System (ADS)

Saeed, Usman; Saleem, Hamid; Shan, Shaukat Ali

2018-01-01

Shear-flow-driven instability and a modified nonlinear dust acoustic wave (mDAW) are investigated in a dusty plasma. In the nonlinear regime a one dimensional mDAW produces pulse-type solitons and in the two-dimensional case, the dipolar vortex solutions are obtained. This investigation is relevant to magnetospheres of planets such as Saturn and Jupiter as well as dusty interstellar clouds. Here, the theoretical model is applied to Saturn's F-rings, and shape of the nonlinear electric field structures is discussed.

On framing potential features of SWCNTs and MWCNTs in mixed convective flow

NASA Astrophysics Data System (ADS)

Hayat, T.; Ullah, Siraj; Khan, M. Ijaz; Alsaedi, A.

2018-03-01

Our target in this research article is to elaborate the characteristics of Darcy-Forchheimer relation in carbon-water nanoliquid flow induced by impermeable stretched cylinder. Energy expression is modeled through viscous dissipation and nonlinear thermal radiation. Application of appropriate transformations yields nonlinear ODEs through nonlinear PDEs. Shooting technique is adopted for the computations of nonlinear ODEs. Importance of influential variables for velocity and thermal fields is elaborated graphically. Moreover rate of heat transfer and drag force are calculated and demonstrated through Tables. Our analysis reports that velocity is higher for ratio of rate constant and buoyancy factor when compared with porosity and volume fraction.

Vortex-induced vibrations mitigation through a nonlinear energy sink

NASA Astrophysics Data System (ADS)

Dai, H. L.; Abdelkefi, A.; Wang, L.

2017-01-01

The passive suppression mechanism of the vortex-induced vibrations (VIV) of the cylinder by means of an essentially nonlinear element, the nonlinear energy sink (NES) is investigated. The flow-induced loads on the cylinder are modeled using a prevalent van der Pol oscillator which is experimentally validated, coupling to the structural vibrations in the presence of the NES structure. Based on the coupled nonlinear governing equations of motion, the performed analysis indicates that the mass and damping of NES have significant effects on the coupled frequency and damping of the aero-elastic system, leading to the shift of synchronization region and mitigation of vibration responses. It is demonstrated that the coupled system of flow-cylinder-NES behaves resonant interactions, showing periodic, aperiodic, and multiple stable responses which depend on the values of the NES parameters. In addition, it is found that the occurrence of multiple stable responses can enhance the nonlinear energy pumping effect, resulting in the increment of transferring energy from the flow via the cylinder to the NES, which is related to the essential nonlinearity of the sink stiffness. This results in a significant reduction in the VIV amplitudes of the primary circular cylinder for appropriate NES parameter values.

Chaos, patterns, coherent structures, and turbulence: Reflections on nonlinear science.

PubMed

Ecke, Robert E

2015-09-01

The paradigms of nonlinear science were succinctly articulated over 25 years ago as deterministic chaos, pattern formation, coherent structures, and adaptation/evolution/learning. For chaos, the main unifying concept was universal routes to chaos in general nonlinear dynamical systems, built upon a framework of bifurcation theory. Pattern formation focused on spatially extended nonlinear systems, taking advantage of symmetry properties to develop highly quantitative amplitude equations of the Ginzburg-Landau type to describe early nonlinear phenomena in the vicinity of critical points. Solitons, mathematically precise localized nonlinear wave states, were generalized to a larger and less precise class of coherent structures such as, for example, concentrated regions of vorticity from laboratory wake flows to the Jovian Great Red Spot. The combination of these three ideas was hoped to provide the tools and concepts for the understanding and characterization of the strongly nonlinear problem of fluid turbulence. Although this early promise has been largely unfulfilled, steady progress has been made using the approaches of nonlinear science. I provide a series of examples of bifurcations and chaos, of one-dimensional and two-dimensional pattern formation, and of turbulence to illustrate both the progress and limitations of the nonlinear science approach. As experimental and computational methods continue to improve, the promise of nonlinear science to elucidate fluid turbulence continues to advance in a steady manner, indicative of the grand challenge nature of strongly nonlinear multi-scale dynamical systems.

A nonperturbative approximation for the moderate Reynolds number Navier–Stokes equations

PubMed Central

Roper, Marcus; Brenner, Michael P.

2009-01-01

The nonlinearity of the Navier–Stokes equations makes predicting the flow of fluid around rapidly moving small bodies highly resistant to all approaches save careful experiments or brute force computation. Here, we show how a linearization of the Navier–Stokes equations captures the drag-determining features of the flow and allows simplified or analytical computation of the drag on bodies up to Reynolds number of order 100. We illustrate the utility of this linearization in 2 practical problems that normally can only be tackled with sophisticated numerical methods: understanding flow separation in the flow around a bluff body and finding drag-minimizing shapes. PMID:19211800

A nonperturbative approximation for the moderate Reynolds number Navier-Stokes equations.

PubMed

Roper, Marcus; Brenner, Michael P

2009-03-03

The nonlinearity of the Navier-Stokes equations makes predicting the flow of fluid around rapidly moving small bodies highly resistant to all approaches save careful experiments or brute force computation. Here, we show how a linearization of the Navier-Stokes equations captures the drag-determining features of the flow and allows simplified or analytical computation of the drag on bodies up to Reynolds number of order 100. We illustrate the utility of this linearization in 2 practical problems that normally can only be tackled with sophisticated numerical methods: understanding flow separation in the flow around a bluff body and finding drag-minimizing shapes.

Regression modeling of ground-water flow

USGS Publications Warehouse

Cooley, R.L.; Naff, R.L.

1985-01-01

Nonlinear multiple regression methods are developed to model and analyze groundwater flow systems. Complete descriptions of regression methodology as applied to groundwater flow models allow scientists and engineers engaged in flow modeling to apply the methods to a wide range of problems. Organization of the text proceeds from an introduction that discusses the general topic of groundwater flow modeling, to a review of basic statistics necessary to properly apply regression techniques, and then to the main topic: exposition and use of linear and nonlinear regression to model groundwater flow. Statistical procedures are given to analyze and use the regression models. A number of exercises and answers are included to exercise the student on nearly all the methods that are presented for modeling and statistical analysis. Three computer programs implement the more complex methods. These three are a general two-dimensional, steady-state regression model for flow in an anisotropic, heterogeneous porous medium, a program to calculate a measure of model nonlinearity with respect to the regression parameters, and a program to analyze model errors in computed dependent variables such as hydraulic head. (USGS)

Bubble deformations and segmented flows in corrugated microchannels at large capillary numbers

NASA Astrophysics Data System (ADS)

Sauzade, Martin; Cubaud, Thomas

2018-03-01

We experimentally investigate the interaction between individual bubble deformations and collective distortions of segmented flows in nonlinear microfluidic geometries. Using highly viscous carrier fluids, we study the evolution of monodisperse trains of gas bubbles from a square to a smoothly corrugated microchannel characterized with a series of extensions and constrictions along the flow path. The hysteresis in the bubble shape between accelerating and decelerating flow fields is shown to increase with the capillary number. Measurements of instantaneous bubble velocities reveal the presence of a capillary pull that produces a nonmonotonic behavior for the front velocity in accelerating flow regions. Functional relationships are developed for predicting the morphology and dynamics of viscous multiphase flow patterns at the pore scale.

Stability and nonlinear adjustment of vortices in Keplerian flows

NASA Astrophysics Data System (ADS)

Bodo, G.; Tevzadze, A.; Chagelishvili, G.; Mignone, A.; Rossi, P.; Ferrari, A.

2007-11-01

Aims:We investigate the stability, nonlinear development and equilibrium structure of vortices in a background shearing Keplerian flow Methods: We make use of high-resolution global two-dimensional compressible hydrodynamic simulations. We introduce the concept of nonlinear adjustment to describe the transition of unbalanced vortical fields to a long-lived configuration. Results: We discuss the conditions under which vortical perturbations evolve into long-lived persistent structures and we describe the properties of these equilibrium vortices. The properties of equilibrium vortices appear to be independent from the initial conditions and depend only on the local disk parameters. In particular we find that the ratio of the vortex size to the local disk scale height increases with the decrease of the sound speed, reaching values well above the unity. The process of spiral density wave generation by the vortex, discussed in our previous work, appear to maintain its efficiency also at nonlinear amplitudes and we observe the formation of spiral shocks attached to the vortex. The shocks may have important consequences on the long term vortex evolution and possibly on the global disk dynamics. Conclusions: Our study strengthens the arguments in favor of anticyclonic vortices as the candidates for the promotion of planetary formation. Hydrodynamic shocks that are an intrinsic property of persistent vortices in compressible Keplerian flows are an important contributor to the overall balance. These shocks support vortices against viscous dissipation by generating local potential vorticity and should be responsible for the eventual fate of the persistent anticyclonic vortices. Numerical codes have be able to resolve shock waves to describe the vortex dynamics correctly.

Influence of nonlinear thermal radiation and viscous dissipation on three-dimensional flow of Jeffrey nano fluid over a stretching sheet in the presence of Joule heating

NASA Astrophysics Data System (ADS)

Ganesh Kumar, K.; Rudraswamy, N. G.; Gireesha, B. J.; Krishnamurthy, M. R.

2017-09-01

Present exploration discusses the combined effect of viscous dissipation and Joule heating on three dimensional flow and heat transfer of a Jeffrey nanofluid in the presence of nonlinear thermal radiation. Here the flow is generated over bidirectional stretching sheet in the presence of applied magnetic field by accounting thermophoresis and Brownian motion of nanoparticles. Suitable similarity transformations are employed to reduce the governing partial differential equations into coupled nonlinear ordinary differential equations. These nonlinear ordinary differential equations are solved numerically by using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. Graphically results are presented and discussed for various parameters. Validation of the current method is proved by comparing our results with the existing results under limiting situations. It can be concluded that combined effect of Joule and viscous heating increases the temperature profile and thermal boundary layer thickness.

Non-Darcy flow of water-based carbon nanotubes with nonlinear radiation and heat generation/absorption

NASA Astrophysics Data System (ADS)

Hayat, T.; Ullah, Siraj; Khan, M. Ijaz; Alsaedi, A.; Zaigham Zia, Q. M.

2018-03-01

Here modeling and computations are presented to introduce the novel concept of Darcy-Forchheimer three-dimensional flow of water-based carbon nanotubes with nonlinear thermal radiation and heat generation/absorption. Bidirectional stretching surface induces the flow. Darcy's law is commonly replace by Forchheimer relation. Xue model is implemented for nonliquid transport mechanism. Nonlinear formulation based upon conservation laws of mass, momentum and energy is first modeled and then solved by optimal homotopy analysis technique. Optimal estimations of auxiliary variables are obtained. Importance of influential variables on the velocity and thermal fields is interpreted graphically. Moreover velocity and temperature gradients are discussed and analyzed. Physical interpretation of influential variables is examined.

Analysis of High Order Difference Methods for Multiscale Complex Compressible Flows

NASA Technical Reports Server (NTRS)

Sjoegreen, Bjoern; Yee, H. C.; Tang, Harry (Technical Monitor)

2002-01-01

Accurate numerical simulations of complex multiscale compressible viscous flows, especially high speed turbulence combustion and acoustics, demand high order schemes with adaptive numerical dissipation controls. Standard high resolution shock-capturing methods are too dissipative to capture the small scales and/or long-time wave propagations without extreme grid refinements and small time steps. An integrated approach for the control of numerical dissipation in high order schemes with incremental studies was initiated. Here we further refine the analysis on, and improve the understanding of the adaptive numerical dissipation control strategy. Basically, the development of these schemes focuses on high order nondissipative schemes and takes advantage of the progress that has been made for the last 30 years in numerical methods for conservation laws, such as techniques for imposing boundary conditions, techniques for stability at shock waves, and techniques for stable and accurate long-time integration. We concentrate on high order centered spatial discretizations and a fourth-order Runge-Kutta temporal discretizations as the base scheme. Near the bound-aries, the base scheme has stable boundary difference operators. To further enhance stability, the split form of the inviscid flux derivatives is frequently used for smooth flow problems. To enhance nonlinear stability, linear high order numerical dissipations are employed away from discontinuities, and nonlinear filters are employed after each time step in order to suppress spurious oscillations near discontinuities to minimize the smearing of turbulent fluctuations. Although these schemes are built from many components, each of which is well-known, it is not entirely obvious how the different components be best connected. For example, the nonlinear filter could instead have been built into the spatial discretization, so that it would have been activated at each stage in the Runge-Kutta time stepping. We could think of a mechanism that activates the split form of the equations only at some parts of the domain. Another issue is how to define good sensors for determining in which parts of the computational domain a certain feature should be filtered by the appropriate numerical dissipation. For the present study we employ a wavelet technique introduced in as sensors. Here, the method is briefly described with selected numerical experiments.

Pressure-dependent surface viscosity and its surprising consequences in interfacial lubrication flows

NASA Astrophysics Data System (ADS)

Manikantan, Harishankar; Squires, Todd M.

2017-02-01

The surface shear rheology of many insoluble surfactants depends strongly on the surface pressure (or concentration) of that surfactant. Here we highlight the dramatic consequences that surface-pressure-dependent surface viscosities have on interfacially dominant flows, by considering lubrication-style geometries within high Boussinesq (Bo) number flows. As with three-dimensional lubrication, high-Bo surfactant flows through thin gaps give high surface pressures, which in turn increase the local surface viscosity, further amplifying lubrication stresses and surface pressures. Despite their strong nonlinearity, the governing equations are separable, so that results from two-dimensional Newtonian lubrication analyses may be immediately adapted to treat surfactant monolayers with a general functional form of ηs(Π ) . Three paradigmatic systems are analyzed to reveal qualitatively new features: a maximum, self-limiting value for surfactant fluxes and particle migration velocities appears for Π -thickening surfactants, and kinematic reversibility is broken for the journal bearing and for suspensions more generally.

Erosion by an Alpine glacier.

PubMed

Herman, Frédéric; Beyssac, Olivier; Brughelli, Mattia; Lane, Stuart N; Leprince, Sébastien; Adatte, Thierry; Lin, Jiao Y Y; Avouac, Jean-Philippe; Cox, Simon C

2015-10-09

Assessing the impact of glaciation on Earth's surface requires understanding glacial erosion processes. Developing erosion theories is challenging because of the complex nature of the erosion processes and the difficulty of examining the ice/bedrock interface of contemporary glaciers. We demonstrate that the glacial erosion rate is proportional to the ice-sliding velocity squared, by quantifying spatial variations in ice-sliding velocity and the erosion rate of a fast-flowing Alpine glacier. The nonlinear behavior implies a high erosion sensitivity to small variations in topographic slope and precipitation. A nonlinear rate law suggests that abrasion may dominate over other erosion processes in fast-flowing glaciers. It may also explain the wide range of observed glacial erosion rates and, in part, the impact of glaciation on mountainous landscapes during the past few million years. Copyright © 2015, American Association for the Advancement of Science.

Derivation of nonlinear wave equations for ultrasound beam in nonuniform bubbly liquids

NASA Astrophysics Data System (ADS)

Kanagawa, Tetsuya; Yano, Takeru; Kawahara, Junya; Kobayashi, Kazumichi; Watanabe, Masao; Fujikawa, Shigeo

2012-09-01

Weakly nonlinear propagation of diffracted ultrasound beams in a nonuniform bubbly liquid is theoretically studied based on the method of multiple scales with the set of scaling relations of some physical parameters. It is assumed that the spatial distribution of the number density of bubbles in an initial state at rest is a slowly varying function of space coordinates and the amplitude of its variation is small compared with a mean number density. As a result, a Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation with dispersion and nonuniform effects for a low frequency case and a nonlinear Schrödinger (NLS) equation with dissipation, diffraction, and nonuniform effects for a high frequency case, are derived from the basic equations of bubbly flows.

Documentation of computer program VS2D to solve the equations of fluid flow in variably saturated porous media

USGS Publications Warehouse

Lappala, E.G.; Healy, R.W.; Weeks, E.P.

1987-01-01

This report documents FORTRAN computer code for solving problems involving variably saturated single-phase flow in porous media. The flow equation is written with total hydraulic potential as the dependent variable, which allows straightforward treatment of both saturated and unsaturated conditions. The spatial derivatives in the flow equation are approximated by central differences, and time derivatives are approximated either by a fully implicit backward or by a centered-difference scheme. Nonlinear conductance and storage terms may be linearized using either an explicit method or an implicit Newton-Raphson method. Relative hydraulic conductivity is evaluated at cell boundaries by using either full upstream weighting, the arithmetic mean, or the geometric mean of values from adjacent cells. Nonlinear boundary conditions treated by the code include infiltration, evaporation, and seepage faces. Extraction by plant roots that is caused by atmospheric demand is included as a nonlinear sink term. These nonlinear boundary and sink terms are linearized implicitly. The code has been verified for several one-dimensional linear problems for which analytical solutions exist and against two nonlinear problems that have been simulated with other numerical models. A complete listing of data-entry requirements and data entry and results for three example problems are provided. (USGS)

Using the nonlinear aquifer storage-discharge relationship to simulate the base flow of glacier- and snowmelt-dominated basins in northwest China

NASA Astrophysics Data System (ADS)

Gan, R.; Luo, Y.

2013-09-01

Base flow is an important component in hydrological modeling. This process is usually modeled by using the linear aquifer storage-discharge relation approach, although the outflow from groundwater aquifers is nonlinear. To identify the accuracy of base flow estimates in rivers dominated by snowmelt and/or glacier melt in arid and cold northwestern China, a nonlinear storage-discharge relationship for use in SWAT (Soil Water Assessment Tool) modeling was developed and applied to the Manas River basin in the Tian Shan Mountains. Linear reservoir models and a digital filter program were used for comparisons. Meanwhile, numerical analysis of recession curves from 78 river gauge stations revealed variation in the parameters of the nonlinear relationship. It was found that the nonlinear reservoir model can improve the streamflow simulation, especially for low-flow period. The higher Nash-Sutcliffe efficiency, logarithmic efficiency, and volumetric efficiency, and lower percent bias were obtained when compared to the one-linear reservoir approach. The parameter b of the aquifer storage-discharge function varied mostly between 0.0 and 0.1, which is much smaller than the suggested value of 0.5. The coefficient a of the function is related to catchment properties, primarily the basin and glacier areas.

Nonlinear spatial evolution of inviscid instabilities on hypersonic boundary layers

NASA Technical Reports Server (NTRS)

Wundrow, David W.

1996-01-01

The spatial development of an initially linear vorticity-mode instability on a compressible flat-plate boundary layer is considered. The analysis is done in the framework of the hypersonic limit where the free-stream Mach number M approaches infinity. Nonlinearity is shown to become important locally, in a thin critical layer, when sigma, the deviation of the phase speed from unity, becomes o(M(exp -8/7)) and the magnitude of the pressure fluctuations becomes 0(sigma(exp 5/2)M(exp 2)). The unsteady flow outside the critical layer takes the form of a linear instability wave but with its amplitude completely determined by the nonlinear flow within the critical layer. The coupled set of equations which govern the critical-layer dynamics reflect a balance between spatial-evolution, (linear and nonlinear) convection and nonlinear vorticity-generation terms. The numerical solution to these equations shows that nonlinear effects produce a dramatic reduction in the instability-wave amplitude.

Acoustic response of Helmholtz dampers in the presence of hot grazing flow

NASA Astrophysics Data System (ADS)

Ćosić, B.; Wassmer, D.; Terhaar, S.; Paschereit, C. O.

2015-01-01

Thermoacoustic instabilities are high amplitude instabilities of premixed gas turbine combustors. Cooled passive dampers are used to attenuate or suppress these instabilities in the combustion chamber. For the first time, the influence of temperature differences between the grazing flow in the combustor and the cross-flow emanating from the Helmholtz damper is comprehensively investigated in the linear and nonlinear amplitude regime. The flow field inside the resonator and in the vicinity of the neck is measured with high-speed particle image velocimetry for various amplitudes and at different momentum-flux ratios of grazing and purging flow. Seeding is used as a tracer to qualitatively assess the mixing of the grazing and purging flow as well as the ingestion into the neck of the resonator. Experimentally, the acoustic response for various temperature differences between grazing and purging flow is investigated. The multi-microphone method, in combination with two microphones flush-mounted in the resonator volume and two microphones in the plane of the resonator entrance, is used to determine the impedance of the Helmholtz resonator in the linear and nonlinear amplitude regime for various temperatures and different momentum-flux ratios. Additionally, a thermocouple was used to measure the temperature in the neck. The acoustic response and the temperature measurements are used to obtain the virtual neck length and the effective area jump from a detailed impedance model. This model is extended to include the observed acoustic energy dissipation caused by the density gradients at the neck vicinity. A clear correlation between temperature differences and changes of the mass end-correction is confirmed. The capabilities of the impedance model are demonstrated.

Nonlinear convective flows in a two-layer system under the action of spatial temperature modulation of heat release/consumption at the interface

NASA Astrophysics Data System (ADS)

Simanovskii, Ilya B.; Viviani, Antonio; Dubois, Frank

2018-06-01

An influence of a spatial temperature modulation of the interfacial heat release/consumption on nonlinear convective flows in the 47v2 silicone oil - water system, is studied. Rigid heat-insulated lateral walls, corresponding to the case of closed cavities, have been considered. Transitions between the flows with different spatial structures, have been investigated. It is shown that the spatial modulation can change the sequence of bifurcations and lead to the appearance of specific steady and oscillatory flows in the system.

Nonlinear deformation and localized failure of bacterial streamers in creeping flows

PubMed Central

Biswas, Ishita; Ghosh, Ranajay; Sadrzadeh, Mohtada; Kumar, Aloke

2016-01-01

We investigate the failure of bacterial floc mediated streamers in a microfluidic device in a creeping flow regime using both experimental observations and analytical modeling. The quantification of streamer deformation and failure behavior is possible due to the use of 200 nm fluorescent polystyrene beads which firmly embed in the extracellular polymeric substance (EPS) and act as tracers. The streamers, which form soon after the commencement of flow begin to deviate from an apparently quiescent fully formed state in spite of steady background flow and limited mass accretion indicating significant mechanical nonlinearity. This nonlinear behavior shows distinct phases of deformation with mutually different characteristic times and comes to an end with a distinct localized failure of the streamer far from the walls. We investigate this deformation and failure behavior for two separate bacterial strains and develop a simplified but nonlinear analytical model describing the experimentally observed instability phenomena assuming a necking route to instability. Our model leads to a power law relation between the critical strain at failure and the fluid velocity scale exhibiting excellent qualitative and quantitative agreeing with the experimental rupture behavior. PMID:27558511

Chemical reaction and heat generation/absorption aspects in MHD nonlinear convective flow of third grade nanofluid over a nonlinear stretching sheet with variable thickness

NASA Astrophysics Data System (ADS)

Qayyum, Sajid; Hayat, Tasawar; Alsaedi, Ahmed

Nonlinear thermal radiation and chemical reaction in magnetohydrodynamic (MHD) flow of third grade nanofluid over a stretching sheet with variable thickness are addressed. Heat generation/absorption and nonlinear convection are considered. The sheet moves with nonlinear velocity. Sheet is convectively heated. In addition zero mass flux condition for nanoparticle concentration is imposed. Results for velocity, temperature, concentration, skin friction and local Nusselt number are presented and examined. It is found that velocity and boundary layer thickness are increasing for Reynolds number. Temperature is a increasing function of the heat generation/absorption parameter while it causes a decrease in the heat transfer rate. Moreover effect of Brownian motion and chemical reaction on the concentration are quite reverse.

Richtmyer-Meshkov evolution under steady shock conditions in the high-energy-density regime

DOE PAGES

Di Stefano, C. A.; Malamud, G.; Kuranz, C. C.; ...

2015-03-17

This work presents direct experimental evidence of long-predicted nonlinear aspects of the Richtmyer-Meshkov (RM) process, in which new modes first arise from the coupling of initially-present modes, and in which shorter-wavelength modes are eventually overtaken by longer-wavelength modes. This is accomplished using a technique we developed employing a long driving laser pulse to create a strong (Mach ~ 8) shock across a well-characterized material interface seeded by a two-mode sinusoidal perturbation. Furthermore, this technique further permits the shock to be sustained, without decay of the high-energy-density flow conditions, long enough for the system to evolve into the nonlinear phase.

Estimation of suspended-sediment rating curves and mean suspended-sediment loads

USGS Publications Warehouse

Crawford, Charles G.

1991-01-01

A simulation study was done to evaluate: (1) the accuracy and precision of parameter estimates for the bias-corrected, transformed-linear and non-linear models obtained by the method of least squares; (2) the accuracy of mean suspended-sediment loads calculated by the flow-duration, rating-curve method using model parameters obtained by the alternative methods. Parameter estimates obtained by least squares for the bias-corrected, transformed-linear model were considerably more precise than those obtained for the non-linear or weighted non-linear model. The accuracy of parameter estimates obtained for the biascorrected, transformed-linear and weighted non-linear model was similar and was much greater than the accuracy obtained by non-linear least squares. The improved parameter estimates obtained by the biascorrected, transformed-linear or weighted non-linear model yield estimates of mean suspended-sediment load calculated by the flow-duration, rating-curve method that are more accurate and precise than those obtained for the non-linear model.

Reduced order modeling and active flow control of an inlet duct

NASA Astrophysics Data System (ADS)

Ge, Xiaoqing

Many aerodynamic applications require the modeling of compressible flows in or around a body, e.g., the design of aircraft, inlet or exhaust duct, wind turbines, or tall buildings. Traditional methods use wind tunnel experiments and computational fluid dynamics (CFD) to investigate the spatial and temporal distribution of the flows. Although they provide a great deal of insight into the essential characteristics of the flow field, they are not suitable for control analysis and design due to the high physical/computational cost. Many model reduction methods have been studied to reduce the complexity of the flow model. There are two main approaches: linearization based input/output modeling and proper orthogonal decomposition (POD) based model reduction. The former captures mostly the local behavior near a steady state, which is suitable to model laminar flow dynamics. The latter obtains a reduced order model by projecting the governing equation onto an "optimal" subspace and is able to model complex nonlinear flow phenomena. In this research we investigate various model reduction approaches and compare them in flow modeling and control design. We propose an integrated model-based control methodology and apply it to the reduced order modeling and active flow control of compressible flows within a very aggressive (length to exit diameter ratio, L/D, of 1.5) inlet duct and its upstream contraction section. The approach systematically applies reduced order modeling, estimator design, sensor placement and control design to improve the aerodynamic performance. The main contribution of this work is the development of a hybrid model reduction approach that attempts to combine the best features of input/output model identification and POD method. We first identify a linear input/output model by using a subspace algorithm. We next project the difference between CFD response and the identified model response onto a set of POD basis. This trajectory is fit to a nonlinear dynamical model to augment the linear input/output model. Thus, the full system is decomposed into a dominant linear subsystem and a low order nonlinear subsystem. The hybrid model is then used for control design and compared with other modeling methods in CFD simulations. Numerical results indicate that the hybrid model accurately predicts the nonlinear behavior of the flow for a 2D diffuser contraction section model. It also performs best in terms of feedback control design and learning control. Since some outputs of interest (e.g., the AIP pressure recovery) are not observable during normal operations, static and dynamic estimators are designed to recreate the information from available sensor measurements. The latter also provides a state estimation for feedback controller. Based on the reduced order models and estimators, different controllers are designed to improve the aerodynamic performance of the contraction section and inlet duct. The integrated control methodology is evaluated with CFD simulations. Numerical results demonstrate the feasibility and efficacy of the active flow control based on reduced order models. Our reduced order models not only generate a good approximation of the nonlinear flow dynamics over a wide input range, but also help to design controllers that significantly improve the flow response. The tools developed for model reduction, estimator and control design can also be applied to wind tunnel experiment.

Current structure of strongly nonlinear interfacial solitary waves

NASA Astrophysics Data System (ADS)

Semin, Sergey; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim; Churaev, Egor

2015-04-01

The characteristics of highly nonlinear solitary internal waves (solitons) in two-layer flow are computed within the fully nonlinear Navier-Stokes equations with use of numerical model of the Massachusetts Institute of Technology (MITgcm). The verification and adaptation of the model is based on the data from laboratory experiments [Carr & Davies, 2006]. The present paper also compares the results of our calculations with the computations performed in the framework of the fully nonlinear Bergen Ocean Model [Thiem et al, 2011]. The comparison of the computed soliton parameters with the predictions of the weakly nonlinear theory based on the Gardner equation is given. The occurrence of reverse flow in the bottom layer directly behind the soliton is confirmed in numerical simulations. The trajectories of Lagrangian particles in the internal soliton on the surface, on the interface and near the bottom are computed. The results demonstrated completely different trajectories at different depths of the model area. Thus, in the surface layer is observed the largest displacement of Lagrangian particles, which can be more than two and a half times larger than the characteristic width of the soliton. Located at the initial moment along the middle pycnocline fluid particles move along the elongated vertical loop at a distance of not more than one third of the width of the solitary wave. In the bottom layer of the fluid moves in the opposite direction of propagation of the internal wave, but under the influence of the reverse flow, when the bulk of the velocity field of the soliton ceases to influence the trajectory, it moves in the opposite direction. The magnitude of displacement of fluid particles in the bottom layer is not more than the half-width of the solitary wave. 1. Carr, M., and Davies, P.A. The motion of an internal solitary wave of depression over a fixed bottom boundary in a shallow, two-layer fluid. Phys. Fluids, 2006, vol. 18, No. 1, 1 - 10. 2. Thiem, O., Carr, M., Berntsen, J., and Davies, P.A. Numerical simulation of internal solitary wave-induced reverse flow and associated vortices in a shallow, two-layer fluid benthic boundary layer. Ocean Dynamics, 2011, vol. 61, No. 6, 857 - 872.

Dynamics of homogeneous shear turbulence: A key role of the nonlinear transverse cascade in the bypass concept.

PubMed

Mamatsashvili, G; Khujadze, G; Chagelishvili, G; Dong, S; Jiménez, J; Foysi, H

2016-08-01

To understand the mechanism of the self-sustenance of subcritical turbulence in spectrally stable (constant) shear flows, we performed direct numerical simulations of homogeneous shear turbulence for different aspect ratios of the flow domain with subsequent analysis of the dynamical processes in spectral or Fourier space. There are no exponentially growing modes in such flows and the turbulence is energetically supported only by the linear growth of Fourier harmonics of perturbations due to the shear flow non-normality. This non-normality-induced growth, also known as nonmodal growth, is anisotropic in spectral space, which, in turn, leads to anisotropy of nonlinear processes in this space. As a result, a transverse (angular) redistribution of harmonics in Fourier space is the main nonlinear process in these flows, rather than direct or inverse cascades. We refer to this type of nonlinear redistribution as the nonlinear transverse cascade. It is demonstrated that the turbulence is sustained by a subtle interplay between the linear nonmodal growth and the nonlinear transverse cascade. This course of events reliably exemplifies a well-known bypass scenario of subcritical turbulence in spectrally stable shear flows. These two basic processes mainly operate at large length scales, comparable to the domain size. Therefore, this central, small wave number area of Fourier space is crucial in the self-sustenance; we defined its size and labeled it as the vital area of turbulence. Outside the vital area, the nonmodal growth and the transverse cascade are of secondary importance: Fourier harmonics are transferred to dissipative scales by the nonlinear direct cascade. Although the cascades and the self-sustaining process of turbulence are qualitatively the same at different aspect ratios, the number of harmonics actively participating in this process (i.e., the harmonics whose energies grow more than 10% of the maximum spectral energy at least once during evolution) varies, but always remains quite large (equal to 36, 86, and 209) in the considered here three aspect ratios. This implies that the self-sustenance of subcritical turbulence cannot be described by low-order models.

Dynamics of homogeneous shear turbulence: A key role of the nonlinear transverse cascade in the bypass concept

NASA Astrophysics Data System (ADS)

Mamatsashvili, G.; Khujadze, G.; Chagelishvili, G.; Dong, S.; Jiménez, J.; Foysi, H.

2016-08-01

To understand the mechanism of the self-sustenance of subcritical turbulence in spectrally stable (constant) shear flows, we performed direct numerical simulations of homogeneous shear turbulence for different aspect ratios of the flow domain with subsequent analysis of the dynamical processes in spectral or Fourier space. There are no exponentially growing modes in such flows and the turbulence is energetically supported only by the linear growth of Fourier harmonics of perturbations due to the shear flow non-normality. This non-normality-induced growth, also known as nonmodal growth, is anisotropic in spectral space, which, in turn, leads to anisotropy of nonlinear processes in this space. As a result, a transverse (angular) redistribution of harmonics in Fourier space is the main nonlinear process in these flows, rather than direct or inverse cascades. We refer to this type of nonlinear redistribution as the nonlinear transverse cascade. It is demonstrated that the turbulence is sustained by a subtle interplay between the linear nonmodal growth and the nonlinear transverse cascade. This course of events reliably exemplifies a well-known bypass scenario of subcritical turbulence in spectrally stable shear flows. These two basic processes mainly operate at large length scales, comparable to the domain size. Therefore, this central, small wave number area of Fourier space is crucial in the self-sustenance; we defined its size and labeled it as the vital area of turbulence. Outside the vital area, the nonmodal growth and the transverse cascade are of secondary importance: Fourier harmonics are transferred to dissipative scales by the nonlinear direct cascade. Although the cascades and the self-sustaining process of turbulence are qualitatively the same at different aspect ratios, the number of harmonics actively participating in this process (i.e., the harmonics whose energies grow more than 10% of the maximum spectral energy at least once during evolution) varies, but always remains quite large (equal to 36, 86, and 209) in the considered here three aspect ratios. This implies that the self-sustenance of subcritical turbulence cannot be described by low-order models.

A comparative numerical analysis of linear and nonlinear aerodynamic sound generation by vortex disturbances in homentropic constant shear flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hau, Jan-Niklas, E-mail: hau@fdy.tu-darmstadt.de; Oberlack, Martin; GSC CE, Technische Universität Darmstadt, Dolivostraße 15, 64293 Darmstadt

2015-12-15

Aerodynamic sound generation in shear flows is investigated in the light of the breakthrough in hydrodynamics stability theory in the 1990s, where generic phenomena of non-normal shear flow systems were understood. By applying the thereby emerged short-time/non-modal approach, the sole linear mechanism of wave generation by vortices in shear flows was captured [G. D. Chagelishvili, A. Tevzadze, G. Bodo, and S. S. Moiseev, “Linear mechanism of wave emergence from vortices in smooth shear flows,” Phys. Rev. Lett. 79, 3178-3181 (1997); B. F. Farrell and P. J. Ioannou, “Transient and asymptotic growth of two-dimensional perturbations in viscous compressible shear flow,” Phys.more » Fluids 12, 3021-3028 (2000); N. A. Bakas, “Mechanism underlying transient growth of planar perturbations in unbounded compressible shear flow,” J. Fluid Mech. 639, 479-507 (2009); and G. Favraud and V. Pagneux, “Superadiabatic evolution of acoustic and vorticity perturbations in Couette flow,” Phys. Rev. E 89, 033012 (2014)]. Its source is the non-normality induced linear mode-coupling, which becomes efficient at moderate Mach numbers that is defined for each perturbation harmonic as the ratio of the shear rate to its characteristic frequency. Based on the results by the non-modal approach, we investigate a two-dimensional homentropic constant shear flow and focus on the dynamical characteristics in the wavenumber plane. This allows to separate from each other the participants of the dynamical processes — vortex and wave modes — and to estimate the efficacy of the process of linear wave-generation. This process is analyzed and visualized on the example of a packet of vortex modes, localized in both, spectral and physical, planes. Further, by employing direct numerical simulations, the wave generation by chaotically distributed vortex modes is analyzed and the involved linear and nonlinear processes are identified. The generated acoustic field is anisotropic in the wavenumber plane, which results in highly directional linear sound radiation, whereas the nonlinearly generated waves are almost omni-directional. As part of this analysis, we compare the effectiveness of the linear and nonlinear mechanisms of wave generation within the range of validity of the rapid distortion theory and show the dominance of the linear aerodynamic sound generation. Finally, topological differences between the linear source term of the acoustic analogy equation and of the anisotropic non-normality induced linear mechanism of wave generation are found.« less

Investigations of the role of nonlinear couplings in structure formation and transport regulation in plasma turbulence

NASA Astrophysics Data System (ADS)

Holland, Christopher George

Studies of nonlinear couplings and dynamics in plasma turbulence are presented. Particular areas of focus are analytic studies of coherent structure formation in electron temperature gradient turbulence, measurement of nonlinear energy transfer in simulations of plasma turbulence, and bispectral analysis of experimental and computational data. The motivation for these works has been to develop and expand the existing theories of plasma transport, and verify the nonlinear predictions of those theories in simulation and experiment. In Chapter II, we study electromagnetic secondary instabilities of electron temperature gradient turbulence. The growth rate for zonal flow generation via modulational instability of electromagnetic ETG turbulence is calculated, as well as that for zonal (magnetic) field generation. In Chapter III, the stability and saturation of streamers in ETG turbulence is considered, and shown to depend sensitively upon geometry and the damping rates of the Kelvin-Helmholtz mode. Requirements for a credible theory of streamer transport are presented. In addition, a self-consistent model for interactions between ETG and ITG (ion temperature gradient) turbulence is presented. In Chapter IV, the nonlinear transfer of kinetic and internal energy is measured in simulations of plasma turbulence. The regulation of turbulence by radial decorrelation due to zonal flows and generation of zonal flows via the Reynolds stress are explicitly demonstrated, and shown to be symmetric facets of a single nonlinear process. Novel nonlinear saturation mechanisms for zonal flows are discussed. In Chapter V, measurements of fluctuation bicoherence in the edge of the DIII-D tokamak are presented. It is shown that the bicoherence increases transiently before a L-H transition, and decays to its initial value after the barrier has formed. The increase in bicoherence is localized to the region where the transport barrier forms, and shows strong coupling between well-separated frequencies. These results are qualitatively reproduced in a simple numerical "thought experiment," described in Chapter VI, which suggests that zonal flows may trigger the L-H transition.

Observation of Dispersive Shock Waves, Solitons, and Their Interactions in Viscous Fluid Conduits.

PubMed

Maiden, Michelle D; Lowman, Nicholas K; Anderson, Dalton V; Schubert, Marika E; Hoefer, Mark A

2016-04-29

Dispersive shock waves and solitons are fundamental nonlinear excitations in dispersive media, but dispersive shock wave studies to date have been severely constrained. Here, we report on a novel dispersive hydrodynamic test bed: the effectively frictionless dynamics of interfacial waves between two high viscosity contrast, miscible, low Reynolds number Stokes fluids. This scenario is realized by injecting from below a lighter, viscous fluid into a column filled with high viscosity fluid. The injected fluid forms a deformable pipe whose diameter is proportional to the injection rate, enabling precise control over the generation of symmetric interfacial waves. Buoyancy drives nonlinear interfacial self-steepening, while normal stresses give rise to the dispersion of interfacial waves. Extremely slow mass diffusion and mass conservation imply that the interfacial waves are effectively dissipationless. This enables high fidelity observations of large amplitude dispersive shock waves in this spatially extended system, found to agree quantitatively with a nonlinear wave averaging theory. Furthermore, several highly coherent phenomena are investigated including dispersive shock wave backflow, the refraction or absorption of solitons by dispersive shock waves, and the multiphase merging of two dispersive shock waves. The complex, coherent, nonlinear mixing of dispersive shock waves and solitons observed here are universal features of dissipationless, dispersive hydrodynamic flows.

Detecting determinism with improved sensitivity in time series: rank-based nonlinear predictability score.

PubMed

Naro, Daniel; Rummel, Christian; Schindler, Kaspar; Andrzejak, Ralph G

2014-09-01

The rank-based nonlinear predictability score was recently introduced as a test for determinism in point processes. We here adapt this measure to time series sampled from time-continuous flows. We use noisy Lorenz signals to compare this approach against a classical amplitude-based nonlinear prediction error. Both measures show an almost identical robustness against Gaussian white noise. In contrast, when the amplitude distribution of the noise has a narrower central peak and heavier tails than the normal distribution, the rank-based nonlinear predictability score outperforms the amplitude-based nonlinear prediction error. For this type of noise, the nonlinear predictability score has a higher sensitivity for deterministic structure in noisy signals. It also yields a higher statistical power in a surrogate test of the null hypothesis of linear stochastic correlated signals. We show the high relevance of this improved performance in an application to electroencephalographic (EEG) recordings from epilepsy patients. Here the nonlinear predictability score again appears of higher sensitivity to nonrandomness. Importantly, it yields an improved contrast between signals recorded from brain areas where the first ictal EEG signal changes were detected (focal EEG signals) versus signals recorded from brain areas that were not involved at seizure onset (nonfocal EEG signals).

Detecting determinism with improved sensitivity in time series: Rank-based nonlinear predictability score

NASA Astrophysics Data System (ADS)

Naro, Daniel; Rummel, Christian; Schindler, Kaspar; Andrzejak, Ralph G.

2014-09-01

The rank-based nonlinear predictability score was recently introduced as a test for determinism in point processes. We here adapt this measure to time series sampled from time-continuous flows. We use noisy Lorenz signals to compare this approach against a classical amplitude-based nonlinear prediction error. Both measures show an almost identical robustness against Gaussian white noise. In contrast, when the amplitude distribution of the noise has a narrower central peak and heavier tails than the normal distribution, the rank-based nonlinear predictability score outperforms the amplitude-based nonlinear prediction error. For this type of noise, the nonlinear predictability score has a higher sensitivity for deterministic structure in noisy signals. It also yields a higher statistical power in a surrogate test of the null hypothesis of linear stochastic correlated signals. We show the high relevance of this improved performance in an application to electroencephalographic (EEG) recordings from epilepsy patients. Here the nonlinear predictability score again appears of higher sensitivity to nonrandomness. Importantly, it yields an improved contrast between signals recorded from brain areas where the first ictal EEG signal changes were detected (focal EEG signals) versus signals recorded from brain areas that were not involved at seizure onset (nonfocal EEG signals).

Seasonal flows of international British Columbia-Alaska rivers: The nonlinear influence of ocean-atmosphere circulation patterns

USGS Publications Warehouse

Fleming, Sean W.; Hood, Eran; Dalhke, Helen; O'Neel, Shad

2016-01-01

The northern portion of the Pacific coastal temperate rainforest (PCTR) is one of the least anthropogenically modified regions on earth and remains in many respects a frontier area to science. Rivers crossing the northern PCTR, which is also an international boundary region between British Columbia, Canada and Alaska, USA, deliver large freshwater and biogeochemical fluxes to the Gulf of Alaska and establish linkages between coastal and continental ecosystems. We evaluate interannual flow variability in three transboundary PCTR watersheds in response to El Niño-Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO), Arctic Oscillation (AO), and North Pacific Gyre Oscillation (NPGO). Historical hydroclimatic datasets from both Canada and the USA are analyzed using an up-to-date methodological suite accommodating both seasonally transient and highly nonlinear teleconnections. We find that streamflow teleconnections occur over particular seasonal windows reflecting the intersection of specific atmospheric and terrestrial hydrologic processes. The strongest signal is a snowmelt-driven flow timing shift resulting from ENSO- and PDO-associated temperature anomalies. Autumn rainfall runoff is also modulated by these climate modes, and a glacier-mediated teleconnection contributes to a late-summer ENSO-flow association. Teleconnections between AO and freshet flows reflect corresponding temperature and precipitation anomalies. A coherent NPGO signal is not clearly evident in streamflow. Linear and monotonically nonlinear teleconnections were widely identified, with less evidence for the parabolic effects that can play an important role elsewhere. The streamflow teleconnections did not vary greatly between hydrometric stations, presumably reflecting broad similarities in watershed characteristics. These results establish a regional foundation for both transboundary water management and studies of long-term hydroclimatic and environmental change.

Active Control of Panel Vibrations Induced by a Boundary Layer Flow

NASA Technical Reports Server (NTRS)

Chow, Pao-Liu

1998-01-01

In recent years, active and passive control of sound and vibration in aeroelastic structures have received a great deal of attention due to many potential applications to aerospace and other industries. There exists a great deal of research work done in this area. Recent advances in the control of sound and vibration can be found in the several conference proceedings. In this report we will summarize our research findings supported by the NASA grant NAG-1-1175. The problems of active and passive control of sound and vibration has been investigated by many researchers for a number of years. However, few of the articles are concerned with the sound and vibration with flow-structure interaction. Experimental and numerical studies on the coupling between panel vibration and acoustic radiation due to flow excitation have been done by Maestrello and his associates at NASA/Langley Research Center. Since the coupled system of nonlinear partial differential equations is formidable, an analytical solution to the full problem seems impossible. For this reason, we have to simplify the problem to that of the nonlinear panel vibration induced by a uniform flow or a boundary-layer flow with a given wall pressure distribution. Based on this simplified model, we have been able to study the control and stabilization of the nonlinear panel vibration, which have not been treated satisfactorily by other authors. The vibration suppression will clearly reduce the sound radiation power from the panel. The major research findings will be presented in the next three sections. In Section II we shall describe our results on the boundary control of nonlinear panel vibration, with or without flow excitation. Section III is concerned with active control of the vibration and sound radiation from a nonlinear elastic panel. A detailed description of our work on the parametric vibrational control of nonlinear elastic panel will be presented in Section IV. This paper will be submitted to the Journal of Acoustic Society of America for publication.

Evolution of Channels Draining Mount St. Helens: Linking Non-Linear and Rapid, Threshold Responses

NASA Astrophysics Data System (ADS)

Simon, A.

2010-12-01

The catastrophic eruption of Mount St. Helens buried the valley of the North Fork Toutle River (NFT) to a depth of up to 140 m. Initial integration of a new drainage network took place episodically by the “filling and spilling” (from precipitation and seepage) of depressions formed during emplacement of the debris avalanche deposit. Channel incision to depths of 20-30 m occurred in the debris avalanche and extensive pyroclastic flow deposits, and headward migration of the channel network followed, with complete integration taking place within 2.5 years. Downstream reaches were converted from gravel-cobble streams with step-pool sequences to smoothed, infilled channels dominated by sand-sized materials. Subsequent channel evolution was dominated by channel widening with the ratio of changes in channel width to changes in channel depth ranging from about 60 to 100. Widening resulted in significant adjustment of hydraulic variables that control sediment-transport rates. For a given discharge over time, flow depths were reduced, relative roughness increased and flow velocity and boundary shear stress decreased non-linearly. These changes, in combination with coarsening of the channel bed with time resulted in systematically reduced rates of degradation (in upstream reaches), aggradation (in downstream reaches) and sediment-transport rates through much of the 1990s. Vertical adjustments were, therefore, easy to characterize with non-linear decay functions with bed-elevation attenuating with time. An empirical model of bed-level response was then created by plotting the total dimensionless change in elevation against river kilometer for both initial and secondary vertical adjustments. High magnitude events generated from the generated from upper part of the mountain, however, can cause rapid (threshold) morphologic changes. For example, a rain-on-snow event in November 2006 caused up to 9 m of incision along a 6.5 km reach of Loowit Creek and the upper NFT. The event triggered a debris flow which cutoff tributary channels to Glacier Creek and redirected Step and Loowit Creeks thereby forcing enhanced flow volumes through the main channel. Very coarse, armored bed materials were mobilized allowing for deep incision into the substrate. Incision continues today at slower rates but it is again the lateral shifting and widening of the channels that is dominant. Low and moderate flows undercut the toe of 30 m-high pyroclastic flow deposits causing significant erosion. As the channel continues to widen incision will attenuate non-linearly. Channels such as the multiple Step Creek channels will coalesce as narrow ridges erode by undercutting and mass failure much as reaches of lower Loowit Creek did in the late 1980’s. The resulting enlarged and over-widened sections will then again (as in downstream reaches) have lowered transporting power.

Direct numerical simulations of premixed autoignition in compressible uniformly-sheared turbulence

NASA Astrophysics Data System (ADS)

Towery, Colin; Darragh, Ryan; Poludnenko, Alexei; Hamlington, Peter

2017-11-01

High-speed combustion systems, such as scramjet engines, operate at high temperatures and pressures, extremely short combustor residence times, very high rates of shear stress, and intense turbulent mixing. As a result, the reacting flow can be premixed and have highly-compressible turbulence fluctuations. We investigate the effects of compressible turbulence on the ignition delay time, heat-release-rate (HRR) intermittency, and mode of autoignition of premixed Hydrogen-air fuel in uniformly-sheared turbulence using new three-dimensional direct numerical simulations with a multi-step chemistry mechanism. We analyze autoignition in both the Eulerian and Lagrangian reference frames at eight different turbulence Mach numbers, Mat , spanning the quasi-isentropic, linear thermodynamic, and nonlinear compressibility regimes, with eddy shocklets appearing in the nonlinear regime. Results are compared to our previous study of premixed autoignition in isotropic turbulence at the same Mat and with a single-step reaction mechanism. This previous study found large decreases in delay times and large increases in HRR intermittency between the linear and nonlinear compressibility regimes and that detonation waves could form in both regimes.

Nonlinear Response of Iceberg Melting to Ocean Currents

NASA Astrophysics Data System (ADS)

Cenedese, C.; FitzMaurice, A.; Straneo, F.

2017-12-01

Icebergs calving into Greenlandic Fjords frequently experience strongly sheared flows over their draft, but the impact of this flow past the iceberg on the melt plumes generated along the iceberg sides is not fully captured by existing parameterizations. We present a series of novel laboratory experiments to determine the dependence of side submarine melt rates on a background flow. We show, for the first time, that two distinct regimes of melting exist depending on the melt plume behavior (side-attached or side-detached). These two regimes produce a nonlinear dependence of melt rate on velocity, and different distributions of meltwater in the water column. Iceberg meltwater may either be confined to a thin surface layer, when the melt plumes are side-attached, or mixed down to the iceberg draft, when the melt plumes are side-detached. In a two-layer vertically sheared flow the average flow speed in existing melt parameterizations gives an underestimate of the submarine melt rate, in part due to the nonlinearity of the dependence of melt rate on flow speed, but also because vertical shear in the velocity profile fundamentally changes the flow splitting around the ice block and consequently the velocity felt by the ice surface. Including this nonlinear velocity dependence in melting parameterizations applied to observed icebergs increases iceberg side melt in the attached regime, improving agreement with observations of iceberg submarine melt rates. We show that both attached and detached plume regimes are relevant to icebergs observed in a Greenland fjord.

Nonlinear dynamics and intermittency in a turbulent reacting wake with density ratio as bifurcation parameter

NASA Astrophysics Data System (ADS)

Suresha, Suhas; Sujith, R. I.; Emerson, Benjamin; Lieuwen, Tim

2016-10-01

The flame or flow behavior of a turbulent reacting wake is known to be fundamentally different at high and low values of flame density ratio (ρu/ρb ), as the flow transitions from globally stable to unstable. This paper analyzes the nonlinear dynamics present in a bluff-body stabilized flame, and identifies the transition characteristics in the wake as ρu/ρb is varied over a Reynolds number (based on the bluff-body lip velocity) range of 1000-3300. Recurrence quantification analysis (RQA) of the experimentally obtained time series of the flame edge fluctuations reveals that the time series is highly aperiodic at high values of ρu/ρb and transitions to increasingly correlated or nearly periodic behavior at low values. From the RQA of the transverse velocity time series, we observe that periodicity in the flame oscillations are related to periodicity in the flow. Therefore, we hypothesize that this transition from aperiodic to nearly periodic behavior in the flame edge time series is a manifestation of the transition in the flow from globally stable, convective instability to global instability as ρu/ρb decreases. The recurrence analysis further reveals that the transition in periodicity is not a sudden shift; rather it occurs through an intermittent regime present at low and intermediate ρu/ρb . During intermittency, the flow behavior switches between aperiodic oscillations, reminiscent of a globally stable, convective instability, and periodic oscillations, reminiscent of a global instability. Analysis of the distribution of the lengths of the periodic regions in the intermittent time series and the first return map indicate the presence of type-II intermittency.

Flow and diffusion of high-stakes test scores.

PubMed

Marder, M; Bansal, D

2009-10-13

We apply visualization and modeling methods for convective and diffusive flows to public school mathematics test scores from Texas. We obtain plots that show the most likely future and past scores of students, the effects of random processes such as guessing, and the rate at which students appear in and disappear from schools. We show that student outcomes depend strongly upon economic class, and identify the grade levels where flows of different groups diverge most strongly. Changing the effectiveness of instruction in one grade naturally leads to strongly nonlinear effects on student outcomes in subsequent grades.

Nonlinear dynamics of an elliptic vortex embedded in an oscillatory shear flow.

PubMed

Ryzhov, Eugene A

2017-11-01

The nonlinear dynamics of an elliptic vortex subjected to a time-periodic linear external shear flow is studied numerically. Making use of the ideas from the theory of nonlinear resonance overlaps, the study focuses on the appearance of chaotic regimes in the ellipse dynamics. When the superimposed flow is stationary, two general types of the steady-state phase portrait are considered: one that features a homoclinic separatrix delineating bounded and unbounded phase trajectories and one without a separatrix (all the phase trajectories are bounded in a periodic domain). When the external flow is time-periodic, the ensuing nonlinear dynamics differs significantly in both cases. For the case with a separatrix and two distinct types of phase trajectories: bounded and unbounded, the effect of the most influential nonlinear resonance with the winding number of 1:1 is analyzed in detail. Namely, the process of occupying the central stability region associated with the steady-state elliptic critical point by the stability region associated with the nonlinear resonance of 1:1 as the perturbation frequency gradually varies is investigated. A stark increase in the persistence of the central regular dynamics region against perturbation when the resonance of 1:1 associated stability region occupies the region associated with the steady-state elliptic critical point is observed. An analogous persistence of the regular motion occurs for higher perturbation frequencies when the corresponding stability islands reach the central stability region associated with the steady-state elliptic point. An analysis for the case with the resonance of 1:2 is presented. For the second case with only bounded phase trajectories and, therefore, no separatrix, the appearance of much bigger stability islands associated with nonlinear resonances compared with the case with a separatrix is reported.

Stabilization of domain walls between traveling waves by nonlinear mode coupling in Taylor-Couette flow.

PubMed

Heise, M; Hoffmann, Ch; Abshagen, J; Pinter, A; Pfister, G; Lücke, M

2008-02-15

We present a new mechanism that allows the stable existence of domain walls between oppositely traveling waves in pattern-forming systems far from onset. It involves a nonlinear mode coupling that results directly from the nonlinearities in the underlying momentum balance. Our work provides the first observation and explanation of such strongly nonlinearly driven domain walls that separate structured states by a phase generating or annihilating defect. Furthermore, the influence of a symmetry breaking externally imposed flow on the wave domains and the domain walls is studied. The results are obtained for vortex waves in the Taylor-Couette system by combining numerical simulations of the full Navier-Stokes equations and experimental measurements.

Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-01-01

The propagation of three-dimensional nonlinear irrotational flow of an inviscid and incompressible fluid of the long waves in dispersive shallow-water approximation is analyzed. The problem formulation of the long waves in dispersive shallow-water approximation lead to fifth-order Kadomtsev-Petviashvili (KP) dynamical equation by applying the reductive perturbation theory. By using an extended auxiliary equation method, the solitary travelling-wave solutions of the two-dimensional nonlinear fifth-order KP dynamical equation are derived. An analytical as well as a numerical solution of the two-dimensional nonlinear KP equation are obtained and analyzed with the effects of external pressure flow.

On MHD nonlinear stretching flow of Powell-Eyring nanomaterial

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Sajjad, Rai; Muhammad, Taseer; Alsaedi, Ahmed; Ellahi, Rahmat

This communication addresses the magnetohydrodynamic (MHD) flow of Powell-Eyring nanomaterial bounded by a nonlinear stretching sheet. Novel features regarding thermophoresis and Brownian motion are taken into consideration. Powell-Eyring fluid is electrically conducted subject to non-uniform applied magnetic field. Assumptions of small magnetic Reynolds number and boundary layer approximation are employed in the mathematical development. Zero nanoparticles mass flux condition at the sheet is selected. Adequate transformation yield nonlinear ordinary differential systems. The developed nonlinear systems have been computed through the homotopic approach. Effects of different pertinent parameters on velocity, temperature and concentration fields are studied and analyzed. Further numerical data of skin friction and heat transfer rate is also tabulated and interpreted.

Geostrophic adjustment in a shallow-water numerical model as it relates to thermospheric dynamics

NASA Technical Reports Server (NTRS)

Larsen, M. F.; Mikkelsen, I. S.

1986-01-01

The theory of geostrophic adjustment and its application to the dynamics of the high latitude thermosphere have been discussed in previous papers based on a linearized treatment of the fluid dynamical equations. However, a linearized treatment is only valid for small Rossby numbers given by Ro = V/fL, where V is the wind speed, f is the local value of the Coriolis parameter, and L is a characteristic horizontal scale for the flow. For typical values in the auroral zone, the approximation is not reasonable for wind speeds greater than 25 m/s or so. A shallow-water (one layer) model was developed that includes the spherical geometry and full nonlinear dynamics in the momentum equations in order to isolate the effects of the nonlinearities on the adjustment process. A belt of accelerated winds between 60 deg and 70 deg latitude was used as the initial condition. The adjustment process was found to proceed as expected from the linear formulation, but that an asymmetry between the response for an eastward and westward flow results from the nonlineawr curvature (centrifugal) terms. In general, the amplitude of an eastward flowing wind will be less after adjustment than a westward wind. For instance, if the initial wind velocity is 300 m/s, the linearized theory predicts a final wind speed of 240 m/s, regardless of the flow direction. However, the nonlinear curvature terms modify the response and produce a final wind speed of only 200 m/s for an initial eastward wind and a final wind speed of almost 300 m/s for an initial westward flow direction. Also, less gravity wave energy is produced by the adjustment of the westward flow than by the adjustment of the eastward flow. The implications are that the response of the thermosphere should be significantly different on the dawn and dusk sides of the auroral oval. Larger flow velocities would be expected on the dusk side since the plasma will accelerate the flow in a westward direction in that sector.

Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier–Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balajewicz, Maciej; Tezaur, Irina; Dowell, Earl

For a projection-based reduced order model (ROM) of a fluid flow to be stable and accurate, the dynamics of the truncated subspace must be taken into account. This paper proposes an approach for stabilizing and enhancing projection-based fluid ROMs in which truncated modes are accounted for a priori via a minimal rotation of the projection subspace. Attention is focused on the full non-linear compressible Navier–Stokes equations in specific volume form as a step toward a more general formulation for problems with generic non-linearities. Unlike traditional approaches, no empirical turbulence modeling terms are required, and consistency between the ROM and themore » Navier–Stokes equation from which the ROM is derived is maintained. Mathematically, the approach is formulated as a trace minimization problem on the Stiefel manifold. As a result, the reproductive as well as predictive capabilities of the method are evaluated on several compressible flow problems, including a problem involving laminar flow over an airfoil with a high angle of attack, and a channel-driven cavity flow problem.« less

Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier–Stokes equations

DOE PAGES

Balajewicz, Maciej; Tezaur, Irina; Dowell, Earl

2016-05-25

For a projection-based reduced order model (ROM) of a fluid flow to be stable and accurate, the dynamics of the truncated subspace must be taken into account. This paper proposes an approach for stabilizing and enhancing projection-based fluid ROMs in which truncated modes are accounted for a priori via a minimal rotation of the projection subspace. Attention is focused on the full non-linear compressible Navier–Stokes equations in specific volume form as a step toward a more general formulation for problems with generic non-linearities. Unlike traditional approaches, no empirical turbulence modeling terms are required, and consistency between the ROM and themore » Navier–Stokes equation from which the ROM is derived is maintained. Mathematically, the approach is formulated as a trace minimization problem on the Stiefel manifold. As a result, the reproductive as well as predictive capabilities of the method are evaluated on several compressible flow problems, including a problem involving laminar flow over an airfoil with a high angle of attack, and a channel-driven cavity flow problem.« less

On nonlinear Tollmien-Schlichting/vortex interaction in three-dimensional boundary layers

NASA Technical Reports Server (NTRS)

Davis, Dominic A. R.; Smith, Frank T.

1993-01-01

The instability of an incompressible three-dimensional boundary layer (that is, one with cross-flow) is considered theoretically and computationally in the context of vortex/wave interactions. Specifically the work centers on two low amplitude, lower-branch Tollmien-Schlichting waves which mutually interact to induce a weak longitudinal vortex flow; the vortex motion, in turn, gives rise to significant wave-modulation via wall-shear forcing. The characteristic Reynolds number is taken as a large parameter and, as a consequence, the waves' and the vortex motion are governed primarily by triple-deck theory. The nonlinear interaction is captured by a viscous partial-differential system for the vortex coupled with a pair of amplitude equations for each wave pressure. Three distinct possibilities were found to emerge for the nonlinear behavior of the flow solution downstream - an algebraic finite-distance singularity, far downstream saturation or far-downstream wave-decay (leaving pure vortex flow) - depending on the input conditions, the wave angles, and the size of the cross-flow.

Nonlinear Convective Flows in a Laterally Heated Two-Layer System with a Temperature-Dependent Heat Release/Consumption at the Interface

NASA Astrophysics Data System (ADS)

Simanovskii, Ilya; Viviani, Antonio; Dubois, Frank; Queeckers, Patrick

2018-01-01

Nonlinear convective flows developed under the joint action of buoyant and thermocapillary effects in a laterally heated two-layer system filling the closed cavity, have been investigated. The influence of a temperature-dependent interfacial heat release/consumption on nonlinear steady and oscillatory regimes, has been studied. It is shown that sufficiently strong temperature dependence of interfacial heat sinks and heat sources can change the sequence of bifurcations and lead to the development of specific oscillatory regimes in the system.

Flow-pattern identification and nonlinear dynamics of gas-liquid two-phase flow in complex networks.

PubMed

Gao, Zhongke; Jin, Ningde

2009-06-01

The identification of flow pattern is a basic and important issue in multiphase systems. Because of the complexity of phase interaction in gas-liquid two-phase flow, it is difficult to discern its flow pattern objectively. In this paper, we make a systematic study on the vertical upward gas-liquid two-phase flow using complex network. Three unique network construction methods are proposed to build three types of networks, i.e., flow pattern complex network (FPCN), fluid dynamic complex network (FDCN), and fluid structure complex network (FSCN). Through detecting the community structure of FPCN by the community-detection algorithm based on K -mean clustering, useful and interesting results are found which can be used for identifying five vertical upward gas-liquid two-phase flow patterns. To investigate the dynamic characteristics of gas-liquid two-phase flow, we construct 50 FDCNs under different flow conditions, and find that the power-law exponent and the network information entropy, which are sensitive to the flow pattern transition, can both characterize the nonlinear dynamics of gas-liquid two-phase flow. Furthermore, we construct FSCN and demonstrate how network statistic can be used to reveal the fluid structure of gas-liquid two-phase flow. In this paper, from a different perspective, we not only introduce complex network theory to the study of gas-liquid two-phase flow but also indicate that complex network may be a powerful tool for exploring nonlinear time series in practice.

Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation

NASA Astrophysics Data System (ADS)

Kamchatnov, A. M.; Kuo, Y.-H.; Lin, T.-C.; Horng, T.-L.; Gou, S.-C.; Clift, R.; El, G. A.; Grimshaw, R. H. J.

2013-12-01

Transcritical flow of a stratified fluid past a broad localised topographic obstacle is studied analytically in the framework of the forced extended Korteweg--de Vries (eKdV), or Gardner, equation. We consider both possible signs for the cubic nonlinear term in the Gardner equation corresponding to different fluid density stratification profiles. We identify the range of the input parameters: the oncoming flow speed (the Froude number) and the topographic amplitude, for which the obstacle supports a stationary localised hydraulic transition from the subcritical flow upstream to the supercritical flow downstream. Such a localised transcritical flow is resolved back into the equilibrium flow state away from the obstacle with the aid of unsteady coherent nonlinear wave structures propagating upstream and downstream. Along with the regular, cnoidal undular bores occurring in the analogous problem for the single-layer flow modeled by the forced KdV equation, the transcritical internal wave flows support a diverse family of upstream and downstream wave structures, including solibores, rarefaction waves, reversed and trigonometric undular bores, which we describe using the recent development of the nonlinear modulation theory for the (unforced) Gardner equation. The predictions of the developed analytic construction are confirmed by direct numerical simulations of the forced Gardner equation for a broad range of input parameters.

EDITORIAL: Measurement techniques for multiphase flows Measurement techniques for multiphase flows

NASA Astrophysics Data System (ADS)

Okamoto, Koji; Murai, Yuichi

2009-11-01

Research on multiphase flows is very important for industrial applications, including power stations, vehicles, engines, food processing and so on. Multiphase flows originally have nonlinear features because of multiphase systems. The interaction between the phases plays a very interesting role in the flows. The nonlinear interaction causes the multiphase flows to be very complicated. Therefore techniques for measuring multiphase flows are very useful in helping to understand the nonlinear phenomena. The state-of-the-art measurement techniques were presented and discussed at the sixth International Symposium on Measurement Techniques for Multiphase Flows (ISMTMF2008) held in Okinawa, Japan, on 15-17 December 2008. This special feature of Measurement Science and Technology includes selected papers from ISMTMF2008. Okinawa has a long history as the Ryukyus Kingdom. China, Japan and many western Pacific countries have had cultural and economic exchanges through Okinawa for over 1000 years. Much technical and scientific information was exchanged at the symposium in Okinawa. The proceedings of ISMTMF2008 apart from these special featured papers were published in Journal of Physics: Conference Series vol. 147 (2009). We would like to express special thanks to all the contributors to the symposium and this special feature. This special feature will be a milestone in measurement techniques for multiphase flows.

Nonlinear Stability and Structure of Compressible Reacting Mixing Layers

NASA Technical Reports Server (NTRS)

Day, M. J.; Mansour, N. N.; Reynolds, W. C.

2000-01-01

The parabolized stability equations (PSE) are used to investigate issues of nonlinear flow development and mixing in compressible reacting shear layers. Particular interest is placed on investigating the change in flow structure that occurs when compressibility and heat release are added to the flow. These conditions allow the 'outer' instability modes- one associated with each of the fast and slow streams-to dominate over the 'central', Kelvin-Helmholtz mode that unaccompanied in incompressible nonreacting mixing layers. Analysis of scalar probability density functions in flows with dominant outer modes demonstrates the ineffective, one-sided nature of mixing that accompany these flow structures. Colayer conditions, where two modes have equal growth rate and the mixing layer is formed by two sets of vortices, offer some opportunity for mixing enhancement. Their extent, however, is found to be limited in the mixing layer's parameter space. Extensive validation of the PSE technique also provides a unique perspective on central- mode vortex pairing, further supporting the view that pairing is primarily governed perspective sheds insight on how linear stability theory is able to provide such an accurate prediction of experimentally-observed, fully nonlinear flow phenomenon.

Numerical Investigations of High Pressure Acoustic Waves in Resonators

NASA Technical Reports Server (NTRS)

Athavale, Mahesh; Pindera, Maciej; Daniels, Christopher C.; Steinetz, Bruce M.

2004-01-01

This presentation presents work on numerical investigations of nonlinear acoustic phenomena in resonators that can generate high-pressure waves using acoustic forcing of the flow. Time-accurate simulations of the flow in a closed cone resonator were performed at different oscillation frequencies and amplitudes, and the numerical results for the resonance frequency and fluid pressure increase match the GRC experimental data well. Work on cone resonator assembly simulations has started and will involve calculations of the flow through the resonator assembly with and without acoustic excitation. A new technique for direct calculation of resonance frequency of complex shaped resonators is also being investigated. Script-driven command procedures will also be developed for optimization of the resonator shape for maximum pressure increase.

Long-lived fluctuations driven by shear flows

NASA Astrophysics Data System (ADS)

Kim, J.-H.; Horton, W.; Morrison, P.; Chagelishvili, G. D.; Gogoberidze, G.; Dahlburg, R.

2004-11-01

In flows that are stable in accordance to the Rayleigh criterion there are long lived transient fluctuations that can lead to the onset of turbulence. We show examples of transitions to turbulence due to the positive nonlinear feedback from the transients. Simulations show that the intensity of the nonlinear decay processes depends on the angle between wave vectors of the interacting spatial Fourier harmonics. Positive nonlinear feedback occurs when vorticities of the perturbation are the same direction. Above some amplitude the cyclonic perturbation is self-sustained due to the feedback loop. Generalization and applications of the simulations for atmospheric and plasma flows are discussed. This work was supported in part by the Department of Energy Grant No. DE-FG03-96ER-54346 and ISTC Grant G-5333.

Non-linear osmosis

PubMed Central

Diamond, Jared M.

1966-01-01

1. The relation between osmotic gradient and rate of osmotic water flow has been measured in rabbit gall-bladder by a gravimetric procedure and by a rapid method based on streaming potentials. Streaming potentials were directly proportional to gravimetrically measured water fluxes. 2. As in many other tissues, water flow was found to vary with gradient in a markedly non-linear fashion. There was no consistent relation between the water permeability and either the direction or the rate of water flow. 3. Water flow in response to a given gradient decreased at higher osmolarities. The resistance to water flow increased linearly with osmolarity over the range 186-825 m-osM. 4. The resistance to water flow was the same when the gall-bladder separated any two bathing solutions with the same average osmolarity, regardless of the magnitude of the gradient. In other words, the rate of water flow is given by the expression (Om — Os)/[Ro′ + ½k′ (Om + Os)], where Ro′ and k′ are constants and Om and Os are the bathing solution osmolarities. 5. Of the theories advanced to explain non-linear osmosis in other tissues, flow-induced membrane deformations, unstirred layers, asymmetrical series-membrane effects, and non-osmotic effects of solutes could not explain the results. However, experimental measurements of water permeability as a function of osmolarity permitted quantitative reconstruction of the observed water flow—osmotic gradient curves. Hence non-linear osmosis in rabbit gall-bladder is due to a decrease in water permeability with increasing osmolarity. 6. The results suggest that aqueous channels in the cell membrane behave as osmometers, shrinking in concentrated solutions of impermeant molecules and thereby increasing membrane resistance to water flow. A mathematical formulation of such a membrane structure is offered. PMID:5945254

Pressure-anisotropy-induced nonlinearities in the kinetic magnetorotational instability

NASA Astrophysics Data System (ADS)

Squire, J.; Quataert, E.; Kunz, M. W.

2017-12-01

In collisionless and weakly collisional plasmas, such as hot accretion flows onto compact objects, the magnetorotational instability (MRI) can differ significantly from the standard (collisional) MRI. In particular, pressure anisotropy with respect to the local magnetic-field direction can both change the linear MRI dispersion relation and cause nonlinear modifications to the mode structure and growth rate, even when the field and flow perturbations are very small. This work studies these pressure-anisotropy-induced nonlinearities in the weakly nonlinear, high-ion-beta regime, before the MRI saturates into strong turbulence. Our goal is to better understand how the saturation of the MRI in a low-collisionality plasma might differ from that in the collisional regime. We focus on two key effects: (i) the direct impact of self-induced pressure-anisotropy nonlinearities on the evolution of an MRI mode, and (ii) the influence of pressure anisotropy on the `parasitic instabilities' that are suspected to cause the mode to break up into turbulence. Our main conclusions are: (i) The mirror instability regulates the pressure anisotropy in such a way that the linear MRI in a collisionless plasma is an approximate nonlinear solution once the mode amplitude becomes larger than the background field (just as in magnetohyrodynamics). This implies that differences between the collisionless and collisional MRI become unimportant at large amplitudes. (ii) The break up of large-amplitude MRI modes into turbulence via parasitic instabilities is similar in collisionless and collisional plasmas. Together, these conclusions suggest that the route to magnetorotational turbulence in a collisionless plasma may well be similar to that in a collisional plasma, as suggested by recent kinetic simulations. As a supplement to these findings, we offer guidance for the design of future kinetic simulations of magnetorotational turbulence.

Towards adjoint-based inversion for rheological parameters in nonlinear viscous mantle flow

NASA Astrophysics Data System (ADS)

Worthen, Jennifer; Stadler, Georg; Petra, Noemi; Gurnis, Michael; Ghattas, Omar

2014-09-01

We address the problem of inferring mantle rheological parameter fields from surface velocity observations and instantaneous nonlinear mantle flow models. We formulate this inverse problem as an infinite-dimensional nonlinear least squares optimization problem governed by nonlinear Stokes equations. We provide expressions for the gradient of the cost functional of this optimization problem with respect to two spatially-varying rheological parameter fields: the viscosity prefactor and the exponent of the second invariant of the strain rate tensor. Adjoint (linearized) Stokes equations, which are characterized by a 4th order anisotropic viscosity tensor, facilitates efficient computation of the gradient. A quasi-Newton method for the solution of this optimization problem is presented, which requires the repeated solution of both nonlinear forward Stokes and linearized adjoint Stokes equations. For the solution of the nonlinear Stokes equations, we find that Newton’s method is significantly more efficient than a Picard fixed point method. Spectral analysis of the inverse operator given by the Hessian of the optimization problem reveals that the numerical eigenvalues collapse rapidly to zero, suggesting a high degree of ill-posedness of the inverse problem. To overcome this ill-posedness, we employ Tikhonov regularization (favoring smooth parameter fields) or total variation (TV) regularization (favoring piecewise-smooth parameter fields). Solution of two- and three-dimensional finite element-based model inverse problems show that a constant parameter in the constitutive law can be recovered well from surface velocity observations. Inverting for a spatially-varying parameter field leads to its reasonable recovery, in particular close to the surface. When inferring two spatially varying parameter fields, only an effective viscosity field and the total viscous dissipation are recoverable. Finally, a model of a subducting plate shows that a localized weak zone at the plate boundary can be partially recovered, especially with TV regularization.

Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow

NASA Astrophysics Data System (ADS)

Mamatsashvili, G.; Stefani, F.; Guseva, A.; Avila, M.

2018-01-01

Magnetorotational instability (MRI) is one of the fundamental processes in astrophysics, driving angular momentum transport and mass accretion in a wide variety of cosmic objects. Despite much theoretical/numerical and experimental efforts over the last decades, its saturation mechanism and amplitude, which sets the angular momentum transport rate, remains not well understood, especially in the limit of high resistivity, or small magnetic Prandtl numbers typical to interiors (dead zones) of protoplanetary disks, liquid cores of planets and liquid metals in laboratory. Using direct numerical simulations, in this paper we investigate the nonlinear development and saturation properties of the helical magnetorotational instability (HMRI)—a relative of the standard MRI—in a magnetized Taylor-Couette flow at very low magnetic Prandtl number (correspondingly at low magnetic Reynolds number) relevant to liquid metals. For simplicity, the ratio of azimuthal field to axial field is kept fixed. From the linear theory of HMRI, it is known that the Elsasser number, or interaction parameter determines its growth rate and plays a special role in the dynamics. We show that this parameter is also important in the nonlinear problem. By increasing its value, a sudden transition from weakly nonlinear, where the system is slightly above the linear stability threshold, to strongly nonlinear, or turbulent regime occurs. We calculate the azimuthal and axial energy spectra corresponding to these two regimes and show that they differ qualitatively. Remarkably, the nonlinear state remains in all cases nearly axisymmetric suggesting that this HMRI-driven turbulence is quasi two-dimensional in nature. Although the contribution of non-axisymmetric modes increases moderately with the Elsasser number, their total energy remains much smaller than that of the axisymmetric ones.

The U.S. Geological Survey Modular Ground-Water Model - PCGN: A Preconditioned Conjugate Gradient Solver with Improved Nonlinear Control

USGS Publications Warehouse

Naff, Richard L.; Banta, Edward R.

2008-01-01

The preconditioned conjugate gradient with improved nonlinear control (PCGN) package provides addi-tional means by which the solution of nonlinear ground-water flow problems can be controlled as compared to existing solver packages for MODFLOW. Picard iteration is used to solve nonlinear ground-water flow equations by iteratively solving a linear approximation of the nonlinear equations. The linear solution is provided by means of the preconditioned conjugate gradient algorithm where preconditioning is provided by the modi-fied incomplete Cholesky algorithm. The incomplete Cholesky scheme incorporates two levels of fill, 0 and 1, in which the pivots can be modified so that the row sums of the preconditioning matrix and the original matrix are approximately equal. A relaxation factor is used to implement the modified pivots, which determines the degree of modification allowed. The effects of fill level and degree of pivot modification are briefly explored by means of a synthetic, heterogeneous finite-difference matrix; results are reported in the final section of this report. The preconditioned conjugate gradient method is coupled with Picard iteration so as to efficiently solve the nonlinear equations associated with many ground-water flow problems. The description of this coupling of the linear solver with Picard iteration is a primary concern of this document.

A nonlinear approach to transition in subcritical plasmas with sheared flow

NASA Astrophysics Data System (ADS)

Pringle, Chris C. T.; McMillan, Ben F.; Teaca, Bogdan

2017-12-01

In many plasma systems, introducing a small background shear flow is enough to stabilize the system linearly. The nonlinear dynamics are much less sensitive to sheared flows than the average linear growth rates, and very small amplitude perturbations can lead to sustained turbulence. We explore the general problem of characterizing how and when the transition from near-laminar states to sustained turbulence occurs, with a model of the interchange instability being used as a concrete example. These questions are fundamentally nonlinear, and the answers must go beyond the linear transient amplification of small perturbations. Two methods that account for nonlinear interactions are therefore explored here. The first method explored is edge tracking, which identifies the boundary between the basins of attraction of the laminar and turbulent states. Here, the edge is found to be structured around an exact, localized, traveling wave solution that is qualitatively similar to avalanche-like bursts seen in the turbulent regime. The second method is an application of nonlinear, non-modal stability theory which allows us to identify the smallest disturbances which can trigger turbulence (the minimal seed for the problem) and hence to quantify how stable the laminar regime is. The results obtained from these fully nonlinear methods provide confidence in the derivation of a semi-analytic approximation for the minimal seed.

The Accuracy of Shock Capturing in Two Spatial Dimensions

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Casper, Jay H.

1997-01-01

An assessment of the accuracy of shock capturing schemes is made for two-dimensional steady flow around a cylindrical projectile. Both a linear fourth-order method and a nonlinear third-order method are used in this study. It is shown, contrary to conventional wisdom, that captured two-dimensional shocks are asymptotically first-order, regardless of the design accuracy of the numerical method. The practical implications of this finding are discussed in the context of the efficacy of high-order numerical methods for discontinuous flows.

Flow characteristics of bounded self-organized dust vortex in a complex plasma

NASA Astrophysics Data System (ADS)

Laishram, Modhuchandra; Sharma, D.; Chattopdhyay, P. K.; Kaw, P. K.

2018-01-01

Dust clouds are often formed in many dusty plasma experiments, when micron size dust particles introduced in the plasma are confined by spatial non-uniformities of the potential. These formations show self-organized patterns like vortex or circulation flows. Steady-state equilibrium dynamics of such dust clouds is analyzed by 2D hydrodynamics for varying Reynolds number, Re, when the cloud is confined in an azimuthally symmetric cylindrical setup by an effective potential and is in a dynamic equilibrium with an unbounded sheared plasma flow. The nonconservative forcing due to ion flow shear generates finite vorticity in the confined dust clouds. In the linear limit (Re ≪ 1), the collective flow is characterized by a single symmetric and elongated vortex with scales correlating with the driving field and those generated by friction with the boundaries. However in the high Re limit, (Re ≥ 1), the nonlinear inertial transport (u . ∇u) is effective and the vortex structure is characterized by an asymmetric equilibrium and emergence of a circular core region with uniform vorticity, over which the viscous stress is negligible. The core domain is surrounded by a virtual boundary of highly convective flow followed by thin shear layers filled with low-velocity co- and counter-rotating vortices, enabling the smooth matching with external boundary conditions. In linear regime, the effective boundary layer thickness is recovered to scale with the dust kinematic viscosity as Δr ≈ μ1/3 and is modified as Δr ≈ (μL∥/u)1/2 in the nonlinear regime through a critical kinematic viscosity μ∗ that signifies a structural bifurcation of the flow field solutions. The flow characteristics recovered are relevant to many microscopic biological processes at lower Re, as well as gigantic vortex flows such as Jovian great red spot and white ovals at higher Re.

A highly accurate symmetric optical flow based high-dimensional nonlinear spatial normalization of brain images.

PubMed

Wen, Ying; Hou, Lili; He, Lianghua; Peterson, Bradley S; Xu, Dongrong

2015-05-01

Spatial normalization plays a key role in voxel-based analyses of brain images. We propose a highly accurate algorithm for high-dimensional spatial normalization of brain images based on the technique of symmetric optical flow. We first construct a three dimension optical model with the consistency assumption of intensity and consistency of the gradient of intensity under a constraint of discontinuity-preserving spatio-temporal smoothness. Then, an efficient inverse consistency optical flow is proposed with aims of higher registration accuracy, where the flow is naturally symmetric. By employing a hierarchical strategy ranging from coarse to fine scales of resolution and a method of Euler-Lagrange numerical analysis, our algorithm is capable of registering brain images data. Experiments using both simulated and real datasets demonstrated that the accuracy of our algorithm is not only better than that of those traditional optical flow algorithms, but also comparable to other registration methods used extensively in the medical imaging community. Moreover, our registration algorithm is fully automated, requiring a very limited number of parameters and no manual intervention. Copyright © 2015 Elsevier Inc. All rights reserved.

Development of a linearized unsteady Euler analysis for turbomachinery blade rows

NASA Technical Reports Server (NTRS)

Verdon, Joseph M.; Montgomery, Matthew D.; Kousen, Kenneth A.

1995-01-01

A linearized unsteady aerodynamic analysis for axial-flow turbomachinery blading is described in this report. The linearization is based on the Euler equations of fluid motion and is motivated by the need for an efficient aerodynamic analysis that can be used in predicting the aeroelastic and aeroacoustic responses of blade rows. The field equations and surface conditions required for inviscid, nonlinear and linearized, unsteady aerodynamic analyses of three-dimensional flow through a single, blade row operating within a cylindrical duct, are derived. An existing numerical algorithm for determining time-accurate solutions of the nonlinear unsteady flow problem is described, and a numerical model, based upon this nonlinear flow solver, is formulated for the first-harmonic linear unsteady problem. The linearized aerodynamic and numerical models have been implemented into a first-harmonic unsteady flow code, called LINFLUX. At present this code applies only to two-dimensional flows, but an extension to three-dimensions is planned as future work. The three-dimensional aerodynamic and numerical formulations are described in this report. Numerical results for two-dimensional unsteady cascade flows, excited by prescribed blade motions and prescribed aerodynamic disturbances at inlet and exit, are also provided to illustrate the present capabilities of the LINFLUX analysis.

Using Nonlinearity and Contact Lines to Control Fluid Flow in Microgravity

NASA Technical Reports Server (NTRS)

Perlin, M.; Schultz, W. W.; Bian, X.; Agarwal, M.

2002-01-01

Slug flows in a tube are affected by surface tension and contact lines, especially under microgravity. Numerical analyses and experiments are conducted of slug flows in small-diameter tubes with horizontal, inclined and vertical orientations. A PID-controlled, meter-long platform capable of following specified motions is used. An improved understanding of the contact line boundary condition for steady and unsteady contact-line motion is expected. Lastly, a direct fluid-handling method using nonlinear oscillatory motion of a tube is presented.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Isa, Sharena Mohamad; Ali, Anati

In this paper, the hydromagnetic flow of dusty fluid over a vertical stretching sheet with thermal radiation is investigated. The governing partial differential equations are reduced to nonlinear ordinary differential equations using similarity transformation. These nonlinear ordinary differential equations are solved numerically using Runge-Kutta Fehlberg fourth-fifth order method (RKF45 Method). The behavior of velocity and temperature profiles of hydromagnetic fluid flow of dusty fluid is analyzed and discussed for different parameters of interest such as unsteady parameter, fluid-particle interaction parameter, the magnetic parameter, radiation parameter and Prandtl number on the flow.

Magnetohydrodynamic viscous flow over a nonlinearly moving surface: Closed-form solutions

NASA Astrophysics Data System (ADS)

Fang, Tiegang

2014-05-01

In this paper, the magnetohydrodynamic (MHD) flow over a nonlinearly (power-law velocity) moving surface is investigated analytically and solutions are presented for a few special conditions. The solutions are obtained in closed forms with hyperbolic functions. The effects of the magnetic, the wall moving, and the mass transpiration parameters are discussed. These solutions are important to show the flow physics as well as to be used as bench mark problems for numerical validation and development of new solution schemes.

Fluid simulation of tokamak ion temperature gradient turbulence with zonal flow closure model

NASA Astrophysics Data System (ADS)

Yamagishi, Osamu; Sugama, Hideo

2016-03-01

Nonlinear fluid simulation of turbulence driven by ion temperature gradient modes in the tokamak fluxtube configuration is performed by combining two different closure models. One model is a gyrofluid model by Beer and Hammett [Phys. Plasmas 3, 4046 (1996)], and the other is a closure model to reproduce the kinetic zonal flow response [Sugama et al., Phys. Plasmas 14, 022502 (2007)]. By including the zonal flow closure, generation of zonal flows, significant reduction in energy transport, reproduction of the gyrokinetic transport level, and nonlinear upshift on the critical value of gradient scale length are observed.

Fluid simulation of tokamak ion temperature gradient turbulence with zonal flow closure model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yamagishi, Osamu, E-mail: yamagisi@nifs.ac.jp; Sugama, Hideo

Nonlinear fluid simulation of turbulence driven by ion temperature gradient modes in the tokamak fluxtube configuration is performed by combining two different closure models. One model is a gyrofluid model by Beer and Hammett [Phys. Plasmas 3, 4046 (1996)], and the other is a closure model to reproduce the kinetic zonal flow response [Sugama et al., Phys. Plasmas 14, 022502 (2007)]. By including the zonal flow closure, generation of zonal flows, significant reduction in energy transport, reproduction of the gyrokinetic transport level, and nonlinear upshift on the critical value of gradient scale length are observed.

Axisymmetric Powell-Eyring fluid flow over a stretching sheet with a convective boundary condition and suction effects

NASA Astrophysics Data System (ADS)

Nasir, Nor Ain Azeany Mohd; Ishak, Anuar; Pop, Ioan

2018-04-01

In this paper, the heat and mass transfer of an axisymmetric Powell-Eyring fluid flow over a stretching sheet with a convective boundary condition and suction effects are investigated. An appropriate similarity transformation is used to reduce the highly non-linear partial differential equation into second and third order non-linear ordinary differential equations. Numerical solutions of the reduced governing equations are computed numerically by utilizing the MATLAB's built-in boundary value problem solver, bvp4c. The physical significance of various parameters such as Biot number, fluid parameters and Prandtl number on the velocity and temperature evolution profiles are illustrated graphically. The effects of these governing parameters on the skin friction coefficient and the local Nusselt number are also displayed graphically. It is noticed that the Powell-Eyring fluid parameter gives significant influence on the rates of heat and mass transfer of the fluid.

Nonlinear response of dense colloidal suspensions under oscillatory shear: mode-coupling theory and Fourier transform rheology experiments.

PubMed

Brader, J M; Siebenbürger, M; Ballauff, M; Reinheimer, K; Wilhelm, M; Frey, S J; Weysser, F; Fuchs, M

2010-12-01

Using a combination of theory, experiment, and simulation we investigate the nonlinear response of dense colloidal suspensions to large amplitude oscillatory shear flow. The time-dependent stress response is calculated using a recently developed schematic mode-coupling-type theory describing colloidal suspensions under externally applied flow. For finite strain amplitudes the theory generates a nonlinear response, characterized by significant higher harmonic contributions. An important feature of the theory is the prediction of an ideal glass transition at sufficiently strong coupling, which is accompanied by the discontinuous appearance of a dynamic yield stress. For the oscillatory shear flow under consideration we find that the yield stress plays an important role in determining the nonlinearity of the time-dependent stress response. Our theoretical findings are strongly supported by both large amplitude oscillatory experiments (with Fourier transform rheology analysis) on suspensions of thermosensitive core-shell particles dispersed in water and Brownian dynamics simulations performed on a two-dimensional binary hard-disk mixture. In particular, theory predicts nontrivial values of the exponents governing the final decay of the storage and loss moduli as a function of strain amplitude which are in good agreement with both simulation and experiment. A consistent set of parameters in the presented schematic model achieves to jointly describe linear moduli, nonlinear flow curves, and large amplitude oscillatory spectroscopy.

Onset of chaos in helical vortex breakdown at low Reynolds number

NASA Astrophysics Data System (ADS)

Pasche, S.; Avellan, F.; Gallaire, F.

2018-06-01

The nonlinear dynamics of a swirling wake flow stemming from a Graboswksi-Berger vortex [Grabowski and Berger, J. Fluid Mech. 75, 525 (1976), 10.1017/S0022112076000360] in a semi-infinite domain is addressed at low Reynolds numbers for a fixed swirl number S =1.095 , defined as the ratio between the characteristic tangential velocity and the centerline axial velocity. In this system, only pure hydrodynamic instabilities develop and interact through the quadratic nonlinearities of the Navier-Stokes equations. Such interactions lead to the onset of chaos at a Reynolds value of Re=220 . This chaotic state is reached by following a Ruelle-Takens-Newhouse scenario, which is initiated by a Hopf bifurcation (the spiral vortex breakdown) as the Reynolds number increases. At larger Reynolds value, a frequency synchronization regime appears followed by a chaotic state again. This scenario is corroborated by nonlinear time series analyses. Stability analysis around the time-average flow and temporal-azimuthal Fourier decomposition of the nonlinear flow distributions both identify successfully the developing vortices and provide deeper insight into the development of the flow patterns leading to this route to chaos. Three single-helical vortices are involved: the primary spiral associated with the spiral vortex breakdown, a downstream spiral, and a near-wake spiral. As the Reynolds number increases, the frequencies of these vortices become closer, increasing their interactions by nonlinearity to eventually generate a strong chaotic axisymmetric oscillation.

Models for short-wave instability in inviscid shear flows

NASA Astrophysics Data System (ADS)

Grimshaw, Roger

1999-11-01

The generation of instability in an invsicid fluid occurs by a resonance between two wave modes, where here the resonance occurs by a coincidence of phase speeds for a finite, non-zero wavenumber. We show that in the weakly nonlinear limit, the appropriate model consists of two coupled equations for the envelopes of the wave modes, in which the nonlinear terms are balanced with low-order cross-coupling linear dispersive terms rather than the more familiar high-order terms which arise in the nonlinear Schrodinger equation, for instance. We will show that this system may either contain gap solitons as solutions in the linearly stable case, or wave breakdown in the linearly unstable case. In this latter circumstance, the system either exhibits wave collapse in finite time, or disintegration into fine-scale structures.

Using nonlinear ac electrokinetics vortex flow to enhance catalytic activities of sol-gel encapsulated trypsin in microfluidic devices

PubMed Central

Wang, Shau-Chun; Chen, Hsiao-Ping; Lai, Yi-Wen; Chau, Lai-Kwan; Chuang, Yu-Chun; Chen, Yi-Jie

2007-01-01

A novel microstirring strategy is applied to accelerate the digestion rate of the substrate Nα-benzoyl-L-arginine-4-nitroanilide (L-BAPA) catalyzed by sol-gel encapsulated trypsin. We use an ac nonlinear electrokinetic vortex flow to stir the solution in a microfluidic reaction chamber to reduce the diffusion length between the immobilized enzyme and substrate in the solution. High-intensity nonlinear electroosmotic microvortices, with angular speeds in excess of 1 cm∕s, are generated around a small (∼1.2 mm) conductive ion exchange granule when ac electric fields (133 V∕cm) are applied across a miniature chamber smaller than 10 μl. Coupling between these microvortices and the on-and-off electrophoretic motion of the granule in low frequency (0.1 Hz) ac fields produces chaotic stream lines to stir substrate molecules sufficiently. We demonstrate that, within a 5-min digestion period, the catalytic reaction rate of immobilized trypsin increases almost 30-fold with adequate reproducibility (15%) due to sufficient stirring action through the introduction of the nonlinear electrokinetic vortices. In contrast, low-frequency ac electroosmotic flow without the granule, provides limited stirring action and increases the reaction rate approximately ninefold with barely acceptable reproducibility (30%). Dye molecules are used to characterize the increases in solute diffusivity in the reaction reservoir in which sol-gel particles are placed, with and without the presence of granule, and compared with the static case. The solute diffusivity enhancement data show respective increases of ∼30 and ∼8 times, with and without the presence of granule. These numbers are consistent with the ratios of the enhanced reaction rate. PMID:19693360

Using nonlinear ac electrokinetics vortex flow to enhance catalytic activities of sol-gel encapsulated trypsin in microfluidic devices.

PubMed

Wang, Shau-Chun; Chen, Hsiao-Ping; Lai, Yi-Wen; Chau, Lai-Kwan; Chuang, Yu-Chun; Chen, Yi-Jie

2007-09-04

A novel microstirring strategy is applied to accelerate the digestion rate of the substrate N(alpha)-benzoyl-L-arginine-4-nitroanilide (L-BAPA) catalyzed by sol-gel encapsulated trypsin. We use an ac nonlinear electrokinetic vortex flow to stir the solution in a microfluidic reaction chamber to reduce the diffusion length between the immobilized enzyme and substrate in the solution. High-intensity nonlinear electroosmotic microvortices, with angular speeds in excess of 1 cms, are generated around a small ( approximately 1.2 mm) conductive ion exchange granule when ac electric fields (133 Vcm) are applied across a miniature chamber smaller than 10 mul. Coupling between these microvortices and the on-and-off electrophoretic motion of the granule in low frequency (0.1 Hz) ac fields produces chaotic stream lines to stir substrate molecules sufficiently. We demonstrate that, within a 5-min digestion period, the catalytic reaction rate of immobilized trypsin increases almost 30-fold with adequate reproducibility (15%) due to sufficient stirring action through the introduction of the nonlinear electrokinetic vortices. In contrast, low-frequency ac electroosmotic flow without the granule, provides limited stirring action and increases the reaction rate approximately ninefold with barely acceptable reproducibility (30%). Dye molecules are used to characterize the increases in solute diffusivity in the reaction reservoir in which sol-gel particles are placed, with and without the presence of granule, and compared with the static case. The solute diffusivity enhancement data show respective increases of approximately 30 and approximately 8 times, with and without the presence of granule. These numbers are consistent with the ratios of the enhanced reaction rate.

Mathematical problems arising in interfacial electrohydrodynamics

NASA Astrophysics Data System (ADS)

Tseluiko, Dmitri

In this work we consider the nonlinear stability of thin films in the presence of electric fields. We study a perfectly conducting thin film flow down an inclined plane in the presence of an electric field which is uniform in its undisturbed state, and normal to the plate at infinity. In addition, the effect of normal electric fields on films lying above, or hanging from, horizontal substrates is considered. Systematic asymptotic expansions are used to derive fully nonlinear long wave model equations for the scaled interface motion and corresponding flow fields. For the case of an inclined plane, higher order terms are need to be retained to regularize the problem in the sense that the long wave approximation remains valid for long times. For the case of a horizontal plane the fully nonlinear evolution equation which is derived at the leading order, is asymptotically correct and no regularization procedure is required. In both physical situations, the effect of the electric field is to introduce a non-local term which arises from the potential region above the liquid film, and enters through the electric Maxwell stresses at the interface. This term is always linearly destabilizing and produces growth rates proportional to the cubic power of the wavenumber - surface tension is included and provides a short wavelength cut-off, that is, all sufficiently short waves are linearly stable. For the case of film flow down an inclined plane, the fully nonlinear equation can produce singular solutions (for certain parameter values) after a finite time, even in the absence of an electric field. This difficulty is avoided at smaller amplitudes where the weakly nonlinear evolution is governed by an extension of the Kuramoto-Sivashinsky (KS) equation. Global existence and uniqueness results are proved, and refined estimates of the radius of the absorbing ball in L2 are obtained in terms of the parameters of the equations for a generalized class of modified KS equations. The established estimates are compared with numerical solutions of the equations which in turn suggest an optimal upper bound for the radius of the absorbing ball. A scaling argument is used to explain this, and a general conjecture is made based on extensive computations. We also carry out a complete study of the nonlinear behavior of competing physical mechanisms: long wave instability above a critical Reynolds number, short wave damping due to surface tension and intermediate growth due to the electric field. Through a combination of analysis and extensive numerical experiments, we elucidate parameter regimes that support non-uniform travelling waves, time-periodic travelling waves and complex nonlinear dynamics including chaotic interfacial oscillations. It is established that a sufficiently high electric field will drive the system to chaotic oscillations, even when the Reynolds number is smaller than the critical value below which the non-electrified problem is linearly stable. A particular case of this is Stokes flow, which is known to be stable for this class of problems (an analogous statement holds for horizontally supported films also). Our theoretical results indicate that such highly stable flows can be rendered unstable by using electric fields. This opens the way for possible heat and mass transfer applications which can benefit significantly from interfacial oscillations and interfacial turbulence. For the case of a horizontal plane, a weakly nonlinear theory is not possible due to the absence of the shear flow generated by the gravitational force along the plate when the latter is inclined. We study the fully nonlinear equation, which in this case is asymptotically correct and is obtained at the leading order. The model equation describes both overlying and hanging films - in the former case gravity is stabilizing while in the latter it is destabilizing. The numerical and theoretical analysis of the fully nonlinear evolution is complicated by the fact that the coefficients of the highest order terms (surface tension in this instance) are nonlinear. We implement a fully implicit two level numerical scheme and perform numerical experiments. We also prove global boundedness of positive periodic smooth solutions, using an appropriate energy functional. This global boundedness result is seen in all our numerical results. Through a combination of analysis and extensive numerical experiments we present evidence for global existence of positive smooth solutions. This means, in turn, that the film does not touch the wall in finite time but asymptotically at infinite time. Numerical solutions are presented to support such phenomena.

A drop in uniaxial and biaxial nonlinear extensional flows

NASA Astrophysics Data System (ADS)

Favelukis, M.

2017-08-01

In this theoretical report, we explore small deformations of an initially spherical drop subjected to uniaxial or biaxial nonlinear extensional creeping flows. The problem is governed by the capillary number (Ca), the viscosity ratio (λ), and the nonlinear intensity of the flow (E). When the extensional flow is linear (E = 0), the familiar internal circulations are obtained and the same is true with E > 0, except that the external and internal flow rates increase with increasing E. If E < 0, the external flow consists of some unconnected regions leading to the same number of internal circulations (-3/7 < E < 0) or twice the number of internal circulations (E < -3/7), when compared to the linear case. The shape of the deformed drop is represented in terms of a modified Taylor deformation parameter, and the conditions for the breakup of the drop by a center pinching mechanism are also established. When the flow is linear (E = 0), the literature predicts prolate spheroidal drops for uniaxial flows (Ca > 0) and oblate spheroidal drops for biaxial flows (Ca < 0). For the same |Ca|, if E > 0, the drop is more elongated than the linear case, while E < 0 results in less elongated drops than the linear case. Compared to the linear case, for both uniaxial and biaxial extensional flows, E > 0 tends to facilitate drop breakup, while E < 0 makes drop breakup more difficult.

Continuation Power Flow with Variable-Step Variable-Order Nonlinear Predictor

NASA Astrophysics Data System (ADS)

Kojima, Takayuki; Mori, Hiroyuki

This paper proposes a new continuation power flow calculation method for drawing a P-V curve in power systems. The continuation power flow calculation successively evaluates power flow solutions through changing a specified value of the power flow calculation. In recent years, power system operators are quite concerned with voltage instability due to the appearance of deregulated and competitive power markets. The continuation power flow calculation plays an important role to understand the load characteristics in a sense of static voltage instability. In this paper, a new continuation power flow with a variable-step variable-order (VSVO) nonlinear predictor is proposed. The proposed method evaluates optimal predicted points confirming with the feature of P-V curves. The proposed method is successfully applied to IEEE 118-bus and IEEE 300-bus systems.

Stochastic Estimation and Non-Linear Wall-Pressure Sources in a Separating/Reattaching Flow

NASA Technical Reports Server (NTRS)

Naguib, A.; Hudy, L.; Humphreys, W. M., Jr.

2002-01-01

Simultaneous wall-pressure and PIV measurements are used to study the conditional flow field associated with surface-pressure generation in a separating/reattaching flow established over a fence-with-splitter-plate geometry. The conditional flow field is captured using linear and quadratic stochastic estimation based on the occurrence of positive and negative pressure events in the vicinity of the mean reattachment location. The results shed light on the dominant flow structures associated with significant wall-pressure generation. Furthermore, analysis based on the individual terms in the stochastic estimation expansion shows that both the linear and non-linear flow sources of the coherent (conditional) velocity field are equally important contributors to the generation of the conditional surface pressure.

DNS of Laminar-Turbulent Transition in Swept-Wing Boundary Layers

NASA Technical Reports Server (NTRS)

Duan, L.; Choudhari, M.; Li, F.

2014-01-01

Direct numerical simulation (DNS) is performed to examine laminar to turbulent transition due to high-frequency secondary instability of stationary crossflow vortices in a subsonic swept-wing boundary layer for a realistic natural-laminar-flow airfoil configuration. The secondary instability is introduced via inflow forcing and the mode selected for forcing corresponds to the most amplified secondary instability mode that, in this case, derives a majority of its growth from energy production mechanisms associated with the wall-normal shear of the stationary basic state. An inlet boundary condition is carefully designed to allow for accurate injection of instability wave modes and minimize acoustic reflections at numerical boundaries. Nonlinear parabolized stability equation (PSE) predictions compare well with the DNS in terms of modal amplitudes and modal shape during the strongly nonlinear phase of the secondary instability mode. During the transition process, the skin friction coefficient rises rather rapidly and the wall-shear distribution shows a sawtooth pattern that is analogous to the previously documented surface flow visualizations of transition due to stationary crossflow instability. Fully turbulent features are observed in the downstream region of the flow.

Thermal radiation and heat generation/absorption aspects in third grade magneto-nanofluid over a slendering stretching sheet with Newtonian conditions

NASA Astrophysics Data System (ADS)

Qayyum, Sajid; Hayat, Tasawar; Alsaedi, Ahmed

2018-05-01

Mathematical modeling for magnetohydrodynamic (MHD) radiative flow of third grade nano-material bounded by a nonlinear stretching sheet with variable thickness is introduced. The sheet moves with nonlinear velocity. Definitions of thermal radiation and heat generation/absorption are utilized in the energy expression. Intention in present investigation is to develop a model for nanomaterial comprising Brownian motion and thermophoresis phenomena. Newtonian conditions for heat and mass species are imposed. Governing equations of the locally similar flow are attempted through a homotopic technique and behaviors of involved variables on the flow fields are displayed graphically. It is revealed that increasing values of thermal conjugate variable corresponds to high temperature. Numerical investigation are explored to obtain the results of skin friction coefficient and local Nusselt and Sherwood numbers. It is revealed that velocity field reduces in the frame of magnetic variable while reverse situation is observed due to mixed convection parameter. Here qualitative behaviors of thermal field and heat transfer rate are opposite for thermophoresis variable. Moreover nanoparticle concentration and local Sherwood number via Brownian motion parameter are opposite.

Acceleration of incremental-pressure-correction incompressible flow computations using a coarse-grid projection method

NASA Astrophysics Data System (ADS)

Kashefi, Ali; Staples, Anne

2016-11-01

Coarse grid projection (CGP) methodology is a novel multigrid method for systems involving decoupled nonlinear evolution equations and linear elliptic equations. The nonlinear equations are solved on a fine grid and the linear equations are solved on a corresponding coarsened grid. Mapping functions transfer data between the two grids. Here we propose a version of CGP for incompressible flow computations using incremental pressure correction methods, called IFEi-CGP (implicit-time-integration, finite-element, incremental coarse grid projection). Incremental pressure correction schemes solve Poisson's equation for an intermediate variable and not the pressure itself. This fact contributes to IFEi-CGP's efficiency in two ways. First, IFEi-CGP preserves the velocity field accuracy even for a high level of pressure field grid coarsening and thus significant speedup is achieved. Second, because incremental schemes reduce the errors that arise from boundaries with artificial homogenous Neumann conditions, CGP generates undamped flows for simulations with velocity Dirichlet boundary conditions. Comparisons of the data accuracy and CPU times for the incremental-CGP versus non-incremental-CGP computations are presented.

MHD Flow and Heat Transfer Characteristics in a Casson Liquid Film Towards an Unsteady Stretching Sheet with Temperature-Dependent Thermal Conductivity

NASA Astrophysics Data System (ADS)

Mahmoud, Mostafa A. A.; Megahed, Ahmed M.

2017-10-01

Theoretical and numerical outcomes of the non-Newtonian Casson liquid thin film fluid flow owing to an unsteady stretching sheet which exposed to a magnetic field, Ohmic heating and slip velocity phenomena is reported here. The non-Newtonian thermal conductivity is imposed and treated as it vary with temperature. The nonlinear partial differential equations governing the non-Newtonian Casson thin film fluid are simplified into a group of highly nonlinear ordinary differential equations by using an adequate dimensionless transformations. With this in mind, the numerical solutions for the ordinary conservation equations are found using an accurate shooting iteration technique together with the Runge-Kutta algorithm. The lineaments of the thin film flow and the heat transfer characteristics for the pertinent parameters are discussed through graphs. The results obtained here detect many concern for the local Nusselt number and the local skin-friction coefficient in which they may be beneficial for the material processing industries. Furthermore, in some special conditions, the present problem has an excellent agreement with previously published work.

On a Model of a Nonlinear Feedback System for River Flow Prediction

NASA Astrophysics Data System (ADS)

Ozaki, T.

1980-02-01

A nonlinear system with feedback is proposed as a dynamic model for the hydrological system, whose input is the rainfall and whose output is the discharge of river flow. Parameters and orders of the model are estimated using Akaike's information criterion. Its application to the prediction of daily discharges of Kanna River and Bird Creek is discussed.

Non-Darcy Forchheimer flow of ferromagnetic second grade fluid

NASA Astrophysics Data System (ADS)

Hayat, T.; Ahmad, Salman; Khan, M. Ijaz; Alsaedi, A.

This article discusses impacts of thermal radiation, viscous dissipation and magnetic dipole in flow of second grade fluid saturating porous medium. Porous medium is characterized by nonlinear Darcy-Forchheimer relation. Relevant nonlinear ordinary differential systems after using appropriate transformations are solved numerically. Shooting technique is implemented for the numerical treatment. Temperature, velocity, skin fraction and Nusselt number are analyzed.

Entropy generation minimization (EGM) of nanofluid flow by a thin moving needle with nonlinear thermal radiation

NASA Astrophysics Data System (ADS)

Waleed Ahmed Khan, M.; Ijaz Khan, M.; Hayat, T.; Alsaedi, A.

2018-04-01

Entropy generation minimization (EGM) and heat transport in nonlinear radiative flow of nanomaterials over a thin moving needle has been discussed. Nonlinear thermal radiation and viscous dissipation terms are merged in the energy expression. Water is treated as ordinary fluid while nanomaterials comprise titanium dioxide, copper and aluminum oxide. The nonlinear governing expressions of flow problems are transferred to ordinary ones and then tackled for numerical results by Built-in-shooting technique. In first section of this investigation, the entropy expression is derived as a function of temperature and velocity gradients. Geometrical and physical flow field variables are utilized to make it nondimensionalized. An entropy generation analysis is utilized through second law of thermodynamics. The results of temperature, velocity, concentration, surface drag force and heat transfer rate are explored. Our outcomes reveal that surface drag force and Nusselt number (heat transfer) enhanced linearly for higher nanoparticle volume fraction. Furthermore drag force decays for aluminum oxide and it enhances for copper nanoparticles. In addition, the lowest heat transfer rate is achieved for higher radiative parameter. Temperature field is enhanced with increase in temperature ratio parameter.

Application of Linear and Non-Linear Harmonic Methods for Unsteady Transonic Flow

NASA Astrophysics Data System (ADS)

Gundevia, Rayomand

This thesis explores linear and non-linear computational methods for solving unsteady flow. The eventual goal is to apply these methods to two-dimensional and three-dimensional flutter predictions. In this study the quasi-one-dimensional nozzle is used as a framework for understanding these methods and their limitations. Subsonic and transonic cases are explored as the back-pressure is forced to oscillate with known amplitude and frequency. A steady harmonic approach is used to solve this unsteady problem for which perturbations are said to be small in comparison to the mean flow. The use of a linearized Euler equations (LEE) scheme is good at capturing the flow characteristics but is limited by accuracy to relatively small amplitude perturbations. The introduction of time-averaged second-order terms in the Non-Linear Harmonic (NLH) method means that a better approximation of the mean-valued solution, upon which the linearization is based, can be made. The nonlinear time-accurate Euler solutions are used for comparison and to establish the regimes of unsteadiness for which these schemes fails. The usefulness of the LEE and NLH methods lie in the gains in computational efficiency over the full equations.

Prospectus: towards the development of high-fidelity models of wall turbulence at large Reynolds number

NASA Astrophysics Data System (ADS)

Klewicki, J. C.; Chini, G. P.; Gibson, J. F.

2017-03-01

Recent and on-going advances in mathematical methods and analysis techniques, coupled with the experimental and computational capacity to capture detailed flow structure at increasingly large Reynolds numbers, afford an unprecedented opportunity to develop realistic models of high Reynolds number turbulent wall-flow dynamics. A distinctive attribute of this new generation of models is their grounding in the Navier-Stokes equations. By adhering to this challenging constraint, high-fidelity models ultimately can be developed that not only predict flow properties at high Reynolds numbers, but that possess a mathematical structure that faithfully captures the underlying flow physics. These first-principles models are needed, for example, to reliably manipulate flow behaviours at extreme Reynolds numbers. This theme issue of Philosophical Transactions of the Royal Society A provides a selection of contributions from the community of researchers who are working towards the development of such models. Broadly speaking, the research topics represented herein report on dynamical structure, mechanisms and transport; scale interactions and self-similarity; model reductions that restrict nonlinear interactions; and modern asymptotic theories. In this prospectus, the challenges associated with modelling turbulent wall-flows at large Reynolds numbers are briefly outlined, and the connections between the contributing papers are highlighted.

Fluid-structure interaction for nonlinear response of shells conveying pulsatile flow

NASA Astrophysics Data System (ADS)

Tubaldi, Eleonora; Amabili, Marco; Païdoussis, Michael P.

2016-06-01

Circular cylindrical shells with flexible boundary conditions conveying pulsatile flow and subjected to pulsatile pressure are investigated. The equations of motion are obtained based on the nonlinear Novozhilov shell theory via Lagrangian approach. The flow is set in motion by a pulsatile pressure gradient. The fluid is modeled as a Newtonian pulsatile flow and it is formulated using a hybrid model that contains the unsteady effects obtained from the linear potential flow theory and the pulsatile viscous effects obtained from the unsteady time-averaged Navier-Stokes equations. A numerical bifurcation analysis employs a refined reduced order model to investigate the dynamic behavior. The case of shells containing quiescent fluid subjected to the action of a pulsatile transmural pressure is also addressed. Geometrically nonlinear vibration response to pulsatile flow and transmural pressure are here presented via frequency-response curves and time histories. The vibrations involving both a driven mode and a companion mode, which appear due to the axial symmetry, are also investigated. This theoretical framework represents a pioneering study that could be of great interest for biomedical applications. In particular, in the future, a more refined model of the one here presented will possibly be applied to reproduce the dynamic behavior of vascular prostheses used for repairing and replacing damaged and diseased thoracic aorta in cases of aneurysm, dissection or coarctation. For this purpose, a pulsatile time-dependent blood flow model is here considered by applying physiological waveforms of velocity and pressure during the heart beating period. This study provides, for the first time in literature, a fully coupled fluid-structure interaction model with deep insights in the nonlinear vibrations of circular cylindrical shells subjected to pulsatile pressure and pulsatile flow.

Linear and nonlinear stability criteria for compressible MHD flows in a gravitational field

NASA Astrophysics Data System (ADS)

Moawad, S. M.; Moawad

2013-10-01

The equilibrium and stability properties of ideal magnetohydrodynamics (MHD) of compressible flow in a gravitational field with a translational symmetry are investigated. Variational principles for the steady-state equations are formulated. The MHD equilibrium equations are obtained as critical points of a conserved Lyapunov functional. This functional consists of the sum of the total energy, the mass, the circulation along field lines (cross helicity), the momentum, and the magnetic helicity. In the unperturbed case, the equilibrium states satisfy a nonlinear second-order partial differential equation (PDE) associated with hydrodynamic Bernoulli law. The PDE can be an elliptic or a parabolic equation depending on increasing the poloidal flow speed. Linear and nonlinear Lyapunov stability conditions under translational symmetric perturbations are established for the equilibrium states.

New thermodynamics of entropy generation minimization with nonlinear thermal radiation and nanomaterials

NASA Astrophysics Data System (ADS)

Hayat, T.; Khan, M. Ijaz; Qayyum, Sumaira; Alsaedi, A.; Khan, M. Imran

2018-03-01

This research addressed entropy generation for MHD stagnation point flow of viscous nanofluid over a stretching surface. Characteristics of heat transport are analyzed through nonlinear radiation and heat generation/absorption. Nanoliquid features for Brownian moment and thermophoresis have been considered. Fluid in the presence of constant applied inclined magnetic field is considered. Flow problem is mathematically modeled and governing expressions are changed into nonlinear ordinary ones by utilizing appropriate transformations. The effects of pertinent variables on velocity, nanoparticle concentration and temperature are discussed graphically. Furthermore Brownian motion and thermophoresis effects on entropy generation and Bejan number have been examined. Total entropy generation is inspected through various flow variables. Consideration is mainly given to the convergence process. Velocity, temperature and mass gradients at the surface of sheet are calculated numerically.

NR-code: Nonlinear reconstruction code

NASA Astrophysics Data System (ADS)

Yu, Yu; Pen, Ue-Li; Zhu, Hong-Ming

2018-04-01

NR-code applies nonlinear reconstruction to the dark matter density field in redshift space and solves for the nonlinear mapping from the initial Lagrangian positions to the final redshift space positions; this reverses the large-scale bulk flows and improves the precision measurement of the baryon acoustic oscillations (BAO) scale.

Investigation of scaling characteristics for defining design environments due to transient ground winds and near-field, nonlinear acoustic fields

NASA Technical Reports Server (NTRS)

Shih, C. C.

1973-01-01

In order to establish a foundation of scaling laws for the highly nonlinear waves associated with the launch vehicle, the basic knowledge of the relationships among the paramaters pertinent to the energy dissipation process associated with the propagation of nonlinear pressure waves in thermoviscous media is required. The problem of interest is to experimentally investigate the temporal and spacial velocity profiles of fluid flow in a 3-inch open-end pipe of various lengths, produced by the propagation of nonlinear pressure waves for various diaphragm burst pressures of a pressure wave generator. As a result, temporal and spacial characteristics of wave propagation for a parametric set of nonlinear pressure waves in the pipe containing air under atmospheric conditions were determined. Velocity measurements at five sections along the pipes of up to 210 ft. in length were made with hot-film anemometers for five pressure waves produced by a piston. The piston was derived with diaphragm burst pressures at 20, 40, 60, 80 and 100 psi in the driver chamber of the pressure wave generator.

Single axis control of ball position in magnetic levitation system using fuzzy logic control

NASA Astrophysics Data System (ADS)

Sahoo, Narayan; Tripathy, Ashis; Sharma, Priyaranjan

2018-03-01

This paper presents the design and real time implementation of Fuzzy logic control(FLC) for the control of the position of a ferromagnetic ball by manipulating the current flowing in an electromagnet that changes the magnetic field acting on the ball. This system is highly nonlinear and open loop unstable. Many un-measurable disturbances are also acting on the system, making the control of it highly complex but interesting for any researcher in control system domain. First the system is modelled using the fundamental laws, which gives a nonlinear equation. The nonlinear model is then linearized at an operating point. Fuzzy logic controller is designed after studying the system in closed loop under PID control action. The controller is then implemented in real time using Simulink real time environment. The controller is tuned manually to get a stable and robust performance. The set point tracking performance of FLC and PID controllers were compared and analyzed.

Finite element flow analysis; Proceedings of the Fourth International Symposium on Finite Element Methods in Flow Problems, Chuo University, Tokyo, Japan, July 26-29, 1982

NASA Astrophysics Data System (ADS)

Kawai, T.

Among the topics discussed are the application of FEM to nonlinear free surface flow, Navier-Stokes shallow water wave equations, incompressible viscous flows and weather prediction, the mathematical analysis and characteristics of FEM, penalty function FEM, convective, viscous, and high Reynolds number FEM analyses, the solution of time-dependent, three-dimensional and incompressible Navier-Stokes equations, turbulent boundary layer flow, FEM modeling of environmental problems over complex terrain, and FEM's application to thermal convection problems and to the flow of polymeric materials in injection molding processes. Also covered are FEMs for compressible flows, including boundary layer flows and transonic flows, hybrid element approaches for wave hydrodynamic loadings, FEM acoustic field analyses, and FEM treatment of free surface flow, shallow water flow, seepage flow, and sediment transport. Boundary element methods and FEM computational technique topics are also discussed. For individual items see A84-25834 to A84-25896

Weakly nonlinear dynamics of near-CJ detonation waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bdzil, J.B.; Klein, R.

1993-01-01

The renewed interest in safety issues for large scale industrial devices and in high speed combustion has driven recent intense efforts to gain a deeper theoretical understanding of detonation wave dynamics. Linear stability analyses, weakly nonlinear bifurcation calculations as well as full scale multi-dimensional direct numerical simulations have been pursued for a standard model problem based on the reactive Euler equations for an ideal gas with constant specific heat capacities and simplified chemical reaction models. Most of these studies are concerned with overdriven detonations. This is true despite the fact that the majority of all detonations observed in nature aremore » running at speeds close to the Chapman-Jouguet (CJ) limit value. By focusing on overdriven waves one removes an array of difficulties from the analysis that is associated with the sonic flow conditions in the wake of a CJ-detonation. In particular, the proper formulation of downstream boundary conditions in the CJ-case is a yet unsolved analytical problem. A proper treatment of perturbations in the back of a Chapman-Jouguet detonation has to account for two distinct weakly nonlinear effects in the forward acoustic wave component. The first is a nonlinear interactionof highly temperature sensitive chemistry with the forward acoustic wave component in a transonic boundary layer near the end of the reaction zone. The second is a cumulative three-wave-resonance in the sense of Majda et al. which is active in the near-sonic burnt gas flow and which is essentially independent of the details of the chemical model. In this work, we consider detonations in mixtures with moderate state sensitivity of the chemical reactions. Then, the acoustic perturbations do not influence the chemistry at the order considered and we may concentrate on the second effect; the three-wave resonance.« less

Weakly nonlinear dynamics of near-CJ detonation waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bdzil, J.B.; Klein, R.

1993-02-01

The renewed interest in safety issues for large scale industrial devices and in high speed combustion has driven recent intense efforts to gain a deeper theoretical understanding of detonation wave dynamics. Linear stability analyses, weakly nonlinear bifurcation calculations as well as full scale multi-dimensional direct numerical simulations have been pursued for a standard model problem based on the reactive Euler equations for an ideal gas with constant specific heat capacities and simplified chemical reaction models. Most of these studies are concerned with overdriven detonations. This is true despite the fact that the majority of all detonations observed in nature aremore » running at speeds close to the Chapman-Jouguet (CJ) limit value. By focusing on overdriven waves one removes an array of difficulties from the analysis that is associated with the sonic flow conditions in the wake of a CJ-detonation. In particular, the proper formulation of downstream boundary conditions in the CJ-case is a yet unsolved analytical problem. A proper treatment of perturbations in the back of a Chapman-Jouguet detonation has to account for two distinct weakly nonlinear effects in the forward acoustic wave component. The first is a nonlinear interactionof highly temperature sensitive chemistry with the forward acoustic wave component in a transonic boundary layer near the end of the reaction zone. The second is a cumulative three-wave-resonance in the sense of Majda et al. which is active in the near-sonic burnt gas flow and which is essentially independent of the details of the chemical model. In this work, we consider detonations in mixtures with moderate state sensitivity of the chemical reactions. Then, the acoustic perturbations do not influence the chemistry at the order considered and we may concentrate on the second effect; the three-wave resonance.« less

Energy Accumulation and Emanation at Low Latitudes. Part II: Nonlinear Response to Strong Episodic Equatorial Forcing.

NASA Astrophysics Data System (ADS)

Chang, Hai-Ru; Webster, Peter J.

1990-11-01

A fully nonlinear model is used to reexamine the impact of a zonally varying basic state on the propagation characteristics of latitudinally equatorially trapped modes. Linear studies have shown that such modes are longitudinally trapped in regions of negative stretching deformation of the equatorial time-mean zonal flow (i.e., where Ux < 0) forming `accumulation' regions of wave action flux. Furthermore, the accumulation regions tend to act as local emanation regions to the extratropics. These physical communications between the tropics and extratropics are referred to as fast teleconnections due to their rapidity (periods of days to weeks) compared to the much slower climatological differences in the mean states such as occur between El Niño and La Niña. The latter form of communication between low and high latitudes, which is induced by very low frequency SST changes, is referred to as a slow teleconnection.It is generally found that accumulation and emanation regions are present in the nonlinear regime with much the same character as with the linear model. The similarity exists even when realistic forcing functions are used with amplitudes and temporal and spatial characteristics that correspond to impulsive convection in the western Pacific Ocean. A description of the convection is given. A diagnosis of the linear and nonlinear results shows that, in the tropics, the linear advection by the mean flow plays a dominant role and probably is the reason for the great similarity of the linear and nonlinear tropical atmosphere. However, there are some differences between the linear and nonlinear results. Nonlinear waves appear to propagate more rapidly through the maximum westerlies along the equator and with less difficulty than linear waves. The differences that do occur arise from the nonlinear changes in the tropical mass field, especially in the accumulation zone. Differences between linear and nonlinear responses in the midlatitude response to equatorial forcing appear to reflect changes in the tropics. Nonlinear maxima occur poleward of the region of tropical westerlies but only after accumulation has occurred along the equator.The results of the study are used to discuss the problem of why there is considerable similarity between simple linear models and more sophisticated nonlinear models. Such similarity would probably explain why the NMC and the NEPRF global models exhibit phase locked responses in the middle latitudes to imposed and impulsive tropical forcing. The role of fast teleconnenions in the longer term general circulation of the atmosphere is discussed, especially during El Niño and La Niña. Whereas an aggregate role for the fast teleconnections in producing very slowly evolving climate features remains obscure, it does appear that the accumulation-emanation theory may infer different routings for transient communications between the tropics and higher latitudes and vice vera depending upon the state of the basic flow.

The Magnetohydrodynamic Kelvin-Helmholtz Instability: A Three-dimensional Study of Nonlinear Evolution

NASA Astrophysics Data System (ADS)

Ryu, Dongsu; Jones, T. W.; Frank, Adam

2000-12-01

We investigate through high-resolution three-dimensional simulations the nonlinear evolution of compressible magnetohydrodynamic flows subject to the Kelvin-Helmholtz instability. As in our earlier work, we have considered periodic sections of flows that contain a thin, transonic shear layer but are otherwise uniform. The initially uniform magnetic field is parallel to the shear plane but oblique to the flow itself. We confirm in three-dimensional flows the conclusion from our two-dimensional work that even apparently weak magnetic fields embedded in Kelvin-Helmholtz unstable plasma flows can be fundamentally important to nonlinear evolution of the instability. In fact, that statement is strengthened in three dimensions by this work because it shows how field-line bundles can be stretched and twisted in three dimensions as the quasi-two-dimensional Cat's Eye vortex forms out of the hydrodynamical motions. In our simulations twisting of the field may increase the maximum field strength by more than a factor of 2 over the two-dimensional effect. If, by these developments, the Alfvén Mach number of flows around the Cat's Eye drops to unity or less, our simulations suggest that magnetic stresses will eventually destroy the Cat's Eye and cause the plasma flow to self-organize into a relatively smooth and apparently stable flow that retains memory of the original shear. For our flow configurations, the regime in three dimensions for such reorganization is 4<~MAx<~50, expressed in terms of the Alfvén Mach number of the original velocity transition and the initial Alfvén speed projected to the flow plan. When the initial field is stronger than this, the flow either is linearly stable (if MAx<~2) or becomes stabilized by enhanced magnetic tension as a result of the corrugated field along the shear layer before the Cat's Eye forms (if MAx>~2). For weaker fields the instability remains essentially hydrodynamic in early stages, and the Cat's Eye is destroyed by the hydrodynamic secondary instabilities of a three-dimensional nature. Then, the flows evolve into chaotic structures that approach decaying isotropic turbulence. In this stage, there is considerable enhancement to the magnetic energy due to stretching, twisting, and turbulent amplification, which is retained long afterward. The magnetic energy eventually catches up to the kinetic energy, and the nature of flows becomes magnetohydrodynamic. Decay of the magnetohydrodynamic turbulence is enhanced by dissipation accompanying magnetic reconnection. Hence, in three dimensions as in two dimensions, very weak fields do not modify substantially the character of the flow evolution but do increase global dissipation rates.

Variation character of stagnation point heat flux for hypersonic pointed bodies from continuum to rarefied flow states and its bridge function study

NASA Astrophysics Data System (ADS)

Wang, Zhihui; Bao, Lin; Tong, Binggang

2009-12-01

This paper is a research on the variation character of stagnation point heat flux for hypersonic pointed bodies from continuum to rarefied flow states by using theoretical analysis and numerical simulation methods. The newly developed near space hypersonic cruise vehicles have sharp noses and wingtips, which desires exact and relatively simple methods to estimate the stagnation point heat flux. With the decrease of the curvature radius of the leading edge, the flow becomes rarefied gradually, and viscous interaction effects and rarefied gas effects come forth successively, which results in that the classical Fay-Riddell equation under continuum hypothesis will become invalid and the variation of stagnation point heat flux is characterized by a new trend. The heat flux approaches the free molecular flow limit instead of an infinite value when the curvature radius of the leading edge tends to 0. The physical mechanism behind this phenomenon remains in need of theoretical study. Firstly, due to the fact that the whole flow regime can be described by Boltzmann equation, the continuum and rarefied flow are analyzed under a uniform framework. A relationship is established between the molecular collision insufficiency in rarefied flow and the failure of Fourier’s heat conduction law along with the increasing significance of the nonlinear heat flux. Then based on an inspiration drew from Burnett approximation, control factors are grasped and a specific heat flux expression containing the nonlinear term is designed in the stagnation region of hypersonic leading edge. Together with flow pattern analysis, the ratio of nonlinear to linear heat flux W r is theoretically obtained as a parameter which reflects the influence of nonlinear factors, i.e. a criterion to classify the hypersonic rarefied flows. Ultimately, based on the characteristic parameter W r , a bridge function with physical background is constructed, which predicts comparative reasonable results in coincidence well with DSMC and experimental data in the whole flow regime.

Some recent applications of Navier-Stokes codes to rotorcraft

NASA Technical Reports Server (NTRS)

Mccroskey, W. J.

1992-01-01

Many operational limitations of helicopters and other rotary-wing aircraft are due to nonlinear aerodynamic phenomena incuding unsteady, three-dimensional transonic and separated flow near the surfaces and highly vortical flow in the wakes of rotating blades. Modern computational fluid dynamics (CFD) technology offers new tools to study and simulate these complex flows. However, existing Euler and Navier-Stokes codes have to be modified significantly for rotorcraft applications, and the enormous computational requirements presently limit their use in routine design applications. Nevertheless, the Euler/Navier-Stokes technology is progressing in anticipation of future supercomputers that will enable meaningful calculations to be made for complete rotorcraft configurations.

Nonlinear aeroelastic analysis, flight dynamics, and control of a complete aircraft

NASA Astrophysics Data System (ADS)

Patil, Mayuresh Jayawant

The focus of this research was to analyze a high-aspect-ratio wing aircraft flying at low subsonic speeds. Such aircraft are designed for high-altitude, long-endurance missions. Due to the high flexibility and associated wing deformation, accurate prediction of aircraft response requires use of nonlinear theories. Also strong interactions between flight dynamics and aeroelasticity are expected. To analyze such aircraft one needs to have an analysis tool which includes the various couplings and interactions. A theoretical basis has been established for a consistent analysis which takes into account, (i) material anisotropy, (ii) geometrical nonlinearities of the structure, (iii) rigid-body motions, (iv) unsteady flow behavior, and (v) dynamic stall. The airplane structure is modeled as a set of rigidly attached beams. Each of the beams is modeled using the geometrically exact mixed variational formulation, thus taking into account geometrical nonlinearities arising due to large displacements and rotations. The cross-sectional stiffnesses are obtained using an asymptotically exact analysis, which can model arbitrary cross sections and material properties. An aerodynamic model, consisting of a unified lift model, a consistent combination of finite-state inflow model and a modified ONERA dynamic stall model, is coupled to the structural system to determine the equations of motion. The results obtained indicate the necessity of including nonlinear effects in aeroelastic analysis. Structural geometric nonlinearities result in drastic changes in aeroelastic characteristics, especially in case of high-aspect-ratio wings. The nonlinear stall effect is the dominant factor in limiting the amplitude of oscillation for most wings. The limit cycle oscillation (LCO) phenomenon is also investigated. Post-flutter and pre-flutter LCOs are possible depending on the disturbance mode and amplitude. Finally, static output feedback (SOF) controllers are designed for flutter suppression and gust alleviation. SOF controllers are very simple and thus easy to implement. For the case considered, SOF controllers with proper choice of sensors give results comparable to full state feedback (linear quadratic regulator) designs.

The Evolution of Modulated Wavetrains Into Turbulent Spots

NASA Technical Reports Server (NTRS)

Gaster, M.

2007-01-01

Experiment are being carried out to study the process by which th almost periodic disturbance waves generated naturally by the freestream evolve into turbulence. The boundary layer on a flat plate has been used for this study. The novelty of the approach is in the form of artificial excitation that is used. In this work the flow is excited artificially by deterministic white noise. The weak T-S wave created develops down stream, becomes nonlinear and blows up locally onto a highly distorted flow. These large local distortions of the mean flow allow very high frequency disturbances to grow and form into small turbulent spots. The spots arise from the excitation, and if the same noise sequence is repeated a spot will form at the same position and time instant relative to the excitation.

The nonlinear interaction of Tollmien-Schlichting waves and Taylor-Goertler vortices in curved channel flows

NASA Technical Reports Server (NTRS)

Hall, P.; Smith, F. T.

1987-01-01

It is known that a viscous fluid flow with curved streamlines can support both Tollmien-Schlichting and Taylor-Goertler instabilities. In a situation where both modes are possible on the basis of linear theory a nonlinear theory must be used to determine the effect of the interaction of the instabilities. The details of this interaction are of practical importance because of its possible catastrophic effects on mechanisms used for laminar flow control. This interaction is studied in the context of fully developed flows in curved channels. A part form technical differences associated with boundary layer growth the structures of the instabilities in this flow are very similar to those in the practically more important external boundary layer situation. The interaction is shown to have two distinct phases depending on the size of the disturbances. At very low amplitudes two oblique Tollmein-Schlichting waves interact with a Goertler vortex in such a manner that the amplitudes become infinite at a finite time. This type of interaction is described by ordinary differential amplitude equations with quadratic nonlinearities.

Wave phenomena in a high Reynolds number compressible boundary layer

NASA Technical Reports Server (NTRS)

Bayliss, A.; Maestrello, L.; Parikh, P.; Turkel, E.

1985-01-01

Growth of unstable disturbances in a high Reynolds number compressible boundary layer is numerically simulated. Localized periodic surface heating and cooling as a means of active control of these disturbances is studied. It is shown that compressibility in itself stabilizes the flow but at a lower Mach number, significant nonlinear distortions are produced. Phase cancellation is shown to be an effective mechanism for active boundary layer control.

Nonlinear travelling waves in rotating Hagen–Poiseuille flow

NASA Astrophysics Data System (ADS)

Pier, Benoît; Govindarajan, Rama

2018-03-01

The dynamics of viscous flow through a rotating pipe is considered. Small-amplitude stability characteristics are obtained by linearizing the Navier–Stokes equations around the base flow and solving the resulting eigenvalue problems. For linearly unstable configurations, the dynamics leads to fully developed finite-amplitude perturbations that are computed by direct numerical simulations of the complete Navier–Stokes equations. By systematically investigating all linearly unstable combinations of streamwise wave number k and azimuthal mode number m, for streamwise Reynolds numbers {{Re}}z ≤slant 500 and rotational Reynolds numbers {{Re}}{{Ω }} ≤slant 500, the complete range of nonlinear travelling waves is obtained and the associated flow fields are characterized.

Wave-induced response of a floating two-dimensional body with a moonpool

PubMed Central

Fredriksen, Arnt G.; Kristiansen, Trygve; Faltinsen, Odd M.

2015-01-01

Regular wave-induced behaviour of a floating stationary two-dimensional body with a moonpool is studied. The focus is on resonant piston-mode motion in the moonpool and rigid-body motions. Dedicated two-dimensional experiments have been performed. Two numerical hybrid methods, which have previously been applied to related problems, are further developed. Both numerical methods couple potential and viscous flow. The semi-nonlinear hybrid method uses linear free-surface and body-boundary conditions. The other one uses fully nonlinear free-surface and body-boundary conditions. The harmonic polynomial cell method solves the Laplace equation in the potential flow domain, while the finite volume method solves the Navier–Stokes equations in the viscous flow domain near the body. Results from the two codes are compared with the experimental data. The nonlinear hybrid method compares well with the data, while certain discrepancies are observed for the semi-nonlinear method. In particular, the roll motion is over-predicted by the semi-nonlinear hybrid method. Error sources in the semi-nonlinear hybrid method are discussed. The moonpool strongly affects heave motions in a frequency range around the piston-mode resonance frequency of the moonpool. No resonant water motions occur in the moonpool at the piston-mode resonance frequency. Instead large moonpool motions occur at a heave natural frequency associated with small damping near the piston-mode resonance frequency. PMID:25512594

Response of corrugated fiberboard to moisture flow : a 3-D finite element transient nonlinear analysis

Treesearch

Adeeb A. Rahman; Thomas J. Urbanik; Mustafa Mahamid

2003-01-01

Collapse of fiberboard packaging boxes, in the shipping industry, due to rise in humidity conditions is common and very costly. A 3D FE nonlinear model is developed to predict the moisture flow throughout a corrugated packaging fiberboard sandwich structure. The model predicts how the moisture diffusion will permeate through the layers of a fiberboard (medium and...

On the nonlinear three dimensional instability of Stokes layers and other shear layers to pairs of oblique waves

NASA Technical Reports Server (NTRS)

Wu, Xuesong; Lee, Sang Soo; Cowley, Stephen J.

1992-01-01

The nonlinear evolution of a pair of initially oblique waves in a high Reynolds Number Stokes layer is studied. Attention is focused on times when disturbances of amplitude epsilon have O(epsilon(exp 1/3)R) growth rates, where R is the Reynolds number. The development of a pair of oblique waves is then controlled by nonlinear critical-layer effects. Viscous effects are included by studying the distinguished scaling epsilon = O(R(exp -1)). This leads to a complicated modification of the kernel function in the integro-differential amplitude equation. When viscosity is not too large, solutions to the amplitude equation develop a finite-time singularity, indicating that an explosive growth can be introduced by nonlinear effects; we suggest that such explosive growth can lead to the bursts observed in experiments. Increasing the importance of viscosity generally delays the occurrence of the finite-time singularity, and sufficiently large viscosity may lead to the disturbance decaying exponentially. For the special case when the streamwise and spanwise wavenumbers are equal, the solution can evolve into a periodic oscillation. A link between the unsteady critical-layer approach to high-Reynolds-number flow instability, and the wave vortex approach is identified.

Reduced-Order Modeling for Flutter/LCO Using Recurrent Artificial Neural Network

NASA Technical Reports Server (NTRS)

Yao, Weigang; Liou, Meng-Sing

2012-01-01

The present study demonstrates the efficacy of a recurrent artificial neural network to provide a high fidelity time-dependent nonlinear reduced-order model (ROM) for flutter/limit-cycle oscillation (LCO) modeling. An artificial neural network is a relatively straightforward nonlinear method for modeling an input-output relationship from a set of known data, for which we use the radial basis function (RBF) with its parameters determined through a training process. The resulting RBF neural network, however, is only static and is not yet adequate for an application to problems of dynamic nature. The recurrent neural network method [1] is applied to construct a reduced order model resulting from a series of high-fidelity time-dependent data of aero-elastic simulations. Once the RBF neural network ROM is constructed properly, an accurate approximate solution can be obtained at a fraction of the cost of a full-order computation. The method derived during the study has been validated for predicting nonlinear aerodynamic forces in transonic flow and is capable of accurate flutter/LCO simulations. The obtained results indicate that the present recurrent RBF neural network is accurate and efficient for nonlinear aero-elastic system analysis

Solving Nonlinear Euler Equations with Arbitrary Accuracy

NASA Technical Reports Server (NTRS)

Dyson, Rodger W.

2005-01-01

A computer program that efficiently solves the time-dependent, nonlinear Euler equations in two dimensions to an arbitrarily high order of accuracy has been developed. The program implements a modified form of a prior arbitrary- accuracy simulation algorithm that is a member of the class of algorithms known in the art as modified expansion solution approximation (MESA) schemes. Whereas millions of lines of code were needed to implement the prior MESA algorithm, it is possible to implement the present MESA algorithm by use of one or a few pages of Fortran code, the exact amount depending on the specific application. The ability to solve the Euler equations to arbitrarily high accuracy is especially beneficial in simulations of aeroacoustic effects in settings in which fully nonlinear behavior is expected - for example, at stagnation points of fan blades, where linearizing assumptions break down. At these locations, it is necessary to solve the full nonlinear Euler equations, and inasmuch as the acoustical energy is of the order of 4 to 5 orders of magnitude below that of the mean flow, it is necessary to achieve an overall fractional error of less than 10-6 in order to faithfully simulate entropy, vortical, and acoustical waves.

Effects of plasma shaping on nonlinear gyrokinetic turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Belli, E. A.; Hammett, G. W.; Dorland, W.

The effects of flux surface shape on the gyrokinetic stability and transport of tokamak plasmas are studied using the GS2 code [M. Kotschenreuther, G. Rewoldt, and W. M. Tang, Comput. Phys. Commun. 88, 128 (1995); W. Dorland, F. Jenko, M. Kotschenreuther, and B. N. Rogers, Phys. Rev. Lett. 85, 5579 (2000)]. Studies of the scaling of nonlinear turbulence with shaping parameters are performed using analytic equilibria based on interpolations of representative shapes of the Joint European Torus [P. H. Rebut and B. E. Keen, Fusion Technol. 11, 13 (1987)]. High shaping is found to be a stabilizing influence on bothmore » the linear ion-temperature-gradient (ITG) instability and the nonlinear ITG turbulence. For the parameter regime studied here, a scaling of the heat flux with elongation of {chi}{approx}{kappa}{sup -1.5} or {kappa}{sup -2.0}, depending on the triangularity, is observed at fixed average temperature gradient. While this is not as strong as empirical elongation scalings, it is also found that high shaping results in a larger Dimits upshift of the nonlinear critical temperature gradient due to an enhancement of the Rosenbluth-Hinton residual zonal flows.« less

Fluctuation-induced shear flow and energy transfer in plasma interchange turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, B.; Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139; Sun, C. K.

2015-11-15

Fluctuation-induced E × B shear flow and energy transfer for plasma interchange turbulence are examined in a flux-driven system with both closed and open magnetic field lines. The nonlinear evolution of interchange turbulence shows the presence of two confinement regimes characterized by low and high E × B flow shear. In the first regime, the large-scale turbulent convection is dominant and the mean E × B shear flow is at a relatively low level. By increasing the heat flux above a certain threshold, the increased turbulent intensity gives rise to the transfer of energy from fluctuations to mean E ×more » B flows. As a result, a transition to the second regime occurs, in which a strong mean E × B shear flow is generated.« less

Targeting specific azimuthal modes using wall changes in turbulent pipe flow

NASA Astrophysics Data System (ADS)

van Buren, Tyler; Hellström, Leo; Marusic, Ivan; Smits, Alexander

2017-11-01

We experimentally study turbulent pipe flow at Re =3486 using stereoscopic particle image velocimetry. Using pipe inserts with non-circular geometry to perturb the flow upstream of the measurement location, we excite specific naturally occurring energetic modes. We consider inserts that directly manipulate the flow momentum (vortex generators), and/or induce secondary flows through Reynolds stresses (sinusoidally varying wall shape). These inserts substantially change the mean flow, and produce distinct regions of low and high momentum corresponding to the mode being excited. The inserts add energy in the targeted modes while simultaneously reducing the energy in the non-excited azimuthal modes. In addition, inserts designed to excite two modes simultaneously exhibit non-linear interactions. Supported under ONR Grant N00014-15-1-2402, Program Manager/Director Thomas Fu and the Australian Research Council.

Kolmogorov Turbulence Defeated by Anderson Localization for a Bose-Einstein Condensate in a Sinai-Oscillator Trap

NASA Astrophysics Data System (ADS)

Ermann, Leonardo; Vergini, Eduardo; Shepelyansky, Dima L.

2017-08-01

We study the dynamics of a Bose-Einstein condensate in a Sinai-oscillator trap under a monochromatic driving force. Such a trap is formed by a harmonic potential and a repulsive disk located in the center vicinity corresponding to the first experiments of condensate formation by Ketterle and co-workers in 1995. We allow that the external driving allows us to model the regime of weak wave turbulence with the Kolmogorov energy flow from low to high energies. We show that in a certain regime of weak driving and weak nonlinearity such a turbulent energy flow is defeated by the Anderson localization that leads to localization of energy on low energy modes. This is in a drastic contrast to the random phase approximation leading to energy flow to high modes. A critical threshold is determined above which the turbulent flow to high energies becomes possible. We argue that this phenomenon can be studied with ultracold atoms in magneto-optical traps.

Ultrafast electrokinetics.

PubMed

Rouhi Youssefi, Mehrnaz; Diez, Francisco Javier

2016-03-01

The influence of a high electric field applied on both fluid flow and particle velocities is quantified at large Peclet numbers. The experiments involved simultaneous particle image velocimetry and flow rate measurements. These are conducted in polydimethylsiloxane channels with spherical nonconducting polystyrene particles and DI water as the background flow. The high electric field tests produced up to three orders of magnitude higher electrokinetic velocities than any previous reports. The maximum electroosmotic velocity and electrophoretic velocity measured were 3.55 and 2.3 m/s. Electrophoretic velocities are measured over the range of 100 V/cm < E < 250 000 V/cm. The results are separated according to the different nonlinear theoretical models, including low and high Peclet numbers, and weak and strong concentration polarization. They show good agreement with the models. Such fast velocities could be used for flow separation, mixing, transport, control, and manipulation of suspended particles as well as microthrust generation among other applications. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Kolmogorov Turbulence Defeated by Anderson Localization for a Bose-Einstein Condensate in a Sinai-Oscillator Trap.

PubMed

Ermann, Leonardo; Vergini, Eduardo; Shepelyansky, Dima L

2017-08-04

We study the dynamics of a Bose-Einstein condensate in a Sinai-oscillator trap under a monochromatic driving force. Such a trap is formed by a harmonic potential and a repulsive disk located in the center vicinity corresponding to the first experiments of condensate formation by Ketterle and co-workers in 1995. We allow that the external driving allows us to model the regime of weak wave turbulence with the Kolmogorov energy flow from low to high energies. We show that in a certain regime of weak driving and weak nonlinearity such a turbulent energy flow is defeated by the Anderson localization that leads to localization of energy on low energy modes. This is in a drastic contrast to the random phase approximation leading to energy flow to high modes. A critical threshold is determined above which the turbulent flow to high energies becomes possible. We argue that this phenomenon can be studied with ultracold atoms in magneto-optical traps.

Shear wave velocity variation across the Taupo Volcanic Zone, New Zealand, from receiver function inversion

USGS Publications Warehouse

Bannister, S.; Bryan, C.J.; Bibby, H.M.

2004-01-01

The Taupo Volcanic Zone (TVZ), New Zealand is a region characterized by very high magma eruption rates and extremely high heat flow, which is manifest in high-temperature geothermal waters. The shear wave velocity structure across the region is inferred using non-linear inversion of receiver functions, which were derived from teleseismic earthquake data. Results from the non-linear inversion, and from forward synthetic modelling, indicate low S velocities at ???6- 16 km depth near the Rotorua and Reporoa calderas. We infer these low-velocity layers to represent the presence of high-level bodies of partial melt associated with the volcanism. Receiver functions at other stations are complicated by reverberations associated with near-surface sedimentary layers. The receiver function data also indicate that the Moho lies between 25 and 30 km, deeper than the 15 ?? 2 km depth previously inferred for the crust-mantle boundary beneath the TVZ. ?? 2004 RAS.

Multi-Scale Long-Range Magnitude and Sign Correlations in Vertical Upward Oil-Gas-Water Three-Phase Flow

NASA Astrophysics Data System (ADS)

Zhao, An; Jin, Ning-de; Ren, Ying-yu; Zhu, Lei; Yang, Xia

2016-01-01

In this article we apply an approach to identify the oil-gas-water three-phase flow patterns in vertical upwards 20 mm inner-diameter pipe based on the conductance fluctuating signals. We use the approach to analyse the signals with long-range correlations by decomposing the signal increment series into magnitude and sign series and extracting their scaling properties. We find that the magnitude series relates to nonlinear properties of the original time series, whereas the sign series relates to the linear properties. The research shows that the oil-gas-water three-phase flows (slug flow, churn flow, bubble flow) can be classified by a combination of scaling exponents of magnitude and sign series. This study provides a new way of characterising linear and nonlinear properties embedded in oil-gas-water three-phase flows.

Stability investigations of relaxing molecular gas flows. Results and perspectives

NASA Astrophysics Data System (ADS)

Grigor'ev, Yurii N.; Ershov, Igor V.

2017-10-01

This article presents results of systematic investigations of a dissipative effect which manifests itself as the growth of hydrodynamic stability and suppression of turbulence in relaxing molecular gas flows. The effect can be a new way for control stability and laminar turbulent transition in aerodynamic flows. The consideration of suppression of inviscid acoustic waves in 2D shear flows is presented. Nonlinear evolution of large-scale vortices and Kelvin — Helmholtz waves in relaxing shear flows are studied. Critical Reynolds numbers in supersonic Couette flows are calculated analytically and numerically within the framework of both classical linear and nonlinear energy hydrodynamic stability theories. The calculations clearly show that the relaxation process can appreciably delay the laminar-turbulent transition. The aim of this article is to show the new dissipative effect, which can be used for flow control and laminarization.

Nonlinear saturation of the Rayleigh instability due to oscillatory flow in a liquid-lined tube

NASA Astrophysics Data System (ADS)

Halpern, David; Grotberg, James B.

2003-10-01

In this paper, the stability of core annular flows consisting of two immiscible fluids in a cylindrical tube with circular cross-section is examined. Such flows are important in a wide range of industrial and biomedical applications. For example, in secondary oil recovery, water is pumped into the well to displace the remaining oil. It is also of relevance in the lung, where a thin liquid film coats the inner surface of the small airways of the lungs. In both cases, the flow is influenced by a surface-tension instability, which may induce the breakup of the core fluid into short plugs, reducing the efficiency of the oil recovery, or blocking the passage of air in the lung thus inducing airway closure. We consider the stability of a thin film coating the inner surface of a rigid cylindrical tube with the less viscous fluid in the core. For thick enough films, the Rayleigh instability forms a liquid bulge that can grow to eventually create a plug blocking the tube. The analysis explores the effect of an oscillatory core flow on the interfacial dynamics and particularly the nonlinear stabilization of the bulge. The oscillatory core flow exerts tangential and normal stresses on the interface between the two fluids that are simplified by uncoupling the core and film analyses in the thin-film high-frequency limit of the governing equations. Lubrication theory is used to derive a nonlinear evolution equation for the position of the air liquid interface which includes the effects of the core flow. It is shown that the core flow can prevent plug formation of the more viscous film layer by nonlinear saturation of the capillary instability. The stabilization mechanism is similar to that of a reversing butter knife, where the core shear wipes the growing liquid bulge back on to the tube wall during the main tidal volume stroke, but allows it to grow back as the stoke and shear turn around. To be successful, the leading film thickness ahead of the bulge must be smaller than the trailing film thickness behind it, a requirement necessitating a large enough core capillary number which promotes a large core shear stress on the interface. The core capillary number is defined to be the ratio of core viscous forces to surface tension forces. When this process is tuned correctly, the two phases balance and there is no net growth of the liquid bulge over one cycle. We find that there is a critical frequency above which plug formation does not occur, and that this critical frequency increases as the tidal volume amplitude of the core flow decreases.

Mastodon

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coleman, Justin Leigh; Veeraraghavan, Swetha; Bolisetti, Chandrakanth

MASTODON has the capability to model stochastic nonlinear soil-structure interaction (NLSSI) in a dynamic probabilistic risk assessment framework. The NLSSI simulations include structural dynamics, time integration, dynamic porous media flow, nonlinear hysteretic soil constitutive models, geometric nonlinearities (gapping, sliding, and uplift). MASTODON is also the MOOSE based master application for dynamic PRA of external hazards.

Numerical Simulations of Laminar Air-Water Flow of a Non-linear Progressive Wave at Low Wind Speed

NASA Astrophysics Data System (ADS)

Wen, X.; Mobbs, S.

2014-03-01

A numerical simulation for two-dimensional laminar air-water flow of a non-linear progressive water wave with large steepness is performed when the background wind speed varies from zero to the wave phase speed. It is revealed that in the water the difference between the analytical solution of potential flow and numerical solution of viscous flow is very small, indicating that both solutions of the potential flow and viscous flow describe the water wave very accurately. In the air the solutions of potential and viscous flows are very different due to the effects of viscosity. The velocity distribution in the airflow is strongly influenced by the background wind speed and it is found that three wind speeds, , (the maximum orbital velocity of a water wave), and (the wave phase speed), are important in distinguishing different features of the flow patterns.

Non-linear dynamics and alternating 'flip' solutions in ferrofluidic Taylor-Couette flow

NASA Astrophysics Data System (ADS)

Altmeyer, Sebastian

2018-04-01

This study treats with the influence of a symmetry-breaking transversal magnetic field on the nonlinear dynamics of ferrofluidic Taylor-Couette flow - flow confined between two concentric independently rotating cylinders. We detected alternating 'flip' solutions which are flow states featuring typical characteristics of slow-fast-dynamics in dynamical systems. The flip corresponds to a temporal change in the axial wavenumber and we find them to appear either as pure 2-fold axisymmetric (due to the symmetry-breaking nature of the applied transversal magnetic field) or involving non-axisymmetric, helical modes in its interim solution. The latter ones show features of typical ribbon solutions. In any case the flip solutions have a preferential first axial wavenumber which corresponds to the more stable state (slow dynamics) and second axial wavenumber, corresponding to the short appearing more unstable state (fast dynamics). However, in both cases the flip time grows exponential with increasing the magnetic field strength before the flip solutions, living on 2-tori invariant manifolds, cease to exist, with lifetime going to infinity. Further we show that ferrofluidic flow turbulence differ from the classical, ordinary (usually at high Reynolds number) turbulence. The applied magnetic field hinders the free motion of ferrofluid partials and therefore smoothen typical turbulent quantities and features so that speaking of mildly chaotic dynamics seems to be a more appropriate expression for the observed motion.

A bioconvection model for a squeezing flow of nanofluid between parallel plates in the presence of gyrotactic microorganisms

NASA Astrophysics Data System (ADS)

Bin-Mohsin, Bandar; Ahmed, Naveed; Adnan; Khan, Umar; Tauseef Mohyud-Din, Syed

2017-04-01

This article deals with the bioconvection flow in a parallel-plate channel. The plates are parallel and the flowing fluid is saturated with nanoparticles, and water is considered as a base fluid because microorganisms can survive only in water. A highly nonlinear and coupled system of partial differential equations presenting the model of bioconvection flow between parallel plates is reduced to a nonlinear and coupled system (nondimensional bioconvection flow model) of ordinary differential equations with the help of feasible nondimensional variables. In order to find the convergent solution of the system, a semi-analytical technique is utilized called variation of parameters method (VPM). Numerical solution is also computed and the Runge-Kutta scheme of fourth order is employed for this purpose. Comparison between these solutions has been made on the domain of interest and found to be in excellent agreement. Also, influence of various parameters has been discussed for the nondimensional velocity, temperature, concentration and density of the motile microorganisms both for suction and injection cases. Almost inconsequential influence of thermophoretic and Brownian motion parameters on the temperature field is observed. An interesting variation are inspected for the density of the motile microorganisms due to the varying bioconvection parameter in suction and injection cases. At the end, we make some concluding remarks in the light of this article.

Koopman operator theory: Past, present, and future

NASA Astrophysics Data System (ADS)

Brunton, Steven; Kaiser, Eurika; Kutz, Nathan

2017-11-01

Koopman operator theory has emerged as a dominant method to represent nonlinear dynamics in terms of an infinite-dimensional linear operator. The Koopman operator acts on the space of all possible measurement functions of the system state, advancing these measurements with the flow of the dynamics. A linear representation of nonlinear dynamics has tremendous potential to enable the prediction, estimation, and control of nonlinear systems with standard textbook methods developed for linear systems. Dynamic mode decomposition has become the leading data-driven method to approximate the Koopman operator, although there are still open questions and challenges around how to obtain accurate approximations for strongly nonlinear systems. This talk will provide an introductory overview of modern Koopman operator theory, reviewing the basics and describing recent theoretical and algorithmic developments. Particular emphasis will be placed on the use of data-driven Koopman theory to characterize and control high-dimensional fluid dynamic systems. This talk will also address key advances in the rapidly growing fields of machine learning and data science that are likely to drive future developments.

Edge localized mode rotation and the nonlinear dynamics of filaments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Morales, J. A.; Bécoulet, M.; Garbet, X.

2016-04-15

Edge Localized Modes (ELMs) rotating precursors were reported few milliseconds before an ELM crash in several tokamak experiments. Also, the reversal of the filaments rotation at the ELM crash is commonly observed. In this article, we present a mathematical model that reproduces the rotation of the ELM precursors as well as the reversal of the filaments rotation at the ELM crash. Linear ballooning theory is used to establish a formula estimating the rotation velocity of ELM precursors. The linear study together with nonlinear magnetohydrodynamic simulations give an explanation to the rotations observed experimentally. Unstable ballooning modes, localized at the pedestal,more » grow and rotate in the electron diamagnetic direction in the laboratory reference frame. Approaching the ELM crash, this rotation decreases corresponding to the moment when the magnetic reconnection occurs. During the highly nonlinear ELM crash, the ELM filaments are cut from the main plasma due to the strong sheared mean flow that is nonlinearly generated via the Maxwell stress tensor.« less

How Artificial Should the Treatment of a Plasma's Viscosity Be?

NASA Astrophysics Data System (ADS)

Whitney, K. G.; Velikovich, A. L.; Thornhill, J. W.; Davis, J.

1999-11-01

Electron viscosity dominates over ion viscosity and is important in describing the generation of shock fronts in highly ionizable plasmas. The sizes of shock front jumps in electron and ion temperature are determined from the magnitudes of the heat flow vector and pressure tensor, which, in turn, acquire non-negligible nonlinear contributions from the temperature and density gradients when these gradients are large. Thus, a consistent treatment of steep gradient formation in plasmas must come from investigations that include the effects of these nonlinear contributions to heat and momentum transport. Coefficients for each of five nonlinear contributions to the pressure tensor for an (r,z) Z-pinch geometry are presented and discussed in this talk. Hydrodynamic code calculations generally are not designed to provide a testbed for directly evaluating the kinetic energy dissipation that occurs at shock fronts; therefore, the strength of these nonlinear pressure tensor terms will be estimated by post-processing a Z-pinch hydrodynamics calculation and a steady-state planar shock wave calculation.

Nonlinear Solver Approaches for the Diffusive Wave Approximation to the Shallow Water Equations

NASA Astrophysics Data System (ADS)

Collier, N.; Knepley, M.

2015-12-01

The diffusive wave approximation to the shallow water equations (DSW) is a doubly-degenerate, nonlinear, parabolic partial differential equation used to model overland flows. Despite its challenges, the DSW equation has been extensively used to model the overland flow component of various integrated surface/subsurface models. The equation's complications become increasingly problematic when ponding occurs, a feature which becomes pervasive when solving on large domains with realistic terrain. In this talk I discuss the various forms and regularizations of the DSW equation and highlight their effect on the solvability of the nonlinear system. In addition to this analysis, I present results of a numerical study which tests the applicability of a class of composable nonlinear algebraic solvers recently added to the Portable, Extensible, Toolkit for Scientific Computation (PETSc).

Distributed Parameter Analysis of Pressure and Flow Disturbances in Rocket Propellant Feed Systems

NASA Technical Reports Server (NTRS)

Dorsch, Robert G.; Wood, Don J.; Lightner, Charlene

1966-01-01

A digital distributed parameter model for computing the dynamic response of propellant feed systems is formulated. The analytical approach used is an application of the wave-plan method of analyzing unsteady flow. Nonlinear effects are included. The model takes into account locally high compliances at the pump inlet and at the injector dome region. Examples of the calculated transient and steady-state periodic responses of a simple hypothetical propellant feed system to several types of disturbances are presented. Included are flow disturbances originating from longitudinal structural motion, gimbaling, throttling, and combustion-chamber coupling. The analytical method can be employed for analyzing developmental hardware and offers a flexible tool for the calculation of unsteady flow in these systems.

Utilizing High-Performance Computing to Investigate Parameter Sensitivity of an Inversion Model for Vadose Zone Flow and Transport

NASA Astrophysics Data System (ADS)

Fang, Z.; Ward, A. L.; Fang, Y.; Yabusaki, S.

2011-12-01

High-resolution geologic models have proven effective in improving the accuracy of subsurface flow and transport predictions. However, many of the parameters in subsurface flow and transport models cannot be determined directly at the scale of interest and must be estimated through inverse modeling. A major challenge, particularly in vadose zone flow and transport, is the inversion of the highly-nonlinear, high-dimensional problem as current methods are not readily scalable for large-scale, multi-process models. In this paper we describe the implementation of a fully automated approach for addressing complex parameter optimization and sensitivity issues on massively parallel multi- and many-core systems. The approach is based on the integration of PNNL's extreme scale Subsurface Transport Over Multiple Phases (eSTOMP) simulator, which uses the Global Array toolkit, with the Beowulf-Cluster inspired parallel nonlinear parameter estimation software, BeoPEST in the MPI mode. In the eSTOMP/BeoPEST implementation, a pre-processor generates all of the PEST input files based on the eSTOMP input file. Simulation results for comparison with observations are extracted automatically at each time step eliminating the need for post-process data extractions. The inversion framework was tested with three different experimental data sets: one-dimensional water flow at Hanford Grass Site; irrigation and infiltration experiment at the Andelfingen Site; and a three-dimensional injection experiment at Hanford's Sisson and Lu Site. Good agreements are achieved in all three applications between observations and simulations in both parameter estimates and water dynamics reproduction. Results show that eSTOMP/BeoPEST approach is highly scalable and can be run efficiently with hundreds or thousands of processors. BeoPEST is fault tolerant and new nodes can be dynamically added and removed. A major advantage of this approach is the ability to use high-resolution geologic models to preserve the spatial structure in the inverse model, which leads to better parameter estimates and improved predictions when using the inverse-conditioned realizations of parameter fields.

Unsteady density-current equations for highly curved terrain

NASA Technical Reports Server (NTRS)

Sivakumaran, N. S.; Dressler, R. F.

1989-01-01

New nonlinear partial differential equations containing terrain curvature and its rate of change are derived that describe the flow of an atmospheric density current. Unlike the classical hydraulic-type equations for density currents, the new equations are valid for two-dimensional, gradually varied flow over highly curved terrain, hence suitable for computing unsteady (or steady) flows over arbitrary mountain/valley profiles. The model assumes the atmosphere above the density current exerts a known arbitrary variable pressure upon the unknown interface. Later this is specialized to the varying hydrostatic pressure of the atmosphere above. The new equations yield the variable velocity distribution, the interface position, and the pressure distribution that contains a centrifugal component, often significantly larger than its hydrostatic component. These partial differential equations are hyperbolic, and the characteristic equations and characteristic directions are derived. Using these to form a characteristic mesh, a hypothetical unsteady curved-flow problem is calculated, not based upon observed data, merely as an example to illustrate the simplicity of their application to unsteady flows over mountains.

Center for the Study of Plasma Microturbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Parker, Scott E.

We have discovered a possible "natural fueling" mechanism in tokamak fusion reactors using large scale gyrokinetic turbulence simulation. In the presence of a heat flux dominated tokamak plasma, cold ions naturally pinch radially inward. If cold DT fuel is introduced near the edge using shallow pellet injection, the cold fuel will pinch inward, at the expense of hot helium ash going radially outward. By adjusting the cold DT fuel concentration, the core DT density profiles can be maintained. We have also shown that cold source ions from edge recycling of cold neutrals are pinched radially inward. This mechanism may bemore » important for fully understanding the edge pedestal buildup after an ELM crash. Work includes benchmarking the gyrokinetic turbulence codes in the electromagnetic regime. This includes cyclone base case parameters with an increasing plasma beta. The code comparisons include GEM, GYRO and GENE. There is good linear agreement between the codes using the Cyclone base case, but including electromagnetics and scanning the plasma beta. All the codes have difficulty achieving nonlinear saturation as the kinetic ballooning limit is approached. GEM does not saturate well when beta gets above about 1/2 of the ideal ballooning limit. We find that the lack of saturation is due to the long wavelength k{sub y} modes being nonlinearly pumped to high levels. If the fundamental k{sub y} mode is zeroed out, higher values of beta nonlinearly saturate well. Additionally, there have been studies to better understand CTEM nonlinear saturation and the importance of zonal flows. We have continued our investigation of trapped electron mode (TEM) turbulence. More recently, we have focused on the nonlinear saturation of TEM turbulence. An important feature of TEM is that in many parameter regimes, the zonal flow is unimportant. We find that when zonal flows are unimportant, zonal density is the dominant saturation mechanism. We developed a simple theory that agrees with the simulation and predicts zonal density generation and feedback stabilization of the most unstable mode even in the absence of zonal flow. We are using GEM to simulate NSTX discharges. We have also done verification and validation on DIII-D. Good agreement with GYRO and DIII-D flux levels were reported in the core region.« less

Multiscale limited penetrable horizontal visibility graph for analyzing nonlinear time series

NASA Astrophysics Data System (ADS)

Gao, Zhong-Ke; Cai, Qing; Yang, Yu-Xuan; Dang, Wei-Dong; Zhang, Shan-Shan

2016-10-01

Visibility graph has established itself as a powerful tool for analyzing time series. We in this paper develop a novel multiscale limited penetrable horizontal visibility graph (MLPHVG). We use nonlinear time series from two typical complex systems, i.e., EEG signals and two-phase flow signals, to demonstrate the effectiveness of our method. Combining MLPHVG and support vector machine, we detect epileptic seizures from the EEG signals recorded from healthy subjects and epilepsy patients and the classification accuracy is 100%. In addition, we derive MLPHVGs from oil-water two-phase flow signals and find that the average clustering coefficient at different scales allows faithfully identifying and characterizing three typical oil-water flow patterns. These findings render our MLPHVG method particularly useful for analyzing nonlinear time series from the perspective of multiscale network analysis.

Sensitivity analysis for aeroacoustic and aeroelastic design of turbomachinery blades

NASA Technical Reports Server (NTRS)

Lorence, Christopher B.; Hall, Kenneth C.

1995-01-01

A new method for computing the effect that small changes in the airfoil shape and cascade geometry have on the aeroacoustic and aeroelastic behavior of turbomachinery cascades is presented. The nonlinear unsteady flow is assumed to be composed of a nonlinear steady flow plus a small perturbation unsteady flow that is harmonic in time. First, the full potential equation is used to describe the behavior of the nonlinear mean (steady) flow through a two-dimensional cascade. The small disturbance unsteady flow through the cascade is described by the linearized Euler equations. Using rapid distortion theory, the unsteady velocity is split into a rotational part that contains the vorticity and an irrotational part described by a scalar potential. The unsteady vorticity transport is described analytically in terms of the drift and stream functions computed from the steady flow. Hence, the solution of the linearized Euler equations may be reduced to a single inhomogeneous equation for the unsteady potential. The steady flow and small disturbance unsteady flow equations are discretized using bilinear quadrilateral isoparametric finite elements. The nonlinear mean flow solution and streamline computational grid are computed simultaneously using Newton iteration. At each step of the Newton iteration, LU decomposition is used to solve the resulting set of linear equations. The unsteady flow problem is linear, and is also solved using LU decomposition. Next, a sensitivity analysis is performed to determine the effect small changes in cascade and airfoil geometry have on the mean and unsteady flow fields. The sensitivity analysis makes use of the nominal steady and unsteady flow LU decompositions so that no additional matrices need to be factored. Hence, the present method is computationally very efficient. To demonstrate how the sensitivity analysis may be used to redesign cascades, a compressor is redesigned for improved aeroelastic stability and two different fan exit guide vanes are redesigned for reduced downstream radiated noise. In addition, a framework detailing how the two-dimensional version of the method may be used to redesign three-dimensional geometries is presented.

Flow Shear Effects in the Onset Physics of Resistive MHD Instabilities in Tokamaks. Final report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brennan, Dylan P.

The progress in this research centers around the computational analysis of flow shear effects in the onset of a 3/2 mode driven by a 1/1 mode in DIII-D equilibria. The initial idea was to try and calculate, via nonlinear simulations with NIMROD, the effects of rotation shear on driven 3/2 and 2/1 seed island physics, in experimentally relevant DIIID equilibria. The simulations indicated that very small seed islands were directly driven, as shielding between the sawtooth and the surfaces is significant at the high Lundquist numbers of the experiment. Instead, long after the initial crash the difference in linear stabilitymore » of the 3/2, which remained prevalent despite the flattening of the core profiles from the sawtooth, contributed to a difference in the eventual seed island evolution. Essentially the seed islands grew or decayed long after the sawtooth crash, and not directly from it. Effectively the dominant 1/1 mode was found to be dragging the coupled modes surrounding it at a high rate through the plasma at their surfaces. The 1/1 mode is locked to the local frame of the plasma in the core, where the flow rate is greatest. The resonant perturbations at the surrounding surfaces propagate in the 'high slip regime' in the language of Fitzpatrick. Peaked flux averaged jxb forces (see Figs. 1 and 2) agree with localized flow modifications at the surfaces in analogy with Ebrahimi, PRL 2007. We track the mode into nonlinear saturation and have found oscillatory states in the evolution. During a visit (11/09) to Tulsa by R.J. LaHaye (GA), it became clear that similar oscillatory states are observed in DIII-D for these types of discharges.« less

Detecting influential observations in nonlinear regression modeling of groundwater flow

USGS Publications Warehouse

Yager, Richard M.

1998-01-01

Nonlinear regression is used to estimate optimal parameter values in models of groundwater flow to ensure that differences between predicted and observed heads and flows do not result from nonoptimal parameter values. Parameter estimates can be affected, however, by observations that disproportionately influence the regression, such as outliers that exert undue leverage on the objective function. Certain statistics developed for linear regression can be used to detect influential observations in nonlinear regression if the models are approximately linear. This paper discusses the application of Cook's D, which measures the effect of omitting a single observation on a set of estimated parameter values, and the statistical parameter DFBETAS, which quantifies the influence of an observation on each parameter. The influence statistics were used to (1) identify the influential observations in the calibration of a three-dimensional, groundwater flow model of a fractured-rock aquifer through nonlinear regression, and (2) quantify the effect of omitting influential observations on the set of estimated parameter values. Comparison of the spatial distribution of Cook's D with plots of model sensitivity shows that influential observations correspond to areas where the model heads are most sensitive to certain parameters, and where predicted groundwater flow rates are largest. Five of the six discharge observations were identified as influential, indicating that reliable measurements of groundwater flow rates are valuable data in model calibration. DFBETAS are computed and examined for an alternative model of the aquifer system to identify a parameterization error in the model design that resulted in overestimation of the effect of anisotropy on horizontal hydraulic conductivity.

Nonlinear Dynamics of a Spring-Supported Piston in a Vibrated Liquid-Filled Housing: II. Experiments

NASA Astrophysics Data System (ADS)

O'Hern, T. J.; Torczynski, J. R.; Clausen, J. R.

2016-11-01

The nonlinear dynamics of a piston supported by a spring in a vibrated liquid-filled housing is investigated experimentally. The housing containing the piston and the liquid is subjected to vibrations along its axis. A post fixed to the housing penetrates a hole through the piston and produces a flow resistance that depends on piston position. Flexible bellows attached to the housing ends enable the piston, liquid, and bellows to execute a collective motion that forces little liquid through the flow resistance. The low damping of this motion leads to a resonance, at which the flow-resistance nonlinearity produces a net force on the piston that can cause it to compress its spring. Experiments are performed to investigate the nonlinear dynamics of this system, and these results are compared to theoretical and numerical results. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Comparison of linear and nonlinear models for coherent hemodynamics spectroscopy (CHS)

NASA Astrophysics Data System (ADS)

Sassaroli, Angelo; Kainerstorfer, Jana; Fantini, Sergio

2015-03-01

A recently proposed linear time-invariant hemodynamic model for coherent hemodynamics spectroscopy1 (CHS) relates the tissue concentrations of oxy- and deoxy-hemoglobin (outputs of the system) to given dynamics of the tissue blood volume, blood flow and rate constant of oxygen diffusion (inputs of the system). This linear model was derived in the limit of "small" perturbations in blood flow velocity. We have extended this model to a more general model (which will be referred to as the nonlinear extension to the original model) that yields the time-dependent changes of oxy and deoxy-hemoglobin concentrations in response to arbitrary dynamic changes in capillary blood flow velocity. The nonlinear extension to the model relies on a general solution of the partial differential equation that governs the spatio-temporal behavior of oxygen saturation of hemoglobin in capillaries and venules on the basis of dynamic (or time resolved) blood transit time. We show preliminary results where the CHS spectra obtained from the linear and nonlinear models are compared to quantify the limits of applicability of the linear model.

Spatial variation of vessel grouping in the xylem of Betula platyphylla Roth.

PubMed

Zhao, Xiping

2016-01-01

Vessel grouping in angiosperms may improve hydraulic integration and increase the spread of cavitations through redundancy pathways. Although disputed, it is increasingly attracting research interest as a potentially significant hydraulic trait. However, the variation of vessel grouping in a tree is poorly understood. I measured the number of solitary and grouped vessels in the xylem of Betula platyphylla Roth. from the pith to the bark along the water flow path. The vessel grouping parameters included the mean number of vessels per vessel group (VG), percentage of solitary vessels (SVP), percentage of radial multiple vessels (MVP), and percentage of cluster vessels (CVP). The effects of cambial age (CA) and flow path-length (PL) on the vessel grouping were analyzed using a linear mixed model.VG and CVP increased nonlinearly, SVP decreased nonlinearly with PL. In trunks and branches, VG and CVP decreased nonlinearly, and SVP increased nonlinearly with CA. In roots, the parameters had no change with CA. MVP was almost constant with PL or CA. The results suggest that vessel grouping has a nonrandom variation pattern, which is affected deeply by cambial age and water flow path.

Drag reduction in channel flow using nonlinear control

NASA Technical Reports Server (NTRS)

Keefe, Laurence R.

1993-01-01

Two nonlinear control schemes have been applied to the problem of drag reduction in channel flow. Both schemes have been tested using numerical simulations at a mass flux Reynolds numbers of 4408, utilizing 2D nonlinear neutral modes for goal dynamics. The OGY-method, which requires feedback, reduces drag to 60-80 percent of the turbulent value at the same Reynolds number, and employs forcing only within a thin region near the wall. The H-method, or model-based control, fails to achieve any drag reduction when starting from a fully turbulent initial condition, but shows potential for suppressing or retarding laminar-to-turbulent transition by imposing instead a transition to a low drag, nonlinear traveling wave solution to the Navier-Stokes equation. The drag in this state corresponds to that achieved by the OGY-method. Model-based control requires no feedback, but in experiments to date has required the forcing be imposed within a thicker layer than the OGY-method. Control energy expenditures in both methods are small, representing less than 0.1 percent of the uncontrolled flow's energy.

Elastic turbulence in entangled semi-dilute DNA solutions measured with optical coherence tomography velocimetry.

PubMed

Malm, A V; Waigh, T A

2017-04-26

The flow instabilities of solutions of high molecular weight DNA in the entangled semi-dilute concentration regime were investigated using optical coherence tomography velocimetry, a technique that provides high spatial (probe volumes of 3.4 pL) and temporal resolution (sub μs) information on the flow behaviour of complex fluids in a rheometer. The velocity profiles of the opaque DNA solutions (high and low salt) were measured as a function of the distance across the gap of a parallel plate rheometer, and their evolution over time was measured. At lower DNA concentrations and low shear rates, the velocity fluctuations were well described by Gaussian functions and the velocity gradient was uniform across the rheometer gap, which is expected for Newtonian flows. As the DNA concentration and shear rate were increased there was a stable wall slip regime followed by an evolving wall slip regime, which is finally followed by the onset of elastic turbulence. Strain localization (shear banding) is observed on the boundaries of the flows at intermediate shear rates, but decreases in the high shear elastic turbulence regime, where bulk strain localization occurs. A dynamic phase diagram for non-linear flow was created to describe the different behaviours.

An eigenvalue approach for the automatic scaling of unknowns in model-based reconstructions: Application to real-time phase-contrast flow MRI.

PubMed

Tan, Zhengguo; Hohage, Thorsten; Kalentev, Oleksandr; Joseph, Arun A; Wang, Xiaoqing; Voit, Dirk; Merboldt, K Dietmar; Frahm, Jens

2017-12-01

The purpose of this work is to develop an automatic method for the scaling of unknowns in model-based nonlinear inverse reconstructions and to evaluate its application to real-time phase-contrast (RT-PC) flow magnetic resonance imaging (MRI). Model-based MRI reconstructions of parametric maps which describe a physical or physiological function require the solution of a nonlinear inverse problem, because the list of unknowns in the extended MRI signal equation comprises multiple functional parameters and all coil sensitivity profiles. Iterative solutions therefore rely on an appropriate scaling of unknowns to numerically balance partial derivatives and regularization terms. The scaling of unknowns emerges as a self-adjoint and positive-definite matrix which is expressible by its maximal eigenvalue and solved by power iterations. The proposed method is applied to RT-PC flow MRI based on highly undersampled acquisitions. Experimental validations include numerical phantoms providing ground truth and a wide range of human studies in the ascending aorta, carotid arteries, deep veins during muscular exercise and cerebrospinal fluid during deep respiration. For RT-PC flow MRI, model-based reconstructions with automatic scaling not only offer velocity maps with high spatiotemporal acuity and much reduced phase noise, but also ensure fast convergence as well as accurate and precise velocities for all conditions tested, i.e. for different velocity ranges, vessel sizes and the simultaneous presence of signals with velocity aliasing. In summary, the proposed automatic scaling of unknowns in model-based MRI reconstructions yields quantitatively reliable velocities for RT-PC flow MRI in various experimental scenarios. Copyright © 2017 John Wiley & Sons, Ltd.

Nonlinear oscillatory rheology and structure of wormlike micellar solutions and colloidal suspensions

NASA Astrophysics Data System (ADS)

Gurnon, Amanda Kate

The complex, nonlinear flow behavior of soft materials transcends industrial applications, smart material design and non-equilibrium thermodynamics. A long-standing, fundamental challenge in soft-matter science is establishing a quantitative connection between the deformation field, local microstructure and macroscopic dynamic flow properties i.e., the rheology. Soft materials are widely used in consumer products and industrial processes including energy recovery, surfactants for personal healthcare (e.g. soap and shampoo), coatings, plastics, drug delivery, medical devices and therapeutics. Oftentimes, these materials are processed by, used during, or exposed to non-equilibrium conditions for which the transient response of the complex fluid is critical. As such, designing new dynamic experiments is imperative to testing these materials and further developing micromechanical models to predict their transient response. Two of the most common classes of these soft materials stand as the focus of the present research; they are: solutions of polymer-like micelles (PLM or also known as wormlike micelles, WLM) and concentrated colloidal suspensions. In addition to their varied applications these two different classes of soft materials are also governed by different physics. In contrast, to the shear thinning behavior of the WLMs at high shear rates, the near hard-sphere colloidal suspensions are known to display increases, sometimes quite substantial, in viscosity (known as shear thickening). The stress response of these complex fluids derive from the shear-induced microstructure, thus measurements of the microstructure under flow are critical for understanding the mechanisms underlying the complex, nonlinear rheology of these complex fluids. A popular micromechanical model is reframed from its original derivation for predicting steady shear rheology of polymers and WLMs to be applicable to weakly nonlinear oscillatory shear flow. The validity, utility and limits of this constitutive model are tested by comparison with experiments on model WLM solutions. Further comparisons to the nonlinear oscillatory shear responses measured from colloidal suspensions establishes this analysis as a promising, quantitative method for understanding the underlying mechanisms responsible for the nonlinear dynamic response of complex fluids. A new experimental technique is developed to measure the microstructure of complex fluids during steady and transient shear flow using small-angle neutron scattering (SANS). The Flow-SANS experimental method is now available to the broader user communities at the NIST Center for Neutron Research, Gaithersburg, MD and the Institut Laue-Langevin, Grenoble, France. Using this new method, a model shear banding WLM solution is interrogated under steady and oscillatory shear. For the first time, the flow-SANS methods identify new metastable states for shear banding WLM solutions, thus establishing the method as capable of probing new states not accessible using traditional steady or linear oscillatory shear methods. The flow-induced three-dimensional microstructure of a colloidal suspension under steady and dynamic oscillatory shear is also measured using these rheo- and flow-SANS methods. A new structure state is identified in the shear thickening regime that proves critical for defining the "hydrocluster" microstructure state of the suspension that is responsible for shear thickening. For both the suspensions and the WLM solutions, stress-SANS rules with the measured microstructures define the individual stress components arising separately from conservative and hydrodynamic forces and these are compared with the macroscopic rheology. Analysis of these results defines the crucial length- and time-scales of the transient microstructure response. The novel dynamic microstructural measurements presented in this dissertation provide new insights into the complexities of shear thickening and shear banding flow phenomena, which are effects observed more broadly across many different types of soft materials. Consequently, the microstructure-rheology property relationships developed for these two classes of complex fluids will aid in the testing and advancement of micromechanical constitutive model development, smart material design, industrial processing and fundamental non-equilibrium thermodynamic research of a broad range of soft materials.

Nonlinear interfacial stability of core-annular film flows in the presence of surfactants

NASA Astrophysics Data System (ADS)

Kas-Danouche, Said A.

This work is an analytical and computational study of the nonlinear interfacial instabilities found in core-annular flows in the presence of surfactants. Core-annular flows arise when two immiscible fluids (for example water and oil) are caused to flow in a pipe under the action of an axial pressure gradient. In one typical type of flow regime, the fluids arrange themselves so that the less viscous (e.g. water) lies in the region of high shear near the pipe wall, with the more viscous fluid occupying the core region. Technologically, this arrangement provides an advantage since the highly viscous fluid is lubricated by the less viscous annulus and for a given pressure gradient the core-fluid flux can be greatly increased. The stability of these flows is of fundamental scientific and practical importance. The sharp interface between the two phases can become unstable by several physical mechanisms and one such mechanism of practical importance is surface tension. In this work we incorporate into our model the effects of insoluble surfactants on the instability. The full problem is derived with particular emphasis paid to the surfactant transport equation which is novel. We then carry out an asymptotic solution of the problem when the annular layer is thin compared to the core-fluid radius and for waves which are of the order of the pipe radius (that is long compared to the annular layer thickness); these scales are in accord with both linear theory as well as experimental observations. The result of the matched asymptotic analysis is a system of coupled nonlinear partial differential equations for the interfacial amplitude and the surfactant concentration on the interface. In the absence of surfactants, the system reduces to the Kuramoto-Sivashinsky equation which has been extensively studied as a paradigm for one-dimensional turbulence in dissipative systems. The surfactant modifies the flow by inducing Marangoni forces along the interface which in turn modify both the velocities and interfacial amplitudes. There are two parameters present in the nonlinear system, the length of the system and a surface Peclet number which measures the diffusion of surfactant on the interface. In order to gain an understanding of the dynamics, we carry out extensive computations using accurate and stable numerical methods capable of following the solution for long times. We map out the dynamics by numerically solving initial value problems on spatially periodic domains where the length of the system is the bifurcation parameter, keeping the Peclet number fixed and equal to one. We find that surfactant acts to suppress chaotic behavior found in its absence for extensive ranges of the bifurcation parameter. The new flow consists of successive windows (in parameter space) of steady-state traveling waves separated by time-periodic attractors. As the length of the system increases a self-similar structure has been found to govern the shapes of the traveling waves as we move from a given window to a lower one. This is elucidated analytically and numerically.

Influence of equilibrium shear flow in the parallel magnetic direction on edge localized mode crash

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luo, Y.; Xiong, Y. Y.; Chen, S. Y., E-mail: sychen531@163.com

2016-04-15

The influence of the parallel shear flow on the evolution of peeling-ballooning (P-B) modes is studied with the BOUT++ four-field code in this paper. The parallel shear flow has different effects in linear simulation and nonlinear simulation. In the linear simulations, the growth rate of edge localized mode (ELM) can be increased by Kelvin-Helmholtz term, which can be caused by the parallel shear flow. In the nonlinear simulations, the results accord with the linear simulations in the linear phase. However, the ELM size is reduced by the parallel shear flow in the beginning of the turbulence phase, which is recognizedmore » as the P-B filaments' structure. Then during the turbulence phase, the ELM size is decreased by the shear flow.« less

Unsteady Transonic Flow Past Airfoils in Rigid Body Motion.

DTIC Science & Technology

1981-03-01

coordinate system. Numerical experiments show that the scheme is very stable and is able to resolve the highly non- linear transonic effects for flutter...Numerical experiments show that the scheme is very stable and is able to resolve the highly nonlinear transonic effects for flutter analysis within...of attack, the angle between the flight direction and the airfoil chord. The effect of chanqinthe angle of attack of a conventional symmetric airfoil

An optimization model for the US Air-Traffic System

NASA Technical Reports Server (NTRS)

Mulvey, J. M.

1986-01-01

A systematic approach for monitoring U.S. air traffic was developed in the context of system-wide planning and control. Towards this end, a network optimization model with nonlinear objectives was chosen as the central element in the planning/control system. The network representation was selected because: (1) it provides a comprehensive structure for depicting essential aspects of the air traffic system, (2) it can be solved efficiently for large scale problems, and (3) the design can be easily communicated to non-technical users through computer graphics. Briefly, the network planning models consider the flow of traffic through a graph as the basic structure. Nodes depict locations and time periods for either individual planes or for aggregated groups of airplanes. Arcs define variables as actual airplanes flying through space or as delays across time periods. As such, a special case of the network can be used to model the so called flow control problem. Due to the large number of interacting variables and the difficulty in subdividing the problem into relatively independent subproblems, an integrated model was designed which will depict the entire high level (above 29000 feet) jet route system for the 48 contiguous states in the U.S. As a first step in demonstrating the concept's feasibility a nonlinear risk/cost model was developed for the Indianapolis Airspace. The nonlinear network program --NLPNETG-- was employed in solving the resulting test cases. This optimization program uses the Truncated-Newton method (quadratic approximation) for determining the search direction at each iteration in the nonlinear algorithm. It was shown that aircraft could be re-routed in an optimal fashion whenever traffic congestion increased beyond an acceptable level, as measured by the nonlinear risk function.

Effects of discrete-electrode arrangement on traveling-wave electroosmotic pumping

NASA Astrophysics Data System (ADS)

Liu, Weiyu; Shao, Jinyou; Ren, Yukun; Wu, Yupan; Wang, Chunhui; Ding, Haitao; Jiang, Hongyuan; Ding, Yucheng

2016-09-01

Traveling-wave electroosmotic (TWEO) pumping arises from the action of an imposed traveling-wave (TW) electric field on its own induced charge in the diffuse double layer, which is formed on top of an electrode array immersed in electrolyte solutions. Such a traveling field can be merely realized in practice by a discrete electrode array upon which the corresponding voltages of correct phase are imposed. By employing the theory of linear and weakly nonlinear double-layer charging dynamics, a physical model incorporating both the nonlinear surface capacitance of diffuse layer and Faradaic current injection is developed herein in order to quantify the changes in TWEO pumping performance from a single-mode TW to discrete electrode configuration. Benefiting from the linear analysis, we investigate the influence of using discrete electrode array to create the TW signal on the resulting fluid motion, and several approaches are suggested to improve the pumping performance. In the nonlinear regime, our full numerical analysis considering the intervening isolation spacing indicates that a practical four-phase discrete electrode configuration of equal electrode and gap width exhibits stronger nonlinearity than expected from the idealized pump applied with a single-mode TW in terms of voltage-dependence of the ideal pumping frequency and peak flow rate, though it has a much lower pumping performance. For model validation, pumping of electrolytes by TWEO is achieved over a confocal spiral four-phase electrode array covered by an insulating microchannel; measurement of flow velocity indicates the modified nonlinear theory considering moderate Faradaic conductance is indeed a more accurate physical description of TWEO. These results offer useful guidelines for designing high-performance TWEO microfluidic pumps with discrete electrode array.

Stabilization of Hypersonic Boundary Layers by Linear and Nonlinear Optimal Perturbations

NASA Technical Reports Server (NTRS)

Paredes, Pedro; Choudhari, Meelan M.; Li, Fei

2017-01-01

The effect of stationary, finite-amplitude, linear and nonlinear optimal perturbations on the modal disturbance growth in a Mach 6 axisymmetric flow over a 7 deg. half-angle cone with 0:126 mm nose radius and 0:305 m length is investigated. The freestream parameters (M = 6, Re(exp 1) = 18 x 10(exp. 6) /m) are selected to match the flow conditions of a previous experiment in the VKI H3 hypersonic tunnel. Plane-marching parabolized stability equations are used in conjunction with a partial-differential equation based planar eigenvalue analysis to characterize the boundary layer instability in the presence of azimuthally periodic streaks. The streaks are observed to stabilize nominally planar Mack mode instabilities, although oblique Mack mode and first-mode disturbances are destabilized. Experimentally measured transition onset in the absence of any streaks correlates with an amplification factor of N = 6 for the planar Mack modes. For high enough streak amplitudes, the transition threshold of N = 6 is not reached by the Mack mode instabilities within the length of the cone; however, subharmonic first-mode instabilities, which are destabilized by the presence of the streaks, do reach N = 6 near the end of the cone. The highest stabilization is observed at streak amplitudes of approximately 20 percent of the freestream velocity. Because the use of initial disturbance profiles based on linear optimal growth theory may yield suboptimal control in the context of nonlinear streaks, the computational predictions are extended to nonlinear optimal growth theory. Results show that by using nonlinearly optimal perturbation leads to slightly enhanced stabilization of plane Mack mode disturbances as well as reduced destabilization of subharmonic first-mode disturbances.

Numerical Simulation of a High Mach Number Jet Flow

NASA Technical Reports Server (NTRS)

Hayder, M. Ehtesham; Turkel, Eli; Mankbadi, Reda R.

1993-01-01

The recent efforts to develop accurate numerical schemes for transition and turbulent flows are motivated, among other factors, by the need for accurate prediction of flow noise. The success of developing high speed civil transport plane (HSCT) is contingent upon our understanding and suppression of the jet exhaust noise. The radiated sound can be directly obtained by solving the full (time-dependent) compressible Navier-Stokes equations. However, this requires computational storage that is beyond currently available machines. This difficulty can be overcome by limiting the solution domain to the near field where the jet is nonlinear and then use acoustic analogy (e.g., Lighthill) to relate the far-field noise to the near-field sources. The later requires obtaining the time-dependent flow field. The other difficulty in aeroacoustics computations is that at high Reynolds numbers the turbulent flow has a large range of scales. Direct numerical simulations (DNS) cannot obtain all the scales of motion at high Reynolds number of technological interest. However, it is believed that the large scale structure is more efficient than the small-scale structure in radiating noise. Thus, one can model the small scales and calculate the acoustically active scales. The large scale structure in the noise-producing initial region of the jet can be viewed as a wavelike nature, the net radiated sound is the net cancellation after integration over space. As such, aeroacoustics computations are highly sensitive to errors in computing the sound sources. It is therefore essential to use a high-order numerical scheme to predict the flow field. The present paper presents the first step in a ongoing effort to predict jet noise. The emphasis here is in accurate prediction of the unsteady flow field. We solve the full time-dependent Navier-Stokes equations by a high order finite difference method. Time accurate spatial simulations of both plane and axisymmetric jet are presented. Jet Mach numbers of 1.5 and 2.1 are considered. Reynolds number in the simulations was about a million. Our numerical model is based on the 2-4 scheme by Gottlieb & Turkel. Bayliss et al. applied the 2-4 scheme in boundary layer computations. This scheme was also used by Ragab and Sheen to study the nonlinear development of supersonic instability waves in a mixing layer. In this study, we present two dimensional direct simulation results for both plane and axisymmetric jets. These results are compared with linear theory predictions. These computations were made for near nozzle exit region and velocity in spanwise/azimuthal direction was assumed to be zero.

Theoretical and Experimental Study on Wide Range Optical Fiber Turbine Flow Sensor.

PubMed

Du, Yuhuan; Guo, Yingqing

2016-07-15

In this paper, a novel fiber turbine flow sensor was proposed and demonstrated for liquid measurement with optical fiber, using light intensity modulation to measure the turbine rotational speed for converting to flow rate. The double-circle-coaxial (DCC) fiber probe was introduced in frequency measurement for the first time. Through the divided ratio of two rings light intensity, the interference in light signals acquisition can be eliminated. To predict the characteristics between the output frequency and flow in the nonlinear range, the turbine flow sensor model was built. Via analyzing the characteristics of turbine flow sensor, piecewise linear equations were achieved in expanding the flow measurement range. Furthermore, the experimental verification was tested. The results showed that the flow range ratio of DN20 turbine flow sensor was improved 2.9 times after using piecewise linear in the nonlinear range. Therefore, combining the DCC fiber sensor and piecewise linear method, it can be developed into a strong anti-electromagnetic interference(anti-EMI) and wide range fiber turbine flowmeter.

Theoretical and Experimental Study on Wide Range Optical Fiber Turbine Flow Sensor

PubMed Central

Du, Yuhuan; Guo, Yingqing

2016-01-01

In this paper, a novel fiber turbine flow sensor was proposed and demonstrated for liquid measurement with optical fiber, using light intensity modulation to measure the turbine rotational speed for converting to flow rate. The double-circle-coaxial (DCC) fiber probe was introduced in frequency measurement for the first time. Through the divided ratio of two rings light intensity, the interference in light signals acquisition can be eliminated. To predict the characteristics between the output frequency and flow in the nonlinear range, the turbine flow sensor model was built. Via analyzing the characteristics of turbine flow sensor, piecewise linear equations were achieved in expanding the flow measurement range. Furthermore, the experimental verification was tested. The results showed that the flow range ratio of DN20 turbine flow sensor was improved 2.9 times after using piecewise linear in the nonlinear range. Therefore, combining the DCC fiber sensor and piecewise linear method, it can be developed into a strong anti-electromagnetic interference(anti-EMI) and wide range fiber turbine flowmeter. PMID:27428976

Towards a Highly Efficient Meshfree Simulation of Non-Newtonian Free Surface Ice Flow: Application to the Haut Glacier d'Arolla

NASA Astrophysics Data System (ADS)

Shcherbakov, V.; Ahlkrona, J.

2016-12-01

In this work we develop a highly efficient meshfree approach to ice sheet modeling. Traditionally mesh based methods such as finite element methods are employed to simulate glacier and ice sheet dynamics. These methods are mature and well developed. However, despite of numerous advantages these methods suffer from some drawbacks such as necessity to remesh the computational domain every time it changes its shape, which significantly complicates the implementation on moving domains, or a costly assembly procedure for nonlinear problems. We introduce a novel meshfree approach that frees us from all these issues. The approach is built upon a radial basis function (RBF) method that, thanks to its meshfree nature, allows for an efficient handling of moving margins and free ice surface. RBF methods are also accurate and easy to implement. Since the formulation is stated in strong form it allows for a substantial reduction of the computational cost associated with the linear system assembly inside the nonlinear solver. We implement a global RBF method that defines an approximation on the entire computational domain. This method exhibits high accuracy properties. However, it suffers from a disadvantage that the coefficient matrix is dense, and therefore the computational efficiency decreases. In order to overcome this issue we also implement a localized RBF method that rests upon a partition of unity approach to subdivide the domain into several smaller subdomains. The radial basis function partition of unity method (RBF-PUM) inherits high approximation characteristics form the global RBF method while resulting in a sparse system of equations, which essentially increases the computational efficiency. To demonstrate the usefulness of the RBF methods we model the velocity field of ice flow in the Haut Glacier d'Arolla. We assume that the flow is governed by the nonlinear Blatter-Pattyn equations. We test the methods for different basal conditions and for a free moving surface. Both RBF methods are compared with a classical finite element method in terms of accuracy and efficiency. We find that the RBF methods are more efficient than the finite element method and well suited for ice dynamics modeling, especially the partition of unity approach.

Efficient Nonlinear Atomization Model for Thin 3D Free Liquid Films

NASA Astrophysics Data System (ADS)

Mehring, Carsten

2007-03-01

Reviewed is a nonlinear reduced-dimension thin-film model developed by the author and aimed at the prediction of spray formation from thin films such as those found in gas-turbine engines (e.g., prefilming air-blast atomizers), heavy-fuel-oil burners (e.g., rotary-cup atomizers) and in the paint industry (e.g., flat-fan atomizers). Various implementations of the model focusing on different model-aspects, i.e., effect of film geometry, surface tension, liquid viscosity, coupling with surrounding gas-phase flow, influence of long-range intermolecular forces during film rupture are reviewed together with a validation of the nonlinear wave propagation characteristics predicted by the model for inviscid planar films using a two-dimensional vortex- method. An extension and generalization of the current nonlinear film model for implementation into a commercial flow- solver is outlined.

Nonlinear Thermal Instability in Compressible Viscous Flows Without Heat Conductivity

NASA Astrophysics Data System (ADS)

Jiang, Fei

2018-04-01

We investigate the thermal instability of a smooth equilibrium state, in which the density function satisfies Schwarzschild's (instability) condition, to a compressible heat-conducting viscous flow without heat conductivity in the presence of a uniform gravitational field in a three-dimensional bounded domain. We show that the equilibrium state is linearly unstable by a modified variational method. Then, based on the constructed linearly unstable solutions and a local well-posedness result of classical solutions to the original nonlinear problem, we further construct the initial data of linearly unstable solutions to be the one of the original nonlinear problem, and establish an appropriate energy estimate of Gronwall-type. With the help of the established energy estimate, we finally show that the equilibrium state is nonlinearly unstable in the sense of Hadamard by a careful bootstrap instability argument.

Stagnation point flow of wormlike micellar solutions in a microfluidic cross-slot device: effects of surfactant concentration and ionic environment.

PubMed

Haward, Simon J; McKinley, Gareth H

2012-03-01

We employ the techniques of microparticle image velocimetry and full-field birefringence microscopy combined with mechanical measurements of the pressure drop to perform a detailed characterization of the extensional rheology and elastic flow instabilities observed for a range of wormlike micellar solutions flowing through a microfluidic cross-slot device. As the flow rate through the device is increased, the flow first bifurcates from a steady symmetric to a steady asymmetric configuration characterized by a birefringent strand of highly aligned micellar chains oriented along the shear-free centerline of the flow field. At higher flow rates the flow becomes three dimensional and time dependent and is characterized by aperiodic spatiotemporal fluctuations of the birefringent strand. The extensional properties and critical conditions for the onset of flow instabilities in the fluids are highly dependent on the fluid formulation (surfactant concentration and ionic strength) and the resulting changes in the linear viscoelasticity and nonlinear shear rheology of the fluids. By combining the measurements of critical conditions for the flow transitions with the viscometric material properties and the degree of shear-thinning characterizing each test fluid, it is possible to construct a stability diagram for viscoelastic flow of complex fluids in the cross-slot geometry.

Wave-induced response of a floating two-dimensional body with a moonpool.

PubMed

Fredriksen, Arnt G; Kristiansen, Trygve; Faltinsen, Odd M

2015-01-28

Regular wave-induced behaviour of a floating stationary two-dimensional body with a moonpool is studied. The focus is on resonant piston-mode motion in the moonpool and rigid-body motions. Dedicated two-dimensional experiments have been performed. Two numerical hybrid methods, which have previously been applied to related problems, are further developed. Both numerical methods couple potential and viscous flow. The semi-nonlinear hybrid method uses linear free-surface and body-boundary conditions. The other one uses fully nonlinear free-surface and body-boundary conditions. The harmonic polynomial cell method solves the Laplace equation in the potential flow domain, while the finite volume method solves the Navier-Stokes equations in the viscous flow domain near the body. Results from the two codes are compared with the experimental data. The nonlinear hybrid method compares well with the data, while certain discrepancies are observed for the semi-nonlinear method. In particular, the roll motion is over-predicted by the semi-nonlinear hybrid method. Error sources in the semi-nonlinear hybrid method are discussed. The moonpool strongly affects heave motions in a frequency range around the piston-mode resonance frequency of the moonpool. No resonant water motions occur in the moonpool at the piston-mode resonance frequency. Instead large moonpool motions occur at a heave natural frequency associated with small damping near the piston-mode resonance frequency. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

A note on the solutions of some nonlinear equations arising in third-grade fluid flows: an exact approach.

PubMed

Aziz, Taha; Mahomed, F M

2014-01-01

In this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. We obtain some simple closed-form steady-state solutions of these reduced equations. Our solutions are valid for the whole domain [0,∞) and also satisfy the physical boundary conditions. We also present the numerical solutions for some of the underlying equations. The graphs corresponding to the essential physical parameters of the flow are presented and discussed.

Laboratory Study of Magnetorotational Instability and Hydrodynamic Stability at Large Reynolds Numbers

NASA Technical Reports Server (NTRS)

Ji, H.; Burin, M.; Schartman, E.; Goodman, J.; Liu, W.

2006-01-01

Two plausible mechanisms have been proposed to explain rapid angular momentum transport during accretion processes in astrophysical disks: nonlinear hydrodynamic instabilities and magnetorotational instability (MRI). A laboratory experiment in a short Taylor-Couette flow geometry has been constructed in Princeton to study both mechanisms, with novel features for better controls of the boundary-driven secondary flows (Ekman circulation). Initial results on hydrodynamic stability have shown negligible angular momentum transport in Keplerian-like flows with Reynolds numbers approaching one million, casting strong doubt on the viability of nonlinear hydrodynamic instability as a source for accretion disk turbulence.

A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach

PubMed Central

Mahomed, F. M.

2014-01-01

In this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. We obtain some simple closed-form steady-state solutions of these reduced equations. Our solutions are valid for the whole domain [0,∞) and also satisfy the physical boundary conditions. We also present the numerical solutions for some of the underlying equations. The graphs corresponding to the essential physical parameters of the flow are presented and discussed. PMID:25143962

Physical Limits on the Predictability of Erosion and Sediment Transport by Landslides and Debris Flows

NASA Astrophysics Data System (ADS)

Iverson, R. M.

2015-12-01

Episodic landslides and debris flows play a key role in sculpting many steep landscapes, and they also pose significant natural hazards. Field evidence, laboratory experiments, and theoretical analyses show that variations in the quantity, speed, and distance of sediment transport by landslides and debris flows can depend strongly on nuanced differences in initial conditions. Moreover, initial conditions themselves can be strongly dependent on the geological legacy of prior events. The scope of these dependencies is revealed by the results of landslide dynamics experiments [Iverson et al., Science, 2000], debris-flow erosion experiments [Iverson et al., Nature Geosci., 2011], and numerical simulations of the highly destructive 2014 Oso, Washington, landslide [Iverson et al., Earth Planet. Sci. Let., 2015]. In each of these cases, feedbacks between basal sediment deformation and pore-pressure generation cause the speed and distance of sediment transport to be very sensitive to subtle differences in the ambient sediment porosity and water content. On the other hand, the onset of most landslides and debris flows depends largely on pore-water pressure distributions and only indirectly on sediment porosity and water content. Thus, even if perfect predictions of the locations and timing of landslides and debris flows were available, the dynamics of the events - and their consequent hazards and sediment transport - would be difficult to predict. This difficulty is a manifestation of the nonlinear physics involved, rather than of poor understanding of those physics. Consequently, physically based models for assessing the hazards and sediment transport due to landslides and debris flows must take into account both evolving nonlinear dynamics and inherent uncertainties about initial conditions. By contrast, landscape evolution models that use prescribed algebraic formulas to represent sediment transport by landslides and debris flows lack a sound physical basis.

Analysis and prediction of flow from local source in a river basin using a Neuro-fuzzy modeling tool.

PubMed

Aqil, Muhammad; Kita, Ichiro; Yano, Akira; Nishiyama, Soichi

2007-10-01

Traditionally, the multiple linear regression technique has been one of the most widely used models in simulating hydrological time series. However, when the nonlinear phenomenon is significant, the multiple linear will fail to develop an appropriate predictive model. Recently, neuro-fuzzy systems have gained much popularity for calibrating the nonlinear relationships. This study evaluated the potential of a neuro-fuzzy system as an alternative to the traditional statistical regression technique for the purpose of predicting flow from a local source in a river basin. The effectiveness of the proposed identification technique was demonstrated through a simulation study of the river flow time series of the Citarum River in Indonesia. Furthermore, in order to provide the uncertainty associated with the estimation of river flow, a Monte Carlo simulation was performed. As a comparison, a multiple linear regression analysis that was being used by the Citarum River Authority was also examined using various statistical indices. The simulation results using 95% confidence intervals indicated that the neuro-fuzzy model consistently underestimated the magnitude of high flow while the low and medium flow magnitudes were estimated closer to the observed data. The comparison of the prediction accuracy of the neuro-fuzzy and linear regression methods indicated that the neuro-fuzzy approach was more accurate in predicting river flow dynamics. The neuro-fuzzy model was able to improve the root mean square error (RMSE) and mean absolute percentage error (MAPE) values of the multiple linear regression forecasts by about 13.52% and 10.73%, respectively. Considering its simplicity and efficiency, the neuro-fuzzy model is recommended as an alternative tool for modeling of flow dynamics in the study area.

Transition of planar Couette flow at infinite Reynolds numbers.

PubMed

Itano, Tomoaki; Akinaga, Takeshi; Generalis, Sotos C; Sugihara-Seki, Masako

2013-11-01

An outline of the state space of planar Couette flow at high Reynolds numbers (Re<10^{5}) is investigated via a variety of efficient numerical techniques. It is verified from nonlinear analysis that the lower branch of the hairpin vortex state (HVS) asymptotically approaches the primary (laminar) state with increasing Re. It is also predicted that the lower branch of the HVS at high Re belongs to the stability boundary that initiates a transition to turbulence, and that one of the unstable manifolds of the lower branch of HVS lies on the boundary. These facts suggest HVS may provide a criterion to estimate a minimum perturbation arising transition to turbulent states at the infinite Re limit.

Thermal maturity patterns of Cretaceous and Tertiary rocks, San Juan Basin, Colorado and New Mexico

USGS Publications Warehouse

Law, B.E.

1992-01-01

Horizontal and vertical thermal maturity patterns and time-temperature modeling indicate that the high levels of thermal maturity in the northern part of the basin are due to either: 1) convective heat transfer associated with a deeply buried heat source located directly below the northern part of the basin or 2) the circulation of relatively hot fluids into the basin from a heat source north of the basin located near the San Juan Mountains. Time-temperature and kinetic modeling of nonlinear Rm profiles indicates that present-day heat flow is insufficient to account for the measured levels of thermal maturity. Furthermore, in order to match nonlinear Rm profiles, it is necessary to assign artifically high thermal-conductivity values to some of the stratigraphic units. These unrealistically high thermal conductivities are interpreted as evidence of convective heat transfer. -from Author

On a PLIF quantification methodology in a nonlinear dye response regime

NASA Astrophysics Data System (ADS)

Baj, P.; Bruce, P. J. K.; Buxton, O. R. H.

2016-06-01

A new technique of planar laser-induced fluorescence calibration is presented in this work. It accounts for a nonlinear dye response at high concentrations, an illumination light attenuation and a secondary fluorescence's influence in particular. An analytical approximation of a generic solution of the Beer-Lambert law is provided and utilized for effective concentration evaluation. These features make the technique particularly well suited for high concentration measurements, or those with a large range of concentration values, c, present (i.e. a high dynamic range of c). The method is applied to data gathered in a water flume experiment where a stream of a fluorescent dye (rhodamine 6G) was released into a grid-generated turbulent flow. Based on these results, it is shown that the illumination attenuation and the secondary fluorescence introduce a significant error into the data quantification (up to 15 and 80 %, respectively, for the case considered in this work) unless properly accounted for.

Sparsity enabled cluster reduced-order models for control

NASA Astrophysics Data System (ADS)

Kaiser, Eurika; Morzyński, Marek; Daviller, Guillaume; Kutz, J. Nathan; Brunton, Bingni W.; Brunton, Steven L.

2018-01-01

Characterizing and controlling nonlinear, multi-scale phenomena are central goals in science and engineering. Cluster-based reduced-order modeling (CROM) was introduced to exploit the underlying low-dimensional dynamics of complex systems. CROM builds a data-driven discretization of the Perron-Frobenius operator, resulting in a probabilistic model for ensembles of trajectories. A key advantage of CROM is that it embeds nonlinear dynamics in a linear framework, which enables the application of standard linear techniques to the nonlinear system. CROM is typically computed on high-dimensional data; however, access to and computations on this full-state data limit the online implementation of CROM for prediction and control. Here, we address this key challenge by identifying a small subset of critical measurements to learn an efficient CROM, referred to as sparsity-enabled CROM. In particular, we leverage compressive measurements to faithfully embed the cluster geometry and preserve the probabilistic dynamics. Further, we show how to identify fewer optimized sensor locations tailored to a specific problem that outperform random measurements. Both of these sparsity-enabled sensing strategies significantly reduce the burden of data acquisition and processing for low-latency in-time estimation and control. We illustrate this unsupervised learning approach on three different high-dimensional nonlinear dynamical systems from fluids with increasing complexity, with one application in flow control. Sparsity-enabled CROM is a critical facilitator for real-time implementation on high-dimensional systems where full-state information may be inaccessible.

MHD stagnation-point flow over a nonlinearly shrinking sheet with suction effect

NASA Astrophysics Data System (ADS)

Awaludin, Izyan Syazana; Ahmad, Rokiah; Ishak, Anuar

2018-04-01

The stagnation point flow over a shrinking permeable sheet in the existence of magnetic field is numerically investigated in this paper. The system of partial differential equations are transformed to a nonlinear ordinary differential equation using similarity transformation and is solved numerically using the boundary value problem solver, bvp4c, in Matlab software. It is found that dual solutions exist for a certain range of the shrinking strength.

Determination of the equation parameters of carbon flow curves and estimated carbon flow and CO2 emissions from broiler production.

PubMed

Henn, J D; Bockor, L; Borille, R; Coldebella, A; Ribeiro, A M L; Kessler, A M

2015-09-01

The objective of this study was to determine the equation parameters of carbon (i.e., C) flow curves and to estimate C flow and carbon dioxide (i.e., CO2) emissions from the production of 1- to 49-day-old broilers from different genetic strains. In total, 384 1-day-old chicks were used, distributed into 4 groups: high-performance males (Cobb-M) and females (Cobb-F), and intermediate-performance males (C44-M) and females (C44-F), with 6 replicates/treatment according to a completely randomized study design. Carbon intake and retention were calculated based on diet and body C composition, and expired C was stoichiometrically estimated as digestible C intake-C retention-C in the urine. Litter C emission was estimated as initial litter C+C in the excreta-final litter C. Carbon flow curves were determined fitting data by nonlinear regression using the Gompertz function. Expired CO2 was calculated based on expired C. The applied nonlinear model presented goodness-of-fit for all responses (R2>0.99). Carbon dioxide production was highly correlated with growth rate. At 42 d age, CO2 expiration (g/bird) was 3,384.4 for Cobb-M, 2,947.9 for Cobb-F, 2,512.5 for C44-M, and 2185.1 for C44-F. Age also significantly affected CO2 production: to achieve 2.0 kg BW, CO2 expiration (g/bird) was 1,794.3 for Cobb-M, 2,016.5 for Cobb-F, 2617.7 for C44-M, and 3,092.3 for C44-F. The obtained equations present high predictability to estimate individual CO2 emissions in strains of Cobb and C44 broilers of any weight, or age, reared between 1 and 49 d age. © 2015 Poultry Science Association Inc.

Linear and nonlinear dynamics of current-driven waves in dusty plasmas

NASA Astrophysics Data System (ADS)

Ahmad, Ali; Ali Shan, S.; Haque, Q.; Saleem, H.

2012-09-01

The linear and nonlinear dynamics of a recently proposed plasma mode of dusty plasma is studied using kappa distribution for electrons. This electrostatic wave can propagate in the plasma due to the sheared flow of electrons and ions parallel to the external magnetic field in the presence of stationary dust. The coupling of this wave with the usual drift wave and ion acoustic wave is investigated. D'Angelo's mode is also modified in the presence of superthermal electrons. In the nonlinear regime, the wave can give rise to dipolar vortex structures if the shear in flow is weaker and tripolar vortices if the flow has steeper gradient. The results have been applied to Saturn's magnetosphere corresponding to negatively charged dust grains. But the theoretical model is applicable for positively charged dust as well. This work will be useful for future observations and studies of dusty environments of planets and comets.

A Class of Exact Solutions of the Boussinesq Equation for Horizontal and Sloping Aquifers

NASA Astrophysics Data System (ADS)

Bartlett, M. S.; Porporato, A.

2018-02-01

The nonlinear equation of Boussinesq (1877) is a foundational approach for studying groundwater flow through an unconfined aquifer, but solving the full nonlinear version of the Boussinesq equation remains a challenge. Here, we present an exact solution to the full nonlinear Boussinesq equation that not only applies to sloping aquifers but also accounts for source and sink terms such as bedrock seepage, an often significant flux in headwater catchments. This new solution captures the hysteretic relationship (a loop rating curve) between the groundwater flow rate and the water table height, which may be used to provide a more realistic representation of streamflow and groundwater dynamics in hillslopes. In addition, the solution provides an expression where the flow recession varies based on hillslope parameters such as bedrock slope, bedrock seepage, aquifer recharge, plant transpiration, and other factors that vary across landscape types.

Nonlinear Dynamics of Turbulent Thermals in Shear Flow

NASA Astrophysics Data System (ADS)

Ingel, L. Kh.

2018-03-01

The nonlinear integral model of a turbulent thermal is extended to the case of the horizontal component of its motion relative to the medium (e.g., thermal floating-up in shear flow). In contrast to traditional models, the possibility of a heat source in the thermal is taken into account. For a piecewise constant vertical profile of the horizontal velocity of the medium and a constant vertical velocity shear, analytical solutions are obtained which describe different modes of dynamics of thermals. The nonlinear interaction between the horizontal and vertical components of thermal motion is studied because each of the components influences the rate of entrainment of the surrounding medium, i.e., the growth rate of the thermal size and, hence, its mobility. It is shown that the enhancement of the entrainment of the medium due to the interaction between the thermal and the cross flow can lead to a significant decrease in the mobility of the thermal.

Analysis of Three-Dimensional, Nonlinear Development of Wave-Like Structure in a Compressible Round Jet

NASA Technical Reports Server (NTRS)

Dahl, Milo D.; Mankbadi, Reda R.

2002-01-01

An analysis of the nonlinear development of the large-scale structures or instability waves in compressible round jets was conducted using the integral energy method. The equations of motion were decomposed into two sets of equations; one set governing the mean flow motion and the other set governing the large-scale structure motion. The equations in each set were then combined to derive kinetic energy equations that were integrated in the radial direction across the jet after the boundary-layer approximations were applied. Following the application of further assumptions regarding the radial shape of the mean flow and the large structures, equations were derived that govern the nonlinear, streamwise development of the large structures. Using numerically generated mean flows, calculations show the energy exchanges and the effects of the initial amplitude on the coherent structure development in the jet.

Model and Comparative Study for Flow of Viscoelastic Nanofluids with Cattaneo-Christov Double Diffusion

PubMed Central

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Alsaedi, Ahmed

2017-01-01

Here two classes of viscoelastic fluids have been analyzed in the presence of Cattaneo-Christov double diffusion expressions of heat and mass transfer. A linearly stretched sheet has been used to create the flow. Thermal and concentration diffusions are characterized firstly by introducing Cattaneo-Christov fluxes. Novel features regarding Brownian motion and thermophoresis are retained. The conversion of nonlinear partial differential system to nonlinear ordinary differential system has been taken into place by using suitable transformations. The resulting nonlinear systems have been solved via convergent approach. Graphs have been sketched in order to investigate how the velocity, temperature and concentration profiles are affected by distinct physical flow parameters. Numerical values of skin friction coefficient and heat and mass transfer rates at the wall are also computed and discussed. Our observations demonstrate that the temperature and concentration fields are decreasing functions of thermal and concentration relaxation parameters. PMID:28046011

Numerical solution of turbulent flow past a backward facing step using a nonlinear K-epsilon model

NASA Technical Reports Server (NTRS)

Speziale, C. G.; Ngo, Tuan

1987-01-01

The problem of turbulent flow past a backward facing step is important in many technological applications and has been used as a standard test case to evaluate the performance of turbulence models in the prediction of separated flows. It is well known that the commonly used kappa-epsilon (and K-l) models of turbulence yield inaccurate predictions for the reattachment points in this problem. By an analysis of the mean vorticity transport equation, it will be argued that the intrinsically inaccurate prediction of normal Reynolds stress differences by the Kappa-epsilon and K-l models is a major contributor to this problem. Computations using a new nonlinear kappa-epsilon model (which alleviates this deficiency) are made with the TEACH program. Comparisons are made between the improved results predicted by this nonlinear kappa-epsilon model and those obtained from the linear kappa-epsilon model as well as from second-order closure models.

Numerical study of Free Convective Viscous Dissipative flow along Vertical Cone with Influence of Radiation using Network Simulation method

NASA Astrophysics Data System (ADS)

Kannan, R. M.; Pullepu, Bapuji; Immanuel, Y.

2018-04-01

A two dimensional mathematical model is formulated for the transient laminar free convective flow with heat transfer over an incompressible viscous fluid past a vertical cone with uniform surface heat flux with combined effects of viscous dissipation and radiation. The dimensionless boundary layer equations of the flow which are transient, coupled and nonlinear Partial differential equations are solved using the Network Simulation Method (NSM), a powerful numerical technique which demonstrates high efficiency and accuracy by employing the network simulator computer code Pspice. The velocity and temperature profiles have been investigated for various factors, namely viscous dissipation parameter ε, Prandtl number Pr and radiation Rd are analyzed graphically.

Subcritical Transition in Channel Flows

NASA Astrophysics Data System (ADS)

Maestri, Joseph; Hall, Philip

2014-11-01

Exact-coherent structures, or colloquially non-linear solutions to the Navier-Stokes equations, have been the subject of great interest over the past decade due to their relevance in understanding the process of transition to turbulence in shear flows. Over the past few years the relationship between high Reynolds number vortex-wave interaction theory and such states has been elucidated in a number of papers and has provided a solid asymptotic framework to understand the so-called self-sustaining process that maintains such structures. In this talk, we will discuss this relationship before talking about recent work on solving the vortex-wave interaction equations using numerical techniques in order to propose laminar-flow control techniques.

Adaptive probabilistic collocation based Kalman filter for unsaturated flow problem

NASA Astrophysics Data System (ADS)

Man, J.; Li, W.; Zeng, L.; Wu, L.

2015-12-01

The ensemble Kalman filter (EnKF) has gained popularity in hydrological data assimilation problems. As a Monte Carlo based method, a relatively large ensemble size is usually required to guarantee the accuracy. As an alternative approach, the probabilistic collocation based Kalman filter (PCKF) employs the Polynomial Chaos to approximate the original system. In this way, the sampling error can be reduced. However, PCKF suffers from the so called "cure of dimensionality". When the system nonlinearity is strong and number of parameters is large, PCKF is even more computationally expensive than EnKF. Motivated by recent developments in uncertainty quantification, we propose a restart adaptive probabilistic collocation based Kalman filter (RAPCKF) for data assimilation in unsaturated flow problem. During the implementation of RAPCKF, the important parameters are identified and active PCE basis functions are adaptively selected. The "restart" technology is used to alleviate the inconsistency between model parameters and states. The performance of RAPCKF is tested by unsaturated flow numerical cases. It is shown that RAPCKF is more efficient than EnKF with the same computational cost. Compared with the traditional PCKF, the RAPCKF is more applicable in strongly nonlinear and high dimensional problems.

Perturbation theory and numerical modelling of weakly and moderately nonlinear incompressible Richtmyer-Meshkov instability

NASA Astrophysics Data System (ADS)

Herrmann, M.; Velikovich, A. L.; Abarzhi, S. I.

2014-10-01

A study of incompressible two-dimensional Richtmyer-Meshkov instability by means of high-order Eulerian perturbation theory and numerical simulations is reported. Nonlinear corrections to Richtmyer's impulsive formula for the bubble and spike growth rates have been calculated analytically for arbitrary Atwood number and an explicit formula has been obtained for it in the Boussinesq limit. Conditions for early-time acceleration and deceleration of the bubble and the spike have been derived. In our simulations we have solved 2D unsteady Navier-Stokes equations for immiscible incompressible fluids using the finite volume fractional step flow solver NGA developed by, coupled to the level set based interface solver LIT,. The impact of small amounts of viscosity and surface tension on the RMI flow dynamics is studied numerically. Simulation results are compared to the theory to demonstrate successful code verification and highlight the influence of the theory's ideal inviscid flow assumption. Theoretical time histories of the interface curvature at the bubble and spike tip and the profiles of vertical and horizontal velocities have been favorably compared to simulation results, which converge to the theoretical predictions as the Reynolds and Weber numbers are increased. Work supported by the US DOE/NNSA.

Nonlinear dynamics of coiling, and mounding in viscoelastic jets

NASA Astrophysics Data System (ADS)

Majmudar, Trushant; Ober, Thomas; McKinley, Gareth

2009-11-01

Free surface continuous jets of non-Newtonian fluids, although relevant for many industrial processes like bottle filling, remain poorly understood in terms of fundamental fluid dynamics. Here we present a systematic study of the effect of viscoelasticity on the dynamics of continuous jets of worm-like micellar surfactant solutions of varying viscosities and elasticities, and model yield-stress fluids. We systematically vary the height of the drop and the flow rate in order to study the effects of varying geometric and kinematic parameters. We observe that for fluids with higher elastic relaxation times, folding is the preferred mode. In contrast, for low elasticity fluids we observe complex nonlinear dynamics consisting of coiling, folding, and irregular meandering as the height of the fall increases. Beyond this regime, the jet dynamics smoothly crosses over to exhibit the ``leaping shampoo" or the Kaye effect. Upon increasing the flow rate to very high values, the ``leaping shampoo" state disappears and is replaced by a pronounced mounding or ``heaping". A subsequent increase in the flow rate results in finger-like protrusions to emerge out of the mound and climb up towards the nozzle. This novel transition is currently under investigation and remains a theoretical challenge.

Numerical simulation of the free surface and water inflow of a slope, considering the nonlinear flow properties of gravel layers: a case study

NASA Astrophysics Data System (ADS)

Yang, Bin; Yang, Tianhong; Xu, Zenghe; Liu, Honglei; Shi, Wenhao; Yang, Xin

2018-02-01

Groundwater is an important factor of slope stability, and 90% of slope failures are related to the influence of groundwater. In the past, free surface calculations and the prediction of water inflow were based on Darcy's law. However, Darcy's law for steady fluid flow is a special case of non-Darcy flow, and many types of non-Darcy flows occur in practical engineering applications. In this paper, based on the experimental results of laboratory water seepage tests, the seepage state of each soil layer in the open-pit slope of the Yanshan Iron Mine, China, were determined, and the seepage parameters were obtained. The seepage behaviour in the silt layer, fine sand layer, silty clay layer and gravelly clay layer followed the traditional Darcy law, while the gravel layers showed clear nonlinear characteristics. The permeability increases exponentially and the non-Darcy coefficient decreases exponentially with an increase in porosity, and the relation among the permeability, the porosity and the non-Darcy coefficient is investigated. A coupled mathematical model is established for two flow fields, on the basis of Darcy flow in the low-permeability layers and Forchheimer flow in the high-permeability layers. In addition, the effect of the seepage in the slope on the transition from Darcy flow to Forchheimer flow was considered. Then, a numerical simulation was conducted by using finite-element software (FELAC 2.2). The results indicate that the free surface calculated by the Darcy-Forchheimer model is in good agreement with the in situ measurements; however, there is an evident deviation of the simulation results from the measured data when the Darcy model is used. Through a parameter sensitivity analysis of the gravel layers, it can be found that the height of the overflow point and the water inflow calculated by the Darcy-Forchheimer model are consistently less than those of the Darcy model, and the discrepancy between these two models increases as the permeability increases. The necessity of adopting the Darcy-Forchheimer model was explained. The Darcy-Forchheimer model would be applicable in slope engineering applications with highly permeable rock.

Numerical simulation of the free surface and water inflow of a slope, considering the nonlinear flow properties of gravel layers: a case study.

PubMed

Yang, Bin; Yang, Tianhong; Xu, Zenghe; Liu, Honglei; Shi, Wenhao; Yang, Xin

2018-02-01

Groundwater is an important factor of slope stability, and 90% of slope failures are related to the influence of groundwater. In the past, free surface calculations and the prediction of water inflow were based on Darcy's law. However, Darcy's law for steady fluid flow is a special case of non-Darcy flow, and many types of non-Darcy flows occur in practical engineering applications. In this paper, based on the experimental results of laboratory water seepage tests, the seepage state of each soil layer in the open-pit slope of the Yanshan Iron Mine, China, were determined, and the seepage parameters were obtained. The seepage behaviour in the silt layer, fine sand layer, silty clay layer and gravelly clay layer followed the traditional Darcy law, while the gravel layers showed clear nonlinear characteristics. The permeability increases exponentially and the non-Darcy coefficient decreases exponentially with an increase in porosity, and the relation among the permeability, the porosity and the non-Darcy coefficient is investigated. A coupled mathematical model is established for two flow fields, on the basis of Darcy flow in the low-permeability layers and Forchheimer flow in the high-permeability layers. In addition, the effect of the seepage in the slope on the transition from Darcy flow to Forchheimer flow was considered. Then, a numerical simulation was conducted by using finite-element software (FELAC 2.2). The results indicate that the free surface calculated by the Darcy-Forchheimer model is in good agreement with the in situ measurements; however, there is an evident deviation of the simulation results from the measured data when the Darcy model is used. Through a parameter sensitivity analysis of the gravel layers, it can be found that the height of the overflow point and the water inflow calculated by the Darcy-Forchheimer model are consistently less than those of the Darcy model, and the discrepancy between these two models increases as the permeability increases. The necessity of adopting the Darcy-Forchheimer model was explained. The Darcy-Forchheimer model would be applicable in slope engineering applications with highly permeable rock.

Numerical simulation of the free surface and water inflow of a slope, considering the nonlinear flow properties of gravel layers: a case study

PubMed Central

Yang, Bin; Xu, Zenghe; Liu, Honglei; Shi, Wenhao; Yang, Xin

2018-01-01

Groundwater is an important factor of slope stability, and 90% of slope failures are related to the influence of groundwater. In the past, free surface calculations and the prediction of water inflow were based on Darcy's law. However, Darcy's law for steady fluid flow is a special case of non-Darcy flow, and many types of non-Darcy flows occur in practical engineering applications. In this paper, based on the experimental results of laboratory water seepage tests, the seepage state of each soil layer in the open-pit slope of the Yanshan Iron Mine, China, were determined, and the seepage parameters were obtained. The seepage behaviour in the silt layer, fine sand layer, silty clay layer and gravelly clay layer followed the traditional Darcy law, while the gravel layers showed clear nonlinear characteristics. The permeability increases exponentially and the non-Darcy coefficient decreases exponentially with an increase in porosity, and the relation among the permeability, the porosity and the non-Darcy coefficient is investigated. A coupled mathematical model is established for two flow fields, on the basis of Darcy flow in the low-permeability layers and Forchheimer flow in the high-permeability layers. In addition, the effect of the seepage in the slope on the transition from Darcy flow to Forchheimer flow was considered. Then, a numerical simulation was conducted by using finite-element software (FELAC 2.2). The results indicate that the free surface calculated by the Darcy–Forchheimer model is in good agreement with the in situ measurements; however, there is an evident deviation of the simulation results from the measured data when the Darcy model is used. Through a parameter sensitivity analysis of the gravel layers, it can be found that the height of the overflow point and the water inflow calculated by the Darcy–Forchheimer model are consistently less than those of the Darcy model, and the discrepancy between these two models increases as the permeability increases. The necessity of adopting the Darcy–Forchheimer model was explained. The Darcy–Forchheimer model would be applicable in slope engineering applications with highly permeable rock. PMID:29515904

Implicit high-order discontinuous Galerkin method with HWENO type limiters for steady viscous flow simulations

NASA Astrophysics Data System (ADS)

Jiang, Zhen-Hua; Yan, Chao; Yu, Jian

2013-08-01

Two types of implicit algorithms have been improved for high order discontinuous Galerkin (DG) method to solve compressible Navier-Stokes (NS) equations on triangular grids. A block lower-upper symmetric Gauss-Seidel (BLU-SGS) approach is implemented as a nonlinear iterative scheme. And a modified LU-SGS (LLU-SGS) approach is suggested to reduce the memory requirements while retain the good convergence performance of the original LU-SGS approach. Both implicit schemes have the significant advantage that only the diagonal block matrix is stored. The resulting implicit high-order DG methods are applied, in combination with Hermite weighted essentially non-oscillatory (HWENO) limiters, to solve viscous flow problems. Numerical results demonstrate that the present implicit methods are able to achieve significant efficiency improvements over explicit counterparts and for viscous flows with shocks, and the HWENO limiters can be used to achieve the desired essentially non-oscillatory shock transition and the designed high-order accuracy simultaneously.

Fully localised nonlinear energy growth optimals in pipe flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pringle, Chris C. T.; Willis, Ashley P.; Kerswell, Rich R.

A new, fully localised, energy growth optimal is found over large times and in long pipe domains at a given mass flow rate. This optimal emerges at a threshold disturbance energy below which a nonlinear version of the known (streamwise-independent) linear optimal [P. J. Schmid and D. S. Henningson, “Optimal energy density growth in Hagen-Poiseuille flow,” J. Fluid Mech. 277, 192–225 (1994)] is selected and appears to remain the optimal up until the critical energy at which transition is triggered. The form of this optimal is similar to that found in short pipes [Pringle et al., “Minimal seeds for shearmore » flow turbulence: Using nonlinear transient growth to touch the edge of chaos,” J. Fluid Mech. 702, 415–443 (2012)], but now with full localisation in the streamwise direction. This fully localised optimal perturbation represents the best approximation yet of the minimal seed (the smallest perturbation which is arbitrarily close to states capable of triggering a turbulent episode) for “real” (laboratory) pipe flows. Dependence of the optimal with respect to several parameters has been computed and establishes that the structure is robust.« less

The interplay between the kinetic nonlinear frequency shift and the flowing gradient in stimulated Brillouin scattering

NASA Astrophysics Data System (ADS)

Wang, Q.; Y Zheng, C.; Liu, Z. J.; Xiao, C. Z.; Feng, Q. S.; Zhang, H. C.; He, X. T.

2018-02-01

The effect of the kinetic nonlinear frequency shift (KNFS) on backward stimulated Brillouin scattering (SBS) in homogeneous plasmas and inhomogeneous flowing plasmas is investigated by three-wave coupled-mode equations. When the positive contribution to the KNFS from electrons as well as the negative contribution from ions is included, the net KNFS can become positive at a large electron-ion temperature ratio {{ZT}}e/{T}i. In homogeneous plasmas, KNFS can greatly reduce the SBS reflectivity at low or large {{ZT}}e/{T}i but has a weak effect on SBS at {{ZT}}e/{T}i where the positive frequency shifts from electrons almost cancels out the negative shifts from ions. In inhomogeneous plasmas, the net negative frequency shift can enhance the backward SBS reflectivity for the negative gradient of the plasma flowing, and can suppress the reflectivity for the positive case. On the contrary, the net positive frequency can suppress the reflectivity for the negative case of the flowing gradient and enhance the reflectivity for the positive case. This indicates that the SBS in inhomogeneous flowing plasmas can be controlled by changing the sign of the nonlinear frequency shift.

Thermodynamics of random reaction networks.

PubMed

Fischer, Jakob; Kleidon, Axel; Dittrich, Peter

2015-01-01

Reaction networks are useful for analyzing reaction systems occurring in chemistry, systems biology, or Earth system science. Despite the importance of thermodynamic disequilibrium for many of those systems, the general thermodynamic properties of reaction networks are poorly understood. To circumvent the problem of sparse thermodynamic data, we generate artificial reaction networks and investigate their non-equilibrium steady state for various boundary fluxes. We generate linear and nonlinear networks using four different complex network models (Erdős-Rényi, Barabási-Albert, Watts-Strogatz, Pan-Sinha) and compare their topological properties with real reaction networks. For similar boundary conditions the steady state flow through the linear networks is about one order of magnitude higher than the flow through comparable nonlinear networks. In all networks, the flow decreases with the distance between the inflow and outflow boundary species, with Watts-Strogatz networks showing a significantly smaller slope compared to the three other network types. The distribution of entropy production of the individual reactions inside the network follows a power law in the intermediate region with an exponent of circa -1.5 for linear and -1.66 for nonlinear networks. An elevated entropy production rate is found in reactions associated with weakly connected species. This effect is stronger in nonlinear networks than in the linear ones. Increasing the flow through the nonlinear networks also increases the number of cycles and leads to a narrower distribution of chemical potentials. We conclude that the relation between distribution of dissipation, network topology and strength of disequilibrium is nontrivial and can be studied systematically by artificial reaction networks.

Thermodynamics of Random Reaction Networks

PubMed Central

Fischer, Jakob; Kleidon, Axel; Dittrich, Peter

2015-01-01

Reaction networks are useful for analyzing reaction systems occurring in chemistry, systems biology, or Earth system science. Despite the importance of thermodynamic disequilibrium for many of those systems, the general thermodynamic properties of reaction networks are poorly understood. To circumvent the problem of sparse thermodynamic data, we generate artificial reaction networks and investigate their non-equilibrium steady state for various boundary fluxes. We generate linear and nonlinear networks using four different complex network models (Erdős-Rényi, Barabási-Albert, Watts-Strogatz, Pan-Sinha) and compare their topological properties with real reaction networks. For similar boundary conditions the steady state flow through the linear networks is about one order of magnitude higher than the flow through comparable nonlinear networks. In all networks, the flow decreases with the distance between the inflow and outflow boundary species, with Watts-Strogatz networks showing a significantly smaller slope compared to the three other network types. The distribution of entropy production of the individual reactions inside the network follows a power law in the intermediate region with an exponent of circa −1.5 for linear and −1.66 for nonlinear networks. An elevated entropy production rate is found in reactions associated with weakly connected species. This effect is stronger in nonlinear networks than in the linear ones. Increasing the flow through the nonlinear networks also increases the number of cycles and leads to a narrower distribution of chemical potentials. We conclude that the relation between distribution of dissipation, network topology and strength of disequilibrium is nontrivial and can be studied systematically by artificial reaction networks. PMID:25723751

Impact of conditions at start-up on thermovibrational convective flow.

PubMed

Melnikov, D E; Shevtsova, V M; Legros, J C

2008-11-01

The development of thermovibrational convection in a cubic cell filled with high Prandtl number liquid (isopropanol) is studied. Direct nonlinear simulations are performed by solving three-dimensional Navier-Stokes equations in the Boussinesq approximation. The cell is subjected to high frequency periodic oscillations perpendicular to the applied temperature gradient under zero gravity. Two types of vibrations are imposed: either as a sine or cosine function of time. It is shown that the initial vibrational phase plays a significant role in the transient behavior of thermovibrational convective flow. Such knowledge is important to interpret correctly short-duration experimental results performed in microgravity, among which the most accessible are drop towers ( approximately 5s) and parabolic flights ( approximately 20s) . It is obtained that under sine vibrations, the flow reaches steady state within less than one thermal time. Under cosine acceleration, this time is 2 times longer. For cosine excitations, the Nusselt number is approximately 10 times smaller in comparison with the sine case. Besides, in the case of cosine, the Nusselt number oscillates with double frequency. However, at the steady state, time-averaged and oscillatory characteristics of the flow are independent of the vibrational start-up. The only feature that always differs the two cases is the phase difference between the velocity, temperature, and accelerations. We have found that due to nonlinear response of the system to the imposed vibrations, the phase shift between velocity and temperature is never equal exactly to pi2 , at least in weightlessness. Thus, heat transport always exists from the beginning of vibrations, although it might be weak.

A method for measuring the nonlinear response in dielectric spectroscopy through third harmonics detection.

PubMed

Thibierge, C; L'Hôte, D; Ladieu, F; Tourbot, R

2008-10-01

We present a high sensitivity method allowing the measurement of the nonlinear dielectric susceptibility of an insulating material at finite frequency. It has been developed for the study of dynamic heterogeneities in supercooled liquids using dielectric spectroscopy at frequencies 0.05 Hz < or = f < or = 3x10(4) Hz. It relies on the measurement of the third harmonics component of the current flowing out of a capacitor. We first show that standard laboratory electronics (amplifiers and voltage sources) nonlinearities lead to limits on the third harmonics measurements that preclude reaching the level needed by our physical goal, a ratio of the third harmonics to the fundamental signal about 10(-7). We show that reaching such a sensitivity needs a method able to get rid of the nonlinear contributions both of the measuring device (lock-in amplifier) and of the excitation voltage source. A bridge using two sources fulfills only the first of these two requirements, but allows to measure the nonlinearities of the sources. Our final method is based on a bridge with two plane capacitors characterized by different dielectric layer thicknesses. It gets rid of the source and amplifier nonlinearities because in spite of a strong frequency dependence of the capacitor impedance, it is equilibrated at any frequency. We present the first measurements of the physical nonlinear response using our method. Two extensions of the method are suggested.

A 2D nonlinear multiring model for blood flow in large elastic arteries

NASA Astrophysics Data System (ADS)

Ghigo, Arthur R.; Fullana, Jose-Maria; Lagrée, Pierre-Yves

2017-12-01

In this paper, we propose a two-dimensional nonlinear ;multiring; model to compute blood flow in axisymmetric elastic arteries. This model is designed to overcome the numerical difficulties of three-dimensional fluid-structure interaction simulations of blood flow without using the over-simplifications necessary to obtain one-dimensional blood flow models. This multiring model is derived by integrating over concentric rings of fluid the simplified long-wave Navier-Stokes equations coupled to an elastic model of the arterial wall. The resulting system of balance laws provides a unified framework in which both the motion of the fluid and the displacement of the wall are dealt with simultaneously. The mathematical structure of the multiring model allows us to use a finite volume method that guarantees the conservation of mass and the positivity of the numerical solution and can deal with nonlinear flows and large deformations of the arterial wall. We show that the finite volume numerical solution of the multiring model provides at a reasonable computational cost an asymptotically valid description of blood flow velocity profiles and other averaged quantities (wall shear stress, flow rate, ...) in large elastic and quasi-rigid arteries. In particular, we validate the multiring model against well-known solutions such as the Womersley or the Poiseuille solutions as well as against steady boundary layer solutions in quasi-rigid constricted and expanded tubes.

Experimental and Model Studies on Loading Path-Dependent and Nonlinear Gas Flow Behavior in Shale Fractures

NASA Astrophysics Data System (ADS)

Li, Honglian; Lu, Yiyu; Zhou, Lei; Tang, Jiren; Han, Shuaibin; Ao, Xiang

2018-01-01

Interest in shale gas as an energy source is growing worldwide. Because the rock's natural fracture system can contribute to gas production, it is important to understand the flow behavior of natural fractures in shale. Previous studies on the flow characteristics in shale fractures were limited and did not consider the effect of nonlinearity. To understand the basic mechanics of the gas flow behavior in shale fractures, laboratory investigations with consideration of the fluid pressure gradient, the confining stress, the loading history and the fracture geometry were conducted in this paper. Izbash's equation was used to analyze the nonlinearity of the flow. The results show that the behavior of the friction factors is similar to that shown in flow tests in smooth and rough pipes. The increase of the confining stress and the irreversible damage to the shale decreased the hydraulic aperture and increased the relative roughness. Thus, turbulent flow could appear at a low Reynolds number, resulting in a significant pressure loss. The limits of the cubic law and the existing correction factor for transmissivity are discussed. It is found that the previous friction models overestimate the friction factor in the laminar regime and underestimate the friction factor in the turbulent regime. For this reason, a new friction model based on a linear combination of the Reynolds number and the relative roughness was developed.

A comparative study of the effects of cone-plate and parallel-plate geometries on rheological properties under oscillatory shear flow

NASA Astrophysics Data System (ADS)

Song, Hyeong Yong; Salehiyan, Reza; Li, Xiaolei; Lee, Seung Hak; Hyun, Kyu

2017-11-01

In this study, the effects of cone-plate (C/P) and parallel-plate (P/P) geometries were investigated on the rheological properties of various complex fluids, e.g. single-phase (polymer melts and solutions) and multiphase systems (polymer blend and nanocomposite, and suspension). Small amplitude oscillatory shear (SAOS) tests were carried out to compare linear rheological responses while nonlinear responses were compared using large amplitude oscillatory shear (LAOS) tests at different frequencies. Moreover, Fourier-transform (FT)-rheology method was used to analyze the nonlinear responses under LAOS flow. Experimental results were compared with predictions obtained by single-point correction and shear rate correction. For all systems, SAOS data measured by C/P and P/P coincide with each other, but results showed discordance between C/P and P/P measurements in the nonlinear regime. For all systems except xanthan gum solutions, first-harmonic moduli were corrected using a single horizontal shift factor, whereas FT rheology-based nonlinear parameters ( I 3/1, I 5/1, Q 3, and Q 5) were corrected using vertical shift factors that are well predicted by single-point correction. Xanthan gum solutions exhibited anomalous corrections. Their first-harmonic Fourier moduli were superposed using a horizontal shift factor predicted by shear rate correction applicable to highly shear thinning fluids. The distinguished corrections were observed for FT rheology-based nonlinear parameters. I 3/1 and I 5/1 were superposed by horizontal shifts, while the other systems displayed vertical shifts of I 3/1 and I 5/1. Q 3 and Q 5 of xanthan gum solutions were corrected using both horizontal and vertical shift factors. In particular, the obtained vertical shift factors for Q 3 and Q 5 were twice as large as predictions made by single-point correction. Such larger values are rationalized by the definitions of Q 3 and Q 5. These results highlight the significance of horizontal shift corrections in nonlinear oscillatory shear data.

Flow Equation Approach to the Statistics of Nonlinear Dynamical Systems

NASA Astrophysics Data System (ADS)

Marston, J. B.; Hastings, M. B.

2005-03-01

The probability distribution function of non-linear dynamical systems is governed by a linear framework that resembles quantum many-body theory, in which stochastic forcing and/or averaging over initial conditions play the role of non-zero . Besides the well-known Fokker-Planck approach, there is a related Hopf functional methodootnotetextUriel Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, 1995) chapter 9.5.; in both formalisms, zero modes of linear operators describe the stationary non-equilibrium statistics. To access the statistics, we investigate the method of continuous unitary transformationsootnotetextS. D. Glazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993); Phys. Rev. D 49, 4214 (1994). (also known as the flow equation approachootnotetextF. Wegner, Ann. Phys. 3, 77 (1994).), suitably generalized to the diagonalization of non-Hermitian matrices. Comparison to the more traditional cumulant expansion method is illustrated with low-dimensional attractors. The treatment of high-dimensional dynamical systems is also discussed.

IMEX HDG-DG: A coupled implicit hybridized discontinuous Galerkin and explicit discontinuous Galerkin approach for Euler systems on cubed sphere.

NASA Astrophysics Data System (ADS)

Kang, S.; Muralikrishnan, S.; Bui-Thanh, T.

2017-12-01

We propose IMEX HDG-DG schemes for Euler systems on cubed sphere. Of interest is subsonic flow, where the speed of the acoustic wave is faster than that of the nonlinear advection. In order to simulate these flows efficiently, we split the governing system into stiff part describing the fast waves and non-stiff part associated with nonlinear advection. The former is discretized implicitly with HDG method while explicit Runge-Kutta DG discretization is employed for the latter. The proposed IMEX HDG-DG framework: 1) facilitates high-order solution both in time and space; 2) avoids overly small time stepsizes; 3) requires only one linear system solve per time step; and 4) relatively to DG generates smaller and sparser linear system while promoting further parallelism owing to HDG discretization. Numerical results for various test cases demonstrate that our methods are comparable to explicit Runge-Kutta DG schemes in terms of accuracy, while allowing for much larger time stepsizes.

Robust ion current oscillations under a steady electric field: An ion channel analog.

PubMed

Yan, Yu; Wang, Yunshan; Senapati, Satyajyoti; Schiffbauer, Jarrod; Yossifon, Gilad; Chang, Hsueh-Chia

2016-08-01

We demonstrate a nonlinear, nonequilibrium field-driven ion flux phenomenon, which unlike Teorell's nonlinear multiple field theory, requires only the application of one field: robust autonomous current-mass flux oscillations across a porous monolith coupled to a capillary with a long air bubble, which mimics a hydrophobic protein in an ion channel. The oscillations are driven by the hysteretic wetting dynamics of the meniscus when electro-osmotic flow and pressure driven backflow, due to bubble expansion, compete to approach zero mass flux within the monolith. Delayed rupture of the film around the advancing bubble cuts off the electric field and switches the monolith mass flow from the former to the latter. The meniscus then recedes and repairs the rupture to sustain an oscillation for a range of applied fields. This generic mechanism shares many analogs with current oscillations in cell membrane ion channel. At sufficiently high voltage, the system undergoes a state transition characterized by appearance of the ubiquitous 1/f power spectrum.

Nonlinear (time domain) and linearized (time and frequency domain) solutions to the compressible Euler equations in conservation law form

NASA Technical Reports Server (NTRS)

Sreenivas, Kidambi; Whitfield, David L.

1995-01-01

Two linearized solvers (time and frequency domain) based on a high resolution numerical scheme are presented. The basic approach is to linearize the flux vector by expressing it as a sum of a mean and a perturbation. This allows the governing equations to be maintained in conservation law form. A key difference between the time and frequency domain computations is that the frequency domain computations require only one grid block irrespective of the interblade phase angle for which the flow is being computed. As a result of this and due to the fact that the governing equations for this case are steady, frequency domain computations are substantially faster than the corresponding time domain computations. The linearized equations are used to compute flows in turbomachinery blade rows (cascades) arising due to blade vibrations. Numerical solutions are compared to linear theory (where available) and to numerical solutions of the nonlinear Euler equations.

High-intensity discharge lamp and Duffing oscillator—Similarities and differences

NASA Astrophysics Data System (ADS)

Baumann, Bernd; Schwieger, Joerg; Stein, Ulrich; Hallerberg, Sarah; Wolff, Marcus

2017-12-01

The processes inside the arc tube of high-intensity discharge lamps are investigated using finite element simulations. The behavior of the gas mixture inside the arc tube is governed by differential equations describing mass, energy, and charge conservation, as well as the Helmholtz equation for the acoustic pressure and the Reynolds equations for the flow driven by buoyancy and Reynolds stresses. The model is highly nonlinear and requires a recursion procedure to account for the impact of acoustic streaming on the temperature and other fields. The investigations reveal the presence of a hysteresis and the corresponding jump phenomenon, quite similar to a Duffing oscillator. The similarities and, in particular, the differences of the nonlinear behavior of the high-intensity discharge lamp to that of a Duffing oscillator are discussed. For large amplitudes, the high-intensity discharge lamp exhibits a stiffening effect in contrast to the Duffing oscillator. It is speculated on how the stiffening might affect hysteresis suppression.

Quantitative real-time in vivo detection of magnetic nanoparticles by their nonlinear magnetization

NASA Astrophysics Data System (ADS)

Nikitin, M. P.; Torno, M.; Chen, H.; Rosengart, A.; Nikitin, P. I.

2008-04-01

A novel method of highly sensitive quantitative detection of magnetic nanoparticles (MP) in biological tissues and blood system has been realized and tested in real time in vivo experiments. The detection method is based on nonlinear magnetic properties of MP and the related device can record a very small relative variation of nonlinear magnetic susceptibility up to 10-8 at room temperature, providing sensitivity of several nanograms of MP in 0.1ml volume. Real-time quantitative in vivo measurements of dynamics of MP concentration in blood flow have been performed. A catheter that carried the blood flow of a rat passed through the measuring device. After an MP injection, the quantity of MP in the circulating blood was continuously recorded. The method has also been used to evaluate the MP distribution between rat's organs. Its sensitivity was compared with detection of the radioactive MP based on isotope of Fe59. The comparison of magnetic and radioactive signals in the rat's blood and organ samples demonstrated similar sensitivity for both methods. However, the proposed magnetic method is much more convenient as it is safe, less expensive, and provides real-time measurements in vivo. Moreover, the sensitivity of the method can be further improved by optimization of the device geometry.

A high-order gas-kinetic Navier-Stokes flow solver

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li Qibing, E-mail: lqb@tsinghua.edu.c; Xu Kun, E-mail: makxu@ust.h; Fu Song, E-mail: fs-dem@tsinghua.edu.c

2010-09-20

The foundation for the development of modern compressible flow solver is based on the Riemann solution of the inviscid Euler equations. The high-order schemes are basically related to high-order spatial interpolation or reconstruction. In order to overcome the low-order wave interaction mechanism due to the Riemann solution, the temporal accuracy of the scheme can be improved through the Runge-Kutta method, where the dynamic deficiencies in the first-order Riemann solution is alleviated through the sub-step spatial reconstruction in the Runge-Kutta process. The close coupling between the spatial and temporal evolution in the original nonlinear governing equations seems weakened due to itsmore » spatial and temporal decoupling. Many recently developed high-order methods require a Navier-Stokes flux function under piece-wise discontinuous high-order initial reconstruction. However, the piece-wise discontinuous initial data and the hyperbolic-parabolic nature of the Navier-Stokes equations seem inconsistent mathematically, such as the divergence of the viscous and heat conducting terms due to initial discontinuity. In this paper, based on the Boltzmann equation, we are going to present a time-dependent flux function from a high-order discontinuous reconstruction. The theoretical basis for such an approach is due to the fact that the Boltzmann equation has no specific requirement on the smoothness of the initial data and the kinetic equation has the mechanism to construct a dissipative wave structure starting from an initially discontinuous flow condition on a time scale being larger than the particle collision time. The current high-order flux evaluation method is an extension of the second-order gas-kinetic BGK scheme for the Navier-Stokes equations (BGK-NS). The novelty for the easy extension from a second-order to a higher order is due to the simple particle transport and collision mechanism on the microscopic level. This paper will present a hierarchy to construct such a high-order method. The necessity to couple spatial and temporal evolution nonlinearly in the flux evaluation can be clearly observed through the numerical performance of the scheme for the viscous flow computations.« less

Rossby and drift wave turbulence and zonal flows: The Charney-Hasegawa-Mima model and its extensions

NASA Astrophysics Data System (ADS)

Connaughton, Colm; Nazarenko, Sergey; Quinn, Brenda

2015-12-01

A detailed study of the Charney-Hasegawa-Mima model and its extensions is presented. These simple nonlinear partial differential equations suggested for both Rossby waves in the atmosphere and drift waves in a magnetically-confined plasma, exhibit some remarkable and nontrivial properties, which in their qualitative form, survive in more realistic and complicated models. As such, they form a conceptual basis for understanding the turbulence and zonal flow dynamics in real plasma and geophysical systems. Two idealised scenarios of generation of zonal flows by small-scale turbulence are explored: a modulational instability and turbulent cascades. A detailed study of the generation of zonal flows by the modulational instability reveals that the dynamics of this zonal flow generation mechanism differ widely depending on the initial degree of nonlinearity. The jets in the strongly nonlinear case further roll up into vortex streets and saturate, while for the weaker nonlinearities, the growth of the unstable mode reverses and the system oscillates between a dominant jet, which is slightly inclined to the zonal direction, and a dominant primary wave. A numerical proof is provided for the extra invariant in Rossby and drift wave turbulence-zonostrophy. While the theoretical derivations of this invariant stem from the wave kinetic equation which assumes weak wave amplitudes, it is shown to be relatively well-conserved for higher nonlinearities also. Together with the energy and enstrophy, these three invariants cascade into anisotropic sectors in the k-space as predicted by the Fjørtoft argument. The cascades are characterised by the zonostrophy pushing the energy to the zonal scales. A small scale instability forcing applied to the model has demonstrated the well-known drift wave-zonal flow feedback loop. The drift wave turbulence is generated from this primary instability. The zonal flows are then excited by either one of the generation mechanisms, extracting energy from the drift waves as they grow. Eventually the turbulence is completely suppressed and the zonal flows saturate. The turbulence spectrum is shown to diffuse in a manner which has been mathematically predicted. The insights gained from this simple model could provide a basis for equivalent studies in more sophisticated plasma and geophysical fluid dynamics models in an effort to fully understand the zonal flow generation, the turbulent transport suppression and the zonal flow saturation processes in both the plasma and geophysical contexts as well as other wave and turbulence systems where order evolves from chaos.

Nonlinear dynamics of shells conveying pulsatile flow with pulse-wave propagation. Theory and numerical results for a single harmonic pulsation

NASA Astrophysics Data System (ADS)

Tubaldi, Eleonora; Amabili, Marco; Païdoussis, Michael P.

2017-05-01

In deformable shells conveying pulsatile flow, oscillatory pressure changes cause local movements of the fluid and deformation of the shell wall, which propagate downstream in the form of a wave. In biomechanics, it is the propagation of the pulse that determines the pressure gradient during the flow at every location of the arterial tree. In this study, a woven Dacron aortic prosthesis is modelled as an orthotropic circular cylindrical shell described by means of the Novozhilov nonlinear shell theory. Flexible boundary conditions are considered to simulate connection with the remaining tissue. Nonlinear vibrations of the shell conveying pulsatile flow and subjected to pulsatile pressure are investigated taking into account the effects of the pulse-wave propagation. For the first time in literature, coupled fluid-structure Lagrange equations of motion for a non-material volume with wave propagation in case of pulsatile flow are developed. The fluid is modeled as a Newtonian inviscid pulsatile flow and it is formulated using a hybrid model based on the linear potential flow theory and considering the unsteady viscous effects obtained from the unsteady time-averaged Navier-Stokes equations. Contributions of pressure and velocity propagation are also considered in the pressure drop along the shell and in the pulsatile frictional traction on the internal wall in the axial direction. A numerical bifurcation analysis employs a refined reduced order model to investigate the dynamic behavior of a pressurized Dacron aortic graft conveying blood flow. A pulsatile time-dependent blood flow model is considered by applying the first harmonic of the physiological waveforms of velocity and pressure during the heart beating period. Geometrically nonlinear vibration response to pulsatile flow and transmural pulsatile pressure, considering the propagation of pressure and velocity changes inside the shell, is here presented via frequency-response curves, time histories, bifurcation diagrams and Poincaré maps. It is shown that traveling waves of pressure and velocity cause a delay in the radial displacement of the shell at different values of the axial coordinate. The effect of different pulse wave velocities is also studied. Comparisons with the corresponding ideal case without wave propagation (i.e. with the same pulsatile velocity and pressure at any point of the shell) are here discussed. Bifurcation diagrams of Poincaré maps obtained from direct time integration have been used to study the system in the spectral neighborhood of the fundamental natural frequency. By increasing the forcing frequency, the response undergoes very complex nonlinear dynamics (chaos, amplitude modulation and period-doubling bifurcation), here deeply investigated.

A nonlinear model for analysis of slug-test data

USGS Publications Warehouse

McElwee, C.D.; Zenner, M.A.

1998-01-01

While doing slug tests in high-permeability aquifers, we have consistently seen deviations from the expected response of linear theoretical models. Normalized curves do not coincide for various initial heads, as would be predicted by linear theories, and are shifted to larger times for higher initial heads. We have developed a general nonlinear model based on the Navier-Stokes equation, nonlinear frictional loss, non-Darcian flow, acceleration effects, radius changes in the well bore, and a Hvorslev model for the aquifer, which explains these data features. The model produces a very good fit for both oscillatory and nonoscillatory field data, using a single set of physical parameters to predict the field data for various initial displacements at a given well. This is in contrast to linear models which have a systematic lack of fit and indicate that hydraulic conductivity varies with the initial displacement. We recommend multiple slug tests with a considerable variation in initial head displacement to evaluate the possible presence of nonlinear effects. Our conclusion is that the nonlinear model presented here is an excellent tool to analyze slug tests, covering the range from the underdamped region to the overdamped region.

Hyperchaotic Dynamics for Light Polarization in a Laser Diode

NASA Astrophysics Data System (ADS)

Bonatto, Cristian

2018-04-01

It is shown that a highly randomlike behavior of light polarization states in the output of a free-running laser diode, covering the whole Poincaré sphere, arises as a result from a fully deterministic nonlinear process, which is characterized by a hyperchaotic dynamics of two polarization modes nonlinearly coupled with a semiconductor medium, inside the optical cavity. A number of statistical distributions were found to describe the deterministic data of the low-dimensional nonlinear flow, such as lognormal distribution for the light intensity, Gaussian distributions for the electric field components and electron densities, Rice and Rayleigh distributions, and Weibull and negative exponential distributions, for the modulus and intensity of the orthogonal linear components of the electric field, respectively. The presented results could be relevant for the generation of single units of compact light source devices to be used in low-dimensional optical hyperchaos-based applications.

GA-optimized feedforward-PID tracking control for a rugged electrohydraulic system design.

PubMed

Sarkar, B K; Mandal, P; Saha, R; Mookherjee, S; Sanyal, D

2013-11-01

Rugged electrohydraulic systems are preferred for remote and harsh applications. Despite the low bandwidth, large deadband and flow nonlinearities in proportional valves valve and highly nonlinear friction in industry-grade cylinders that comprise rugged systems, their maintenance are much easier than very sophisticated and delicate servocontrol and servocylinder systems. With the target of making the easily maintainable system to perform comparably to a servosystem, a feedforward control has been designed here for compensating the nonlinearities. A PID feedback of the piston displacement has been employed in tandem for absorbing the unmodeled effects. All the controller parameters have been optimized by a real-coded genetic algorithm. The agreement between the achieved real-time responses for step and sinusoidal demands with those achieved by modern servosystems clearly establishes the acceptability of the controller design. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Wave dynamics in an extended macroscopic traffic flow model with periodic boundaries

NASA Astrophysics Data System (ADS)

Wang, Yu-Qing; Chu, Xing-Jian; Zhou, Chao-Fan; Yan, Bo-Wen; Jia, Bin; Fang, Chen-Hao

2018-06-01

Motivated by the previous traffic flow model considering the real-time traffic state, a modified macroscopic traffic flow model is established. The periodic boundary condition is applied to the car-following model. Besides, the traffic state factor R is defined in order to correct the real traffic conditions in a more reasonable way. It is a key step that we introduce the relaxation time as a density-dependent function and provide corresponding evolvement of traffic flow. Three different typical initial densities, namely the high density, the medium one and the low one, are intensively investigated. It can be found that the hysteresis loop exists in the proposed periodic-boundary system. Furthermore, the linear and nonlinear stability analyses are performed in order to test the robustness of the system.

The NCOREL computer program for 3D nonlinear supersonic potential flow computations

NASA Technical Reports Server (NTRS)

Siclari, M. J.

1983-01-01

An innovative computational technique (NCOREL) was established for the treatment of three dimensional supersonic flows. The method is nonlinear in that it solves the nonconservative finite difference analog of the full potential equation and can predict the formation of supercritical cross flow regions, embedded and bow shocks. The method implicitly computes a conical flow at the apex (R = 0) of a spherical coordinate system and uses a fully implicit marching technique to obtain three dimensional cross flow solutions. This implies that the radial Mach number must remain supersonic. The cross flow solutions are obtained by using type dependent transonic relaxation techniques with the type dependency linked to the character of the cross flow velocity (i.e., subsonic/supersonic). The spherical coordinate system and marching on spherical surfaces is ideally suited to the computation of wing flows at low supersonic Mach numbers due to the elimination of the subsonic axial Mach number problems that exist in other marching codes that utilize Cartesian transverse marching planes.

Excitation of nonlinear wave patterns in flowing complex plasmas

NASA Astrophysics Data System (ADS)

Jaiswal, S.; Bandyopadhyay, P.; Sen, A.

2018-01-01

We describe experimental observations of nonlinear wave structures excited by a supersonic mass flow of dust particles over an electrostatic potential hill in a dusty plasma medium. The experiments have been carried out in a Π- shaped experimental (DPEx) device in which micron sized Kaolin particles are embedded in a DC glow discharge Argon plasma. An equilibrium dust cloud is formed by maintaining the pumping speed and gas flow rate and the dust flow is induced either by suddenly reducing the height of a potential hill or by suddenly reducing the gas flow rate. For a supersonic flow of the dust fluid precursor solitons are seen to propagate in the upstream direction while wake structures propagate in the downstream direction. For flow speeds with a Mach number greater than 2 the dust particles flowing over the potential hill give rise to dispersive dust acoustic shock waves. The experimental results compare favorably with model theories based on forced K-dV and K-dV Burger's equations.

High Reynolds number analysis of flat plate and separated afterbody flow using non-linear turbulence models

NASA Technical Reports Server (NTRS)

Carlson, John R.

1996-01-01

The ability of the three-dimensional Navier-Stokes method, PAB3D, to simulate the effect of Reynolds number variation using non-linear explicit algebraic Reynolds stress turbulence modeling was assessed. Subsonic flat plate boundary-layer flow parameters such as normalized velocity distributions, local and average skin friction, and shape factor were compared with DNS calculations and classical theory at various local Reynolds numbers up to 180 million. Additionally, surface pressure coefficient distributions and integrated drag predictions on an axisymmetric nozzle afterbody were compared with experimental data from 10 to 130 million Reynolds number. The high Reynolds data was obtained from the NASA Langley 0.3m Transonic Cryogenic Tunnel. There was generally good agreement of surface static pressure coefficients between the CFD and measurement. The change in pressure coefficient distributions with varying Reynolds number was similar to the experimental data trends, though slightly over-predicting the effect. The computational sensitivity of viscous modeling and turbulence modeling are shown. Integrated afterbody pressure drag was typically slightly lower than the experimental data. The change in afterbody pressure drag with Reynolds number was small both experimentally and computationally, even though the shape of the distribution was somewhat modified with Reynolds number.

Role of zonal flows in trapped electron mode turbulence through nonlinear gyrokinetic particle and continuum simulationa)

NASA Astrophysics Data System (ADS)

Ernst, D. R.; Lang, J.; Nevins, W. M.; Hoffman, M.; Chen, Y.; Dorland, W.; Parker, S.

2009-05-01

Trapped electron mode (TEM) turbulence exhibits a rich variety of collisional and zonal flow physics. This work explores the parametric variation of zonal flows and underlying mechanisms through a series of linear and nonlinear gyrokinetic simulations, using both particle-in-cell and continuum methods. A new stability diagram for electron modes is presented, identifying a critical boundary at ηe=1, separating long and short wavelength TEMs. A novel parity test is used to separate TEMs from electron temperature gradient driven modes. A nonlinear scan of ηe reveals fine scale structure for ηe≳1, consistent with linear expectation. For ηe<1, zonal flows are the dominant saturation mechanism, and TEM transport is insensitive to ηe. For ηe>1, zonal flows are weak, and TEM transport falls inversely with a power law in ηe. The role of zonal flows appears to be connected to linear stability properties. Particle and continuum methods are compared in detail over a range of ηe=d ln Te/d ln ne values from zero to five. Linear growth rate spectra, transport fluxes, fluctuation wavelength spectra, zonal flow shearing spectra, and correlation lengths and times are in close agreement. In addition to identifying the critical parameter ηe for TEM zonal flows, this paper takes a challenging step in code verification, directly comparing very different methods of simulating simultaneous kinetic electron and ion dynamics in TEM turbulence.

Energetics of slope flows: linear and weakly nonlinear solutions of the extended Prandtl model

NASA Astrophysics Data System (ADS)

Güttler, Ivan; Marinović, Ivana; Večenaj, Željko; Grisogono, Branko

2016-07-01

The Prandtl model succinctly combines the 1D stationary boundary-layer dynamics and thermodynamics of simple anabatic and katabatic flows over uniformly inclined surfaces. It assumes a balance between the along-the-slope buoyancy component and adiabatic warming/cooling, and the turbulent mixing of momentum and heat. In this study, energetics of the Prandtl model is addressed in terms of the total energy (TE) concept. Furthermore, since the authors recently developed a weakly nonlinear version of the Prandtl model, the TE approach is also exercised on this extended model version, which includes an additional nonlinear term in the thermodynamic equation. Hence, interplay among diffusion, dissipation and temperature-wind interaction of the mean slope flow is further explored. The TE of the nonlinear Prandtl model is assessed in an ensemble of solutions where the Prandtl number, the slope angle and the nonlinearity parameter are perturbed. It is shown that nonlinear effects have the lowest impact on variability in the ensemble of solutions of the weakly nonlinear Prandtl model when compared to the other two governing parameters. The general behavior of the nonlinear solution is similar to the linear solution, except that the maximum of the along-the-slope wind speed in the nonlinear solution reduces for larger slopes. Also, the dominance of PE near the sloped surface, and the elevated maximum of KE in the linear and nonlinear energetics of the extended Prandtl model are found in the PASTEX-94 measurements. The corresponding level where KE>PE most likely marks the bottom of the sublayer subject to shear-driven instabilities. Finally, possible limitations of the weakly nonlinear solutions of the extended Prandtl model are raised. In linear solutions, the local storage of TE term is zero, reflecting the stationarity of solutions by definition. However, in nonlinear solutions, the diffusion, dissipation and interaction terms (where the height of the maximum interaction is proportional to the height of the low-level jet by the factor ≈4/9) do not balance and the local storage of TE attains non-zero values. In order to examine the issue of non-stationarity, the inclusion of velocity-pressure covariance in the momentum equation is suggested for future development of the extended Prandtl model.

Groundwater-Surface Water Interaction: A Case Study of Embankment Dam Safety Assessment in Sweden.

NASA Astrophysics Data System (ADS)

Ferdos, F.; Dargahi, B.

2015-12-01

Seepage, when excessive and unimpeded, can cause embankment dam failure. Such failures are often initiated by internal erosion and piping. Modelling these phenomena in embankment dams, accounting for the groundwater-surface water interactions, is crucial when performing dam safety assessments. The aim of this study was to evaluate the applicability of modelling seepage flows in multi-region dams using a finite element based multi-physics model. The model was applied to the Trängslet dam, the largest dam in Sweden. The objectives were to analyze the characteristics of both the flow and the surface-ground water interactions occurring in the dam, including: i) the saturated and unsaturated laminar flow regimes within the dam body, ii) the non-linear through-flow in the dam shoulders' coarse material, iii) the influence of the surface waves in the reservoir on the seepage flow by coupling the physics to a hydrodynamic interface, and iv) the influence of a conceptual "erosion tunnel" on the seepage flow and its interaction with the surface water flow by coupling the physics to a CFD interface. The focus of the study was on the influence of the transient water head boundary condition, surface waves and the internal erosion tunnel on the location of the phreatic line and the seepage flow rate. The simulated seepage flow of the dam in its original condition tallied with the monitoring measurements (40-70 l/s). The main feature found was the relatively high position of the phreatic line, which could compromise the stability of the dam. The combination of the seepage model with the reservoir hydrodynamics indicated a negligible influence of the surface waves on seepage flow. Results from the combination of the seepage model with fluid dynamics indicated that a conceptual "erosion tunnel" placed within the dam, even as high as in the unsaturated zone, significantly affects the phreatic line's position. This also causes the seepage flow to increase by several orders of magnitude, resulting in non-linear turbulent flow regimes in the downstream shoulder of the dam and, ultimately, dam failure. While the modelling was limited by a lack of reliable geometrical and geotechnical data, the results of the study do highlight the importance of including groundwater-surface water interactions in dam safety assessments.

Nonlinear radiative heat flux and heat source/sink on entropy generation minimization rate

NASA Astrophysics Data System (ADS)

Hayat, T.; Khan, M. Waleed Ahmed; Khan, M. Ijaz; Alsaedi, A.

2018-06-01

Entropy generation minimization in nonlinear radiative mixed convective flow towards a variable thicked surface is addressed. Entropy generation for momentum and temperature is carried out. The source for this flow analysis is stretching velocity of sheet. Transformations are used to reduce system of partial differential equations into ordinary ones. Total entropy generation rate is determined. Series solutions for the zeroth and mth order deformation systems are computed. Domain of convergence for obtained solutions is identified. Velocity, temperature and concentration fields are plotted and interpreted. Entropy equation is studied through nonlinear mixed convection and radiative heat flux. Velocity and temperature gradients are discussed through graphs. Meaningful results are concluded in the final remarks.

Nonlinear Gravitational and Radiation Aspects in Nanoliquid with Exponential Space Dependent Heat Source and Variable Viscosity

NASA Astrophysics Data System (ADS)

Gireesha, B. J.; Kumar, P. B. Sampath; Mahanthesh, B.; Shehzad, S. A.; Abbasi, F. M.

2018-05-01

The nonlinear convective flow of kerosene-Alumina nanoliquid subjected to an exponential space dependent heat source and temperature dependent viscosity is investigated here. This study is focuses on augmentation of heat transport rate in liquid propellant rocket engine. The kerosene-Alumina nanoliquid is considered as the regenerative coolant. Aspects of radiation and viscous dissipation are also covered. Relevant nonlinear system is solved numerically via RK based shooting scheme. Diverse flow fields are computed and examined for distinct governing variables. We figured out that the nanoliquid's temperature increased due to space dependent heat source and radiation aspects. The heat transfer rate is higher in case of changeable viscosity than constant viscosity.

Nonlinear Gravitational and Radiation Aspects in Nanoliquid with Exponential Space Dependent Heat Source and Variable Viscosity

NASA Astrophysics Data System (ADS)

Gireesha, B. J.; Kumar, P. B. Sampath; Mahanthesh, B.; Shehzad, S. A.; Abbasi, F. M.

2018-02-01

The nonlinear convective flow of kerosene-Alumina nanoliquid subjected to an exponential space dependent heat source and temperature dependent viscosity is investigated here. This study is focuses on augmentation of heat transport rate in liquid propellant rocket engine. The kerosene-Alumina nanoliquid is considered as the regenerative coolant. Aspects of radiation and viscous dissipation are also covered. Relevant nonlinear system is solved numerically via RK based shooting scheme. Diverse flow fields are computed and examined for distinct governing variables. We figured out that the nanoliquid's temperature increased due to space dependent heat source and radiation aspects. The heat transfer rate is higher in case of changeable viscosity than constant viscosity.

On compressible and piezo-viscous flow in thin porous media.

PubMed

Pérez-Ràfols, F; Wall, P; Almqvist, A

2018-01-01

In this paper, we study flow through thin porous media as in, e.g. seals or fractures. It is often useful to know the permeability of such systems. In the context of incompressible and iso-viscous fluids, the permeability is the constant of proportionality relating the total flow through the media to the pressure drop. In this work, we show that it is also relevant to define a constant permeability when compressible and/or piezo-viscous fluids are considered. More precisely, we show that the corresponding nonlinear equation describing the flow of any compressible and piezo-viscous fluid can be transformed into a single linear equation. Indeed, this linear equation is the same as the one describing the flow of an incompressible and iso-viscous fluid. By this transformation, the total flow can be expressed as the product of the permeability and a nonlinear function of pressure, which represents a generalized pressure drop.

Prospectus: towards the development of high-fidelity models of wall turbulence at large Reynolds number

PubMed Central

Klewicki, J. C.; Chini, G. P.; Gibson, J. F.

2017-01-01

Recent and on-going advances in mathematical methods and analysis techniques, coupled with the experimental and computational capacity to capture detailed flow structure at increasingly large Reynolds numbers, afford an unprecedented opportunity to develop realistic models of high Reynolds number turbulent wall-flow dynamics. A distinctive attribute of this new generation of models is their grounding in the Navier–Stokes equations. By adhering to this challenging constraint, high-fidelity models ultimately can be developed that not only predict flow properties at high Reynolds numbers, but that possess a mathematical structure that faithfully captures the underlying flow physics. These first-principles models are needed, for example, to reliably manipulate flow behaviours at extreme Reynolds numbers. This theme issue of Philosophical Transactions of the Royal Society A provides a selection of contributions from the community of researchers who are working towards the development of such models. Broadly speaking, the research topics represented herein report on dynamical structure, mechanisms and transport; scale interactions and self-similarity; model reductions that restrict nonlinear interactions; and modern asymptotic theories. In this prospectus, the challenges associated with modelling turbulent wall-flows at large Reynolds numbers are briefly outlined, and the connections between the contributing papers are highlighted. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’. PMID:28167585

Prospectus: towards the development of high-fidelity models of wall turbulence at large Reynolds number.

PubMed

Klewicki, J C; Chini, G P; Gibson, J F

2017-03-13

Recent and on-going advances in mathematical methods and analysis techniques, coupled with the experimental and computational capacity to capture detailed flow structure at increasingly large Reynolds numbers, afford an unprecedented opportunity to develop realistic models of high Reynolds number turbulent wall-flow dynamics. A distinctive attribute of this new generation of models is their grounding in the Navier-Stokes equations. By adhering to this challenging constraint, high-fidelity models ultimately can be developed that not only predict flow properties at high Reynolds numbers, but that possess a mathematical structure that faithfully captures the underlying flow physics. These first-principles models are needed, for example, to reliably manipulate flow behaviours at extreme Reynolds numbers. This theme issue of Philosophical Transactions of the Royal Society A provides a selection of contributions from the community of researchers who are working towards the development of such models. Broadly speaking, the research topics represented herein report on dynamical structure, mechanisms and transport; scale interactions and self-similarity; model reductions that restrict nonlinear interactions; and modern asymptotic theories. In this prospectus, the challenges associated with modelling turbulent wall-flows at large Reynolds numbers are briefly outlined, and the connections between the contributing papers are highlighted.This article is part of the themed issue 'Toward the development of high-fidelity models of wall turbulence at large Reynolds number'. © 2017 The Author(s).

Asymptotic research of transonic gas flows

NASA Astrophysics Data System (ADS)

Velmisov, Petr A.; Tamarova, Yuliya A.

2017-12-01

The article is dedicated to the development asymptotic theory of gas flowing at speed next to sound velocity, particularly of gas transonic flows, i.e. the flows, containing both, subsonic and supersonic areas. The main issue, when styding such flows, are nonlinearity and combined type of equations, describing the transonic flow. Based on asymptotic nonlinear equation obtained in the article, the gas transonic flows is studied, considering transverse disturbance with respect to the main flow. The asymptotic conditions at shock-wave front and conditions on the streamlined surface are found. Moreover, the equation of sound surface and asymptotic formula defining the pressure are recorded. Several exact particular solutions of such equation are given, and their application to solve several tasks of transonic aerodynamics is indicated. Specifically, the polynomial form solution describing gas axisymmetric flows in Laval nozzles with constant acceleration in direction of the nozzle's axis and flow swirling is obtained. The solutions describing the unsteady flow along the channels between spinning surfaces are presented. The asymptotic equation is obtained, describing the flow, appearing during non-separated and separated flow past, closely approximated to cylindrical one. Specific solutions are given, based on which the examples of steady flow are formed.

Shear-Flow Instability Saturation by Stable Modes: Hydrodynamics and Gyrokinetics

NASA Astrophysics Data System (ADS)

Fraser, Adrian; Pueschel, M. J.; Terry, P. W.; Zweibel, E. G.

2017-10-01

We present simulations of shear-driven instabilities, focusing on the impact of nonlinearly excited, large-scale, linearly stable modes on the nonlinear cascade, momentum transport, and secondary instabilities. Stable modes, which have previously been shown to significantly affect instability saturation [Fraser et al. PoP 2017], are investigated in a collisionless, gyrokinetic, periodic zonal flow using the Gene code by projecting the results of nonlinear simulations onto a basis of linear eigenmodes that includes both stable and unstable modes. Benchmarking growth rates against previous gyrokinetic studies and an equivalent fluid system demonstrates comparable linear dynamics in the fluid and gyrokinetic systems. Cases of driven and decaying shear-flow turbulence are compared in Gene by using a Krook operator as an effective forcing. For comparison with existing hydrodynamic and MHD shear-flow instability studies, we present results for the shear layer obtained by similar means with the code Dedalus. Supported by U.S. DOE Grant No. DE-FG02-89ER53291, the NSF, and UW-Madison.

Effect of homogenous-heterogeneous reactions on MHD Prandtl fluid flow over a stretching sheet

NASA Astrophysics Data System (ADS)

Khan, Imad; Malik, M. Y.; Hussain, Arif; Salahuddin, T.

An analysis is performed to explore the effects of homogenous-heterogeneous reactions on two-dimensional flow of Prandtl fluid over a stretching sheet. In present analysis, we used the developed model of homogeneous-heterogeneous reactions in boundary layer flow. The mathematical configuration of presented flow phenomenon yields the nonlinear partial differential equations. Using scaling transformations, the governing partial differential equations (momentum equation and homogenous-heterogeneous reactions equations) are transformed into non-linear ordinary differential equations (ODE's). Then, resulting non-linear ODE's are solved by computational scheme known as shooting method. The quantitative and qualitative manners of concerned physical quantities (velocity, concentration and drag force coefficient) are examined under prescribed physical constrained through figures and tables. It is observed that velocity profile enhances verses fluid parameters α and β while Hartmann number reduced it. The homogeneous and heterogeneous reactions parameters have reverse effects on concentration profile. Concentration profile shows retarding behavior for large values of Schmidt number. Skin fraction coefficient enhances with increment in Hartmann number H and fluid parameter α .

Pressure fluctuations and time scales in turbulent channel flow

NASA Astrophysics Data System (ADS)

Septham, Kamthon; Morrison, Jonathan; Diwan, Sourabh

2015-11-01

Pressure fluctuations in turbulent channel flow subjected to globally stabilising linear feedback control are investigated at Reτ = 400 . The passivity-based control is adopted and explained by the conservative characteristics of the nonlinear terms contributing to the Reynolds-Orr equation (Sharma et al. Phys. Fluids 2011). The linear control operates via vU' ; the maximum forcing is located at y+ ~ 20 , corresponding to the location of the maximum in the mean-square pressure gradient. The responses of the rapid (linear) and slow (nonlinear) pressure fluctuations to the linear control are investigated using the Green's function representations. It demonstrates that the linear control operates via the linear source terms of the Poisson equation for pressure fluctuations. Landahl's timescales of the minimal flow unit (MFU) in turbulent channel flow are examined at y+ = 20 . It shows that the timescales of MFU agree well with the theoretical values proposed by Landahl (1993). Therefore, the effectiveness of the linear control to attenuate wall turbulence is explained by Landahl's theory for timescales, in that the control proceeds via the shear interaction timescale which is significantly shorter than both the nonlinear and viscous timescales.

Chaotic structures of nonlinear magnetic fields. I - Theory. II - Numerical results

NASA Technical Reports Server (NTRS)

Lee, Nam C.; Parks, George K.

1992-01-01

A study of the evolutionary properties of nonlinear magnetic fields in flowing MHD plasmas is presented to illustrate that nonlinear magnetic fields may involve chaotic dynamics. It is shown how a suitable transformation of the coupled equations leads to Duffing's form, suggesting that the behavior of the general solution can also be chaotic. Numerical solutions of the nonlinear magnetic field equations that have been cast in the form of Duffing's equation are presented.

Hydrodynamic optical soliton tunneling

NASA Astrophysics Data System (ADS)

Sprenger, P.; Hoefer, M. A.; El, G. A.

2018-03-01

A notion of hydrodynamic optical soliton tunneling is introduced in which a dark soliton is incident upon an evolving, broad potential barrier that arises from an appropriate variation of the input signal. The barriers considered include smooth rarefaction waves and highly oscillatory dispersive shock waves. Both the soliton and the barrier satisfy the same one-dimensional defocusing nonlinear Schrödinger (NLS) equation, which admits a convenient dispersive hydrodynamic interpretation. Under the scale separation assumption of nonlinear wave (Whitham) modulation theory, the highly nontrivial nonlinear interaction between the soliton and the evolving hydrodynamic barrier is described in terms of self-similar, simple wave solutions to an asymptotic reduction of the Whitham-NLS partial differential equations. One of the Riemann invariants of the reduced modulation system determines the characteristics of a soliton interacting with a mean flow that results in soliton tunneling or trapping. Another Riemann invariant yields the tunneled soliton's phase shift due to hydrodynamic interaction. Soliton interaction with hydrodynamic barriers gives rise to effects that include reversal of the soliton propagation direction and spontaneous soliton cavitation, which further suggest possible methods of dark soliton control in optical fibers.

Hydrodynamic optical soliton tunneling.

PubMed

Sprenger, P; Hoefer, M A; El, G A

2018-03-01

A notion of hydrodynamic optical soliton tunneling is introduced in which a dark soliton is incident upon an evolving, broad potential barrier that arises from an appropriate variation of the input signal. The barriers considered include smooth rarefaction waves and highly oscillatory dispersive shock waves. Both the soliton and the barrier satisfy the same one-dimensional defocusing nonlinear Schrödinger (NLS) equation, which admits a convenient dispersive hydrodynamic interpretation. Under the scale separation assumption of nonlinear wave (Whitham) modulation theory, the highly nontrivial nonlinear interaction between the soliton and the evolving hydrodynamic barrier is described in terms of self-similar, simple wave solutions to an asymptotic reduction of the Whitham-NLS partial differential equations. One of the Riemann invariants of the reduced modulation system determines the characteristics of a soliton interacting with a mean flow that results in soliton tunneling or trapping. Another Riemann invariant yields the tunneled soliton's phase shift due to hydrodynamic interaction. Soliton interaction with hydrodynamic barriers gives rise to effects that include reversal of the soliton propagation direction and spontaneous soliton cavitation, which further suggest possible methods of dark soliton control in optical fibers.

Numerical Simulations of Reacting Flows Using Asynchrony-Tolerant Schemes for Exascale Computing

NASA Astrophysics Data System (ADS)

Cleary, Emmet; Konduri, Aditya; Chen, Jacqueline

2017-11-01

Communication and data synchronization between processing elements (PEs) are likely to pose a major challenge in scalability of solvers at the exascale. Recently developed asynchrony-tolerant (AT) finite difference schemes address this issue by relaxing communication and synchronization between PEs at a mathematical level while preserving accuracy, resulting in improved scalability. The performance of these schemes has been validated for simple linear and nonlinear homogeneous PDEs. However, many problems of practical interest are governed by highly nonlinear PDEs with source terms, whose solution may be sensitive to perturbations caused by communication asynchrony. The current work applies the AT schemes to combustion problems with chemical source terms, yielding a stiff system of PDEs with nonlinear source terms highly sensitive to temperature. Examples shown will use single-step and multi-step CH4 mechanisms for 1D premixed and nonpremixed flames. Error analysis will be discussed both in physical and spectral space. Results show that additional errors introduced by the AT schemes are negligible and the schemes preserve their accuracy. We acknowledge funding from the DOE Computational Science Graduate Fellowship administered by the Krell Institute.

Nonlinear initial-boundary value solutions by the finite element method. [for Navier-Stokes equations of two dimensional flow

NASA Technical Reports Server (NTRS)

Baker, A. J.

1974-01-01

The finite-element method is used to establish a numerical solution algorithm for the Navier-Stokes equations for two-dimensional flows of a viscous compressible fluid. Numerical experiments confirm the advection property for the finite-element equivalent of the nonlinear convection term for both unidirectional and recirculating flowfields. For linear functionals, the algorithm demonstrates good accuracy using coarse discretizations and h squared convergence with discretization refinement.

The Role of Eigensolutions in Nonlinear Inverse Cavity-Flow-Theory. Revision.

DTIC Science & Technology

1985-06-10

The method of Levi Civita is applied to an isolated fully cavitating body at zero cavitation number and adapted to the solution of the inverse...Eigensolutions in Nonlinear Inverse Cavity-Flow Theory [Revised] Abstract: The method of Levi Civita is applied to an isolated fully cavitating body at...problem is not thought * to present much of a challenge at zero cavitation number. In this case, - the classical method of Levi Civita [7] can be

Unstable flow structures in the Blasius boundary layer.

PubMed

Wedin, H; Bottaro, A; Hanifi, A; Zampogna, G

2014-04-01

Finite amplitude coherent structures with a reflection symmetry in the spanwise direction of a parallel boundary layer flow are reported together with a preliminary analysis of their stability. The search for the solutions is based on the self-sustaining process originally described by Waleffe (Phys. Fluids 9, 883 (1997)). This requires adding a body force to the Navier-Stokes equations; to locate a relevant nonlinear solution it is necessary to perform a continuation in the nonlinear regime and parameter space in order to render the body force of vanishing amplitude. Some states computed display a spanwise spacing between streaks of the same length scale as turbulence flow structures observed in experiments (S.K. Robinson, Ann. Rev. Fluid Mech. 23, 601 (1991)), and are found to be situated within the buffer layer. The exact coherent structures are unstable to small amplitude perturbations and thus may be part of a set of unstable nonlinear states of possible use to describe the turbulent transition. The nonlinear solutions survive down to a displacement thickness Reynolds number Re * = 496 , displaying a 4-vortex structure and an amplitude of the streamwise root-mean-square velocity of 6% scaled with the free-stream velocity. At this Re* the exact coherent structure bifurcates supercritically and this is the point where the laminar Blasius flow starts to cohabit the phase space with alternative simple exact solutions of the Navier-Stokes equations.

On the nonlinear development of the most unstable Goertler vortex mode

NASA Technical Reports Server (NTRS)

Denier, James P.; Hall, Philip

1991-01-01

The nonlinear development of the most unstable Gortler vortex mode in boundary layer flows over curved walls is investigated. The most unstable Gortler mode is confined to a viscous wall layer of thickness O(G -1/5) and has spanwise wavelength O(G 11/5); it is, of course, most relevant to flow situations where the Gortler number G is much greater than 1. The nonlinear equations covering the evolution of this mode over an O(G -3/5) streamwise lengthscale are derived and are found to be of a fully nonparallel nature. The solution of these equations is achieved by making use of the numerical scheme used by Hall (1988) for the numerical solution of the nonlinear Gortler equations valid for O(1) Gortler numbers. Thus, the spanwise dependence of the flow is described by a Fourier expansion, whereas the streamwise and normal variations of the flow are dealt with by employing a suitable finite difference discretization of the governing equations. Our calculations demonstrate that, given a suitable initial disturbance, after a brief interval of decay, the energy in all the higher harmonics grows until a singularity is encountered at some downstream position. The structure of the flowfield as this singularity is approached suggests that the singularity is responsible for the vortices, which are initially confined to the thin viscous wall layer, moving away from the wall and into the core of the boundary layer.

Nonlinear Plasma Response to Resonant Magnetic Perturbation in Rutherford Regime

NASA Astrophysics Data System (ADS)

Zhu, Ping; Yan, Xingting; Huang, Wenlong

2017-10-01

Recently a common analytic relation for both the locked mode and the nonlinear plasma response in the Rutherford regime has been developed based on the steady-state solution to the coupled dynamic system of magnetic island evolution and torque balance equations. The analytic relation predicts the threshold and the island size for the full penetration of resonant magnetic perturbation (RMP). It also rigorously proves a screening effect of the equilibrium toroidal flow. In this work, we test the theory by solving for the nonlinear plasma response to a single-helicity RMP of a circular-shaped limiter tokamak equilibrium with a constant toroidal flow, using the initial-value, full MHD simulation code NIMROD. Time evolution of the parallel flow or ``slip frequency'' profile and its asymptotic approach to steady state obtained from the NIMROD simulations qualitatively agree with the theory predictions. Further comparisons are carried out for the saturated island size, the threshold for full mode penetration, as well as the screening effects of equilibrium toroidal flow in order to understand the physics of nonlinear plasma response in the Rutherford regime. Supported by National Magnetic Confinement Fusion Science Program of China Grants 2014GB124002 and 2015GB101004, the 100 Talent Program of the Chinese Academy of Sciences, and U.S. Department of Energy Grants DE-FG02-86ER53218 and DE-FC02-08ER54975.

Recent developments in heterodyne laser interferometry at Harbin Institute of Technology

NASA Astrophysics Data System (ADS)

Hu, P. C.; Tan, J. B. B.; Yang, H. X. X.; Fu, H. J. J.; Wang, Q.

2013-01-01

In order to fulfill the requirements for high-resolution and high-precision heterodyne interferometric technologies and instruments, the laser interferometry group of HIT has developed some novel techniques for high-resolution and high-precision heterodyne interferometers, such as high accuracy laser frequency stabilization, dynamic sub-nanometer resolution phase interpolation and dynamic nonlinearity measurement. Based on a novel lock point correction method and an asymmetric thermal structure, the frequency stabilized laser achieves a long term stability of 1.2×10-8, and it can be steadily stabilized even in the air flowing up to 1 m/s. In order to achieve dynamic sub-nanometer resolution of laser heterodyne interferometers, a novel phase interpolation method based on digital delay line is proposed. Experimental results show that, the proposed 0.62 nm, phase interpolator built with a 64 multiple PLL and an 8-tap digital delay line achieves a static accuracy better than 0.31nm and a dynamic accuracy better than 0.62 nm over the velocity ranging from -2 m/s to 2 m/s. Meanwhile, an accuracy beam polarization measuring setup is proposed to check and ensure the light's polarization state of the dual frequency laser head, and a dynamic optical nonlinearity measuring setup is built to measure the optical nonlinearity of the heterodyne system accurately and quickly. Analysis and experimental results show that, the beam polarization measuring setup can achieve an accuracy of 0.03° in ellipticity angles and an accuracy of 0.04° in the non-orthogonality angle respectively, and the optical nonlinearity measuring setup can achieve an accuracy of 0.13°.

A wind turbine hybrid simulation framework considering aeroelastic effects

NASA Astrophysics Data System (ADS)

Song, Wei; Su, Weihua

2015-04-01

In performing an effective structural analysis for wind turbine, the simulation of turbine aerodynamic loads is of great importance. The interaction between the wake flow and the blades may impact turbine blades loading condition, energy yield and operational behavior. Direct experimental measurement of wind flow field and wind profiles around wind turbines is very helpful to support the wind turbine design. However, with the growth of the size of wind turbines for higher energy output, it is not convenient to obtain all the desired data in wind-tunnel and field tests. In this paper, firstly the modeling of dynamic responses of large-span wind turbine blades will consider nonlinear aeroelastic effects. A strain-based geometrically nonlinear beam formulation will be used for the basic structural dynamic modeling, which will be coupled with unsteady aerodynamic equations and rigid-body rotations of the rotor. Full wind turbines can be modeled by using the multi-connected beams. Then, a hybrid simulation experimental framework is proposed to potentially address this issue. The aerodynamic-dominant components, such as the turbine blades and rotor, are simulated as numerical components using the nonlinear aeroelastic model; while the turbine tower, where the collapse of failure may occur under high level of wind load, is simulated separately as the physical component. With the proposed framework, dynamic behavior of NREL's 5MW wind turbine blades will be studied and correlated with available numerical data. The current work will be the basis of the authors' further studies on flow control and hazard mitigation on wind turbine blades and towers.

Linear and nonlinear stability of the Blasius boundary layer

NASA Technical Reports Server (NTRS)

Bertolotti, F. P.; Herbert, TH.; Spalart, P. R.

1992-01-01

Two new techniques for the study of the linear and nonlinear instability in growing boundary layers are presented. The first technique employs partial differential equations of parabolic type exploiting the slow change of the mean flow, disturbance velocity profiles, wavelengths, and growth rates in the streamwise direction. The second technique solves the Navier-Stokes equation for spatially evolving disturbances using buffer zones adjacent to the inflow and outflow boundaries. Results of both techniques are in excellent agreement. The linear and nonlinear development of Tollmien-Schlichting (TS) waves in the Blasius boundary layer is investigated with both techniques and with a local procedure based on a system of ordinary differential equations. The results are compared with previous work and the effects of non-parallelism and nonlinearity are clarified. The effect of nonparallelism is confirmed to be weak and, consequently, not responsible for the discrepancies between measurements and theoretical results for parallel flow.

The Weakly Nonlinear Magnetorotational Instability in a Global, Cylindrical Taylor–Couette Flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Clark, S. E.; Oishi, Jeffrey S., E-mail: seclark@astro.columbia.edu

We conduct a global, weakly nonlinear analysis of the magnetorotational instability (MRI) in a Taylor–Couette flow. This is a multiscale, perturbative treatment of the nonideal, axisymmetric MRI near threshold, subject to realistic radial boundary conditions and cylindrical geometry. We analyze both the standard MRI, initialized by a constant vertical background magnetic field, and the helical MRI, with an azimuthal background field component. This is the first weakly nonlinear analysis of the MRI in a global Taylor–Couette geometry, as well as the first weakly nonlinear analysis of the helical MRI. We find that the evolution of the amplitude of the standardmore » MRI is described by a real Ginzburg–Landau equation (GLE), whereas the amplitude of the helical MRI takes the form of a complex GLE. This suggests that the saturated state of the helical MRI may itself be unstable on long spatial and temporal scales.« less

On the instability of a three-dimensional attachment-line boundary layer - Weakly nonlinear theory and a numerical approach

NASA Technical Reports Server (NTRS)

Hall, P.; Malik, M. R.

1986-01-01

The instability of a three-dimensional attachment-line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite-amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time-dependent Navier-Stokes equations for the attachment-line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite-amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment-line boundary layer is also investigated.

On the instability of a 3-dimensional attachment line boundary layer: Weakly nonlinear theory and a numerical approach

NASA Technical Reports Server (NTRS)

Hall, P.; Malik, M. R.

1984-01-01

The instability of a three dimensional attachment line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time dependent Navier-Stokes equations for the attachment line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment line boundary layer is also investigated.

A Multi-Scale Integrated Approach to Representing Watershed Systems: Significance and Challenges

NASA Astrophysics Data System (ADS)

Kim, J.; Ivanov, V. Y.; Katopodes, N.

2013-12-01

A range of processes associated with supplying services and goods to human society originate at the watershed level. Predicting watershed response to forcing conditions has been of high interest to many practical societal problems, however, remains challenging due to two significant properties of the watershed systems, i.e., connectivity and non-linearity. Connectivity implies that disturbances arising at any larger scale will necessarily propagate and affect local-scale processes; their local effects consequently influence other processes, and often convey nonlinear relationships. Physically-based, process-scale modeling is needed to approach the understanding and proper assessment of non-linear effects between the watershed processes. We have developed an integrated model simulating hydrological processes, flow dynamics, erosion and sediment transport, tRIBS-OFM-HRM (Triangulated irregular network - based Real time Integrated Basin Simulator-Overland Flow Model-Hairsine and Rose Model). This coupled model offers the advantage of exploring the hydrological effects of watershed physical factors such as topography, vegetation, and soil, as well as their feedback mechanisms. Several examples investigating the effects of vegetation on flow movement, the role of soil's substrate on sediment dynamics, and the driving role of topography on morphological processes are illustrated. We show how this comprehensive modeling tool can help understand interconnections and nonlinearities of the physical system, e.g., how vegetation affects hydraulic resistance depending on slope, vegetation cover fraction, discharge, and bed roughness condition; how the soil's substrate condition impacts erosion processes with an non-unique characteristic at the scale of a zero-order catchment; and how topographic changes affect spatial variations of morphologic variables. Due to feedback and compensatory nature of mechanisms operating in different watershed compartments, our conclusion is that a key to representing watershed systems lies in an integrated, interdisciplinary approach, whereby a physically-based model is used for assessments/evaluations associated with future changes in landuse, climate, and ecosystems.

A study of prediction methods for the high angle-of-attack aerodynamics of straight wings and fighter aircraft

NASA Technical Reports Server (NTRS)

Mcmillan, O. J.; Mendenhall, M. R.; Perkins, S. C., Jr.

1984-01-01

Work is described dealing with two areas which are dominated by the nonlinear effects of vortex flows. The first area concerns the stall/spin characteristics of a general aviation wing with a modified leading edge. The second area concerns the high-angle-of-attack characteristics of high performance military aircraft. For each area, the governing phenomena are described as identified with the aid of existing experimental data. Existing analytical methods are reviewed, and the most promising method for each area used to perform some preliminary calculations. Based on these results, the strengths and weaknesses of the methods are defined, and research programs recommended to improve the methods as a result of better understanding of the flow mechanisms involved.