Accurate solutions for transonic viscous flow over finite wings
NASA Technical Reports Server (NTRS)
Vatsa, V. N.
1986-01-01
An explicit multistage Runge-Kutta type time-stepping scheme is used for solving the three-dimensional, compressible, thin-layer Navier-Stokes equations. A finite-volume formulation is employed to facilitate treatment of complex grid topologies encountered in three-dimensional calculations. Convergence to steady state is expedited through usage of acceleration techniques. Further numerical efficiency is achieved through vectorization of the computer code. The accuracy of the overall scheme is evaluated by comparing the computed solutions with the experimental data for a finite wing under different test conditions in the transonic regime. A grid refinement study ir conducted to estimate the grid requirements for adequate resolution of salient features of such flows.
NASA Astrophysics Data System (ADS)
Stukel, Michael R.; Landry, Michael R.; Ohman, Mark D.; Goericke, Ralf; Samo, Ty; Benitez-Nelson, Claudia R.
2012-03-01
Despite the increasing use of linear inverse modeling techniques to elucidate fluxes in undersampled marine ecosystems, the accuracy with which they estimate food web flows has not been resolved. New Markov Chain Monte Carlo (MCMC) solution methods have also called into question the biases of the commonly used L2 minimum norm (L 2MN) solution technique. Here, we test the abilities of MCMC and L 2MN methods to recover field-measured ecosystem rates that are sequentially excluded from the model input. For data, we use experimental measurements from process cruises of the California Current Ecosystem (CCE-LTER) Program that include rate estimates of phytoplankton and bacterial production, micro- and mesozooplankton grazing, and carbon export from eight study sites varying from rich coastal upwelling to offshore oligotrophic conditions. Both the MCMC and L 2MN methods predicted well-constrained rates of protozoan and mesozooplankton grazing with reasonable accuracy, but the MCMC method overestimated primary production. The MCMC method more accurately predicted the poorly constrained rate of vertical carbon export than the L 2MN method, which consistently overestimated export. Results involving DOC and bacterial production were equivocal. Overall, when primary production is provided as model input, the MCMC method gives a robust depiction of ecosystem processes. Uncertainty in inverse ecosystem models is large and arises primarily from solution under-determinacy. We thus suggest that experimental programs focusing on food web fluxes expand the range of experimental measurements to include the nature and fate of detrital pools, which play large roles in the model.
High order accurate solutions of viscous problems
NASA Technical Reports Server (NTRS)
Hayder, M. E.; Turkel, Eli
1993-01-01
We consider a fourth order extension to MacCormack's scheme. The original extension was fourth order only for the inviscid terms but was second order for the viscous terms. We show how to modify the viscous terms so that the scheme is uniformly fourth order in the spatial derivatives. Applications are given to some boundary layer flows. In addition, for applications to shear flows the effect of the outflow boundary conditions are very important. We compare the accuracy of several of these different boundary conditions for both boundary layer and shear flows. Stretching at the outflow usually increases the oscillations in the numerical solution but the addition of a filtered sponge layer (with or without stretching) reduces such oscillations. The oscillations are generated by insufficient resolution of the shear layer. When the shear layer is sufficiently resolved then oscillations are not generated and there is less of a need for a nonreflecting boundary condition.
Accurate numerical solution of compressible, linear stability equations
NASA Technical Reports Server (NTRS)
Malik, M. R.; Chuang, S.; Hussaini, M. Y.
1982-01-01
The present investigation is concerned with a fourth order accurate finite difference method and its application to the study of the temporal and spatial stability of the three-dimensional compressible boundary layer flow on a swept wing. This method belongs to the class of compact two-point difference schemes discussed by White (1974) and Keller (1974). The method was apparently first used for solving the two-dimensional boundary layer equations. Attention is given to the governing equations, the solution technique, and the search for eigenvalues. A general purpose subroutine is employed for solving a block tridiagonal system of equations. The computer time can be reduced significantly by exploiting the special structure of two matrices.
More-Accurate Model of Flows in Rocket Injectors
NASA Technical Reports Server (NTRS)
Hosangadi, Ashvin; Chenoweth, James; Brinckman, Kevin; Dash, Sanford
2011-01-01
An improved computational model for simulating flows in liquid-propellant injectors in rocket engines has been developed. Models like this one are needed for predicting fluxes of heat in, and performances of, the engines. An important part of predicting performance is predicting fluctuations of temperature, fluctuations of concentrations of chemical species, and effects of turbulence on diffusion of heat and chemical species. Customarily, diffusion effects are represented by parameters known in the art as the Prandtl and Schmidt numbers. Prior formulations include ad hoc assumptions of constant values of these parameters, but these assumptions and, hence, the formulations, are inaccurate for complex flows. In the improved model, these parameters are neither constant nor specified in advance: instead, they are variables obtained as part of the solution. Consequently, this model represents the effects of turbulence on diffusion of heat and chemical species more accurately than prior formulations do, and may enable more-accurate prediction of mixing and flows of heat in rocket-engine combustion chambers. The model has been implemented within CRUNCH CFD, a proprietary computational fluid dynamics (CFD) computer program, and has been tested within that program. The model could also be implemented within other CFD programs.
Accurate description of calcium solvation in concentrated aqueous solutions.
Kohagen, Miriam; Mason, Philip E; Jungwirth, Pavel
2014-07-17
Calcium is one of the biologically most important ions; however, its accurate description by classical molecular dynamics simulations is complicated by strong electrostatic and polarization interactions with surroundings due to its divalent nature. Here, we explore the recently suggested approach for effectively accounting for polarization effects via ionic charge rescaling and develop a new and accurate parametrization of the calcium dication. Comparison to neutron scattering and viscosity measurements demonstrates that our model allows for an accurate description of concentrated aqueous calcium chloride solutions. The present model should find broad use in efficient and accurate modeling of calcium in aqueous environments, such as those encountered in biological and technological applications.
Device accurately measures and records low gas-flow rates
NASA Technical Reports Server (NTRS)
Branum, L. W.
1966-01-01
Free-floating piston in a vertical column accurately measures and records low gas-flow rates. The system may be calibrated, using an adjustable flow-rate gas supply, a low pressure gage, and a sequence recorder. From the calibration rates, a nomograph may be made for easy reduction. Temperature correction may be added for further accuracy.
A new benchmark with high accurate solution for hot-cold fluids mixing
NASA Astrophysics Data System (ADS)
Younes, Anis; Fahs, Marwan; Zidane, Ali; Huggenberger, Peter; Zechner, Eric
2015-09-01
A new benchmark is proposed for the verification of buoyancy-driven flow codes. The benchmark deals with mixing hot and cold fluids from the opposite boundaries of an open channel. A high accurate solution is developed using the Fourier-Galerkin (FG) method and compared to the results of an advanced finite element (FE) model. An excellent agreement is observed between the FG and FE solutions for different Reynolds numbers which demonstrates the viability of the solutions in benchmarking buoyancy-driven flow numerical codes.
ACCURATE CHEMICAL MASTER EQUATION SOLUTION USING MULTI-FINITE BUFFERS
Cao, Youfang; Terebus, Anna; Liang, Jie
2016-01-01
The discrete chemical master equation (dCME) provides a fundamental framework for studying stochasticity in mesoscopic networks. Because of the multi-scale nature of many networks where reaction rates have large disparity, directly solving dCMEs is intractable due to the exploding size of the state space. It is important to truncate the state space effectively with quantified errors, so accurate solutions can be computed. It is also important to know if all major probabilistic peaks have been computed. Here we introduce the Accurate CME (ACME) algorithm for obtaining direct solutions to dCMEs. With multi-finite buffers for reducing the state space by O(n!), exact steady-state and time-evolving network probability landscapes can be computed. We further describe a theoretical framework of aggregating microstates into a smaller number of macrostates by decomposing a network into independent aggregated birth and death processes, and give an a priori method for rapidly determining steady-state truncation errors. The maximal sizes of the finite buffers for a given error tolerance can also be pre-computed without costly trial solutions of dCMEs. We show exactly computed probability landscapes of three multi-scale networks, namely, a 6-node toggle switch, 11-node phage-lambda epigenetic circuit, and 16-node MAPK cascade network, the latter two with no known solutions. We also show how probabilities of rare events can be computed from first-passage times, another class of unsolved problems challenging for simulation-based techniques due to large separations in time scales. Overall, the ACME method enables accurate and efficient solutions of the dCME for a large class of networks. PMID:27761104
Electroosmotic Flow Hysteresis for Dissimilar Anionic Solutions.
Lim, An Eng; Lim, Chun Yee; Lam, Yee Cheong
2016-08-16
Electroosmotic flow (EOF) with two or more fluids is often encountered in various microfluidic applications. However, no investigation has hitherto been conducted to investigate the hysteretic or flow direction-dependent behavior during displacement flow of solutions with dissimilar anion species. In this investigation, EOF of dissimilar anionic solutions was studied experimentally through the current monitoring method and numerically through finite element simulations. As opposed to other conventional displacement flows, EOF involving dissimilar anionic solutions exhibits counterintuitive behavior, whereby the current-time curve does not reach the steady-state value of the displacing electrolyte. Two distinct mechanics have been identified as the causes for this observation: (a) ion concentration adjustment when the displacing anions migrate upstream against EOF due to competition between the gradients of electromigrative and convective fluxes and (b) ion concentration readjustment induced by the static diffusive interfacial region between the dissimilar fluids which can only be propagated throughout the entire microchannel with the presence of EOF. The resultant ion distributions lead to the flow rate to be directional-dependent, indicating that the flow conditions are asymmetric between these two different flow directions. The outcomes of this investigation contribute to the in-depth understanding of flow behavior in microfluidic systems involving inhomogeneous fluids, particularly dissimilar anionic solutions. The understanding of EOF hysteresis is fundamentally important for the accurate prediction of analytes transport in microfluidic devices under EOF. PMID:27426052
A time-accurate implicit method for chemical non-equilibrium flows at all speeds
NASA Technical Reports Server (NTRS)
Shuen, Jian-Shun
1992-01-01
A new time accurate coupled solution procedure for solving the chemical non-equilibrium Navier-Stokes equations over a wide range of Mach numbers is described. The scheme is shown to be very efficient and robust for flows with velocities ranging from M less than or equal to 10(exp -10) to supersonic speeds.
Multigrid solutions of elliptic fluid flow problems
NASA Astrophysics Data System (ADS)
Wright, Nigel George
1988-06-01
An efficient FAS multigrid solution strategy is presented for the accurate and economic simulation of convection dominated flows. The use of a high-order approximation to the convective transport terms found in the governing equations of motion was investigated in conjunction with an unsegregated smoothing technique. Results are presented for a sequence of problems of increasing complexity requiring that careful attention be directed toward the proper treatment of different types of boundary condition. The classical two-dimensional problem of flow in a lid-driven cavity is investigated in depth for flows at Reynolds number of 100, 400 and 1000. This gives an extremely good indication of the power of a multigrid approach. Next, the solution methodology is applied to flow in a three-dimensional lid-driven cavity at different Reynolds numbers, with cross-reference being made to predictions obtained in the corresponding two-dimensional simulations, and to the flow over a step discontinuity in the case of an abruptly expanding channel. Although, at first sight, these problems appear to require only minor extensions to the existing approach, it is found that they are rather more idiosyncratic. Finally, the governing equations and numerical algorithm are extended to encompass the treatment of thermally driven flows. The solution to two such problems is presented and compared with corresponding results obtained by traditional methods.
A high order accurate difference scheme for complex flow fields
Dexun Fu; Yanwen Ma
1997-06-01
A high order accurate finite difference method for direct numerical simulation of coherent structure in the mixing layers is presented. The reason for oscillation production in numerical solutions is analyzed. It is caused by a nonuniform group velocity of wavepackets. A method of group velocity control for the improvement of the shock resolution is presented. In numerical simulation the fifth-order accurate upwind compact difference relation is used to approximate the derivatives in the convection terms of the compressible N-S equations, a sixth-order accurate symmetric compact difference relation is used to approximate the viscous terms, and a three-stage R-K method is used to advance in time. In order to improve the shock resolution the scheme is reconstructed with the method of diffusion analogy which is used to control the group velocity of wavepackets. 18 refs., 12 figs., 1 tab.
Accurate deterministic solutions for the classic Boltzmann shock profile
NASA Astrophysics Data System (ADS)
Yue, Yubei
The Boltzmann equation or Boltzmann transport equation is a classical kinetic equation devised by Ludwig Boltzmann in 1872. It is regarded as a fundamental law in rarefied gas dynamics. Rather than using macroscopic quantities such as density, temperature, and pressure to describe the underlying physics, the Boltzmann equation uses a distribution function in phase space to describe the physical system, and all the macroscopic quantities are weighted averages of the distribution function. The information contained in the Boltzmann equation is surprisingly rich, and the Euler and Navier-Stokes equations of fluid dynamics can be derived from it using series expansions. Moreover, the Boltzmann equation can reach regimes far from the capabilities of fluid dynamical equations, such as the realm of rarefied gases---the topic of this thesis. Although the Boltzmann equation is very powerful, it is extremely difficult to solve in most situations. Thus the only hope is to solve it numerically. But soon one finds that even a numerical simulation of the equation is extremely difficult, due to both the complex and high-dimensional integral in the collision operator, and the hyperbolic phase-space advection terms. For this reason, until few years ago most numerical simulations had to rely on Monte Carlo techniques. In this thesis I will present a new and robust numerical scheme to compute direct deterministic solutions of the Boltzmann equation, and I will use it to explore some classical gas-dynamical problems. In particular, I will study in detail one of the most famous and intrinsically nonlinear problems in rarefied gas dynamics, namely the accurate determination of the Boltzmann shock profile for a gas of hard spheres.
A time-accurate algorithm for chemical non-equilibrium viscous flows at all speeds
NASA Technical Reports Server (NTRS)
Shuen, J.-S.; Chen, K.-H.; Choi, Y.
1992-01-01
A time-accurate, coupled solution procedure is described for the chemical nonequilibrium Navier-Stokes equations over a wide range of Mach numbers. This method employs the strong conservation form of the governing equations, but uses primitive variables as unknowns. Real gas properties and equilibrium chemistry are considered. Numerical tests include steady convergent-divergent nozzle flows with air dissociation/recombination chemistry, dump combustor flows with n-pentane-air chemistry, nonreacting flow in a model double annular combustor, and nonreacting unsteady driven cavity flows. Numerical results for both the steady and unsteady flows demonstrate the efficiency and robustness of the present algorithm for Mach numbers ranging from the incompressible limit to supersonic speeds.
Cartesian Off-Body Grid Adaption for Viscous Time- Accurate Flow Simulation
NASA Technical Reports Server (NTRS)
Buning, Pieter G.; Pulliam, Thomas H.
2011-01-01
An improved solution adaption capability has been implemented in the OVERFLOW overset grid CFD code. Building on the Cartesian off-body approach inherent in OVERFLOW and the original adaptive refinement method developed by Meakin, the new scheme provides for automated creation of multiple levels of finer Cartesian grids. Refinement can be based on the undivided second-difference of the flow solution variables, or on a specific flow quantity such as vorticity. Coupled with load-balancing and an inmemory solution interpolation procedure, the adaption process provides very good performance for time-accurate simulations on parallel compute platforms. A method of using refined, thin body-fitted grids combined with adaption in the off-body grids is presented, which maximizes the part of the domain subject to adaption. Two- and three-dimensional examples are used to illustrate the effectiveness and performance of the adaption scheme.
Highly accurate boronimeter assay of concentrated boric acid solutions
Ball, R.M. )
1992-01-01
The Random-Walk Boronimeter has successfully been used as an on-line indicator of boric acid concentration in an operating commercial pressurized water reactor. The principle has been adapted for measurement of discrete samples to high accuracy and to concentrations up to 6000 ppm natural boron in light water. Boric acid concentration in an aqueous solution is a necessary measurement in many nuclear power plants, particularly those that use boric acid dissolved in the reactor coolant as a reactivity control system. Other nuclear plants use a high-concentration boric acid solution as a backup shutdown system. Such a shutdown system depends on rapid injection of the solution and frequent surveillance of the fluid to ensure the presence of the neutron absorber. The two methods typically used to measure boric acid are the chemical and the physical methods. The chemical method uses titration to determine the ionic concentration of the BO[sub 3] ions and infers the boron concentration. The physical method uses the attenuation of neutrons by the solution and infers the boron concentration from the neutron absorption properties. This paper describes the Random-Walk Boronimeter configured to measure discrete samples to high accuracy and high concentration.
Critical flow: General theory and spurious solutions
Kestin, J.
1991-05-01
It is hardly necessary to emphasize the importance that an accurate prediction of the parameters of critical flow plays in a number of industries, notably in nuclear reactor safety calculations and in metering. In spite of its importance, the literature of the subject still contains erroneous statements. Many of them result from an unjustified belief in the generality of certain conclusions drawn in the elementary study of one-dimensional isentropic flow of a perfect gas with constant specific heats through a convergent-divergent (de Laval) nozzle. This lecture will present a complete and consistent theory of such flows, applicable to any fluid (single- or multiphase) and any channel shape. The study is restricted to the one-dimensional approximation, and, although only adiabatic conditions are discussed, the formalism can be extended to arbitrary conditions at the boundary of the channel. A scrutiny of some of the latest critical reviews of the state of the art of modelling thermal-hydraulic phenomena, especially in the context of LWR safety analysis, reveals the persistence of some misconceptions concerning the nature of the flow and of the relation between the preferred mathematical model and its discretized equivalent. It has recently become clear that the ensemble of trajectories in phase space of a mathematical model, expressed in the form of a set of differential equations, can be radically different from the ensemble of solutions implied in the numerical code, expressed as a set of linear algebraic equations employed in practical applications. This discrepancy becomes acute when critical flow rates are computed under conditions of choked flow. 7 refs.
A time-accurate implicit method for chemically reacting flows at all Mach numbers
NASA Technical Reports Server (NTRS)
Withington, J. P.; Yang, V.; Shuen, J. S.
1991-01-01
The objective of this work is to develop a unified solution algorithm capable of treating time-accurate chemically reacting flows at all Mach numbers, ranging from molecular diffusion velocities to supersonic speeds. A rescaled pressure term is used in the momentum equation to circumvent the singular behavior of pressure at low Mach numbers. A dual time-stepping integration procedure is established. The system eigenvalues become well behaved and have the same order of magnitude, even in the very low Mach number regime. The computational efficiency for moderate and high speed flow is competitive with the conventional density-based scheme. The capabilities of the algorithm are demonstrated by applying it to selected model problems including nozzle flows and flame dynamics.
Accurate, reliable control of process gases by mass flow controllers
Hardy, J.; McKnight, T.
1997-02-01
The thermal mass flow controller, or MFC, has become an instrument of choice for the monitoring and controlling of process gas flow throughout the materials processing industry. These MFCs are used on CVD processes, etching tools, and furnaces and, within the semiconductor industry, are used on 70% of the processing tools. Reliability and accuracy are major concerns for the users of the MFCs. Calibration and characterization technologies for the development and implementation of mass flow devices are described. A test facility is available to industry and universities to test and develop gas floe sensors and controllers and evaluate their performance related to environmental effects, reliability, reproducibility, and accuracy. Additional work has been conducted in the area of accuracy. A gravimetric calibrator was invented that allows flow sensors to be calibrated in corrosive, reactive gases to an accuracy of 0.3% of reading, at least an order of magnitude better than previously possible. Although MFCs are typically specified with accuracies of 1% of full scale, MFCs may often be implemented with unwarranted confidence due to the conventional use of surrogate gas factors. Surrogate gas factors are corrections applied to process flow indications when an MFC has been calibrated on a laboratory-safe surrogate gas, but is actually used on a toxic, or corrosive process gas. Previous studies have indicated that the use of these factors may cause process flow errors of typically 10%, but possibly as great as 40% of full scale. This paper will present possible sources of error in MFC process gas flow monitoring and control, and will present an overview of corrective measures which may be implemented with MFC use to significantly reduce these sources of error.
Accurate blood flow measurements: are artificial tracers necessary?
Poelma, Christian; Kloosterman, Astrid; Hierck, Beerend P; Westerweel, Jerry
2012-01-01
Imaging-based blood flow measurement techniques, such as particle image velocimetry, have become an important tool in cardiovascular research. They provide quantitative information about blood flow, which benefits applications ranging from developmental biology to tumor perfusion studies. Studies using these methods can be classified based on whether they use artificial tracers or red blood cells to visualize the fluid motion. We here present the first direct comparison in vivo of both methods. For high magnification cases, the experiments using red blood cells strongly underestimate the flow (up to 50% in the present case), as compared to the tracer results. For medium magnification cases, the results from both methods are indistinguishable as they give the same underestimation of the real velocities (approximately 33%, based on in vitro reference measurements). These results suggest that flow characteristics reported in literature cannot be compared without a careful evaluation of the imaging characteristics. A method to predict the expected flow averaging behavior for a particular facility is presented.
Control of microorganisms in flowing nutrient solutions.
Evans, R D
1994-11-01
Controlling microorganisms in flowing nutrient solutions involves different techniques when targeting the nutrient solution, hardware surfaces in contact with the solution, or the active root zone. This review presents basic principles and applications of a number of treatment techniques, including disinfection by chemicals, ultrafiltration, ultrasonics, and heat treatment, with emphasis on UV irradiation and ozone treatment. Procedures for control of specific pathogens by nutrient solution conditioning also are reviewed.
Fluid flow in nanopores: Accurate boundary conditions for carbon nanotubes
NASA Astrophysics Data System (ADS)
Sokhan, Vladimir P.; Nicholson, David; Quirke, Nicholas
2002-11-01
Steady-state Poiseuille flow of a simple fluid in carbon nanopores under a gravitylike force is simulated using a realistic empirical many-body potential model for carbon. Building on our previous study of slit carbon nanopores we show that fluid flow in a nanotube is also characterized by a large slip length. By analyzing temporal profiles of the velocity components of particles colliding with the wall we obtain values of the Maxwell coefficient defining the fraction of molecules thermalized by the wall and, for the first time, propose slip boundary conditions for smooth continuum surfaces such that they are equivalent in adsorption, diffusion, and fluid flow properties to fully dynamic atomistic models.
Device for accurately measuring mass flow of gases
Hylton, James O.; Remenyik, Carl J.
1994-01-01
A device for measuring mass flow of gases which utilizes a substantially buoyant pressure vessel suspended within a fluid/liquid in an enclosure. The pressure vessel is connected to a weighing device for continuously determining weight change of the vessel as a function of the amount of gas within the pressure vessel. In the preferred embodiment, this pressure vessel is formed from inner and outer right circular cylindrical hulls, with a volume between the hulls being vented to the atmosphere external the enclosure. The fluid/liquid, normally in the form of water typically with an added detergent, is contained within an enclosure with the fluid/liquid being at a level such that the pressure vessel is suspended beneath this level but above a bottom of the enclosure. The buoyant pressure vessel can be interconnected with selected valves to an auxiliary pressure vessel so that initial flow can be established to or from the auxiliary pressure vessel prior to flow to or from the buoyant pressure vessel.
Device for accurately measuring mass flow of gases
Hylton, J.O.; Remenyik, C.J.
1994-08-09
A device for measuring mass flow of gases which utilizes a substantially buoyant pressure vessel suspended within a fluid/liquid in an enclosure is disclosed. The pressure vessel is connected to a weighing device for continuously determining weight change of the vessel as a function of the amount of gas within the pressure vessel. In the preferred embodiment, this pressure vessel is formed from inner and outer right circular cylindrical hulls, with a volume between the hulls being vented to the atmosphere external the enclosure. The fluid/liquid, normally in the form of water typically with an added detergent, is contained within an enclosure with the fluid/liquid being at a level such that the pressure vessel is suspended beneath this level but above a bottom of the enclosure. The buoyant pressure vessel can be interconnected with selected valves to an auxiliary pressure vessel so that initial flow can be established to or from the auxiliary pressure vessel prior to flow to or from the buoyant pressure vessel. 5 figs.
An accurate adaptive solver for surface-tension-driven interfacial flows
NASA Astrophysics Data System (ADS)
Popinet, Stéphane
2009-09-01
A method combining an adaptive quad/octree spatial discretisation, geometrical Volume-Of-Fluid interface representation, balanced-force continuum-surface-force surface-tension formulation and height-function curvature estimation is presented. The extension of these methods to the quad/octree discretisation allows adaptive variable resolution along the interface and is described in detail. The method is shown to recover exact equilibrium (to machine accuracy) between surface-tension and pressure gradient in the case of a stationary droplet, irrespective of viscosity and spatial resolution. Accurate solutions are obtained for the classical test case of capillary wave oscillations. An application to the capillary breakup of a jet of water in air further illustrates the accuracy and efficiency of the method. The source code of the implementation is freely available as part of the Gerris flow solver.
Approximate Solution for Choked Flow in Gas Seal Pads
NASA Technical Reports Server (NTRS)
Fleming, David P.
2004-01-01
Previous analyses of high pressure seals have considered adiabatic flow with friction but neglected effects of seal rotation. Most of this work analyzed a one-dimensional flow field. This works well to calculate stiffness and leakage of full circular seals, either face seals or annular ring seals. However, it cannot provide accurate results for a rectangular seal pad with its strongly two-dimensional flow field and its reliance on hydrodynamic forces to maintain a full fluid film. On the other hand, solutions of Reynolds lubrication equation have been obtained for the two-dimensional flow in a seal pad. But these solutions do not account for choking which occurs at high seal pressure ratios, nor do they consider the pressure loss that occurs in the entrance region of the flow field. The aim of the present work is to build on the Reynolds equation solution by use of an approximate choked flow analysis. This will account for the pressure losses in the flow entrance region, ensure that fluid velocities remain subsonic, and enable fluid inertial effects within the pad film to be accounted for. Results show that, in general, fluid inertia acts to decrease pad film load capacity and leakage, and increase film stiffness.
NASA Technical Reports Server (NTRS)
Venkatachari, Balaji Shankar; Streett, Craig L.; Chang, Chau-Lyan; Friedlander, David J.; Wang, Xiao-Yen; Chang, Sin-Chung
2016-01-01
Despite decades of development of unstructured mesh methods, high-fidelity time-accurate simulations are still predominantly carried out on structured, or unstructured hexahedral meshes by using high-order finite-difference, weighted essentially non-oscillatory (WENO), or hybrid schemes formed by their combinations. In this work, the space-time conservation element solution element (CESE) method is used to simulate several flow problems including supersonic jet/shock interaction and its impact on launch vehicle acoustics, and direct numerical simulations of turbulent flows using tetrahedral meshes. This paper provides a status report for the continuing development of the space-time conservation element solution element (CESE) numerical and software framework under the Revolutionary Computational Aerosciences (RCA) project. Solution accuracy and large-scale parallel performance of the numerical framework is assessed with the goal of providing a viable paradigm for future high-fidelity flow physics simulations.
Channel Flow of Wormlike Micellar Solutions
NASA Astrophysics Data System (ADS)
Cromer, Michael; Cook, Pam; McKinley, Gareth
2009-11-01
We examine the inhomogeneous response of the VCM model (Vasquez, Cook, McKinley 2006) in steady pressure-driven channel flow. The VCM model, a microstructural network model, was developed to describe concentrated solutions of wormlike micelles. The model comprises of a set of coupled partial differential equations, which incorporate breakage and reforming of two micellar species (a long species `A' and a shorter species `B') in addition to reptative and Rousian stress-relaxation mechanisms. We examine pressure-driven flow in microfluidic devices with rectangular cross-sections as well as with hyperbolic converging/diverging walls. The velocity profile predicted by the VCM model in Poiseuille flow deviates from the parabolic profile expected for a constant viscosity fluid and exhibits strong shear bands near channel walls. This shear-banding is analogous to that seen in circular Taylor-Couette flow and in good qualitative agreement with experimental observations in microfluidic channels. The hyperbolic planar contraction is of special interest due to the dominant contribution of extensional flow along the centerline and the proposed use of such flows as microfluidic extensional rheometers. The model predictions are compared with birefringence measurements of the evolution in the local microstructural orientation of CTAB and CPyCl-based micellar solutions.
Influence of surfactants on unsaturated water flow and solute transport
NASA Astrophysics Data System (ADS)
Karagunduz, Ahmet; Young, Michael H.; Pennell, Kurt D.
2015-04-01
Surfactants can reduce soil water retention by changing the surface tension of water and the contact angle between the liquid and solid phases. As a result, water flow and solute transport in unsaturated soil may be altered in the presence of surfactants. In this study, the effects of a representative nonionic surfactant, Triton X-100, on coupled water flow and nonreactive solute transport during unsaturated flow conditions were evaluated. Batch reactor experiments were conducted to measure the surfactant sorption characteristics, while unsaturated transport experiments were performed in columns packed with 40-270 mesh Ottawa sand at five initial water contents. Following the introduction of surfactant solution, the rate of water percolation through the sand increased; however, this period of rapid water drainage was followed by decreased water percolation due to the reduction in soil water content and the corresponding decrease in unsaturated hydraulic conductivity behind the surfactant front. The observed changes in water percolation occurred sequentially, and resulted in faster nonreactive solute transport than was observed in the absence of surfactant. A one-dimensional mathematical model accurately described coupled water flow, surfactant, and solute transport under most experimental conditions. Differences between model predictions and experimental data were observed in the column study performed at the lowest water content (0.115 cm3/cm3), which was attributed to surfactant adsorption at the air-water interface. These findings demonstrate the potential influence of surfactants additives on unsaturated water flow and solute transport in soils, and demonstrate a methodology to couple these processes in a predictive modeling tool.
A novel numerical technique to obtain an accurate solution to the Thomas-Fermi equation
NASA Astrophysics Data System (ADS)
Parand, Kourosh; Yousefi, Hossein; Delkhosh, Mehdi; Ghaderi, Amin
2016-07-01
In this paper, a new algorithm based on the fractional order of rational Euler functions (FRE) is introduced to study the Thomas-Fermi (TF) model which is a nonlinear singular ordinary differential equation on a semi-infinite interval. This problem, using the quasilinearization method (QLM), converts to the sequence of linear ordinary differential equations to obtain the solution. For the first time, the rational Euler (RE) and the FRE have been made based on Euler polynomials. In addition, the equation will be solved on a semi-infinite domain without truncating it to a finite domain by taking FRE as basic functions for the collocation method. This method reduces the solution of this problem to the solution of a system of algebraic equations. We demonstrated that the new proposed algorithm is efficient for obtaining the value of y'(0) , y(x) and y'(x) . Comparison with some numerical and analytical solutions shows that the present solution is highly accurate.
Unstructured viscous flow solution using adaptive hybrid grids
NASA Technical Reports Server (NTRS)
Galle, Martin
1995-01-01
A three dimensional finite volume scheme based on hybrid grids containing both tetrahedral and hexahedral cells is presented. The application to hybrid grids offers the possibility to combine the flexibility of tetrahedral meshes with the accuracy of hexahedral grids. An algorithm to compute a dual mesh for the entire computational domain was developed. The dual mesh technique guarantees conservation in the whole flow field even at interfaces between hexahedral and tetrahedral domains and enables the employment of an accurate upwind flow solver. The hybrid mesh can be adapted to the solution by dividing cells in areas of insufficient resolution. The method is tested on different viscous and inviscid cases for hypersonic, transonic and subsonic flows.
ASYMPTOTICALLY OPTIMAL HIGH-ORDER ACCURATE ALGORITHMS FOR THE SOLUTION OF CERTAIN ELLIPTIC PDEs
Leonid Kunyansky, PhD
2008-11-26
The main goal of the project, "Asymptotically Optimal, High-Order Accurate Algorithms for the Solution of Certain Elliptic PDE's" (DE-FG02-03ER25577) was to develop fast, high-order algorithms for the solution of scattering problems and spectral problems of photonic crystals theory. The results we obtained lie in three areas: (1) asymptotically fast, high-order algorithms for the solution of eigenvalue problems of photonics, (2) fast, high-order algorithms for the solution of acoustic and electromagnetic scattering problems in the inhomogeneous media, and (3) inversion formulas and fast algorithms for the inverse source problem for the acoustic wave equation, with applications to thermo- and opto- acoustic tomography.
GENERAL SOLUTIONS FOR VISCOPLASTIC DEBRIS FLOW.
Chen, Cheng-lung
1988-01-01
Theoretical velocity profile and theoretical pressure and concentration distributions for (steady) uniform debris flow in wide channels are derived from a generalized viscoplastic fluid (GVF) model without imposing R. A. Bagnold's assumption of constant grain concentration. Good agreement between the theoretical velocity profile and the experimental data of Japanese scientists strongly supports the validity of both the GVF model and the proposed method of solution from the model. It is shown that both E. C. Bingham and Bagnold versions (or submodels) of the GVF model can be used to simulate debris flow at the dynamic state. Although Bagnold's dilatant submodel appears to fit the Japanese data better than the Bingham submodel for flow of noncohesive grains, the choice between them is by no means clear-cut.
Exact solutions to magnetized plasma flow
Wang, Zhehui; Barnes, Cris W.
2001-03-01
Exact analytic solutions for steady-state magnetized plasma flow (MPF) using ideal magnetohydrodynamics formalism are presented. Several cases are considered. When plasma flow is included, a finite plasma pressure gradient {nabla}p can be maintained in a force-free state JxB=0 by the velocity gradient. Both incompressible and compressible MPF examples are discussed for a Taylor-state spheromak B field. A new magnetized nozzle solution is given for compressible plasma when U{parallel}B. Transition from a magnetized nozzle to a magnetic nozzle is possible when the B field is strong enough. No physical nozzle would be needed in the magnetic nozzle case. Diverging-, drum- and nozzle-shaped MPF solutions when U{perpendicular}B are also given. The electric field is needed to balance the UxB term in Ohm's law. The electric field can be generated in the laboratory with the proposed conducting electrodes. If such electric fields also exist in stars and galaxies, such as through a dynamo process, then these solutions can be candidates to explain single and double jets.
NASA Technical Reports Server (NTRS)
Liu, Yen; Vinokur, Marcel
1989-01-01
This paper treats the accurate and efficient calculation of thermodynamic properties of arbitrary gas mixtures for equilibrium flow computations. New improvements in the Stupochenko-Jaffe model for the calculation of thermodynamic properties of diatomic molecules are presented. A unified formulation of equilibrium calculations for gas mixtures in terms of irreversible entropy is given. Using a highly accurate thermo-chemical data base, a new, efficient and vectorizable search algorithm is used to construct piecewise interpolation procedures with generate accurate thermodynamic variable and their derivatives required by modern computational algorithms. Results are presented for equilibrium air, and compared with those given by the Srinivasan program.
NASA Technical Reports Server (NTRS)
Stahara, S. S.; Elliott, J. P.; Spreiter, J. R.
1981-01-01
Perturbation procedures and associated computational codes for determining nonlinear flow solutions were developed to establish a method for minimizing computational requirements associated with parametric studies of transonic flows in turbomachines. The procedure that was developed and evaluated was found to be capable of determining highly accurate approximations to families of strongly nonlinear solutions which are either continuous or discontinuous, and which represent variations in some arbitrary parameter. Coordinate straining is employed to account for the movement of discontinuities and maxima of high gradient regions due to the perturbation. The development and results reported are for the single parameter perturbation problem. Flows past both isolated airfoils and compressor cascades involving a wide variety of flow and geometry parameter changes are reported. Attention is focused in particular on transonic flows which are strongly supercritical and exhibit large surface shock movement over the parametric range studied; and on subsonic flows which display large pressure variations in the stagnation and peak suction pressure regions. Comparisons with the corresponding 'exact' nonlinear solutions indicate a remarkable accuracy and range of validity of such a procedure.
MONA: An accurate two-phase well flow model based on phase slippage
Asheim, H.
1984-10-01
In two phase flow, holdup and pressure loss are related to interfacial slippage. A model based on the slippage concept has been developed and tested using production well data from Forties, the Ekofisk area, and flowline data from Prudhoe Bay. The model developed turned out considerably more accurate than the standard models used for comparison.
Adjustable flow rate controller for polymer solutions
Jackson, Kenneth M.
1981-01-01
An adjustable device for controlling the flow rate of polymer solutions which results in only little shearing of the polymer molecules, said device comprising an inlet manifold, an outlet manifold, a plurality of tubes capable of providing communication between said inlet and outlet manifolds, said tubes each having an internal diameter that is smaller than that of the inlet manifold and large enough to insure that viscosity of the polymer solution passing through each said tube will not be reduced more than about 25 percent, and a valve associated with each tube, said valve being capable of opening or closing communication in that tube between the inlet and outlet manifolds, each said valve when fully open having a diameter that is substantially at least as great as that of the tube with which it is associated.
A new algorithm for generating highly accurate benchmark solutions to transport test problems
Azmy, Y.Y.
1997-06-01
We present a new algorithm for solving the neutron transport equation in its discrete-variable form. The new algorithm is based on computing the full matrix relating the scalar flux spatial moments in all cells to the fixed neutron source spatial moments, foregoing the need to compute the angular flux spatial moments, and thereby eliminating the need for sweeping the spatial mesh in each discrete-angular direction. The matrix equation is solved exactly in test cases, producing a solution vector that is free from iteration convergence error, and subject only to truncation and roundoff errors. Our algorithm is designed to provide method developers with a quick and simple solution scheme to test their new methods on difficult test problems without the need to develop sophisticated solution techniques, e.g. acceleration, before establishing the worthiness of their innovation. We demonstrate the utility of the new algorithm by applying it to the Arbitrarily High Order Transport Nodal (AHOT-N) method, and using it to solve two of Burre`s Suite of Test Problems (BSTP). Our results provide highly accurate benchmark solutions, that can be distributed electronically and used to verify the pointwise accuracy of other solution methods and algorithms.
A flux monitoring method for easy and accurate flow rate measurement in pressure-driven flows.
Siria, Alessandro; Biance, Anne-Laure; Ybert, Christophe; Bocquet, Lydéric
2012-03-01
We propose a low-cost and versatile method to measure flow rate in microfluidic channels under pressure-driven flows, thereby providing a simple characterization of the hydrodynamic permeability of the system. The technique is inspired by the current monitoring method usually employed to characterize electro-osmotic flows, and makes use of the measurement of the time-dependent electric resistance inside the channel associated with a moving salt front. We have successfully tested the method in a micrometer-size channel, as well as in a complex microfluidic channel with a varying cross-section, demonstrating its ability in detecting internal shape variations.
Toward Accurate Modeling of the Effect of Ion-Pair Formation on Solute Redox Potential.
Qu, Xiaohui; Persson, Kristin A
2016-09-13
A scheme to model the dependence of a solute redox potential on the supporting electrolyte is proposed, and the results are compared to experimental observations and other reported theoretical models. An improved agreement with experiment is exhibited if the effect of the supporting electrolyte on the redox potential is modeled through a concentration change induced via ion pair formation with the salt, rather than by only considering the direct impact on the redox potential of the solute itself. To exemplify the approach, the scheme is applied to the concentration-dependent redox potential of select molecules proposed for nonaqueous flow batteries. However, the methodology is general and enables rational computational electrolyte design through tuning of the operating window of electrochemical systems by shifting the redox potential of its solutes; including potentially both salts as well as redox active molecules. PMID:27500744
NASA Astrophysics Data System (ADS)
Rudin, Stephen; Divani, Afshin; Wakhloo, Ajay K.; Lieber, Baruch B.; Granger, William; Bednarek, Daniel R.; Yang, Chang-Ying J.
1998-07-01
Detailed cerebrovascular blood flow can be more accurately determined radiographically from the new droplet tracking method previously introduced by the authors than from standard soluble contrast techniques. For example, arteriovenous malformation (AVM) transit times which are crucial for proper glue embolization treatments, were shown to be about half when using droplets compared to those measured using soluble contrast techniques. In this work, factors such as x-ray pulse duration, frame rate, system spatial resolution (focal spot size), droplet size, droplet and system contrast parameters, and system noise are considered in relation to their affect on the accurate determination of droplet location and velocity.
An exact closed form solution for constant area compressible flow with friction and heat transfer
NASA Technical Reports Server (NTRS)
Sturas, J. I.
1971-01-01
The well-known differential equation for the one-dimensional flow of a compressible fluid with heat transfer and wall friction has no known solution in closed form for the general case. This report presents a closed form solution for the special case of constant heat flux per unit length and constant specific heat. The solution was obtained by choosing the square of a dimensionless flow parameter as one of the independent variables to describe the flow. From this exact solution, an approximate simplified form is derived that is applicable for predicting subsonic flow performance characteristics for many types of constant area passages in internal flow. The data included in this report are considered sufficiently accurate for use as a guide in analyzing and designing internal gas flow systems.
Implicit solution of three-dimensional internal turbulent flows
NASA Technical Reports Server (NTRS)
Michelassi, V.; Liou, M.-S.; Povinelli, Louis A.; Martelli, F.
1991-01-01
The scalar form of the approximate factorization method was used to develop a new code for the solution of three dimensional internal laminar and turbulent compressible flows. The Navier-Stokes equations in their Reynolds-averaged form were iterated in time until a steady solution was reached. Evidence was given to the implicit and explicit artificial damping schemes that proved to be particularly efficient in speeding up convergence and enhancing the algorithm robustness. A conservative treatment of these terms at the domain boundaries was proposed in order to avoid undesired mass and/or momentum artificial fluxes. Turbulence effects were accounted for by the zero-equation Baldwin-Lomax turbulence model and the q-omega two-equation model. The flow in a developing S-duct was then solved in the laminar regime in a Reynolds number (Re) of 790 and in the turbulent regime at Re equals 40,000 by using the Baldwin-Lomax model. The Stanitz elbow was then solved by using an invicid version of the same code at M sub inlet equals 0.4. Grid dependence and convergence rate were investigated, showing that for this solver the implicit damping scheme may play a critical role for convergence characteristics. The same flow at Re equals 2.5 times 10(exp 6) was solved with the Baldwin-Lomax and the q-omega models. Both approaches show satisfactory agreement with experiments, although the q-omega model was slightly more accurate.
NASA Technical Reports Server (NTRS)
Loh, Ching Y.; Jorgenson, Philip C. E.
2007-01-01
A time-accurate, upwind, finite volume method for computing compressible flows on unstructured grids is presented. The method is second order accurate in space and time and yields high resolution in the presence of discontinuities. For efficiency, the Roe approximate Riemann solver with an entropy correction is employed. In the basic Euler/Navier-Stokes scheme, many concepts of high order upwind schemes are adopted: the surface flux integrals are carefully treated, a Cauchy-Kowalewski time-stepping scheme is used in the time-marching stage, and a multidimensional limiter is applied in the reconstruction stage. However even with these up-to-date improvements, the basic upwind scheme is still plagued by the so-called "pathological behaviors," e.g., the carbuncle phenomenon, the expansion shock, etc. A solution to these limitations is presented which uses a very simple dissipation model while still preserving second order accuracy. This scheme is referred to as the enhanced time-accurate upwind (ETAU) scheme in this paper. The unstructured grid capability renders flexibility for use in complex geometry; and the present ETAU Euler/Navier-Stokes scheme is capable of handling a broad spectrum of flow regimes from high supersonic to subsonic at very low Mach number, appropriate for both CFD (computational fluid dynamics) and CAA (computational aeroacoustics). Numerous examples are included to demonstrate the robustness of the methods.
Approximate Analytical Solutions for Hypersonic Flow Over Slender Power Law Bodies
NASA Technical Reports Server (NTRS)
Mirels, Harold
1959-01-01
Approximate analytical solutions are presented for two-dimensional and axisymmetric hypersonic flow over slender power law bodies. Both zero order (M approaches infinity) and first order (small but nonvanishing values of 1/(M(Delta)(sup 2) solutions are presented, where M is free-stream Mach number and Delta is a characteristic slope. These solutions are compared with exact numerical integration of the equations of motion and appear to be accurate particularly when the shock is relatively close to the body.
Approximate Solutions for Flow with a Stretching Boundary due to Partial Slip
Filobello-Nino, U.; Vazquez-Leal, H.; Sarmiento-Reyes, A.; Benhammouda, B.; Jimenez-Fernandez, V. M.; Pereyra-Diaz, D.; Perez-Sesma, A.; Cervantes-Perez, J.; Huerta-Chua, J.; Sanchez-Orea, J.; Contreras-Hernandez, A. D.
2014-01-01
The homotopy perturbation method (HPM) is coupled with versions of Laplace-Padé and Padé methods to provide an approximate solution to the nonlinear differential equation that describes the behaviour of a flow with a stretching flat boundary due to partial slip. Comparing results between approximate and numerical solutions, we concluded that our results are capable of providing an accurate solution and are extremely efficient. PMID:27433526
Invited article: Time accurate mass flow measurements of solid-fueled systems.
Olliges, Jordan D; Lilly, Taylor C; Joslyn, Thomas B; Ketsdever, Andrew D
2008-10-01
A novel diagnostic method is described that utilizes a thrust stand mass balance (TSMB) to directly measure time-accurate mass flow from a solid-fuel thruster. The accuracy of the TSMB mass flow measurement technique was demonstrated in three ways including the use of an idealized numerical simulation, verifying a fluid mass calibration with high-speed digital photography, and by measuring mass loss in more than 30 hybrid rocket motor firings. Dynamic response of the mass balance was assessed through weight calibration and used to derive spring, damping, and mass moment of inertia coefficients for the TSMB. These dynamic coefficients were used to determine the mass flow rate and total mass loss within an acrylic and gaseous oxygen hybrid rocket motor firing. Intentional variations in the oxygen flow rate resulted in corresponding variations in the total propellant mass flow as expected. The TSMB was optimized to determine mass losses of up to 2.5 g and measured total mass loss to within 2.5% of that calculated by a NIST-calibrated digital scale. Using this method, a mass flow resolution of 0.0011 g/s or 2% of the average mass flow in this study has been achieved.
NASA Technical Reports Server (NTRS)
VanZante, Dale E.; Strazisar, Anthony J.; Wood, Jerry R,; Hathaway, Michael D.; Okiishi, Theodore H.
2000-01-01
The tip clearance flows of transonic compressor rotors are important because they have a significant impact on rotor and stage performance. While numerical simulations of these flows are quite sophisticated. they are seldom verified through rigorous comparisons of numerical and measured data because these kinds of measurements are rare in the detail necessary to be useful in high-speed machines. In this paper we compare measured tip clearance flow details (e.g. trajectory and radial extent) with corresponding data obtained from a numerical simulation. Recommendations for achieving accurate numerical simulation of tip clearance flows are presented based on this comparison. Laser Doppler Velocimeter (LDV) measurements acquired in a transonic compressor rotor, NASA Rotor 35, are used. The tip clearance flow field of this transonic rotor was simulated using a Navier-Stokes turbomachinery solver that incorporates an advanced k-epsilon turbulence model derived for flows that are not in local equilibrium. Comparison between measured and simulated results indicates that simulation accuracy is primarily dependent upon the ability of the numerical code to resolve important details of a wall-bounded shear layer formed by the relative motion between the over-tip leakage flow and the shroud wall. A simple method is presented for determining the strength of this shear layer.
A time accurate prediction of the viscous flow in a turbine stage including a rotor in motion
NASA Astrophysics Data System (ADS)
Shavalikul, Akamol
In this current study, the flow field in the Pennsylvania State University Axial Flow Turbine Research Facility (AFTRF) was simulated. This study examined four sets of simulations. The first two sets are for an individual NGV and for an individual rotor. The last two sets use a multiple reference frames approach for a complete turbine stage with two different interface models: a steady circumferential average approach called a mixing plane model, and a time accurate flow simulation approach called a sliding mesh model. The NGV passage flow field was simulated using a three-dimensional Reynolds Averaged Navier-Stokes finite volume solver (RANS) with a standard kappa -- epsilon turbulence model. The mean flow distributions on the NGV surfaces and endwall surfaces were computed. The numerical solutions indicate that two passage vortices begin to be observed approximately at the mid axial chord of the NGV suction surface. The first vortex is a casing passage vortex which occurs at the corner formed by the NGV suction surface and the casing. This vortex is created by the interaction of the passage flow and the radially inward flow, while the second vortex, the hub passage vortex, is observed near the hub. These two vortices become stronger towards the NGV trailing edge. By comparing the results from the X/Cx = 1.025 plane and the X/Cx = 1.09 plane, it can be concluded that the NGV wake decays rapidly within a short axial distance downstream of the NGV. For the rotor, a set of simulations was carried out to examine the flow fields associated with different pressure side tip extension configurations, which are designed to reduce the tip leakage flow. The simulation results show that significant reductions in tip leakage mass flow rate and aerodynamic loss reduction are possible by using suitable tip platform extensions located near the pressure side corner of the blade tip. The computations used realistic turbine rotor inlet flow conditions in a linear cascade arrangement
A fast and accurate method to predict 2D and 3D aerodynamic boundary layer flows
NASA Astrophysics Data System (ADS)
Bijleveld, H. A.; Veldman, A. E. P.
2014-12-01
A quasi-simultaneous interaction method is applied to predict 2D and 3D aerodynamic flows. This method is suitable for offshore wind turbine design software as it is a very accurate and computationally reasonably cheap method. This study shows the results for a NACA 0012 airfoil. The two applied solvers converge to the experimental values when the grid is refined. We also show that in separation the eigenvalues remain positive thus avoiding the Goldstein singularity at separation. In 3D we show a flow over a dent in which separation occurs. A rotating flat plat is used to show the applicability of the method for rotating flows. The shown capabilities of the method indicate that the quasi-simultaneous interaction method is suitable for design methods for offshore wind turbine blades.
A quasilinear model for solute transport under unsaturated flow
Houseworth, J.E.; Leem, J.
2009-05-15
We developed an analytical solution for solute transport under steady-state, two-dimensional, unsaturated flow and transport conditions for the investigation of high-level radioactive waste disposal. The two-dimensional, unsaturated flow problem is treated using the quasilinear flow method for a system with homogeneous material properties. Dispersion is modeled as isotropic and is proportional to the effective hydraulic conductivity. This leads to a quasilinear form for the transport problem in terms of a scalar potential that is analogous to the Kirchhoff potential for quasilinear flow. The solutions for both flow and transport scalar potentials take the form of Fourier series. The particular solution given here is for two sources of flow, with one source containing a dissolved solute. The solution method may easily be extended, however, for any combination of flow and solute sources under steady-state conditions. The analytical results for multidimensional solute transport problems, which previously could only be solved numerically, also offer an additional way to benchmark numerical solutions. An analytical solution for two-dimensional, steady-state solute transport under unsaturated flow conditions is presented. A specific case with two sources is solved but may be generalized to any combination of sources. The analytical results complement numerical solutions, which were previously required to solve this class of problems.
NASA Technical Reports Server (NTRS)
Dougherty, N. S.; Burnette, D. W.; Holt, J. B.; Matienzo, Jose
1993-01-01
Time-accurate unsteady flow simulations are being performed supporting the SRM T+68sec pressure 'spike' anomaly investigation. The anomaly occurred in the RH SRM during the STS-54 flight (STS-54B) but not in the LH SRM (STS-54A) causing a momentary thrust mismatch approaching the allowable limit at that time into the flight. Full-motor internal flow simulations using the USA-2D axisymmetric code are in progress for the nominal propellant burn-back geometry and flow conditions at T+68-sec--Pc = 630 psi, gamma = 1.1381, T(sub c) = 6200 R, perfect gas without aluminum particulate. In a cooperative effort with other investigation team members, CFD-derived pressure loading on the NBR and castable inhibitors was used iteratively to obtain nominal deformed geometry of each inhibitor, and the deformed (bent back) inhibitor geometry was entered into this model. Deformed geometry was computed using structural finite-element models. A solution for the unsteady flow has been obtained for the nominal flow conditions (existing prior to the occurrence of the anomaly) showing sustained standing pressure oscillations at nominally 14.5 Hz in the motor IL acoustic mode that flight and static test data confirm to be normally present at this time. Average mass flow discharged from the nozzle was confirmed to be the nominal expected (9550 lbm/sec). The local inlet boundary condition is being perturbed at the location of the presumed reconstructed anomaly as identified by interior ballistics performance specialist team members. A time variation in local mass flow is used to simulate sudden increase in burning area due to localized propellant grain cracks. The solution will proceed to develop a pressure rise (proportional to total mass flow rate change squared). The volume-filling time constant (equivalent to 0.5 Hz) comes into play in shaping the rise rate of the developing pressure 'spike' as it propagates at the speed of sound in both directions to the motor head end and nozzle. The
Time-accurate Navier-Stokes computations of classical two-dimensional edge tone flow fields
NASA Technical Reports Server (NTRS)
Liu, B. L.; O'Farrell, J. M.; Jones, Jess H.
1990-01-01
Time-accurate Navier-Stokes computations were performed to study a Class II (acoustic) whistle, the edge tone, and gain knowledge of the vortex-acoustic coupling mechanisms driving production of these tones. Results were obtained by solving the full Navier-Stokes equations for laminar compressible air flow of a two-dimensional jet issuing from a slit interacting with a wedge. Cases considered were determined by varying the distance from the slit to the edge. Flow speed was kept constant at 1750 cm/sec as was the slit thickness of 0.1 cm, corresponding to conditions in the experiments of Brown. Excellent agreement was obtained in all four edge tone stage cases between the present computational results and the experimentally obtained results of Brown. Specific edge tone generated phenomena and further confirmation of certain theories concerning these phenomena were brought to light in this analytical simulation of edge tones.
Implicit solution of three-dimensional internal turbulent flows
NASA Technical Reports Server (NTRS)
Michelassi, V.; Liou, M.-S.; Povinelli, L. A.
1990-01-01
The scalar form of the approximate factorization method was used to develop a new code for the solution of three-dimensional internal laminar and turbulent compressible flows. The Navier-Stokes equations in their Reynolds-averaged form are iterated in time until a steady solution is reached. Evidence is given to the implicit and explicit artificial damping schemes that proved to be particularly efficient in speeding up convergence and enhancing the algorithm robustness. A conservative treatment of these terms at domain boundaries is proposed in order to avoid undesired mass and/or momentum artificial fluxes. Turbulence effects are accounted for by the zero-equation Baldwin-Lomax turbulence model and the q-omega two-equation model. For the first, an investigation on the model behavior in case of multiple boundaries is performed. The flow in a developing S-duct is then solved in the laminar regime at Reynolds number (Re) 790 and in the turbulent regime at Re=40,000 using the Baldwin-Lomax model . The Stanitz elbow is then solved using an inviscid version of the same code at M(sub inlet)=0.4. Grid dependence and convergence rate are investigated showing that for this solver the implicit damping scheme may play a critical role for convergence characteristics. The same flow at Re=2.5x10(exp 6) is solved with the Baldwin-Lomax and the q-omega models. Both approaches showed satisfactory agreement with experiments, although the q-omega model is slightly more accurate.
NASA Astrophysics Data System (ADS)
Diwakar, S. V.; Das, Sarit K.; Sundararajan, T.
2009-12-01
A new Quadratic Spline based Interface (QUASI) reconstruction algorithm is presented which provides an accurate and continuous representation of the interface in a multiphase domain and facilitates the direct estimation of local interfacial curvature. The fluid interface in each of the mixed cells is represented by piecewise parabolic curves and an initial discontinuous PLIC approximation of the interface is progressively converted into a smooth quadratic spline made of these parabolic curves. The conversion is achieved by a sequence of predictor-corrector operations enforcing function ( C0) and derivative ( C1) continuity at the cell boundaries using simple analytical expressions for the continuity requirements. The efficacy and accuracy of the current algorithm has been demonstrated using standard test cases involving reconstruction of known static interface shapes and dynamically evolving interfaces in prescribed flow situations. These benchmark studies illustrate that the present algorithm performs excellently as compared to the other interface reconstruction methods available in literature. Quadratic rate of error reduction with respect to grid size has been observed in all the cases with curved interface shapes; only in situations where the interface geometry is primarily flat, the rate of convergence becomes linear with the mesh size. The flow algorithm implemented in the current work is designed to accurately balance the pressure gradients with the surface tension force at any location. As a consequence, it is able to minimize spurious flow currents arising from imperfect normal stress balance at the interface. This has been demonstrated through the standard test problem of an inviscid droplet placed in a quiescent medium. Finally, the direct curvature estimation ability of the current algorithm is illustrated through the coupled multiphase flow problem of a deformable air bubble rising through a column of water.
NASA Astrophysics Data System (ADS)
Zhu, Jun; Chen, Lijun; Ma, Lantao; Li, Dejian; Jiang, Wei; Pan, Lihong; Shen, Huiting; Jia, Hongmin; Hsiang, Chingyun; Cheng, Guojie; Ling, Li; Chen, Shijie; Wang, Jun; Liao, Wenkui; Zhang, Gary
2014-04-01
Defect review is a time consuming job. Human error makes result inconsistent. The defects located on don't care area would not hurt the yield and no need to review them such as defects on dark area. However, critical area defects can impact yield dramatically and need more attention to review them such as defects on clear area. With decrease in integrated circuit dimensions, mask defects are always thousands detected during inspection even more. Traditional manual or simple classification approaches are unable to meet efficient and accuracy requirement. This paper focuses on automatic defect management and classification solution using image output of Lasertec inspection equipment and Anchor pattern centric image process technology. The number of mask defect found during an inspection is always in the range of thousands or even more. This system can handle large number defects with quick and accurate defect classification result. Our experiment includes Die to Die and Single Die modes. The classification accuracy can reach 87.4% and 93.3%. No critical or printable defects are missing in our test cases. The missing classification defects are 0.25% and 0.24% in Die to Die mode and Single Die mode. This kind of missing rate is encouraging and acceptable to apply on production line. The result can be output and reloaded back to inspection machine to have further review. This step helps users to validate some unsure defects with clear and magnification images when captured images can't provide enough information to make judgment. This system effectively reduces expensive inline defect review time. As a fully inline automated defect management solution, the system could be compatible with current inspection approach and integrated with optical simulation even scoring function and guide wafer level defect inspection.
Boraldi, Federica; Bartolomeo, Angelica; De Biasi, Sara; Orlando, Stefania; Costa, Sonia; Cossarizza, Andrea; Quaglino, Daniela
2016-01-01
Introduction Although rare, circulating endothelial and progenitor cells could be considered as markers of endothelial damage and repair potential, possibly predicting the severity of cardiovascular manifestations. A number of studies highlighted the role of these cells in age-related diseases, including those characterized by ectopic calcification. Nevertheless, their use in clinical practice is still controversial, mainly due to difficulties in finding reproducible and accurate methods for their determination. Methods Circulating mature cells (CMC, CD45-, CD34+, CD133-) and circulating progenitor cells (CPC, CD45dim, CD34bright, CD133+) were investigated by polychromatic high-speed flow cytometry to detect the expression of endothelial (CD309+) or osteogenic (BAP+) differentiation markers in healthy subjects and in patients affected by peripheral vascular manifestations associated with ectopic calcification. Results This study shows that: 1) polychromatic flow cytometry represents a valuable tool to accurately identify rare cells; 2) the balance of CD309+ on CMC/CD309+ on CPC is altered in patients affected by peripheral vascular manifestations, suggesting the occurrence of vascular damage and low repair potential; 3) the increase of circulating cells exhibiting a shift towards an osteoblast-like phenotype (BAP+) is observed in the presence of ectopic calcification. Conclusion Differences between healthy subjects and patients with ectopic calcification indicate that this approach may be useful to better evaluate endothelial dysfunction in a clinical context. PMID:27560136
Cao, Youfang; Terebus, Anna; Liang, Jie
2016-01-01
truncation and error analysis methods developed here can be used to ensure accurate direct solutions to the dCME for a large number of stochastic networks. PMID:27105653
Cao, Youfang; Terebus, Anna; Liang, Jie
2016-04-01
truncation and error analysis methods developed here can be used to ensure accurate direct solutions to the dCME for a large number of stochastic networks.
Hong Xinguo; Hao Quan
2009-01-15
In this paper, we report a method of precise in situ x-ray scattering measurements on protein solutions using small stationary sample cells. Although reduction in the radiation damage induced by intense synchrotron radiation sources is indispensable for the correct interpretation of scattering data, there is still a lack of effective methods to overcome radiation-induced aggregation and extract scattering profiles free from chemical or structural damage. It is found that radiation-induced aggregation mainly begins on the surface of the sample cell and grows along the beam path; the diameter of the damaged region is comparable to the x-ray beam size. Radiation-induced aggregation can be effectively avoided by using a two-dimensional scan (2D mode), with an interval as small as 1.5 times the beam size, at low temperature (e.g., 4 deg. C). A radiation sensitive protein, bovine hemoglobin, was used to test the method. A standard deviation of less than 5% in the small angle region was observed from a series of nine spectra recorded in 2D mode, in contrast to the intensity variation seen using the conventional stationary technique, which can exceed 100%. Wide-angle x-ray scattering data were collected at a standard macromolecular diffraction station using the same data collection protocol and showed a good signal/noise ratio (better than the reported data on the same protein using a flow cell). The results indicate that this method is an effective approach for obtaining precise measurements of protein solution scattering.
Orbital Advection by Interpolation: A Fast and Accurate Numerical Scheme for Super-Fast MHD Flows
Johnson, B M; Guan, X; Gammie, F
2008-04-11
In numerical models of thin astrophysical disks that use an Eulerian scheme, gas orbits supersonically through a fixed grid. As a result the timestep is sharply limited by the Courant condition. Also, because the mean flow speed with respect to the grid varies with position, the truncation error varies systematically with position. For hydrodynamic (unmagnetized) disks an algorithm called FARGO has been developed that advects the gas along its mean orbit using a separate interpolation substep. This relaxes the constraint imposed by the Courant condition, which now depends only on the peculiar velocity of the gas, and results in a truncation error that is more nearly independent of position. This paper describes a FARGO-like algorithm suitable for evolving magnetized disks. Our method is second order accurate on a smooth flow and preserves {del} {center_dot} B = 0 to machine precision. The main restriction is that B must be discretized on a staggered mesh. We give a detailed description of an implementation of the code and demonstrate that it produces the expected results on linear and nonlinear problems. We also point out how the scheme might be generalized to make the integration of other supersonic/super-fast flows more efficient. Although our scheme reduces the variation of truncation error with position, it does not eliminate it. We show that the residual position dependence leads to characteristic radial variations in the density over long integrations.
Modeling flow and solute transport in irrigation furrows
Technology Transfer Automated Retrieval System (TEKTRAN)
This paper presents an internally coupled flow and solute transport model for free-draining irrigation furrows. Furrow hydraulics is simulated with a numerical zero-inertia model and solute transport is computed with a model based on a numerical solution of the cross-section averaged advection-dispe...
NASA Astrophysics Data System (ADS)
Park, Jong Ho; Park, Jung Jin; Park, O. Ok; Jin, Chang-Soo; Yang, Jung Hoon
2016-04-01
Because of the rise in renewable energy use, the redox flow battery (RFB) has attracted extensive attention as an energy storage system. Thus, many studies have focused on improving the performance of the felt electrodes used in RFBs. However, existing analysis cells are unsuitable for characterizing felt electrodes because of their complex 3-dimensional structure. Analysis is also greatly affected by the measurement conditions, viz. compression ratio, contact area, and contact strength between the felt and current collector. To address the growing need for practical analytical apparatus, we report a new analysis cell for accurate electrochemical characterization of felt electrodes under various conditions, and compare it with previous ones. In this cell, the measurement conditions can be exhaustively controlled with a compression supporter. The cell showed excellent reproducibility in cyclic voltammetry analysis and the results agreed well with actual RFB charge-discharge performance.
NASA Astrophysics Data System (ADS)
Wosnik, M.; Bachant, P.
2014-12-01
Cross-flow turbines, often referred to as vertical-axis turbines, show potential for success in marine hydrokinetic (MHK) and wind energy applications, ranging from small- to utility-scale installations in tidal/ocean currents and offshore wind. As turbine designs mature, the research focus is shifting from individual devices to the optimization of turbine arrays. It would be expensive and time-consuming to conduct physical model studies of large arrays at large model scales (to achieve sufficiently high Reynolds numbers), and hence numerical techniques are generally better suited to explore the array design parameter space. However, since the computing power available today is not sufficient to conduct simulations of the flow in and around large arrays of turbines with fully resolved turbine geometries (e.g., grid resolution into the viscous sublayer on turbine blades), the turbines' interaction with the energy resource (water current or wind) needs to be parameterized, or modeled. Models used today--a common model is the actuator disk concept--are not able to predict the unique wake structure generated by cross-flow turbines. This wake structure has been shown to create "constructive" interference in some cases, improving turbine performance in array configurations, in contrast with axial-flow, or horizontal axis devices. Towards a more accurate parameterization of cross-flow turbines, an extensive experimental study was carried out using a high-resolution turbine test bed with wake measurement capability in a large cross-section tow tank. The experimental results were then "interpolated" using high-fidelity Navier--Stokes simulations, to gain insight into the turbine's near-wake. The study was designed to achieve sufficiently high Reynolds numbers for the results to be Reynolds number independent with respect to turbine performance and wake statistics, such that they can be reliably extrapolated to full scale and used for model validation. The end product of
An adaptive grid method for computing time accurate solutions on structured grids
NASA Technical Reports Server (NTRS)
Bockelie, Michael J.; Smith, Robert E.; Eiseman, Peter R.
1991-01-01
The solution method consists of three parts: a grid movement scheme; an unsteady Euler equation solver; and a temporal coupling routine that links the dynamic grid to the Euler solver. The grid movement scheme is an algebraic method containing grid controls that generate a smooth grid that resolves the severe solution gradients and the sharp transitions in the solution gradients. The temporal coupling is performed with a grid prediction correction procedure that is simple to implement and provides a grid that does not lag the solution in time. The adaptive solution method is tested by computing the unsteady inviscid solutions for a one dimensional shock tube and a two dimensional shock vortex iteraction.
A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows
NASA Technical Reports Server (NTRS)
Felici, Helene Marie
1992-01-01
A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the Eulerian time-marching procedure and provides a correction of the Eulerian solution. In turn, the Eulerian solutions is used to integrate the Lagrangian state-vector along the particles trajectories. The Lagrangian correction technique does not require any a-priori information on the structure or position of the vortical regions. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers, used as 'accuracy boosters,' take advantage of the accurate convection description of the Lagrangian solution and enhance the vorticity and entropy capturing capabilities of standard Eulerian finite-volume methods. The combined solution procedures is tested in several applications. The convection of a Lamb vortex in a straight channel is used as an unsteady compressible flow preservation test case. The other test cases concern steady incompressible flow calculations and include the preservation of turbulent inlet velocity profile, the swirling flow in a pipe, and the constant stagnation pressure flow and secondary flow calculations in bends. The last application deals with the external flow past a wing with emphasis on the trailing vortex solution. The improvement due to the addition of the Lagrangian correction technique is measured by comparison with analytical solutions when available or with Eulerian solutions on finer grids. The use of the combined Eulerian/Lagrangian scheme results in substantially lower grid resolution requirements than the standard Eulerian scheme for a given solution accuracy.
A comparative study of computational solutions to flow over a backward-facing step
NASA Technical Reports Server (NTRS)
Mizukami, M.; Georgiadis, N. J.; Cannon, M. R.
1993-01-01
A comparative study was conducted for computational fluid dynamic solutions to flow over a backward-facing step. This flow is a benchmark problem, with a simple geometry, but involves complicated flow physics such as free shear layers, reattaching flow, recirculation, and high turbulence intensities. Three Reynolds-averaged Navier-Stokes flow solvers with k-epsilon turbulence models were used, each using a different solution algorithm: finite difference, finite element, and hybrid finite element - finite difference. Comparisons were made with existing experimental data. Results showed that velocity profiles and reattachment lengths were predicted reasonably well by all three methods, while the skin friction coefficients were more difficult to predict accurately. It was noted that, in general, selecting an appropriate solver for each problem to be considered is important.
An improved method for accurate prediction of mass flows through combustor liner holes
Adkins, R.C.; Gueroui, D.
1986-01-01
The objective of this paper is to present a simple approach to the solution of flow through combustor liner holes which can be used by practicing combustor engineers as well as providing the specialist modeler with a convenient boundary condition. For modeling, suppose that all relevant details of the incoming jets can be readily predicted, then the computational boundary can be limited to the inner wall of the liner and to the jets themselves. The scope of this paper is limited to the derivation of a simple analysis, the development of a reliable test technique, and to the correlation of data for plane holes having a diameter which is large when compared to the liner wall thickness. The effect of internal liner flow on the performance of the holes is neglected; this is considered to be justifiable because the analysis terminates at a short distance downstream of the hole and the significantly lower velocities inside the combustor have had little opportunity to have taken any effect. It is intended to extend the procedure to more complex hole forms and flow configurations in later papers.
Accurate determination of plasmid copy number of flow-sorted cells using droplet digital PCR.
Jahn, Michael; Vorpahl, Carsten; Türkowsky, Dominique; Lindmeyer, Martin; Bühler, Bruno; Harms, Hauke; Müller, Susann
2014-06-17
Many biotechnological processes rely on the expression of a plasmid-based target gene. A constant and sufficient number of plasmids per cell is desired for efficient protein production. To date, only a few methods for the determination of plasmid copy number (PCN) are available, and most of them average the PCN of total populations disregarding heterogeneous distributions. Here, we utilize the highly precise quantification of DNA molecules by droplet digital PCR (ddPCR) and combine it with cell sorting using flow cytometry. A duplex PCR assay was set up requiring only 1000 sorted cells for precise determination of PCN. The robustness of this method was proven by thorough optimization of cell sorting, cell disruption, and PCR conditions. When non plasmid-harboring cells of Pseudomonas putida KT2440 were spiked with different dilutions of the expression plasmid pA-EGFP_B, a PCN from 1 to 64 could be accurately detected. As a proof of principle, induced cultures of P. putida KT2440 producing an EGFP-fused model protein by means of the plasmid pA-EGFP_B were investigated by flow cytometry and showed two distinct subpopulations, fluorescent and nonfluorescent cells. These two subpopulations were sorted for PCN determination with ddPCR. A remarkably diverging plasmid distribution was found within the population, with nonfluorescent cells showing a much lower PCN (≤1) than fluorescent cells (PCN of up to 5) under standard conditions.
Aeroacoustic Flow Phenomena Accurately Captured by New Computational Fluid Dynamics Method
NASA Technical Reports Server (NTRS)
Blech, Richard A.
2002-01-01
One of the challenges in the computational fluid dynamics area is the accurate calculation of aeroacoustic phenomena, especially in the presence of shock waves. One such phenomenon is "transonic resonance," where an unsteady shock wave at the throat of a convergent-divergent nozzle results in the emission of acoustic tones. The space-time Conservation-Element and Solution-Element (CE/SE) method developed at the NASA Glenn Research Center can faithfully capture the shock waves, their unsteady motion, and the generated acoustic tones. The CE/SE method is a revolutionary new approach to the numerical modeling of physical phenomena where features with steep gradients (e.g., shock waves, phase transition, etc.) must coexist with those having weaker variations. The CE/SE method does not require the complex interpolation procedures (that allow for the possibility of a shock between grid cells) used by many other methods to transfer information between grid cells. These interpolation procedures can add too much numerical dissipation to the solution process. Thus, while shocks are resolved, weaker waves, such as acoustic waves, are washed out.
Numberical Solution to Transient Heat Flow Problems
ERIC Educational Resources Information Center
Kobiske, Ronald A.; Hock, Jeffrey L.
1973-01-01
Discusses the reduction of the one- and three-dimensional diffusion equation to the difference equation and its stability, convergence, and heat-flow applications under different boundary conditions. Indicates the usefulness of this presentation for beginning students of physics and engineering as well as college teachers. (CC)
Flow behaviour of a POSS biopolymer solution.
Kidane, Asmeret G; Edirisinghe, Mohan J; Bonhoeffer, Philipp; Seifalian, Alexander M
2007-01-01
A non-biodegradable polyhedral oligomeric silsesquioxane (POSS) nanocomposite biopolymer has been developed for fabrication of medical devices and for tissue engineering human organs. The polymer in solution, containing 2 wt% of POSS, has been synthesized, characterized and investigated to determine its key rheological properties. Thus, the variation of shear stress and viscosity as a function of shear rate has been determined at ambient temperature to estimate yield stress and the index of pseudoplasticity, respectively. The temperature dependence of viscosity and the effect of ageing on the viscosity of the polymer have also been investigated. Results are compared with those of a conventional polycarbonate urethane (PCU) polymer solution. The POSS-PCU polymer solution shows near-Newtonian behaviour in the shear rate range to 1000 s(-1), having an apparent viscosity of approximately 3000 mPa s and a pseudoplasticity index of 0.90, decreasing slightly as the polymer solution is aged over 9 months. The temperature dependence of viscosity of the POSS polymer is extremely low and does not change with ageing but the yield strength increases from 2.7 Pa to 8.3 Pa.
Efficient solution of turbulent incompressible separated flows
NASA Astrophysics Data System (ADS)
Michelassi, Vittorio; Martelli, Francesco
A computational method for incompressible separated flows based on two-dimensional approximate factorization is presented. Turbulence effects are accounted for by low-Reynolds number forms of the k-epsilon model. Mass conservation is enforced by the artificial compressibility method. Decoupling and coupling of the equations of motions with the turbulence model equations are investigated. Testing of the coupled solver showed no improvement in convergence or accuracy in comparison to the classical decoupled approach. The solver was then applied to several large-recirculation flows using a modified version of the low-Reynolds-number form of the k-epsilon model proposed by Chien and a two-layer version of the k-epsilon model introduced by Rodi. Both versions gave fast convergence rates and good agreement with experiments.
Flow Battery Solution for Smart Grid Applications
none,
2014-11-30
To address future grid requirements, a U.S. Department of Energy ARRA Storage Demonstration program was launched in 2009 to commercialize promising technologies needed for stronger and more renewables-intensive grids. Raytheon Ktech and EnerVault received a cost-share grant award from the U.S. Department of Energy to develop a grid-scale storage system based on EnerVault’s iron-chromium redox flow battery technology.
Lagrangian solution of supersonic real gas flows
NASA Technical Reports Server (NTRS)
Loh, Ching-Yuen; Liou, Meng-Sing
1993-01-01
The present extention of a Lagrangian approach of the Riemann solution procedure, which was originally proposed for perfect gases, to real gases, is nontrivial and requires the development of an exact real-gas Riemann solver for the Lagrangian form of the conservation laws. Calculations including complex wave interactions of various types were conducted to test the accuracy and robustness of the approach. Attention is given to the case of 2D oblique waves' capture, where a slip line is clearly in evidence; the real gas effect is demonstrated in the case of a generic engine nozzle.
Submicron flow of polymer solutions: slippage reduction due to confinement.
Cuenca, Amandine; Bodiguel, Hugues
2013-03-01
Pressure-driven flows of high molecular weight polyacrylamide solutions are examined in nanoslits using fluorescence photobleaching. The effective viscosity of polymer solutions decreases when the channel height decreases below the micron scale. In addition, the apparent slippage of the solutions is characterized macroscopically on similar surfaces. Though slippage can explain qualitatively the effective viscosity reduction, a quantitative comparison shows that the slip length is greatly reduced below the micron scale. This result indicates that chain migration is suppressed in confined geometries.
Assessment of meanflow solutions for instability analysis of transitioning flows
NASA Technical Reports Server (NTRS)
Iyer, Venkit
1991-01-01
Meanflow solutions of 3D supersonic flow past a cone at incidence and a swept leading edge wing have been obtained by thre methods, viz., boundary-layer, parabolized Navier-Stokes, and thin shear-layer Navier-Stokes solvers. The smoothness and accuracy of the solution profiles are compared with a view to applying the meanflow solution to boundary-layer stability analysis.
An accurate two-phase approximate solution to the acute viral infection model
Perelson, Alan S
2009-01-01
During an acute viral infection, virus levels rise, reach a peak and then decline. Data and numerical solutions suggest the growth and decay phases are linear on a log scale. While viral dynamic models are typically nonlinear with analytical solutions difficult to obtain, the exponential nature of the solutions suggests approximations can be found. We derive a two-phase approximate solution to the target cell limited influenza model and illustrate the accuracy using data and previously established parameter values of six patients infected with influenza A. For one patient, the subsequent fall in virus concentration was not consistent with our predictions during the decay phase and an alternate approximation is derived. We find expressions for the rate and length of initial viral growth in terms of the parameters, the extent each parameter is involved in viral peaks, and the single parameter responsible for virus decay. We discuss applications of this analysis in antiviral treatments and investigating host and virus heterogeneities.
Lewis, E.R.; Schwartz, S.
2010-03-15
Light scattering by aerosols plays an important role in Earth’s radiative balance, and quantification of this phenomenon is important in understanding and accounting for anthropogenic influences on Earth’s climate. Light scattering by an aerosol particle is determined by its radius and index of refraction, and for aerosol particles that are hygroscopic, both of these quantities vary with relative humidity RH. Here exact expressions are derived for the dependences of the radius ratio (relative to the volume-equivalent dry radius) and index of refraction on RH for aqueous solutions of single solutes. Both of these quantities depend on the apparent molal volume of the solute in solution and on the practical osmotic coefficient of the solution, which in turn depend on concentration and thus implicitly on RH. Simple but accurate approximations are also presented for the RH dependences of both radius ratio and index of refraction for several atmospherically important inorganic solutes over the entire range of RH values for which these substances can exist as solution drops. For all substances considered, the radius ratio is accurate to within a few percent, and the index of refraction to within ~0.02, over this range of RH. Such parameterizations will be useful in radiation transfer models and climate models.
Navier-Stokes solutions for flows related to store separation
NASA Technical Reports Server (NTRS)
Baysal, Oktay; Stallings, Robert L., Jr.; Plentovich, Elizabeth B.
1989-01-01
The objective is developing CFD capabilities to obtain solutions for viscous flows about generic configurations of internally and externally carried stores. The emphasis is placed on the supersonic flow regime with extensions being made to the transonic regime. The project is broken into four steps: (1) Cavity flows for internal carriage configurations; (2) High angle of attack flows, which may be experienced during the separation of the stores: (3) Flows about a body near a flat plate for external carriage configurations; and (4) Flows about a body inside or in the proximity of a cavity. Three-dimensional unsteady cavity flow solutions are obtained by an explicit, MacCormack algorithm, EMCAV3, for open, close, and transitional cavities. High angle of attack flows past cylinders are solved by an implicit, upwind algorithm. All the results compare favorably with the experimental data. For flows about multiple body configurations, the Chimera embedding scheme is modified for finite-volume and multigrid algorithms, MaGGiE. Then a finite volume, implicit, upwind, multigrid Navier-Stokes solver which uses on overlapped/embedded and zonal grids, VUMXZ3, is developed from the CFL3D code. Supersonic flows past a cylinder near a flat plate are computed using this code. The results are compared with the experimental data. Currently the VUMXZ3 code is being modified to accomplish step 4 of this project. Wind tunnel experiments are also being conducted for validation purposes.
Free-Flowing Solutions for CFD
NASA Technical Reports Server (NTRS)
2003-01-01
Licensed to over 1,500 customers worldwide, an advanced computational fluid dynamics (CFD) post-processor with a quick learning curve is consistently providing engineering solutions, with just the right balance of visual insight and hard data. FIELDVIEW is the premier product of JMSI, Inc., d.b.a. Intelligent Light, a woman-owned, small business founded in 1994 and located in Lyndhurst, New Jersey. In the early 1990s, Intelligent Light entered into a joint development contract with a research based company to commercialize the post-processing FIELDVIEW code. As Intelligent Light established itself, it purchased the exclusive rights to the code, and structured its business solely around the software technology. As a result, it is enjoying profits and growing at a rate of 25 to 30 percent per year. Advancements made from the earliest commercial launch of FIELDVIEW, all the way up to the recently released versions 8 and 8.2 of the program, have been backed by research collaboration with NASA's Langley Research Center, where some of the world's most progressive work in transient (also known as time-varying) CFD takes place.
Redox flow batteries based on supporting solutions containing chloride
Li, Liyu; Kim, Soowhan; Yang, Zhenguo; Wang, Wei; Nie, Zimin; Chen, Baowei; Zhang, Jianlu; Xia, Guanguang
2015-09-01
Redox flow battery systems having a supporting solution that contains Cl.sup.- ions can exhibit improved performance and characteristics. Furthermore, a supporting solution having mixed SO.sub.4.sup.2- and Cl.sup.- ions can provide increased energy density and improved stability and solubility of one or more of the ionic species in the catholyte and/or anolyte. According to one example, a vanadium-based redox flow battery system is characterized by an anolyte having V.sup.2+ and V.sup.3+ in a supporting solution and a catholyte having V.sup.4+ and V.sup.5+ in a supporting solution. The supporting solution can contain Cl.sup.- ions or a mixture of SO.sub.4.sup.2- and Cl.sup.- ions.
Redox flow batteries based on supporting solutions containing chloride
Li, Liyu; Kim, Soowhan; Yang, Zhenguo; Wang, Wei; Zhang, Jianlu; Chen, Baowei; Nie, Zimin; Xia, Guanguang
2014-01-14
Redox flow battery systems having a supporting solution that contains Cl.sup.- ions can exhibit improved performance and characteristics. Furthermore, a supporting solution having mixed SO.sub.4.sup.2- and Cl.sup.- ions can provide increased energy density and improved stability and solubility of one or more of the ionic species in the catholyte and/or anolyte. According to one example, a vanadium-based redox flow battery system is characterized by an anolyte having V.sup.2+ and V.sup.3+ in a supporting solution and a catholyte having V.sup.4+ and V.sup.5+ in a supporting solution. The supporting solution can contain Cl.sup.- ions or a mixture of SO.sub.4.sup.2- and Cl.sup.- ions.
Redox flow batteries based on supporting solutions containing chloride
Li, Liyu; Kim, Soowhan; Yang, Zhenguo; Wang, Wei; Nie, Zimin; Chen, Baowei; Zhang, Jianlu; Xia, Guanguang
2015-07-07
Redox flow battery systems having a supporting solution that contains Cl.sup.- ions can exhibit improved performance and characteristics. Furthermore, a supporting solution having mixed SO.sub.4.sup.2- and Cl.sup.- ions can provide increased energy density and improved stability and solubility of one or more of the ionic species in the catholyte and/or anolyte. According to one example, a vanadium-based redox flow battery system is characterized by an anolyte having V.sup.2+ and V.sup.3+ in a supporting solution and a catholyte having V.sup.4+ and V.sup.5+ in a supporting solution. The supporting solution can contain Cl.sup.- ions or a mixture of SO.sub.4.sup.2- and Cl.sup.- ions.
An Accurate Solution to the Lotka-Volterra Equations by Modified Homotopy Perturbation Method
NASA Astrophysics Data System (ADS)
Chowdhury, M. S. H.; Rahman, M. M.
In this paper, we suggest a method to solve the multispecies Lotka-Voltera equations. The suggested method, which we call modified homotopy perturbation method, can be considered as an extension of the homotopy perturbation method (HPM) which is very efficient in solving a varety of differential and algebraic equations. The HPM is modified in order to obtain the approximate solutions of Lotka-Voltera equation response in a sequence of time intervals. In particular, the example of two species is considered. The accuracy of this method is examined by comparison with the numerical solution of the Runge-Kutta-Verner method. The results prove that the modified HPM is a powerful tool for the solution of nonlinear equations.
Numerical solutions for heat flow in adhesive lap joints
NASA Technical Reports Server (NTRS)
Howell, P. A.; Winfree, William P.
1992-01-01
The present formulation for the modeling of heat transfer in thin, adhesively bonded lap joints precludes difficulties associated with large aspect ratio grids required by standard FEM formulations. This quasi-static formulation also reduces the problem dimensionality (by one), thereby minimizing computational requirements. The solutions obtained are found to be in good agreement with both analytical solutions and solutions from standard FEM programs. The approach is noted to yield a more accurate representation of heat-flux changes between layers due to a disbond.
Solid rocket booster internal flow analysis by highly accurate adaptive computational methods
NASA Technical Reports Server (NTRS)
Huang, C. Y.; Tworzydlo, W.; Oden, J. T.; Bass, J. M.; Cullen, C.; Vadaketh, S.
1991-01-01
The primary objective of this project was to develop an adaptive finite element flow solver for simulating internal flows in the solid rocket booster. Described here is a unique flow simulator code for analyzing highly complex flow phenomena in the solid rocket booster. New methodologies and features incorporated into this analysis tool are described.
Multiple Solutions of Transonic Flow over NACA0012 Airfoil
NASA Astrophysics Data System (ADS)
Xiong, Juntao; Liu, Ya; Liu, Feng; Luo, Shijun; Zhao, Zijie; Ren, Xudong; Gao, Chao
2012-11-01
Multiple solutions of the small-disturbance potential equation and full potential equation were known for the NACA0012 airfoil in a certain range of transonic Mach numbers and at zero angle of attack. However the multiple solutions for this airfoil were not observed using Euler or Navier-Stokes equations under the above flow conditions. In the present work, both the Unsteady Reynolds-Averaged Navier-Stokes (URANS) computations and transonic wind tunnel experiments are performed under certain Reynolds numbers to further study the problem. The results of the two methods reveal that buffet appears in a narrow Mach number range where the potential flow methods predict multiple solutions. Boundary layer displacement thickness computed from URANS at the same flow condition is used to modify the geometry of the airfoil. Euler equations are then solved for the modified geometry. The results show that the addition of the boundary layer displacement thickness creates multiple solutions for the NACA0012 airfoil. Global linear stability analysis is also performed on the original and the modified airfoils. This shows a close relationship between the viscous unsteady shock buffet phenomenon of transonic airfoil flow and the existence of multiple solutions of the external inviscid flow. Postdoctoral Research Assistant.
Extensional flow of blood analog solutions in microfluidic devices
Sousa, P. C.; Pinho, F. T.; Oliveira, M. S. N.; Alves, M. A.
2011-01-01
In this study, we show the importance of extensional rheology, in addition to the shear rheology, in the choice of blood analog solutions intended to be used in vitro for mimicking the microcirculatory system. For this purpose, we compare the flow of a Newtonian fluid and two well-established viscoelastic blood analog polymer solutions through microfluidic channels containing both hyperbolic and abrupt contractions∕expansions. The hyperbolic shape was selected in order to impose a nearly constant strain rate at the centerline of the microchannels and achieve a quasihomogeneous and strong extensional flow often found in features of the human microcirculatory system such as stenoses. The two blood analog fluids used are aqueous solutions of a polyacrylamide (125 ppm w∕w) and of a xanthan gum (500 ppm w∕w), which were characterized rheologically in steady-shear flow using a rotational rheometer and in extension using a capillary breakup extensional rheometer (CaBER). Both blood analogs exhibit a shear-thinning behavior similar to that of whole human blood, but their relaxation times, obtained from CaBER experiments, are substantially different (by one order of magnitude). Visualizations of the flow patterns using streak photography, measurements of the velocity field using microparticle image velocimetry, and pressure-drop measurements were carried out experimentally for a wide range of flow rates. The experimental results were also compared with the numerical simulations of the flow of a Newtonian fluid and a generalized Newtonian fluid with shear-thinning behavior. Our results show that the flow patterns of the two blood analog solutions are considerably different, despite their similar shear rheology. Furthermore, we demonstrate that the elastic properties of the fluid have a major impact on the flow characteristics, with the polyacrylamide solution exhibiting a much stronger elastic character. As such, these properties must be taken into account in the
Solute transport along preferential flow paths in unsaturated fractures
Su, G.W.; Geller, J.T.; Pruess, K.; Hunt, J.R.
2001-01-01
Laboratory experiments were conducted to study solute transport along preferential flow paths in unsaturated, inclined fractures. Qualitative aspects of solute transport were identified in a miscible dye tracer experiment conducted in a transparent replica of a natural granite fracture. Additional experiments were conducted to measure the breakthrough curves of a conservative tracer introduced into an established preferential flow path in two different fracture replicas and a rock-replica combination. The influence of gravity was investigated by varying fracture inclination. The relationship between the travel times of the solute and the relative influence of gravity was substantially affected by two modes of intermittent flow that occurred: the snapping rivulet and the pulsating blob modes. The measured travel times of the solute were evaluated with three transfer function models: the axial dispersion, the reactors-in-series, and the lognormal models. The three models described the solute travel times nearly equally well. A mechanistic model was also formulated to describe transport when the pulsating blob mode occurred which assumed blobs of water containing solute mixed with residual pools of water along the flow path.
Highly Accurate Beam Torsion Solutions Using the p-Version Finite Element Method
NASA Technical Reports Server (NTRS)
Smith, James P.
1996-01-01
A new treatment of the classical beam torsion boundary value problem is applied. Using the p-version finite element method with shape functions based on Legendre polynomials, torsion solutions for generic cross-sections comprised of isotropic materials are developed. Element shape functions for quadrilateral and triangular elements are discussed, and numerical examples are provided.
Elastic turbulence in curvilinear flows of polymer solutions
NASA Astrophysics Data System (ADS)
Groisman, Alexander; Steinberg, Victor
2004-03-01
Following our first report (A Groisman and V Steinberg 2000 Nature 405 53), we present an extended account of experimental observations of elasticity-induced turbulence in three different systems: a swirling flow between two plates, a Couette-Taylor (CT) flow between two cylinders, and a flow in a curvilinear channel (Dean flow). All three set-ups had a high ratio of the width of the region available for flow to the radius of curvature of the streamlines. The experiments were carried out with dilute solutions of high-molecular-weight polyacrylamide in concentrated sugar syrups. High polymer relaxation time and solution viscosity ensured prevalence of non-linear elastic effects over inertial non-linearity, and development of purely elastic instabilities at low Reynolds number (Re) in all three flows. Above the elastic instability threshold, flows in all three systems exhibit features of developed turbulence. They include: (i) randomly fluctuating fluid motion excited in a broad range of spatial and temporal scales and (ii) significant increase in the rates of momentum and mass transfer (compared with those expected for a steady flow with a smooth velocity profile). Phenomenology, driving mechanisms and parameter dependence of the elastic turbulence are compared with those of the conventional high-Re hydrodynamic turbulence in Newtonian fluids. Some similarities as well as multiple principal differences were found. In two out of three systems (swirling flow between two plates and flow in the curvilinear channel), power spectra of velocity fluctuations decayed rather quickly, following power laws with exponents of about -3.5. It suggests that, being random in time, the flow is rather smooth in space, in the sense that the main contribution to deformation and mixing (and, possibly, elastic energy) is coming from flow at the largest scale of the system. This situation, random in time and smooth in space, is analogous to flows at small scales (below the Kolmogorov
The accurate solution of Poisson's equation by expansion in Chebyshev polynomials
NASA Technical Reports Server (NTRS)
Haidvogel, D. B.; Zang, T.
1979-01-01
A Chebyshev expansion technique is applied to Poisson's equation on a square with homogeneous Dirichlet boundary conditions. The spectral equations are solved in two ways - by alternating direction and by matrix diagonalization methods. Solutions are sought to both oscillatory and mildly singular problems. The accuracy and efficiency of the Chebyshev approach compare favorably with those of standard second- and fourth-order finite-difference methods.
Flow of DNA solutions in a microfluidic gradual contraction
Gulati, Shelly; Muller, Susan J.; Liepmann, Dorian
2015-01-01
The flow of λ-DNA solutions in a gradual micro-contraction was investigated using direct measurement techniques. The effects on DNA transport in microscale flows are significant because the flow behavior is influenced by macromolecular conformations, both viscous and elastic forces dominate inertial forces at this length scale, and the fully extended length of the molecule approaches the characteristic channel length wc (L/wc ∼ 0.13). This study examines the flow of semi-dilute and entangled DNA solutions in a gradual planar micro-contraction for low Reynolds numbers (3.7 × 10−6 < Re < 3.1 × 10−1) and high Weissenberg numbers (0.4 < Wi < 446). The semi-dilute DNA solutions have modest elasticity number, El = Wi/Re = 55, and do not exhibit viscoelastic behavior. For the entangled DNA solutions, we access high elasticity numbers (7.9 × 103 < El < 6.0 × 105). Video microscopy and streak images of entangled DNA solution flow reveal highly elastic behavior evidenced by the presence of large, stable vortices symmetric about the centerline and upstream of the channel entrance. Micro-particle image velocimetry measurements are used to obtain high resolution, quantitative velocity measurements of the vortex growth in this micro-contraction flow. These direct measurements provide a deeper understanding of the underlying physics of macromolecular transport in microfluidic flow, which will enable the realization of enhanced designs of lab-on-a-chip systems. PMID:26392834
NASA Astrophysics Data System (ADS)
Jiao, Jianying; Zhang, Ye
2014-06-01
An inverse method based on local approximate solutions (LAS inverse method) is proposed to invert transient flows in heterogeneous aquifers. Unlike the objective-function-based inversion techniques, the method does not require forward simulations to assess measurement-to-model misfits; thus the knowledge of aquifer initial conditions (IC) and boundary conditions (BC) is not required. Instead, the method employs a set of local approximate solutions of flow to impose continuity of hydraulic head and Darcy fluxes throughout space and time. Given sufficient (but limited) measurements, it yields well-posed systems of nonlinear equations that can be solved efficiently with optimization. Solution of the inversion includes parameters (hydraulic conductivities, specific storage coefficients) and flow field including the unknown IC and BC. Given error-free measurements, the estimated conductivities and specific storages are accurate within 10% of the true values. When increasing measurement errors are imposed, the estimated parameters become less accurate, but the inverse solution is still stable, i.e., parameter, IC, and BC estimation remains bounded. For a problem where parameter variation is unknown, highly parameterized inversion can reveal the underlying parameter structure, whereas equivalent conductivity and average storage coefficient can also be estimated. Because of the physically-based constraints placed in inversion, the number of measurements does not need to exceed the number of parameters for the inverse method to succeed.
Dual Solutions for Nonlinear Flow Using Lie Group Analysis
Awais, Muhammad; Hayat, Tasawar; Irum, Sania; Saleem, Salman
2015-01-01
`The aim of this analysis is to investigate the existence of the dual solutions for magnetohydrodynamic (MHD) flow of an upper-convected Maxwell (UCM) fluid over a porous shrinking wall. We have employed the Lie group analysis for the simplification of the nonlinear differential system and computed the absolute invariants explicitly. An efficient numerical technique namely the shooting method has been employed for the constructions of solutions. Dual solutions are computed for velocity profile of an upper-convected Maxwell (UCM) fluid flow. Plots reflecting the impact of dual solutions for the variations of Deborah number, Hartman number, wall mass transfer are presented and analyzed. Streamlines are also plotted for the wall mass transfer effects when suction and blowing situations are considered. PMID:26575996
Dual Solutions for Nonlinear Flow Using Lie Group Analysis.
Awais, Muhammad; Hayat, Tasawar; Irum, Sania; Saleem, Salman
2015-01-01
`The aim of this analysis is to investigate the existence of the dual solutions for magnetohydrodynamic (MHD) flow of an upper-convected Maxwell (UCM) fluid over a porous shrinking wall. We have employed the Lie group analysis for the simplification of the nonlinear differential system and computed the absolute invariants explicitly. An efficient numerical technique namely the shooting method has been employed for the constructions of solutions. Dual solutions are computed for velocity profile of an upper-convected Maxwell (UCM) fluid flow. Plots reflecting the impact of dual solutions for the variations of Deborah number, Hartman number, wall mass transfer are presented and analyzed. Streamlines are also plotted for the wall mass transfer effects when suction and blowing situations are considered. PMID:26575996
Solutal Marangoni instability in layered two-phase flow
NASA Astrophysics Data System (ADS)
Picardo, Jason; Radhakrishna, T. G.; Pushpavanam, S.
2015-11-01
In this work, the instability of layered two-phase flow caused by the presence of a surface-active solute is studied. The fluids are density matched to focus on surfactant effects. The fluids flow between two flat plates, which are maintained at different solute concentrations. This establishes a constant flux of soluble surfactant from one fluid to the other, in the base state. A linear stability analysis is carried out, supported by energy budget calculations. The flow is first analyzed in the creeping flow regime. Long wave as well as short wave Marangoni instabilities are identified, each with a distinct energy signature. The short wave instability manifests as two distinct modes, characterized by the importance of interfacial deformations or lack thereof. The primary instability switches between these different modes as parameters are varied. The effect of small but finite inertia on these solutal Marangoni modes is then examined. The effect of soluble surfactant on a finte inertia flow is also studied, with focus on the transition from the viscosity-induced instability to solutal Marangoni instability. This analysis is relevant to microfluidic applications, such as solvent extraction, in which mass transfer is carried out between stratified immiscible fluids.
A flux-split solution procedure for unsteady flow calculations
NASA Technical Reports Server (NTRS)
Pordal, H. S.; Khosla, P. K.; Rubin, S. G.
1990-01-01
The solution of reduced Navier Stokes (RNS) equations is considered using a flux-split procedure. Unsteady flow in a two dimensional engine inlet is computed. The problems of unstart and restart are investigated. A sparse matrix direct solver combined with domain decomposition strategy is used to compute the unsteady flow field at each instant of time. Strong shock-boundary layer interaction, time varying shocks and time varying recirculation regions are efficiently captured.
Instabilities in stagnation point flows of polymer solutions
NASA Astrophysics Data System (ADS)
Haward, S. J.; McKinley, G. H.
2013-08-01
A recently developed microfluidic device, the optimized shape cross-slot extensional rheometer or OSCER [S. J. Haward, M. S. N. Oliveira, M. A. Alves, and G. H. McKinley, "Optimized cross-slot flow geometry for microfluidic extensional rheometry," Phys. Rev. Lett. 109, 128301 (2012), 10.1103/PhysRevLett.109.128301], is used to investigate the stability of viscoelastic polymer solutions in an idealized planar stagnation point flow. Aqueous polymer solutions, consisting of poly(ethylene oxide) and of hyaluronic acid with various molecular weights and concentrations, are formulated in order to provide fluids with a wide range of rheological properties. Semi-dilute solutions of high molecular weight polymers provide highly viscoelastic fluids with long relaxation times, which achieve a high Weissenberg number (Wi) at flow rates for which the Reynolds number (Re) remains low; hence the elasticity number El = Wi/Re is high. Lower concentration solutions of moderate molecular weight polymers provide only weakly viscoelastic fluids in which inertia remains important and El is relatively low. Flow birefringence observations are used to visualize the nature of flow instabilities in the fluids as the volumetric flow rate through the OSCER device is steadily incremented. At low Wi and Re, all of the fluids display a steady, symmetric, and uniform "birefringent strand" of highly oriented polymer molecules aligned along the outflowing symmetry axis of the test geometry, indicating the stability of the flow field under such conditions. In fluids of El > 1, we observe steady elastic flow asymmetries beyond a critical Weissenberg number,Wicrit, that are similar in character to those already reported in standard cross-slot geometries [e.g., P. E. Arratia, C. C. Thomas, J. Diorio, and J. P. Gollub, "Elastic instabilities of polymer solutions in cross-channel flow," Phys. Rev. Lett. 96, 144502 (2006), 10.1103/PhysRevLett.96.144502]. However, in fluids with El < 1 we observe a sequence
FLUID FLOW, SOLUTE MIXING AND PRECIPITATION IN POROUS MEDIA
Redden, George D; Y. Fang; T.D. Scheibe; A.M. Tartakovsky; Fox, Don T; Fujita, Yoshiko; White, Timothy A
2006-09-01
Reactions that lead to the formation of mineral precipitates, colloids or growth of biofilms in porous media often depend on the molecular-level diffusive mixing. For example, for the formation of mineral phases, exceeding the saturation index for a mineral is a minimum requirement for precipitation to proceed. Solute mixing frequently occurs at the interface between two solutions each containing one or more soluble reactants, particularly in engineered systems where contaminant degradation or modification or fluid flow are objectives. Although many of the fundamental component processes involved in the deposition or solubilization of solid phases are reasonably well understood, including precipitation equilibrium and kinetics, fluid flow and solute transport, the deposition of chemical precipitates, biofilms and colloidal particles are all coupled to flow, and the science of such coupled processes is not well developed. How such precipitates (and conversely, dissolution of solids) are distributed in the subsurface along flow paths with chemical gradients is a complex and challenging problem. This is especially true in systems that undergo rapid change where equilibrium conditions cannot be assumed, particularly in subsurface systems where reactants are introduced rapidly, compared to most natural flow conditions, and where mixing fronts are generated. Although the concept of dispersion in porous media is frequently used to approximate mixing at macroscopic scales, dispersion does not necessarily describe pore-level or molecular level mixing that must occur for chemical and biological reactions to be possible. An example of coupling between flow, mixing and mineral precipitation, with practical applications to controlling fluid flow or contaminant remediation in subsurface environments is shown in the mixing zone between parallel flowing solutions. Two- and three-dimensional experiments in packed-sand media were conducted where solutions containing calcium and
High-Order Accurate Solutions to the Helmholtz Equation in the Presence of Boundary Singularities
NASA Astrophysics Data System (ADS)
Britt, Darrell Steven, Jr.
Problems of time-harmonic wave propagation arise in important fields of study such as geological surveying, radar detection/evasion, and aircraft design. These often involve highfrequency waves, which demand high-order methods to mitigate the dispersion error. We propose a high-order method for computing solutions to the variable-coefficient inhomogeneous Helmholtz equation in two dimensions on domains bounded by piecewise smooth curves of arbitrary shape with a finite number of boundary singularities at known locations. We utilize compact finite difference (FD) schemes on regular structured grids to achieve highorder accuracy due to their efficiency and simplicity, as well as the capability to approximate variable-coefficient differential operators. In this work, a 4th-order compact FD scheme for the variable-coefficient Helmholtz equation on a Cartesian grid in 2D is derived and tested. The well known limitation of finite differences is that they lose accuracy when the boundary curve does not coincide with the discretization grid, which is a severe restriction on the geometry of the computational domain. Therefore, the algorithm presented in this work combines high-order FD schemes with the method of difference potentials (DP), which retains the efficiency of FD while allowing for boundary shapes that are not aligned with the grid without sacrificing the accuracy of the FD scheme. Additionally, the theory of DP allows for the universal treatment of the boundary conditions. One of the significant contributions of this work is the development of an implementation that accommodates general boundary conditions (BCs). In particular, Robin BCs with discontinuous coefficients are studied, for which we introduce a piecewise parameterization of the boundary curve. Problems with discontinuities in the boundary data itself are also studied. We observe that the design convergence rate suffers whenever the solution loses regularity due to the boundary conditions. This is
Fracture-Flow-Enhanced Solute Diffusion into Fractured Rock
Wu, Yu-Shu; Ye, Ming; Sudicky, E.A.
2007-12-15
We propose a new conceptual model of fracture-flow-enhanced matrix diffusion, which correlates with fracture-flow velocity, i.e., matrix diffusion enhancement induced by rapid fluid flow within fractures. According to the boundary-layer or film theory, fracture flow enhanced matrix diffusion may dominate mass-transfer processes at fracture-matrix interfaces, because rapid flow along fractures results in large velocity and concentration gradients at and near fracture-matrix interfaces, enhancing matrix diffusion at matrix surfaces. In this paper, we present a new formulation of the conceptual model for enhanced fracture-matrix diffusion, and its implementation is discussed using existing analytical solutions and numerical models. In addition, we use the enhanced matrix diffusion concept to analyze laboratory experimental results from nonreactive and reactive tracer breakthrough tests, in an effort to validate the new conceptual model.
Spectrally accurate numerical solution of the single-particle Schrödinger equation
NASA Astrophysics Data System (ADS)
Batcho, P. F.
1998-06-01
We have formulated a three-dimensional fully numerical (i.e., chemical basis-set free) method and applied it to the solution of the single-particle Schrödinger equation. The numerical method combines the rapid ``exponential'' convergence rates of spectral methods with the geometric flexibility of finite-element methods and can be viewed as an extension of the spectral element method. Singularities associated with multicenter systems are efficiently integrated by a Duffy transformation and the discrete operator is formulated by a variational statement. The method is applicable to molecular modeling for quantum chemical calculations on polyatomic systems. The complete system is shown to be efficiently inverted by the preconditioned conjugate gradient method and exponential convergence rates in numerical approximations are demonstrated for suitable benchmark problems including the hydrogenlike orbitals of nitrogen.
Design and Construction Solutions in the Accurate Realization of NCSX Magnetic Fields
Heitzenroeder, P.; Dudek, Lawrence E.; Brooks, Arthur W.; Viola, Michael E.; Brown, Thomas; Neilson, George H.; Zarnstorff, Michael C.; Rej, Donald; Cole,Michael J.; Freudenberg, Kevin D.; Harris J. H.; McGinnis, Gary
2008-09-29
The National Compact Stellarator Experiment, NCSX, is being constructed at the Princeton Plasma Physics Laboratory (PPPL) in partnership with the Oak Ridge national Laboratory. The goal of NCSX is to provide the understanding necessary to develop an attractive, disruption free, steady state compact stellaratorbased reactor design. This paper describes the recently revised designs of the critical interfaces between the modular coils, the construction solutions developed to meet assembly tolerances, and the recently revised trim coil system that provides the required compensation to correct for the “as built” conditions and to allow flexibility in the disposition of as-built conditions. In May, 2008, the sponsor decided to terminate the NCSX project due to growth in the project’s cost and schedule estimates. However significant technical challenges in design and construction were overcome, greatly reducing the risk in the remaining work to complete the project.
Hassouna, M Sabry; Farag, A A
2007-09-01
A wide range of computer vision applications require an accurate solution of a particular Hamilton- Jacobi (HJ) equation, known as the Eikonal equation. In this paper, we propose an improved version of the fast marching method (FMM) that is highly accurate for both 2D and 3D Cartesian domains. The new method is called multi-stencils fast marching (MSFM), which computes the solution at each grid point by solving the Eikonal equation along several stencils and then picks the solution that satisfies the upwind condition. The stencils are centered at each grid point and cover its entire nearest neighbors. In 2D space, 2 stencils cover the 8-neighbors of the point, while in 3D space, 6 stencils cover its 26-neighbors. For those stencils that are not aligned with the natural coordinate system, the Eikonal equation is derived using directional derivatives and then solved using higher order finite difference schemes. The accuracy of the proposed method over the state-of-the-art FMM-based techniques has been demonstrated through comprehensive numerical experiments.
Reference Solutions for Benchmark Turbulent Flows in Three Dimensions
NASA Technical Reports Server (NTRS)
Diskin, Boris; Thomas, James L.; Pandya, Mohagna J.; Rumsey, Christopher L.
2016-01-01
A grid convergence study is performed to establish benchmark solutions for turbulent flows in three dimensions (3D) in support of turbulence-model verification campaign at the Turbulence Modeling Resource (TMR) website. The three benchmark cases are subsonic flows around a 3D bump and a hemisphere-cylinder configuration and a supersonic internal flow through a square duct. Reference solutions are computed for Reynolds Averaged Navier Stokes equations with the Spalart-Allmaras turbulence model using a linear eddy-viscosity model for the external flows and a nonlinear eddy-viscosity model based on a quadratic constitutive relation for the internal flow. The study involves three widely-used practical computational fluid dynamics codes developed and supported at NASA Langley Research Center: FUN3D, USM3D, and CFL3D. Reference steady-state solutions computed with these three codes on families of consistently refined grids are presented. Grid-to-grid and code-to-code variations are described in detail.
NASA Astrophysics Data System (ADS)
Lee, Dongwook
2013-06-01
In this paper, we extend the unsplit staggered mesh scheme (USM) for 2D magnetohydrodynamics (MHD) [D. Lee, A.E. Deane, An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics, J. Comput. Phys. 228 (2009) 952-975] to a full 3D MHD scheme. The scheme is a finite-volume Godunov method consisting of a constrained transport (CT) method and an efficient and accurate single-step, directionally unsplit multidimensional data reconstruction-evolution algorithm, which extends Colella's original 2D corner transport upwind (CTU) method [P. Colella, Multidimensional upwind methods for hyperbolic conservation laws, J. Comput. Phys. 87 (1990) 446-466]. We present two types of data reconstruction-evolution algorithms for 3D: (1) a reduced CTU scheme and (2) a full CTU scheme. The reduced 3D CTU scheme is a variant of a simple 3D extension of Collela's 2D CTU method and is considered as a direct extension from the 2D USM scheme. The full 3D CTU scheme is our primary 3D solver which includes all multidimensional cross-derivative terms for stability. The latter method is logically analogous to the 3D unsplit CTU method by Saltzman [J. Saltzman, An unsplit 3D upwind method for hyperbolic conservation laws, J. Comput. Phys. 115 (1994) 153-168]. The major novelties in our algorithms are twofold. First, we extend the reduced CTU scheme to the full CTU scheme which is able to run with CFL numbers close to unity. Both methods utilize the transverse update technique developed in the 2D USM algorithm to account for transverse fluxes without solving intermediate Riemann problems, which in turn gives cost-effective 3D methods by reducing the total number of Riemann solves. The proposed algorithms are simple and efficient especially when including multidimensional MHD terms that maintain in-plane magnetic field dynamics. Second, we introduce a new CT scheme that makes use of proper upwind information in taking averages of electric fields. Our 3D USM schemes can be easily
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas; Hariharan, S. I.; Maccamy, R. C.
1993-01-01
We consider the solution of scattering problems for the wave equation using approximate boundary conditions at artificial boundaries. These conditions are explicitly viewed as approximations to an exact boundary condition satisfied by the solution on the unbounded domain. We study the short and long term behavior of the error. It is provided that, in two space dimensions, no local in time, constant coefficient boundary operator can lead to accurate results uniformly in time for the class of problems we consider. A variable coefficient operator is developed which attains better accuracy (uniformly in time) than is possible with constant coefficient approximations. The theory is illustrated by numerical examples. We also analyze the proposed boundary conditions using energy methods, leading to asymptotically correct error bounds.
Efficient solutions of two-dimensional incompressible steady viscous flows
NASA Technical Reports Server (NTRS)
Morrison, J. H.; Napolitano, M.
1986-01-01
A simple, efficient, and robust numerical technique is provided for solving two dimensional incompressible steady viscous flows at moderate to high Reynolds numbers. The proposed approach employs an incremental multigrid method and an extrapolation procedure based on minimum residual concepts to accelerate the convergence rate of a robust block-line-Gauss-Seidel solver for the vorticity-stream function Navier-Stokes equations. Results are presented for the driven cavity flow problem using uniform and nonuniform grids and for the flow past a backward facing step in a channel. For this second problem, mesh refinement and Richardson extrapolation are used to obtain useful benchmark solutions in the full range of Reynolds numbers at which steady laminar flow is established.
Preliminary investigation of elongational flow of dilute polymer solutions
NASA Technical Reports Server (NTRS)
Peng, S. T. J.; Landel, R. F.
1976-01-01
A tubeless siphon apparatus has been set up to measure extensional flow. In this apparatus, the liquid is continuously drawn into a capillary and, after steady flow has been established, the tube is raised above the liquid surface. With viscoelastic liquids, the flow continues and a column can be lifted from the reservoir. At the capillary entrance, an oscillating bead of excess liquid collects which interferes with both the flow and the measurements. This can be minimized by careful control of the liquid-column height. For homogeneous solutions, the column is symmetrical and tapers steadily from the liquid surface to the capillary entrance, with no bulging. Preliminary results show tensile viscosities 1000 times that of the Trouton coefficient and having a very strong dependence on deformation rate. A concentration-stretch rate-reduced variable scheme is proposed.
Rapid, high-order accurate calculation of flows due to free source or vortex distributions
NASA Technical Reports Server (NTRS)
Halsey, D.
1981-01-01
Fast Fourier transform (FFT) techniques are applied to the problem of finding the flow due to source or vortex distributions in the field outside an airfoil or other two-dimensional body. Either the complex potential or the complex velocity may be obtained to a high order of accuracy, with computational effort similar to that required by second-order fast Poisson solvers. These techniques are applicable to general flow problems with compressibility and rotation. An example is given of their use for inviscid compressible flow.
NASA Astrophysics Data System (ADS)
Stecca, Guglielmo; Siviglia, Annunziato; Blom, Astrid
2016-07-01
We present an accurate numerical approximation to the Saint-Venant-Hirano model for mixed-sediment morphodynamics in one space dimension. Our solution procedure originates from the fully-unsteady matrix-vector formulation developed in [54]. The principal part of the problem is solved by an explicit Finite Volume upwind method of the path-conservative type, by which all the variables are updated simultaneously in a coupled fashion. The solution to the principal part is embedded into a splitting procedure for the treatment of frictional source terms. The numerical scheme is extended to second-order accuracy and includes a bookkeeping procedure for handling the evolution of size stratification in the substrate. We develop a concept of balancedness for the vertical mass flux between the substrate and active layer under bed degradation, which prevents the occurrence of non-physical oscillations in the grainsize distribution of the substrate. We suitably modify the numerical scheme to respect this principle. We finally verify the accuracy in our solution to the equations, and its ability to reproduce one-dimensional morphodynamics due to streamwise and vertical sorting, using three test cases. In detail, (i) we empirically assess the balancedness of vertical mass fluxes under degradation; (ii) we study the convergence to the analytical linearised solution for the propagation of infinitesimal-amplitude waves [54], which is here employed for the first time to assess a mixed-sediment model; (iii) we reproduce Ribberink's E8-E9 flume experiment [46].
Preliminary investigations into solutal flow about growing tetragonal lysozyme crystals
NASA Technical Reports Server (NTRS)
Pusey, Marc; Witherow, William; Naumann, Robert
1988-01-01
A series of preliminary experiments were done to investigate solutal flow about growing lysozyme crystals and its effects. Density-gradient-driven flow was observed using a schlieren optical system. Crystals used ranged from 0.3 to 1.72 mm across the (110) face, and protein concentrations were from 3.7 to 23.7 mg/ml. The convective plume velocities were found to be from 10 to 50 microns/s, which correlated with those predicted to occur based upon a diffusive-convective model. When microcrystals of lysozyme, less than 20 microns across the (110) face were subjected to directed solution flows, the growth rate was found to rapidly decrease over the 8-20 h course of the experiment. Solution flow rates used ranged from 18 to 40 microns/s, and protein concentrations were from 7.3 to 11.7 mg/ml, conditions typical of larger (greater than 0.5 mm) crystals in the terminal phases of a typical crystal growth procedure.
Tuning-free controller to accurately regulate flow rates in a microfluidic network.
Heo, Young Jin; Kang, Junsu; Kim, Min Jun; Chung, Wan Kyun
2016-01-01
We describe a control algorithm that can improve accuracy and stability of flow regulation in a microfluidic network that uses a conventional pressure pump system. The algorithm enables simultaneous and independent control of fluid flows in multiple micro-channels of a microfluidic network, but does not require any model parameters or tuning process. We investigate robustness and optimality of the proposed control algorithm and those are verified by simulations and experiments. In addition, the control algorithm is compared with a conventional PID controller to show that the proposed control algorithm resolves critical problems induced by the PID control. The capability of the control algorithm can be used not only in high-precision flow regulation in the presence of disturbance, but in some useful functions for lab-on-a-chip devices such as regulation of volumetric flow rate, interface position control of two laminar flows, valveless flow switching, droplet generation and particle manipulation. We demonstrate those functions and also suggest further potential biological applications which can be accomplished by the proposed control framework. PMID:26987587
Tuning-free controller to accurately regulate flow rates in a microfluidic network
Heo, Young Jin; Kang, Junsu; Kim, Min Jun; Chung, Wan Kyun
2016-01-01
We describe a control algorithm that can improve accuracy and stability of flow regulation in a microfluidic network that uses a conventional pressure pump system. The algorithm enables simultaneous and independent control of fluid flows in multiple micro-channels of a microfluidic network, but does not require any model parameters or tuning process. We investigate robustness and optimality of the proposed control algorithm and those are verified by simulations and experiments. In addition, the control algorithm is compared with a conventional PID controller to show that the proposed control algorithm resolves critical problems induced by the PID control. The capability of the control algorithm can be used not only in high-precision flow regulation in the presence of disturbance, but in some useful functions for lab-on-a-chip devices such as regulation of volumetric flow rate, interface position control of two laminar flows, valveless flow switching, droplet generation and particle manipulation. We demonstrate those functions and also suggest further potential biological applications which can be accomplished by the proposed control framework. PMID:26987587
Elastic instabilities in planar elongational flow of monodisperse polymer solutions
Haward, Simon J.; McKinley, Gareth H.; Shen, Amy Q.
2016-01-01
We investigate purely elastic flow instabilities in the almost ideal planar stagnation point elongational flow field generated by a microfluidic optimized-shape cross-slot extensional rheometer (OSCER). We use time-resolved flow velocimetry and full-field birefringence microscopy to study the behavior of a series of well-characterized viscoelastic polymer solutions under conditions of low fluid inertia and over a wide range of imposed deformation rates. At low deformation rates the flow is steady and symmetric and appears Newtonian-like, while at high deformation rates we observe the onset of a flow asymmetry resembling the purely elastic instabilities reported in standard-shaped cross-slot devices. However, for intermediate rates, we observe a new type of elastic instability characterized by a lateral displacement and time-dependent motion of the stagnation point. At the onset of this new instability, we evaluate a well-known dimensionless criterion M that predicts the onset of elastic instabilities based on geometric and rheological scaling parameters. The criterion yields maximum values of M which compare well with critical values of M for the onset of elastic instabilities in viscometric torsional flows. We conclude that the same mechanism of tension acting along curved streamlines governs the onset of elastic instabilities in both extensional (irrotational) and torsional (rotational) viscoelastic flows. PMID:27616181
Elastic instabilities in planar elongational flow of monodisperse polymer solutions
NASA Astrophysics Data System (ADS)
Haward, Simon J.; McKinley, Gareth H.; Shen, Amy Q.
2016-09-01
We investigate purely elastic flow instabilities in the almost ideal planar stagnation point elongational flow field generated by a microfluidic optimized-shape cross-slot extensional rheometer (OSCER). We use time-resolved flow velocimetry and full-field birefringence microscopy to study the behavior of a series of well-characterized viscoelastic polymer solutions under conditions of low fluid inertia and over a wide range of imposed deformation rates. At low deformation rates the flow is steady and symmetric and appears Newtonian-like, while at high deformation rates we observe the onset of a flow asymmetry resembling the purely elastic instabilities reported in standard-shaped cross-slot devices. However, for intermediate rates, we observe a new type of elastic instability characterized by a lateral displacement and time-dependent motion of the stagnation point. At the onset of this new instability, we evaluate a well-known dimensionless criterion M that predicts the onset of elastic instabilities based on geometric and rheological scaling parameters. The criterion yields maximum values of M which compare well with critical values of M for the onset of elastic instabilities in viscometric torsional flows. We conclude that the same mechanism of tension acting along curved streamlines governs the onset of elastic instabilities in both extensional (irrotational) and torsional (rotational) viscoelastic flows.
Elastic instabilities in planar elongational flow of monodisperse polymer solutions.
Haward, Simon J; McKinley, Gareth H; Shen, Amy Q
2016-01-01
We investigate purely elastic flow instabilities in the almost ideal planar stagnation point elongational flow field generated by a microfluidic optimized-shape cross-slot extensional rheometer (OSCER). We use time-resolved flow velocimetry and full-field birefringence microscopy to study the behavior of a series of well-characterized viscoelastic polymer solutions under conditions of low fluid inertia and over a wide range of imposed deformation rates. At low deformation rates the flow is steady and symmetric and appears Newtonian-like, while at high deformation rates we observe the onset of a flow asymmetry resembling the purely elastic instabilities reported in standard-shaped cross-slot devices. However, for intermediate rates, we observe a new type of elastic instability characterized by a lateral displacement and time-dependent motion of the stagnation point. At the onset of this new instability, we evaluate a well-known dimensionless criterion M that predicts the onset of elastic instabilities based on geometric and rheological scaling parameters. The criterion yields maximum values of M which compare well with critical values of M for the onset of elastic instabilities in viscometric torsional flows. We conclude that the same mechanism of tension acting along curved streamlines governs the onset of elastic instabilities in both extensional (irrotational) and torsional (rotational) viscoelastic flows. PMID:27616181
Nonequilibrium thermodynamics of dilute polymer solutions in flow
Latinwo, Folarin; Hsiao, Kai-Wen; Schroeder, Charles M.
2014-11-07
Modern materials processing applications and technologies often occur far from equilibrium. To this end, the processing of complex materials such as polymer melts and nanocomposites generally occurs under strong deformations and flows, conditions under which equilibrium thermodynamics does not apply. As a result, the ability to determine the nonequilibrium thermodynamic properties of polymeric materials from measurable quantities such as heat and work is a major challenge in the field. Here, we use work relations to show that nonequilibrium thermodynamic quantities such as free energy and entropy can be determined for dilute polymer solutions in flow. In this way, we determine the thermodynamic properties of DNA molecules in strong flows using a combination of simulations, kinetic theory, and single molecule experiments. We show that it is possible to calculate polymer relaxation timescales purely from polymer stretching dynamics in flow. We further observe a thermodynamic equivalence between nonequilibrium and equilibrium steady-states for polymeric systems. In this way, our results provide an improved understanding of the energetics of flowing polymer solutions.
NASA Astrophysics Data System (ADS)
Brunker, J.; Beard, P.
2014-03-01
An assessment has been made of various experimental factors affecting the accuracy of flow velocities measured using a pulsed time correlation photoacoustic Doppler technique. In this method, Doppler time shifts are quantified via crosscorrelation of pairs of photoacoustic waveforms generated in moving absorbers using pairs of laser light pulses, and the photoacoustic waves are detected using an ultrasound transducer. The acoustic resolution mode is employed by using the transducer focal width, rather than the large illuminated volume, to define the lateral spatial resolution. This enables penetration depths of several millimetres or centimetres, unlike methods using the optical resolution mode, which limits the maximum penetration depth to approximately 1 mm. In the acoustic resolution mode, it is difficult to detect time shifts in highly concentrated suspensions of flowing absorbers, such as red blood cell suspensions and whole blood, and this challenge supposedly arises because of the lack of spatial heterogeneity. However, by assessing the effect of different absorption coefficients and tube diameters, we offer an alternative explanation relating to light attenuation and parabolic flow. We also demonstrate a new signal processing method that surmounts the previous problem of measurement under-reading. This method is a form of signal range gating and enables mapping of the flow velocity profile across the tube as well as measurement of the average flow velocity. We show that, using our signal processing scheme, it is possible to measure the flow of whole blood using a relatively low frequency detector. This important finding paves the way for application of the technique to measurements of blood flow several centimetres deep in living tissue.
Time-Accurate Computation of Viscous Flow Around Deforming Bodies Using Overset Grids
Fast, P; Henshaw, W D
2001-04-02
Dynamically evolving boundaries and deforming bodies interacting with a flow are commonly encountered in fluid dynamics. However, the numerical simulation of flows with dynamic boundaries is difficult with current methods. We propose a new method for studying such problems. The key idea is to use the overset grid method with a thin, body-fitted grid near the deforming boundary, while using fixed Cartesian grids to cover most of the computational domain. Our approach combines the strengths of earlier moving overset grid methods for rigid body motion, and unstructured grid methods for Aow-structure interactions. Large scale deformation of the flow boundaries can be handled without a global regridding, and in a computationally efficient way. In terms of computational cost, even a full overset grid regridding is significantly cheaper than a full regridding of an unstructured grid for the same domain, especially in three dimensions. Numerical studies are used to verify accuracy and convergence of our flow solver. As a computational example, we consider two-dimensional incompressible flow past a flexible filament with prescribed dynamics.
Finite-amplitude solutions in rotating Hagen-Poiseuille flow
NASA Astrophysics Data System (ADS)
Pier, Benoît; Kumar, Abhishek; Govindarajan, Rama
2015-11-01
While the pipe Poiseuille base flow is linearly stable at all Reynolds numbers, a small amount of rotation of the pipe around its axis induces linear instability beyond a low critical Reynolds number Rc ~= 83 [Pedley, J. Fluid Mech. 1969]. More recently [Fernandez-Feria and del Pino, Phys. Fluids 2002], this configuration has been shown to become absolutely unstable at Reynolds numbers of the same order of magnitude. Using direct numerical simulations, we investigate here finite-amplitude solutions resulting from saturation of exponentially growing small-amplitude initial perturbations. The base flow depends on two dynamical parameters (axial Reynolds number and rotation rate) and the initial perturbation is characterized by its axial wavenumber and its azimuthal mode number. The range of nonlinear waves prevailing in this configuration, the associated nonlinear dispersion relation and the spatial structure of these solutions are systematically obtained by exploring the parameter space. Funding from CEFIPRA is gratefully acknowledged.
General solutions of the Stokes flow --- Lamb's solution and multipole expansion
NASA Astrophysics Data System (ADS)
Ichiki, Kengo
2004-11-01
The objective of this talk is to relate the two major representations of the Stokes flow; Lamb's general solution (Lamb 1932, and Happel and Brenner 1973) and the multipole expansion of the Oseen tensor (Ichiki 2002). For low Reynolds number hydrodynamics, the governing equation is the Stokes equation, which is a linear partial differential equation. The general solution can be obtained by the conventional potential theory and we have a lot of equivalent representations. It is obvious that these various formulations are mathematically equivalent. However, to the author's knowledge, the relations among them are limited (Weinbaum and Ganatos 1990, and Kim and Karrila 1991). Here we write Lamb's solution by Cartesian tensors and express the force moments on particles by the Lamb's solution. Using this relation, we compare the suspension stress expressed by Lamb's solution (Tanksley and Prosperetti 2001) with that by force moments.
A finite element formulation of Euler equations for the solution of steady transonic flows
NASA Technical Reports Server (NTRS)
Ecer, A.; Akay, H. U.
1982-01-01
The main objective of the considered investigation is related to the development of a relaxation scheme for the analysis of inviscid, rotational, transonic flow problems. To formulate the equations of motion for inviscid flows in a fixed coordinate system, an Eulerian type variational principle is required. The derivation of an Eulerian variational principle which is employed in the finite element formulation is discussed. The presented numerical method describes the mathematical formulation and the application of a numerical process for the direct solution of steady Euler equations. The development of the procedure as an extension of existing potential flow formulations provides the applicability of previous procedures, e.g., proper application of the artificial viscosity for supersonic elements, and the accurate modeling of the shock.
Towards Accurate Prediction of Turbulent, Three-Dimensional, Recirculating Flows with the NCC
NASA Technical Reports Server (NTRS)
Iannetti, A.; Tacina, R.; Jeng, S.-M.; Cai, J.
2001-01-01
The National Combustion Code (NCC) was used to calculate the steady state, nonreacting flow field of a prototype Lean Direct Injection (LDI) swirler. This configuration used nine groups of eight holes drilled at a thirty-five degree angle to induce swirl. These nine groups created swirl in the same direction, or a corotating pattern. The static pressure drop across the holes was fixed at approximately four percent. Computations were performed on one quarter of the geometry, because the geometry is considered rotationally periodic every ninety degrees. The final computational grid used was approximately 2.26 million tetrahedral cells, and a cubic nonlinear k - epsilon model was used to model turbulence. The NCC results were then compared to time averaged Laser Doppler Velocimetry (LDV) data. The LDV measurements were performed on the full geometry, but four ninths of the geometry was measured. One-, two-, and three-dimensional representations of both flow fields are presented. The NCC computations compare both qualitatively and quantitatively well to the LDV data, but differences exist downstream. The comparison is encouraging, and shows that NCC can be used for future injector design studies. To improve the flow prediction accuracy of turbulent, three-dimensional, recirculating flow fields with the NCC, recommendations are given.
Fibrillization kinetics of insulin solution in an interfacial shearing flow
NASA Astrophysics Data System (ADS)
Balaraj, Vignesh; McBride, Samantha; Hirsa, Amir; Lopez, Juan
2015-11-01
Although the association of fibril plaques with neurodegenerative diseases like Alzheimer's and Parkinson's is well established, in-depth understanding of the roles played by various physical factors in seeding and growth of fibrils is far from well known. Of the numerous factors affecting this complex phenomenon, the effect of fluid flow and shear at interfaces is paramount as it is ubiquitous and the most varying factor in vivo. Many amyloidogenic proteins have been found to denature upon contact at hydrophobic interfaces due to the self-assembling nature of protein in its monomeric state. Here, fibrillization kinetics of insulin solution is studied in an interfacial shearing flow. The transient surface rheological response of the insulin solution to the flow and its effect on the bulk fibrillization process has been quantified. Minute differences in hydrophobic characteristics between two variants of insulin- Human recombinant and Bovine insulin are found to result in very different responses. Results presented will be in the form of fibrillization assays, images of fibril plaques formed, and changes in surface rheological properties of the insulin solution. The interfacial velocity field, measured from images (via Brewster Angle Microscopy), is compared with computations. Supported by NNX13AQ22G, National Aeronautics and Space Administration.
Solution adaptive grids applied to low Reynolds number flow
NASA Astrophysics Data System (ADS)
de With, G.; Holdø, A. E.; Huld, T. A.
2003-08-01
A numerical study has been undertaken to investigate the use of a solution adaptive grid for flow around a cylinder in the laminar flow regime. The main purpose of this work is twofold. The first aim is to investigate the suitability of a grid adaptation algorithm and the reduction in mesh size that can be obtained. Secondly, the uniform asymmetric flow structures are ideal to validate the mesh structures due to mesh refinement and consequently the selected refinement criteria. The refinement variable used in this work is a product of the rate of strain and the mesh cell size, and contains two variables Cm and Cstr which determine the order of each term. By altering the order of either one of these terms the refinement behaviour can be modified.
High resolution solutions of the Euler equations for vortex flows
NASA Technical Reports Server (NTRS)
Murman, E. M.; Powell, K. G.; Rizzi, A.
1985-01-01
Solutions of the Euler equations are presented for M = 1.5 flow past a 70-degree-swept delta wing. At an angle of attack of 10 degrees, strong leading-edge vortices are produced. Two computational approaches are taken, based upon fully three-dimensional and conical flow theory. Both methods utilize a finite-volume discretization solved by a pseudounsteady multistage scheme. Results from the two approaches are in good agreement. Computations have been done on a 16-million-word CYBER 205 using 196 x 56 x 96 and 128 x 128 cells for the two methods. A sizable data base is generated, and some of the practical aspects of manipulating it are mentioned. The results reveal many interesting physical features of the compressible vortical flow field and also suggest new areas needing research.
Yu, Yang; Zhang, Fan; Gao, Ming-Xin; Li, Hai-Tao; Li, Jing-Xing; Song, Wei; Huang, Xin-Sheng; Gu, Cheng-Xiong
2013-01-01
OBJECTIVES Intraoperative transit time flow measurement (TTFM) is widely used to assess anastomotic quality in coronary artery bypass grafting (CABG). However, in sequential vein grafting, the flow characteristics collected by the conventional TTFM method are usually associated with total graft flow and might not accurately indicate the quality of every distal anastomosis in a sequential graft. The purpose of our study was to examine a new TTFM method that could assess the quality of each distal anastomosis in a sequential graft more reliably than the conventional TTFM approach. METHODS Two TTFM methods were tested in 84 patients who underwent sequential saphenous off-pump CABG in Beijing An Zhen Hospital between April and August 2012. In the conventional TTFM method, normal blood flow in the sequential graft was maintained during the measurement, and the flow probe was placed a few centimetres above the anastomosis to be evaluated. In the new method, blood flow in the sequential graft was temporarily reduced during the measurement by placing an atraumatic bulldog clamp at the graft a few centimetres distal to the anastomosis to be evaluated, while the position of the flow probe remained the same as in the conventional method. This new TTFM method was named the flow reduction TTFM. Graft flow parameters measured by both methods were compared. RESULTS Compared with the conventional TTFM, the flow reduction TTFM resulted in significantly lower mean graft blood flow (P < 0.05); in contrast, yielded significantly higher pulsatility index (P < 0.05). Diastolic filling was not significantly different between the two methods and was >50% in both cases. Interestingly, the flow reduction TTFM identified two defective middle distal anastomoses that the conventional TTFM failed to detect. Graft flows near the defective distal anastomoses were improved substantially after revision. CONCLUSIONS In this study, we found that temporary reduction of graft flow during TTFM seemed to
Exact solutions and physical analogies for unidirectional flows
NASA Astrophysics Data System (ADS)
Bazant, Martin Z.
2016-06-01
Unidirectional flow is the simplest phenomenon of fluid mechanics. Its mathematical description, the Dirichlet problem for Poisson's equation in two dimensions with constant forcing, arises in many physical contexts, such as the torsion of elastic beams, first solved by de Saint-Venant for complex shapes. Here the literature is unified and extended by identifying 17 physical analogies for unidirectional flow and describing their common mathematical structure. Besides classical analogies in fluid and solid mechanics, applications are discussed in stochastic processes (first passage in two dimensions), pattern formation (river growth by erosion), and electrokinetics (ion transport in nanochannels), which also involve Poisson's equation with nonconstant forcing. Methods are given to construct approximate geometries that admit exact solutions, by adding harmonic functions to quadratic forms or by truncating eigenfunction expansions. Exact solutions for given geometries are also derived by conformal mapping. We prove that the remarkable geometrical interpretation of Poiseuille flow in an equilateral triangular pipe (the product of the distances from an interior point to the sides) is only shared by parallel plates and unbounded equilateral wedges (with the third side hidden behind the apex). We also prove Onsager reciprocity for linear electrokinetic phenomena in straight pores of arbitrary shape and surface charge, based on the mathematics of unidirectional flow.
Stability of Inviscid Flow over Airfoils Admitting Multiple Numerical Solutions
NASA Astrophysics Data System (ADS)
Liu, Ya; Xiong, Juntao; Liu, Feng; Luo, Shijun
2012-11-01
Multiple numerical solutions at the same flight condition are found of inviscid transonic flow over certain airfoils (Jameson et al., AIAA 2011-3509) within some Mach number range. Both symmetric and asymmetric solutions exist for a symmetric airfoil at zero angle of attack. Global linear stability analysis of the multiple solutions is conducted. Linear perturbation equations of the Euler equations around a steady-state solution are formed and discretized numerically. An eigenvalue problem is then constructed using the modal analysis approach. Only a small portion of the eigen spectrum is needed and thus can be found efficiently by using Arnoldi's algorithm. The least stable or unstable mode corresponds to the eigenvalue with the largest real part. Analysis of the NACA 0012 airfoil indicates stability of symmetric solutions of the Euler equations at conditions where buffet is found from unsteady Navier-Stokes equations. Euler solutions of the same airfoil but modified to include the displacement thickness of the boundary layer computed from the Navier-Stokes equations, however, exhibit instability based on the present linear stability analysis. Graduate Student.
NASA Technical Reports Server (NTRS)
Hasiuk, Jan; Hindman, Richard; Iversen, James
1988-01-01
The azimuthal-invariant, three-dimensional cylindrical, incompressible Navier-Stokes equations are solved to steady state for a finite-length, physically realistic model. The numerical method relies on an alternating-direction implicit scheme that is formally second-order accurate in space and first-order accurate in time. The equations are linearized and uncoupled by evaluating variable coefficients at the previous time iteration. Wall grid clustering is provided by a Roberts transformation in radial and axial directions. A vorticity-velocity formulation is found to be preferable to a vorticity-streamfunction approach. Subject to no-slip, Dirichlet boundary conditions, except for the inner cylinder rotation velocity (impulsive start-up) and zero-flow initial conditions, nonturbulent solutions are obtained for sub- and supercritical Reynolds numbers of 100 to 400 for a finite geometry where R(outer)/R(inner) = 1.5, H/R(inner) = 0.73, and H/Delta-R = 1.5. An axially-stretched model solution is shown to asymptotically approach the one-dimensional analytic Couette solution at the cylinder midheight. Flowfield change from laminar to Taylor-vortex flow is discussed as a function of Reynolds number. Three-dimensional velocities, vorticity, and streamfunction are presented via two-dimensional graphs and three-dimensional surface and contour plots.
A second-order accurate immersed boundary-lattice Boltzmann method for particle-laden flows
NASA Astrophysics Data System (ADS)
Zhou, Qiang; Fan, Liang-Shih
2014-07-01
A new immersed boundary-lattice Boltzmann method (IB-LBM) is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles. The immersed boundary method (IBM) recently developed by Breugem (2012) [19] is adopted in the present method, development including the retraction technique, the multi-direct forcing method and the direct account of the inertia of the fluid contained within the particles. The present IB-LBM is, however, formulated with further improvement with the implementation of the high-order Runge-Kutta schemes in the coupled fluid-particle interaction. The major challenge to implement high-order Runge-Kutta schemes in the LBM is that the flow information such as density and velocity cannot be directly obtained at a fractional time step from the LBM since the LBM only provides the flow information at an integer time step. This challenge can be, however, overcome as given in the present IB-LBM by extrapolating the flow field around particles from the known flow field at the previous integer time step. The newly calculated fluid-particle interactions from the previous fractional time steps of the current integer time step are also accounted for in the extrapolation. The IB-LBM with high-order Runge-Kutta schemes developed in this study is validated by several benchmark applications. It is demonstrated, for the first time, that the IB-LBM has the capacity to resolve the translational and rotational motion of particles with the second-order accuracy. The optimal retraction distances for spheres and tubes that help the method achieve the second-order accuracy are found to be around 0.30 and -0.47 times of the lattice spacing, respectively. Simulations of the Stokes flow through a simple cubic lattice of rotational spheres indicate that the lift force produced by the Magnus effect can be very significant in view of the magnitude of the drag force when the practical rotating speed of the spheres is encountered. This finding
An Integrated Numerical Hydrodynamic Shallow Flow-Solute Transport Model for Urban Area
NASA Astrophysics Data System (ADS)
Alias, N. A.; Mohd Sidek, L.
2016-03-01
The rapidly changing on land profiles in the some urban areas in Malaysia led to the increasing of flood risk. Extensive developments on densely populated area and urbanization worsen the flood scenario. An early warning system is really important and the popular method is by numerically simulating the river and flood flows. There are lots of two-dimensional (2D) flood model predicting the flood level but in some circumstances, still it is difficult to resolve the river reach in a 2D manner. A systematic early warning system requires a precisely prediction of flow depth. Hence a reliable one-dimensional (1D) model that provides accurate description of the flow is essential. Research also aims to resolve some of raised issues such as the fate of pollutant in river reach by developing the integrated hydrodynamic shallow flow-solute transport model. Presented in this paper are results on flow prediction for Sungai Penchala and the convection-diffusion of solute transports simulated by the developed model.
Recommendations for accurate numerical blood flow simulations of stented intracranial aneurysms.
Janiga, Gábor; Berg, Philipp; Beuing, Oliver; Neugebauer, Mathias; Gasteiger, Rocco; Preim, Bernhard; Rose, Georg; Skalej, Martin; Thévenin, Dominique
2013-06-01
The number of scientific publications dealing with stented intracranial aneurysms is rapidly increasing. Powerful computational facilities are now available; an accurate computational modeling of hemodynamics in patient-specific configurations is, however, still being sought. Furthermore, there is still no general agreement on the quantities that should be computed and on the most adequate analysis for intervention support. In this article, the accurate representation of patient geometry is first discussed, involving successive improvements. Concerning the second step, the mesh required for the numerical simulation is especially challenging when deploying a stent with very fine wire structures. Third, the description of the fluid properties is a major challenge. Finally, a founded quantitative analysis of the simulation results is obviously needed to support interventional decisions. In the present work, an attempt has been made to review the most important steps for a high-quality computational fluid dynamics computation of virtually stented intracranial aneurysms. In consequence, this leads to concrete recommendations, whereby the obtained results are not discussed for their medical relevance but for the evaluation of their quality. This investigation might hopefully be helpful for further studies considering stent deployment in patient-specific geometries, in particular regarding the generation of the most appropriate computational model. PMID:23729530
Cobb, J.W.
1995-02-01
There is an increasing need for more accurate numerical methods for large-scale nonlinear magneto-fluid turbulence calculations. These methods should not only increase the current state of the art in terms of accuracy, but should also continue to optimize other desired properties such as simplicity, minimized computation, minimized memory requirements, and robust stability. This includes the ability to stably solve stiff problems with long time-steps. This work discusses a general methodology for deriving higher-order numerical methods. It also discusses how the selection of various choices can affect the desired properties. The explicit discussion focuses on third-order Runge-Kutta methods, including general solutions and five examples. The study investigates the linear numerical analysis of these methods, including their accuracy, general stability, and stiff stability. Additional appendices discuss linear multistep methods, discuss directions for further work, and exhibit numerical analysis results for some other commonly used lower-order methods.
Multigrid Acceleration of Time-Accurate DNS of Compressible Turbulent Flow
NASA Technical Reports Server (NTRS)
Broeze, Jan; Geurts, Bernard; Kuerten, Hans; Streng, Martin
1996-01-01
An efficient scheme for the direct numerical simulation of 3D transitional and developed turbulent flow is presented. Explicit and implicit time integration schemes for the compressible Navier-Stokes equations are compared. The nonlinear system resulting from the implicit time discretization is solved with an iterative method and accelerated by the application of a multigrid technique. Since we use central spatial discretizations and no artificial dissipation is added to the equations, the smoothing method is less effective than in the more traditional use of multigrid in steady-state calculations. Therefore, a special prolongation method is needed in order to obtain an effective multigrid method. This simulation scheme was studied in detail for compressible flow over a flat plate. In the laminar regime and in the first stages of turbulent flow the implicit method provides a speed-up of a factor 2 relative to the explicit method on a relatively coarse grid. At increased resolution this speed-up is enhanced correspondingly.
An affordable and accurate conductivity probe for density measurements in stratified flows
NASA Astrophysics Data System (ADS)
Carminati, Marco; Luzzatto-Fegiz, Paolo
2015-11-01
In stratified flow experiments, conductivity (combined with temperature) is often used to measure density. The probes typically used can provide very fine spatial scales, but can be fragile, expensive to replace, and sensitive to environmental noise. A complementary instrument, comprising a low-cost conductivity probe, would prove valuable in a wide range of applications where resolving extremely small spatial scales is not needed. We propose using micro-USB cables as the actual conductivity sensors. By removing the metallic shield from a micro-B connector, 5 gold-plated microelectrodes are exposed and available for 4-wire measurements. These have a cell constant ~550m-1, an intrinsic thermal noise of at most 30pA/Hz1/2, as well as sub-millisecond time response, making them highly suitable for many stratified flow measurements. In addition, we present the design of a custom electronic board (Arduino-based and Matlab-controlled) for simultaneous acquisition from 4 sensors, with resolution (in conductivity, and resulting density) exceeding the performance of typical existing probes. We illustrate the use of our conductivity-measuring system through stratified flow experiments, and describe plans to release simple instructions to construct our complete system for around 200.
A second-order accurate immersed boundary-lattice Boltzmann method for particle-laden flows
Zhou, Qiang; Fan, Liang-Shih
2014-07-01
A new immersed boundary-lattice Boltzmann method (IB-LBM) is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles. The immersed boundary method (IBM) recently developed by Breugem (2012) [19] is adopted in the present method, development including the retraction technique, the multi-direct forcing method and the direct account of the inertia of the fluid contained within the particles. The present IB-LBM is, however, formulated with further improvement with the implementation of the high-order Runge–Kutta schemes in the coupled fluid–particle interaction. The major challenge to implement high-order Runge–Kutta schemes in the LBM is that the flow information such as density and velocity cannot be directly obtained at a fractional time step from the LBM since the LBM only provides the flow information at an integer time step. This challenge can be, however, overcome as given in the present IB-LBM by extrapolating the flow field around particles from the known flow field at the previous integer time step. The newly calculated fluid–particle interactions from the previous fractional time steps of the current integer time step are also accounted for in the extrapolation. The IB-LBM with high-order Runge–Kutta schemes developed in this study is validated by several benchmark applications. It is demonstrated, for the first time, that the IB-LBM has the capacity to resolve the translational and rotational motion of particles with the second-order accuracy. The optimal retraction distances for spheres and tubes that help the method achieve the second-order accuracy are found to be around 0.30 and −0.47 times of the lattice spacing, respectively. Simulations of the Stokes flow through a simple cubic lattice of rotational spheres indicate that the lift force produced by the Magnus effect can be very significant in view of the magnitude of the drag force when the practical rotating speed of the spheres is encountered
NASA Astrophysics Data System (ADS)
Liu, Nansheng; Khomami, Bamin
2011-11-01
Despite tremendous progress in development of numerical techniques and constitutive theories for polymeric fluids in the past decade, Direct Numerical Simulation (DNS) of elastic turbulence has posed tremendous challenges to researchers engaged in developing first principles models and simulations that can accurately and robustly predict the dynamical behavior of polymeric flows. In this presentation, we report the first DNS of elastic turbulence in the Taylor-Couette (TC) flow. Specifically, our computations with prototypical constitutive equations for dilute polymeric solutions, such as the FENE-P model are capable of reproducing the essential features of the experimentally observed elastic turbulence in TC flow of this class of fluids, namely, randomly fluctuating fluid motion excited in a broad range of spatial and temporal scales, and a significant increase of the flow resistance. Moreover, the experimentally measured Power Spectral Density of radial velocity fluctuations, i.e., two contiguous regions of power-law decay, -1.1 at lower frequencies and -2.2 at high-frequencies is accurately computed. We would like to thank NSF through grant CBET-0755269 and NSFC through grant NO. 10972211 for supporting of this work.
NASA Astrophysics Data System (ADS)
Katamine, Eiji; Kanai, Ryoma
2015-11-01
This paper presents a numerical solution to shape identification problem of steady-state viscous flow fields. In this study, a shape identification problem is formulated for flow velocity distribution prescribed problem, while the total dissipated energy is constrained to less than a desired value, in the viscous flow field. The square error integral between the actual flow velocity distributions and the prescribed flow velocity distributions in the prescribed sub-domains is used as the objective functional. Shape gradient of the shape identification problem is derived theoretically using the Lagrange multiplier method, adjoint variable method, and the formulae of the material derivative. Reshaping is carried out by the traction method proposed as an approach to solving shape optimization problems. The validity of proposed method is confirmed by results of 2D numerical analysis.
Ma, Rui; Zheng, Chunmiao; Tonkin, Matt; Zachara, John M
2011-04-01
Correct interpretation of tracer test data is critical for understanding transport processes in the subsurface. This task can be greatly complicated by the presence of intraborehole flows in a highly dynamic flow environment. At a new tracer test site (Hanford IFRC) a dynamic flow field created by changes in the stage of the adjacent Columbia River, coupled with a heterogeneous hydraulic conductivity distribution, leads to considerable variations in vertical hydraulic gradients. These variations, in turn, create intraborehole flows in fully-screened (6.5m) observation wells with frequently alternating upward and downward movement. This phenomenon, in conjunction with a highly permeable aquifer formation and small horizontal hydraulic gradients, makes modeling analysis and model calibration a formidable challenge. Groundwater head data alone were insufficient to define the flow model boundary conditions, and the movement of the tracer was highly sensitive to the dynamics of the flow field. This study shows that model calibration can be significantly improved by explicitly considering (a) dynamic flow model boundary conditions and (b) intraborehole flow. The findings from this study underscore the difficulties in interpreting tracer tests and understanding solute transport under highly dynamic flow conditions. PMID:21216023
Ma, Rui; Zheng, Chunmiao; Tonkin, Matthew J.; Zachara, John M.
2011-04-01
Correct interpretation of tracer test data is critical for understanding transport processes in the subsurface. This task can be greatly complicated by the presence of intraborehole flows in a highly dynamic flow environment. At a new tracer test site (Hanford IFRC) a dynamic flow field created by changes in the stage of the adjacent Columbia River, coupled with a heterogeneous hydraulic conductivity distribution, leads to considerable variations in vertical hydraulic gradients. These variations, in turn, create intraborehole flows in fully-screened (6.5 m) observation wells with frequently alternating upward and downward movement. This phenomenon, in conjunction with a highly permeable aquifer formation and small horizontal hydraulic gradients, makes modeling analysis and model calibration a formidable challenge. Groundwater head data alone were insufficient to define the flow model boundary conditions, and the movement of the tracer was highly sensitive to the dynamics of the flow field. This study shows that model calibration can be significantly improved by explicitly considering (a) dynamic flow model boundary conditions and (b) intraborehole flow. The findings from this study underscore the difficulties in interpreting tracer tests and understanding solute transport under highly dynamic flow conditions.
NASA Technical Reports Server (NTRS)
Duque, Earl P. N.; Biswas, Rupak; Strawn, Roger C.
1995-01-01
This paper summarizes a method that solves both the three dimensional thin-layer Navier-Stokes equations and the Euler equations using overset structured and solution adaptive unstructured grids with applications to helicopter rotor flowfields. The overset structured grids use an implicit finite-difference method to solve the thin-layer Navier-Stokes/Euler equations while the unstructured grid uses an explicit finite-volume method to solve the Euler equations. Solutions on a helicopter rotor in hover show the ability to accurately convect the rotor wake. However, isotropic subdivision of the tetrahedral mesh rapidly increases the overall problem size.
NASA Astrophysics Data System (ADS)
Sakai, Yasumasa; Taki, Hirofumi; Kanai, Hiroshi
2016-07-01
In our previous study, the viscoelasticity of the radial artery wall was estimated to diagnose endothelial dysfunction using a high-frequency (22 MHz) ultrasound device. In the present study, we employed a commercial ultrasound device (7.5 MHz) and estimated the viscoelasticity using arterial pressure and diameter, both of which were measured at the same position. In a phantom experiment, the proposed method successfully estimated the elasticity and viscosity of the phantom with errors of 1.8 and 30.3%, respectively. In an in vivo measurement, the transient change in the viscoelasticity was measured for three healthy subjects during flow-mediated dilation (FMD). The proposed method revealed the softening of the arterial wall originating from the FMD reaction within 100 s after avascularization. These results indicate the high performance of the proposed method in evaluating vascular endothelial function just after avascularization, where the function is difficult to be estimated by a conventional FMD measurement.
NASA Astrophysics Data System (ADS)
Messaris, Gerasimos A. T.; Hadjinicolaou, Maria; Karahalios, George T.
2016-08-01
The present work is motivated by the fact that blood flow in the aorta and the main arteries is governed by large finite values of the Womersley number α and for such values of α there is not any analytical solution in the literature. The existing numerical solutions, although accurate, give limited information about the factors that affect the flow, whereas an analytical approach has an advantage in that it can provide physical insight to the flow mechanism. Having this in mind, we seek analytical solution to the equations of the fluid flow driven by a sinusoidal pressure gradient in a slightly curved pipe of circular cross section when the Womersley number varies from small finite to infinite values. Initially the equations of motion are expanded in terms of the curvature ratio δ and the resulting linearized equations are solved analytically in two ways. In the first, we match the solution for the main core to that for the Stokes boundary layer. This solution is valid for very large values of α. In the second, we derive a straightforward single solution valid to the entire flow region and for 8 ≤ α < ∞, a range which includes the values of α that refer to the physiological flows. Each solution contains expressions for the axial velocity, the stream function, and the wall stresses and is compared to the analogous forms presented in other studies. The two solutions give identical results to each other regarding the axial flow but differ in the secondary flow and the circumferential wall stress, due to the approximations employed in the matched asymptotic expansion process. The results on the stream function from the second solution are in agreement with analogous results from other numerical solutions. The second solution predicts that the atherosclerotic plaques may develop in any location around the cross section of the aortic wall unlike to the prescribed locations predicted by the first solution. In addition, it gives circumferential wall stresses
TRIM—3D: a three-dimensional model for accurate simulation of shallow water flow
Casulli, Vincenzo; Bertolazzi, Enrico; Cheng, Ralph T.
1993-01-01
A semi-implicit finite difference formulation for the numerical solution of three-dimensional tidal circulation is discussed. The governing equations are the three-dimensional Reynolds equations in which the pressure is assumed to be hydrostatic. A minimal degree of implicitness has been introduced in the finite difference formula so that the resulting algorithm permits the use of large time steps at a minimal computational cost. This formulation includes the simulation of flooding and drying of tidal flats, and is fully vectorizable for an efficient implementation on modern vector computers. The high computational efficiency of this method has made it possible to provide the fine details of circulation structure in complex regions that previous studies were unable to obtain. For proper interpretation of the model results suitable interactive graphics is also an essential tool.
A second-order accurate kinetic-theory-based method for inviscid compressible flows
NASA Technical Reports Server (NTRS)
Deshpande, Suresh M.
1986-01-01
An upwind method for the numerical solution of the Euler equations is presented. This method, called the kinetic numerical method (KNM), is based on the fact that the Euler equations are moments of the Boltzmann equation of the kinetic theory of gases when the distribution function is Maxwellian. The KNM consists of two phases, the convection phase and the collision phase. The method is unconditionally stable and explicit. It is highly vectorizable and can be easily made total variation diminishing for the distribution function by a suitable choice of the interpolation strategy. The method is applied to a one-dimensional shock-propagation problem and to a two-dimensional shock-reflection problem.
NASA Astrophysics Data System (ADS)
Xu, Li; Weng, Peifen
2014-02-01
An improved fifth-order weighted essentially non-oscillatory (WENO-Z) scheme combined with the moving overset grid technique has been developed to compute unsteady compressible viscous flows on the helicopter rotor in forward flight. In order to enforce periodic rotation and pitching of the rotor and relative motion between rotor blades, the moving overset grid technique is extended, where a special judgement standard is presented near the odd surface of the blade grid during search donor cells by using the Inverse Map method. The WENO-Z scheme is adopted for reconstructing left and right state values with the Roe Riemann solver updating the inviscid fluxes and compared with the monotone upwind scheme for scalar conservation laws (MUSCL) and the classical WENO scheme. Since the WENO schemes require a six point stencil to build the fifth-order flux, the method of three layers of fringes for hole boundaries and artificial external boundaries is proposed to carry out flow information exchange between chimera grids. The time advance on the unsteady solution is performed by the full implicit dual time stepping method with Newton type LU-SGS subiteration, where the solutions of pseudo steady computation are as the initial fields of the unsteady flow computation. Numerical results on non-variable pitch rotor and periodic variable pitch rotor in forward flight reveal that the approach can effectively capture vortex wake with low dissipation and reach periodic solutions very soon.
Lie group analysis and similarity solution for fractional Blasius flow
NASA Astrophysics Data System (ADS)
Pan, Mingyang; Zheng, Liancun; Liu, Fawang; Zhang, Xinxin
2016-08-01
This paper presents an investigation for boundary layer flow of viscoelastic fluids past a flat plate. Fractional-order Blasius equation with spatial fractional Riemann-Liouville derivative is derived firstly by using Lie group transformation. The solution is obtained numerically by the generalized shooting method, employing the shifted Grünwald formula and classical fourth order Runge-Kutta method as the iterative scheme. The effects of the order of fractional derivative and the generalized Reynolds number on the velocity profiles are analyzed and discussed. Numerical results show that the smaller the value of the fractional order derivative leads to the faster velocity of viscoelastic fluids near the plate but not to hold near the outer flow. As the Reynolds number increases, the fluid is moving faster in the whole boundary layer consistently.
Numerical solution of periodic vortical flows about a thin airfoil
NASA Technical Reports Server (NTRS)
Scott, James R.; Atassi, Hafiz M.
1989-01-01
A numerical method is developed for computing periodic, three-dimensional, vortical flows around isolated airfoils. The unsteady velocity is split into a vortical component which is a known function of the upstream flow conditions and the Lagrangian coordinates of the mean flow, and an irrotational field whose potential satisfies a nonconstant-coefficient, inhomogeneous, convective wave equation. Solutions for thin airfoils at zero degrees incidence to the mean flow are presented in this paper. Using an elliptic coordinate transformation, the computational domain is transformed into a rectangle. The Sommerfeld radiation condition is applied to the unsteady pressure on the grid line corresponding to the far field boundary. The results are compared with a Possio solver, and it is shown that for maximum accuracy the grid should depend on both the Mach number and reduced frequency. Finally, in order to assess the range of validity of the classical thin airfoil approximation, results for airfoils with zero thickness are compared with results for airfoils with small thickness.
Fluid flow and solute segregation in EFG crystal growth process
NASA Astrophysics Data System (ADS)
Bunoiu, O.; Nicoara, I.; Santailler, J. L.; Duffar, T.
2005-02-01
The influence of the die geometry and various growth conditions on the fluid flow and on the solute distribution in EFG method has been studied using numerical simulation. The commercial FIDAP software has been used in order to solve the momentum and mass transfer equations in the capillary channel and in the melt meniscus. Two types of shaper design are studied and the results are in good agreement with the void distribution observed in rod-shaped sapphire crystals grown by the EFG method in the various configurations.
New discretization and solution techniques for incompressible viscous flow problems
NASA Technical Reports Server (NTRS)
Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.
1983-01-01
Several topics arising in the finite element solution of the incompressible Navier-Stokes equations are considered. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. The role of artificial viscosity in viscous flow calculations is studied, emphasizing work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some modifications are mentioned.
New discretization and solution techniques for incompressible viscous flow problems
NASA Technical Reports Server (NTRS)
Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.
1983-01-01
This paper considers several topics arising in the finite element solution of the incompressible Navier-Stokes equations. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. Following this, the role of artificial viscosity in viscous flow calculations is studied, emphasizing recent work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some recent modifications are mentioned.
Preferential flow and segregation of porewater solutes in Wetland sediment
Harvey, J.W.; Chambers, R.M.; Hoelscher, J.R.
1995-01-01
Sediment macropores (with effective diameters larger than 100 ??m) comprise 11% of the bulk sediment volume in a tidal freshwater wetland vegetated with Peltandra virginica. In order to determine effects of macroporous sediment structure on solute transport, we conducted a solute tracer experiment in the sediment. The effective transport volume (??eff, the volume of sediment through which solute was transported normalized to sediment bulk volume) was 0.15 cm3 cm-3, which is considerably smaller than the total pore space that is potentially available for transport (porosity of sediment is 0.63 cm3 cm-3). A mean transport time of 13 d was required to flush preferential flow paths in Peltandra hummocks; hydrologic turnover of the volumetrically dominant matrix pores (0.53 cm3 cm-3) was apparently much slower. Based on porewater sampler design and hydrological principles, we suggest that N2-purged tension solution samplers and diffusion equilibrators preferentially sample porewater from macropore and matrix domains, respectively. Dissolved ammonium and orthophosphate concentrations were three-fold higher in matrix pores compared to macropores, which is consistent with our finding that more rapid hydrological flushing occurred in macropores compared to matrix pores. Further evaluation of porewater sampler designs in macroporous sediment is needed to improve studies of hydrologic transport and biogeochemical cycling in wetlands. ?? 1995 Estuarine Research Federation.
RELATIVISTIC GLOBAL SOLUTIONS OF NEUTRINO-DOMINATED ACCRETION FLOWS
Xue Li; Liu Tong; Gu Weimin; Lu Jufu
2013-08-15
Neutrino-dominated accretion flows (NDAFs) around rotating stellar-mass black holes are plausible candidates for the central engines of gamma-ray bursts (GRBs). We investigate one-dimensional global solutions of NDAFs, taking into account general relativity in the Kerr metric, neutrino physics, and nucleosynthesis more precisely than previous works. We calculate 16 solutions with different characterized accretion rates and black hole spins to exhibit the radial distributions of various physical properties in NDAFs. We confirm that the electron degeneracy has important effects in NDAFs and we find that the electron fraction is about 0.46 in the outer region for all 16 solutions. From the perspective of the mass fraction, free nucleons, {sup 4}He, and {sup 5}6Fe dominate in the inner, middle, and outer regions, respectively. The influence of neutrino trapping on the annihilation is of importance for the superhigh accretion ( M-dot =10 M{sub sun} s{sup -1}) and most of the 16 solutions have an adequate annihilation luminosity for GRBs.
Solution of the complete Curtiss-Bird model for polymeric liquids subjected to simple shear flow.
Stephanou, Pavlos S; Kröger, Martin
2016-03-28
The complete kinetic theory model for concentrated polymer solutions and melts proposed by Curtiss and Bird is solved for shear flow: (a) analytically by providing a solution for the single-link (or configurational) distribution function as a real basis spherical harmonics expansion and then calculating the materials functions in shear flow up to second order in the dimensionless shear rate and, (b) numerically via the execution of Brownian dynamics simulations. These two methods are actually complementary to each other as the former is accurate only for small dimensionless shear rates where the latter produces results with increasingly large uncertainties. The analytical expansions of the material functions with respect to the dimensionless shear rate reduce to those of the extensively studied, simplified Curtiss-Bird model when ε' = 0, and to the rigid rod when ε' = 1. It is known that the power-law behavior at high shear rates is very different for these two extremal cases. We employ Brownian dynamics simulation to not only recover the limiting cases but to find a gradual variation of the power-law behaviors at large dimensionless shear rates upon varying ε'. The fact that experimental data are usually located between these two extremes strongly advocates the significance of studying the solution of the Curtiss-Bird model. This is exemplified in this work by comparing the solution of this model with available rheological data for semiflexible biological systems that are clearly not captured by the original Doi-Edwards or simplified Curtiss-Bird models. PMID:27036477
NASA Astrophysics Data System (ADS)
Mathias, Simon A.; Moutsopoulos, Konstantinos N.
2016-07-01
Understanding the hydraulics around injection and production wells in unconfined aquifers associated with rainwater and reclaimed water aquifer storage schemes is an issue of increasing importance. Much work has been done previously to understand the mathematics associated with Darcy's law in this context. However, groundwater flow velocities around injection and production wells are likely to be sufficiently large such as to induce significant non-Darcy effects. This article presents a mathematical analysis to look at Forchheimer's equation in the context of water injection and water production in unconfined aquifers. Three different approximate solutions are derived using quasi-steady-state assumptions and the method of matched asymptotic expansion. The resulting approximate solutions are shown to be accurate for a wide range of practical scenarios by comparison with a finite difference solution to the full problem of concern. The approximate solutions have led to an improved understanding of the flow dynamics. They can also be used as verification tools for future numerical models in this context.
Tranchida, Peter Quinto; Purcaro, Giorgia; Sciarrone, Danilo; Dugo, Paola; Dugo, Giovanni; Mondello, Luigi
2010-09-01
In the present research, a split-flow comprehensive 2-D GC-quadrupole MS (qMS) method was developed using: a primary apolar 30 m×0.25 mm id×0.25 μm d(f) capillary linked, via a T-union, to a secondary polar 1.0 m×0.05 mm id×0.05 μm d(f) capillary and to a 0.10 m×0.05 mm id×0.05 μm d(f) uncoated column segment. The GC×GC-qMS instrument was equipped with two GC ovens and a loop-type modulator. The polar column was connected to the MS, whereas the uncoated column directed most of the first-dimension effluent to waste and enabled the generation of optimum gas velocities in both dimensions, namely circa 20 and 80 cm/s in the first and second dimensions, respectively. The rapid-scanning qMS was operated at a scan speed of 10,000 amu/s, a 25-Hz data acquisition frequency (scan time+interscan time: 40 ms), and with a normal GC mass range (m/z 40-360). Chromatography bands at the second-dimension outlet were never less than 360 ms wide (6σ), enabling the acquisition of at least 10 spectra/peak.
NASA Technical Reports Server (NTRS)
Chang, Chau-Lyan; Venkatachari, Balaji Shankar; Cheng, Gary
2013-01-01
With the wide availability of affordable multiple-core parallel supercomputers, next generation numerical simulations of flow physics are being focused on unsteady computations for problems involving multiple time scales and multiple physics. These simulations require higher solution accuracy than most algorithms and computational fluid dynamics codes currently available. This paper focuses on the developmental effort for high-fidelity multi-dimensional, unstructured-mesh flow solvers using the space-time conservation element, solution element (CESE) framework. Two approaches have been investigated in this research in order to provide high-accuracy, cross-cutting numerical simulations for a variety of flow regimes: 1) time-accurate local time stepping and 2) highorder CESE method. The first approach utilizes consistent numerical formulations in the space-time flux integration to preserve temporal conservation across the cells with different marching time steps. Such approach relieves the stringent time step constraint associated with the smallest time step in the computational domain while preserving temporal accuracy for all the cells. For flows involving multiple scales, both numerical accuracy and efficiency can be significantly enhanced. The second approach extends the current CESE solver to higher-order accuracy. Unlike other existing explicit high-order methods for unstructured meshes, the CESE framework maintains a CFL condition of one for arbitrarily high-order formulations while retaining the same compact stencil as its second-order counterpart. For large-scale unsteady computations, this feature substantially enhances numerical efficiency. Numerical formulations and validations using benchmark problems are discussed in this paper along with realistic examples.
Numerical solution of transonic wing flows using an Euler/Navier-Stokes zonal approach
NASA Technical Reports Server (NTRS)
Holst, T. L.; Gundy, K. L.; Thomas, S. D.; Chaderjian, N. M.; Flores, J.
1985-01-01
Transonic flow fields about wing geometries are computed using an Euler/Navier-Stokes approach in which the flow field is divided into several zones. The grid zones immediately adjacent to the wing surface are suitably clustered and solved with the Navier-Stokes equations. Grid zones removed from the wing are less finely clustered and are solved with the Euler equations. Wind tunnel wall effects are easily and accurately modeled with the new grid-zoning algorithm because the wind tunnel grid is constructed as an exact subset of the corresponding free-air grid. Solutions are obtained that are in good agreement with experiment, including cases with significant wind tunnel wall effects and shock-induced separation on the upper wing surface.
Numerical Solutions of Supersonic and Hypersonic Laminar Compression Corner Flows
NASA Technical Reports Server (NTRS)
Hung, C. M.; MacCormack, R. W.
1976-01-01
An efficient time-splitting, second-order accurate, numerical scheme is used to solve the complete Navier-Stokes equations for supersonic and hypersonic laminar flow over a two-dimensional compression corner. A fine, exponentially stretched mesh spacing is used in the region near the wall for resolving the viscous layer. Good agreement is obtained between the present computed results and experimental measurement for a Mach number of 14.1 and a Reynolds number of 1.04 x 10(exp 5) with wedge angles of 15 deg, 18 deg, and 24 deg. The details of the pressure variation across the boundary layer are given, and a correlation between the leading edge shock and the peaks in surface pressure and heat transfer is observed.
Accurate calculation of Stokes drag for point-particle tracking in two-way coupled flows
NASA Astrophysics Data System (ADS)
Horwitz, J. A. K.; Mani, A.
2016-08-01
In this work, we propose and test a method for calculating Stokes drag applicable to particle-laden fluid flows where two-way momentum coupling is important. In the point-particle formulation, particle dynamics are coupled to fluid dynamics via a source term that appears in the respective momentum equations. When the particle Reynolds number is small and the particle diameter is smaller than the fluid scales, it is common to approximate the momentum coupling source term as the Stokes drag. The Stokes drag force depends on the difference between the undisturbed fluid velocity evaluated at the particle location, and the particle velocity. However, owing to two-way coupling, the fluid velocity is modified in the neighborhood of a particle, relative to its undisturbed value. This causes the computed Stokes drag force to be underestimated in two-way coupled point-particle simulations. We develop estimates for the drag force error as function of the particle size relative to the grid size. Because the disturbance field created by the particle contaminates the surrounding fluid, correctly calculating the drag force cannot be done solely by direct interpolation of the fluid velocity. Instead, we develop a correction method that calculates the undisturbed fluid velocity from the computed disturbed velocity field by adding an estimate of the velocity disturbance created by the particle. The correction scheme is tested for a particle settling in an otherwise quiescent fluid and is found to reduce the error in computed settling velocity by an order of magnitude compared with common interpolation schemes.
Caruso, Carlo; Burriesci, Matthew S.; Cella, Kristen; Pringle, John R.
2015-01-01
In studies of both the establishment and breakdown of cnidarian-dinoflagellate symbiosis, it is often necessary to determine the number of Symbiodinium cells relative to the quantity of host tissue. Ideally, the methods used should be rapid, precise, and accurate. In this study, we systematically evaluated methods for sample preparation and storage and the counting of algal cells using the hemocytometer, a custom image-analysis program for automated counting of the fluorescent algal cells, the Coulter Counter, or the Millipore Guava flow-cytometer. We found that although other methods may have value in particular applications, for most purposes, the Guava flow cytometer provided by far the best combination of precision, accuracy, and efficient use of investigator time (due to the instrument's automated sample handling), while also allowing counts of algal numbers over a wide range and in small volumes of tissue homogenate. We also found that either of two assays of total homogenate protein provided a precise and seemingly accurate basis for normalization of algal counts to the total amount of holobiont tissue. PMID:26291447
Krediet, Cory J; DeNofrio, Jan C; Caruso, Carlo; Burriesci, Matthew S; Cella, Kristen; Pringle, John R
2015-01-01
In studies of both the establishment and breakdown of cnidarian-dinoflagellate symbiosis, it is often necessary to determine the number of Symbiodinium cells relative to the quantity of host tissue. Ideally, the methods used should be rapid, precise, and accurate. In this study, we systematically evaluated methods for sample preparation and storage and the counting of algal cells using the hemocytometer, a custom image-analysis program for automated counting of the fluorescent algal cells, the Coulter Counter, or the Millipore Guava flow-cytometer. We found that although other methods may have value in particular applications, for most purposes, the Guava flow cytometer provided by far the best combination of precision, accuracy, and efficient use of investigator time (due to the instrument's automated sample handling), while also allowing counts of algal numbers over a wide range and in small volumes of tissue homogenate. We also found that either of two assays of total homogenate protein provided a precise and seemingly accurate basis for normalization of algal counts to the total amount of holobiont tissue. PMID:26291447
Parabolized Navier-Stokes solutions of separation and trailing-edge flows
NASA Technical Reports Server (NTRS)
Brown, J. L.
1983-01-01
A robust, iterative solution procedure is presented for the parabolized Navier-Stokes or higher order boundary layer equations as applied to subsonic viscous-inviscid interaction flows. The robustness of the present procedure is due, in part, to an improved algorithmic formulation. The present formulation is based on a reinterpretation of stability requirements for this class of algorithms and requires only second order accurate backward or central differences for all streamwise derivatives. Upstream influence is provided for through the algorithmic formulation and iterative sweeps in x. The primary contribution to robustness, however, is the boundary condition treatment, which imposes global constraints to control the convergence path. Discussed are successful calculations of subsonic, strong viscous-inviscid interactions, including separation. These results are consistent with Navier-Stokes solutions and triple deck theory.
Sun, Fang; Ella-Menye, Jean-Rene; Galvan, Daniel David; Bai, Tao; Hung, Hsiang-Chieh; Chou, Ying-Nien; Zhang, Peng; Jiang, Shaoyi; Yu, Qiuming
2015-03-24
Reliable surface-enhanced Raman scattering (SERS) based biosensing in complex media is impeded by nonspecific protein adsorptions. Because of the near-field effect of SERS, it is challenging to modify SERS-active substrates using conventional nonfouling materials without introducing interference from their SERS signals. Herein, we report a stealth surface modification strategy for sensitive, specific and accurate detection of fructose in protein solutions using SERS by forming a mixed self-assembled monolayer (SAM). The SAM consists of a short zwitterionic thiol, N,N-dimethyl-cysteamine-carboxybetaine (CBT), and a fructose probe 4-mercaptophenylboronic acid (4-MPBA). The specifically designed and synthesized CBT not only resists protein fouling effectively, but also has very weak Raman activity compared to 4-MPBA. Thus, the CBT SAM provides a stealth surface modification to SERS-active substrates. The surface compositions of mixed SAMs were investigated using X-ray photoelectron spectroscopy (XPS) and SERS, and their nonfouling properties were studied with a surface plasmon resonance (SPR) biosensor. The mixed SAM with a surface composition of 94% CBT demonstrated a very low bovine serum albumin (BSA) adsorption (∼3 ng/cm(2)), and moreover, only the 4-MPBA signal appeared in the SERS spectrum. With the use of this surface-modified SERS-active substrate, quantification of fructose over clinically relevant concentrations (0.01-1 mM) was achieved. Partial least-squares regression (PLS) analysis showed that the detection sensitivity and accuracy were maintained for the measurements in 1 mg/mL BSA solutions. This stealth surface modification strategy provides a novel route to introduce nonfouling property to SERS-active substrates for SERS biosensing in complex media.
Invariant solutions organizing turbulence in pipe flow experiments
NASA Astrophysics Data System (ADS)
Altmeyer, Sebastian; Kühnen, Jakob; Schaner, Markus; Hof, Björn
2015-11-01
A large number of unstable invariant solutions, e.g. traveling waves (TWs) or (relative-) periodic orbits, has been discovered and numerically studied in recent years for pipe flow. The proposed role of such states as building blocks of turbulence is however less clear and so far only limited experimental evidence has been provided. In experiments we used a modulated pipe segment to impose a certain symmetry on the experimental velocity field and in the non-modulated downstream pipe traveling waves could be observed persisting for many wavelengths. Measured velocity fields (PIV) were used as initial conditions for a numerical Newton search and converged to the exact invariant traveling wave solutions. All the experimentally observed TW's correspond to lower branch states that are close to the laminar turbulent boundary (edge). Correspondingly in the experiments as the waves proceeded downstream flows would typically relaminarize but occasionally the TW's would grow to turbulence. The latter observation confirms the relevance of these invariant states for the transition process.
Implicit Multigrid Solutions for Compressible Flows in Complex Geometries.
NASA Astrophysics Data System (ADS)
Wang, Lixia
Two implicit multigrid algorithms for the two and three dimensional compressible Euler equations have been developed in this dissertation. First, a diagonal implicit multigrid method is developed for solving a finite-volume approximation to the Euler equations in which the dependent variables are stored at the cell vertices. The spatial derivatives in the two dimensional Euler equations are approximated using a conservative cell-vertex finite volume formulation. Artificial dissipation is provided by adding an adaptive blend of second and fourth differences of the solution to maintain stability and accuracy. A Diagonal Alternating Directional Implicit method is used to advance the solution in time. Rapid convergence to a steady-state solution is achieved with local time stepping and the multigrid algorithm. Results for the transonic flow past the NACA 0012 airfoil are presented to verify the accuracy and efficiency of the scheme. Second, the development of an efficient and flexible multiblock/multigrid Euler solver and its application to realistic engineering problems are presented. A cell-centered finite volume method with a multigrid implementation of the Diagonal Alternating Direction Implicit algorithm is used to solve the Euler equations. A fully conservative inter-block boundary condition, which permits the passage of discontinuities across block boundaries with minimum distortion of the solution, is developed for cases in which the grid lines at the inter-block boundaries can be completely continuous or discontinuous. Information is exchanged between blocks by using surface arrays, which contain all the data needed to update the inter-block boundary conditions. Results demonstrate the feasibility of using the present multi -block/multigrid approach to solve flow problems involving complex geometries. Two dimensional results for several types of grids and various free stream conditions have been presented to verify the accuracy and computational efficiency of
Implicit multigrid solutions for compressible flows in complex geometries
NASA Astrophysics Data System (ADS)
Wang, Lixia
Two implicit multigrid algorithms for the two and three dimensional compressible Euler equations are developed. First, a diagonal implicit multigrid method is developed for solving a finite-volume approximation to the Euler equations in which the dependent variables are stored at the cell vertices. The spatial derivatives in the two dimensional Euler equations are approximated using a conservative cell-vertex finite volume formulation. Artificial dissipation is provided by adding an adaptive blend of second and fourth differences of the solution to maintain stability and accuracy. A diagonal alternating directional implicit method is used to advance the solution in time. Rapid convergence to a steady-state solution is achieved with local time stepping and the multigrid algorithm. Results for the transonic flow past the NACA 0012 airfoil are presented to verify the accuracy and efficiency of the scheme. Second, the development of an efficient and flexible multiblock/multigrid Euler solver and its application to realistic engineering problems are presented. A cell-centered finite volume method with a multigrid implementation of the diagonal alternating direction implicit algorithm is used to solve the Euler equations. A fully conservative interblock boundary condition, which permits the passage of discontinuities across block boundaries with minimum distortion of the solution, is developed for cases in which the grid lines at the interblock boundaries can be completely continuous or discontinuous. Information is exchanged between blocks by using surface arrays, which contain all the data needed to update the interblock boundary conditions. Results demonstrate the feasibility of using the present multiblock/multigrid approach to solve flow problems involving complex geometries. Two dimensional results for several types of grids and various free stream conditions have been presented to verify the accuracy and computational efficiency of the method. The application of
The use of wavelet transforms in the solution of two-phase flow problems
Moridis, G.J.; Nikolaou, M.; You, Yong
1994-10-01
In this paper we present the use of wavelets to solve the nonlinear Partial Differential.Equation (PDE) of two-phase flow in one dimension. The wavelet transforms allow a drastically different approach in the discretization of space. In contrast to the traditional trigonometric basis functions, wavelets approximate a function not by cancellation but by placement of wavelets at appropriate locations. When an abrupt chance, such as a shock wave or a spike, occurs in a function, only local coefficients in a wavelet approximation will be affected. The unique feature of wavelets is their Multi-Resolution Analysis (MRA) property, which allows seamless investigational any spatial resolution. The use of wavelets is tested in the solution of the one-dimensional Buckley-Leverett problem against analytical solutions and solutions obtained from standard numerical models. Two classes of wavelet bases (Daubechies and Chui-Wang) and two methods (Galerkin and collocation) are investigated. We determine that the Chui-Wang, wavelets and a collocation method provide the optimum wavelet solution for this type of problem. Increasing the resolution level improves the accuracy of the solution, but the order of the basis function seems to be far less important. Our results indicate that wavelet transforms are an effective and accurate method which does not suffer from oscillations or numerical smearing in the presence of steep fronts.
Precise and accurate measurement of U and Th isotopes via ICP-MS using a single solution
NASA Astrophysics Data System (ADS)
Mertz-Kraus, R.; Sharp, W. D.; Ludwig, K. R.
2012-04-01
, allowing the sample's 238U/235U ratio to be measured. In step 3, we monitor peak-tails at half-mass positions (229.5, 231.5, 234.5) and on mass 237 while aspirating sample solution. Tail measurement requires a distinct cup configuration to maintain 238U in the cups; however, no sample is consumed during automated cup reconfiguration. We monitor the accuracy of 234U/238U ratios using CRM 145, which gives a weighted mean atom ratio of (5.2846 ± 0.0029) - 10-5 (all errors 2σ), consistent with published and reference values. The reproducibility of 230Th/238U ratios is monitored using the Schwartzwalder Mine secular-equilibrium standard (SM). We detect no bias in 230Th/238U or 234U/238U ratios measured for SM at beam intensities ranging over a factor of four, consistent with accurate correction for IC yields. Aladdin's cave coral (AC-1) was analyzed to check our ICP-MS method (and the preceding purification by ion exchange) on a carbonate and yields a mean age of 125.43 ± 0.38 ka, in agreement with published values. We are currently applying the method to corals, speleothems, pedogenic coatings, and tufas.
Hiruta, Yoshiki; Toh, Sadayoshi
2015-12-01
Two-dimensional Kolmogorov flow in wide periodic boxes is numerically investigated. It is shown that the total flow rate in the direction perpendicular to the force controls the characteristics of the flow, especially the existence of spatially localized solitary solutions such as traveling waves, periodic solutions, and chaotic solutions, which can behave as elementary components of the flow. We propose a procedure to construct approximate solutions consisting of solitary solutions. It is confirmed by direct numerical simulations that these solutions are stable and represent interactions between elementary components such as collisions, coexistence, and collapse of chaos.
NASA Technical Reports Server (NTRS)
Constantinescu, George S.; Lele, S. K.
2001-01-01
Numerical methods for solving the flow equations in cylindrical or spherical coordinates should be able to capture the behavior of the exact solution near the regions where the particular form of the governing equations is singular. In this work we focus on the treatment of these numerical singularities for finite-differences methods by reinterpreting the regularity conditions developed in the context of pseudo-spectral methods. A generally applicable numerical method for treating the singularities present at the polar axis, when nonaxisymmetric flows are solved in cylindrical, coordinates using highly accurate finite differences schemes (e.g., Pade schemes) on non-staggered grids, is presented. Governing equations for the flow at the polar axis are derived using series expansions near r=0. The only information needed to calculate the coefficients in these equations are the values of the flow variables and their radial derivatives at the previous iteration (or time) level. These derivatives, which are multi-valued at the polar axis, are calculated without dropping the accuracy of the numerical method using a mapping of the flow domain from (0,R)*(0,2pi) to (-R,R)*(0,pi), where R is the radius of the computational domain. This allows the radial derivatives to be evaluated using high-order differencing schemes (e.g., compact schemes) at points located on the polar axis. The proposed technique is illustrated by results from simulations of laminar-forced jets and turbulent compressible jets using large eddy simulation (LES) methods. In term of the general robustness of the numerical method and smoothness of the solution close to the polar axis, the present results compare very favorably to similar calculations in which the equations are solved in Cartesian coordinates at the polar axis, or in which the singularity is removed by employing a staggered mesh in the radial direction without a mesh point at r=0, following the method proposed recently by Mohseni and Colonius
Better Strategies for Finite Element Solutions of Variable Viscosity Stokes Flow
NASA Astrophysics Data System (ADS)
Hasenclever, Jörg; Phipps Morgan, Jason; Shi, Chao
2010-05-01
Accurate numerical solution of variable viscosity Stokes Flow is one of the most important issues for better geodynamic understanding of mantle convection and mantle melting. While a good Stokes solver is usually an integral part of a good Navier-Stokes solver, typically Navier-Stokes equations are solved for flow of a fluid with uniform viscosity. The lumped-mass-matrix is an excellent and cheap preconditioner for uniform viscosity Stokes flow (cf. Maday and Patera, 1989), therefore for most applications to Navier-Stokes flow the ‘Stokes' part of the problem is viewed as well-resolved. Unfortunately, the inverse-viscosity-scaled lumped mass matrix does not work nearly as well to precondition Stokes flow in a fluid with strongly varying viscosity. This issue is already central to accurate numerical studies of convection in Earth's silicate-fluid mantle (May and Moresi, 2008; van Geenen et al., 2009; Burstedde et al., 2009) and may become central for researchers investigating Navier-Stokes problems with lateral variations in viscosity. Here we discuss several known computational hurdles to progress, and suggest strategies that offer promise in overcoming them. The choices for solving the discrete pressure equation arising from Stokes flow typically involve several tradeoffs between speed and storage requirements. In exact math, the discrete pressure matrix S is symmetric, so that it should be possible to use a symmetric preconditioned conjugate gradient (CG) Krylov algorithm instead of needing an asymmetric GMRES (cf. Saad, 2003) or GCR (Generalized Conjugate Residual, cf. Van der Vorst, 2003) that would require ~10-50 times more storage of past search directions. However, a CG-like method requires that the action of both S and any pressure preconditioner must be almost perfectly symmetric. This means that we must be very careful about the effects of roundoff in any iterative solver-based pressure preconditioner that may introduce numerically asymmetric operators
The development of solution algorithms for compressible flows
NASA Astrophysics Data System (ADS)
Slack, David Christopher
Three main topics were examined. The first is the development and comparison of time integration schemes on 2-D unstructured meshes. Both explicit and implicit solution grids are presented. Cell centered and cell vertex finite volume upwind schemes using Roe's approximate Riemann solver are developed. The second topic involves an interactive adaptive remeshing algorithm which uses a frontal grid generator and is compared to a single grid calculation. The final topic examined is the capabilities developed for a structured 3-D code called GASP. The capabilities include: generalized chemistry and thermodynamic modeling, space marching, memory management through the use of binary C I/O, and algebraic and two equation eddy viscosity turbulence modeling. Results are given for Mach 1.7 3-D analytic forebody, a Mach 1.38 axisymmetric nozzle with hydrogen-air combustion, a Mach 14.15 deg ramp, and Mach 0.3 viscous flow over a flat plate.
Real-time precision concentration measurement for flowing liquid solutions
NASA Astrophysics Data System (ADS)
Krishna, V.; Fan, C. H.; Longtin, J. P.
2000-10-01
The precise, real-time measurement of liquid concentration is important in fundamental research, chemical analysis, mixing processes, and manufacturing, e.g., in the food and semiconductor industries. This work presents a laser-based, noninvasive technique to measure concentration changes of flowing liquids in real time. The essential components in the system include a 5 mW laser diode coupled to a single-mode optical fiber, a triangular optical cell, and a high-resolution beam position sensor. The instrument provides a large range of concentration measurement, typically 0%-100% for binary liquid mixtures, while providing a resolution on the order of 0.05% concentration or better. The experimental configuration is small, reliable, and inexpensive. Results are presented for NaCl and MgCl2 aqueous solutions with concentrations ranging from 0% to 25%, with very good agreement found between measured and true concentrations.
Exact Integral Solutions for Two-Phase Flow
NASA Astrophysics Data System (ADS)
McWhorter, David B.; Sunada, Daniel K.
1990-03-01
Exact integral solutions for the horizontal, unsteady flow of two viscous, incompressible fluids are derived. Both one-dimensional and radial displacements are calculated with full consideration of capillary drive and for arbitrary capillary-hydraulic properties. One-dimensional, unidirectional displacement of a nonwetting phase is shown to occur increasingly like a shock front as the pore-size distribution becomes wider. This is in contrast to the situation when an inviscid nonwetting phase is displaced. The penetration of a nonwetting phase into porous media otherwise saturated by a wetting phase occurs in narrow, elongate distributions. Such distributions result in rapid and extensive penetration by the nonwetting phase. The process is remarkably sensitive to the capillary-hydraulic properties that determine the value of knw/kw at large wetting phase saturations, a region in which laboratory measurements provide the least resolution. The penetration of a nonwetting phase can be expected to be dramatically affected by the presence of fissures, worm holes, or other macropores. Calculations for radial displacement of a nonwetting phase resident at a small initial saturation show the displacement to be inefficient. The fractional flow of the nonwetting phase falls rapidly and, for a specific example, becomes 1% by the time one pore volume of water has been injected.
NASA Astrophysics Data System (ADS)
Gerke, K.
2012-04-01
Most dye staining experiments in natural soils result in highly heterogeneous flow patterns which are usually explained with presence of preferential flow paths or different kinds of flow instabilities. It is quite logic that soil structure is one of the main factors affecting infiltrations regimes, however the degree of flow stochasticity is not studied enough. In this contribution a substantial amount of large scale (2-4 m lateral excavations) field experiment data is considered (including forested hillslopes and agricultural fields) with special attention to sprinkling of two different staining substances with different dyeing mechanisms (common dye is visible both in adsorbed and in solution states; fluorescent dye - only in solution). The latter method allows an estimation of the flow stability (stochasticity). Most staining field experiments are supported by undisturbed sample collections (laboratory measurements for hydraulic conductivity, water retention curves, X-ray microtomography scans, grain size distributions, etc.). Preliminary results strongly support the evidence of stability of flow under similar precipitation and moisture conditions. Infiltration also correlated with soil structure and microproperties. Numerical modeling using classical approach (single-porosity coupled Richard's and advection-dispersion equations, random hydraulic properties based on log-normal experimentally obtained distribution) fails to describe experimentally obtained staining patterns. Multi-porosity models may provide better tools to account for different soil heterogeneities, but their parameters can not be obtained experimentally. Small scale solutions using pore-network or lattice-Botzmann methods based on microtomography scans are accurate, but computationally expensive (volumes around tens of cm3). Based on field observations a simple cellular automata approach to model staining patterns is developed and tested on experimental data. Our results are much better then
Intercomparison of 3D pore-scale flow and solute transport simulation methods
Mehmani, Yashar; Schoenherr, Martin; Pasquali, Andrea; Perkins, William A.; Kim, Kyungjoo; Perego, Mauro; Parks, Michael L.; Balhoff, Matthew T.; Richmond, Marshall C.; Geier, Martin; Krafczyk, Manfred; Luo, Li -Shi; Tartakovsky, Alexandre M.; Yang, Xiaofan; Scheibe, Timothy D.; Trask, Nathaniel
2015-09-28
Multiple numerical approaches have been developed to simulate porous media fluid flow and solute transport at the pore scale. These include 1) methods that explicitly model the three-dimensional geometry of pore spaces and 2) methods that conceptualize the pore space as a topologically consistent set of stylized pore bodies and pore throats. In previous work we validated a model of the first type, using computational fluid dynamics (CFD) codes employing a standard finite volume method (FVM), against magnetic resonance velocimetry (MRV) measurements of pore-scale velocities. Here we expand that validation to include additional models of the first type based on the lattice Boltzmann method (LBM) and smoothed particle hydrodynamics (SPH), as well as a model of the second type, a pore-network model (PNM). The PNM approach used in the current study was recently improved and demonstrated to accurately simulate solute transport in a two-dimensional experiment. While the PNM approach is computationally much less demanding than direct numerical simulation methods, the effect of conceptualizing complex three-dimensional pore geometries on solute transport in the manner of PNMs has not been fully determined. We apply all four approaches (FVM-based CFD, LBM, SPH and PNM) to simulate pore-scale velocity distributions and (for capable codes) nonreactive solute transport, and intercompare the model results. Comparisons are drawn both in terms of macroscopic variables (e.g., permeability, solute breakthrough curves) and microscopic variables (e.g., local velocities and concentrations). Generally good agreement was achieved among the various approaches, but some differences were observed depending on the model context. The intercomparison work was challenging because of variable capabilities of the codes, and inspired some code enhancements to allow consistent comparison of flow and transport simulations across the full suite of methods. This paper provides support for confidence
Intercomparison of 3D pore-scale flow and solute transport simulation methods
Mehmani, Yashar; Schoenherr, Martin; Pasquali, Andrea; Perkins, William A.; Kim, Kyungjoo; Perego, Mauro; Parks, Michael L.; Balhoff, Matthew T.; Richmond, Marshall C.; Geier, Martin; et al
2015-09-28
Multiple numerical approaches have been developed to simulate porous media fluid flow and solute transport at the pore scale. These include 1) methods that explicitly model the three-dimensional geometry of pore spaces and 2) methods that conceptualize the pore space as a topologically consistent set of stylized pore bodies and pore throats. In previous work we validated a model of the first type, using computational fluid dynamics (CFD) codes employing a standard finite volume method (FVM), against magnetic resonance velocimetry (MRV) measurements of pore-scale velocities. Here we expand that validation to include additional models of the first type based onmore » the lattice Boltzmann method (LBM) and smoothed particle hydrodynamics (SPH), as well as a model of the second type, a pore-network model (PNM). The PNM approach used in the current study was recently improved and demonstrated to accurately simulate solute transport in a two-dimensional experiment. While the PNM approach is computationally much less demanding than direct numerical simulation methods, the effect of conceptualizing complex three-dimensional pore geometries on solute transport in the manner of PNMs has not been fully determined. We apply all four approaches (FVM-based CFD, LBM, SPH and PNM) to simulate pore-scale velocity distributions and (for capable codes) nonreactive solute transport, and intercompare the model results. Comparisons are drawn both in terms of macroscopic variables (e.g., permeability, solute breakthrough curves) and microscopic variables (e.g., local velocities and concentrations). Generally good agreement was achieved among the various approaches, but some differences were observed depending on the model context. The intercomparison work was challenging because of variable capabilities of the codes, and inspired some code enhancements to allow consistent comparison of flow and transport simulations across the full suite of methods. This paper provides support for
Intercomparison of 3D pore-scale flow and solute transport simulation methods
NASA Astrophysics Data System (ADS)
Yang, Xiaofan; Mehmani, Yashar; Perkins, William A.; Pasquali, Andrea; Schönherr, Martin; Kim, Kyungjoo; Perego, Mauro; Parks, Michael L.; Trask, Nathaniel; Balhoff, Matthew T.; Richmond, Marshall C.; Geier, Martin; Krafczyk, Manfred; Luo, Li-Shi; Tartakovsky, Alexandre M.; Scheibe, Timothy D.
2016-09-01
Multiple numerical approaches have been developed to simulate porous media fluid flow and solute transport at the pore scale. These include 1) methods that explicitly model the three-dimensional geometry of pore spaces and 2) methods that conceptualize the pore space as a topologically consistent set of stylized pore bodies and pore throats. In previous work we validated a model of the first type, using computational fluid dynamics (CFD) codes employing a standard finite volume method (FVM), against magnetic resonance velocimetry (MRV) measurements of pore-scale velocities. Here we expand that validation to include additional models of the first type based on the lattice Boltzmann method (LBM) and smoothed particle hydrodynamics (SPH), as well as a model of the second type, a pore-network model (PNM). The PNM approach used in the current study was recently improved and demonstrated to accurately simulate solute transport in a two-dimensional experiment. While the PNM approach is computationally much less demanding than direct numerical simulation methods, the effect of conceptualizing complex three-dimensional pore geometries on solute transport in the manner of PNMs has not been fully determined. We apply all four approaches (FVM-based CFD, LBM, SPH and PNM) to simulate pore-scale velocity distributions and (for capable codes) nonreactive solute transport, and intercompare the model results. Comparisons are drawn both in terms of macroscopic variables (e.g., permeability, solute breakthrough curves) and microscopic variables (e.g., local velocities and concentrations). Generally good agreement was achieved among the various approaches, but some differences were observed depending on the model context. The intercomparison work was challenging because of variable capabilities of the codes, and inspired some code enhancements to allow consistent comparison of flow and transport simulations across the full suite of methods. This study provides support for confidence
Analytical solutions to non-Fickian subsurface dispersion in uniform groundwater flow
Zou, S.; Xia, J.; Koussis, A.D.
1996-01-01
Analytical solutions are obtained by the Fourier transform technique for the one-, two-, and three-dimensional transport of a conservative solute injected instantaneously in a uniform groundwater flow. These solutions account for dispersive non-linearity caused by the heterogeneity of the hydraulic properties of aquifer systems and can be used as building blocks to construct solutions by convolution (principle of superposition) for source conditions other than slug injection. The dispersivity is assumed to vary parabolically with time and is thus constant for the entire system at any given time. Two approaches for estimating time-dependent dispersion parameters are developed for two-dimensional plumes. They both require minimal field tracer test data and, therefore, represent useful tools for assessing real-world aquifer contamination sites. The first approach requires mapped plume-area measurements at two specific times after the tracer injection. The second approach requires concentration-versus-time data from two sampling wells through which the plume passes. Detailed examples and comparisons with other procedures show that the methods presented herein are sufficiently accurate and easier to use than other available methods.
Solution-Adaptive Program for Computing 2D/Axi Viscous Flow
NASA Technical Reports Server (NTRS)
Wood, William A.
2003-01-01
A computer program solves the Navier- Stokes equations governing the flow of a viscous, compressible fluid in an axisymmetric or two-dimensional (2D) setting. To obtain solutions more accurate than those generated by prior such programs that utilize regular and/or fixed computational meshes, this program utilizes unstructured (that is, irregular triangular) computational meshes that are automatically adapted to solutions. The adaptation can refine to regions of high change in gradient or can be driven by a novel residual minimization technique. Starting from an initial mesh and a corresponding data structure, the adaptation of the mesh is controlled by use of minimization functional. Other improvements over prior such programs include the following: (1) Boundary conditions are imposed weakly; that is, following initial specification of solution values at boundary nodes, these values are relaxed in time by means of the same formulations as those used for interior nodes. (2) Eigenvalues are limited in order to suppress expansion shocks. (3) An upwind fluctuation-splitting distribution scheme applied to inviscid flux requires fewer operations and produces less artificial dissipation than does a finite-volume scheme, leading to greater accuracy of solutions.
Block, Stephan; Fast, Björn Johansson; Lundgren, Anders; Zhdanov, Vladimir P.; Höök, Fredrik
2016-01-01
Biological nanoparticles (BNPs) are of high interest due to their key role in various biological processes and use as biomarkers. BNP size and composition are decisive for their functions, but simultaneous determination of both properties with high accuracy remains challenging. Optical microscopy allows precise determination of fluorescence/scattering intensity, but not the size of individual BNPs. The latter is better determined by tracking their random motion in bulk, but the limited illumination volume for tracking this motion impedes reliable intensity determination. Here, we show that by attaching BNPs to a supported lipid bilayer, subjecting them to hydrodynamic flows and tracking their motion via surface-sensitive optical imaging enable determination of their diffusion coefficients and flow-induced drifts, from which accurate quantification of both BNP size and emission intensity can be made. For vesicles, the accuracy of this approach is demonstrated by resolving the expected radius-squared dependence of their fluorescence intensity for radii down to 15 nm. PMID:27658367
NASA Astrophysics Data System (ADS)
Kawai, Soshi; Terashima, Hiroshi; Negishi, Hideyo
2015-11-01
This paper addresses issues in high-fidelity numerical simulations of transcritical turbulent flows at supercritical pressure. The proposed strategy builds on a tabulated look-up table method based on REFPROP database for an accurate estimation of non-linear behaviors of thermodynamic and fluid transport properties at the transcritical conditions. Based on the look-up table method we propose a numerical method that satisfies high-order spatial accuracy, spurious-oscillation-free property, and capability of capturing the abrupt variation in thermodynamic properties across the transcritical contact surface. The method introduces artificial mass diffusivity to the continuity and momentum equations in a physically-consistent manner in order to capture the steep transcritical thermodynamic variations robustly while maintaining spurious-oscillation-free property in the velocity field. The pressure evolution equation is derived from the full compressible Navier-Stokes equations and solved instead of solving the total energy equation to achieve the spurious pressure oscillation free property with an arbitrary equation of state including the present look-up table method. Flow problems with and without physical diffusion are employed for the numerical tests to validate the robustness, accuracy, and consistency of the proposed approach.
2013-01-01
Background The uptake of nanoparticles (NPs) by cells remains to be better characterized in order to understand the mechanisms of potential NP toxicity as well as for a reliable risk assessment. Real NP uptake is still difficult to evaluate because of the adsorption of NPs on the cellular surface. Results Here we used two approaches to distinguish adsorbed fluorescently labeled NPs from the internalized ones. The extracellular fluorescence was either quenched by Trypan Blue or the uptake was analyzed using imaging flow cytometry. We used this novel technique to define the inside of the cell to accurately study the uptake of fluorescently labeled (SiO2) and even non fluorescent but light diffracting NPs (TiO2). Time course, dose-dependence as well as the influence of surface charges on the uptake were shown in the pulmonary epithelial cell line NCI-H292. By setting up an integrative approach combining these flow cytometric analyses with confocal microscopy we deciphered the endocytic pathway involved in SiO2 NP uptake. Functional studies using energy depletion, pharmacological inhibitors, siRNA-clathrin heavy chain induced gene silencing and colocalization of NPs with proteins specific for different endocytic vesicles allowed us to determine macropinocytosis as the internalization pathway for SiO2 NPs in NCI-H292 cells. Conclusion The integrative approach we propose here using the innovative imaging flow cytometry combined with confocal microscopy could be used to identify the physico-chemical characteristics of NPs involved in their uptake in view to redesign safe NPs. PMID:23388071
NASA Astrophysics Data System (ADS)
Chen, Bingyan; Zhu, Changping; Chen, Longwei; Fei, Juntao; Gao, Ying; Wen, Wen; Shan, Minglei; Ren, Zhaoxing
2014-12-01
The organic compounds of p-nitrophenol (PNP) solution was treated by the active species generated in a stirred reactor by an atmospheric pressure plasma jet (APPJ). The emission intensities of hydroxyl (OH), oxygen (O), nitric oxide (NO), hydrogen (H) and molecular (N2) were measured by optical emission spectroscopy (OES). The relations between the flow rates of the PNP solution and degradation, the degradation effects and initial pH value of the solution were also investigated. Experimental results show that there exist intense emissions of O (777.1 nm), N2 (337.1 nm), OH (306-310 nm) and NO band (200-290 nm) in the region of plasma. Given the treatment time and gas flow rate, the degradation increased as a function of discharge energy and solution flow rate, respectively. The solution flow rate for the most efficient degradation ranged from 1.414 m/s to 1.702 m/s, and contributed very little when it exceeded 2.199 m/s. This indicates the existence of diffusion-controlled reactions at a low solution flow rate and activation-controlled reactions at a high solution flow rate. Moreover, increasing or decreasing the initial pH value of neutral PNP solution (pH=5.95) could improve the degradation efficiency. Treated by APPJ, the PNP solutions with different initial pH values of 5.95, 7.47 and 2.78 turned more acidic in the end, while the neutral solution had the lowest degradation efficiency. This work clearly demonstrates the close coupling of active species, photolysis of ultraviolet, the organic solution flow rate and the initial pH value, and thus is helpful in the study of the mechanism and application of plasma in wastewater treatment.
On the analytic structure of the Taylor-Maccoll conical-flow solution
NASA Technical Reports Server (NTRS)
Schwartz, L. W.
1975-01-01
The conical flow solution for axisymmetric supersonic flow past cones has been found to be virtually independent of the ratio of specific heats when normalized in a certain way. A simple rational approximation to this flow is derived. The important singularities and the limiting behavior of the solution are also discussed.
NASA Astrophysics Data System (ADS)
Awojoyogbe, O. B.
2004-08-01
Various biological and physiological properties of living tissue can be studied by means of nuclear magnetic resonance techniques. Unfortunately, the basic physics of extracting the relevant information from the solution of Bloch nuclear magnetic resource (NMR) equations to accurately monitor the clinical state of biological systems is still not yet fully understood. Presently, there are no simple closed solutions known to the Bloch equations for a general RF excitation. Therefore the translational mechanical analysis of the Bloch NMR equations presented in this study, which can be taken as definitions of new functions to be studied in detail may reveal very important information from which various NMR flow parameters can be derived. Fortunately, many of the most important but hidden applications of blood flow parameters can be revealed without too much difficulty if appropriate mathematical techniques are used to solve the equations. In this study we are concerned with a mathematical study of the laws of NMR physics from the point of view of translational mechanical theory. The important contribution of this study is that solutions to the Bloch NMR flow equations do always exist and can be found as accurately as desired. We shall restrict our attention to cases where the radio frequency field can be treated by simple analytical methods. First we shall derive a time dependant second-order non-homogeneous linear differential equation from the Bloch NMR equation in term of the equilibrium magnetization M0, RF B1( t) field, T1 and T2 relaxation times. Then, we would develop a general method of solving the differential equation for the cases when RF B1( t)=0, and when RF B1( t)≠0. This allows us to obtain the intrinsic or natural behavior of the NMR system as well as the response of the system under investigation to a specific influence of external force to the system. Specifically, we consider the case where the RF B1 varies harmonically with time. Here the complete
Cross-flow ultrafiltration of micellar surfactant solutions
Markels, J.H.; Lynn, S.; Radke, C.J.
1995-09-01
A steady-state fouling-resistance and osmotic-pressure model is used to predict flux in the laminar, cross-flow ultrafiltration of micellar cetyl (=hexadecyl)pyridinium chloride (CPC) solutions at 0.01-M NaCl background electrolyte. The model assumes a constant overall hydraulic resistance including the effect of surfactant fouling and native membrane resistance. Measurements of osmotic pressures of CPC solutions at 0.01-M NaCl as a function of surfactant concentration describe the effect of concentration polarization on permeate flux. Two types of asymmetric polyethersulfone membranes are used: 5,000 molecular weight cutoff (MWCO) membranes that allow partial monomer permeation, but quantitatively reject all micelles; 50,000 MWCO membranes that allow some micelle permeation. For the former, the intrinsic rejection coefficient for monomer, measured separately, is sufficient to describe surfactant rejection, without adjustable parameters. Predictions of the volumetric flux of the permeate, including the value of the limiting flux, agree well with the experimental results over the entire range of pressure drop, axial velocity, and bulk surfactant concentration. For the 50,000 MWCO membranes the data are described using a best-fit value of the overall surfactant rejection coefficient. For the first time, unusual behavior is observed experimentally in which the flux levels off with increasing pressure drop across the membrane, only to increase sharply again at higher applied pressure drop. Both effects are in accord with the proposed model. No gel layer need be postulated to explain the flux behavior of either membrane type.
THE FLOW AROUND A COSMIC STRING. I. HYDRODYNAMIC SOLUTION
Beresnyak, Andrey
2015-05-10
Cosmic strings are linear topological defects which are hypothesized to be produced during inflation. Most searches for strings have relied on the string’s lensing of background galaxies or the cosmic microwave background. In this paper, I obtained a solution for the supersonic flow of collisional gas past the cosmic string which has two planar shocks with a shock compression ratio that depends on the angle defect of the string and its speed. The shocks result in the compression and heating of the gas and, given favorable conditions, particle acceleration. Gas heating and over-density in an unusual wedge shape can be detected by observing the Hi line at high redshifts. Particle acceleration can occur in the present-day universe when the string crosses the hot gas contained in galaxy clusters and, since the consequences of such a collision persist for cosmological timescales, could be located by looking at unusual large-scale radio sources situated on a single spatial plane.
Early turbulence in von Karman swirling flow of polymer solutions
NASA Astrophysics Data System (ADS)
Burnishev, Yuri; Steinberg, Victor
2015-01-01
We present quantitative experimental results on the transition to early turbulence in von Karman swirling flow of water- and water-sugar-based polymer solutions compared to the transition to turbulence in their Newtonian solvents by measurements of solely global quantities as torque Γ(t) and pressure p(t) with large statistics as a function of Re. For the first time the transition values of Re_c\\textit{turb} to fully developed turbulence and turbulent drag reduction regime Re_c\\textit{TDR} are obtained as functions of elasticity El by using the solvents with different viscosities and polymer concentrations ϕ. Two scaling regions for fundamental turbulent characteristics are identified and they correspond to the turbulent and TDR regimes. Both Re_c\\textit{turb} and Re_c\\textit{TDR} are found via the dependence of the friction coefficient Cf and Cp, defined through scaled average torque \\barΓ and rms pressure fluctuations p\\textit{rms} , respectively, on Re for different El and ϕ and via the limits of the two scaling regions.
NASA Astrophysics Data System (ADS)
Yang, T. T.; Ntone, F.
1981-05-01
Curved wall diffusers designed by using an inverse method of solution of potential flow theory have been shown to be both short and highly efficient. These features make this type of diffuser attractive in thrust ejector applications. In ejectors, however, the flow at the diffuser inlet is nearly a uniform shear flow. This paper presents a method used in examining the flow velocity along the diffuser wall and some of the analytical results for diffusers designed with potential flow theory and receiving a rotational flow. The inlet flow vorticity and the diffuser area ratios prescribed in the inverse solution of the irrotational flow are the parameters of the study. The geometry of a sample ejector using such a diffuser and its estimated thrust augmentation ratio are also presented.
Viscous flow solutions for slender bodies of revolution at incidence
NASA Technical Reports Server (NTRS)
Vatsa, Veer N.
1991-01-01
Flow over slender prolate spheroids at incidence is examined. The incidence angle is chosen high enough to cause streamwise separation of the flow in addition to crossflow separation generally observed at lower incidence angles. The freestream Mach number for the cases investigated here is subsonic, thus precluding the use of parabolized procedures. Laminar, transitional and turbulent flow cases are investigated.
Flow dynamics and solute transport in unsaturated rock fractures
Su, G. W.
1999-10-01
Rock fractures play an important role in flow and contaminant transport in fractured aquifers, production of oil from petroleum reservoirs, and steam generation from geothermal reservoirs. In this dissertation, phenomenological aspects of flow in unsaturated fractures were studied in visualization experiments conducted on a transparent replica of a natural, rough-walled rock fracture for inlet conditions of constant pressure and flow rate over a range of angles of inclination. The experiments demonstrated that infiltrating liquid proceeds through unsaturated rock fractures along non-uniform, localized preferential flow paths. Even in the presence of constant boundary conditions, intermittent flow was a persistent flow feature observed, where portions of the flow channel underwent cycles of snapping and reforming. Two modes of intermittent flow were observed, the pulsating blob mode and the rivulet snapping mode. A conceptual model for the rivulet snapping mode was proposed and examined using idealized, variable-aperture fractures. The frequency of intermittent flow events was measured in several experiments and related to the capillary and Bond numbers to characterize this flow behavior.
Plasma flow structures as analytical solution of a magneto-hydro-dynamic model with pressure
NASA Astrophysics Data System (ADS)
Paccagnella, R.
2012-03-01
In this work starting from a set of magnetohydrodynamic (MHD) equations that describe the dynamical evolution for the pressure driven resistive/interchange modes in a magnetic confinement system, global solutions for the plasma flow relevant for toroidal pinches like tokamaks and reversed field pinches (RFPs) are derived. Analytical solutions for the flow stream function associated with the dominant modes are presented.
Wexler, Eliezer J.
1989-01-01
Analytical solutions to the advective-dispersive solute transport equation are useful in predicting the fate of solutes in groundwater. Analytical solutions compiled from available literature or derived by the author are presented in this report for a variety of boundary condition types and solute-source configuration in one-, two-, and three-dimensional systems with uniform groundwater flow. A set of user-oriented computer programs was created to evaluate these solutions and to display the results in tabular and computer-graphics format. These programs incorporate many features that enhance their accuracy, ease of use, and versatility. Documentation for the programs describes their operation and required input data, and presents the results of sample problems. Derivations of select solutions, source codes for the computer programs, and samples of program input and output also are described. (USGS)
Wexler, Eliezer J.
1992-01-01
Analytical solutions to the advective-dispersive solute-transport equation are useful in predicting the fate of solutes in ground water. Analytical solutions compiled from available literature or derived by the author are presented for a variety of boundary condition types and solute-source configurations in one-, two-, and three-dimensional systems having uniform ground-water flow. A set of user-oriented computer programs was created to evaluate these solutions and to display the results in tabular and computer-graphics format. These programs incorporate many features that enhance their accuracy, ease of use, and versatility. Documentation for the programs describes their operation and required input data, and presents the results of sample problems. Derivations of selected solutions, source codes for the computer programs, and samples of program input and output also are included.
Water flow and solute transport in floating fen root mats
NASA Astrophysics Data System (ADS)
Stofberg, Sija F.; EATM van der Zee, Sjoerd
2015-04-01
be very similar and likely functionally related. Our experimental field data were used for modelling water flow and solute transport in floating fens, using HYDRUS 2D. Fluctuations of surface water and root mat, as well as geometry and unsaturated zone parameters can have a major influence on groundwater fluctuations and the exchange between rain and surface water and the water in the root mats. In combination with the duration of salt pulses in surface water, and sensitivity of fen plants to salinity (Stofberg et al. 2014, submitted), risks for rare plants can be anticipated.
The accuracy of finite element solutions of Stokes's flow with strongly varying viscosity
NASA Astrophysics Data System (ADS)
Moresi, Louis; Zhong, Shijie; Gurnis, Michael
1996-10-01
We provide benchmark comparisons of two finite element (FE) mantle convection codes, CITCOM and CONMAN, against analytic solutions for Stokes' flow for strongly varying viscosity in the horizontal and vertical directions. The two codes use a similar FE formulation but different methods for solving the resulting equations. They both obtain accurate velocity, pressure and surface topography for viscosity structures which vary rapidly over a short distance, or discontinuously. The benchmarks help determine how many elements are needed to resolve a region of, for example, a convection simulation with high viscosity gradients. The overall accuracy does not depend on the global viscosity variation but on the gradients within individual elements. As a rule of thumb, accuracy can fall below 1% when there is a viscosity variation greater than a factor of two or three in an element. For iterative solution methods, necessary in three-dimensional modelling, these guidelines are required to determine the number of iterations to perform. We discuss a penalty based technique which improves the convergence of iterative solvers for general problems in which high viscosity gradients occurs spontaneously.
NASA Technical Reports Server (NTRS)
Thompson, D. S.
1980-01-01
The full Navier-Stokes equations for incompressible turbulent flow must be solved to accurately represent all flow phenomena which occur in a high Reynolds number incompressible flow. A two layer algebraic eddy viscosity turbulence model is used to represent the Reynolds stress in the primitive variable formulation. The development of the boundary-fitted coordinate systems makes the numerical solution of these equations feasible for arbitrarily shaped bodies. The nondimensional time averaged Navier-Stokes equations, including the turbulence mode, are represented by finite difference approximations in the transformed plane. The resulting coupled system of nonlinear algebraic equations is solved using a point successive over relaxation iteration. The test case considered was a NACA 64A010 airfoil section at an angle of attack of two degrees and a Reynolds number of 2,000,000.
Miyagawa, Yoichi; Morisada, Shintaro; Ohto, Keisuke; Hidetaka, Kawakita
2016-08-01
Separation of colloidal particles in non-Newtonian fluid is important in food engineering. Using hydrodynamic chromatography, colloidal particles and starch granules originating from corn were individually injected into dextran solutions (Mw 2,000,000g/mol) flowing through a coiled tube for efficient size separation. Rheological properties of dextran solutions ranging from 50 to 250g/L were determined, revealing pseudoplastic fluid behavior. Velocity profiles for dextran solution flow in coiled tubes were obtained from rheological power law parameters. Suspensions of colloidal particles of diameters 1.0 and 20μm were individually injected into the dextran flows, demonstrating that dextran solutions at high concentration separated colloidal particles. Starch granules were separated by size using a dextran solution flow (250g/L). Thus, we expect to obtain efficient separation of colloidal particles in foods using highly concentrated dextran solutions. PMID:27112856
Viscous shock layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium
NASA Technical Reports Server (NTRS)
Anderson, E. C.; Moss, J. N.
1975-01-01
The viscous shock layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially symmetric flow fields. Solutions are obtained using an implicit finite difference scheme and results are presented for hypersonic flow over spherically blunted cone configurations at free stream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.
Viscous-shock-layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium
NASA Technical Reports Server (NTRS)
Anderson, E. C.; Moss, J. N.
1975-01-01
The viscous-shock-layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially-symmetric flow fields. Solutions were obtained using an implicit finite-difference scheme and results are presented for hypersonic flow over spherically-blunted cone configurations at freestream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.
Adaptive multigrid domain decomposition solutions for viscous interacting flows
NASA Technical Reports Server (NTRS)
Rubin, Stanley G.; Srinivasan, Kumar
1992-01-01
Several viscous incompressible flows with strong pressure interaction and/or axial flow reversal are considered with an adaptive multigrid domain decomposition procedure. Specific examples include the triple deck structure surrounding the trailing edge of a flat plate, the flow recirculation in a trough geometry, and the flow in a rearward facing step channel. For the latter case, there are multiple recirculation zones, of different character, for laminar and turbulent flow conditions. A pressure-based form of flux-vector splitting is applied to the Navier-Stokes equations, which are represented by an implicit lowest-order reduced Navier-Stokes (RNS) system and a purely diffusive, higher-order, deferred-corrector. A trapezoidal or box-like form of discretization insures that all mass conservation properties are satisfied at interfacial and outflow boundaries, even for this primitive-variable, non-staggered grid computation.
Müller, A J; Torres, M F; Sáez, A E
2004-05-11
It is well-known that solutions of cetyltrimethylammonium p-toluenesulfonate in water exhibit a pronounced shear-thickening phenomenon in a specific concentration range (0.1-0.8%) when they are subjected to simple-shear flows, as a consequence of flow-induced self-assembly of wormlike micelles. This work shows that a strong elongational flow field (opposed-jets flow), applied to the same solutions, does not lead to extension thickening because the extensional flow prevents or destroys micellar association. In flow through a porous medium, a substantial increase in apparent viscosity is observed beyond a critical apparent shear rate, which surpasses increases observed in simple-shear flows. This is explained as the result of a synergistic effect of shear and relatively weak elongation on the solution microstructure.
Analytical solution for two-phase flow in a wellbore using the drift-flux model
Pan, L.; Webb, S.W.; Oldenburg, C.M.
2011-11-01
This paper presents analytical solutions for steady-state, compressible two-phase flow through a wellbore under isothermal conditions using the drift flux conceptual model. Although only applicable to highly idealized systems, the analytical solutions are useful for verifying numerical simulation capabilities that can handle much more complicated systems, and can be used in their own right for gaining insight about two-phase flow processes in wells. The analytical solutions are obtained by solving the mixture momentum equation of steady-state, two-phase flow with an assumption that the two phases are immiscible. These analytical solutions describe the steady-state behavior of two-phase flow in the wellbore, including profiles of phase saturation, phase velocities, and pressure gradients, as affected by the total mass flow rate, phase mass fraction, and drift velocity (i.e., the slip between two phases). Close matching between the analytical solutions and numerical solutions for a hypothetical CO{sub 2} leakage problem as well as to field data from a CO{sub 2} production well indicates that the analytical solution is capable of capturing the major features of steady-state two-phase flow through an open wellbore, and that the related assumptions and simplifications are justified for many actual systems. In addition, we demonstrate the utility of the analytical solution to evaluate how the bottomhole pressure in a well in which CO{sub 2} is leaking upward responds to the mass flow rate of CO{sub 2}-water mixture.
NASA Astrophysics Data System (ADS)
Bhushan, R.; Ng, T. L.
2014-12-01
Accurate stream flow forecasts are critical for reservoir operations for water supply planning. As the world urban population increases, the demand for water in cities is also increasing, making accurate forecasts even more important. However, accurate forecasting of stream flows is difficult owing to short- and long-term weather variations. We propose to reduce this need for accurate stream flow forecasts by augmenting reservoir operations with seawater desalination and wastewater recycling. We develop a robust operating policy for the joint operation of the three sources. With the joint model, we tap into the unlimited reserve of seawater through desalination, and make use of local supplies of wastewater through recycling. However, both seawater desalination and recycling are energy intensive and relatively expensive. Reservoir water on the other hand, is generally cheaper but is limited and variable in its availability, increasing the risk of water shortage during extreme climate events. We operate the joint system by optimizing it using a genetic algorithm to maximize water supply reliability and resilience while minimizing vulnerability subject to a budget constraint and for a given stream flow forecast. To compute the total cost of the system, we take into account the pumping cost of transporting reservoir water to its final destination, and the capital and operating costs of desalinating seawater and recycling wastewater. We produce results for different hydro climatic regions based on artificial stream flows we generate using a simple hydrological model and an autoregressive time series model. The artificial flows are generated from precipitation and temperature data from the Canadian Regional Climate model for present and future scenarios. We observe that the joint operation is able to effectively minimize the negative effects of stream flow forecast uncertainty on system performance at an overall cost that is not significantly greater than the cost of a
High-order exact solutions for pseudo-plane ideal flows
NASA Astrophysics Data System (ADS)
Sun, Che
2016-08-01
A steady pseudo-plane ideal flow (PIF) model is derived from the 3D Euler equations under Boussinesq approximation. The model is solved analytically to yield high-degree polynomial exact solutions. Unlike quadratic flows, the cubic and quartic solutions display reduced geometry in the form of straightline jet, circular vortex, and multipolar strain field. The high-order circular-vortex solutions are vertically aligned and even the non-aligned multipolar strain-field solutions display vertical concentricity. Such geometry reduction is explained by an analytical theorem stating that only straightline jet and circular vortex have functional solutions to the PIF model.
NASA Astrophysics Data System (ADS)
Inaba, Hideo; Aly, Wael I. A.; Haruki, Naoto; Horibe, Akihiko
2005-08-01
The reduction characteristic of turbulent drag and heat transfer of drag reduction surfactant solution flowing in a helically coiled pipe were experimentally investigated. The drag reduction surfactant used in the present study was the amine oxide type nonionic surfactant of oleyldihydroxyethylamineoxide (ODEAO, C22H45NO3=371). The zwitterion surfactant of cetyldimethylaminoaciticacidbetaine (CDMB, C20H41NO2=327) was added by 10% to the ODEAO solution in order to avoid the chemical degradation of ODEAO by ionic impurities in a test tape water. The experiments of flow drag and heat transfer reduction were carried out in the helically coiled pipe of coil to pipe diameter ratio of 37.5 and the helically coiled pipe length to pipe diameter of 1180.5 (pipe diameter of 14.4 mm) at various concentrations, temperatures and flow velocities of the ODEAO surfactant solution. The ODEAO solution showed a non-Newtonian behavior at high concentration of the ODEAO. From the experimental results, it was observed that the friction factor of the ODEAO surfactant solution flowing through the coiled pipe was decreased to a great extent in comparison with water as a Newtonian fluid in the turbulent flow region. Heat transfer measurements for water and the ODEAO solution were performed in both laminar and turbulent flow regions under the uniform heat flux boundary condition. The heat transfer coefficients for the ODEAO solution flow were the same as water flow in the laminar region. On the other hand, heat transfer reduction of the ODEAO solution flow was remarkedly reduced as compared with that of the water flow in the turbulent flow region.
NASA Technical Reports Server (NTRS)
Iyer, V.; Harris, J. E.
1987-01-01
The three-dimensional boundary-layer equations in the limit as the normal coordinate tends to infinity are called the surface Euler equations. The present paper describes an accurate method for generating edge conditions for three-dimensional boundary-layer codes using these equations. The inviscid pressure distribution is first interpolated to the boundary-layer grid. The surface Euler equations are then solved with this pressure field and a prescribed set of initial and boundary conditions to yield the velocities along the two surface coordinate directions. Results for typical wing and fuselage geometries are presented. The smoothness and accuracy of the edge conditions obtained are found to be superior to the conventional interpolation procedures.
Van Gorder, Robert A
2013-04-01
We provide a formulation of the local induction approximation (LIA) for the motion of a vortex filament in the Cartesian reference frame (the extrinsic coordinate system) which allows for scaling of the reference coordinate. For general monotone scalings of the reference coordinate, we derive an equation for the planar solution to the derivative nonlinear Schrödinger equation governing the LIA. We proceed to solve this equation perturbatively in small amplitude through an application of multiple-scales analysis, which allows for accurate computation of the period of the planar vortex filament. The perturbation result is shown to agree strongly with numerical simulations, and we also relate this solution back to the solution obtained in the arclength reference frame (the intrinsic coordinate system). Finally, we discuss nonmonotone coordinate scalings and their application for finding self-intersections of vortex filaments. These self-intersecting vortex filaments are likely unstable and collapse into other structures or dissipate completely.
NASA Technical Reports Server (NTRS)
Parikh, Paresh; Pirzadeh, Shahyar; Loehner, Rainald
1990-01-01
A set of computer programs for 3-D unstructured grid generation, fluid flow calculations, and flow field visualization was developed. The grid generation program, called VGRID3D, generates grids over complex configurations using the advancing front method. In this method, the point and element generation is accomplished simultaneously, VPLOT3D is an interactive, menudriven pre- and post-processor graphics program for interpolation and display of unstructured grid data. The flow solver, VFLOW3D, is an Euler equation solver based on an explicit, two-step, Taylor-Galerkin algorithm which uses the Flux Corrected Transport (FCT) concept for a wriggle-free solution. Using these programs, increasingly complex 3-D configurations of interest to aerospace community were gridded including a complete Space Transportation System comprised of the space-shuttle orbitor, the solid-rocket boosters, and the external tank. Flow solutions were obtained on various configurations in subsonic, transonic, and supersonic flow regimes.
Solution of nonlinear flow equations for complex aerodynamic shapes
NASA Technical Reports Server (NTRS)
Djomehri, M. Jahed
1992-01-01
Solution-adaptive CFD codes based on unstructured methods for 3-D complex geometries in subsonic to supersonic regimes were investigated, and the computed solution data were analyzed in conjunction with experimental data obtained from wind tunnel measurements in order to assess and validate the predictability of the code. Specifically, the FELISA code was assessed and improved in cooperation with NASA Langley and Imperial College, Swansea, U.K.
Application of the lag-after-pulsed-separation (LAPS) flow meter to different protein solutions.
Sengupta, Shramik; Mahmud, Goher; Chiou, Daniel J; Ziaie, Babak; Barocas, Victor H
2005-02-01
A lag after pulsed separation (LAPS) meter was previously developed to measure flow rates of protein solutions. The LAPS meter operates on the time-of-flight principle. An upstream event (electrophoretic concentration of the particles in one section of the device) is detected downstream (by change in ac resistance). The time lag between the event and its detection is inversely proportional to the fluid flow rate. We demonstrate the ability of the LAPS meter to measure the flow rate of solutions containing one or more charged biomacromolecules or particles. A prototype of the LAPS meter was used to measure flow rates of solutions of model proteins [bovine serum albumin (BSA), lysozyme and hemoglobin] and mixtures of BSA and lysozyme. Flow rates of 10-50 microl min(-1)(average velocities of 0.24-1.2 mm s(-1)) were measured. When a single ac measurement was used, the results were solution-dependent, which we attribute to the interface between the protein solution and the ac electrodes. A differential mode, in which the signal from a positive and a negative dc pulse were subtracted from each other, eliminated interfacial effects and led to a single universal (solution-independent) calibration curve. The LAPS meter can be used as a non-invasive, no-moving-parts flow sensor in any microfluidic system (such as drug delivery devices or micro-reactor arrays) where one needs to measure the flow rate of a solution or a suspension containing charged species such as proteins or cells.
Numerical solution of inviscid and viscous laminar and turbulent flow around the airfoil
NASA Astrophysics Data System (ADS)
Slouka, Martin; Kozel, Karel
2016-03-01
This work deals with the 2D numerical solution of inviscid compressible flow and viscous compressible laminar and turbulent flow around the profile. In a case of turbulent flow algebraic Baldwin-Lomax model is used and compared with Wilcox k-omega model. Calculations are done for NACA 0012 and RAE 2822 airfoil profile for the different angles of upstream flow. Numerical results are compared and discussed with experimental data.
Anderson, O.A.
2007-01-31
The well-known Kapchinskij-Vladimirskij (KV) equations are difficult to solve in general, but the problem is simplified for the matched-beam case with sufficient symmetry. They show that the interdependence of the two KV equations is eliminated, so that only one needs to be solved--a great simplification. They present an iterative method of solution which can potentially yield any desired level of accuracy. The lowest level, the well-known smooth approximation, yields simple, explicit results with good accuracy for weak or moderate focusing fields. The next level improves the accuracy for high fields; they previously showed [Part. Accel. 52, 133 (1996)] how to maintain a simple explicit format for the results. That paper used expansion in a small parameter to obtain results of second-level accuracy. The present paper, using straightforward iteration, obtains equations of first, second, and third levels of accuracy. For a periodic lattice with beam matched to lattice, they use the lattice and beam parameters as input and solve for phase advances and envelope functions. They find excellent agreement with numerical solutions over a wide range of beam emittances and intensities.
Anderson, Oscar A.
2006-08-06
The well-known Kapchinskij-Vladimirskij (KV) equations are difficult to solve in general, but the problem is simplified for the matched-beam case with sufficient symmetry. They show that the interdependence of the two KV equations is eliminated, so that only one needs to be solved--a great simplification. They present an iterative method of solution which can potentially yield any desired level of accuracy. The lowest level, the well-known smooth approximation, yields simple, explicit results with good accuracy for weak or moderate focusing fields. The next level improves the accuracy for high fields; they previously showed how to maintain a simple explicit format for the results. That paper used expansion in a small parameter to obtain the second level. The present paper, using straightforward iteration, obtains equations of first, second, and third levels of accuracy. For a periodic lattice with beam matched to lattice, they use the lattice and beam parameters as input and solve for phase advances and envelope waveforms. They find excellent agreement with numerical solutions over a wide range of beam emittances and intensities.
Exact solutions for shapes of two-dimensional bubbles in a corner flow
NASA Astrophysics Data System (ADS)
Zubarev, Nikolay M.; Zubareva, Olga V.
2007-10-01
A one-parameter family of exact solutions for the deformations of two-dimensional bubbles in a corner flow of an ideal liquid is obtained. The solutions correspond to the special case where the pressure inside the bubble equals the stagnation pressure. The parameter of the model is the corner angle. The solution family includes classical McLeod's solution which corresponds to the corner of angle π. For the particular case of a right-angled corner, the solution describes the straining flow past a bubble. In view of the known analogy between the distributions of a planar electric field and the velocity field for a two-dimensional potential flow, our solutions give equilibrium configurations of the surface of a conducting liquid in an external electric field.
Thin airfoil theory based on approximate solution of the transonic flow equation
NASA Technical Reports Server (NTRS)
Spreiter, John R; Alksne, Alberta Y
1957-01-01
A method is presented for the approximate solution of the nonlinear equations transonic flow theory. Solutions are found for two-dimensional flows at a Mach number of 1 and for purely subsonic and purely supersonic flows. Results are obtained in closed analytic form for a large and significant class of nonlifting airfoils. At a Mach number of 1 general expressions are given for the pressure distribution on an airfoil of specified geometry and for the shape of an airfoil having a prescribed pressure distribution. Extensive comparisons are made with available data, particularly for a Mach number of 1, and with existing solutions.
Thin airfoil theory based on approximate solution of the transonic flow equation
NASA Technical Reports Server (NTRS)
Spreiter, John R; Alksne, Alberta Y
1958-01-01
A method is presented for the approximate solution of the nonlinear equations of transonic flow theory. Solutions are found for two-dimensional flows at a Mach number of 1 and for purely subsonic and purely supersonic flows. Results are obtained in closed analytic form for a large and significant class of nonlifting airfoils. At a Mach number of 1 general expressions are given for the pressure distribution on an airfoil of specified geometry and for the shape of an airfoil having a prescribed pressure distribution. Extensive comparisons are made with available data, particularly for a Mach number of 1, and with existing solutions.
Rheological properties and the mechanism of a viscous flow of aqueous pectin solutions
NASA Astrophysics Data System (ADS)
Netesova, G. A.; Kotov, V. V.; Bodyakina, I. M.; Lukin, A. L.
2012-09-01
The rheological properties and mechanisms of a viscous flow of diluted apple pectin solutions are investigated. It is found that the rise in solution viscosity upon an increase in concentration and a drop in temperature is, along with the corresponding degree to which the interaction between pectin molecules and solvent is reduced, associated with the processes of structuring. The entropy of a viscous flow of pectin solutions is found to be positive: it grows with a rise in concentration is virtually temperature independent. It is established that the entropy factor makes the main contribution to the free energy value of a viscous flow.
Low Reynolds number numerical solutions of chaotic flow
NASA Technical Reports Server (NTRS)
Pulliam, Thomas H.
1989-01-01
Numerical computations of two-dimensional flow past an airfoil at low Mach number, large angle of attack, and low Reynolds number are reported which show a sequence of flow states leading from single-period vortex shedding to chaos via the period-doubling mechanism. Analysis of the flow in terms of phase diagrams, Poincare sections, and flowfield variables are used to substantiate these results. The critical Reynolds number for the period-doubling bifurcations is shown to be sensitive to mesh refinement and the influence of large amounts of numerical dissipation. In extreme cases, large amounts of added dissipation can delay or completely eliminate the chaotic response. The effect of artificial dissipation at these low Reynolds numbers is to produce a new effective Reynolds number for the computations.
Analytical Solution for Subsurface Gas Flow to a Well Induced by Surface Pressure Fluctuations
Rossabi, J.
2001-06-20
A simple analytical model is presented for predicting subsurface gas flow to a vadose zone well in response to atmospheric pressure fluctuations (barometric pumping). The effective radial permeability (kr) in the vicinity of the well is determined during model calibration using less than two weeks of data. By combining the flow solution with a solution for the vertical gas pressure, only atmospheric pressure data are required to predict the induced flow through a well. The ability to quantitatively predict naturally induced flow in vadose zone wells by simple and inexpensive measurements is invaluable for systems using barometric pumping for remediation.
Analytical solution for subsurface gas flow to a well induced by surface pressure fluctuations.
Rossabi, Joseph; Falta, Ronald W
2002-01-01
A simple analytical model is presented for predicting subsurface gas flow to a vadose-zone well in response to atmospheric pressure fluctuations (barometric pumping). The effective radial permeability (kr) in the vicinity of the well is determined during model calibration using less than two weeks worth of data. By combining the flow solution with a solution for the vertical gas pressure, only atmospheric pressure data are required to predict the induced flow through a well. The ability to quantitatively predict naturally induced flow in vadose-zone wells by simple and inexpensive measurements is invaluable for systems using barometric pumping for remediation. PMID:11798048
NASA Technical Reports Server (NTRS)
Yu, Sheng-Tao
2001-01-01
This document reports the conclusion and findings of our research activities for this grant. The goal of the project is the development and application of the method of Space-Time Conservation Element and Solution Element, or the CE/SE method, to simulate chemically reacting flows. The product of this project will be a high-fidelity, time-accurate flow solver analyzing unsteady flow fields advanced propulsion concepts, including the low-emission turbojet engine combustion and flow fields of the Pulse Detonation Engines (PDE). Based on the documents and computer software of the CE/SE method that we have received from the CE/SE working group at NASA Lewis, we have focused our research effort on addressing outstanding technical issues related to the extension of the CE/SE method for unsteady, chemically reactive flows. In particular, we have made progresses in the following three aspects: (1) Derivation of the governing equations for reacting flows; (2) Numerical treatments of stiff source terms; and (3) Detailed simulations of ZND detonation waves.
Analytical solutions for flow fields near continuous wall reactive barriers
NASA Astrophysics Data System (ADS)
Klammler, Harald; Hatfield, Kirk
2008-05-01
Permeable reactive barriers (PRBs) are widely applied for in-situ remediation of contaminant plumes transported by groundwater. Besides the goal of a sufficient contaminant remediation inside the reactive cell (residence time) the width of plume intercepted by a PRB is of critical concern. A 2-dimensional analytical approach is applied to determine the flow fields towards rectangular PRBs of the continuous wall (CW) configuration with and without impermeable side walls (but yet no funnel). The approach is based on the conformal mapping technique and assumes a homogeneous aquifer with a uniform ambient flow field. The hydraulic conductivity of the reactive material is furthermore assumed to exceed the conductivity of the aquifer by at least one order of magnitude as to neglect the hydraulic gradient across the reactor. The flow fields are analyzed regarding the widths and shapes of the respective capture zones as functions of the dimensions (aspect ratio) of the reactive cell and the ambient groundwater flow direction. Presented are an improved characterization of the advantages of impermeable side walls, a convenient approach to improved hydraulic design (including basic cost-optimization) and new concepts for monitoring CW PRBs. Water level data from a CW PRB at the Seneca Army Depot site, NY, are used for field demonstration.
Analytical solutions for flow fields near continuous wall reactive barriers.
Klammler, Harald; Hatfield, Kirk
2008-05-26
Permeable reactive barriers (PRBs) are widely applied for in-situ remediation of contaminant plumes transported by groundwater. Besides the goal of a sufficient contaminant remediation inside the reactive cell (residence time) the width of plume intercepted by a PRB is of critical concern. A 2-dimensional analytical approach is applied to determine the flow fields towards rectangular PRBs of the continuous wall (CW) configuration with and without impermeable side walls (but yet no funnel). The approach is based on the conformal mapping technique and assumes a homogeneous aquifer with a uniform ambient flow field. The hydraulic conductivity of the reactive material is furthermore assumed to exceed the conductivity of the aquifer by at least one order of magnitude as to neglect the hydraulic gradient across the reactor. The flow fields are analyzed regarding the widths and shapes of the respective capture zones as functions of the dimensions (aspect ratio) of the reactive cell and the ambient groundwater flow direction. Presented are an improved characterization of the advantages of impermeable side walls, a convenient approach to improved hydraulic design (including basic cost-optimization) and new concepts for monitoring CW PRBs. Water level data from a CW PRB at the Seneca Army Depot site, NY, are used for field demonstration.
NASA Astrophysics Data System (ADS)
Artrith, Nongnuch; Kolpak, Alexie
2014-03-01
The shape, size, and composition of catalyst nanoparticles can have a significant influence on their catalytic activity. Understanding such structure-reactivity relationships is crucial for the optimization of industrial catalysts and the design of novel catalysts with enhanced properties. In this work, we investigate the equilibrium shape and surface structure/composition of Au/Cu nanoparticles in solution, which have recently been shown to be stable and efficient catalysts for CO2 reduction. Using a combination of density functional theory calculations and large-scale Monte-Carlo and molecular dynamics simulations with reactive atomistic potentials, we determine how the nanoparticle shape, surface structure, and surface stoichiometry (i.e., fraction of Au at the surface relative to overall composition), evolve as a function of varying catalytic conditions. We discuss the effects of these changes on the surface electronic structure and binding energies of CO2, H2, and CH3OH. Our results emphasize the important relationships between catalytic environment (e.g., solvent effects), catalyst structure, and catalytic activity. We thank the Schlumberger Foundation Faculty for the Future for financial support. Computing time at XSEDE and NERSC clusters are gratefully acknowledged.
NASA Astrophysics Data System (ADS)
Alcoba, D. R.; Valdemoro, C.; Tel, L. M.; Pérez-Romero, E.
The equation obtained by mapping the matrix representation of the Schrödinger equation with the 2nd-order correlation transition matrix elements into the 2-body space is the so called correlation contracted Schrödinger equation (CCSE) (Alcoba, Phys Rev A 2002, 65, 032519). As shown by Alcoba (Phys Rev A 2002, 65, 032519) the solution of the CCSE coincides with that of the Schrödinger equation. Here the attention is focused in the vanishing hypervirial of the correlation operator (GHV), which can be identified with the anti-Hermitian part of the CCSE. A comparative analysis of the GHV and the anti-Hermitian part of the contracted Schrödinger equation (ACSE) indicates that the former is a stronger stationarity condition than the latter. By applying a Heisenberg-like unitary transformation to the G-particle-hole operator (Valdemoro et al., Phys Rev A 2000, 61, 032507), a good approximation of the expectation value of this operator as well as of the GHV is obtained. The method is illustrated for the case of the Beryllium isoelectronic series as well as for the Li2 and BeH2 molecules. The correlation energies obtained are within 98.80-100.09% of the full-configuration interaction ones. The convergence of these calculations was faster when using the GHV than with the ACSE.
Uniqueness of transonic shock solutions in a duct for steady potential flow
NASA Astrophysics Data System (ADS)
Chen, Gui-Qiang; Yuan, Hairong
We study the uniqueness of solutions with a transonic shock in a duct in a class of transonic shock solutions, which are not necessarily small perturbations of the background solution, for steady potential flow. We prove that, for given uniform supersonic upstream flow in a straight duct, there exists a unique uniform pressure at the exit of the duct such that a transonic shock solution exists in the duct, which is unique modulo translation. For any other given uniform pressure at the exit, there exists no transonic shock solution in the duct. This is equivalent to establishing a uniqueness theorem for a free boundary problem of a partial differential equation of second order in a bounded or unbounded duct. The proof is based on the maximum/comparison principle and a judicious choice of special transonic shock solutions as a comparison solution.
NASA Astrophysics Data System (ADS)
Cote, C. M.; Bristow, K. L.; Ross, P. J.
2000-05-01
Most soils contain preferential flow paths that can impact on solute mobility. Solutes can move rapidly down the preferential flow paths with high pore-water velocities, but can be held in the less permeable region of the soil matrix with low pore-water velocities, thereby reducing the efficiency of leaching. In this study, we conducted leaching experiments with interruption of the flow and drainage of the main flow paths to assess the efficiency of this type of leaching. We compared our experimental results to a simple analytical model, which predicts the influence of the variations in concentration gradients within a single spherical aggregate (SSA) surrounded by preferential flow paths on leaching. We used large (length: 300 mm, diameter: 216 mm) undisturbed field soil cores from two contrasting soil types. To carry out intermittent leaching experiments, the field soil cores were first saturated with tracer solution (CaBr 2), and background solution (CaCl 2) was applied to mimic a leaching event. The cores were then drained at 25- to 30-cm suction to empty the main flow paths to mimic a dry period during which solutes could redistribute within the undrained region. We also conducted continuous leaching experiments to assess the impact of the dry periods on the efficiency of leaching. The flow interruptions with drainage enhanced leaching by 10-20% for our soils, which was consistent with the model's prediction, given an optimised "equivalent aggregate radius" for each soil. This parameter quantifies the time scales that characterise diffusion within the undrained region of the soil, and allows us to calculate the duration of the leaching events and interruption periods that would lead to more efficient leaching. Application of these methodologies will aid development of strategies for improving management of chemicals in soils, needed in managing salts in soils, in improving fertiliser efficiency, and in reclaiming contaminated soils.
A GENERAL MASS-CONSERVATIVE NUMERICAL SOLUTION FOR THE UNSATURATED FLOW EQUATION
Numerical approximations based on different forms of the governing partial differential equation can lead to significantly different results for unsaturated flow problems. Numerical solution based on the standard h-based form of Richards equation generally yields poor results, ch...
ERIC Educational Resources Information Center
Sanger, Michael J.; Greenbowe, Thomas J.
1997-01-01
Examines students' misconceptions and proposed mechanisms related to current flow in electrolyte solutions and the salt bridge. Confirms reported misconceptions and identifies several new ones. Discusses probable sources of misconceptions and some methods for preventing them. Contains 27 references. (JRH)
Solution of non-isoenergetic supersonic flows by method of characteristics, volume 3
NASA Technical Reports Server (NTRS)
Prozan, R. J.
1972-01-01
The calculation of supersonic flow fields by the method of characteristics. The theoretical approach to the solution of these flow fields and a computer program to implement the numerical solution of the flow equations are discussed. This versatile program has a flexible set of boundary conditions enabling the calculation of nozzles, plumes and many other complex flow fields. A complete derivation of the equations of motion for reacting gas systems is presented. An important consequence of this derivation is that, for the reaction assumptions which were made, the thermochemistry was shown to be uncoupled from the flow solution and as such could be solved separately. The methods of characteristics equations are shown to be formally the same for ideal, frozen, and equilibrium reacting gas mixtures.
Solution of Reactive Compressible Flows Using an Adaptive Wavelet Method
NASA Astrophysics Data System (ADS)
Zikoski, Zachary; Paolucci, Samuel; Powers, Joseph
2008-11-01
This work presents numerical simulations of reactive compressible flow, including detailed multicomponent transport, using an adaptive wavelet algorithm. The algorithm allows for dynamic grid adaptation which enhances our ability to fully resolve all physically relevant scales. The thermodynamic properties, equation of state, and multicomponent transport properties are provided by CHEMKIN and TRANSPORT libraries. Results for viscous detonation in a H2:O2:Ar mixture, and other problems in multiple dimensions, are included.
NASA Astrophysics Data System (ADS)
Ngo-Cong, D.; Mohammed, F. J.; Strunin, D. V.; Skvortsov, A. T.; Mai-Duy, N.; Tran-Cong, T.
2015-06-01
The contaminant transport process governed by the advection-diffusion equation plays an important role in modelling industrial and environmental flows. In this article, our aim is to accurately reduce the 2-D advection-diffusion equation governing the dispersion of a contaminant in a turbulent open channel flow to its 1-D approximation. The 1-D model helps to quickly estimate the horizontal size of contaminant clouds based on the values of the model coefficients. We derive these coefficients analytically and investigate numerically the model convergence. The derivation is based on the centre manifold theory to obtain successively more accurate approximations in a consistent manner. Two types of the average velocity profile are considered: the classical logarithmic profile and the power profile. We further develop the one-dimensional integrated radial basis function network method as a numerical approach to obtain the numerical solutions to both the original 2-D equation and the approximate 1-D equations. We compare the solutions of the original models with their centre-manifold approximations at very large Reynolds numbers. The numerical results obtained from the approximate 1-D models are in good agreement with those of the original 2-D model for both the logarithmic and power velocity profiles.
New exact solution of the problem of rotationally symmetric Couette-Poiseuille flow
NASA Astrophysics Data System (ADS)
Aristov, S. N.; Knyazev, D. V.
2007-09-01
An exact solution is obtained for the problem of steady-state viscous incompressible flow under a pressure difference in the gap between coaxial cylinders for the case where the inner cylinder rotates at a constant angular velocity. The solution differs from the classical Couette-Poiseuille result by the presence of radial mass transfer, which provides for interaction between the poloidal and azimuthal circulations. The flow rate is found to depend linearly on the angular velocity of rotation of the inner cylinder.
The Analytical Solutions for Magnetohydrodynamic Flow of a Third Order Fluid in a Porous Medium
NASA Astrophysics Data System (ADS)
Hayat, Tasawar; Ellahi, Rahmat; Mahomed, Fazal Mehmood
2009-10-01
An analysis has been carried out for flow and heat transfer characteristics in a third grade fluid between two porous plates. The electrically conducting fluid fills the porous medium. The solutions have been developed for small porosity and magnetic field. Three flow problems are investigated and analytical expressions for the velocity field and temperature distribution are given for each case. Moreover, we recover and extend the results of Siddiqui et al. [1] by presenting exact solutions for the governing equations derived in [1].
NASA Astrophysics Data System (ADS)
Ryu, Jaiyoung; Hu, Xiao; Shadden, Shawn C.
2014-11-01
The cerebral circulation is unique in its ability to maintain blood flow to the brain under widely varying physiologic conditions. Incorporating this autoregulatory response is critical to cerebral blood flow modeling, as well as investigations into pathological conditions. We discuss a one-dimensional nonlinear model of blood flow in the cerebral arteries that includes coupling of autoregulatory lumped parameter networks. The model is tested to reproduce a common clinical test to assess autoregulatory function - the carotid artery compression test. The change in the flow velocity at the middle cerebral artery (MCA) during carotid compression and release demonstrated strong agreement with published measurements. The model is then used to investigate vasospasm of the MCA, a common clinical concern following subarachnoid hemorrhage. Vasospasm was modeled by prescribing vessel area reduction in the middle portion of the MCA. Our model showed similar increases in velocity for moderate vasospasms, however, for serious vasospasm (~ 90% area reduction), the blood flow velocity demonstrated decrease due to blood flow rerouting. This demonstrates a potentially important phenomenon, which otherwise would lead to false-negative decisions on clinical vasospasm if not properly anticipated.
Solution of transonic flows by an integro-differential equation method
NASA Technical Reports Server (NTRS)
Ogana, W.
1978-01-01
Solutions of steady transonic flow past a two-dimensional airfoil are obtained from a singular integro-differential equation which involves a tangential derivative of the perturbation velocity potential. Subcritical flows are solved by taking central differences everywhere. For supercritical flows with shocks, central differences are taken in subsonic flow regions and backward differences in supersonic flow regions. The method is applied to a nonlifting parabolic-arc airfoil and to a lifting NACA 0012 airfoil. Results compare favorably with those of finite-difference schemes.
NASA Technical Reports Server (NTRS)
Mcfarland, E. R.
1981-01-01
A solution method was developed for calculating compressible inviscid flow through a linear cascade of arbitrary blade shapes. The method uses advanced surface singularity formulations which were adapted from those in current external flow analyses. The resulting solution technique provides a fast flexible calculation for flows through turbomachinery blade rows. The solution method and some examples of the method's capabilities are presented.
An analytical solution for transient flow of Bingham viscoplastic materials in rock fractures
Amadei, B.; Savage, W.Z.
2001-01-01
We present below an analytical solution to model the one-dimensional transient flow of a Bingham viscoplastic material in a fracture with parallel walls (smooth or rough) that is subjected to an applied pressure gradient. The solution models the acceleration and the deceleration of the material as the pressure gradient changes with time. Two cases are considered: A pressure gradient applied over a finite time interval and an applied pressure gradient that is constant over time. The solution is expressed in dimensionless form and can therefore be used for a wide range of Bingham viscoplastic materials. The solution is also capable of capturing the transition that takes place in a fracture between viscoplastic flow and rigid plug flow. Also, it shows the development of a rigid central layer in fractures, the extent of which depends on the fluid properties (viscosity and yield stress), the magnitude of the pressure gradient, and the fracture aperture and surface roughness. Finally, it is shown that when a pressure gradient is applied and kept constant, the solution for the fracture flow rate converges over time to a steady-state solution that can be defined as a modified cubic law. In this case, the fracture transmissivity is found to be a non-linear function of the head gradient. This solution provides a tool for a better understanding of the flow of Bingham materials in rock fractures, interfaces, and cracks. ?? 2001 Elsevier Science Ltd. All rights reserved.
Comparison of NACA 0012 Laminar Flow Solutions: Structured and Unstructured Grid Methods
NASA Technical Reports Server (NTRS)
Swanson, R. C.; Langer, S.
2016-01-01
In this paper we consider the solution of the compressible Navier-Stokes equations for a class of laminar airfoil flows. The principal objective of this paper is to demonstrate that members of this class of laminar flows have steady-state solutions. These laminar airfoil flow cases are often used to evaluate accuracy, stability and convergence of numerical solution algorithms for the Navier-Stokes equations. In recent years, such flows have also been used as test cases for high-order numerical schemes. While generally consistent steady-state solutions have been obtained for these flows using higher order schemes, a number of results have been published with various solutions, including unsteady ones. We demonstrate with two different numerical methods and a range of meshes with a maximum density that exceeds 8 × 106 grid points that steady-state solutions are obtained. Furthermore, numerical evidence is presented that even when solving the equations with an unsteady algorithm, one obtains steady-state solutions.
NASA Technical Reports Server (NTRS)
Low, B. C.; Tsinganos, K.
1986-01-01
In the case of an establishment of theoretical models of the hydromagnetic solar wind, the inclusion of the effects of the magnetic field in the solar wind makes it extremely dificult to solve the mathematical problem. This paper has the objective to present a set of particular analytic solutions. The general formulation of Tsinganos (1982) is used to identify a class of analytic solutions to the equations of steady hydromagnetic flows in spherical coordinates. Flow in an open magnetic field are studied, taking into account the problem in dimensionless form, the special case of radial flows with alpha = 0, general radial flows, illustrative examples for flows in which alpha is not equal to 0, a parametric study of nonradial flows in which alpha is not equal to zero, variations in the parameter nu, and variations in the initial speed eta.
Analytical solution of laminar-laminar stratified two-phase flows with curved interfaces
Brauner, N.; Rovinsky, J.; Maron, D.M.
1995-09-01
The present study represents a complete analytical solution for laminar two-phase flows with curved interfaces. The solution of the Navier-Stokes equations for the two-phases in bipolar coordinates provides the `flow monograms` describe the relation between the interface curvature and the insitu flow geometry when given the phases flow rates and viscosity ratios. Energy considerations are employed to construct the `interface monograms`, whereby the characteristic interfacial curvature is determined in terms of the phases insitu holdup, pipe diameter, surface tension, fluids/wall adhesion and gravitation. The two monograms are then combined to construct the system `operational monogram`. The `operational monogram` enables the determination of the interface configuration, the local flow characteristics, such as velocity profiles, wall and interfacial shear stresses distribution as well as the integral characteristics of the two-phase flow: phases insitu holdup and pressure drop.
Exact solution of cilia induced flow of a Jeffrey fluid in an inclined tube.
Maqbool, K; Shaheen, S; Mann, A B
2016-01-01
The present study investigated the cilia induced flow of MHD Jeffrey fluid through an inclined tube. This study is carried out under the assumptions of long wavelength and low Reynolds number approximations. Exact solutions for the velocity profile, pressure rise, pressure gradient, volume flow rate and stream function are obtained. Effects of pertinent physical parameters on the computational results are presented graphically. PMID:27610298
An analytical solution for Dean flow in curved ducts with rectangular cross section
NASA Astrophysics Data System (ADS)
Norouzi, M.; Biglari, N.
2013-05-01
In this paper, a full analytical solution for incompressible flow inside the curved ducts with rectangular cross-section is presented for the first time. The perturbation method is applied to solve the governing equations and curvature ratio is considered as the perturbation parameter. The previous perturbation solutions are usually restricted to the flow in curved circular or annular pipes related to the overly complex form of solutions or singularity situation for flow in curved ducts with non-circular shapes of cross section. This issue specifies the importance of analytical studies in the field of Dean flow inside the non-circular ducts. In this study, the main flow velocity, stream function of lateral velocities (secondary flows), and flow resistance ratio in rectangular curved ducts are obtained analytically. The effect of duct curvature and aspect ratio on flow field is investigated as well. Moreover, it is important to mention that the current analytical solution is able to simulate the Taylor-Görtler and Dean vortices (vortices in stable and unstable situations) in curved channels.
Numerical solution of compressible viscous flows at high Reynolds numbers
NASA Technical Reports Server (NTRS)
Maccormack, R. W.
1981-01-01
A new numerical method which was used to reduce the computation time required in fluid dynamics to solve the Navier-Stokes equations at flight Reynolds numbers is described. The method is the implicit analogue of the explicit finite different method. It uses this as its first stage, while the second stage removes the restrictive stability condition by recasting the difference equations in an implicit form. The resulting matrix equations to be solved are either upper or lower block bidiagonal equations. The new method makes it possible and practical to calculate many important three dimensional, high Reynolds number flow fields on computers.
Concentration polarization of interacting solute particles in cross-flow membrane filtration
Bhattacharjee, S.; Kim, A.S.; Elimelech, M.
1999-04-01
A theoretical approach for predicting the influence of interparticle interactions on concentration polarization and the ensuing permeate flux decline during cross-flow membrane filtration of charged solute particles is presented. The Ornstein-Zernike integral equation is solved using appropriate closures corresponding to hard-spherical and long-range solute-solute interactions to predict the radial distribution function of the solute particles in a concentrated solution (dispersion). Two properties of the solution, namely the osmotic pressure and the diffusion coefficient, are determined on the basis of the radial distribution function at different solute concentrations. Incorporation of the concentration dependence of these two properties in the concentration polarization model comprising the convective-diffusion equation and the osmotic-pressure governed permeate flux equation leads to the coupled prediction of the solute concentration profile and the local permeate flux. The approach leads to a direct quantitative incorporation of solute-solute interactions in the framework of a standard theory of concentration polarization. The developed model is used to study the effects of ionic strength and electrostatic potential on the variations of solute diffusivity and osmotic pressure. Finally, the combined influence of these two properties on the permeate flux decline behavior during cross-flow membrane filtration of charged solute particles is predicted.
Solutions and procedures to assure the flow in deepwater conditions
Gomes, M.G.F.M.; Pereira, F.B.; Lino, A.C.F.
1996-12-31
Petrobras has been developing deep water oil fields located in Campos Basin, a vanguard subsea project which faces big challenges, one of them wax deposition in production flowlines. So, since 1990, Petrobras has been studying methods to prevent and remove paraffin-wax deposits. Tests of techniques based on chemical inhibition of crystal growth, thermo-chemical cleaning (SGN), mechanical cleaning (pigging), electrical heating and thermal insulation were done and the main results obtained at CENPES (Petrobras R and D Center) started to be used in the field in 1993. This paper presents solutions and procedures which has been used to minimize oil production losses at Campos Basin -- Brazil.
Travelling-wave solutions bifurcating from relative periodic orbits in plane Poiseuille flow
NASA Astrophysics Data System (ADS)
Rawat, Subhandu; Cossu, Carlo; Rincon, François
2016-06-01
Travelling-wave solutions are shown to bifurcate from relative periodic orbits in plane Poiseuille flow at Re = 2000 in a saddle-node infinite-period bifurcation. These solutions consist in self-sustaining sinuous quasi-streamwise streaks and quasi-streamwise vortices located in the bulk of the flow. The lower branch travelling-wave solutions evolve into spanwise localized states when the spanwise size Lz of the domain in which they are computed is increased. On the contrary, the upper branch of travelling-wave solutions develops multiple streaks when Lz is increased. Upper-branch travelling-wave solutions can be continued into coherent solutions to the filtered equations used in large-eddy simulations where they represent turbulent coherent large-scale motions.
The effect of viscosity on steady transonic flow with a nodal solution topology
NASA Technical Reports Server (NTRS)
Owocki, Stanley P.; Zank, Gary P.
1991-01-01
The effect of viscosity on a steady, transonic flow for which the inviscid limit has a nodal solution topology near the critical point is investigated. For the accelerating case, viscous solutions tend to repel each other, so that a very delicate choice of initial conditions is required to prevent them from diverging. Only the two critical solutions extend to arbitrarily large distances into both the subsonic and supersonic flows. For the decelerating case, the solutions tend to attract, and so an entire two-parameter family of solutions now extends over large distances. The general effect of viscosity on the solution degeneracy of a nodal topology is thus to reduce or limit it for the accelerating case and to enhance it for the decelerating case. The astrophysical implications of these findings are addressed.
A Note on Exact Solutions for the Unsteady Free Convection Flow of a Jeffrey Fluid
NASA Astrophysics Data System (ADS)
Khan, Ilyas
2015-06-01
In this note, we investigate the unsteady free convection flow of a Jeffrey fluid past an infinite isothermal vertical plate. Exact solutions are obtained using the Laplace transform technique. These solutions are expressed in terms of exponential and complementary error functions, and satisfy all imposed initial and boundary conditions as well as the governing equations. The expression for the shear stress is also evaluated. The corresponding solutions for a Newtonian fluid can be easily obtained as a special case. It is found from the velocity and shear stress solutions that they strongly depend on the material parameters of a Jeffrey fluid. The exact solutions obtained here can be used as a benchmark for checking the correctness of other approximate or numerical solutions. In addition, this note will help in understanding the characteristics of non-Newtonian fluid flows that are subject to free convection due to buoyancy force.
Streamwise-Localized Solutions at the Onset of Turbulence in Pipe Flow
NASA Astrophysics Data System (ADS)
Avila, M.; Mellibovsky, F.; Roland, N.; Hof, B.
2013-05-01
Although the equations governing fluid flow are well known, there are no analytical expressions that describe the complexity of turbulent motion. A recent proposition is that in analogy to low dimensional chaotic systems, turbulence is organized around unstable solutions of the governing equations which provide the building blocks of the disordered dynamics. We report the discovery of periodic solutions which just like intermittent turbulence are spatially localized and show that turbulent transients arise from one such solution branch.
STUDIES ON THE ANOMALOUS VISCOSITY AND FLOW-BIREFRINGENCE OF PROTEIN SOLUTIONS
Lawrence, A. S. C.; Needham, Joseph; Shen, Shih-Chang
1944-01-01
1. A coaxial viscosimeter which permits the simultaneous determination of relative and anomalous viscosity and of flow-birefringence is described. Flow-anomaly and flow-birefringence are regarded as characteristic of elongated micelles and molecules. 2. Such methods have been applied to dilute solutions of proteins. The conditions under which the coaxial (Couette) viscosimeter measures the viscosity of the bulk phase and the surface film phase respectively have been investigated and are described. 3. The general behaviour of protein solutions subjected to shear is summarised. PMID:19873384
NASA Astrophysics Data System (ADS)
Faug, Thierry
2015-12-01
In the present paper, flows of granular materials impacting wall-like obstacles down inclines are described by depth-averaged analytic solutions. Particular attention is paid to extending the existing depth-averaged equations initially developed for frictionless and incompressible fluids down a horizontal plane. The effects of the gravitational acceleration along the slope, and of the retarding acceleration caused by friction as well, are systematically taken into account. The analytic solutions are then used to revisit existing data on rigid walls impacted by granular flows. This approach allows establishing a complete phase diagram for granular flow-wall interaction.
A pressure based method for the solution of viscous incompressible turbomachinery flows
NASA Technical Reports Server (NTRS)
Hobson, Garth Victor; Lakshminarayana, B.
1991-01-01
A new technique was developed for the solution of the incompressible Navier-Stokes equations. The numerical technique, derived from a pressure substitution method (PSM), overcomes many of the deficiencies of the pressure correction method. This technique allows for the direct solution of the actual pressure in the form of a Poisson equation which is derived from the pressure weighted substitution of the full momentum equations into the continuity equation. Two dimensional internal flows are computed with this method. The prediction of cascade performance is presented. The extention of the pressure correction method for the solution of three dimensional flows is also presented.
Evaluation of alkanolamine solutions for carbon dioxide removal in cross-flow rotating packed beds.
Lin, Chia-Chang; Lin, Yu-Hong; Tan, Chung-Sung
2010-03-15
The removal of CO(2) from a 10 vol% CO(2) gas by chemical absorption with 30 wt% alkanolamine solutions containing monoethanolamine (MEA), piperazine (PZ), and 2-amino-2-methyl-1-propanol (AMP) in the cross-flow rotating packed bed (RPB) was investigated. The CO(2) removal efficiency increased with rotor speed, liquid flow rate and inlet liquid temperature. However, the CO(2) removal efficiency decreased with gas flow rate. Also, the CO(2) removal efficiency was independent of inlet gas temperature. The 30 wt% alkanolamine solutions containing PZ with MEA were the appropriate absorbents compared with the single alkanolamine (MEA, AMP) and the mixed alkanolamine solutions containing AMP with MEA. A higher portion of PZ in alkanolamine solutions was more favorable to CO(2) removal. Owing to less contact time in the cross-flow RPB, alkanolamines having high reaction rates with CO(2) are suggested to be used. For the mixed alkanolamine solution containing 12 wt% PZ and 18 wt% MEA, the highest gas flow rate allowed to achieve the CO(2) removal efficiency more than 90% at a liquid flow rate of 0.54 L/min was of 29 L/min. The corresponding height of a transfer unit (HTU) was found to be less than 5.0 cm, lower than that in the conventional packed bed.
Upscaling of Solute Transport in Heterogeneous Media with Non-uniform Flow and Dispersion Fields
Xu, Zhijie; Meakin, Paul
2013-10-01
An analytical and computational model for non-reactive solute transport in periodic heterogeneous media with arbitrary non-uniform flow and dispersion fields within the unit cell of length ε is described. The model lumps the effect of non-uniform flow and dispersion into an effective advection velocity Ve and an effective dispersion coefficient De. It is shown that both Ve and De are scale-dependent (dependent on the length scale of the microscopic heterogeneity, ε), dependent on the Péclet number Pe, and on a dimensionless parameter α that represents the effects of microscopic heterogeneity. The parameter α, confined to the range of [-0.5, 0.5] for the numerical example presented, depends on the flow direction and non-uniform flow and dispersion fields. Effective advection velocity Ve and dispersion coefficient De can be derived for any given flow and dispersion fields, and . Homogenized solutions describing the macroscopic variations can be obtained from the effective model. Solutions with sub-unit-cell accuracy can be constructed by homogenized solutions and its spatial derivatives. A numerical implementation of the model compared with direct numerical solutions using a fine grid, demonstrated that the new method was in good agreement with direct solutions, but with significant computational savings.
NASA Technical Reports Server (NTRS)
Desmarais, R. N.
1982-01-01
The method is capable of generating approximations of arbitrary accuracy. It is based on approximating the algebraic part of the nonelementary integrals in the kernel by exponential functions and then integrating termwise. The exponent spacing in the approximation is a geometric sequence. The coefficients and exponent multiplier of the exponential approximation are computed by least squares so the method is completely automated. Exponential approximates generated in this manner are two orders of magnitude more accurate than the exponential approximation that is currently most often used for this purpose. The method can be used to generate approximations to attain any desired trade-off between accuracy and computing cost.
NASA Astrophysics Data System (ADS)
Wong, S.; Craig, J. R.
2009-05-01
Recently, Wong S. & J.R. Craig [Computational Methods in Water Resources XVII International Conference, 2008] have developed a semi-analytic series (SAS) solution method for simulating 2D steady-state groundwater flow in multi-layer aquifers with natural unconformity. The advantages of the approach include the capability to predict groundwater flow in aquifer systems with a geometrically complex structure, i.e., layers that are contiguous but vary (sometimes dramatically) in thickness across the modelled domain. The SAS approach is unorthodox compared to numerical scheme such as finite element (FE) method when handling an aquifer basin with contiguous layers. This research attempts to compare the robustness of the SAS solution with that of the FE solution under variety of different geometric conditions, including the increasing of system aspect ratios and the inclusion of pinching layers. It was found that the SAS approach is a useful benchmarking tool and that for contiguous layers, both FE methods continue to be highly accurate at even large aspect ratios. Based on the benchmarking experiments, some rules of thumb for mesh generation in FE models of regional aquifer systems with both contiguous and discontiguous layering are identified.
Elasto-inertial particle focusing under the viscoelastic flow of DNA solution in a square channel.
Kim, Bookun; Kim, Ju Min
2016-03-01
Particle focusing is an essential step in a wide range of applications such as cell counting and sorting. Recently, viscoelastic particle focusing, which exploits the spatially non-uniform viscoelastic properties of a polymer solution under Poiseuille flow, has attracted much attention because the particles are focused along the channel centerline without any external force. Lateral particle migration in polymer solutions in square channels has been studied due to its practical importance in lab-on-a-chip applications. However, there are still many questions about how the rheological properties of the medium alter the equilibrium particle positions and about the flow rate ranges for particle focusing. In this study, we investigated lateral particle migration in a viscoelastic flow of DNA solution in a square microchannel. The elastic property is relevant due to the long relaxation time of a DNA molecule, even when the DNA concentration is extremely low. Further, the shear viscosity of the solution is essentially constant irrespective of shear rate. Our current results demonstrate that the particles migrate toward the channel centerline and the four corners of a square channel in the dilute DNA solution when the inertia is negligible (elasticity-dominant flow). As the flow rate increases, the multiple equilibrium particle positions are reduced to a single file along the channel centerline, due to the elasto-inertial particle focusing mechanism. The current results support that elasto-inertial particle focusing mechanism is a universal phenomenon in a viscoelastic fluid with constant shear viscosity (Boger fluid). Also, the effective flow rate ranges for three-dimensional particle focusing in the DNA solution were significantly higher and wider than those for the previous synthetic polymer solution case, which facilitates high throughput analysis of particulate systems. In addition, we demonstrated that the DNA solution can be applied to focus a wide range of
D4Z - a new renumbering for iterative solution of ground-water flow and solute- transport equations
Kipp, K.L.; Russell, T.F.; Otto, J.S.
1992-01-01
D4 zig-zag (D4Z) is a new renumbering scheme for producing a reduced matrix to be solved by an incomplete LU preconditioned, restarted conjugate-gradient iterative solver. By renumbering alternate diagonals in a zig-zag fashion, a very low sensitivity of convergence rate to renumbering direction is obtained. For two demonstration problems involving groundwater flow and solute transport, iteration counts are related to condition numbers and spectra of the reduced matrices.
Applications of an adaptive unstructured solution algorithm to the analysis of high speed flows
NASA Technical Reports Server (NTRS)
Thareja, R. R.; Prabhu, R. K.; Morgan, K.; Peraire, J.; Peiro, J.
1990-01-01
An upwind cell-centered scheme for the solution of steady laminar viscous high-speed flows is implemented on unstructured two-dimensional meshes. The first-order implementation employs Roe's (1981) approximate Riemann solver, and a higher-order extension is produced by using linear reconstruction with limiting. The procedure is applied to the solution of inviscid subsonic flow over an airfoil, inviscid supersonic flow past a cylinder, and viscous hypersonic flow past a double ellipse. A detailed study is then made of a hypersonic laminar viscous flow on a 24-deg compression corner. It is shown that good agreement is achieved with previous predictions using finite-difference and finite-volume schemes. However, these predictions do not agree with experimental observations. With refinement of the structured grid at the leading edge, good agreement with experimental observations for the distributions of wall pressure, heating rate and skin friction is obtained.
Zhi-Gang Feng
2012-05-31
The simulation of particulate flows for industrial applications often requires the use of two-fluid models, where the solid particles are considered as a separate continuous phase. One of the underlining uncertainties in the use of the two-fluid models in multiphase computations comes from the boundary condition of the solid phase. Typically, the gas or liquid fluid boundary condition at a solid wall is the so called no-slip condition, which has been widely accepted to be valid for single-phase fluid dynamics provided that the Knudsen number is low. However, the boundary condition for the solid phase is not well understood. The no-slip condition at a solid boundary is not a valid assumption for the solid phase. Instead, several researchers advocate a slip condition as a more appropriate boundary condition. However, the question on the selection of an exact slip length or a slip velocity coefficient is still unanswered. Experimental or numerical simulation data are needed in order to determinate the slip boundary condition that is applicable to a two-fluid model. The goal of this project is to improve the performance and accuracy of the boundary conditions used in two-fluid models such as the MFIX code, which is frequently used in multiphase flow simulations. The specific objectives of the project are to use first principles embedded in a validated Direct Numerical Simulation particulate flow numerical program, which uses the Immersed Boundary method (DNS-IB) and the Direct Forcing scheme in order to establish, modify and validate needed energy and momentum boundary conditions for the MFIX code. To achieve these objectives, we have developed a highly efficient DNS code and conducted numerical simulations to investigate the particle-wall and particle-particle interactions in particulate flows. Most of our research findings have been reported in major conferences and archived journals, which are listed in Section 7 of this report. In this report, we will present a
NASA Astrophysics Data System (ADS)
Ben Slimene, Erij; Lassabatere, Laurent; Winiarski, Thierry; Gourdon, Remy
2016-04-01
The understanding of the fate of pollutants in the vadose zone is a prerequisite to manage soil and groundwater quality. Water infiltrates into the soil and carries a large amount of pollutants (heavy metals, organic compounds, etc.). The quality of groundwater depends on the capability of soils to remove pollutants while water infiltrates. The capability of soils to remove pollutants depends not only on their geochemical properties and affinity with pollutants but also on the quality of the contact between the reactive particles of the soil and pollutants. In such a context, preferential flows are the worst scenario since they prevent pollutants from reaching large parts of the soil including reactive zones that could serve for pollutant removal. The negative effects of preferential flow have already been pointed out by several studies. In this paper, we investigate numerically the effect of the establishment of preferential flow in a numerical section (13.5m long and 2.5m deep) that mimics a strongly heterogeneous deposit. The modelled deposit is made of several lithofacies with contrasting hydraulic properties. The numerical study proves that this strong contrast in hydraulic properties triggers the establishment of preferential flow (capillary barriers and funneled flow). Preferential flow develops mainly for low initial water contents and low fluxes imposed at the soil surface. The impact of these flows on solute transfer is also investigated as a function of solute reactivity and affinity to soil sorption sites. Modeled results clearly show that solute transport is greatly impacted by flow heterogeneity. Funneled flows have the same impacts as water fractionation into mobile and immobile transfer with a fast transport of solutes by preferential flow and solute diffusion to zones where the flow is slower. Such a pattern greatly impacts retention and reduces the access of pollutants into large parts of the soil. Retention is thus greatly reduced at the section
Code and Solution Verification of 3D Numerical Modeling of Flow in the Gust Erosion Chamber
NASA Astrophysics Data System (ADS)
Yuen, A.; Bombardelli, F. A.
2014-12-01
Erosion microcosms are devices commonly used to investigate the erosion and transport characteristics of sediments at the bed of rivers, lakes, or estuaries. In order to understand the results these devices provide, the bed shear stress and flow field need to be accurately described. In this research, the UMCES Gust Erosion Microcosm System (U-GEMS) is numerically modeled using Finite Volume Method. The primary aims are to simulate the bed shear stress distribution at the surface of the sediment core/bottom of the microcosm, and to validate the U-GEMS produces uniform bed shear stress at the bottom of the microcosm. The mathematical model equations are solved by on a Cartesian non-uniform grid. Multiple numerical runs were developed with different input conditions and configurations. Prior to developing the U-GEMS model, the General Moving Objects (GMO) model and different momentum algorithms in the code were verified. Code verification of these solvers was done via simulating the flow inside the top wall driven square cavity on different mesh sizes to obtain order of convergence. The GMO model was used to simulate the top wall in the top wall driven square cavity as well as the rotating disk in the U-GEMS. Components simulated with the GMO model were rigid bodies that could have any type of motion. In addition cross-verification was conducted as results were compared with numerical results by Ghia et al. (1982), and good agreement was found. Next, CFD results were validated by simulating the flow within the conventional microcosm system without suction and injection. Good agreement was found when the experimental results by Khalili et al. (2008) were compared. After the ability of the CFD solver was proved through the above code verification steps. The model was utilized to simulate the U-GEMS. The solution was verified via classic mesh convergence study on four consecutive mesh sizes, in addition to that Grid Convergence Index (GCI) was calculated and based on
Similarity Solutions of the Compressible Flow Equations for a General Equation of State
NASA Astrophysics Data System (ADS)
Boyd, Zachary; Ramsey, Scott; Baty, Roy
2015-11-01
The Euler compressible flow equations admit discontinuous (e.g. shock) solutions regardless of the equation of state (EOS) used to close them. In addition, certain classes of initial conditions and EOS admit special flows known as similarity solutions, including some containing shocks. These are useful (1) as test problems for hydrocodes, (2) as intermediate asymptotic estimates for non-symmetric problems, and (3) in forecasting experimental results. To date, the vast majority of work pertaining to similarity solutions of the Euler equations has been accomplished in the context of the ideal gas EOS; the case where the material is arbitrary is less well-understood. In this work, we classify using Lie-group analysis those materials which admit similarity solutions. We also indicate how such solutions may be found for a variety of materials of interest, including those characterized by particular forms of the Gruneisen EOS. Graduate Student Department of Mathematics, UCLA.
Macropore system characteristics controls on non-reactive solute transport at different flow rates
NASA Astrophysics Data System (ADS)
Larsbo, Mats; Koestel, John
2014-05-01
Preferential flow and transport in macroporous soils are important pathways for the leaching of agrochemicals through soils. Preferential solute transport in soil is to a large extent determined by the macropore system characteristics and the water flow conditions. The importance of different characteristics of the macropore system is likely to vary with the flow conditions. The objective of this study was to determine which properties of the macropore system that control the shape of non-reactive tracer solute breakthrough curves at different steady-state flow rates. We sampled five undisturbed columns (20 cm high, 20 cm diameter) from the soil surface of four soils with clay contents between 21 and 50 %. Solute transport experiments were carried out under unsaturated conditions at 2, 4, 6, 8 and 12 mm h-1 flow rates. For each flow rate a pulse of potassium bromide solution was applied at the soil surface and the electrical conductivity was measured with high temporal resolution in the column effluent. We used the 5 % arrival time and the holdback factor to estimate the degree of preferential transport from the resulting breakthrough curves. Unsaturated hydraulic conductivities were measured at the soil surface of the columns using a tension disc infiltrometer. The macropore system was imaged by industrial X-ray computed tomography at a resolution of 125 μm in all directions. Measures of the macropore system characteristics including measures of pore continuity were calculated from these images using the ImageJ software. Results show that the degree of preferential transport is generally increasing with flow rate when larger pores become active in the transport. The degree of preferential flow was correlated to measures of macropore topology. This study show that conclusions drawn from experiments carried out at one flow rate should generally not be extrapolated to other flow rates.
Coppola, Antonio; Comegna, Vincenzo; Basile, Angelo; Lamaddalena, Nicola; Severino, Gerardo
2009-02-16
Soils often exhibit a variety of small-scale heterogeneities such as inter-aggregate pores and voids which partition flow into separate regions. In this paper a methodological approach is discussed for characterizing the hydrological behaviour of a heterogeneous clayey-sandy soil in the presence of structural inter-aggregate pores. For the clay soil examined, it was demonstrated that, coupling the transfer function approach for analyzing BTCs and water retention data obtained with different methods from laboratory studies captures the bimodal geometry of the porous system along with the related existence of fast and slow flow paths. To be effectively and reliably applied this approach requires that the predominant effects of the soil hydrological behaviour near saturation be supported by accurate experimental data of both breakthrough curves (BTCs) and hydraulic functions for high water content values. This would allow the separation of flow phases and hence accurate identification of the processes and related parameters. PMID:19042056
NASA Astrophysics Data System (ADS)
Liu, Wei; Wen, Jizhou; Chao, Jiangyue; Yin, Weiyou; Shen, Chen; Lai, Dayi; Lin, Chao-Hsin; Liu, Junjie; Sun, Hejiang; Chen, Qingyan
2012-09-01
Flow fields in commercial airliner cabins are crucial for creating a thermally comfortable and healthy cabin environment. Flow fields depend on the thermo-fluid boundary conditions at the diffusers, in addition to the cabin geometry and furnishing. To study the flow fields in cabins, this paper describes a procedure to obtain the cabin geometry, boundary conditions at the diffusers, and flow fields. This investigation used a laser tracking system and reverse engineering to generate a digital model of an MD-82 aircraft cabin. Even though the measuring error by the system was very small, approximations and assumptions were needed to reduce the workload and data size. The geometric model can also be easily used to calculate the space volume. A combination of hot-sphere anemometers (HSA) and ultrasonic anemometers (UA) were applied to obtain the velocity magnitude, velocity direction, and turbulence intensity at the diffusers. The measured results indicate that the flow boundary conditions in a real cabin were rather complex and the velocity magnitude, velocity direction, and turbulence intensity varied significantly from one slot opening to another. UAs were also applied to measure the three-dimensional air velocity at 20 Hz, which could also be used to determine the turbulence intensity. Due to the instability of the flow, it should at least be measured for 4 min to obtain accurate averaged velocity and turbulence information. It was found that the flow fields were of low speed and high turbulence intensity. This study provides high quality data for validating Computational Fluid Dynamics (CFD) models, including cabin geometry, boundary conditions of diffusers, and high-resolution flow field in the first-class cabin of a functional MD-82 commercial airliner.
Diffusional solute flux during osmotic water flow across the human red cell membrane.
Brahm, J; Galey, W R
1987-05-01
The effect of solvent drag on the unidirectional efflux of labeled water, urea, and chloride from human red cells was studied by means of the continuous flow tube method under conditions of osmotic equilibrium and net volume flow. Solvent (water) flow out of cells was created by mixing cells equilibrated in 100 mM salt solution with a 200-mM or 250-mM salt solution, while flow of water into cells was obtained by equilibrating the cells in the higher concentration and mixing them with the 100-mM solution. Control experiments constitute measurements of efflux of [14C]ethanol in normal cells and 3H2O in cells treated with p-chloromercuribenzosulfonate under the conditions described above. In both instances, the solute is known to penetrate the membrane through nonporous pathways. As anticipated, the tracer flux of neither urea nor chloride showed any dependence on net solvent flow, regardless of the direction. If one assumes the recently reported reflection coefficient for urea of 0.7, the urea tracer flux should change by at least 24% under volume flow conditions. Since such changes would be easily detected with our method, we conclude that the pathways for water, for urea, and for chloride are functionally separated. PMID:3037007
Sheng, F.; Wang, K.; Zhang, R.; Liu, H.H.
2009-03-15
Preferential flow and solute transport are common processes in the unsaturated soil, in which distributions of soil water content and solute concentrations are often characterized as fractal patterns. An active region model (ARM) was recently proposed to describe the preferential flow and transport patterns. In this study, ARM governing equations were derived to model the preferential soil water flow and solute transport processes. To evaluate the ARM equations, dye infiltration experiments were conducted, in which distributions of soil water content and Cl{sup -} concentration were measured. Predicted results using the ARM and the mobile-immobile region model (MIM) were compared with the measured distributions of soil water content and Cl{sup -} concentration. Although both the ARM and the MIM are two-region models, they are fundamental different in terms of treatments of the flow region. The models were evaluated based on the modeling efficiency (ME). The MIM provided relatively poor prediction results of the preferential flow and transport with negative ME values or positive ME values less than 0.4. On the contrary, predicted distributions of soil water content and Cl- concentration using the ARM agreed reasonably well with the experimental data with ME values higher than 0.8. The results indicated that the ARM successfully captured the macroscopic behavior of preferential flow and solute transport in the unsaturated soil.
A 3D-CFD code for accurate prediction of fluid flows and fluid forces in seals
NASA Technical Reports Server (NTRS)
Athavale, M. M.; Przekwas, A. J.; Hendricks, R. C.
1994-01-01
Current and future turbomachinery requires advanced seal configurations to control leakage, inhibit mixing of incompatible fluids and to control the rotodynamic response. In recognition of a deficiency in the existing predictive methodology for seals, a seven year effort was established in 1990 by NASA's Office of Aeronautics Exploration and Technology, under the Earth-to-Orbit Propulsion program, to develop validated Computational Fluid Dynamics (CFD) concepts, codes and analyses for seals. The effort will provide NASA and the U.S. Aerospace Industry with advanced CFD scientific codes and industrial codes for analyzing and designing turbomachinery seals. An advanced 3D CFD cylindrical seal code has been developed, incorporating state-of-the-art computational methodology for flow analysis in straight, tapered and stepped seals. Relevant computational features of the code include: stationary/rotating coordinates, cylindrical and general Body Fitted Coordinates (BFC) systems, high order differencing schemes, colocated variable arrangement, advanced turbulence models, incompressible/compressible flows, and moving grids. This paper presents the current status of code development, code demonstration for predicting rotordynamic coefficients, numerical parametric study of entrance loss coefficients for generic annular seals, and plans for code extensions to labyrinth, damping, and other seal configurations.
A tale of two solutes: Dual-domain flow and the role of the mass transfer coefficient
NASA Astrophysics Data System (ADS)
Callaghan, M. V.; Bishop, J. M.; Cey, E. E.; Bentley, L. R.
2011-12-01
' histories were different because of the difference in their distribution at the beginning of the experiment. Dual-permeability water flow and solute transport has been modeled using the HYDRUS software package. The numerical model was calibrated to both the observed salt and tracer concentrations, and, consequently, the distinct behavior of the two solutes. The numerical modeling results indicate that salt and tracer transport are sensitive to the mass transfer coefficient between matrix and macropore domains and, consequently, proper selection of the coefficient value is key to the accurate prediction of transport in dual permeability media.
Stratified flow over topography: time-dependent comparisons between model solutions and observations
NASA Astrophysics Data System (ADS)
Cummins, Patrick F.
2000-12-01
Detailed observations of stratified flow over a sill in Knight Inlet, British Columbia are compared with numerical solutions from a two-dimensional primitive equation model. The comparison focuses on the establishment of the high drag state over the sill in response to a time-varying barotropic forcing associated with an ebbing tidal flow. The results show that the model solution evolves to a hydraulically controlled, high drag state that is similar to the observed one. However, the model evolution to this state occurs rapidly through an overturning internal wave response with subsequent convective mixing. On the other hand, the observations show a more gradual evolution with no apparent overturning. It is suggested that flow separation in the lee of the sill crest, which typically is not well represented in models of stratified flow, likely exerts a strong control on the rate and manner in which the high drag state becomes established.
Kogi, Osamu; Kim, Haeng-Boo; Kitamura, Noboru
2002-07-01
A microspectroscopy system combined with a fluid manifold was developed to manipulate and analyze "single" living cells. A sample buffer solution containing living cells was introduced into a flow cell set on a thermostated microscope stage and a few cells were allowed to attach to the bottom wall of the flow cell. With these living cells being attached to the wall, other floating cells were pumped out by flowing a buffer solution. These procedures made it possible to keep a few cells in the flow cell and to analyze single cells by fluorescence microspectroscopy. The technique was applied to study the time course of staining processes of single living yeast (Saccharomyces cerevisiae) cells by using two types of a fluorescent probe. The present methodology was shown to be of primary importance for obtaining biochemical/physiological information on single living cells and also for studying cell-to-cell variations in several characteristics.
Emergence of spatio-temporal dynamics from exact coherent solutions in pipe flow
NASA Astrophysics Data System (ADS)
Ritter, Paul; Mellibovsky, Fernando; Avila, Marc
2016-08-01
Turbulent-laminar patterns are ubiquitous near transition in wall-bounded shear flows. Despite recent progress in describing their dynamics in analogy to non-equilibrium phase transitions, there is no theory explaining their emergence. Dynamical-system approaches suggest that invariant solutions to the Navier–Stokes equations, such as traveling waves and relative periodic orbits in pipe flow, act as building blocks of the disordered dynamics. While recent studies have shown how transient chaos arises from such solutions, the ensuing dynamics lacks the strong fluctuations in size, shape and speed of the turbulent spots observed in experiments. We here show that chaotic spots with distinct dynamical and kinematic properties merge in phase space and give rise to the enhanced spatio-temporal patterns observed in pipe flow. This paves the way for a dynamical-system foundation to the phenomenology of turbulent-laminar patterns in wall-bounded extended shear flows.
Emergence of spatio-temporal dynamics from exact coherent solutions in pipe flow
NASA Astrophysics Data System (ADS)
Ritter, Paul; Mellibovsky, Fernando; Avila, Marc
2016-08-01
Turbulent-laminar patterns are ubiquitous near transition in wall-bounded shear flows. Despite recent progress in describing their dynamics in analogy to non-equilibrium phase transitions, there is no theory explaining their emergence. Dynamical-system approaches suggest that invariant solutions to the Navier-Stokes equations, such as traveling waves and relative periodic orbits in pipe flow, act as building blocks of the disordered dynamics. While recent studies have shown how transient chaos arises from such solutions, the ensuing dynamics lacks the strong fluctuations in size, shape and speed of the turbulent spots observed in experiments. We here show that chaotic spots with distinct dynamical and kinematic properties merge in phase space and give rise to the enhanced spatio-temporal patterns observed in pipe flow. This paves the way for a dynamical-system foundation to the phenomenology of turbulent-laminar patterns in wall-bounded extended shear flows.
Application of the homotopy method for analytical solution of non-Newtonian channel flows
NASA Astrophysics Data System (ADS)
Roohi, Ehsan; Kharazmi, Shahab; Farjami, Yaghoub
2009-06-01
This paper presents the homotopy series solution of the Navier-Stokes and energy equations for non-Newtonian flows. Three different problems, Couette flow, Poiseuille flow and Couette-Poiseuille flow have been investigated. For all three cases, the nonlinear momentum and energy equations have been solved using the homotopy method and analytical approximations for the velocity and the temperature distribution have been obtained. The current results agree well with those obtained by the homotopy perturbation method derived by Siddiqui et al (2008 Chaos Solitons Fractals 36 182-92). In addition to providing analytical solutions, this paper draws attention to interesting physical phenomena observed in non-Newtonian channel flows. For example, it is observed that the velocity profile of non-Newtonian Couette flow is indistinctive from the velocity profile of the Newtonian one. Additionally, we observe flow separation in non-Newtonian Couette-Poiseuille flow even though the pressure gradient is negative (favorable). We provide physical reasoning for these unique phenomena.
Transonic small disturbances equation applied to the solution of two-dimensional nonsteady flows
NASA Technical Reports Server (NTRS)
Couston, M.; Angelini, J. J.; Mulak, P.
1980-01-01
Transonic nonsteady flows are of large practical interest. Aeroelastic instability prediction, control figured vehicle techniques or rotary wings in forward flight are some examples justifying the effort undertaken to improve knowledge of these problems is described. The numerical solution of these problems under the potential flow hypothesis is described. The use of an alternating direction implicit scheme allows the efficient resolution of the two dimensional transonic small perturbations equation.
Prusa, J. . Dept. of Mechanical Engineering); Manglik, R.M. . Dept. of Mechanical, Industrial, and Nuclear Engineering)
1994-08-01
Methods that predict heat transfer rates in thermally developing flows, important in engineering design, are often compared with the classical Graetz problem. Surprisingly, numerical solutions to this problem generally do not give accurate results in the entrance region. This inaccuracy stems from the existence of a singularity at the tube inlet. By adopting a fundamental approach based upon singular perturbation theory, the heat transfer process in the tube entrance has been analyzed to bring out the asymptotic boundary layer structure of the generalized problem with non-Newtonian flows. Using a standard finite difference method with only 21 radial nodes, results within 0.3% of the exact solution to the Graetz problem (Newtonian limit of generalized power law fluid flows) are obtained. Compared with previous numerical solutions reported in the literature, these results are an order of magnitude improvement in the accuracy with an order of magnitude decrease in the required number of radial nodes. Also, the number of radial nodes does not have to be increased in the present method to maintain this high level of accuracy as the initial singularity is approached. Solutions for power law, non-Newtonian fluid flows are presented, and generalized correlations are given for predicting Nusselt numbers in both the thermal entrance region and fully developed flows with 0 < n [<=] [infinity].
NASA Astrophysics Data System (ADS)
Voorhies, Goerte V.; Nishihama, Masahiro
1994-04-01
The effects of laterally homogeneous mantle electrical conductivity have been included in steady, frozen-flux core surface flow estimation along with refinements in method and weighting. The refined method allows simultaneous solution for both the initial radial geomagnetic field component at the core-mantle boundary and the subadjacent fluid motion; it also features Gauss' method for solving the nonlinear inverse problem associated with steady motional induction. The trade-off between spatial complexity of the derived flows and misfit to the weighted Definitive Geomagnetic Reference Field models is studied for various mantle conductivity profiles. For simple flow and a fixed initial geomagnetic condition a fairly high deep-mantle conductivity performs better than either insulating or weakly conducting profiles; however, a thin, very high conductivity layer at the base of the mantle performs almost as well. Simultaneous solution for both initial geomagnetic field and fluid flow reduces the misfit per degree of freedom even more than does changing the mantle conductivity profile. Moreover, when both core field and flow are estimated, the performance of the solutions and the derived flows become insensitive to the conductivity profile.
NASA Technical Reports Server (NTRS)
Voorhies, Coerte V.; Nishihama, Masahiro
1993-01-01
The effects of laterally homogeneous mantle electrical conductivity were included in steady, frozen-flux core surface flow estimation along with refinements in method and weighting. The refined method allows simultaneous solution for both the initial radial geomagnetic field component at the core-mantle boundary (CMB) and the sub-adjacent fluid motion; it also features Gauss' method for solving the non-linear inverse problem associated with steady motional induction. The tradeoff between spatial complexity of the derived flows and misfit to the weighted Definitive Geomagnetic Reference Field models (DGRF's) is studied for various mantle conductivity profiles. For simple flow and a fixed initial geomagnetic condition, a fairly high deep-mantle conductivity performs better than either insulating or weakly conducting profiles; however, a thin, very high conductivity layer at the base of the mantle performs almost as well. Simultaneous solution for both initial geomagnetic field and flow reduces the misfit per degree of freedom even more than does changing the mantle conductivity profile. Moreover, when both core field and flow are estimated, the performance of the solutions and the derived flows become insensitive to the conductivity profile.
Raymond, Yves; Champagne, Claude P
2015-04-01
The goals of this study were to evaluate the precision and accuracy of flow cytometry (FC) methodologies in the evaluation of populations of probiotic bacteria (Lactobacillus rhamnosus R0011) in two commercial dried forms, and ascertain the challenges in enumerating them in a chocolate matrix. FC analyses of total (FC(T)) and viable (FC(V)) counts in liquid or dried cultures were almost two times more precise (reproducible) than traditional direct microscopic counts (DCM) or colony forming units (CFU). With FC, it was possible to ascertain low levels of dead cells (FC(D)) in fresh cultures, which is not possible with traditional CFU and DMC methodologies. There was no interference of chocolate solids on FC counts of probiotics when inoculation was above 10(7) bacteria per g. Addition of probiotics in chocolate at 40 °C resulted in a 37% loss in viable cells. Blending of the probiotic powder into chocolate was not uniform which raised a concern that the precision of viable counts could suffer. FCT data can serve to identify the correct inoculation level of a sample, and viable counts (FCV or CFU) can subsequently be better interpreted.
{N} =2 supersymmetric Janus solutions and flows: from gauged supergravity to M theory
NASA Astrophysics Data System (ADS)
Pilch, Krzysztof; Tyukov, Alexander; Warner, Nicholas P.
2016-05-01
We investigate a family of SU(3)×U(1)×U(1)-invariant holographic flows and Janus solutions obtained from gauged {N} = 8 supergravity in four dimensions. We give complete details of how to use the uplift formulae to obtain the corresponding solutions in M theory. While the flow solutions appear to be singular from the four-dimensional perspective, we find that the eleven-dimensional solutions are much better behaved and give rise to interesting new classes of compactification geometries that are smooth, up to orbifolds, in the infra-red limit. Our solutions involve new phases in which M2 branes polarize partially or even completely into M5 branes. We derive the eleven-dimensional supersymmetries and show that the eleven-dimensional equations of motion and BPS equations are indeed satisfied as a consequence of their four-dimensional counterparts. Apart from elucidating a whole new class of eleven-dimensional Janus and flow solutions, our work provides extensive and highly non-trivial tests of the recently-derived uplift formulae.
NASA Technical Reports Server (NTRS)
Weinberg, B. C.; Mcdonald, H.
1982-01-01
A numerical scheme is developed for solving the time dependent, three dimensional compressible viscous flow equations to be used as an aid in the design of helicopter rotors. In order to further investigate the numerical procedure, the computer code developed to solve an approximate form of the three dimensional unsteady Navier-Stokes equations employing a linearized block implicit technique in conjunction with a QR operator scheme is tested. Results of calculations are presented for several two dimensional boundary layer flows including steady turbulent and unsteady laminar cases. A comparison of fourth order and second order solutions indicate that increased accuracy can be obtained without any significant increases in cost (run time). The results of the computations also indicate that the computer code can be applied to more complex flows such as those encountered on rotating airfoils. The geometry of a symmetric NACA four digit airfoil is considered and the appropriate geometrical properties are computed.
NASA Technical Reports Server (NTRS)
Reed, D. A.; Patrick, M. L.
1985-01-01
The applicability of static data flow architectures to the iterative solution of sparse linear systems of equations is investigated. An analytic performance model of a static data flow computation is developed. This model includes both spatial parallelism, concurrent execution in multiple PE's, and pipelining, the streaming of data from array memories through the PE's. The performance model is used to analyze a row partitioned iterative algorithm for solving sparse linear systems of algebraic equations. Based on this analysis, design parameters for the static data flow architecture as a function of matrix sparsity and dimension are proposed.
Solutions of turbulent backward-facing step flow with heat transfer using the finite volume method
Horstman, R.H.; Cochran, R.J.; Emergy, A.F.
1995-12-31
The heated turbulent flow over a backward-facing step is numerically solved using the commercial computational fluid dynamics program FLUENT. The methods used here consist of the default power-law upwinding scheme, default multigrid equation solution method and a standard k-{var_epsilon} turbulence model with wall functions. A total of four separate cases are reported. The four cases consist of combinations of partially and fully developed flow at the inlet with uniform or developed temperature profiles. Three mesh refinements are reported for each flow.
New developmnts in flow measurement technology provide solutions to difficult process applications
Rose, C.; Vass, G.
1995-12-31
This paper describes some new methods developed in the last few years that allow solutions to historically difficult flow measurement applications. Some of these applications are: measuring the flow from a piston pump, long term reliable operation on a process that tends to coat out on the pipeline, monitoring flow in partially-filled lines, and the measurement of fluids with solids in high speed batching applications. The new methods adapt basic electromagnetic flowmeter (magmeter) technology, with new approaches in sensor and electronics design, allowing these difficult applications to succeed. Applicable industries are Chemical, Food & Beverage, Water & Waste, and allied process industries. Successful applications will be cited regarding this topic.
Pseudo-direct solution to the boundary-layer equations for separated flow
NASA Technical Reports Server (NTRS)
Arieli, R.; Murphy, J. D.
1979-01-01
This paper describes a procedure for the automatic iteration of an inverse boundary-layer technique to a prescribed pressure distribution in a separated flow. The technique is demonstrated by computation of two transonic airfoil flows and two externally generated shock boundary-layer interaction flows. These results are compared to experimental data and to solutions of the full Navier-Stokes equations. These comparisons indicate that substantial economies can be obtained by applying methods like the present, in lieu of full Navier-Stokes methods, in zonal calculation schemes for design purposes. The optimization technique leading to convergence is described in detail and a table of typical computation time is presented.
Calculation procedures for potential and viscous flow solutions for engine inlets
NASA Technical Reports Server (NTRS)
Albers, J. A.; Stockman, N. O.
1973-01-01
The method and basic elements of computer solutions for both potential flow and viscous flow calculations for engine inlets are described. The procedure is applicable to subsonic conventional (CTOL), short-haul (STOL), and vertical takeoff (VTOL) aircraft engine nacelles operating in a compressible viscous flow. The calculated results compare well with measured surface pressure distributions for a number of model inlets. The paper discusses the uses of the program in both the design and analysis of engine inlets, with several examples given for VTOL lift fans, acoustic splitters, and for STOL engine nacelles. Several test support applications are also given.
NASA Astrophysics Data System (ADS)
Dryahina, K.; Spanel, P.
2005-07-01
A method to calculate diffusion coefficients of ions important for the selected ion flow tube mass spectrometry, SIFT-MS, is presented. The ions, on which this method is demonstrated, include the SIFT-MS precursors H3O+(H2O)0,1,2,3, NO.+(H2O)0,1,2 and O2+ and the product ions relevant to analysis of breath trace metabolites ammonia (NH3+(H2O)0,1,2, NH4+(H2O)0,1,2), acetaldehyde (C2H4OH+(H2O)0,1,2), acetone (CH3CO+, (CH3)2CO+, (CH3)2COH+(H2O)0,1, (CH3)2CO.NO+), ethanol (C2H5OHH+(H2O)0,1,2) and isoprene (C5H7+, C5H8+, C5H9+). Theoretical model of the (12, 4) potential for interaction between the ions and the helium atoms is used, with the repulsive part approximated by the mean hard-sphere cross section and the attractive part describing ion-induced dipole interactions. The reduced zero-field mobilities at 300 K are calculated using the Viehland and Mason theory [L.A. Viehland, S.L. Lin, E.A. Mason, At. Data Nucl. Data Tables, 60 (1995) 37-95], parameterised by a simple formula as a function of the mean hard-sphere cross section, and converted to diffusion coefficients using the Einstein relation. The method is tested on a set of experimental data for simple ions and cluster ions.
Numerical study of wave effects on groundwater flow and solute transport in a laboratory beach.
Geng, Xiaolong; Boufadel, Michel C; Xia, Yuqiang; Li, Hailong; Zhao, Lin; Jackson, Nancy L; Miller, Richard S
2014-09-01
A numerical study was undertaken to investigate the effects of waves on groundwater flow and associated inland-released solute transport based on tracer experiments in a laboratory beach. The MARUN model was used to simulate the density-dependent groundwater flow and subsurface solute transport in the saturated and unsaturated regions of the beach subjected to waves. The Computational Fluid Dynamics (CFD) software, Fluent, was used to simulate waves, which were the seaward boundary condition for MARUN. A no-wave case was also simulated for comparison. Simulation results matched the observed water table and concentration at numerous locations. The results revealed that waves generated seawater-groundwater circulations in the swash and surf zones of the beach, which induced a large seawater-groundwater exchange across the beach face. In comparison to the no-wave case, waves significantly increased the residence time and spreading of inland-applied solutes in the beach. Waves also altered solute pathways and shifted the solute discharge zone further seaward. Residence Time Maps (RTM) revealed that the wave-induced residence time of the inland-applied solutes was largest near the solute exit zone to the sea. Sensitivity analyses suggested that the change in the permeability in the beach altered solute transport properties in a nonlinear way. Due to the slow movement of solutes in the unsaturated zone, the mass of the solute in the unsaturated zone, which reached up to 10% of the total mass in some cases, constituted a continuous slow release of solutes to the saturated zone of the beach. This means of control was not addressed in prior studies.
Dynamic dissolution of halite rock during flow of diluted saline solutions
NASA Astrophysics Data System (ADS)
Weisbrod, N.; Alon-Mordish, C.; Yechieli, Y.
2010-12-01
Continuous recession of the Dead Sea (DS) water level influences the location of the underground interface between fresh aquifer water and DS water (DSW). As the interface moves, salt layers are exposed to and potentially dissolved by dilute solutions. This process has resulted in the formation of hundreds of sinkholes along the DS shore during the last decade. Very little is known about the dynamics of salt dissolution during flow of dilute saline solution. Patterns and kinetics of halite dissolution were examined during the flow of unsaturated DSW solutions in a series of laboratory experiments. Flow experiments were carried out in natural halite cores taken from boreholes drilled along the DS shore (15-30 m deep). First, the permeability of the core was determined using 100% DSW. Next, 100% DSW was replaced by diluted DSW and changes in permeability and flow were studied. Dissolution patterns were monitored by digital camera and computerized tomography (CT). The mass of NaCl dissolved from the core was determined based on outlet solution density. In one set of experiments, a 2-mm wide channel was drilled through the length of the entire core prior to flow to study dissolution along a preexisting channel. Our results show that above a critical flow velocity (0.01ml/min), dissolution developed along preferential pathways and formed distinct channels. The channel structure related to the halite properties and internal heterogeneities. Under flow velocity less than 0.01 ml/min, dissolution developed as a propagating front. At these low velocities, salt reprecipitation in pores often resulted in clogging and cessation of flow through the salt core. The effect of solution density on the dissolution pattern was also found to be important, as more channels developed upward due to gravitational fractionation. In summary, our results suggest that dissolution through massive salt layers will occur in very specific locations where resistance to flow is at a minimum. These
Testing and benchmarking of a three-dimensional groundwater flow and solute transport model
Sims, P.N.; Andersen, P.F.; Faust, C.R.; Stephenson, D.E.
1988-12-31
A three-dimensional finite-difference model was developed to simulate groundwater flow and solute transport. The model is intended for application to a variety of groundwater resource and solute migration evaluations, including several complex sites at the Savannah River Plant (SRP). Because the model, FTWORK, is relatively new, there is a need to provide confidence in the model results. Methodologies that test models include comparisons with analytical solutions, comparisons with empirical data, and checking that conservation properties hold. Another level of testing is the comparison of one code against another. This paper describes the testing and benchmarking procedure used to verify the validate FTWORK.
Analytical and Numerical Solutions of a Generalized Hyperbolic Non-Newtonian Fluid Flow
NASA Astrophysics Data System (ADS)
Pakdemirli, Mehmet; Sarı, Pınar; Solmaz, Bekir
2010-03-01
The generalized hyperbolic non-Newtonian fluid model first proposed by Al-Zahrani [J. Petroleum Sci. Eng. 17, 211 (1997)] is considered. This model was successfully applied to some drilling fluids with a better performance in relating shear stress and velocity gradient compared to power-law and the Hershel-Bulkley model. Special flow geometries namely pipe flow, parallel plate flow, and flow between two rotating cylinders are treated. For the first two cases, analytical solutions of velocity profiles and discharges in the form of integrals are presented. These quantities are calculated by numerically evaluating the integrals. For the flow between two rotating cylinders, the differential equation is solved by the Runge-Kutta method combined with shooting. For all problems, the power-law approximation of the model is compared with the generalized hyperbolic model, too.
Analytical solution for two-dimensional groundwater flow in presence of two isopotential lines
NASA Astrophysics Data System (ADS)
Holzbecher, Ekkehard
2005-12-01
The groundwater flow pattern is examined in an idealized situation, which is an approximation for situations as found at the confluence of rivers or where streams flow into or out of a lake or at peninsulas or bays. Two isopotential lines meet at an angle α; it is assumed that the aquifer is well connected to all surface water bodies. Moreover, groundwater flow is determined by a base flow component and recharge or pumping wells. The flow field is constructed using superposition of analytical solutions and conformal mapping. Classical results for α = π concerning the onset of bank filtration and the length of the infiltration zone are extended for the general case. Finally, an outlook is given on general problem setups, for which the proposed methodology can be applied too.
NASA Technical Reports Server (NTRS)
Liu, C. H.; Wong, T. C.; Kandil, O. A.
1988-01-01
The two-dimensional flow over a blunt leading-edge plate is simulated on the basis of an Euler/Navier-Stokes zonal scheme. The scheme uses an implicit upwind finite-volume scheme, which is based on the van Leer flux-vector splitting. It is shown that the Euler/Navier-Stokes zonal scheme with downstream boundary-layer compatibility conditions is accurate and efficient.
Influence of spatial and temporal flow variability on solute transport in catchments
NASA Astrophysics Data System (ADS)
Selroos, Jan-Olof; Destouni, Georgia
2015-04-01
The present study quantifies the separate and combined effects of spatial and temporal variability of waterborne solute transport through catchments. The questions addressed are whether, when and why different types of variability may dominate catchment-scale transport. We utilize a versatile numerical solute transport code with a particle-based Monte Carlo time domain random walk method to simulate waterborne transport through a generic catchment. The methodology is exemplified by performing simulations using data on spatiotemporal flow and transport variability from direct stream discharge observations and independently calculated advective solute travel time distributions for catchments within the water management district Northern Baltic Proper (NBP) in Mid-Eastern Sweden. A main conclusion of the study is that projections of catchment mass loading based on spatial variability alone are robust estimates of long-term average solute transport development. This is especially true when annually aggregated mass load rather than finer temporal resolution of mass flux is considered. Temporal variability yields short-term fluctuations around the long-term average solute breakthrough development, and earlier or later arrival than the latter, depending on the timing and duration of solute input relative to the temporal flow variability. The exact temporal characteristics of future solute breakthroughs are thus fundamentally uncertain but their statistical expectation may be well quantified by only spatial variability account.
NASA Astrophysics Data System (ADS)
Danish, Mohammad; Kumar, Shashi; Kumar, Surendra
2012-03-01
Exact analytical solutions for the velocity profiles and flow rates have been obtained in explicit forms for the Poiseuille and Couette-Poiseuille flow of a third grade fluid between two parallel plates. These exact solutions match well with their numerical counter parts and are better than the recently developed approximate analytical solutions. Besides, effects of various parameters on the velocity profile and flow rate have been studied.
Practical aspects of spatially high accurate methods
NASA Technical Reports Server (NTRS)
Godfrey, Andrew G.; Mitchell, Curtis R.; Walters, Robert W.
1992-01-01
The computational qualities of high order spatially accurate methods for the finite volume solution of the Euler equations are presented. Two dimensional essentially non-oscillatory (ENO), k-exact, and 'dimension by dimension' ENO reconstruction operators are discussed and compared in terms of reconstruction and solution accuracy, computational cost and oscillatory behavior in supersonic flows with shocks. Inherent steady state convergence difficulties are demonstrated for adaptive stencil algorithms. An exact solution to the heat equation is used to determine reconstruction error, and the computational intensity is reflected in operation counts. Standard MUSCL differencing is included for comparison. Numerical experiments presented include the Ringleb flow for numerical accuracy and a shock reflection problem. A vortex-shock interaction demonstrates the ability of the ENO scheme to excel in simulating unsteady high-frequency flow physics.
Elongational flow of solutions of poly(ethylene oxide) and sulfonated surfactants.
Smitter, L M; Ruiz, J C; Torres, M E; Müller, A J; Sáez, A E
2002-07-15
In this work, the elongational flow behavior of aqueous solutions of poly(ethylene oxide) (PEO) was studied in the presence of sulfonated surfactants. The technique of opposed-jets flow was used to generate an elongational flow field in which pressure drops were measured as a function of strain rates. The surfactants used were sodium dodecyl benzene sulfonate (SDBS) and an alpha-olefin sulfonate (AOS). Solutions of PEO and other flexible polymers exhibit extension thickening in opposed-jets flow due to the formation of transient networks of entangled molecules. This effect is present at concentrations below the static coil overlap concentration, due to the changes in molecular conformation induced by the flow. When SDBS or AOS are added to PEO solutions at low concentrations, the extension thickening weakens due to an increase in PEO intramolecular interactions that lead to coil contraction. This occurs until the surfactant concentration is close to the critical aggregation concentration reported in the literature. Further addition of surfactant induces the formation of intermolecular interactions as the PEO molecules are expanded by the electrostatic repulsion between attached micellar aggregates, with an associated strengthening of extension thickening. Intramolecular effects were not seen beyond a specific PEO concentration.
Direct estimation of mass flow and diffusion of nitrogen compounds in solution and soil.
Oyewole, Olusegun Ayodeji; Inselsbacher, Erich; Näsholm, Torgny
2014-02-01
Plant nutrient uptake from soil is mainly governed by diffusion and transpirationally induced mass flow, but the current methods for assessing the relative importance of these processes are indirect. We developed a microdialysis method using solutions of different osmotic potentials as perfusates to simulate diffusion and mass flow processes, and assessed how induced mass flow affected fluxes of nitrogen (N) compounds in solution and in boreal forest soil. Varying the osmotic potential of perfusates induced vertical fluxes in the direction of the dialysis membranes at rates of between 1 × 10(-8) and 3 × 10(-7) m s(-1) , thus covering the estimated range of water velocities perpendicular to root surfaces and induced by transpiration. Mass flow increased N fluxes in solution but even more so in soil. This effect was explained by an indirect effect of mass flow on rates of diffusive fluxes, possibly caused by the formation of steeper gradients in concentrations of N compounds from membrane surfaces out in the soil. Our results suggest that transpiration may be an essential driver of plant N acquisition.
Direct estimation of mass flow and diffusion of nitrogen compounds in solution and soil.
Oyewole, Olusegun Ayodeji; Inselsbacher, Erich; Näsholm, Torgny
2014-02-01
Plant nutrient uptake from soil is mainly governed by diffusion and transpirationally induced mass flow, but the current methods for assessing the relative importance of these processes are indirect. We developed a microdialysis method using solutions of different osmotic potentials as perfusates to simulate diffusion and mass flow processes, and assessed how induced mass flow affected fluxes of nitrogen (N) compounds in solution and in boreal forest soil. Varying the osmotic potential of perfusates induced vertical fluxes in the direction of the dialysis membranes at rates of between 1 × 10(-8) and 3 × 10(-7) m s(-1) , thus covering the estimated range of water velocities perpendicular to root surfaces and induced by transpiration. Mass flow increased N fluxes in solution but even more so in soil. This effect was explained by an indirect effect of mass flow on rates of diffusive fluxes, possibly caused by the formation of steeper gradients in concentrations of N compounds from membrane surfaces out in the soil. Our results suggest that transpiration may be an essential driver of plant N acquisition. PMID:24134319
Genesis of Streamwise-Localized Solutions from Globally Periodic Traveling Waves in Pipe Flow
NASA Astrophysics Data System (ADS)
Chantry, M.; Willis, A. P.; Kerswell, R. R.
2014-04-01
The aim in the dynamical systems approach to transitional turbulence is to construct a scaffold in phase space for the dynamics using simple invariant sets (exact solutions) and their stable and unstable manifolds. In large (realistic) domains where turbulence can coexist with laminar flow, this requires identifying exact localized solutions. In wall-bounded shear flows, the first of these has recently been found in pipe flow, but questions remain as to how they are connected to the many known streamwise-periodic solutions. Here we demonstrate that the origin of the first localized solution is in a modulational symmetry-breaking Hopf bifurcation from a known global traveling wave that has twofold rotational symmetry about the pipe axis. Similar behavior is found for a global wave of threefold rotational symmetry, this time leading to two localized relative periodic orbits. The clear implication is that many global solutions should be expected to lead to more realistic localized counterparts through such bifurcations, which provides a constructive route for their generation.
Solute dispersion under electric and pressure driven flows; pore scale processes
NASA Astrophysics Data System (ADS)
Li, Shuai; Raoof, Amir; Schotting, Ruud
2014-09-01
Solute dispersion is one of the major mixing mechanisms in transport through porous media, originating from velocity variations at different scales, starting from the pore scale. Different driving forces, such as pressure driven flow (PDF) and electro-osmotic flow (EOF), establish different velocity profiles within individual pores, resulting in different spreading of solutes at this scale. While the velocity profile in PDF is parabolic due to the wall friction effects, the velocity in EOF is typically plug flow, due to the wall charge effects. In this study, we applied a pore network modeling formulation to simulate the velocity field driven by pressure and electric potential to calculate and compare the corresponding average solute dispersivity values. The influence of different driving forces on the hydrodynamic dispersion of a tracer solute is investigated. Applying the pore network modeling, we could capture the velocity variations among different pores, which is the main contribution for the dispersion coefficient. The correlation between pore velocities against pore sizes is found to be different for EOF and PDF, causing different solute dispersion coefficients. The results can provide insight into modeling of electrokinetic remediation for contaminant cleanup in low permeable soils.
Dual-Code Solution Strategy for Chemically-Reacting Hypersonic Flows
NASA Technical Reports Server (NTRS)
Wood, William A.; Eberhardt, Scott
1995-01-01
A new procedure seeks to combine the thin-layer Navier-Stokes solver LAURA with the parabolized Navier-Stokes solver UPS for the aerothermodynamic solution of chemically-reacting air flow fields. The interface protocol is presented and the method is applied to two slender, blunted shapes. Both axisymmetric and three-dimensional solutions are included with surface pressure and heat transfer comparisons between the present method and previously published results. The case of Mach 25 flow over an axisymmetric six degree sphere-cone with a non-catalytic wall is considered to 100 nose radii. A stability bound on the marching step size was observed with this case and is attributed to chemistry effects resulting from the non-catalytic wall boundary condition. A second case with Mach 28 flow over a sphere-cone-cylinder-flare configuration is computed at both two and five degree angles of attack with a fully-catalytic wall. Surface pressures are seen to be within five percent with the present method compared to the baseline LAURA solution and heat transfers are within 10 percent. The effect of grid resolution is investigated in both the radial and streamwise directions. The procedure demonstrates significant, order of magnitude reductions in solution time and required memory for the three-dimensional case in comparison to an all thin-layer Navier-Stokes solution.
NASA Astrophysics Data System (ADS)
de Monserrat, Albert; Morgan, Jason P.; Taramón, Jorge M.; Hall, Robert
2016-04-01
This work focuses on improving current 2D numerical approaches to modeling the boundary conditions associated with computing accurate deformation and melting associated with continental rifting. Recent models primarily use far-field boundary conditions that have been used for decades with little assessment of their effects on asthenospheric flow beneath the rifting region. All are extremely oversimplified. All are likely to significantly shape the pattern of asthenospheric flow beneath the stretching lithosphere which is associated with pressure-release melting and rift volcanism. The choice of boundary conditions may lead to different predictions of asthenospheric flow and melting associated with lithospheric stretching and breakup. We also find that they may affect the mode of crustal stretching. Here we discuss a suite of numerical experiments using a Lagrangian formulation, that compare these choices to likely more realistic boundary condition choices like the analytical solution for flow associated with two diverging plates stretching over a finite-width region. We also compare embedded and nested meshes with a high-resolution 2-D region within a cartesian 'whole mantle cross-section' box. Our initial results imply that the choice of far-field boundary conditions does indeed significantly influence predicted melting distributions and melt volumes associated with continental breakup. For calculations including asthenospheric melting, the 'finite width plate spreading' and embedded rifting boundary condition treatments lead to significantly smaller BC-influenced signals when using high-resolution calculation regions of order ~1000 km wide and 600 km deep within a lower resolution box of the order of >5000 km wide and 2800 km. We recommend their use when models are attempting to resolve the effects of asthenosphere flow and melting. We also discuss several examples of typical numerical 'artifacts' related to 'edge convection' at the sides of the stretching region
Flow-enhanced solution printing of all-polymer solar cells.
Diao, Ying; Zhou, Yan; Kurosawa, Tadanori; Shaw, Leo; Wang, Cheng; Park, Steve; Guo, Yikun; Reinspach, Julia A; Gu, Kevin; Gu, Xiaodan; Tee, Benjamin C K; Pang, Changhyun; Yan, Hongping; Zhao, Dahui; Toney, Michael F; Mannsfeld, Stefan C B; Bao, Zhenan
2015-08-12
Morphology control of solution coated solar cell materials presents a key challenge limiting their device performance and commercial viability. Here we present a new concept for controlling phase separation during solution printing using an all-polymer bulk heterojunction solar cell as a model system. The key aspect of our method lies in the design of fluid flow using a microstructured printing blade, on the basis of the hypothesis of flow-induced polymer crystallization. Our flow design resulted in a ∼90% increase in the donor thin film crystallinity and reduced microphase separated donor and acceptor domain sizes. The improved morphology enhanced all metrics of solar cell device performance across various printing conditions, specifically leading to higher short-circuit current, fill factor, open circuit voltage and significantly reduced device-to-device variation. We expect our design concept to have broad applications beyond all-polymer solar cells because of its simplicity and versatility.
Numerical solutions of three-dimensional MHD flows in strong non-uniform transverse magnetic fields
Hua, T.Q.; Walker, J.S.
1988-07-01
Magnetohydrodynamic flows of liquid metals in thin conducting ducts of various geometries in the presence of strong nonuniform transverse magnetic fields are examined. The interaction parameter and Hartmann number are assumed to be large, whereas the magnetic Reynolds number is assumed to be small. Under these assumptions, viscous and inertial effects are confined in very thin boundary layers adjacent to the walls. At walls parallel to the magnetic field lines, as at the side walls of a rectangular duct, the boundary layers (side layers) carry a significant fraction of the volumetric flow rate in the form of high velocity jets. This paper describes the analysis and summarizes the numerical methods for obtaining 3-D solutions (core solutions) for flow parameters outside these layers, without solving explicitly for the layers themselves. 13 refs., 1 fig.
Flow-enhanced solution printing of all-polymer solar cells
Diao, Ying; Zhou, Yan; Kurosawa, Tadanori; Shaw, Leo; Wang, Cheng; Park, Steve; Guo, Yikun; Reinspach, Julia A.; Gu, Kevin; Gu, Xiaodan; Tee, Benjamin C. K.; Pang, Changhyun; Yan, Hongping; Zhao, Dahui; Toney, Michael F.; Mannsfeld, Stefan C. B.; Bao, Zhenan
2015-08-12
Morphology control of solution coated solar cell materials presents a key challenge limiting their device performance and commercial viability. Here we present a new concept for controlling phase separation during solution printing using an all-polymer bulk heterojunction solar cell as a model system. The key aspect of our method lies in the design of fluid flow using a microstructured printing blade, on the basis of the hypothesis of flow-induced polymer crystallization. Our flow design resulted in a similar to 90% increase in the donor thin film crystallinity and reduced microphase separated donor and acceptor domain sizes. The improved morphology enhanced all metrics of solar cell device performance across various printing conditions, specifically leading to higher short-circuit current, fill factor, open circuit voltage and significantly reduced device-to-device variation. However, we expect our design concept to have broad applications beyond all-polymer solar cells because of its simplicity and versatility.
Flow-enhanced solution printing of all-polymer solar cells
Diao, Ying; Zhou, Yan; Kurosawa, Tadanori; Shaw, Leo; Wang, Cheng; Park, Steve; Guo, Yikun; Reinspach, Julia A.; Gu, Kevin; Gu, Xiaodan; Tee, Benjamin C. K.; Pang, Changhyun; Yan, Hongping; Zhao, Dahui; Toney, Michael F.; Mannsfeld, Stefan C. B.; Bao, Zhenan
2015-01-01
Morphology control of solution coated solar cell materials presents a key challenge limiting their device performance and commercial viability. Here we present a new concept for controlling phase separation during solution printing using an all-polymer bulk heterojunction solar cell as a model system. The key aspect of our method lies in the design of fluid flow using a microstructured printing blade, on the basis of the hypothesis of flow-induced polymer crystallization. Our flow design resulted in a ∼90% increase in the donor thin film crystallinity and reduced microphase separated donor and acceptor domain sizes. The improved morphology enhanced all metrics of solar cell device performance across various printing conditions, specifically leading to higher short-circuit current, fill factor, open circuit voltage and significantly reduced device-to-device variation. We expect our design concept to have broad applications beyond all-polymer solar cells because of its simplicity and versatility. PMID:26264528
An Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids
NASA Technical Reports Server (NTRS)
Nielsen, Eric J.; Lu, James; Park, Michael A.; Darmofal, David L.
2003-01-01
An algorithm for solving the discrete adjoint system based on an unstructured-grid discretization of the Navier-Stokes equations is presented. The method is constructed such that an adjoint solution exactly dual to a direct differentiation approach is recovered at each time step, yielding a convergence rate which is asymptotically equivalent to that of the primal system. The new approach is implemented within a three-dimensional unstructured-grid framework and results are presented for inviscid, laminar, and turbulent flows. Improvements to the baseline solution algorithm, such as line-implicit relaxation and a tight coupling of the turbulence model, are also presented. By storing nearest-neighbor terms in the residual computation, the dual scheme is computationally efficient, while requiring twice the memory of the flow solution. The scheme is expected to have a broad impact on computational problems related to design optimization as well as error estimation and grid adaptation efforts.
Malmström, Maria E; Destouni, Georgia; Martinet, Philippe
2004-05-01
Many environmental problems require assessment of extensive reaction systems within natural subsurface flow systems exhibiting large physical and biogeochemical heterogeneity. We present an approach to couple stochastic advective-reactive modeling of physical solute transport (LaSAR) with the geochemical model PHREEQC for modeling solute concentrations in systems with variable flow velocity and multicomponent reactions. PHREEQC allows for general and flexible quantification of a multitude of linear and nonlinear geochemical processes, while LaSAR efficiently handles field-scale solute spreading in stochastic heterogeneous flow fields. The combined LaSAR-PHREEQC approach requires very modest computational efforts, thereby allowing a large number of reactive transport problems to be readily assessed and facilitating handling of quantifiable uncertainty in environmental model applications. Computational efficiency and explicit handling of field-scale dispersion without introduction of excessive fluid mixing that may impair model results are general advantages of the LaSAR compared with alternative solute transport modeling approaches. The LaSAR-PHREEQC approach is restricted to steady or unidirectional flow fields, and our specific application examples are limited to homogeneous reaction systems without local or transverse dispersion-diffusion, although these are not general methodological limitations. As a comprehensive application example, we simulate the spreading of acid mine drainage in a groundwater focusing on Zn2+ and including relevant, major-component geochemistry. Model results show that Zn2+ may be substantially attenuated by both sorption and precipitation, with flow heterogeneity greatly affecting expected solute concentrations downstream of the mine waste deposit in both cases. PMID:15180064
Dynamic dissolution of halite rock during flow of diluted saline solutions
NASA Astrophysics Data System (ADS)
Weisbrod, N.; Alon-Mordish, C.; Konen, E.; Yechieli, Y.
2012-05-01
The dynamic dissolution pattern of halite salt rocks taken from coreholes near the Dead Sea was studied in laboratory-scale experiments. When unsaturated solution (with respect to halite) flowed through salt cores, dissolution developed along preferential flow pathways in a channel structure. The channel structure was related to the salt's properties and internal heterogeneities, flow velocity and impact of gravity. Preferential dissolution pathways developed in areas of minimum resistance to flow, such as large-pore networks and cracks. Nevertheless, in many cases no structural heterogeneity was observed along the dissolution channels prior to the experiments. The initial formation of channels took place above a critical flow velocity; below this threshold, dissolution developed as a slowly propagating front. In these cases, salt re-precipitation resulted in clogging and cessation of flow through a few of the salt cores. Solution density was found to be important, as evidenced by the fact that more channels developed upward than downward, due to gravitational fractionation. The development of dissolution channels could have very important implications for the overall permeability of the salt layer in general, and the use of salt formations for industrial waste storage and the development of sinkholes along the Dead Sea shore in particular.
Weir, Alexander J; Sayer, Robin; Cheng-Xiang Wang; Parks, Stuart
2015-08-01
Medical phantoms are frequently required to verify image and signal processing systems, and are often used to support algorithm development for a wide range of imaging and blood flow assessments. A phantom with accurate scattering properties is a crucial requirement when assessing the effects of multi-path propagation channels during the development of complex signal processing techniques for Transcranial Doppler (TCD) ultrasound. The simulation of physiological blood flow in a phantom with tissue and blood equivalence can be achieved using a variety of techniques. In this paper, poly (vinyl alcohol) cryogel (PVA-C) tissue mimicking material (TMM) is evaluated in conjunction with a number of potential scattering agents. The acoustic properties of the TMMs are assessed and an acoustic velocity of 1524ms(-1), an attenuation coefficient of (0:49) × 10(-4)fdBm(1)Hz(-1), a characteristic impedance of (1.72) × 10(6)Kgm(-2)s(-1) and a backscatter coefficient of (1.12) × 10(-28)f(4)m(-1)Hz(-4)sr(-1) were achieved using 4 freeze-thaw cycles and an aluminium oxide (Al(2)O(3)) scattering agent. This TMM was used to make an anatomically realistic wall-less flow phantom for studying the effects of multipath propagation in TCD ultrasound.
Zhang, Chun-Yang; Yang, Kun
2010-05-01
Due to their unique optical and electronic properties, quantum dots (QDs) have been widely used in a variety of biosensors for sensitive detection of biomarkers and small molecules. However, single QD exhibits dynamic fluctuation of fluorescence intensity (i.e., blinking) with the transition between on and off states, which adversely influences the development of QD-based optical biosensors. Therefore, the methods for efficient evaluation of on-state QD are especially important and highly desirable. In this paper, a novel and unique approach based on single-molecule two-color coincidence detection is developed to simply and accurately evaluate the on-state QDs in a microfluidic flow. Our results demonstrate that improved QDs in the on state are detected in a microfluidic flow in comparison with that in the Brownian motion state, thus paving the way to the development of single QD-based biosensors for sensitive detection of low-abundance biomolecules. This single-molecule two-color coincidence detection has been applied for the homegeneous detection of nucleic acids in a microfluidic flow with the detection sensitivity of 5.0 fM.
Majer, G.; Zick, K.
2015-04-28
A pulsed field gradient spin-echo nuclear magnetic resonance (NMR) sequence with solvent suppression (PGSE-WATERGATE) was applied to accurately measure the diffusion coefficients of Rhodamine 6G (Rh6G) in low-concentration aqueous solutions. Three samples with Rh6G concentrations of C{sub Rh6G} = 1, 4.5, and 25 μM were investigated. The precise determination of the diffusion coefficients in this low-concentration range was made possible by using a cryogenically cooled NMR probe and by the effective solvent suppression of the PGSE-WATERGATE sequence. The present results bridge the gap between diffusion data measured by fluorescence correlation spectroscopy in the single molecule limit and diffusivities obtained by pulsed field gradient NMR (PFG-NMR) without solvent suppression at higher concentrations. To further extend the concentration range, the diffusion coefficient of Rh6G was also measured on a sample with C{sub Rh6G} = 410 μM by PFG-NMR. The overall concentration dependence of the Rh6G diffusion at 25 °C is discussed in terms of dimerization of the Rh6G molecules. The concentration-dependent monomer/dimer proportion is deduced from the diffusion data.
Combined LAURA-UPS solution procedure for chemically-reacting flows. M.S. Thesis
NASA Technical Reports Server (NTRS)
Wood, William A.
1994-01-01
A new procedure seeks to combine the thin-layer Navier-Stokes solver LAURA with the parabolized Navier-Stokes solver UPS for the aerothermodynamic solution of chemically-reacting air flowfields. The interface protocol is presented and the method is applied to two slender, blunted shapes. Both axisymmetric and three dimensional solutions are included with surface pressure and heat transfer comparisons between the present method and previously published results. The case of Mach 25 flow over an axisymmetric six degree sphere-cone with a noncatalytic wall is considered to 100 nose radii. A stability bound on the marching step size was observed with this case and is attributed to chemistry effects resulting from the noncatalytic wall boundary condition. A second case with Mach 28 flow over a sphere-cone-cylinder-flare configuration is computed at both two and five degree angles of attack with a fully-catalytic wall. Surface pressures are seen to be within five percent with the present method compared to the baseline LAURA solution and heat transfers are within 10 percent. The effect of grid resolution is investigated and the nonequilibrium results are compared with a perfect gas solution, showing that while the surface pressure is relatively unchanged by the inclusion of reacting chemistry the nonequilibrium heating is 25 percent higher. The procedure demonstrates significant, order of magnitude reductions in solution time and required memory for the three dimensional case over an all thin-layer Navier-Stokes solution.
NASA Astrophysics Data System (ADS)
Chen, Po-Chia; Chuang, Mo-Hsiung; Tan, Yih-Chi
2014-05-01
In recent years the urban and industrial developments near the coastal area are rapid and therefore the associated population grows dramatically. More and more water demand for human activities, agriculture irrigation, and aquaculture relies on heavy pumping in coastal area. The decline of groundwater table may result in the problems of seawater intrusion and/or land subsidence. Since the 1950s, numerous studies focused on the effect of tidal fluctuation on the groundwater flow in the coastal area. Many studies concentrated on the developments of one-dimensional (1D) and two-dimensional (2D) analytical solutions describing the tide-induced head fluctuations. For example, Jacob (1950) derived an analytical solution of 1D groundwater flow in a confined aquifer with a boundary condition subject to sinusoidal oscillation. Jiao and Tang (1999) derived a 1D analytical solution of a leaky confined aquifer by considered a constant groundwater head in the overlying unconfined aquifer. Jeng et al. (2002) studied the tidal propagation in a coupled unconfined and confined costal aquifer system. Sun (1997) presented a 2D solution for groundwater response to tidal loading in an estuary. Tang and Jiao (2001) derived a 2D analytical solution in a leaky confined aquifer system near open tidal water. This study aims at developing a general analytical solution describing the head fluctuations in a 2D estuarine aquifer system consisted of an unconfined aquifer, a confined aquifer, and an aquitard between them. Both the confined and unconfined aquifers are considered to be anisotropic. The predicted head fluctuations from this solution will compare with the simulation results from the MODFLOW program. In addition, the solutions mentioned above will be shown to be special cases of the present solution. Some hypothetical cases regarding the head fluctuation in costal aquifers will be made to investigate the dynamic effects of water table fluctuation, hydrogeological conditions, and
NASA Astrophysics Data System (ADS)
Bonilla, Jose; Kalwa, Fritz; Händel, Falk; Binder, Martin; Stefan, Catalin
2016-04-01
The Dupuit-Thiem equation is normally used to assess flow towards a pumping well in unconfined aquifers under steady-state conditions. For the formulation of the equation it is assumed that flow is laminar, radial and horizontal towards the well. It is well known that these assumptions are not met in the vicinity of the well; some authors restrict the application of the equation only to a radius larger than 1.5-fold the aquifer thickness. In this study, the equation accuracy to predict the pressure head is evaluated as a simple and quick analytical method to describe the flow pattern for different injection rates in the LSAW. A laboratory scale aquifer-well system (LSAW) was implemented to study the aquifer recharge through wells. The LSAW consists of a 1.0 m-diameter tank with a height of 1.1 meters, filled with sand and a screened well in the center with a diameter of 0.025 m. A regulated outflow system establishes a controlled water level at the tank wall to simulate various aquifer thicknesses. The pressure head at the bottom of the tank along one axis can be measured to assess the flow profile every 0.1 m between the well and the tank wall. In order to evaluate the accuracy of the Dupuit-Thiem equation, a combination of different injection rates and aquifer thicknesses were simulated in the LSAW. Contrary to what was expected (significant differences between the measured and calculated pressure heads in the well), the absolute difference between the calculated and measured pressure head is less than 10%. Beside this, the highest differences are not observed in the well itself, but in the near proximity of it, at a radius of 0.1 m. The results further show that the difference between the calculated and measured pressure heads tends to decrease with higher flow rates. Despite its limitations (assumption of laminar and horizontal flow throughout the whole aquifer), the Dupuit-Thiem equation is considered to accurately represent the flow system in the LSAW.
Slender-Body Theory Based On Approximate Solution of the Transonic Flow Equation
NASA Technical Reports Server (NTRS)
Spreiter, John R.; Alksne, Alberta Y.
1959-01-01
Approximate solution of the nonlinear equations of the small disturbance theory of transonic flow are found for the pressure distribution on pointed slender bodies of revolution for flows with free-stream, Mach number 1, and for flows that are either purely subsonic or purely supersonic. These results are obtained by application of a method based on local linearization that was introduced recently in the analysis of similar problems in two-dimensional flows. The theory is developed for bodies of arbitrary shape, and specific results are given for cone-cylinders and for parabolic-arc bodies at zero angle of attack. All results are compared either with existing theoretical results or with experimental data.
Application of a solution adaptive grid scheme, SAGE, to complex three-dimensional flows
NASA Technical Reports Server (NTRS)
Davies, Carol B.; Venkatapathy, Ethiraj
1991-01-01
A new three-dimensional (3D) adaptive grid code based on the algebraic, solution-adaptive scheme of Nakahashi and Deiwert is developed and applied to a variety of problems. The new computer code, SAGE, is an extension of the same-named two-dimensional (2D) solution-adaptive program that has already proven to be a powerful tool in computational fluid dynamics applications. The new code has been applied to a range of complex three-dimensional, supersonic and hypersonic flows. Examples discussed are a tandem-slot fuel injector, the hypersonic forebody of the Aeroassist Flight Experiment (AFE), the 3D base flow behind the AFE, the supersonic flow around a 3D swept ramp and a generic, hypersonic, 3D nozzle-plume flow. The associated adapted grids and the solution enhancements resulting from the grid adaption are presented for these cases. Three-dimensional adaption is more complex than its 2D counterpart, and the complexities unique to the 3D problems are discussed.
Second-order small-disturbance solutions for hypersonic flow over power-law bodies
NASA Technical Reports Server (NTRS)
Townsend, J. C.
1975-01-01
Similarity solutions were found which give the adiabatic flow of an ideal gas about two-dimensional and axisymmetric power-law bodies at infinite Mach number to second order in the body slenderness parameter. The flow variables were expressed as a sum of zero-order and perturbation similarity functions for which the axial variations in the flow equations separated out. The resulting similarity equations were integrated numerically. The solutions, which are universal functions, are presented in graphic and tabular form. To avoid a singularity in the calculations, the results are limited to body power-law exponents greater than about 0.85 for the two-dimensional case and 0.75 for the axisymmetric case. Because of the entropy layer induced by the nose bluntness (for power-law bodies other than cones and wedges), only the pressure function is valid at the body surface. The similarity results give excellent agreement with the exact solutions for inviscid flow over wedges and cones having half-angles up to about 20 deg. They give good agreement with experimental shock-wave shapes and surface-pressure distributions for 3/4-power axisymmetric bodies, considering that Mach number and boundary-layer displacement effects are not included in the theory.
Implicit unified gas-kinetic scheme for steady state solutions in all flow regimes
NASA Astrophysics Data System (ADS)
Zhu, Yajun; Zhong, Chengwen; Xu, Kun
2016-06-01
This paper presents an implicit unified gas-kinetic scheme (UGKS) for non-equilibrium steady state flow computation. The UGKS is a direct modeling method for flow simulation in all regimes with the updates of both macroscopic flow variables and microscopic gas distribution function. By solving the macroscopic equations implicitly, a predicted equilibrium state can be obtained first through iterations. With the newly predicted equilibrium state, the evolution equation of the gas distribution function and the corresponding collision term can be discretized in a fully implicit way for fast convergence through iterations as well. The lower-upper symmetric Gauss-Seidel (LU-SGS) factorization method is implemented to solve both macroscopic and microscopic equations, which improves the efficiency of the scheme. Since the UGKS is a direct modeling method and its physical solution depends on the mesh resolution and the local time step, a physical time step needs to be fixed before using an implicit iterative technique with a pseudo-time marching step. Therefore, the physical time step in the current implicit scheme is determined by the same way as that in the explicit UGKS for capturing the physical solution in all flow regimes, but the convergence to a steady state speeds up through the adoption of a numerical time step with large CFL number. Many numerical test cases in different flow regimes from low speed to hypersonic ones, such as the Couette flow, cavity flow, and the flow passing over a cylinder, are computed to validate the current implicit method. The overall efficiency of the implicit UGKS can be improved by one or two orders of magnitude in comparison with the explicit one.
Flow and solute transport through a levee separating fluids with different densities
NASA Astrophysics Data System (ADS)
Brooker, Andrew M. H.; Townley, Lloyd R.
1994-06-01
Steady seepage through a levee or a dam separating reservoirs with different levels and densities is shown to result in five possible flow configurations. If densities are equal, the problem reduces to the classical problem of flow through a dam. If the lower reservoir is less dense, a stationary wedge may or may not form inside the levee near the downgradient reservoir level. If the lower reservoir is more dense, a wedge forms near the toe of the levee, as in the classical problem of saltwater intrusion. Another possibility is that the dense wedge can connect the two reservoirs, thus allowing bidirectional flow. Conditions are derived which define when these different flow configurations occur. For the case of a rectangular dam with vertical walls a closed form solution is obtained for the net mass flux between the reservoirs. Net volumetric flux is determined analytically for all flow configurations except the case of bidirectional flow. The expression for volumetric flux is a generalization of a result based on the Dupuit assumption for the case of constant density. A range of parameters is identified in which net volumetric flux is in one direction and net mass flux in the other. A numerical model based on the boundary integral equation method allows calculation of net volumetric flux for the case of bidirectional flow and also allows simulation of more complex levee geometries. The solution has direct application to levees separating ponds in solar salt production, to the causeway across the Great Salt Lake in Utah, and to the role of exchange flows in the genesis of evaporites in nearshore lagoons.
Multigrid solution of incompressible turbulent flows by using two-equation turbulence models
Zheng, X.; Liu, C.; Sung, C.H.
1996-12-31
Most of practical flows are turbulent. From the interest of engineering applications, simulation of realistic flows is usually done through solution of Reynolds-averaged Navier-Stokes equations and turbulence model equations. It has been widely accepted that turbulence modeling plays a very important role in numerical simulation of practical flow problem, particularly when the accuracy is of great concern. Among the most used turbulence models today, two-equation models appear to be favored for the reason that they are more general than algebraic models and affordable with current available computer resources. However, investigators using two-equation models seem to have been more concerned with the solution of N-S equations. Less attention is paid to the solution method for the turbulence model equations. In most cases, the turbulence model equations are loosely coupled with N-S equations, multigrid acceleration is only applied to the solution of N-S equations due to perhaps the fact the turbulence model equations are source-term dominant and very stiff in sublayer region.
Analytical Solution to the Riemann Problem of Three-Phase Flow in Porous Media
Juanes, Ruben; Patzek, Tadeusz W.
2002-09-26
In this paper we study one-dimensional three-phase flow through porous media of immiscible, incompressible fluids. The model uses the common multiphase flow extension of Darcy's equation, and does not include gravity and capillarity effects. Under these conditions, the mathematical problem reduces to a 2 x 2 system of conservation laws whose essential features are: (1) the system is strictly hyperbolic; (2) both characteristic fields are nongenuinely nonlinear, with single, connected inflection loci. These properties, which are natural extensions of the two-phase flow model, ensure that the solution is physically sensible. We present the complete analytical solution to the Riemann problem (constant initial and injected states) in detail, and describe the characteristic waves that may arise, concluding that only nine combinations of rarefactions, shocks and rarefaction-shocks are possible. We demonstrate that assuming the saturation paths of the solution are straightlines may result in inaccurate predictions for some realistic systems. Efficient algorithms for computing the exact solution are also given, making the analytical developments presented here readily applicable to interpretation of lab displacement experiments, and implementation of streamline simulators.
Constraints on flows in Horava-Lifshitz gravity by classical solutions
Kim, Taekyung; Kim, Yoonbai
2010-11-15
We find exact static stringy solutions of Horava-Lifshitz gravity with the projectability condition but imposing the detailed balance condition near the UV fixed point, and propose a method on constraining the possible pattern of flows in Horava-Lifshitz gravity by using the obtained classical solutions. In the obtained vacuum solutions, the parameters related to the speed of the graviton and the coefficients of quartic spatial derivative terms lead to intriguing effects: the change of graviton speed yields a surplus angle and the quartic derivatives make the square of effective electric charge negative. The result of a few tests based on the geometries of a cone, an excess cone, a black string, and a charged (black) string seems suggestive. For example, the flow of constant graviton speed and variable Newton's coupling can be favored in the vicinity of an IR fixed point, but the conclusion is indistinct and far from definite yet. Together with the numerous classical solutions, static or time dependent, which have already been found, the accumulated data from various future tests will give some hints in constraining the flow patterns more deterministic.
NASA Astrophysics Data System (ADS)
Chang, Ching-Min; Yeh, Hund-Der
2016-09-01
This work describes an investigation of the spatial statistical structure of specific discharge field and solute transport process of a nonreactive solute at the field scale through a heterogeneous deformable porous medium. The flow field is driven by a vertical gradient in the excess pore water pressure induced by a step increase in load applied on the upper part of a finite-thickness aquifer. The non-stationary spectral representation is adopted to characterize the spatial covariance of the specific discharge field necessary for the development of the solute particle trajectory statistics using the Lagrangian formalism. We show that the statistics of the specific discharge and particle trajectory derived herein are non-stationary and functions of the coefficient of soil compressibility, μ. The effect of μ on the relative variation of specific discharge and the solute particle trajectory statistics are analyzed upon evaluating our expressions.
Long-time behavior of solution for the compressible nematic liquid crystal flows in R3
NASA Astrophysics Data System (ADS)
Gao, Jincheng; Tao, Qiang; Yao, Zheng-an
2016-08-01
In this paper, we investigate the global existence and long-time behavior of classical solution for the compressible nematic liquid crystal flows in three-dimensional whole space. First of all, the global existence of classical solution is established under the condition that the initial data are close to the constant equilibrium state in HN (R3) (N ≥ 3)-framework. Then, one establishes algebraic time decay for the classical solution by weighted energy method. Finally, the algebraic decay rate of classical solution in Lp (R3)-norm with 2 ≤ p ≤ ∞ and optimal decay rate of their spatial derivative in L2 (R3)-norm are obtained if the initial perturbation belong to L1 (R3) additionally.
NASA Astrophysics Data System (ADS)
Li, Y.; Ma, X.; Su, N.
2013-12-01
The movement of water and solute into and through the vadose zone is, in essence, an issue of immiscible displacement in pore-space network of a soil. Therefore, multiphase flow and transport in porous media, referring to three medium: air, water, and the solute, pose one of the largest unresolved challenges for porous medium fluid seepage. However, this phenomenon has always been largely neglected. It is expected that a reliable analysis model of the multi-phase flow in soil can truly reflect the process of natural movement about the infiltration, which is impossible to be observed directly. In such cases, geophysical applications of the nuclear magnetic resonance (NMR) provides the opportunity to measure the water movements into soils directly over a large scale from tiny pore to regional scale, accordingly enable it available both on the laboratory and on the field. In addition, the NMR provides useful information about the pore space properties. In this study, we proposed both laboratory and field experiments to measure the multi-phase flow parameters, together with optimize the model in computer programming based on the fractional partial differential equations (fPDE). In addition, we establish, for the first time, an infiltration model including solute flowing with water, which has huge influence on agriculture and soil environment pollution. Afterwards, with data collected from experiments, we simulate the model and analyze the spatial variability of parameters. Simulations are also conducted according to the model to evaluate the effects of airflow on water infiltration and other effects such as solute and absorption. It has significant meaning to oxygen irrigation aiming to higher crop yield, and shed more light into the dam slope stability. In summary, our framework is a first-time model added in solute to have a mathematic analysis with the fPDE and more instructive to agriculture activities.
Flow of Viscoelastic Wormlike Micelle Solutions through a Periodic Array of Cylinders
NASA Astrophysics Data System (ADS)
Moss, Geoffrey R.; Rothstein, Jonathan P.
2008-07-01
Solutions of self-assembled wormlike micelles are used with ever increasing frequency in a multitude of consumer products ranging from cosmetic to industrial applications. Owing to the wide range of applications, flows of interest are often complex in nature; exhibiting both extensional and shear regions that can make modeling and prediction both challenging and valuable. Adding to the complexity, the micellear dynamics are continually changing, resulting in a number of interesting phenomena, such as shear banding and extensional flow instabilities. In this paper, we present the results of our investigation into the flow fields generated by a controllable and idealized semi-porous media: a periodic array of cylinders (PAC). Our test channel geometry consists of six equally spaced cylinders, arranged perpendicular to the flow. By systematically varying the Deborah number, the flow kinematics, stability and pressure drop were measured. We present evidence of the onset of shear banding above a critical Deborah number as seen by a deviation from the expected Newtonian response of the fluid. A combination of particle image velocimetry (PIV) in conjunction with flush mount pressure transducers were used to fully characterize the flow, and measure the pressure drop generated by the PAC, while flow induced birefringence (FIB) measurements were used to determine micelle deformation and alignment.
Buoyancy-driven flow in a peat moss layer as a mechanism for solute transport
Rappoldt, Cornelis; Pieters, Gert-Jan J. M.; Adema, Erwin B.; Baaijens, Gerrit J.; Grootjans, Ab P.; van Duijn, Cornelis J.
2003-01-01
Transport of nutrients, CO2, methane, and oxygen plays an important ecological role at the surface of wetland ecosystems. A possibly important transport mechanism in a water-saturated peat moss layer (usually Sphagnum cuspidatum) is nocturnal buoyancy flow, the downward flow of relatively cold surface water, and the upward flow of warm water induced by nocturnal cooling. Mathematical stability analysis showed that buoyancy flow occurs in a cooling porous layer if the system's Rayleigh number (Ra) exceeds 25. For a temperature difference of 10 K between day and night, a typical Ra value for a peat moss layer is 80, which leads to quickly developing buoyancy cells. Numerical simulation demonstrated that fluid flow leads to a considerable mixing of water. Temperature measurements in a cylindrical peat sample of 50-cm height and 35-cm diameter were in agreement with the theoretical results. The nocturnal flow and the associated mixing of the water represent a mechanism for solute transport in water-saturated parts of peat land and in other types of terrestrializing vegetation. This mechanism may be particularly important in continental wetlands, where Ra values in summer are often much larger than the threshold for fluid flow. PMID:14657381
Parkhurst, David L.; Kipp, Kenneth L.; Charlton, Scott R.
2010-01-01
The computer program PHAST (PHREEQC And HST3D) simulates multicomponent, reactive solute transport in three-dimensional saturated groundwater flow systems. PHAST is a versatile groundwater flow and solute-transport simulator with capabilities to model a wide range of equilibrium and kinetic geochemical reactions. The flow and transport calculations are based on a modified version of HST3D that is restricted to constant fluid density and constant temperature. The geochemical reactions are simulated with the geochemical model PHREEQC, which is embedded in PHAST. Major enhancements in PHAST Version 2 allow spatial data to be defined in a combination of map and grid coordinate systems, independent of a specific model grid (without node-by-node input). At run time, aquifer properties are interpolated from the spatial data to the model grid; regridding requires only redefinition of the grid without modification of the spatial data. PHAST is applicable to the study of natural and contaminated groundwater systems at a variety of scales ranging from laboratory experiments to local and regional field scales. PHAST can be used in studies of migration of nutrients, inorganic and organic contaminants, and radionuclides; in projects such as aquifer storage and recovery or engineered remediation; and in investigations of the natural rock/water interactions in aquifers. PHAST is not appropriate for unsaturated-zone flow, multiphase flow, or density-dependent flow. A variety of boundary conditions are available in PHAST to simulate flow and transport, including specified-head, flux (specified-flux), and leaky (head-dependent) conditions, as well as the special cases of rivers, drains, and wells. Chemical reactions in PHAST include (1) homogeneous equilibria using an ion-association or Pitzer specific interaction thermodynamic model; (2) heterogeneous equilibria between the aqueous solution and minerals, ion exchange sites, surface complexation sites, solid solutions, and gases; and
Field-scale experiments of unsaturated flow and solute transport in a heterogeneous porous medium
NASA Astrophysics Data System (ADS)
Nichol, Craig; Smith, Leslie; Beckie, Roger
2005-05-01
A multiyear flow and conservative tracer test has been carried out in unsaturated mine waste rock to examine the physical mechanisms by which water moves through this coarse, heterogeneous, granular material. The experimental system has a footprint of 8 m × 8 m, is 5 m high, and is built on a contiguous grid of 16 zero-tension lysimeters. A chloride tracer was applied during a single rainfall event. Subsequently, the system has been subject to both natural and applied rainfall events in which no further tracer was added. Water flow and tracer transport is monitored using in situ measurements of moisture content, matric suction, and soil water solution samplers. Results demonstrate for transient infiltration conditions the influence and interaction of matrix flow in a heterogeneous granular matrix, preferential flow in macropores, and noncapillary pathways. Tracer migration through preferential flow paths dominates the initial and peak breakthrough concentrations. Point measurements of tracer concentration from in situ solution samplers yield a relatively poor indication of the flux-averaged transport of mass that is recorded at the base of the experiment, in addition to overestimating the stored mass and underestimating residence time.
Segregation behavior of magnetic ions in continuous flowing solution under gradient magnetic field
NASA Astrophysics Data System (ADS)
Bing, Ji; Ping, Wu; Han, Ren; Shiping, Zhang; Abdul, Rehman; Li, Wang
2016-07-01
The research of magnetic separation starts from magnetic solid particles to nanoparticles, and in the research progress, particles become smaller gradually with the development of application of magnetic separation technology. Nevertheless, little experimental study of magnetic separation of molecules and ions under continuous flowing conditions has been reported. In this work, we designed a magnetic device and a “layered” flow channel to study the magnetic separation at the ionic level in continuous flowing solution. A segregation model was built to discuss the segregation behavior as well as the factors that may affect the separation. The magnetic force was proved to be the driving force which plays an indispensable role leading to the segregation and separation. The flow velocity has an effect on the segregation behavior of magnetic ions, which determines the separation result. On the other hand, the optimum flow velocity which makes maximum separation is related to the initial concentration of solution. Project supported by the National Natural Science Foundation of China (Grant No. 51276016).
Dynamics of polymer solutions and polymer/vesicle mixtures during microchannel flow
NASA Astrophysics Data System (ADS)
Graham, Michael; Anekal, Samartha; Hernandez-Ortiz, Juan
2008-11-01
Addition of small amounts of long-chain polymers to blood has been found to have dramatic effects on its flow in the microcirculation. To address the mechanisms underlying these phenomena, we use a real-space P^3M method for Stokes flow including Brownian fluctuations to study the dynamics of polymer solutions and polymer/vesicle mixtures in microscale flows. Both a simple slit geometry and a grooved cavity flow are studied and polymer concentrations from ultradilute up to near the overlap concentration are considered. As concentration increases, the hydrodynamic migration effects observed in dilute solution unidirectional flows become less prominent, virtually vanishing as the overlap concentration is approached. In a grooved channel geometry, the groove is almost completely depleted of polymer chains at high Weissenberg number in the dilute limit, but at finite concentration this depletion effect is dramatically reduced. In suspensions of vesicles, the presence of polymer molecules has a substantial effect on the dynamics of pair collisions and on migration of the vesicles from microchannel walls.
An inverse problem solution to the flow of tracers in naturally fractured reservoirs
Jetzabeth Ramirez S.; Fernando Samaniego V.; Fernando Rodriguez; Jesus Rivera R.
1994-01-20
This paper presents a solution for the inverse problem to the flow of tracers in naturally fractured reservoirs. The models considered include linear flow in vertical fractures, radial flow in horizontal fractures, and cubic block matrix-fracture geometry. The Rosenbrock method for nonlinear regression used in this study, allowed the estimation of up to six parameters for the cubic block matrix fracture geometry. The nonlinear regression for the three cases was carefully tested against syntetical tracer concentration responses affected by random noise, with the objective of simulating as close as possible step injection field data. Results were obtained within 95 percent confidence limits. The sensitivity of the inverse problem solution on the main parameters that describe this flow problem was investigated. The main features of the nonlinear regression program used in this study are also discussed. The procedure of this study can be applied to interpret tracer tests in naturally fractured reservoirs, allowing the estimation of fracture and matrix parameters of practical interest (longitudinal fracture dispersivity alpha, matrix porosity phi2, fracture half-width w, matrix block size d, matrix diffusion coefficient D2 and the adsorption constant kd). The methodology of this work offers a practical alternative for tracer flow tests interpretation to other techniques.
Parallel Finite Element Solution of 3D Rayleigh-Benard-Marangoni Flows
NASA Technical Reports Server (NTRS)
Carey, G. F.; McLay, R.; Bicken, G.; Barth, B.; Pehlivanov, A.
1999-01-01
A domain decomposition strategy and parallel gradient-type iterative solution scheme have been developed and implemented for computation of complex 3D viscous flow problems involving heat transfer and surface tension effects. Details of the implementation issues are described together with associated performance and scalability studies. Representative Rayleigh-Benard and microgravity Marangoni flow calculations and performance results on the Cray T3D and T3E are presented. The work is currently being extended to tightly-coupled parallel "Beowulf-type" PC clusters and we present some preliminary performance results on this platform. We also describe progress on related work on hierarchic data extraction for visualization.
Numerical solution of a three-dimensional cubic cavity flow by using the Boltzmann equation
NASA Technical Reports Server (NTRS)
Hwang, Danny P.
1992-01-01
A three-dimensional cubic cavity flow has been analyzed for diatomic gases by using the Boltzmann equation with the Bhatnagar-Gross-Krook (B-G-K) model. The method of discrete ordinate was applied, and the diffuse reflection boundary condition was assumed. The results, which show a consistent trend toward the Navier-Stokes solution as the Knudson number is reduced, give us confidence to apply the method to a three-dimensional geometry for practical predictions of rarefied-flow characteristics. The CPU time and the main memory required for a three-dimensional geometry using this method seem reasonable.
Over-reflection of slow magnetosonic waves by homogeneous shear flow: Analytical solution
Dimitrov, Z. D.; Maneva, Y. G.; Hristov, T. S.; Mishonov, T. M.
2011-08-15
We have analyzed the amplification of slow magnetosonic (or pseudo-Alfvenic) waves (SMW) in incompressible shear flow. As found here, the amplification depends on the component of the wave-vector perpendicular to the direction of the shear flow. Earlier numerical results are consistent with the general analytic solution for the linearized magnetohydrodynamic equations, derived here for the model case of pure homogeneous shear (without Coriolis force). An asymptotically exact analytical formula for the amplification coefficient is derived for the case when the amplification is sufficiently large.
Temperature and heat transfer solutions for aeromagnetic dusty-gas flow
Chamkha, A.J. )
1993-09-01
Based on temperature and heat transfer solutions derived by Chamkha (1992) for aeromagnetic dusty-gas flows (such as are occurring in many industrial processes), this paper investigates the effect of a transverse magnetic field on the temperature profile, and the wall heat transfer for flow of a dusty gas past an infinite porous flat plate. The fluid phase is assumed to be incompressible and electrically conducting, and the particle phase is assumed to be incompressible and electrically nonconducing; it is also assumed that there is no radiative heat transfer from one particle to another and that the particles do not interact with each other. 6 refs.
Jackman, A.P.; Walters, R.A.; Kennedy, V.C.
1984-01-01
Models describing low-flow transport of conservative (nonreactive) and reactive solutes, which adsorb on the streambed, are developed and tested. Temporary storage within the bed plays an important role in solute movement. Three different models of bed-storage processes are developed for conservative solutes. One model assumes the bed is a well-mixed, nondiffusing, nonreacting zone. Solute flux into the bed is then proportional to the difference between stream and bed-solute concentrations. A second model assumes that solute is transported within the bed by a vertical diffusion process. The bed-solute concentration, which matches the stream concentration at the interface, varies with depth in the bed according to Fick 's law. A third model assumes convection in the downstream direction occurs in certain parts of the bed, while the mechanism of the first model functions elsewhere. Storage of absorbing species is assumed to occur by equilibrium adsorption within streambed particles. Uptake rate is described by an intraparticle diffusion process. Model equations were solved using finite element numerical methods. Models were calibrated using data from a 24-hour injection of conservative chloride and adsorptive Sr ions at Uvas Creek near Morgan Hill, California. All models predict well except for some overestimation by the adsorption model during dieaway. (USGS)
NASA Technical Reports Server (NTRS)
Farrell, C.; Adamczyk, J.
1981-01-01
The three-dimensional flow in a turbomachinery blade row was approximated by correcting for streamtube convergence and radius change in the throughflow direction. The method is a fully conservative solution of the full potential equation incorporating the finite volume technique on body fitted periodic mesh, with an artificial density imposed in the transonic region to insure stability and the capture of shock waves. Comparison of results for several supercritical blades shows good agreement with their hodograph solutions. Other calculations for these profiles as well as standard NACA blade sections indicate that this is a useful scheme analyzing both the design and off-design performance of turbomachinery blading.
NASA Astrophysics Data System (ADS)
Vijayakumar, M.; Li, Liyu; Graff, Gordon; Liu, Jun; Zhang, Huamin; Yang, Zhenguo; Hu, Jian Zhi
The V 5+ electrolyte solution from Vanadium Redox Flow Batteries was studied by variable temperature 17O and 51V Nuclear Magnetic Resonance (NMR) spectroscopy and density functional theory (DFT) based computational modeling. It was found that the V 5+ species exist as hydrated penta co-ordinated vanadate ion, i.e. [VO 2(H 2O) 3] 1+. This hydrated structure is not stable at elevated temperature and change into neutral H 3VO 4 molecule via a deprotonation process and subsequently leading to the observed V 2O 5 precipitation in V 5+ electrolyte solutions.
Yuan, Qiao-ying; Zhang, Ling; Xiao, Dan; Zhao, Kun; Lin, Chun; Si, Liang-yi
2014-01-01
Because of the limitations of existing methods and techniques for directly obtaining real-time blood data, no accurate microflow in vivo real-time analysis method exists. To establish a novel technical platform for real-time in vivo detection and to analyze average blood pressure and other blood flow parameters, a small, accurate, flexible, and nontoxic Fabry-Perot fiber sensor was designed. The carotid sheath was implanted through intubation of the rabbit carotid artery (n = 8), and the blood pressure and other detection data were determined directly through the veins. The fiber detection results were compared with test results obtained using color Doppler ultrasound and a physiological pressure sensor recorder. Pairwise comparisons among the blood pressure results obtained using the three methods indicated that real-time blood pressure information obtained through the fiber sensor technique exhibited better correlation than the data obtained with the other techniques. The highest correlation (correlation coefficient of 0.86) was obtained between the fiber sensor and pressure sensor. The blood pressure values were positively related to the total cholesterol level, low-density lipoprotein level, number of red blood cells, and hemoglobin level, with correlation coefficients of 0.033, 0.129, 0.358, and 0.373, respectively. The blood pressure values had no obvious relationship with the number of white blood cells and high-density lipoprotein and had a negative relationship with triglyceride levels, with a correlation coefficient of –0.031. The average ambulatory blood pressure measured by the fiber sensor exhibited a negative correlation with the quantity of blood platelets (correlation coefficient of −0.839, P<0.05). The novel fiber sensor can thus obtain in vivo blood pressure data accurately, stably, and in real time; the sensor can also determine the content and status of the blood flow to some extent. Therefore, the fiber sensor can obtain partially real
Yuan, Qiao-ying; Zhang, Ling; Xiao, Dan; Zhao, Kun; Lin, Chun; Si, Liang-yi
2014-01-01
Because of the limitations of existing methods and techniques for directly obtaining real-time blood data, no accurate microflow in vivo real-time analysis method exists. To establish a novel technical platform for real-time in vivo detection and to analyze average blood pressure and other blood flow parameters, a small, accurate, flexible, and nontoxic Fabry-Perot fiber sensor was designed. The carotid sheath was implanted through intubation of the rabbit carotid artery (n = 8), and the blood pressure and other detection data were determined directly through the veins. The fiber detection results were compared with test results obtained using color Doppler ultrasound and a physiological pressure sensor recorder. Pairwise comparisons among the blood pressure results obtained using the three methods indicated that real-time blood pressure information obtained through the fiber sensor technique exhibited better correlation than the data obtained with the other techniques. The highest correlation (correlation coefficient of 0.86) was obtained between the fiber sensor and pressure sensor. The blood pressure values were positively related to the total cholesterol level, low-density lipoprotein level, number of red blood cells, and hemoglobin level, with correlation coefficients of 0.033, 0.129, 0.358, and 0.373, respectively. The blood pressure values had no obvious relationship with the number of white blood cells and high-density lipoprotein and had a negative relationship with triglyceride levels, with a correlation coefficient of -0.031. The average ambulatory blood pressure measured by the fiber sensor exhibited a negative correlation with the quantity of blood platelets (correlation coefficient of -0.839, P<0.05). The novel fiber sensor can thus obtain in vivo blood pressure data accurately, stably, and in real time; the sensor can also determine the content and status of the blood flow to some extent. Therefore, the fiber sensor can obtain partially real
NASA Technical Reports Server (NTRS)
Garrick, I E; Kaplan, Carl
1944-01-01
The differential equation of Chaplygin's jet problem is utilized to give a systematic development of particular solutions of the hodograph flow equations, which extends the treatment of Chaplygin into the supersonic range and completes the set of particular solutions. The particular solutions serve to place on a reasonable basis the use of velocity correction formulas for the comparison of incompressible and compressible flows. It is shown that the geometric-mean type of velocity correction formula introduced in part I has significance as an over-all type of approximation in the subsonic range. A brief review of general conditions limiting the potential flow of an adiabatic compressible fluid is given and application is made to the particular solutions, yielding conditions for the existence of singular loci in the supersonic range. The combining of particular solutions in accordance with prescribed boundary flow conditions is not treated in the present paper.
NASA Technical Reports Server (NTRS)
Garrick, I. E.; Kaplan, Carl
1944-01-01
The differential equation of Chaplygin's jet problem is utilized to give a systematic development of particular solutions of the hodograph flow equations, which extends the treatment of Chaplygin into the supersonic range and completes the set of particular solutions. The particular solutions serve to place on a reasonable basis the use of velocity correction formulas for the comparison of incompressible and compressible flows. It is shown that the geometric-mean type of velocity correction formula introduced in part I has significance as an over-all type of approximation in the subsonic range. A brief review of general conditions limiting the potential flow of an adiabatic compressible fluid is given and application is made to the particular solutions, yielding conditions for the existence of singular loci in the supersonic range. The combining of particular solutions in accordance with prescribed boundary flow conditions is not treated in the present paper.
STUDIES ON THE ANOMALOUS VISCOSITY AND FLOW-BIREFRINGENCE OF PROTEIN SOLUTIONS
Lawrence, A. S. C.; Miall, Margaret; Needham, Joseph; Shen, Shih-Chang
1944-01-01
1. An extensive investigation has been made of protein particle shape using the methods of flow-birefringence and anomalous viscosity measurement in the coaxial cell. 2. As a result of investigations on a number of proteins, it is concluded that they may be divided into four groups. Group A consists of those which show flow-anomaly both in the bulk phase and in the surface film. These also show flow-birefringence in the bulk phase. Examples: tobacco mosaic disease virus nucleoprotein; myosin. Though corpuscular proteins, they have elongated particles before denaturation. Group B consists of those which show flow-anomaly only (in the first instance) in the surface film, and no flow-birefringence in the bulk phase. They are probably close to spherical in shape in solution, but form elongated particles as they denature in the surface film. After this process has been completed, they may show flow-anomaly also in the bulk phase. Some proteins show flow-anomaly in the surface film immediately it forms, others only show it after a certain time has elapsed for the building up of the film. We designate the former as group B1 and the latter as group B2. Group B1, immediate surface film flow-anomaly. Examples: serum euglobulin, amphibian embryo euglobulin b. Group B2, slowly appearing surface film flow-anomaly. After the film has once been fully formed and then dispersed by shaking, the solution may have the properties of that of a protein in group B1; i.e., anomalous flow in the film may occur immediately on testing in the viscosimeter. Examples: avian ovalbumin, amphibian embryo pseudoglobulin. Group C consists of those proteins which show flow-anomaly neither in the bulk phase nor in the surface film, under the conditions used by us. They are probably close to spherical in shape. Examples: insulin, methaemoglobin, amphibian embryo euglobulin c, mucoproteins. 3. The theoretical significance of protein fibre molecules, whether native or formed by denaturation in the living
NASA Astrophysics Data System (ADS)
Wang, Li-yong; Li, Le; Zhang, Zhi-hua
2016-09-01
Hot compression tests of Ti-6Al-4V alloy in a wide temperature range of 1023-1323 K and strain rate range of 0.01-10 s-1 were conducted by a servo-hydraulic and computer-controlled Gleeble-3500 machine. In order to accurately and effectively characterize the highly nonlinear flow behaviors, support vector regression (SVR) which is a machine learning method was combined with genetic algorithm (GA) for characterizing the flow behaviors, namely, the GA-SVR. The prominent character of GA-SVR is that it with identical training parameters will keep training accuracy and prediction accuracy at a stable level in different attempts for a certain dataset. The learning abilities, generalization abilities, and modeling efficiencies of the mathematical regression model, ANN, and GA-SVR for Ti-6Al-4V alloy were detailedly compared. Comparison results show that the learning ability of the GA-SVR is stronger than the mathematical regression model. The generalization abilities and modeling efficiencies of these models were shown as follows in ascending order: the mathematical regression model < ANN < GA-SVR. The stress-strain data outside experimental conditions were predicted by the well-trained GA-SVR, which improved simulation accuracy of the load-stroke curve and can further improve the related research fields where stress-strain data play important roles, such as speculating work hardening and dynamic recovery, characterizing dynamic recrystallization evolution, and improving processing maps.
NASA Astrophysics Data System (ADS)
Wang, Li-yong; Li, Le; Zhang, Zhi-hua
2016-07-01
Hot compression tests of Ti-6Al-4V alloy in a wide temperature range of 1023-1323 K and strain rate range of 0.01-10 s-1 were conducted by a servo-hydraulic and computer-controlled Gleeble-3500 machine. In order to accurately and effectively characterize the highly nonlinear flow behaviors, support vector regression (SVR) which is a machine learning method was combined with genetic algorithm (GA) for characterizing the flow behaviors, namely, the GA-SVR. The prominent character of GA-SVR is that it with identical training parameters will keep training accuracy and prediction accuracy at a stable level in different attempts for a certain dataset. The learning abilities, generalization abilities, and modeling efficiencies of the mathematical regression model, ANN, and GA-SVR for Ti-6Al-4V alloy were detailedly compared. Comparison results show that the learning ability of the GA-SVR is stronger than the mathematical regression model. The generalization abilities and modeling efficiencies of these models were shown as follows in ascending order: the mathematical regression model < ANN < GA-SVR. The stress-strain data outside experimental conditions were predicted by the well-trained GA-SVR, which improved simulation accuracy of the load-stroke curve and can further improve the related research fields where stress-strain data play important roles, such as speculating work hardening and dynamic recovery, characterizing dynamic recrystallization evolution, and improving processing maps.
Liang, Qin-Qin; Li, Yong-Sheng
2013-12-01
An accurate and rapid method and a system to determine protein content using asynchronous-injection alternating merging zone flow-injection spectrophotometry based on reaction between coomassie brilliant blue G250 (CBBG) and protein was established. Main merit of our approach is that it can avoid interferences of other nitric-compounds in samples, such as melamine and urea. Optimized conditions are as follows: Concentrations of CBBG, polyvinyl alcohol (PVA), NaCl and HCl are 150 mg/l, 30 mg/l, 0.1 mol/l and 1.0% (v/v), respectively; volumes of the sample and reagent are 150 μl and 30 μl, respectively; length of a reaction coil is 200 cm; total flow rate is 2.65 ml/min. The linear range of the method is 0.5-15 mg/l (BSA), its detection limit is 0.05 mg/l, relative standard deviation is less than 1.87% (n=11), and analytical speed is 60 samples per hour.
NASA Technical Reports Server (NTRS)
Edwards, Jack R.; Mcrae, D. Scott
1991-01-01
An efficient method for computing two-dimensional compressible Navier-Stokes flow fields is presented. The solution algorithm is a fully-implicit approximate factorization technique based on an unsymmetric line Gauss-Seidel splitting of the equation system Jacobian matrix. Convergence characteristics are improved by the addition of acceleration techniques based on Shamanskii's method for nonlinear equations and Broyden's quasi-Newton update. Characteristic-based differencing of the equations is provided by means of Van Leer's flux vector splitting. In this investigation, emphasis is placed on the fast and accurate computation of shock-wave-boundary layer interactions with and without slot suction effects. In the latter context, a set of numerical boundary conditions for simulating the transpiration flow in an open slot is devised. Both laminar and turbulent cases are considered, with turbulent closure provided by a modified Cebeci-Smith algebraic model. Comparisons with computational and experimental data sets are presented for a variety of interactions, and a fully-coupled simulation of a plenum chamber/inlet flowfield with shock interaction and suction is also shown and discussed.
Numerical solutions for a flow with mixed convection in a vertical geometry
NASA Astrophysics Data System (ADS)
Torczynski, J. R.
The K-12 Aerospace Heat Transfer Committee of the American Society of Mechanical Engineers recently specified a computational benchmark problem involving steady incompressible laminar flow with mixed convection using the Boussinesq approximation in a two-dimensional backstep geometry. FIDAP v6.0 (Fluid Dynamics International) and NEKTON v2.85 (Nektonics, Fluent) are capable of simulating situations with this type of coupled fluid flow and heat transfer. FIDAP uses conventional finite elements and has both steady and transient solvers, whereas NEKTON uses spectral elements with a transient solver (for large problems). Numerical solutions to the benchmark problem are obtained with both of these codes, and grid-refinement studies are performed to verify that grid-independence is achieved. The grid-independent solutions from both codes are found to be in excellent agreement with each other and with results in the archival literature regarding velocity and temperature profiles and the locations of separation and reattachment points.
Comparing the Titrations of Mixed-Acid Solutions Using Dropwise and Constant-Flow Techniques
NASA Astrophysics Data System (ADS)
Charlesworth, Paul; Seguin, Matthew J.; Chesney, David J.
2003-11-01
A mixed-acid solution containing hydrochloric and phosphoric acids was used to determine the error associated with performing a real-time titration. The results were compared against those obtained by performing the titration in a more traditional dropwise addition of titrant near the equivalence points. It was found that the real-time techniques resulted in significantly decreased analysis times while maintaining a low experimental error. The constant-flow techniques were implemented into two different levels of chemistry. It was found that students could successfully utilize the modified experiments. Problems associated with the techniques, major sources of error, and their solutions are discussed. In both cases, the use of the constant-flow setup has increased student recollection of key concepts, such as pKa determination, proper indicator choice, and recognizing the shape of specific titration curves by increasing student interest in the experiment.
Wall Slip during the Flow of Carbopol Solutions through a Parallel Plate Channel
NASA Astrophysics Data System (ADS)
de Souza Mendes, Paulo R.; Pédron, Jonathan; Pereira, Renata A. B.
2008-07-01
Experiments were performed to investigate the phenomenon of wall slip during the flow of aqueous solutions of carbopol through a parallel plate channel. The Reynolds number is low for all cases investigated, to ensure negligible development length. In the experiments, the pressure drop is measured for different flow rate values, and the results are presented in the form of curves of dimensionless average velocity versus dimensionless wall shear stress. We also performed experiments with glycerol, and the results agreed with the analytical solution available in the literature. Moreover, this agreement ensures the absence of wall slip for this Newtonian case. Comparisons between the experimental and numerical results show that (apparent) wall slip occurs when the wall shear stress is below a threshold stress of a few times the yield stress. Above this threshold, the numerical and experimental curves tend to merge.
Simulation of unsteady flow and solute transport in a tidal river network
Zhan, X.
2003-01-01
A mathematical model and numerical method for water flow and solute transport in a tidal river network is presented. The tidal river network is defined as a system of open channels of rivers with junctions and cross sections. As an example, the Pearl River in China is represented by a network of 104 channels, 62 nodes, and a total of 330 cross sections with 11 boundary section for one of the applications. The simulations are performed with a supercomputer for seven scenarios of water flow and/or solute transport in the Pearl River, China, with different hydrological and weather conditions. Comparisons with available data are shown. The intention of this study is to summarize previous works and to provide a useful tool for water environmental management in a tidal river network, particularly for the Pearl River, China.
Investigation of ALEGRA shock hydrocode algorithms using an exact free surface jet flow solution.
Hanks, Bradley Wright.; Robinson, Allen C
2014-01-01
Computational testing of the arbitrary Lagrangian-Eulerian shock physics code, ALEGRA, is presented using an exact solution that is very similar to a shaped charge jet flow. The solution is a steady, isentropic, subsonic free surface flow with significant compression and release and is provided as a steady state initial condition. There should be no shocks and no entropy production throughout the problem. The purpose of this test problem is to present a detailed and challenging computation in order to provide evidence for algorithmic strengths and weaknesses in ALEGRA which should be examined further. The results of this work are intended to be used to guide future algorithmic improvements in the spirit of test-driven development processes.
Analytical solution to the equations for parallel-flow four-channel heat exchangers
Malinowski, L.
2000-04-01
Assuming that the thermophysical parameters of the fluids are independent on temperature, the stationary temperature field in a parallel-flow multi-channel heat exchanger can be described by a set of linear differential equations of the first order with constant coefficients. A compact analytical solution to this set is presented for the case of four-channel exchangers and simple eigenvalues of the coefficient matrix of the set.
Numerical solution of fluid flow and heat tranfer problems with surface radiation
NASA Technical Reports Server (NTRS)
Ahuja, S.; Bhatia, K.
1995-01-01
This paper presents a numerical scheme, based on the finite element method, to solve strongly coupled fluid flow and heat transfer problems. The surface radiation effect for gray, diffuse and isothermal surfaces is considered. A procedure for obtaining the view factors between the radiating surfaces is discussed. The overall solution strategy is verified by comparing the available results with those obtained using this approach. An analysis of a thermosyphon is undertaken and the effect of considering the surface radiation is clearly explained.
Global solution to a hyperbolic problem arising in the modeling of blood flow in circulatory systems
NASA Astrophysics Data System (ADS)
Ruan, Weihua; Clark, M. E.; Zhao, Meide; Curcio, Anthony
2007-07-01
This paper considers a system of first-order, hyperbolic, partial differential equations in the domain of a one-dimensional network. The system models the blood flow in human circulatory systems as an initial-boundary-value problem with boundary conditions of either algebraic or differential type. The differential equations are nonhomogeneous with frictional damping terms and the state variables are coupled at internal junctions. The existence and uniqueness of the local classical solution have been established in our earlier work [W. Ruan, M.E. Clark, M. Zhao, A. Curcio, A hyperbolic system of equations of blood flow in an arterial network, J. Appl. Math. 64 (2) (2003) 637-667; W. Ruan, M.E. Clark, M. Zhao, A. Curcio, Blood flow in a network, Nonlinear Anal. Real World Appl. 5 (2004) 463-485; W. Ruan, M.E. Clark, M. Zhao, A. Curcio, A quasilinear hyperbolic system that models blood flow in a network, in: Charles V. Benton (Ed.), Focus on Mathematical Physics Research, Nova Science Publishers, Inc., New York, 2004, pp. 203-230]. This paper continues the analysis and gives sufficient conditions for the global existence of the classical solution. We prove that the solution exists globally if the boundary data satisfy the dissipative condition (2.3) or (3.2), and the norms of the initial and forcing functions in a certain Sobolev space are sufficiently small. This is only the first step toward establishing the global existence of the solution to physiologically realistic models, because, in general, the chosen dissipative conditions (2.3) and (3.2) do not appear to hold for the originally proposed boundary conditions (1.3)-(1.12).
Solute transport processes in flow-event-driven stream-aquifer interaction
NASA Astrophysics Data System (ADS)
Xie, Yueqing; Cook, Peter G.; Simmons, Craig T.
2016-07-01
The interaction between streams and groundwater controls key features of the stream hydrograph and chemograph. Since surface runoff is usually less saline than groundwater, flow events are usually accompanied by declines in stream salinity. In this paper, we use numerical modelling to show that, at any particular monitoring location: (i) the increase in stream stage associated with a flow event will precede the decrease in solute concentration (arrival time lag for solutes); and (ii) the decrease in stream stage following the flow peak will usually precede the subsequent return (increase) in solute concentration (return time lag). Both arrival time lag and return time lag increase with increasing wave duration. However, arrival time lag decreases with increasing wave amplitude, whereas return time lag increases. Furthermore, while arrival time lag is most sensitive to parameters that control river velocity (channel roughness and stream slope), return time lag is most sensitive to groundwater parameters (aquifer hydraulic conductivity, recharge rate, and dispersitivity). Additionally, the absolute magnitude of the decrease in river concentration is sensitive to both river and groundwater parameters. Our simulations also show that in-stream mixing is dominated by wave propagation and bank storage processes, and in-stream dispersion has a relatively minor effect on solute concentrations. This has important implications for spreading of contaminants released to streams. Our work also demonstrates that a high contribution of pre-event water (or groundwater) within the flow hydrograph can be caused by the combination of in-stream and bank storage exchange processes, and does not require transport of pre-event water through the catchment.
An analytic solution for periodic thermally-driven flows over an infinite slope
NASA Astrophysics Data System (ADS)
Zardi, Dino; Serafin, Stefano
2013-04-01
The flow generated along an infinite slope in an unperturbed stably stratified atmosphere at rest by a time periodic surface temperature forcing is examined. Following Defant (1949), a set of equations is derived which extends Prandtl's (1942) theory to allow for nonstationary conditions. Uniform boundary conditions are conducive to an along-slope parallel flow, governed by a periodically reversing local imbalance between along-slope advection and slope-normal fluxes of momentum and heat. Solutions include both a transient part and a subsequent periodic regime. The former can only be expressed in an integral form, whereas the latter is a combination of exponential and sine or cosine functions of time and height normal to the slope. Key parameters are the quantity Nα = N sinα (where α is the slope angle, and N is the Brunt-Väisälä frequency of the unperturbed atmosphere) and the angular frequency of the driving surface temperature cycle, ?. Three different flow regimes may occur, namely subcritical (Nα < ?), critical (Nα = ?) and supercritical (Nα > ?). The properties of the solutions in each regime are examined and discussed. The relationship between the present solutions and the earlier time-dependent slope flow model by Defant (1949) is also discussed. References Defant, F., 1949: Zur Theorie der Hangwinde, nebst Bemerkungen zur Theorie der Berg- und Talwinde. [A theory of slope winds, along with remarks on the theory of mountain winds and valley winds]. Arch. Meteor. Geophys. Bioclimatol., Ser. A, 1, 421-450 (Theoretical and Applied Climatology). [English translation: Whiteman, C.D., and E. Dreiseitl, 1984: Alpine meteorology: Translations of classic contributions by A. Wagner, E. Ekhart and F. Defant. PNL-5141 / ASCOT-84-3. Pacific Northwest Laboratory, Richland, Washington, 121 pp]. Prandtl, L., 1942: Strömungslehre [Flow Studies]. Vieweg und Sohn, Braunschweig, 382 pp.
Dual-permeability model for water flow and solute transport in shrinking soils
NASA Astrophysics Data System (ADS)
Coppola, Antonio; Gerke, Horst; Comegna, Alessandro; Basile, Angelo
2014-05-01
A dual-permeability approach was extended to describe preferential water flow and solute transport in shrinking soils. In the approach, the soil is treated as a dual-permeability bulk porous medium consisting of dynamic interacting matrix and fractures pore domains. Water flow and solute transport in both the domains are described by the Richards' equation and advection-dispersion equation, respectively. In the model the contributions of the two regions to water flow and solute transport is changed dynamically according to the shrinkage characteristic exhibited under soil drying. Aggregate deformation during wetting/drying cycles is assumed to change only the relative proportions of voids in the fractures and in the aggregates, while the total volume of pores (and thus the layer thickness) remains unchanged. Thus, the partial contributions of the fracture and aggregate domains, are now a function of the water content (or the pressure head h), while their sum, the bulk porosity, is assumed to be constant. Any change in the aggregate contribution to total porosity is directly converted into a proportional change in the fracture porosity. This means that bulk volume change during shrinkage is mainly determined by change in crack volume rather than by change in layer thickness. This simplified approach allows dealing with an expansive soil as with a macroscopically rigid soil. The model was already tested by investigating whether and how well hydraulic characteristics obtained under the assumption of "dynamic" dual-permeability hydraulic parameterizations, or, alternatively, assuming the rigidity of the porous medium, reproduced measured soil water contents in a shrinking soil. Here we will discuss theoretical implications of the model in terms of relative importance of the parameters involved. The relative importance will be evaluated for different flow and transport processes and for different initial and top boundary conditions. Key words: Preferential flow and
Effects of alongshore morphology on groundwater flow and solute transport in a nearshore aquifer
NASA Astrophysics Data System (ADS)
Zhang, Ying; Li, Ling; Erler, Dirk V.; Santos, Isaac; Lockington, David
2016-02-01
Variations of beach morphology in both the cross-shore and alongshore directions, associated with tidal creeks, are common at natural coasts, as observed at a field site on the east coast of Rarotonga, Cook Islands. Field investigations and three-dimensional (3-D) numerical simulations were conducted to study the nearshore groundwater flow and solute transport in such a system. The results show that the beach morphology, combined with tides, induced a significant alongshore flow and modified local pore water circulation and salt transport in the intertidal zone substantially. The bathymetry and hydraulic head of the creek enabled further and more rapid landward intrusion of seawater along the creek than in the aquifer, which created alongshore hydraulic gradient and solute concentration gradient to drive pore water flow and salt transport in the alongshore direction within the aquifer. The effects of the creek led to the formation of a saltwater plume in groundwater at an intermediate depth between fresher water zones on a cross-shore transect. The 3-D pore water flow in the nearshore zone was also complicated by the landward hydraulic head condition, resulting in freshwater drainage across the inland section of the creek while seawater infiltrating the seaward section. These results provided new insights into the complexity, intensity, and time scales of mixing among fresh groundwater, recirculating seawater and creek water in three dimensions. The 3-D characteristics of nearshore pore water flow and solute transport have important implications for studies of submarine groundwater discharge and associated chemical input to the coastal sea, and for evaluation of the beach habitat conditions.
Flow and Reactive Transport of Miscible and Immiscible Solutions in Fractured & Porous Media
NASA Astrophysics Data System (ADS)
Ryerson, F. J.; Ezzedine, S. M.; Antoun, T.
2012-12-01
Miscible and immiscible flows are important phenomena encountered in many industrial and engineering applications such as hydrothermal systems, oil and gas reservoirs, salt/water intrusion, geological carbon sequestration etc… Under the influence of gravity, the flow of fluids with sufficiently large density ratios may become unstable leading to instabilities, mixing and in some instances reactions at the interfacial contact between fluids. Flow is governed by a combination of momentum and mass conservation equations that describe the flow of the fluid phase and a convection-diffusion equation describing the change of concentration in the fluid phase. When hydrodynamic instabilities develop it may be difficult to use standard grid-based methods to model miscible/immiscible flow because the domains occupied by fluids evolve constantly with time. In the current study, adaptive mesh refinement finite elements method has been used to solve for flow and transport equations. Furthermore, a particle tracking scheme has also been implemented to track the kinematics of swarm of particles injected into the porous fractured media to quantify surface area, sweeping zones, and their impact on porosity changes. Spatial and temporal moments of the fingering instabilities and the development of reaction zones and the impact of kinetic reaction at the fluid/solution interfaces have also been analyzed. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Time-dependent rotating stratified shear flow: exact solution and stability analysis.
Salhi, A; Cambon, C
2007-01-01
A solution of the Euler equations with Boussinesq approximation is derived by considering unbounded flows subjected to spatially uniform density stratification and shear rate that are time dependent [S(t)= partial differentialU3/partial differentialx2]. In addition to vertical stratification with constant strength N(v)2, this base flow includes an additional, horizontal, density gradient characterized by N(h)2(t). The stability of this flow is then analyzed: When the vertical stratification is stabilizing, there is a simple harmonic motion of the horizontal stratification N(h)2(t) and of the shear rate S(t), but this flow is unstable to certain disturbances, which are amplified by a Floquet mechanism. This analysis may involve an additional Coriolis effect with Coriolis parameter f, so that governing dimensionless parameters are a modified Richardson number, R=[S(0)2+N(h)4(0)/N(v)2]1/2, and f(v)=f/N(v), as well as the initial phase of the periodic shear rate. Parametric resonance between the inertia-gravity waves and the oscillating shear is demonstrated from the dispersion relation in the limit R-->0. The parametric instability has connection with both baroclinic and elliptical flow instabilities, but can develop from a very different base flow.
Multidimensional self-similar analytical solutions of two-phase flow in porous media
NASA Astrophysics Data System (ADS)
Fučík, Radek; Illangasekare, Tissa H.; Beneš, Michal
2016-04-01
In general, analytical solutions serve a useful purpose to obtain better insights and to verify numerical codes. For flow of two incompressible and immiscible phases in homogeneous porous media without gravity, one such method that neglects capillary pressure in the solution was first developed by Buckley and Leverett (1942). Subsequently, McWhorter and Sunada (1990) derived an exact solution for the one and two dimensional cases that factored in capillary effects. This solution used a similarity transform that allowed to reduce the governing equations into a single ordinary differential equation (ODE) that can be further integrated into an equivalent integral equation. We present a revision to McWhorter and Sunada solution by extending the self-similar solution into a general multidimensional space. Inspired by the derivation proposed by McWhorter and Sunada (1990), we integrate the resulting ODE in the third and higher dimensions into a new integral equation that can be subsequently solved iteratively by means of numerical integration. We developed implementations of the iterative schemes for one- and higher dimensional cases that can be accessed online on the authors' website.
Approximation of traveling wave solutions in wall-bounded flows using resolvent modes
NASA Astrophysics Data System (ADS)
McKeon, Beverley; Graham, Michael; Moarref, Rashad; Park, Jae Sung; Sharma, Ati; Willis, Ashley
2014-11-01
Significant recent attention has been devoted to computing and understanding exact traveling wave solutions of the Navier-Stokes equations. These solutions can be interpreted as the state-space skeleton of turbulence and are attractive benchmarks for studying low-order models of wall turbulence. Here, we project such solutions onto the velocity response (or resolvent) modes supplied by the gain-based resolvent analysis outlined by McKeon & Sharma (JFM, 2010). We demonstrate that in both pipe (Pringle et al., Phil. Trans. R. Soc. A, 2009) and channel (Waleffe, JFM, 2001) flows, the solutions can be well-described by a small number of resolvent modes. Analysis of the nonlinear forcing modes sustaining these solutions reveals the importance of small amplitude forcing, consistent with the large amplifications admitted by the resolvent operator. We investigate the use of resolvent modes as computationally cheap ``seeds'' for the identification of further traveling wave solutions. The support of AFOSR under Grants FA9550-09-1-0701, FA9550-12-1-0469, FA9550-11-1-0094 and FA9550-14-1-0042 (program managers Rengasamy Ponnappan, Doug Smith and Gregg Abate) is gratefully acknowledged.
Semi-analytical solutions of groundwater flow in multi-zone (patchy) wedge-shaped aquifers
NASA Astrophysics Data System (ADS)
Samani, Nozar; Sedghi, Mohammad M.
2015-03-01
Alluvial fans are potential sites of potable groundwater in many parts of the world. Characteristics of alluvial fans sediments are changed radially from high energy coarse-grained deposition near the apex to low energy fine-grained deposition downstream so that patchy wedge-shaped aquifers with radial heterogeneity are formed. The hydraulic parameters of the aquifers (e.g. hydraulic conductivity and specific storage) change in the same fashion. Analytical or semi-analytical solutions of the flow in wedge-shaped aquifers are available for homogeneous cases. In this paper we derive semi-analytical solutions of groundwater flow to a well in multi-zone wedge-shaped aquifers. Solutions are provided for three wedge boundary configurations namely: constant head-constant head wedge, constant head-barrier wedge and barrier-barrier wedge. Derivation involves the use of integral transforms methods. The effect of heterogeneity ratios of zones on the response of the aquifer is examined. The results are presented in form of drawdown and drawdown derivative type curves. Heterogeneity has a significant effect on over all response of the pumped aquifer. Solutions help understanding the behavior of heterogeneous multi-zone aquifers for sustainable development of the groundwater resources in alluvial fans.
Generalization of one-dimensional solute transport: A stochastic-convective flow conceptualization
NASA Astrophysics Data System (ADS)
Simmons, C. S.
1986-04-01
A stochastic-convective representation of one-dimensional solute transport is derived. It is shown to conceptually encompass solutions of the conventional convection-dispersion equation. This stochastic approach, however, does not rely on the assumption that dispersive flux satisfies Fick's diffusion law. Observable values of solute concentration and flux, which together satisfy a conservation equation, are expressed as expectations over a flow velocity ensemble, representing the inherent random processess that govern dispersion. Solute concentration is determined by a Lagrangian pdf for random spatial displacements, while flux is determined by an equivalent Eulerian pdf for random travel times. A condition for such equivalence is derived for steady nonuniform flow, and it is proven that both Lagrangian and Eulerian pdfs are required to account for specified initial and boundary conditions on a global scale. Furthermore, simplified modeling of transport is justified by proving that an ensemble of effectively constant velocities always exists that constitutes an equivalent representation. An example of how a two-dimensional transport problem can be reduced to a single-dimensional stochastic viewpoint is also presented to further clarify concepts.
Helical Groundwater Flow in Braided-River Sediments and its Effects on Solute Mixing
NASA Astrophysics Data System (ADS)
Arie Cirpka, Olaf; Bennett, Jeremy Paul; Haslauer, Claus; Ye, Yu; Rolle, Massimo; Chiogna, Gabriele
2016-04-01
Spatially variable orientation of anisotropy can cause helical flow in porous media. In previous studies (Chiogna et al., 2015; Cirpka et al., 2015; see also Figure 1), we analyzed hydraulic conductivity fields with blockwise constant anisotropic correlation structure showing that macroscopically helical flow evolves, and leads to enhanced solute dilution in steady-state advective-dispersive transport. While these studies demonstrated the potential importance of helical flow in heterogeneous porous media, the likelihood of its occurrence remained unclear. In particular, natural sediments do not exhibit extended stripes of materials with diagonally oriented internal anisotropy. In the present study, we generated realistic looking sedimentary structures mimicking scour fills that may be created in braided-river sediments. The individual geobodies are filled with anisotropic porous material. Cross-sections show typical cross-bedding. In particular we analyzed how the variability in bulk hydraulic conductivity between the geobodies and the differences in the orientation of anisotropy affect flow and transverse solute mixing. While the variance of log-hydraulic conductivity controls longitudinal spreading, the variability in the orientation of anisotropy is decisive for folding and mixing perpendicular to the mean flow direction. The importance of non-stationary anisotropy for transverse mixing poses a challenge for the hydraulic characterization of sediments when predicting lengths of mixing-controlled quasi steady-state plumes. References [1] O.A. Cirpka, G. Chiogna, M. Rolle, A. Bellin: Transverse mixing in three-dimensional non-stationary anisotropic heterogeneous porous media. Water Resour. Res. 51(1): 241-260 (2015). [2] G. Chiogna, O.A. Cirpka, M. Rolle, A. Bellin: Helical flow in three-dimensional non-stationary anisotropic heterogeneous porous media. Water Resour. Res. 51(1): 261-280 (2015).
Impact of microbial growth on water flow and solute transport in unsaturated porous media
Yarwood, R. R.; Rockhold, M. L.; Niemet, M. R.; Selker, John S.; Bottomley, Peter J.
2006-10-05
A novel analytical method was developed that permitted real-time, noninvasive measurements of microbial growth and associated changes in hydrodynamic properties in porous media under unsaturated flowing conditions. Salicylate-induced, lux gene-based bioluminescence was used to quantify the temporal and spatial development of colonization over a seven day time course. Water contents were determined daily by measuring light transmission through the system. Hydraulic flow paths were determined daily by pulsing a bromophenol blue dye solution through the colonized region of the sand. Bacterial growth and accumulation had a significant impact on the hydraulic properties of the porous media. Microbial colonization caused localized drying within the colonized zone, with decreases in saturation approaching 50% of antecedent values, and a 25% lowering of the capillary fringe height. Flow was retarded within the colonized zone and diverted around it. The apparent solute velocity through the colonized region was reduced from 0.41 cm min 1 (R2 = 0.99) to 0.25 cm min 1 (R2 = 0.99) by the sixth day of the experiment, associated with maximum population densities that would occupy about 7% of the available pore space within the colonized region. Changes in the extent of colonization occurred over the course of the experiment, including upward migration against flow. The distribution of cells was not determined by water flow alone, but rather by a dynamic interaction between water flow and microbial growth. This experimental system provides rich data sets for the testing of conceptualizations expressed through numerical modeling.
STUDIES ON THE ANOMALOUS VISCOSITY AND FLOW-BIREFRINGENCE OF PROTEIN SOLUTIONS
Dainty, Mary; Kleinzeller, Arnost; Lawrence, A. S. C.; Miall, Margaret; Needham, Joseph; Needham, Dorothy M.; Shen, Shih-Chang
1944-01-01
1. An investigation of the physicochemical properties of myosin has been carried out. Prepared under standard conditions, the ratio of flow-birefringence to protein concentration is uniform. The effect of electrolytes, pH, and urea on the flow-birefringence and viscosity (relative and anomalous) of myosin has been examined. 2. Decrease or abolition of flow-birefringence does not necessarily imply far reaching denaturation, since such effects can be reversed by a variety of means. 3. When a myosin solution is treated with adenosinetriphosphate, its flow-birefringence is decreased (average 48 per cent), its anomalous viscosity is retained, and its relative viscosity is decreased (average 14 per cent). The full effect of adenosinetriphosphate is obtained at 0.004 M; a molarity very much less than that of other substances which decrease the flow-birefringence of myosin. 4. The changes in the physicochemical properties of myosin brought about by adenosinetriphosphate are spontaneously reversible, and are connected with the enzymatic action of the protein as adenosinetriphosphatase. 5. Effects similar to those of adenosinetriphosphate on the physicochemical properties of purified myosin have been obtained so far only with inosinetriphosphate. 6. Inorganic phosphate is split off by myosin from inosinetriphosphate as well as from adenosinetriphosphate. Inorganic triphosphate is split by 1 to 2 per cent solution of three times precipitated myosin. 7. Adenosinediphosphate and inorganic triphosphate act as competitive inhibitors with adenosinetriphosphate, blocking the fall of flow-birefringence. 8. The implications of the results, and the conception of active enzymic groups attached to proteins participating in cell structure, whether contractile or non-contractile, are discussed in relation to present views on muscle physiology and other biological problems. PMID:19873391
Canonical solutions for unsteady flow fields. M.S. Thesis - George Washington Univ.
NASA Technical Reports Server (NTRS)
Liu, G. C.
1984-01-01
The initial value problem of one-dimensional gas-dynamics involving discontinuous, nonuniform initial data is discussed. Canonical solutions which are valid in a small x, t region aroung a discontinuity, and which include the first order effects of nonuniformities in the data, are derived explicitly. The theory is derived by considering a group of elementary piston problems. Solutions with a shock or with a centered expansion wave are worked out individually in order to relate initial flow properties and their gradients to the speed and acceleration of the discontinuity waves. They are then combined to represent the solution of a general initial value problem by regarding the piston path as a contact line. In addition, problems with chemical reaction are discussed in terms of elementary piston problems which involve strong detonation waves, Chapman-Jouguet detonation waves, and deflagration waves.
Solutions of multidimensional partial differential equations representable as a one-dimensional flow
NASA Astrophysics Data System (ADS)
Zenchuk, A. I.
2014-03-01
We propose an algorithm for reducing an (M+ 1)-dimensional nonlinear partial differential equation (PDE) representable in the form of a one-dimensional flow ut + (u, ux uxx,…) = 0 (where w is an arbitrary local function of u and its xi derivatives, i = 1,…, M) to a family of M-dimensional nonlinear PDEs F(u,w) = 0, where F is a general (or particular) solution of a certain second-order two-dimensional nonlinear PDE. In particular, the M-dimensional PDE might turn out to be an ordinary differential equation, which can be integrated in some cases to obtain explicit solutions of the original (M+ 1)-dimensional equation. Moreover, a spectral parameter can be introduced in the function F, which leads to a linear spectral equation associated with the original equation. We present simplest examples of nonlinear PDEs together with their explicit solutions.
The velocity equations for dilatant granular flow and a new exact solution
NASA Astrophysics Data System (ADS)
Hill, J. M.; Katoanga, T. L.
For axially symmetric flow of dilatant granular materials, the velocity equations uncouple from the stress equations in certain plastic regimes, and assuming dilatant double shearing a set of three first order partial differential equations are obtained. These equations turn out to be deceptive because although simple in appearance, the determination of simple exact solutions is non-trivial. Here we show that all the known functional forms of existing solutions also arise systematically by consideration of the "optimal systems" of the classical Lie symmetries which indicates that any further solution types most likely arise from non-classical symmetries. For one of the known families we present a special case which admits a particularly simple closed form expression, which has not been previously given in the literature. For this particular special case the integral curves (streamlines) can be readily obtained as well as a simple analytical "approximation" for the particle paths. The streamlines and the validity of the analytical approximation are shown graphically.
NASA Technical Reports Server (NTRS)
Chen, Y. K.; Henline, W. D.
1993-01-01
The general boundary conditions including mass and energy balances of chemically equilibrated or nonequilibrated gas adjacent to ablating surfaces have been derived. A computer procedure based on these conditions was developed and interfaced with the Navier-Stokes solver for predictions of the flow field, surface temperature, and surface ablation rates over re-entry space vehicles with ablating Thermal Protection Systems (TPS). The Navier-Stokes solver with general surface thermochemistry boundary conditions can predict more realistic solutions and provide useful information for the design of TPS. A test case with a proposed hypersonic test vehicle configuration and associated free stream conditions was developed. Solutions with various surface boundary conditions were obtained, and the effect of nonequilibrium gas as well as surface chemistry on surface heating and ablation rate were examined. The solutions of the GASP code with complete ablating surface conditions were compared with those of the ASC code. The direction of future work is also discussed.
Parkhurst, David L.; Kipp, Kenneth L.; Engesgaard, Peter; Charlton, Scott R.
2004-01-01
The computer program PHAST simulates multi-component, reactive solute transport in three-dimensional saturated ground-water flow systems. PHAST is a versatile ground-water flow and solute-transport simulator with capabilities to model a wide range of equilibrium and kinetic geochemical reactions. The flow and transport calculations are based on a modified version of HST3D that is restricted to constant fluid density and constant temperature. The geochemical reactions are simulated with the geochemical model PHREEQC, which is embedded in PHAST. PHAST is applicable to the study of natural and contaminated ground-water systems at a variety of scales ranging from laboratory experiments to local and regional field scales. PHAST can be used in studies of migration of nutrients, inorganic and organic contaminants, and radionuclides; in projects such as aquifer storage and recovery or engineered remediation; and in investigations of the natural rock-water interactions in aquifers. PHAST is not appropriate for unsaturated-zone flow, multiphase flow, density-dependent flow, or waters with high ionic strengths. A variety of boundary conditions are available in PHAST to simulate flow and transport, including specified-head, flux, and leaky conditions, as well as the special cases of rivers and wells. Chemical reactions in PHAST include (1) homogeneous equilibria using an ion-association thermodynamic model; (2) heterogeneous equilibria between the aqueous solution and minerals, gases, surface complexation sites, ion exchange sites, and solid solutions; and (3) kinetic reactions with rates that are a function of solution composition. The aqueous model (elements, chemical reactions, and equilibrium constants), minerals, gases, exchangers, surfaces, and rate expressions may be defined or modified by the user. A number of options are available to save results of simulations to output files. The data may be saved in three formats: a format suitable for viewing with a text editor; a
A dual-permeability approach to preferential water flow and solute transport in shrinking soils
NASA Astrophysics Data System (ADS)
Coppola, Antonio; dragonetti, giovanna; Comegna, Alessandro; Gerke, Horst H.; Basile, Angelo
2016-04-01
The pore systems in most natural soils is dynamically changing due to alternating swelling and shrinkage processes, which induces changes in pore volume and pore size distribution including deformations in pore geometry. This is a serious difficulty for modeling flow and transport in dual permeability approaches, as it will also require that the geometrical deformation of both the soil matrix and the fracture porous systems be taken into account, as well as the dynamics of soil hydraulic properties in response to the domain deformations. This study follows up a previous work by the same authors extending the classical rigid (RGD) approach formerly proposed by Gerke and van Genuchten, to account for shrinking effects (SHR) in modeling water flow and solute transport in dual-permeability porous media. In this study we considered three SHR scenarios, assuming that aggregate shrinkage may change either: (i) the hydraulic properties of the two pore domains, (ii) their relative fractions, and (iii) both, hydraulic properties and fractions of the two domains. The objective was to compare simulation results obtained under the RGD and the SHR assumptions to illustrate the impact of matrix volume changes on water storage, water fluxes and solute concentrations during: 1) An infiltration process bringing an initially dry soil to saturation, 2) A drainage process starting from an initially saturated soil. For an infiltration process, the simulated wetting front and the solute concentration propagation velocity, as well as the water fluxes, water and solute exchange rates, for the three SHR scenarios significantly deviated from the RGD. By contrast, relatively similar water content profiles evolved under all scenarios during drying. Overall, compared to the RGD approach, the effect of changing the hydraulic properties and the weight of the two domains according to the shrinkage behavior of the soil aggregates induced a much more rapid response in terms of water fluxes and
NASA Astrophysics Data System (ADS)
Frampton, Andrew; Destouni, Georgia
2016-04-01
In cold regions, flow in the unsaturated zone is highly dynamic with seasonal variability and changes in temperature, moisture, and heat and water fluxes, all of which affect ground freeze-thaw processes and influence transport of inert and reactive waterborne substances. In arctic permafrost environments, near-surface groundwater flow is further restricted to a relatively shallow and seasonally variable active layer, confined by perennially frozen ground below. The active layer is typically partially saturated with ice, liquid water and air, and is strongly dependent on seasonal temperature fluctuations, thermal forcing and infiltration patterns. Here there is a need for improved understanding of the mechanisms controlling subsurface solute transport in the partially saturated active layer zone. Studying solute transport in cold regions is relevant to improve the understanding of how natural and anthropogenic pollution may change as activities in arctic and sub-arctic regions increase. It is also particularly relevant for understanding how dissolved carbon is transported in coupled surface and subsurface hydrological systems under climate change, in order to better understand the permafrost-hydrological-carbon climate feedback. In this contribution subsurface solute transport under surface warming and degrading permafrost conditions is studied using a physically based model of coupled cryotic and hydrogeological flow processes combined with a particle tracking method. Changes in subsurface water flows and solute transport travel times are analysed for different modelled geological configurations during a 100-year warming period. Results show that for all simulated cases, the minimum and mean travel times increase non-linearly with warming irrespective of geological configuration and heterogeneity structure. The travel time changes are shown to depend on combined warming effects of increase in pathway length due to deepening of the active layer, reduced transport
NASA Technical Reports Server (NTRS)
Hamilton, H. Harris, II; Millman, Daniel R.; Greendyke, Robert B.
1992-01-01
A computer code was developed that uses an implicit finite-difference technique to solve nonsimilar, axisymmetric boundary layer equations for both laminar and turbulent flow. The code can treat ideal gases, air in chemical equilibrium, and carbon tetrafluoride (CF4), which is a useful gas for hypersonic blunt-body simulations. This is the only known boundary layer code that can treat CF4. Comparisons with experimental data have demonstrated that accurate solutions are obtained. The method should prove useful as an analysis tool for comparing calculations with wind tunnel experiments and for making calculations about flight vehicles where equilibrium air chemistry assumptions are valid.
Colloid release and clogging in porous media: Effects of solution ionic strength and flow velocity.
Torkzaban, Saeed; Bradford, Scott A; Vanderzalm, Joanne L; Patterson, Bradley M; Harris, Brett; Prommer, Henning
2015-10-01
The release and retention of in-situ colloids in aquifers play an important role in the sustainable operation of managed aquifer recharge (MAR) schemes. The processes of colloid release, retention, and associated permeability changes in consolidated aquifer sediments were studied by displacing native groundwater with reverse osmosis-treated (RO) water at various flow velocities. Significant amounts of colloid release occurred when: (i) the native groundwater was displaced by RO-water with a low ionic strength (IS), and (ii) the flow velocity was increased in a stepwise manner. The amount of colloid release and associated permeability reduction upon RO-water injection depended on the initial clay content of the core. The concentration of released colloids was relatively low and the permeability reduction was negligible for the core sample with a low clay content of about 1.3%. In contrast, core samples with about 6 and 7.5% clay content exhibited: (i) close to two orders of magnitude increase in effluent colloid concentration and (ii) more than 65% permeability reduction. Incremental improvement in the core permeability was achieved when the flow velocity increased, whereas a short flow interruption provided a considerable increase in the core permeability. This dependence of colloid release and permeability changes on flow velocity and colloid concentration was consistent with colloid retention and release at pore constrictions due to the mechanism of hydrodynamic bridging. A mathematical model was formulated to describe the processes of colloid release, transport, retention at pore constrictions, and subsequent permeability changes. Our experimental and modeling results indicated that only a small fraction of the in-situ colloids was released for any given change in the IS or flow velocity. Comparison of the fitted and experimentally measured effluent colloid concentrations and associated changes in the core permeability showed good agreement, indicating that the
Colloid release and clogging in porous media: Effects of solution ionic strength and flow velocity.
Torkzaban, Saeed; Bradford, Scott A; Vanderzalm, Joanne L; Patterson, Bradley M; Harris, Brett; Prommer, Henning
2015-10-01
The release and retention of in-situ colloids in aquifers play an important role in the sustainable operation of managed aquifer recharge (MAR) schemes. The processes of colloid release, retention, and associated permeability changes in consolidated aquifer sediments were studied by displacing native groundwater with reverse osmosis-treated (RO) water at various flow velocities. Significant amounts of colloid release occurred when: (i) the native groundwater was displaced by RO-water with a low ionic strength (IS), and (ii) the flow velocity was increased in a stepwise manner. The amount of colloid release and associated permeability reduction upon RO-water injection depended on the initial clay content of the core. The concentration of released colloids was relatively low and the permeability reduction was negligible for the core sample with a low clay content of about 1.3%. In contrast, core samples with about 6 and 7.5% clay content exhibited: (i) close to two orders of magnitude increase in effluent colloid concentration and (ii) more than 65% permeability reduction. Incremental improvement in the core permeability was achieved when the flow velocity increased, whereas a short flow interruption provided a considerable increase in the core permeability. This dependence of colloid release and permeability changes on flow velocity and colloid concentration was consistent with colloid retention and release at pore constrictions due to the mechanism of hydrodynamic bridging. A mathematical model was formulated to describe the processes of colloid release, transport, retention at pore constrictions, and subsequent permeability changes. Our experimental and modeling results indicated that only a small fraction of the in-situ colloids was released for any given change in the IS or flow velocity. Comparison of the fitted and experimentally measured effluent colloid concentrations and associated changes in the core permeability showed good agreement, indicating that the
Xu, Wentao; Cheng, Nan; Huang, Kunlun; Lin, Yuehe; Wang, Chenguang; Xu, Yuancong; Zhu, Longjiao; Du, Dan; Luo, Yunbo
2016-06-15
Many types of diagnostic technologies have been reported for DNA methylation, but they require a standard curve for quantification or only show moderate accuracy. Moreover, most technologies have difficulty providing information on the level of methylation at specific contiguous multi-sites, not to mention easy-to-use detection to eliminate labor-intensive procedures. We have addressed these limitations and report here a cascade strategy that combines proportion competitive quantitative PCR (PCQ-PCR) and lateral flow nucleic acid biosensor (LFNAB), resulting in accurate and easy-to-use assessment. The P16 gene with specific multi-methylated sites, a well-studied tumor suppressor gene, was used as the target DNA sequence model. First, PCQ-PCR provided amplification products with an accurate proportion of multi-methylated sites following the principle of proportionality, and double-labeled duplex DNA was synthesized. Then, a LFNAB strategy was further employed for amplified signal detection via immune affinity recognition, and the exact level of site-specific methylation could be determined by the relative intensity of the test line and internal reference line. This combination resulted in all recoveries being greater than 94%, which are pretty satisfactory recoveries in DNA methylation assessment. Moreover, the developed cascades show significantly high usability as a simple, sensitive, and low-cost tool. Therefore, as a universal platform for sensing systems for the detection of contiguous multi-sites of DNA methylation without external standards and expensive instrumentation, this PCQ-PCR-LFNAB cascade method shows great promise for the point-of-care diagnosis of cancer risk and therapeutics.
Johnston, M; Jung, Y
2014-06-01
Purpose: Arterial spin labeling (ASL) is an MRI perfusion imaging method from which quantitative cerebral blood flow (CBF) maps can be calculated. Acquisition with variable post-labeling delays (PLD) and variable TRs allows for arterial transit time (ATT) mapping and leads to more accurate CBF quantification with a scan time saving of 48%. In addition, T1 and M0 maps can be obtained without a separate scan. In order to accurately estimate ATT and T1 of brain tissue from the ASL data, variable labeling durations were invented, entitled variable-bolus ASL. Methods: All images were collected on a healthy subject with a 3T Siemens Skyra scanner. Variable-bolus Psuedo-continuous ASL (PCASL) images were collected with 7 TI times ranging 100-4300ms in increments of 700ms with TR ranging 1000-5200ms. All boluses were 1600ms when the TI allowed, otherwise the bolus duration was 100ms shorter than the TI. All TI times were interleaved to reduce sensitivity to motion. Voxel-wise T1 and M0 maps were estimated using a linear least squares fitting routine from the average singal from each TI time. Then pairwise subtraction of each label/control pair and averaging for each TI time was performed. CBF and ATT maps were created using the standard model by Buxton et al. with a nonlinear fitting routine using the T1 tissue map. Results: CBF maps insensitive to ATT were produced along with ATT maps. Both maps show patterns and averages consistent with literature. The T1 map also shows typical T1 contrast. Conclusion: It has been demonstrated that variablebolus ASL produces CBF maps free from the errors due to ATT and tissue T1 variations and provides M0, T1, and ATT maps which have potential utility. This is accomplished with a single scan in a feasible scan time (under 6 minutes) with low sensivity to motion.
NASA Astrophysics Data System (ADS)
Sebben, Megan L.; Werner, Adrian D.
2016-08-01
Preferential flow features (PFFs, e.g. fractures and faults) are common features in rocks that otherwise have significant matrix permeability. Despite this, few studies have explored the influence of a PFF on the distribution of solute plumes in permeable rock formations, and the current understanding of PFF effects on solute plumes is based almost entirely on low-permeability rock matrices. This research uses numerical modelling to examine solute plumes that pass through a PFF in permeable rock, to explore the PFF's influence on plume migration. The study adopts intentionally simplified arrangements involving steady-state solute plumes in idealised, moderate-to-high-permeability rock aquifers containing a single PFF. A range of matrix-PFF permeability ratios (4.9 × 10-6-2.5 × 10-2), typical of fractured sedimentary aquifers, is considered. The results indicate that for conditions representative of high-to-moderate-permeability sedimentary rock matrices containing a medium-sized fracture, the effect of the PFF on solute plume displacement and spreading can be considerable. For example, plumes are between 1.3 and 19 times wider than in associated porous media only scenarios, and medium-sized PFFs in moderately permeable matrices can reduce the maximum solute concentration by up to 104 times. Plume displacement and spreading is lower in aquifers of higher matrix-PFF permeability ratios, and where solute plumes are more dispersed at the point of intersection with the PFF. Asymmetry in the plume caused by the passage through the PFF is more pronounced for more dispersive plumes. The current study demonstrates that PFFs most likely govern solute plume characteristics in typical permeable matrices, given that a single PFF of aperture representing a medium-sized fracture (i.e. 5.0 × 10-4m) produces the equivalent spreading effects of 0.22-7.88 m of plume movement through the permeable matrix.
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
Impact of water table fluctuations on water flow and solute transport in different porous media
NASA Astrophysics Data System (ADS)
Rühle, Franziska; Zentner, Nadine; Stumpp, Christine
2013-04-01
The interface between saturated and unsaturated zone is dynamic and varies spatially and temporally resulting in fluctuations of the water table. Still, little is known about transport processes under transient flow conditions at this interface and how the processes are affected by altering the water table. In order to understand transport and fate of dissolved contaminants into the groundwater and consequently the quality of groundwater, improved understanding about hydrological processes at the dynamic interface between unsaturated and saturated zone is needed. The objective of this study was to investigate the impact of water table fluctuations on one-dimensional vertical flow and solute transport in different sediments. Therefore, flow-through columns (length=50cm, diameter=9cm), filled with glass beads of different grain sizes (smaller=0.4-0.6mm, coarser=1.0-1.5mm), were constantly irrigated at 12 cm/d. Several multi-tracer experiments were conducted with a statically fixed water table and compared to experiments where the water table was fluctuated in upward and downward direction. Data modeling was performed with a lumped parameter model to simulate hydrological fluxes and to determine transport parameters. Our results showed that most tracer breakthrough curves were well simulated indicating that the systems were at steady state. The results showed that under certain hydrological conditions water table fluctuations lead to increased dispersivity. It is suggested that a falling water table can cause increased spreading when the decline is faster than the water flux resulting in a more extensive solute distribution over depth. Further, it was observed that a rising water table can cause higher tracer spreading due to diffusive solute exchange in coarse sediments with immobile water regions. In conclusion, spatial and temporal variability of the interface between vadose zone and groundwater contribute to spreading of solutes and therefore have to be considered
On the propagation of diel signals in river networks using analytic solutions of flow equations
NASA Astrophysics Data System (ADS)
Fonley, Morgan; Mantilla, Ricardo; Small, Scott J.; Curtu, Rodica
2016-07-01
Several authors have reported diel oscillations in streamflow records and have hypothesized that these oscillations are linked to evapotranspiration cycles in the watershed. The timing of oscillations in rivers, however, lags behind those of temperature and evapotranspiration in hillslopes. Two hypotheses have been put forth to explain the magnitude and timing of diel streamflow oscillations during low-flow conditions. The first suggests that delays between the peaks and troughs of streamflow and daily evapotranspiration are due to processes occurring in the soil as water moves toward the channels in the river network. The second posits that they are due to the propagation of the signal through the channels as water makes its way to the outlet of the basin. In this paper, we design and implement a theoretical model to test these hypotheses. We impose a baseflow signal entering the river network and use a linear transport equation to represent flow along the network. We develop analytic streamflow solutions for the case of uniform velocities in space over all river links. We then use our analytic solution to simulate streamflows along a self-similar river network for different flow velocities. Our results show that the amplitude and time delay of the streamflow solution are heavily influenced by transport in the river network. Moreover, our equations show that the geomorphology and topology of the river network play important roles in determining how amplitude and signal delay are reflected in streamflow signals. Finally, we have tested our theoretical formulation in the Dry Creek Experimental Watershed, where oscillations are clearly observed in streamflow records. We find that our solution produces streamflow values and fluctuations that are similar to those observed in the summer of 2011.
Semi-analytical solution of groundwater flow in a leaky aquifer system subject to bending effect
NASA Astrophysics Data System (ADS)
Yu, Chia-Chi; Yang, Shaw-Yang; Yeh, Hund-Der
2013-04-01
SummaryThe bending of aquitard like a plate due to aquifer pumping and compression is often encountered in many practical problems of subsurface flow. This reaction will have large influence on the release of the volume of water from the aquifer, which is essential for the planning and management of groundwater resources in aquifers. However, the groundwater flow induced by pumping in a leaky aquifer system is often assumed that the total stress of aquifer maintains constant all the time and the mechanical behavior of the aquitard formation is negligible. Therefore, this paper devotes to the investigation of the effect of aquitard bending on the drawdown distribution in a leaky aquifer system, which is obviously of interest in groundwater hydrology. Based on the work of Wang et al. (2004) this study develops a mathematical model for investigating the impacts of aquitard bending and leakage rate on the drawdown of the confined aquifer due to a constant-rate pumping in the leaky aquifer system. This model contains three equations; two flow equations delineate the transient drawdown distributions in the aquitard and the confined aquifer, while the other describes the vertical displacement in response to the aquitard bending. For the case of no aquitard bending, this new solution can reduce to the Hantush Laplace-domain solution (Hantush, 1960). On the other hand, this solution without the leakage effect can reduce to the time domain solution of Wang et al. (2004). The results show that the aquifer drawdown is influenced by the bending effect at early time and by the leakage effect at late time. The results of sensitivity analysis indicate that the aquifer compaction is sensitive only at early time, causing less amount of water released from the pumped aquifer than that predicted by the traditional groundwater theory. The dimensionless drawdown is rather sensitive to aquitard's hydraulic conductivity at late time. Additionally, both the hydraulic conductivity and
On the Solution of the Three-Dimensional Flowfield About a Flow-Through Nacelle. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Compton, William Bernard
1985-01-01
The solution of the three dimensional flow field for a flow through nacelle was studied. Both inviscid and viscous inviscid interacting solutions were examined. Inviscid solutions were obtained with two different computational procedures for solving the three dimensional Euler equations. The first procedure employs an alternating direction implicit numerical algorithm, and required the development of a complete computational model for the nacelle problem. The second computational technique employs a fourth order Runge-Kutta numerical algorithm which was modified to fit the nacelle problem. Viscous effects on the flow field were evaluated with a viscous inviscid interacting computational model. This model was constructed by coupling the explicit Euler solution procedure with a flag entrainment boundary layer solution procedure in a global iteration scheme. The computational techniques were used to compute the flow field for a long duct turbofan engine nacelle at free stream Mach numbers of 0.80 and 0.94 and angles of attack of 0 and 4 deg.
A closed-form solution for steady-state coupled phloem/xylem flow using the Lambert-W function.
Hall, A J; Minchin, P E H
2013-12-01
A closed-form solution for steady-state coupled phloem/xylem flow is presented. This incorporates the basic Münch flow model of phloem transport, the cohesion model of xylem flow, and local variation in the xylem water potential and lateral water flow along the transport pathway. Use of the Lambert-W function allows this solution to be obtained under much more general and realistic conditions than has previously been possible. Variation in phloem resistance (i.e. viscosity) with solute concentration, and deviations from the Van't Hoff expression for osmotic potential are included. It is shown that the model predictions match those of the equilibrium solution of a numerical time-dependent model based upon the same mechanistic assumptions. The effect of xylem flow upon phloem flow can readily be calculated, which has not been possible in any previous analytical model. It is also shown how this new analytical solution can handle multiple sources and sinks within a complex architecture, and can describe competition between sinks. The model provides new insights into Münch flow by explicitly including interactions with xylem flow and water potential in the closed-form solution, and is expected to be useful as a component part of larger numerical models of entire plants.
Extensional flow of hyaluronic acid solutions in an optimized microfluidic cross-slot devicea
Haward, S. J.; Jaishankar, A.; Oliveira, M. S. N.; Alves, M. A.; McKinley, G. H.
2013-01-01
We utilize a recently developed microfluidic device, the Optimized Shape Cross-slot Extensional Rheometer (OSCER), to study the elongational flow behavior and rheological properties of hyaluronic acid (HA) solutions representative of the synovial fluid (SF) found in the knee joint. The OSCER geometry is a stagnation point device that imposes a planar extensional flow with a homogenous extension rate over a significant length of the inlet and outlet channel axes. Due to the compressive nature of the flow generated along the inlet channels, and the planar elongational flow along the outlet channels, the flow field in the OSCER device can also be considered as representative of the flow field that arises between compressing articular cartilage layers of the knee joints during running or jumping movements. Full-field birefringence microscopy measurements demonstrate a high degree of localized macromolecular orientation along streamlines passing close to the stagnation point of the OSCER device, while micro-particle image velocimetry is used to quantify the flow kinematics. The stress-optical rule is used to assess the local extensional viscosity in the elongating fluid elements as a function of the measured deformation rate. The large limiting values of the dimensionless Trouton ratio, Tr ∼ O(50), demonstrate that these fluids are highly extensional-thickening, providing a clear mechanism for the load-dampening properties of SF. The results also indicate the potential for utilizing the OSCER in screening of physiological SF samples, which will lead to improved understanding of, and therapies for, disease progression in arthritis sufferers. PMID:24738010
Extensional flow of hyaluronic acid solutions in an optimized microfluidic cross-slot device.
Haward, S J; Jaishankar, A; Oliveira, M S N; Alves, M A; McKinley, G H
2013-07-01
We utilize a recently developed microfluidic device, the Optimized Shape Cross-slot Extensional Rheometer (OSCER), to study the elongational flow behavior and rheological properties of hyaluronic acid (HA) solutions representative of the synovial fluid (SF) found in the knee joint. The OSCER geometry is a stagnation point device that imposes a planar extensional flow with a homogenous extension rate over a significant length of the inlet and outlet channel axes. Due to the compressive nature of the flow generated along the inlet channels, and the planar elongational flow along the outlet channels, the flow field in the OSCER device can also be considered as representative of the flow field that arises between compressing articular cartilage layers of the knee joints during running or jumping movements. Full-field birefringence microscopy measurements demonstrate a high degree of localized macromolecular orientation along streamlines passing close to the stagnation point of the OSCER device, while micro-particle image velocimetry is used to quantify the flow kinematics. The stress-optical rule is used to assess the local extensional viscosity in the elongating fluid elements as a function of the measured deformation rate. The large limiting values of the dimensionless Trouton ratio, Tr ∼ O(50), demonstrate that these fluids are highly extensional-thickening, providing a clear mechanism for the load-dampening properties of SF. The results also indicate the potential for utilizing the OSCER in screening of physiological SF samples, which will lead to improved understanding of, and therapies for, disease progression in arthritis sufferers.
Schvidler, M.; Karasaki, K.
2011-06-15
In previous papers (Shvidler and Karasaki, 1999, 2001, 2005, and 2008) we presented and analyzed an approach for finding the general forms of exactly averaged equations of flow and transport in porous media. We studied systems of basic equations for steady flow with sources in unbounded domains with stochastically homogeneous conductivity fields. A brief analysis of exactly averaged equations of nonsteady flow and nonreactive solute transport was also presented. At the core of this approach is the existence of appropriate random Green's functions. For example, we showed that in the case of a 3-dimensional unbounded domain the existence of appropriate random Green's functions is sufficient for finding the exact nonlocal averaged equations for flow velocity using the operator with a unique kernel-vector. Examination of random fields with global symmetry (isotropy, transversal isotropy and orthotropy) makes it possible to describe significantly different types of averaged equations with nonlocal unique operators. It is evident that the existence of random Green's functions for physical linear processes is equivalent to assuming the existence of some linear random operators for appropriate stochastic equations. If we restricted ourselves to this assumption only, as we have done in this paper, we can study the processes in any dimensional bounded or unbounded fields and in addition, cases in which the random fields of conductivity and porosity are stochastically nonhomogeneous, nonglobally symmetrical, etc.. It is clear that examining more general cases involves significant difficulty and constricts the analysis of structural types for the processes being studied. Nevertheless, we show that we obtain the essential information regarding averaged equations for steady and transient flow, as well as for solute transport.
Exact solutions for the flow of non-Newtonian fluid with fractional derivative in an annular pipe
NASA Astrophysics Data System (ADS)
Tong, Dengke; Wang, Ruihe; Yang, Heshan
2005-08-01
This paper deals with some unsteady unidirectional transient flows of Oldroyd-B fluid in an annular pipe. The fractional calculus approach in the constitutive relationship model Oldroyd-B fluid is introduced and a generalized Jeffreys model with the fractional calculus has been built. Exact solutions of some unsteady flows of Oldroyd-B fluid in an annular pipe are obtained by using Hankel transform and Laplace transform for fractional calculus. The following four problems have been studied: (1) Poiseuille flow due to a constant pressure gradient; (2) axial Couette flow in an annulus; (3) axial Couette flow in an annulus due to a longitudinal constant shear; (4) Poiseuille flow due to a constant pressure gradient and a longitudinal constant shear. The well-known solutions for Navier-Stokes fluid, as well as those corresponding to a Maxwell fluid and a second grade one, appear as limited cases of our solutions.
Local velocity measurements in heterogeneous and time-dependent flows of a micellar solution.
Decruppe, J P; Greffier, O; Manneville, S; Lerouge, S
2006-06-01
We present and discuss the results of pointwise velocity measurements performed on a viscoelastic micellar solution made of cetyltrimethylammonium bromide and sodium salicylate in water, respectively, at the concentrations of 50 and 100 mmol. The sample is contained in a Couette device and subjected to flow in the strain controlled mode. This particular solution shows shear banding and, in a narrow range of shear rates at the right end of the stress plateau, apparent shear thickening occurs. Time-dependent recordings of the shear stress in this range reveal that the flow has become unstable and that large sustained oscillations of the shear stress and of the first normal stresses difference emerge and grow in the flow. Local pointwise velocity measurements clearly reveal a velocity profile typical of shear banding when the imposed shear rate belongs to the plateau, but also important wall slip in the entire range of velocity gradients investigated. In the oscillations regime, the velocity is recorded as a function of time at a fixed point close to the rotor of the Couette device. The time-dependent velocity profile reveals random fluctuations but, from time to time, sharp decreases much larger than the standard deviation are observed. An attempt is made to correlate these strong variations with the stress oscillations and a correlation coefficient r is computed. However, the small value found for the coefficient r does not allow us to draw a final conclusion as concerns the correlation between stress oscillations and velocity fast decreases.
A master dynamic flow diagram for the shear thickening transition in micellar solutions.
Bautista, F; Tepale, N; Fernández, V V A; Landázuri, G; Hernández, E; Macías, E R; Soltero, J F A; Escalante, J I; Manero, O; Puig, J E
2016-01-01
The shear thickening behavior of dilute micellar solutions of hexadecyltrimethylammonium-type surfactants with different counterions (tosylate, 3- and 4-fluorobenzoate, vinylbenzoate and salicylate) and of n-alkyltetradecylammonium bromide (CnTAB), with n = 14, 16 and 18, is examined here. These solutions undergo a shear thickening transition due to the formation of shear-induced structures (SISs) in the shear range studied. Here we report a relationship between the shear thickening intensity and the differences in the hydrophobicity of counterions according to the Hofmeister-like anion series, which leads to a master flow diagram. This master flow diagram is produced by plotting a normalized shear thickening intensity (Iη - 1)/(Imax - 1) versus CD/CD,max, where Iη is the shear-thickening intensity, defined as the largest viscosity obtained in the shear-thickening transition (STT) at a given surfactant concentration CD divided by the Newtonian viscosity η0, and Imax is the largest intensity value obtained in the STT at a surfactant concentration CD,max. The master flow diagram is built using several cetyltrimethylammonium-type surfactants with different counterions, according to a Hofmeister-like series, and by n-alkyltetradecylammonium bromide surfactants with different alkyl chain lengths.
Flow-enhanced solution printing of all-polymer solar cells
Diao, Ying; Zhou, Yan; Kurosawa, Tadanori; Shaw, Leo; Wang, Cheng; Park, Steve; Guo, Yikun; Reinspach, Julia A.; Gu, Kevin; Gu, Xiaodan; et al
2015-08-12
Morphology control of solution coated solar cell materials presents a key challenge limiting their device performance and commercial viability. Here we present a new concept for controlling phase separation during solution printing using an all-polymer bulk heterojunction solar cell as a model system. The key aspect of our method lies in the design of fluid flow using a microstructured printing blade, on the basis of the hypothesis of flow-induced polymer crystallization. Our flow design resulted in a similar to 90% increase in the donor thin film crystallinity and reduced microphase separated donor and acceptor domain sizes. The improved morphology enhancedmore » all metrics of solar cell device performance across various printing conditions, specifically leading to higher short-circuit current, fill factor, open circuit voltage and significantly reduced device-to-device variation. However, we expect our design concept to have broad applications beyond all-polymer solar cells because of its simplicity and versatility.« less
Perturbation solution for the viscoelastic 3D flow around a rigid sphere subject to simple shear
NASA Astrophysics Data System (ADS)
Housiadas, Kostas D.; Tanner, Roger I.
2011-08-01
We study the steady, three-dimensional creeping, and viscoelastic flow around a freely rotating rigid sphere subject to simple shear flow imposed at infinity. The viscoelasticity of the ambient fluid is modeled using the second-order-fluid model, the Upper Convected Maxwell, the exponential affine Phan-Thien-Tanner, and the Giesekus constitutive equations. A spherical coordinate system with origin at the center of the sphere is used to describe the flow field. The solution of the governing equations is expanded as a series for small values of the Deborah number. The resulting sequence of differential equations is solved analytically up to second order and numerically up to fourth order in Deborah number by employing fully spectral representations for all the primary variables. In particular, Chebyshev polynomials are used in the radial coordinate and the double Fourier series in the longitudinal and latitudinal coordinates. The numerical results up to second-order agree within machine accuracy with the available analytical solutions clearly indicating the correctness and accuracy of the numerical method developed here. Analytical expressions for the angular velocity of the rigid sphere up to fourth order, which show the slowdown of the rotation of the sphere with respect to the Newtonian creeping case, are also derived. For small Deborah numbers, these expressions, along with those presented in a recent letter [Housiadas and Tanner, Phys. Fluids 23, 051702 (2011)] are in agreement with the few available experimental data and numerical results.
Solution-Adaptive Cartesian Cell Approach for Viscous and Inviscid Flows
NASA Technical Reports Server (NTRS)
Coirier, William J.; Powell, Kenneth G.
1996-01-01
A Cartesian cell-based approach for adaptively refined solutions of the Euler and Navier-Stokes equations in two dimensions is presented. Grids about geometrically complicated bodies are generated automatically, by the recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal cut cells are created using modified polygon-clipping algorithms. The grid is stored in a binary tree data structure that provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite volume formulation. The convective terms are upwinded: A linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The results of a study comparing the accuracy and positivity of two classes of cell-centered, viscous gradient reconstruction procedures is briefly summarized. Adaptively refined solutions of the Navier-Stokes equations are shown using the more robust of these gradient reconstruction procedures, where the results computed by the Cartesian approach are compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.
Hydrodynamic dispersion of a neutral non-reacting solute in electroosmotic flow
S. K. Griffiths; R. H. Nilson
1999-06-01
Analytical methods are employed to determine the axial dispersion of a neutral non-reacting solute in an incompressible electroosmotic flow. In contrast to previous approaches, the dispersion is obtained here by solving the time-dependent diffusion-advection equation in transformed spatial and temporal coordinates to obtain the two-dimensional late-time concentration field. The coefficient of dispersion arises as a separation eigenvalue, and its value is obtained as a necessary condition for satisfying all of the required boundary conditions. Solutions based on the Debye-Huckel approximation are presented for both a circular tube and a channel of infinite width. These results recover the well-known solutions for dispersion in pressure-driven flows when the Debye length is very large. In this limit, the axial dispersion is proportional to the square of the Peclet number based on the characteristic transverse dimension of the tube or channel. In the tilt of very small Debye lengths, the authors find that the dispersion varies as the square of the Peclet number based on the Debye length. Simple approximations to the coefficient of dispersion as a function of the Debye length and Peclet number are also presented.
NASA Astrophysics Data System (ADS)
Guevara, Carlos; Graf, Thomas
2013-04-01
Subsurface water systems are endangered due to salt water intrusion in coastal aquifers, leachate infiltration from waste disposal sites and salt transport in agricultural sites. This leads to the situation where more dense fluid overlies a less dense fluid creating a density gradient. Under certain conditions this density gradient produces instabilities in form dense plume fingers that move downwards. This free convection increases solute transport over large distances and shorter times. In cases where a significantly larger density gradient exists, the effect of free convection on transport is non-negligible. The assumption of a constant density distribution in space and time is no longer valid. Therefore variable-density flow must be considered. The flow equation and the transport equation govern the numerical modeling of variable-density flow and solute transport. Computer simulation programs mathematically describe variable-density flow using the Oberbeck-Boussinesq Approximation (OBA). Three levels of simplifications can de considered, which are denoted by OB1, OB2 and OB3. OB1 is the usually applied simplification where variable density is taken into account in the hydraulic potential. In OB2 variable density is considered in the flow equation and in OB3 variable density is additionally considered in the transport equation. Using the results from a laboratory-scale experiment of variable-density flow and solute transport (Simmons et al., Transp. Porous Medium, 2002) it is investigated which level of mathematical accuracy is required to represent the physical experiment the most accurate. Differences between the physical and mathematical model are evaluated using qualitative indicators (e.g. mass fluxes, Nusselt number). Results show that OB1 is required for small density gradients and OB3 is required for large density gradients.
Impact of water table fluctuations on water flow and solute transport in 1D column systems
NASA Astrophysics Data System (ADS)
Rühle, F.; Stumpp, C.
2012-04-01
Although hydrological processes and mass fluxes in the unsaturated and saturated zone have been well studied separately, little is known about transition processes between these zones. Since the transition zone is dynamic and varies spatially and temporally with fluctuations of the water table, water flow and solute transport are believed to vary dynamically, too. This may influence the transport and fate of dissolved contaminants and consequently the quality of groundwater. In order to protect and maintain drinking water resources, improved understanding about hydrological processes at the dynamic interface between the unsaturated and saturated zone is needed. The objective of this study was to investigate the impact of water table fluctuations on one-dimensional vertical flow and solute transport in laboratory column systems. Therefore, two flow-through columns were constantly irrigated with groundwater at an infiltration rate of 4.7 cm/d. In one column the water table was kept statically fixed in the middle, in the other column the water table was continually fluctuated by regularly raising and lowering the outflow tube. Several multi-tracer experiments were conducted and compared injecting the tracers bromide, deuterium and 18-oxygen at different water levels. Data modelling was performed with a lumped parameter model to simulate the hydrological fluxes. Our results showed that at static water table and similar water fluxes in both columns, structural heterogeneities due to packing lead to differences in solute transport, e.g. different dispersivity. Tracer breakthrough curves were well simulated with the lumped parameter model indicating that the systems were at steady state. When the water table was fluctuated small differences in solute transport were observed. Even with a fluctuating water table the lumped parameter model yielded high modelling accuracy and indicated that under certain hydrological conditions water table fluctuations lead to slightly
NASA Technical Reports Server (NTRS)
Gupta, R. N.; Moss, J. N.; Simmonds, A. L.
1982-01-01
Two flow-field codes employing the time- and space-marching numerical techniques were evaluated. Both methods were used to analyze the flow field around a massively blown Jupiter entry probe under perfect-gas conditions. In order to obtain a direct point-by-point comparison, the computations were made by using identical grids and turbulence models. For the same degree of accuracy, the space-marching scheme takes much less time as compared to the time-marching method and would appear to provide accurate results for the problems with nonequilibrium chemistry, free from the effect of local differences in time on the final solution which is inherent in time-marching methods. With the time-marching method, however, the solutions are obtainable for the realistic entry probe shapes with massive or uniform surface blowing rates; whereas, with the space-marching technique, it is difficult to obtain converged solutions for such flow conditions. The choice of the numerical method is, therefore, problem dependent. Both methods give equally good results for the cases where results are compared with experimental data.
Interface evolution of a particle in a supersaturated solution affected by a far-field uniform flow
NASA Astrophysics Data System (ADS)
Chen, Ming-Wen; Wang, Zi-Dong
2013-09-01
The effect of far-field uniform flow on the morphological evolution of a spherical particle in a supersaturated solution affected by a far-field uniform flow is studied by using the matched asymptotic expansion method. The analytical solution for the interface shape, concentration field, and interface velocity of the particle growth shows that the convection induced by the far-field uniform flow facilitates the growth of the spherical particle, the upstream flow imposed on the particle enhances the growth velocity of the interface when the flow comes in, the downstream flow lowers the growth velocity of the surface when the flow goes out, and the interface morphology evolves into a peach-like shape.
CFEST Coupled Flow, Energy & Solute Transport Version CFEST005 User’s Guide
Freedman, Vicky L.; Chen, Yousu; Gilca, Alex; Cole, Charles R.; Gupta, Sumant K.
2006-07-20
The CFEST (Coupled Flow, Energy, and Solute Transport) simulator described in this User’s Guide is a three-dimensional finite-element model used to evaluate groundwater flow and solute mass transport. Confined and unconfined aquifer systems, as well as constant and variable density fluid flows can be represented with CFEST. For unconfined aquifers, the model uses a moving boundary for the water table, deforming the numerical mesh so that the uppermost nodes are always at the water table. For solute transport, changes in concentra¬tion of a single dissolved chemical constituent are computed for advective and hydrodynamic transport, linear sorption represented by a retardation factor, and radioactive decay. Although several thermal parameters described in this User’s Guide are required inputs, thermal transport has not yet been fully implemented in the simulator. Once fully implemented, transport of thermal energy in the groundwater and solid matrix of the aquifer can also be used to model aquifer thermal regimes. The CFEST simulator is written in the FORTRAN 77 language, following American National Standards Institute (ANSI) standards. Execution of the CFEST simulator is controlled through three required text input files. These input file use a structured format of associated groups of input data. Example input data lines are presented for each file type, as well as a description of the structured FORTRAN data format. Detailed descriptions of all input requirements, output options, and program structure and execution are provided in this User’s Guide. Required inputs for auxillary CFEST utilities that aide in post-processing data are also described. Global variables are defined for those with access to the source code. Although CFEST is a proprietary code (CFEST, Inc., Irvine, CA), the Pacific Northwest National Laboratory retains permission to maintain its own source, and to distribute executables to Hanford subcontractors.
A solution procedure for two- and three-dimensional unsteady viscous flows
NASA Astrophysics Data System (ADS)
Weinberg, B. C.; McDonald, H.; Shamroth, S. J.
1985-01-01
An efficient computational procedure for solving three-dimensional unsteady turbulent flows is described. The consistently split Linearized Block Implicit (LBI) scheme is used in conjunction with the QR operator scheme to solve an approximate form of the Navier-Stokes equations in generalized nonorthogonal coordinates employing physical velocity components. As a demonstration calculation the turbulent oscillating flow over a flat plate corresponding to the experiment of Karlsson is considered in both two and three dimensions. New inflow boundary conditions are proposed which yield physically plausible solutions near the upstream boundary. The results obtained agree both qualitatively and quantitatively with Karlsson's data and shed new light on the controversy concerning the interpretation of the skin friction phase angle as a function of reduced frequency.
Analytical solutions for flow in porous media with multicomponent cation exchange reactions
NASA Astrophysics Data System (ADS)
Venkatraman, Ashwin; Hesse, Marc A.; Lake, Larry W.; Johns, Russell T.
2014-07-01
Multicomponent cation exchange reactions have important applications in groundwater remediation, disposal of nuclear wastes as well as enhanced oil recovery. The hyperbolic theory of conservation laws can be used to explain the nature of displacements observed during flow with cation exchange reactions between flowing aqueous phase and stationary solid phase. Analytical solutions have been developed to predict the effluent profiles for a particular case of heterovalent cations (Na+, Ca2+ and Mg2+) and an anion (Cl-) for any combination of constant injection and constant initial composition using this theory. We assume local equilibrium, neglect dispersion and model the displacement as a Riemann problem using mass action laws, the charge conservation equation and the cation exchange capacity equation. The theoretical predictions have been compared with experimental data available at two scales—the laboratory scale and the field scale. The theory agrees well with the experimental data at both scales. Analytical theory predictions show good agreement with numerical model, developed using finite differences.
Parallel solution of high-order numerical schemes for solving incompressible flows
NASA Technical Reports Server (NTRS)
Milner, Edward J.; Lin, Avi; Liou, May-Fun; Blech, Richard A.
1993-01-01
A new parallel numerical scheme for solving incompressible steady-state flows is presented. The algorithm uses a finite-difference approach to solving the Navier-Stokes equations. The algorithms are scalable and expandable. They may be used with only two processors or with as many processors as are available. The code is general and expandable. Any size grid may be used. Four processors of the NASA LeRC Hypercluster were used to solve for steady-state flow in a driven square cavity. The Hypercluster was configured in a distributed-memory, hypercube-like architecture. By using a 50-by-50 finite-difference solution grid, an efficiency of 74 percent (a speedup of 2.96) was obtained.
NASA Technical Reports Server (NTRS)
Karageorghis, Andreas; Phillips, Timothy N.
1990-01-01
The numerical simulation of steady planar two-dimensional, laminar flow of an incompressible fluid through an abruptly contracting channel using spectral domain decomposition methods is described. The key features of the method are the decomposition of the flow region into a number of rectangular subregions and spectral approximations which are pointwise C(1) continuous across subregion interfaces. Spectral approximations to the solution are obtained for Reynolds numbers in the range 0 to 500. The size of the salient corner vortex decreases as the Reynolds number increases from 0 to around 45. As the Reynolds number is increased further the vortex grows slowly. A vortex is detected downstream of the contraction at a Reynolds number of around 175 that continues to grow as the Reynolds number is increased further.
Numerical solutions of the Navier-Stokes equations for transonic afterbody flows
NASA Technical Reports Server (NTRS)
Swanson, R. C., Jr.
1980-01-01
The time dependent Navier-Stokes equations in mass averaged variables are solved for transonic flow over axisymmetric boattail plume simulator configurations. Numerical solution of these equations is accomplished with the unsplit explict finite difference algorithm of MacCormack. A grid subcycling procedure and computer code vectorization are used to improve computational efficiency. The two layer algebraic turbulence models of Cebeci-Smith and Baldwin-Lomax are employed for investigating turbulence closure. Two relaxation models based on these baseline models are also considered. Results in the form of surface pressure distribution for three different circular arc boattails at two free stream Mach numbers are compared with experimental data. The pressures in the recirculating flow region for all separated cases are poorly predicted with the baseline turbulence models. Significant improvements in the predictions are usually obtained by using the relaxation models.
Exact Solutions for Stokes' Flow of a Non-Newtonian Nanofluid Model: A Lie Similarity Approach
NASA Astrophysics Data System (ADS)
Aziz, Taha; Aziz, A.; Khalique, C. M.
2016-07-01
The fully developed time-dependent flow of an incompressible, thermodynamically compatible non-Newtonian third-grade nanofluid is investigated. The classical Stokes model is considered in which the flow is generated due to the motion of the plate in its own plane with an impulsive velocity. The Lie symmetry approach is utilised to convert the governing nonlinear partial differential equation into different linear and nonlinear ordinary differential equations. The reduced ordinary differential equations are then solved by using the compatibility and generalised group method. Exact solutions for the model equation are deduced in the form of closed-form exponential functions which are not available in the literature before. In addition, we also derived the conservation laws associated with the governing model. Finally, the physical features of the pertinent parameters are discussed in detail through several graphs.
Fluid flow and sand production in heavy-oil reservoirs under solution-gas drive
Smith, G.E.
1988-05-01
The production of heavy oil in Canada has led to a number of anomalous results, most of which have been excused as high-permeability channels resulting from sand production. The methods of soil mechanics predict gross formation failure resulting from high fluid compressability, small cohesion, and high viscosity. Gross failure results in excellent productivity but reduced in-situ stress (and fracture stress). Solution-gas drive in these reservoirs involves simultaneous-mixture flow of a gas as very tiny little bubbles entrained in heavy oil. Stress, geometry, and permeability alteration resulting from matrix deformation combined with peculiar pressure-depended multiphase-flow properties result in a new model of reservoir performance. A field observation of stress modification is discussed, as are the contributions of the four components discussed previously to the observed phenomena.
Coupled turbulent flow, heat, and solute transport in continuous casting processes
NASA Astrophysics Data System (ADS)
Aboutalebi, M. Reza; Hasan, M.; Guthrie, R. I. L.
1995-08-01
A fully coupled fluid flow, heat, and solute transport model was developed to analyze turbulent flow, solidification, and evolution of macrosegregation in a continuous billet caster. Transport equations of total mass, momentum, energy, and species for a binary iron-carbon alloy system were solved using a continuum model, wherein the equations are valid for the solid, liquid, and mushy zones in the casting. A modified version of the low-Reynolds number k-ɛ model was adopted to incorporate turbulence effects on transport processes in the system. A control-volume-based finite-difference procedure was employed to solve the conservation equations associated with appropriate boundary conditions. Because of high nonlinearity in the system of equations, a number of techniques were used to accelerate the convergence process. The effects of the parameters such as casting speed, steel grade, nozzle configuration on flow pattern, solidification profile, and carbon segregation were investigated. From the computed flow pattern, the trajectory of inclusion particles, as well as the density distribution of the particles, was calculated. Some of the computed results were compared with available experimental measurements, and reasonable agreements were obtained.
Analytical solution of two-fluid electro-osmotic flows of viscoelastic fluids.
Afonso, A M; Alves, M A; Pinho, F T
2013-04-01
This paper presents an analytical model that describes a two-fluid electro-osmotic flow of stratified fluids with Newtonian or viscoelastic rheological behavior. This is the principle of operation of an electro-osmotic two-fluid pump as proposed by Brask et al. [Tech. Proc. Nanotech., 1, 190-193, 2003], in which an electrically non-conducting fluid is transported by the interfacial dragging viscous force of a conducting fluid that is driven by electro-osmosis. The electric potential in the conducting fluid and the analytical steady flow solution of the two-fluid electro-osmotic stratified flow in a planar microchannel are presented by assuming a planar interface between the two immiscible fluids with Newtonian or viscoelastic rheological behavior. The effects of fluid rheology, shear viscosity ratio, holdup and interfacial zeta potential are analyzed to show the viability of this technique, where an enhancement of the flow rate is observed as the shear-thinning effects are increased.
Mustafa, Meraj; Farooq, Muhammad A.; Hayat, Tasawar; Alsaedi, Ahmed
2013-01-01
This investigation is concerned with the stagnation-point flow of nanofluid past an exponentially stretching sheet. The presence of Brownian motion and thermophoretic effects yields a coupled nonlinear boundary-value problem (BVP). Similarity transformations are invoked to reduce the partial differential equations into ordinary ones. Local similarity solutions are obtained by homotopy analysis method (HAM), which enables us to investigate the effects of parameters at a fixed location above the sheet. The numerical solutions are also derived using the built-in solver bvp4c of the software MATLAB. The results indicate that temperature and the thermal boundary layer thickness appreciably increase when the Brownian motion and thermophoresis effects are strengthened. Moreover the nanoparticles volume fraction is found to increase when the thermophoretic effect intensifies. PMID:23671576
Mustafa, Meraj; Farooq, Muhammad A; Hayat, Tasawar; Alsaedi, Ahmed
2013-01-01
This investigation is concerned with the stagnation-point flow of nanofluid past an exponentially stretching sheet. The presence of Brownian motion and thermophoretic effects yields a coupled nonlinear boundary-value problem (BVP). Similarity transformations are invoked to reduce the partial differential equations into ordinary ones. Local similarity solutions are obtained by homotopy analysis method (HAM), which enables us to investigate the effects of parameters at a fixed location above the sheet. The numerical solutions are also derived using the built-in solver bvp4c of the software MATLAB. The results indicate that temperature and the thermal boundary layer thickness appreciably increase when the Brownian motion and thermophoresis effects are strengthened. Moreover the nanoparticles volume fraction is found to increase when the thermophoretic effect intensifies.
Simulation of bead-and-spring chain models for semidilute polymer solutions in shear flow
NASA Astrophysics Data System (ADS)
Fetsko, S. W.; Cummings, P. T.
1994-11-01
We report preliminary results of simulations of the steady-state rheological behavior for semidilute polymer solutions of head-and-spring chain models in planar Couette now. The simulations include examination of the effects of excluded volume. hydrodynamic interactions and density. Hydrodynamic interactions are modeled by the Rotne -Prager Yamakawa tensor. The simulations are based on the nonequilibrium Brownian dynamics algorithm of Ermak and McCammon. In addition to the spring potential between neighboring beads in the chain. the interaction between any two beads in the solution is modeled using a shifted, repulsive Leonard-Jones potential. Lees Edward sliding brick boundary conditions are used for consistency with the Couette flow field.
Optical windows for a flow cell to contain aqueous solutions at high pressure and temperature
NASA Astrophysics Data System (ADS)
Bowers, W. J., Jr.; Bean, V. E.; Hurst, W. S.
1995-02-01
A flow cell to contain aqueous solutions at pressures up to 40 MPa and temperatures up to 600 °C that is equipped with sapphire windows for the transmission of visible light is described. There are four windows, two for the entrance and exit of a laser beam, and two located at 90° that feature f/1 (53° included angle) collection apertures with a 9 mm diameter unobstructed view for Raman spectroscopy, absorption measurements, or studies using full-field back illumination. The window-to-metal seals are gold o-rings; the metal-to-metal seals are gaskets prepared by pressing a gold o-ring onto a gold foil washer. This cell has been used for two years for Raman studies of aqueous solutions at high pressures and temperatures both below and above the supercritical point of water.
NASA Technical Reports Server (NTRS)
Hanson, R. K.; Presley, L. L.; Williams, E. V.
1972-01-01
The method of characteristics for a chemically reacting gas is used in the construction of the time-dependent, one-dimensional flow field resulting from the normal reflection of an incident shock wave at the end wall of a shock tube. Nonequilibrium chemical reactions are allowed behind both the incident and reflected shock waves. All the solutions are evaluated for oxygen, but the results are generally representative of any inviscid, nonconducting, and nonradiating diatomic gas. The solutions clearly show that: (1) both the incident- and reflected-shock chemical relaxation times are important in governing the time to attain steady state thermodynamic properties; and (2) adjacent to the end wall, an excess-entropy layer develops wherein the steady state values of all the thermodynamic variables except pressure differ significantly from their corresponding Rankine-Hugoniot equilibrium values.
Solutions with special functions for time fractional free convection flow of Brinkman-type fluid
NASA Astrophysics Data System (ADS)
Ali, Farhad; Aftab Alam Jan, Syed; Khan, Ilyas; Gohar, Madeha; Ahmad Sheikh, Nadeem
2016-09-01
The objective of this paper is to report the combined effect of heat and mass diffusion on time fractional free convectional incompressible flow of Brinkman-type fluid over an oscillating plate in the presence of first-order chemical reaction. The Laplace transform has been used to obtain the exact solutions for the fractional-order distributions. Exact expressions for temperature, concentration and velocity have been presented in terms of special functions. For instance, we presented temperature in terms of Wright function, concentration in the form of Fox- H function and velocity in terms of Mittag-Leffler and general Wright functions. The effects of various physical parameters on the fluid motion are sketched and discussed graphically. The present solutions have been reduced by taking one or more parameters approaching to zero and an excellent agreement is observed with the published work. The numerical results for skin-friction, Nusselt and Sherwood numbers have been shown in tabular form.
Similar solutions for viscous hypersonic flow over a slender three-fourths-power body of revolution
NASA Technical Reports Server (NTRS)
Lin, Chin-Shun
1987-01-01
For hypersonic flow with a shock wave, there is a similar solution consistent throughout the viscous and inviscid layers along a very slender three-fourths-power body of revolution The strong pressure interaction problem can then be treated by the method of similarity. Numerical calculations are performed in the viscous region with the edge pressure distribution known from the inviscid similar solutions. The compressible laminar boundary-layer equations are transformed into a system of ordinary differential equations. The resulting two-point boundary value problem is then solved by the Runge-Kutta method with a modified Newton's method for the corresponding boundary conditions. The effects of wall temperature, mass bleeding, and body transverse curvature are investigated. The induced pressure, displacement thickness, skin friction, and heat transfer due to the previously mentioned parameters are estimated and analyzed.
NASA Technical Reports Server (NTRS)
Farrell, C.; Adamczyk, J.
1981-01-01
A reliable method is presented for calculating the flowfield about a cascade of arbitrary 2-D airfoils. The method approximates the three-dimensional flow in a turbomachinery blade row by correcting for streamtube convergence and radius change in the throughflow direction. The method is a fully conservative solution of the full potential equation incorporating the finite volume technique on a body-fitted periodic mesh, with an artificial density imposed in the transonic region to ensure stability and the capture of shock waves. Comparison of results for several supercritical blades shows good agreement with their hodograph solutions. Other calculations for these profiles as well as standard NACA blade sections indicate that this is a useful scheme for analyzing both the design and off-design performance of turbomachinery blading.
Transonic Navier-Stokes solutions of three-dimensional afterbody flows
NASA Technical Reports Server (NTRS)
Compton, William B., III; Thomas, James L.; Abeyounis, William K.; Mason, Mary L.
1989-01-01
The performance of a three-dimensional Navier-Stokes solution technique in predicting the transonic flow past a nonaxisymmetric nozzle was investigated. The investigation was conducted at free-stream Mach numbers ranging from 0.60 to 0.94 and an angle of attack of 0 degrees. The numerical solution procedure employs the three-dimensional, unsteady, Reynolds-averaged Navier-Stokes equations written in strong conservation form, a thin layer assumption, and the Baldwin-Lomax turbulence model. The equations are solved by using the finite-volume principle in conjunction with an approximately factored upwind-biased numerical algorithm. In the numerical procedure, the jet exhaust is represented by a solid sting. Wind-tunnel data with the jet exhaust simulated by high pressure air were also obtained to compare with the numerical calculations.
Least-squares finite element solutions for three-dimensional backward-facing step flow
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Hou, Lin-Jun; Lin, Tsung-Liang
1993-01-01
Comprehensive numerical solutions of the steady state incompressible viscous flow over a three-dimensional backward-facing step up to Re equals 800 are presented. The results are obtained by the least-squares finite element method (LSFEM) which is based on the velocity-pressure-vorticity formulation. The computed model is of the same size as that of Armaly's experiment. Three-dimensional phenomena are observed even at low Reynolds number. The calculated values of the primary reattachment length are in good agreement with experimental results.
Parallel solution of optimal shape design problem governed by Helmholtz/potential flow equations
Maekinen, R.A.E.; Toivanen, J.
1995-12-01
Computation of a wave scattered by a flying obstacle is a problem of great practical importance. We consider in this paper the numerical solution of a shape optimization problem for a lifting 2D airfoil in a distributed computing environment. A mathematical model describing of the Helmholtz equation {Delta}u + {omega}{sup 2}u = 0 with suitable boundary conditions on the profile and in the infinity. For potential flow the pressure distribution p on the profile is obtained by solving two Laplace equations on the computational domain.
SOLA-VOF: A solution algorithm for transient fluid flow with multiple free boundaries
NASA Astrophysics Data System (ADS)
Nichols, B. D.; Hirt, C. W.; Hotchkiss, R. S.
1980-08-01
A computer program is presented for the solution of two dimensional transient fluid flow with free boundaries. The SOLA-VOF program, which is based on the concept of a fractional volume of fluid is more flexible and efficient than other methods for treating arbitrary free boundaries. Its basic model of operation is for single fluid calculations having multiple free surfaces. However, SOLA-VOF can also be used for calculations involving two fluids separated by a sharp interface. In either case, the fluids may be treated as incompressible or as having limited compressibility. Surface tension forces with wall adhesion are permitted in both cases.
Line relaxation methods for the solution of 2D and 3D compressible flows
NASA Technical Reports Server (NTRS)
Hassan, O.; Probert, E. J.; Morgan, K.; Peraire, J.
1993-01-01
An implicit finite element based algorithm for the compressible Navier-Stokes equations is outlined, and the solution of the resulting equation by a line relaxation on general meshes of triangles or tetrahedra is described. The problem of generating and adapting unstructured meshes for viscous flows is reexamined, and an approach for both 2D and 3D simulations is proposed. An efficient approach appears to be the use of an implicit/explicit procedure, with the implicit treatment being restricted to those regions of the mesh where viscous effects are known to be dominant. Numerical examples demonstrating the computational performance of the proposed techniques are given.
Exact solutions of the problem of free-boundary unsteady flows
NASA Astrophysics Data System (ADS)
Karabut, Evgenii
2013-06-01
Some approach to the solution of boundary value problems for finding functions that are analytical in a wedge is proposed. If the ratio of the angle at the wedge vertex to the number π is rational, then the boundary value problem is reduced to the finite system of ordinary differential equations. Such approach, applied to the problem of inertial motion of a liquid wedge, made it possible to sum the series with small denominators arising in the problem and find four exact examples of self-similar flows with a free boundary.
Dynamic ultramicroscopy of laser-induced flows in colloidal solutions of plasmon-resonance particles
Fedosov, I V; Tuchin, V V; Nefedov, I S; Khlebtsov, B N
2008-06-30
A method is proposed for visualisation of the velocity fields of colloidal plasmon-resonance nanoparticles moving in a laser beam. The method uses the particle image velocimetry for processing ultramicroscopic images. Particles in a thick layer of colloidal solution are illuminated by a slit laser ultramicroscopic source with a large numerical aperture providing a high contrast of particle images and visualisation of the transverse velocity distribution in laser-induced flows with a high spatial resolution. (special issue devoted to application of laser technologies in biophotonics and biomedical studies)
Accretion Flow Properties of MAXI J1543–564 during 2011 Outburst from the TCAF Solution
NASA Astrophysics Data System (ADS)
Chatterjee, Debjit; Debnath, Dipak; Chakrabarti, Sandip K.; Mondal, Santanu; Jana, Arghajit
2016-08-01
We derive accretion flow properties of the transient black hole candidate (BHC) MAXI J1543–564 using the RXTE data. We use the two-component advective flow (TCAF) solution to fit the data of the initial rising phase of outburst (from 2011 May 10 to 15). The 2.5–25 keV spectra are fitted using the TCAF solution fits file as a local additive table model in XSPEC. We extract physical flow parameters such as the two-component (Keplerian disk and sub-Keplerian halo) accretion rates and size and the property of the Compton cloud (post-shock region close to a black hole). Similar to other classical transient BHCs, monotonic evolution of low-frequency quasi-periodic oscillations (QPOs) is observed during the rising phase of the outburst, which is fitted with the propagating oscillatory shock (POS) model, which describes how the Compton cloud properties change from day to day. From the nature of variations of TCAF model fitted physical flow parameters and QPOs, we only found hard-intermediate and soft-intermediate spectral states during this phase of the outburst under study. We also calculated the frequency of the dominating QPOs from the TCAF model fitted shock parameters and found that they roughly match with the observed and POS model fitted values. From our spectro-temporal study of the source with TCAF and POS models, the most probable mass of the BHC is found to be 12.6–14.0 M ⊙, or {13}-0.4+1.0 {M}ȯ .
Accretion Flow Properties of MAXI J1543-564 during 2011 Outburst from the TCAF Solution
NASA Astrophysics Data System (ADS)
Chatterjee, Debjit; Debnath, Dipak; Chakrabarti, Sandip K.; Mondal, Santanu; Jana, Arghajit
2016-08-01
We derive accretion flow properties of the transient black hole candidate (BHC) MAXI J1543-564 using the RXTE data. We use the two-component advective flow (TCAF) solution to fit the data of the initial rising phase of outburst (from 2011 May 10 to 15). The 2.5-25 keV spectra are fitted using the TCAF solution fits file as a local additive table model in XSPEC. We extract physical flow parameters such as the two-component (Keplerian disk and sub-Keplerian halo) accretion rates and size and the property of the Compton cloud (post-shock region close to a black hole). Similar to other classical transient BHCs, monotonic evolution of low-frequency quasi-periodic oscillations (QPOs) is observed during the rising phase of the outburst, which is fitted with the propagating oscillatory shock (POS) model, which describes how the Compton cloud properties change from day to day. From the nature of variations of TCAF model fitted physical flow parameters and QPOs, we only found hard-intermediate and soft-intermediate spectral states during this phase of the outburst under study. We also calculated the frequency of the dominating QPOs from the TCAF model fitted shock parameters and found that they roughly match with the observed and POS model fitted values. From our spectro-temporal study of the source with TCAF and POS models, the most probable mass of the BHC is found to be 12.6-14.0 M ⊙, or {13}-0.4+1.0 {M}⊙ .
NASA Astrophysics Data System (ADS)
Cornaton, F. J.
2012-03-01
Environmental fluid circulations are very often characterized by analyzing the fate and behavior of natural and anthropogenic tracers. Among these tracers, age is taken as an ideal tracer which can yield interesting diagnoses, as for example the characterization of the mixing and renewal of water masses, of the fate and mixing of contaminants, or the calibration of hydrodispersive parameters used by numerical models. Such diagnoses are of great interest in atmospheric and ocean circulation sciences, as well in surface and subsurface hydrology. The temporal evolution of groundwater age and its frequency distributions can display important changes as flow regimes vary due to natural change in climate and hydrologic conditions and/or human induced pressures on the resource to satisfy the water demand. Groundwater age being nowadays frequently used to investigate reservoir properties and recharge conditions, special attention needs to be put on the way this property is characterized, would it be using isotopic methods or mathematical modeling. Steady state age frequency distributions can be modeled using standard numerical techniques since the general balance equation describing age transport under steady state flow conditions is exactly equivalent to a standard advection-dispersion equation. The time-dependent problem is however described by an extended transport operator that incorporates an additional coordinate for water age. The consequence is that numerical solutions can hardly be achieved, especially for real 3-D applications over large time periods of interest. A novel algorithm for solving the age distribution problem under time-varying flow regimes is presented and, for some specific configurations, extended to the problem of generalized component exposure time. The algorithm combines the Laplace transform technique applied to the age (or exposure time) coordinate with standard time-marching schemes. The method is validated and illustrated using analytical
Schermeyer, Marie-Therese; Sigloch, Heike; Bauer, Katharina C; Oelschlaeger, Claude; Hubbuch, Jürgen
2016-03-01
This study aims at defining rheological parameters for the characterization of highly concentrated protein solutions. As a basis for comparing rheological behavior with protein solution characteristics the protein phase behavior of Lysozyme from chicken egg white with concentrations up to 225 mg/mL, changing pH values and additive concentrations was studied in a microbatch scale format. The prepared phase diagrams, scored after 40 days (t40) give insights into the kind and kinetics of the phase transitions that occur. Oscillatory frequency sweep measurements of samples with exactly the same conditions were conducted immediately after preparation (t0). The protein solutions behave viscoelastic and show a characteristic curve shape of the storage modulus (G') and the loss modulus (G″). The graphs provide information about the cross-linking degree of the respective sample. The measured rheological parameters were sensitive concerning solution composition, protein concentration and solution inner structure. The rheological moduli G' and G″ and especially the ratio of these parameters over a frequency range from 100 to 40000 rad/sec give information about the aggregation tendency of the protein under tested conditions. We succeeded to correlate protein phase behavior with the defined rheological key parameter ωCO. This point represents the frequency value of the intersection point from G' and G″. In our study Lysozyme expressed a ωCO threshold value of 20000 rad/sec as a lower limit for stable protein solutions. The predictability of lysozyme aggregation tendency and crystallization by means of squeeze flow rheometry is shown. PMID:26375304
NASA Astrophysics Data System (ADS)
Wissmeier, L. C.; Barry, D. A.
2009-12-01
Computer simulations of water availability and quality play an important role in state-of-the-art water resources management. However, many of the most utilized software programs focus either on physical flow and transport phenomena (e.g., MODFLOW, MT3DMS, FEFLOW, HYDRUS) or on geochemical reactions (e.g., MINTEQ, PHREEQC, CHESS, ORCHESTRA). In recent years, several couplings between both genres of programs evolved in order to consider interactions between flow and biogeochemical reactivity (e.g., HP1, PHWAT). Software coupling procedures can be categorized as ‘close couplings’, where programs pass information via the memory stack at runtime, and ‘remote couplings’, where the information is exchanged at each time step via input/output files. The former generally involves modifications of software codes and therefore expert programming skills are required. We present a generic recipe for remotely coupling the PHREEQC geochemical modeling framework and flow and solute transport (FST) simulators. The iterative scheme relies on operator splitting with continuous re-initialization of PHREEQC and the FST of choice at each time step. Since PHREEQC calculates the geochemistry of aqueous solutions in contact with soil minerals, the procedure is primarily designed for couplings to FST’s for liquid phase flow in natural environments. It requires the accessibility of initial conditions and numerical parameters such as time and space discretization in the input text file for the FST and control of the FST via commands to the operating system (batch on Windows; bash/shell on Unix/Linux). The coupling procedure is based on PHREEQC’s capability to save the state of a simulation with all solid, liquid and gaseous species as a PHREEQC input file by making use of the dump file option in the TRANSPORT keyword. The output from one reaction calculation step is therefore reused as input for the following reaction step where changes in element amounts due to advection
Performance of the analytical solutions for Taylor dispersion process in open channel flow
NASA Astrophysics Data System (ADS)
Zeng, L.; Wu, Zi; Fu, Xudong; Wang, Guangqian
2015-09-01
The present paper provides a systematical analysis for concentration distribution of Taylor dispersion in laminar open channel flow, seeking fundamental understandings for the physical process of solute transport that generally applies to natural rivers. As a continuation and a direct numerical verification of the previous theoretical work (Wu, Z., Chen, G.Q., 2014. Journal of Hydrology, 519: 1974-1984.), in this paper we attempt to understand that to what extent the obtained analytical solutions are valid for the multi-dimensional concentration distribution, which is vital for the key conclusion of the so-called slow-decaying transient effect. It is shown that as a first estimation, even asymptotically, the longitudinal skewness of the concentration distribution should be incorporated to predict the vertical concentration correctly. Thus the traditional truncation of the concentration expansion is considered to be insufficient for the first estimation. The analytical solution by the two-scale perturbation analysis with modifications up to the second order is shown to be a most economical solution to give a reasonably good prediction.
Three-terminal capacitance cell for stopped-flow measurements of very dilute solutions
NASA Astrophysics Data System (ADS)
Tjahjono, Martin; Davis, Thomas; Garland, Marc
2007-02-01
A capacitance cell has been designed, constructed, and tested for stopped-flow measurements of very dilute low-relative permittivity liquid solutions. The capacitance cell utilizes a three-terminal design and is connected to ultrahigh sensitivity capacitance bridge. The cell was designed for operating conditions T ≈243.15-373.15K and P ≈0-1MPa and tested with pure anhydrous cyclohexane and with dilute acetone/cyclohexane solutions at 298.15K and 0.1MPa under an argon blanket in a thermostated bath with a temperature variation of <0.001K. Details of the design and materials of construction are reported. The measured relative permittivity of cyclohexane was 2.015 565, in agreement with the literature, and the long term variation of the measurement was ±5×10-6. The relative permittivities of the acetone/cyclohexane solutions were very linear (R2=0.9997) in the measured interval of 0.001-0.008mole fraction. These measurements confirm that the design specifications for stability and resolution/sensitivity of better than 1×10-5 have been realized. Finally, the present online capacitance cell was connected online to an ultrasensitive densitometer and ultrasensitive refractometer and binary acetone/cyclohexane solutions were measured. The measurements of density, refractive index, and relative permittivity were combined to provide a dipole moment of acetone of 2.750±0.005D, which is in good agreement with literature.
Preferential flow and solute transport in a large lysimeter, under controlled boundary conditions.
NASA Astrophysics Data System (ADS)
Schoen, R.; Gaudet, J. P.; Bariac, T.
1999-02-01
Laboratory studies of solute transport in soils (soil columns) are not totally representative of field conditions (spatial variability, soil structure etc.). Field studies hardly allow quantification of fluxes and mechanisms. In this article, and intermediate approach is suggested, using a lysimeter (1.7 m 3) of an almost undisturbed soil, with controlled boundary conditions, the aim being to be able to quantify fluxes and mechanisms at a scale closer to field conditions, thus yielding results that better depict reality. Two experiments, with constant water fluxes of 1.05 and 1.48 mm h -1 were conducted. Solutes were introduced as concentration pulses. Species 2H 2O, C1 - and Br - were used as tracers, and K +, NH 4+, NO 3-, atrazine as interactive and/or reactive solutes. Elution curves were analyzed by the method of moments. Results show that about 20% of the water are immobile. As a consequence of anion exclusion, anion tracers appear at the outlet with an advance of about 10% in time as compared to isotopic tracers. The added NH 4+is mostly nitrified, and K + undergoes cation exchange with Ca 2+ and Mg 2+. Under our experimental conditions, leaching of atrazine is significant with low degradation. A third experiment was conducted, in which the flow was interrupted while the solute peak was within the lysimeter, and 400 soil samples were extracted from the lysimeter. Soil-water content distributions exhibit coefficients of variation within layers between 5% and 27%. Concentration distributions exhibit coefficients of variation within layers between 22% and 59%. There is no correlation between concentration and water content. The observed spatial variability suggests the occurrence of preferential flow. Concentrations in suction cups were 55%-136% of those measured in corresponding soil samples.
Mineral/solution reaction rates in a mixed flow reactor: Wollastonite hydrolysis
NASA Astrophysics Data System (ADS)
Rimstidt, J. Donald; Dove, Patricia M.
1986-11-01
A newly developed mixed flow reactor was used to measure the rate of hydrolysis of wollastonite over the pH range of 3 to 8. This design avoids abrasion of the solid sample by confining it within a nylon mesh while the reacting solution is circulated over it by a stirrer. The rate of reaction was determined from the difference of the compositions of the input and output solutions following the methods used by chemical engineers for the analysis of mixed flow reactors, also called continuously stirred tank reactors (CSTR). This apparatus, constructed from easily obtainable parts, avoids many of the problems inherent in studying mineral/solution reaction kinetics in batch reactors. The hydrolysis of wollastonite CaSiO3 + 2 H+ + H2O = Ca2+ + H4SiO4 can be fit to a rate law of the form: dnH+/ dt = kadKH+mH+/(1.0 + KH+mH+) where kad = 9.80 × 10 -8molm-2sec-1 and KH+ = 2.08 × 10 5. Over the pH range of 4 to 7, the data also may fit a simple linear form: dnH+/ dt = - Ak+( aH+) 0.40 where k+ = 3.80 × 10 -6 sec -1 at 25°C. The presence of calcium ion in the solution at concentrations up to 1.0 mol kg -1 produces only a minor reduction of the reaction rate. The activation energy for this reaction is 79.2 kJ mol -1. Examination of the surfaces of the reacted grains showed no evidence of incongruent reaction leading to a product layer but did show the extensive development of etch pits leading to a rapid increase in the specific surface area. At large extents of reaction at low pH, diffusion of ions into or from these deep etch pits may limit the reaction rate.
Quasi 3D modeling of water flow and solute transport in vadose zone and groundwater
NASA Astrophysics Data System (ADS)
Yakirevich, A.; Kuznetsov, M.; Weisbrod, N.; Pachepsky, Y. A.
2013-12-01
The complexity of subsurface flow systems calls for a variety of concepts leading to the multiplicity of simplified flow models. One commonly used simplification is based on the assumption that lateral flow and transport in unsaturated zone is insignificant unless the capillary fringe is involved. In such cases the flow and transport in the unsaturated zone above groundwater level can be simulated as a 1D phenomenon, whereas through groundwater they are viewed as 2D or 3D phenomena. A new approach for a numerical scheme for 3D variably saturated flow and transport is presented. A Quasi-3D approach allows representing flow in the 'vadose zone - aquifer' system by a series of 1D Richards' equations solved in variably-saturated zone and by 3D-saturated flow equation in groundwater (modified MODFLOW code). The 1D and 3D equations are coupled at the phreatic surface in a way that aquifer replenishment is calculated using the Richards' equation, and solving for the moving water table does not require definition of the specific yield parameter. The 3D advection-dispersion equation is solved in the entire domain by the MT3D code. Using implicit finite differences approximation to couple processes in the vadose zone and groundwater provides mass conservation and increase of computational efficiency. The above model was applied to simulate the impact of irrigation on groundwater salinity in the Alto Piura aquifer (Northern Peru). Studies on changing groundwater quality in arid and semi-arid lands show that irrigation return flow is one of the major factors contributing to aquifer salinization. Existing mathematical models do not account explicitly for the solute recycling during irrigation on a daily scale. Recycling occurs throughout the unsaturated and saturated zones, as function of the solute mass extracted from pumping wells. Salt concentration in irrigation water is calculated at each time step as a function of concentration of both surface water and groundwater
Herrero, Pol; Bäuerlein, Patrick S; Emke, Erik; Marcé, Rosa M; de Voogt, Pim
2015-04-29
In order to assess the environmental risks of a compound it is imperative to have suitable and reliable techniques for its determination in environmental matrices. In this paper, we focused on a method development for the recently introduced online coupling of a field flow fractionation (FFF) system to an Orbitrap-HRMS, that allows the simultaneous size and concentration determination of different aqueous fullerene aggregates and their concentrations in different size fractions. A 0.05% NH4OH solution in water was identified as the best carrier liquid for the analysis of the three different aqueous fullerene suspensions (C60 [60], [6,6]-phenyl-C61 butyric acid methyl ester ([60]PCBM) and [6,6]-(bis)phenyl-C61 butyric acid methyl ester ([60]bisPCBM)). The multi-angle light scattering (MALS) data received after employing the ammonia solution was consistent with both the theory and calibration using well defined Au and latex particles. The LODs obtained using Orbitrap HRMS detection were 0.1 μg L(-1) for an injection volume of 100 μL which are significantly better than the LODs obtained by using UV (20 μg L(-1)) and MALS detectors (5 μg L(-1)). However, these LODs can be further improved as in theory there is no limit to the amount of sample that can be injected into the FFF. Environmental samples (river and sewage water) were spiked with fullerenes and the fractograms obtained for these samples revealed that the matrix does affect the size of fullerene aggregates. Information on the size distribution can be useful for the risk assessment of these particles.
Symmetry-plane model of 3D Euler flows: Mapping to regular systems and numerical solutions of blowup
NASA Astrophysics Data System (ADS)
Mulungye, Rachel M.; Lucas, Dan; Bustamante, Miguel D.
2014-11-01
We introduce a family of 2D models describing the dynamics on the so-called symmetry plane of the full 3D Euler fluid equations. These models depend on a free real parameter and can be solved analytically. For selected representative values of the free parameter, we apply the method introduced in [M.D. Bustamante, Physica D: Nonlinear Phenom. 240, 1092 (2011)] to map the fluid equations bijectively to globally regular systems. By comparing the analytical solutions with the results of numerical simulations, we establish that the numerical simulations of the mapped regular systems are far more accurate than the numerical simulations of the original systems, at the same spatial resolution and CPU time. In particular, the numerical integrations of the mapped regular systems produce robust estimates for the growth exponent and singularity time of the main blowup quantity (vorticity stretching rate), converging well to the analytically-predicted values even beyond the time at which the flow becomes under-resolved (i.e. the reliability time). In contrast, direct numerical integrations of the original systems develop unstable oscillations near the reliability time. We discuss the reasons for this improvement in accuracy, and explain how to extend the analysis to the full 3D case. Supported under the programme for Research in Third Level Institutions (PRTLI) Cycle 5 and co-funded by the European Regional Development Fund.
NASA Technical Reports Server (NTRS)
Penny, M. M.; Smith, S. D.; Anderson, P. G.; Sulyma, P. R.; Pearson, M. L.
1976-01-01
A numerical solution for chemically reacting supersonic gas-particle flows in rocket nozzles and exhaust plumes was described. The gas-particle flow solution is fully coupled in that the effects of particle drag and heat transfer between the gas and particle phases are treated. Gas and particles exchange momentum via the drag exerted on the gas by the particles. Energy is exchanged between the phases via heat transfer (convection and/or radiation). Thermochemistry calculations (chemical equilibrium, frozen or chemical kinetics) were shown to be uncoupled from the flow solution and, as such, can be solved separately. The solution to the set of governing equations is obtained by utilizing the method of characteristics. The equations cast in characteristic form are shown to be formally the same for ideal, frozen, chemical equilibrium and chemical non-equilibrium reacting gas mixtures. The particle distribution is represented in the numerical solution by a finite distribution of particle sizes.
NASA Technical Reports Server (NTRS)
Kumar, A.; Tiwari, S. N.
1980-01-01
Laminar and turbulent flow-field solutions with coupled carbon-phenolic mass injection are presented for the forebody of a probe entering a nominal Jupiter atmosphere. Solutions are obtained for a 35-degree hyperboloid and for a 45-degree spherically blunted cone using a time-dependent, finite-difference method. The radiative heating rates for the coupled laminar flow are significantly reduced as compared to the corresponding no-blowing case; however, for the coupled turbulent flow, it is found that the surface radiative heating rates are substantially increased and often exceed the corresponding no-blowing values. Turbulence is found to have no effect on the surface radiative heating rates for the no-blowing solutions. The present results are compared with the other available solutions, and some additional solutions are presented.
Boutron, P
1984-04-01
It is generally assumed that when cells are cooled at rates close to those corresponding to the maximum of survival, once supercooling has ceased, above the eutectic melting temperature the extracellular ice is in equilibrium with the residual solution. This did not seem evident to us due to the difficulty of ice crystallization in cryoprotective solutions. The maximum quantities of ice crystallized in glycerol and 1,2-propanediol solutions have been calculated from the area of the solidification and fusion peaks obtained with a Perkin-Elmer DSC-2 differential scanning calorimeter. The accuracy has been improved by several corrections: better defined baseline, thermal variation of the heat of fusion of the ice, heat of solution of the water from its melting with the residual solution. More ice crystallizes in the glycerol than in the 1,2-propanediol solutions, of which the amorphous residue contains about 40 to 55% 1,2-propanediol. The equilibrium values are unknown in the presence of 1,2-propanediol. With glycerol, in our experiments, the maximum is first lower than the equilibrium but approaches it as the concentration increases. It is not completely determined by the colligative properties of the solutes.
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.
Hydroplaning of subaqueous debris flows and glide blocks: Analytical solutions and discussion
NASA Astrophysics Data System (ADS)
Harbitz, Carl B.; Parker, Gary; ElverhøI, Anders; Marr, Jeffrey G.; Mohrig, David; Harff, Peter A.
2003-07-01
Subaqueous debris flows often attain significantly higher velocities and longer run-out distances than their subaerial counterparts in spite of increased viscous drag and reduced effective gravity due to buoyancy. Recent experimental research suggests that a basal lubricating layer of water associated with hydroplaning decouples the sediments from the bed, resulting in a dramatic reduction of the basal shear stress. Hydroplaning thus provides an explanation for these observations. The conditions for onset of hydroplaning are discussed in terms of critical densimetric Froude number. The stress reduction due to a lubricating layer of water or mud slurry is studied via equilibrium solutions for a two-layer Couette flow. The calculations reveal that the stresses in both the low-viscosity lubricating layer and the high-viscosity deforming deposits below it are substantially reduced. The principles of laminar boundary layers are used to develop an equilibrium solution for the steady motion of a hydroplaning debris glide block. This adjusted version of lubrication theory properly accounts for hydroplaning associated with a dynamic pressure generated at the head of the block. Example calculations at both laboratory and field scale support the experimental results of reduced bed friction, limited erosion, sediment rheology independence, and high velocities. The results also reveal the possibility for a net up-slope discharge in the lubricating layer.
Zheng, Chunmiao; Gorelick, Steven M
2003-01-01
Several recent studies at the Macrodispersion Experiment (MADE) site in Columbus, Mississippi, have indicated that the relative preferential flowpaths and flow barriers resulting from decimeter-scale aquifer heterogeneities appear to have a dominant effect on plume-scale solute transport. Numerical experiments are thus conducted in this study to explore the key characteristics of solute transport in two-dimensional flow fields influenced by decimeter-scale preferential flowpaths. A hypothetical but geologically plausible network of 10 cm wide channels of high hydraulic conductivity is used to represent the relative preferential flowpaths embedded in an otherwise homogeneous aquifer. When the hydraulic conductivity in the channels is 100 times greater than that in the remaining portion of the aquifer, the calculated concentration distributions under three source configurations all exhibit highly asymmetrical, non-Gaussian patterns. These patterns, with peak concentrations close to the source and extensive spreading downgradient, resemble that observed at the MADE site tracer tests. When the contrast between the channel and nonchannel hydraulic conductivities is reduced to 30:1 from 100:1, the calculated mass distribution curve starts to approach a Gaussian one with the peak concentration near the central portion of the plume. Additional analysis based on a field-scale model demonstrates that the existence of decimeter-scale preferential flowpaths can have potentially far-reaching implications for ground water remediation. Failure to account for them in numerical simulation could lead to overestimation of the effectiveness of the remedial measure under consideration.
Goedbloed, J. P.
2009-12-15
A new method of systematically constructing the full structure of the complex magnetohydrodynamic spectra of stationary flows is presented. It is based on the self-adjointness of the generalized force operator G and the Doppler-Coriolis shift operator U, and the associated quadratic forms for the normalized energy W and the normalized Doppler-Coriolis shift V, which may be constructed for all complex values of omega if the original eigenvalue problem is converted into a one-sided boundary value problem. This turns W into a complex expression, while V remains real. Whereas the solution path P{sub s} of stable modes is just the real axis, the solution path P{sub u} of unstable modes in the complex omega plane is found by requiring that the solution-averaged Doppler-Coriolis shifted real part of the frequency vanishes, sigma-V[xi(omega)]=0, or that the energy is real, Im W[xi(omega)]=0. The location of the eigenvalues on these solution paths is determined by two quadratic forms, which may straightforwardly be evaluated in any of the finite element spectral codes in existence. A new oscillation theorem is proved about the monotonicity of complex eigenvalues for one-dimensional systems. Instead of counting internal nodes of the real displacement vector xi (as in static plasmas), it is based on counting the zeros of the alternating ratio, or alternator, Rident toxi/PI of the boundary values of the complex functions xi and the total pressure perturbation PI, which is real on the solution path. This finally provides the generalization of the basic structural properties of the magnetohydrodynamic spectrum of static plasmas, which has been known for a long time, to stationary plasmas.
Ketterer, M.E.; Kozerski, G.E.; Ritacco, R.; Painuly, P.
1997-01-01
Application of a prototype capillary free-flow electrophoresis (CFFE) device for separation of different solution species of Co, Cr, and As is explored. A unique free-flow electrophoresis (FFE) design is employed, which makes use of internal capillary cooling tubes to minimize thermal convection due to Joule heating.
Chen, Cheng; Lau, Boris L.; Gaillard, J.-F.; Packman, A.I.
2010-01-22
Deposition of colloidal particles is one of many processes that lead to the evolution of the structure of natural porous media in groundwater aquifers, oil reservoirs, and sediment beds. Understanding of the mechanisms and effects of this type of structural evolution has been limited by a lack of direct observations of pore structure. Here, synchrotron X-ray difference microtomography (XDMT) was used to resolve the temporal evolution of pore structure and the distribution of colloidal deposits within a granular porous medium. Column filtration experiments were performed to observe the deposition of relatively high concentrations of colloidal zirconia (200 mg/l of particles having diameter {approx}1 {micro}m) in a packed bed of glass beads (diameters 210-300 {micro}m). Noninvasive XDMT imaging of the pore structure was performed three separate times during each column experiment. The structural information observed at each time was used to define internal boundary conditions for three-dimensional lattice Boltzmann (LB) simulations that show how the evolving pore structure affects pore fluid flow and solute transport. While the total deposit mass increased continuously over time, colloid deposition was observed to be highly heterogeneous and local colloid detachment was observed at some locations in a low ionic strength medium. LB simulations indicated that particle accumulation greatly reduced the permeability of the porous medium while increasing the tortuosity. The colloidal deposits also increased the spatial variability in pore water velocities, leading to higher dispersion coefficients. Anomalous dispersion behavior was investigated by simulation at the scale of the experimental system: weak tailing was found in the clean bed case, and the extent of tailing greatly increased following colloid deposition because of the development of extensive no-flow regions. As a result of this coupling between pore fluid flow, colloid accumulation, and the pore geometry
NASA Astrophysics Data System (ADS)
Weidman, P. D.; Ishak, Anuar
2015-08-01
New solutions of flow induced by a biorthogonally stretching surface are reported. The flexible membrane has linear stretching rate a along the x-axis and b along the y-axis. A similarity reduction of the Navier-Stokes equations yields a coupled pair of ordinary differential equations governed the single parameter α = b / a . Dual solutions are found in the region αt < α ⩽ 1 , where αt = - 0.2514 . One of the two components of the dual solutions exhibits algebraic decay in the far field. It appears that no self-similar solutions exist for α <αt . It is also shown that the exact solution for flow induced by a unilaterally stretching sheet due to Crane has dual solutions with algebraic decay in the far field.
NASA Technical Reports Server (NTRS)
Mcmillin, S. Naomi; Thomas, James L.; Murman, Earll M.
1990-01-01
An Euler flow solver and a thin layer Navier-Stokes flow solver were used to numerically simulate the supersonic leeside flow fields over delta wings which were observed experimentally. Three delta wings with 75, 67.5, and 60 deg leading edge sweeps were computed over an angle-of-attack range of 4 to 20 deg at a Mach number 2.8. The Euler code and Navier-Stokes code predict equally well the primary flow structure where the flow is expected to be separated or attached at the leading edge based on the Stanbrook-Squire boundary. The Navier-Stokes code is capable of predicting both the primary and the secondary flow features for the parameter range investigated. For those flow conditions where the Euler code did not predict the correct type of primary flow structure, the Navier-Stokes code illustrated that the flow structure is sensitive to boundary layer model. In general, the laminar Navier-Stokes solutions agreed better with the experimental data, especially for the lower sweep delta wings. The computational results and a detailed re-examination of the experimental data resulted in a refinement of the flow classifications. This refinement in the flow classification results in the separation bubble with the shock flow type as the intermediate flow pattern between separated and attached flows.
Benchmark Study of 3D Pore-scale Flow and Solute Transport Simulation Methods
NASA Astrophysics Data System (ADS)
Scheibe, T. D.; Yang, X.; Mehmani, Y.; Perkins, W. A.; Pasquali, A.; Schoenherr, M.; Kim, K.; Perego, M.; Parks, M. L.; Trask, N.; Balhoff, M.; Richmond, M. C.; Geier, M.; Krafczyk, M.; Luo, L. S.; Tartakovsky, A. M.
2015-12-01
Multiple numerical approaches have been developed to simulate porous media fluid flow and solute transport at the pore scale. These include 1) methods that explicitly model the three-dimensional geometry of pore spaces and 2) methods that conceptualize the pore space as a topologically consistent set of stylized pore bodies and pore throats. In previous work we validated a model of the first type, using computational fluid dynamics (CFD) codes employing standard finite volume method (FVM), against magnetic resonance velocimetry (MRV) measurements of pore-scale velocities. Here we expand that benchmark study to include additional models of the first type based on the immersed-boundary method (IMB), lattice Boltzmann method (LBM), and smoothed particle hydrodynamics (SPH), as well as a model of the second type, a pore-network model (PNM). While the PNM approach is computationally much less demanding than direct numerical simulation methods, the effect of conceptualizing complex three-dimensional pore geometries in the manner of PNMs has not been fully determined. We apply all five approaches (FVM-based CFD, IMB, LBM, SPH and PNM) to simulate pore-scale velocity distributions and nonreactive solute transport, and intercompare the model results. Comparisons are drawn both in terms of macroscopic variables (e.g., permeability, solute breakthrough curves) and microscopic variables (e.g., local velocities and concentrations). Generally good agreement was achieved among the various approaches, but some differences were observed depending on the model context. The benchmark study was challenging because of variable capabilities of the codes, and inspired some code enhancements to allow consistent comparison of flow and transport simulations across the full suite of methods. This study provides support for confidence in a variety of pore-scale modeling methods, and motivates further development and application of pore-scale simulation methods.
NASA Astrophysics Data System (ADS)
Wen, Yue-hua; Cheng, Jie; Zhang, Li; Yan, Xu; Yang, Yu-sheng
The effects of the presence of additives like lead and tungstate ions in flowing alkaline zincate solutions on suppressing spongy zinc electrogrowth are examined. The results show that the two additives with optimal concentrations in flowing electrolytes can suppress spongy zinc initiation and propagation. And, the two additives can bring about more uniform and compact deposits and, thereby, reduce spongy zinc growth. The influence of lead and tungstate ions on the zinc deposition/dissolution is evaluated by cyclic voltammetry. It also shows that the addition of the two additives is largely a blocking action, and the co-deposition of lead and zinc ions may occur. The performance of the zinc-air flow battery with zinc regeneration electrolysis is determined. It shows that by the addition of 0.6 M Na 2WO 4 or 10 -4 M to 10 -3 M lead, compact or mixed compact-spongy zinc deposits are created and the favorable charge/discharge performance of the battery is achieved with an energy efficiency of approximately 60%.
Hubig, Michael; Suchandt, Steffen; Adam, Nico
2004-10-01
Phase unwrapping (PU) represents an important step in synthetic aperture radar interferometry (InSAR) and other interferometric applications. Among the different PU methods, the so called branch-cut approaches play an important role. In 1996 M. Costantini [Proceedings of the Fringe '96 Workshop ERS SAR Interferometry (European Space Agency, Munich, 1996), pp. 261-272] proposed to transform the problem of correctly placing branch cuts into a minimum cost flow (MCF) problem. The crucial point of this new approach is to generate cost functions that represent the a priori knowledge necessary for PU. Since cost functions are derived from measured data, they are random variables. This leads to the question of MCF solution stability: How much can the cost functions be varied without changing the cheapest flow that represents the correct branch cuts? This question is partially answered: The existence of a whole linear subspace in the space of cost functions is shown; this subspace contains all cost differences by which a cost function can be changed without changing the cost difference between any two flows that are discharging any residue configuration. These cost differences are called strictly stable cost differences. For quadrangular nonclosed networks (the most important type of MCF networks for interferometric purposes) a complete classification of strictly stable cost differences is presented. Further, the role of the well-known class of node potentials in the framework of strictly stable cost differences is investigated, and information on the vector-space structure representing the MCF environment is provided. PMID:15497426
Analytical solutions for flow fields near drain-and-gate reactive barriers.
Klammler, Harald; Hatfield, Kirk; Kacimov, Anvar
2010-01-01
Permeable reactive barriers (PRBs) are a popular technology for passive contaminant remediation in aquifers through installation of reactive materials in the pathway of a plume. Of fundamental importance are the degree of remediation inside the reactor (residence time) and the portion of groundwater intercepted by a PRB (capture width). Based on a two-dimensional conformal mapping approach (previously used in related work), the latter is studied in the present work for drain-and-gate (DG) PRBs, which may possess a collector and a distributor drain ("full" configuration) or a collector drain only ("simple" configuration). Inherent assumptions are a homogeneous unbounded aquifer with a uniform far field, in which highly permeable drains establish constant head boundaries. Solutions for aquifer flow fields in terms of the complex potential are derived, illustrated, and analyzed for doubly symmetric DG configurations and arbitrary reactor hydraulic resistance as well as ambient groundwater flow direction. A series of practitioner-friendly charts for capture width is given to assist in PRB design and optimization without requiring complex mathematics. DG PRBs are identified as more susceptible to flow divergence around the reactor than configurations using impermeable side structures (e.g., funnel-and-gate), and deployment of impermeable walls on drains is seen to mitigate this problem under certain circumstances.
Microstructure and Rheology of a Flow-Induced Structured Phase in Wormlike Micellar Solutions
Cardiel Rivera, Joshua J.; Dohnalkova, Alice; Dubash, Neville; Zhao, Ya; Cheung, Perry; Shen, Amy
2013-04-30
Surfactant molecules found in soaps and detergents can self-assemble into a great variety of morphologies (e.g., spherical micelles, cylindrical micelles, and lamellar phases). The resulting morphology is highly affected by ionic strength, temperature, and flow conditions. In particular, cylindrical micelles in the presence of inorganic or organic salts can self-assemble into large flexible and elongated wormlike micelles. In equilibrium, the wormlike micelles transition from slightly entangled to branched and, finally, to multi-connected structures with increasing salt concentration. In our work, by introducing external flow conditions via microfluidics, these micellar structures can follow very different trajectories on the phase map and new nanoporous structures can be created. This flow induced approach offers great potential to create novel materials and nanoporous scaffolds from wormlike micelles under ambient temperature and pressure, without any chemical and thermal means (1). As a result, this work provides attractive solutions for synthesizing new biocompatible materials under ambient conditions with biosensing, encapsulation, catalysis, photonics, and self-healing applications.
Souza, W.R.; Voss, C.I.
1987-01-01
The groundwater system in southern Oahu, Hawaii consists of a thick, areally extensive freshwater lens overlying a zone of transition to a thick saltwater body. This system is analyzed in cross section with a variable-density groundwater flow and solute transport model on a regional scale. The simulation is difficult, because the coastal aquifer system has a saltwater transition zone that is broadly dispersed near the discharge area, but is very sharply defined inland. Steady-state simulation analysis of the transition zone in the layered basalt aquifer of southern Oahu indicates that a small transverse dispersivity is characteristic of horizontal regional flow. Further, in this system flow is generally parallel to isochlors and steady-state behavior is insensitive to the longitudinal dispersivity. Parameter analysis identifies that only six parameters control the complex hydraulics of the system: horizontal and vertical hydraulic conductivity of the basalt aquifer; hydraulic conductivity of the confining "caprock" layer; leakance below the caprock; specific yield; and aquifer matrix compressibility. The best-fitting models indicate the horizontal hydraulic conductivity is significantly greater than the vertical hydraulic conductivity. These models give values for specific yield and aquifer compressibility which imply a considerable degree of compressive storage in the water table aquifer. ?? 1987.
Maryshev, Boris S; Lyubimova, Tatyana P
2016-06-01
In the present paper we consider slow filtration of a mixture through a close porous filter. The heavy solute penetrates slowly into the porous filter due to the external vertical filtration flow and diffusion. This process is accompanied by the formation of the domain with heavy fluid near the upper boundary of the filter. The developed stratification, at which the heavy fluid is located above the light fluid, is unstable. When the mass of the heavy fluid exceeds the critical value, one can observe the onset of the Rayleigh-Taylor instability. Due to the above peculiarities we can distinguish between two regimes of vertical filtration: 1) homogeneous seepage and 2) convective filtration. When considering the filtration process it is necessary to take into account the diffusion accompanied by the immobilization effect (or sorption) of the solute. The immobilization is described by the linear MIM (mobile/immobile media) model. It has been shown that the immobilization slows down the process of forming the unstable stratification. The purpose of the paper is to find the stability conditions for homogeneous vertical seepage of he solute into the close porous filter. The linear stability problem is solved using the quasi-static approach. The critical times of instability are estimated. The stability maps are plotted in the space of system parameters. The applicability of quasi-static approach is substantiated by direct numerical simulation of the full nonlinear equations. PMID:27349555
Katabatic Flow: A Closed-Form Solution with Spatially-Varying Eddy Diffusivities
NASA Astrophysics Data System (ADS)
Giometto, M. G.; Grandi, R.; Fang, J.; Monkewitz, P. A.; Parlange, M. B.
2016-08-01
The Nieuwstadt closed-form solution for the stationary Ekman layer is generalized for katabatic flows within the conceptual framework of the Prandtl model. The proposed solution is valid for spatially-varying eddy viscosity and diffusivity (O'Brien type) and constant Prandtl number (Pr). Variations in the velocity and buoyancy profiles are discussed as a function of the dimensionless model parameters z_0 ≡ hat{z}_0 hat{N}^2 Pr sin {(α )} |hat{b}_s |^{-1} and λ ≡ hat{u}_{ref}hat{N} √{Pr} |hat{b}_s |^{-1} , where hat{z}_0 is the hydrodynamic roughness length, hat{N} is the Brunt-Väisälä frequency, α is the surface sloping angle, hat{b}_s is the imposed surface buoyancy, and hat{u}_{ref} is a reference velocity scale used to define eddy diffusivities. Velocity and buoyancy profiles show significant variations in both phase and amplitude of extrema with respect to the classic constant K model and with respect to a recent approximate analytic solution based on the Wentzel-Kramers-Brillouin theory. Near-wall regions are characterized by relatively stronger surface momentum and buoyancy gradients, whose magnitude is proportional to z_0 and to λ . In addition, slope-parallel momentum and buoyancy fluxes are reduced, the low-level jet is further displaced toward the wall, and its peak velocity depends on both z_0 and λ.
On a difficulty in eigenfunction expansion solutions for the start-up of fluid flow
NASA Astrophysics Data System (ADS)
Christov, Ivan C.
2015-11-01
Most mathematics and engineering textbooks describe the process of ``subtracting off'' the steady state of a linear parabolic partial differential equation as a technique for obtaining a boundary-value problem with homogeneous boundary conditions that can be solved by separation of variables (i.e., eigenfunction expansions). While this method produces the correct solution for the start-up of the flow of, e.g., a Newtonian fluid between parallel plates, it can lead to erroneous solutions to the corresponding problem for a class of non-Newtonian fluids. We show that the reason for this is the non-rigorous enforcement of the start-up condition in the textbook approach, which leads to a violation of the principle of causality. Nevertheless, these boundary-value problems can be solved correctly using eigenfunction expansions, and we present the formulation that makes this possible (in essence, an application of Duhamel's principle). The solutions obtained by this new approach are shown to agree identically with those obtained by using the Laplace transform in time only, a technique that enforces the proper start-up condition implicitly (hence, the same error cannot be committed). Supported, in part, by NSF Grant DMS-1104047 and the U.S. DOE (Contract No. DE-AC52-06NA25396) through the LANL/LDRD Program.
NASA Astrophysics Data System (ADS)
Pantellini, Filippo; Griton, Léa
2016-10-01
The spatial structure of a steady state plasma flow is shaped by the standing modes with local phase velocity exactly opposite to the flow velocity. The general procedure of finding the wave vectors of all possible standing MHD modes in any given point of a stationary flow requires numerically solving an algebraic equation. We present the graphical procedure (already mentioned by some authors in the 1960's) along with the exact solution for the Alfvén mode and approximate analytic solutions for both fast and slow modes. The technique can be used to identify MHD modes in space and laboratory plasmas as well as in numerical simulations.
SOLA-DM: A numerical solution algorithm for transient three-dimensional flows
Wilson, T.L.; Nichols, B.D.; Hirt, C.W.; Stein, L.R.
1988-02-01
SOLA-DM is a three-dimensional time-explicit, finite-difference, Eulerian, fluid-dynamics computer code for solving the time-dependent incompressible Navier-Stokes equations. The solution algorithm (SOLA) evolved from the marker-and-cell (MAC) method, and the code is highly vectorized for efficient performance on a Cray computer. The computational domain is discretized by a mesh of parallelepiped cells in either cartesian or cylindrical geometry. The primary hydrodynamic variables for approximating the solution of the momentum equations are cell-face-centered velocity components and cell-centered pressures. Spatial accuracy is selected by the user to be first or second order; the time differencing is first-order accurate. The incompressibility condition results in an elliptic equation for pressure that is solved by a conjugate gradient method. Boundary conditions of five general types may be chosen: free-slip, no-slip, continuative, periodic, and specified pressure. In addition, internal mesh specifications to model obstacles and walls are provided. SOLA-DM also solves the equations for discrete particle dynamics, permitting the transport of marker particles or other solid particles through the fluid to be modeled. 7 refs., 7 figs.
NASA Astrophysics Data System (ADS)
Inaba, Hideo; Miyahara, Satoshi; Takeya, Kengo
Supercooling characteristics of three kinds of organic water solutions (D-Sorbitol, Glycerol, Glucose) in a forced flow were investigated experimentally. The critical condition of ice nucleation in a cooled circular tube was examined for concentration of water solution and cooling temperature under various Reynolds numbers. It was found that the flow velocity and cooling temperature conditions in a laminar flow region. However, in a turbulent flow region, the critical degree of supercooling was influenced by the flow velocity and cooling temperature. As a result, non-dimensional correlation equations for the critical condition of ice formation were derived in the laminar and turbulent flow region as a function of some non-dimensional parameters. While the ice making efficiency of D-Sorbitol water solution was measured under various Reynolds numbers and cooling temperature conditions on the stable supercooling condition. The ice making efficiency of supercooled organic water solution was influenced by the degree of the supercooling based on the mixed organic water solution temperature at the outlet of the inner tube.
Accretion Flow Dynamics of MAXI J1836-194 During Its 2011 Outburst from TCAF Solution
NASA Astrophysics Data System (ADS)
Jana, Arghajit; Debnath, Dipak; Chakrabarti, Sandip K.; Mondal, Santanu; Molla, Aslam Ali
2016-03-01
The Galactic transient X-ray binary MAXI J1836-194 was discovered on 2011 August 29. Here we make a detailed study of the spectral and timing properties of its 2011 outburst using archival data from the RXTE Proportional Counter Array instrument. The evolution of accretion flow dynamics of the source during the outburst through spectral analysis with Chakrabarti-Titarchuk’s two-component advective flow (TCAF) solution as a local table model in XSPEC. We also fitted spectra with combined disk blackbody and power-law models and compared it with the TCAF model fitted results. The source is found to be in hard and hard-intermediate spectral states only during the entire phase of this outburst. No soft or soft-intermediate spectral states are observed. This could be due to the fact that this object belongs to a special class of sources (e.g., MAXI J1659-152, Swift J1753.5-0127, etc.) that have very short orbital periods and that the companion is profusely mass-losing or the disk is immersed inside an excretion disk. In these cases, flows in the accretion disk are primarily dominated by low viscous sub-Keplerian flow and the Keplerian rate is not high enough to initiate softer states. Low-frequency quasi-periodic oscillations (QPOs) are observed sporadically although as in normal outbursts of transient black holes, monotonic evolutions of QPO frequency during both rising and declining phases are observed. From the TCAF fits, we find the mass of the black hole in the range of 7.5-11 M⊙, and from time differences between peaks of the Keplerian and sub-Keplerian accretion rates we obtain a viscous timescale for this particular outburst, ˜10 days.
NASA Astrophysics Data System (ADS)
Zhao, Yuqing; Zhang, You-Kuan; Liang, Xiuyu
2016-08-01
A semi-analytical solution was presented for groundwater flow due to pumping in a leaky sloping fault-zone aquifer surrounded by permeable matrices. The flow in the aquifer was descried by a three-dimensional flow equation, and the flow in the upper and lower matrix blocks are described by a one-dimensional flow equation. A first-order free-water surface equation at the outcrop of the fault-zone aquifer was used to describe the water table condition. The Laplace domain solution was derived using Laplace transform and finite Fourier transform techniques and the semi-analytical solutions in the real time domain were evaluated using the numerical inverse Laplace transform method. The solution was in excellent agreement with Theis solution combined with superposition principle as well as the solution of Huang et al. (2014). It was found that the drawdown increases as the sloping angle of the aquifer increases in early time and the impact of the angle is insignificant after pumping for a long time. The free-water surface boundary as additional source recharges the fault aquifer and significantly affect the drawdown at later time. The surrounding permeable matrices have a strong influence on drawdown but this influence can be neglected when the ratio of the specific storage and the ratio of the hydraulic conductivity of the matrices to those of the fault aquifer are less than 0.001.
NASA Technical Reports Server (NTRS)
Landahl, M.; Loefgren, P.
1973-01-01
A second-order theory for supersonic flow past slender bodies is presented. Through the introduction of characteristic coordinates as independent variables and the expansion procedure proposed by Lin and Oswatitsch, a uniformly valid solution is obtained for the whole flow field in the axisymmetric case and for far field in the general three-dimensional case. For distances far from the body the theory is an extension of Whitham's first-order solution and for the domain close to the body it is a modification of Van Dyke's second-order solution in the axisymmetric case. From the theory useful formulas relating flow deflections to the Whitham F-function are derived, which permits one to determine the sonic boom strength from wind tunnel measurements fairly close to the body.
NASA Astrophysics Data System (ADS)
Shaha, Poly Rani; Rudro, Sajal Kanti; Poddar, Nayan Kumar; Mondal, Rabindra Nath
2016-07-01
The study of flows through coiled ducts and channels has attracted considerable attention not only because of their ample applications in Chemical, Mechanical, Civil, Nuclear and Biomechanical engineering but also because of their ample applications in other areas, such as blood flow in the veins and arteries of human and other animals. In this paper, a numerical study is presented for the fully developed two-dimensional flow of viscous incompressible fluid through a loosely coiled rectangular duct of large aspect ratio. Numerical calculations are carried out by using a spectral method, and covering a wide range of the Dean number, Dn, for two types of curvatures of the duct. The main concern of the present study is to find out effects of curvature as well as formation of secondary vortices on unsteady solutions whether the unsteady flow is steady-state, periodic, multi-periodic or chaotic, if Dn is increased. Time evolution calculations as well as their phase spaces are performed with a view to study the non-linear behavior of the unsteady solutions, and it is found that the steady-state flow turns into chaotic flow through various flow instabilities, if Dn is increased no matter what the curvature is. It is found that the unsteady flow is a steady-state solution for small Dn's and oscillates periodically or non-periodically (chaotic) between two- and twelve-vortex solutions, if Dn is increased. It is also found that the chaotic solution is weak for small Dn's but strong as Dn becomes large. Axial flow distribution is also investigated and shown in contour plots.
Hollingsworth, Jennifer A.; Palaniappan, Kumaranand; Laocharoensuk, Rawiwan; Smith, Nickolaus A.; Dickerson, Robert M.; Casson, Joanna L.; Baldwin, Jon K.
2012-06-07
Semiconductor nanowires (SC-NWs) have potential applications in diverse technologies from nanoelectronics and photonics to energy harvesting and storage due to their quantum-confined opto-electronic properties coupled with their highly anisotropic shape. Here, we explore new approaches to an important solution-based growth method known as solution-liquid-solid (SLS) growth. In SLS, molecular precursors are reacted in the presence of low-melting metal nanoparticles that serve as molten fluxes to catalyze the growth of the SC-NWs. The mechanism of growth is assumed to be similar to that of vapor-liquid-solid (VLS) growth, with the clear distinctions of being conducted in solution in the presence of coordinating ligands and at relatively lower temperatures (<300 C). The resultant SC-NWs are soluble in common organic solvents and solution processable, offering advantages such as simplified processing, scale-up, ultra-small diameters for quantum-confinement effects, and flexible choice of materials from group III-V to groups II-VI, IV-VI, as well as truly ternary I-III-VI semiconductors as we recently demonstrates. Despite these advantages of SLS growth, VLS offers several clear opportunities not allowed by conventional SLS. Namely, VLS allows sequential addition of precursors for facile synthesis of complex axial heterostructures. In addition, growth proceeds relatively slowly compared to SLS, allowing clear assessments of growth kinetics. In order to retain the materials and processing flexibility afforded by SLS, but add the elements of controlled growth afforded by VLS, we transformed SLS into a flow based method by adapting it to synthesis in a microfluidic system. By this new method - so-called 'flow-SLS' (FSLS) - we have now demonstrated unprecedented fabrication of multi-segmented SC-NWs, e.g., 8-segmented CdSe/ZnSe defined by either compositionally abrupt or alloyed interfaces as a function of growth conditions. In addition, we have studied growth rates as a
Preferential water and solute fluxes in a model macropored porous medium as a function of flow rate
NASA Astrophysics Data System (ADS)
batany, stephane; Peyneau, Pierre-Emmanuel; Lassabatere, Laurent; Bechet, Beatrice; Faure, Pamela; Dangla, Patrick
2016-04-01
Macropores in soils can induce preferential flow and increase solute transport. Close to water saturation, most of the water flows through macropores at a much higher rate than it would in the same soil without any macropore. Preferential flow and water infiltration in soils with macropores have been investigated with different modeling approaches. Most of these are based on dual porosity or dual permeability approaches. These approaches consider that macropored soils are constituted by the association of two regions exchanging water, a matrix and a macropore domain, both of them obeying Darcy's law. Nevertheless, these approaches restrict preferential flow to the macropore domain and cannot simulate any enhancement of flow in the matrix surrounding the macropores. However, this hypothesis has been strongly questioned by several studies that had investigated solute transfer in macropored soils for which solute breakthrough curves (BTCs) were in complete disagreement with the flow restriction to the macropore domain. Thus, the understanding of water infiltration in soils requires more investigations regarding the effect of macropore and cracks in soils. The proposed paper aims at investigating water flow and tracer transport in a water saturated model macropored system as a function of the flow rate. Various solutes were injected in a 5 cm diameter, 14.5 cm high column filled with 425-800 μm diameter glass beads glued together. A 3 mm diameter Teflon rod inserted along the axis of the column during the preparation of the system was removed after the consolidation of the porous medium to create a macropore. Several flow rates - always ensuring a laminar flow - were tested, from values for which the diffusion transport rate is similar to the advective transport rate to values several orders of magnitude higher for which advection dominates. For all flow rates, solute BTCs were analyzed using the moment method and MIM model to quantify the volume of water visited by
Chen, K.F.; Olson, C.A.
1983-09-01
One reliable method that can be used to verify the solution scheme of a computer code is to compare the code prediction to a simplified problem for which an analytic solution can be derived. An analytic solution for the axial pressure drop as a function of the flow was obtained for the simplified problem of homogeneous equilibrium two-phase flow in a vertical, heated channel with a cosine axial heat flux shape. This analytic solution was then used to verify the predictions of the CONDOR computer code, which is used to evaluate the thermal-hydraulic performance of boiling water reactors. The results show excellent agreement between the analytic solution and CONDOR prediction.
Chen, K.F.; Olson, C.A.
1983-09-01
One reliable method that can be used to verify the solution scheme of a computer code is to compare the code prediction to a simplified problem for which an analytic solution can be derived. An analytic solution for the axial pressure drop as a function of the flow was obtained for the simplified problem of homogeneous equilibrium two-phase flow in a vertical, heated channel with a cosine axial heat flux shape. This analytic solution was then used to verify the predictions of the CONDOR computer code, which is used to evaluate the thermal-hydraulic performance of boiling water reactors. The results show excellent agreement between the analytic solution and CONDOR prediction.
Borges, Sivanildo S; Vieira, Gláucia P; Reis, Boaventura F
2007-01-01
In this work, an automatic device to deliver titrant solution into a titration chamber with the ability to determine the dispensed volume of solution, with good precision independent of both elapsed time and flow rate, is proposed. A glass tube maintained at the vertical position was employed as a container for the titrant solution. Electronic devices were coupled to the glass tube in order to control its filling with titrant solution, as well as the stepwise solution delivering into the titration chamber. The detection of the titration end point was performed employing a photometer designed using a green LED (lambda=545 nm) and a phototransistor. The titration flow system comprised three-way solenoid valves, which were assembled to allow that the steps comprising the solution container loading and the titration run were carried out automatically. The device for the solution volume determination was designed employing an infrared LED (lambda=930 nm) and a photodiode. When solution volume delivered from proposed device was within the range of 5 to 105 mul, a linear relationship (R = 0.999) between the delivered volumes and the generated potential difference was achieved. The usefulness of the proposed device was proved performing photometric titration of hydrochloric acid solution with a standardized sodium hydroxide solution and using phenolphthalein as an external indicator. The achieved results presented relative standard deviation of 1.5%. PMID:18317510
Numerical solution of non-isothermal non-adiabatic flow of real gases in pipelines
NASA Astrophysics Data System (ADS)
Bermúdez, Alfredo; López, Xián; Vázquez-Cendón, M. Elena
2016-10-01
A finite volume scheme for the numerical solution of a mathematical model for non-isothermal non-adiabatic compressible flow of a real gas in a pipeline is introduced. In order to make an upwind discretization of the flux, the Q-scheme of van Leer is used. Unlike standard Euler equations, the model takes into account wall friction, variable height and heat transfer between the pipe and the environment. Since all these terms are sources, in order to get a well-balanced scheme they are discretized by making a similar upwinding to the one in the flux term. The performance of the overall method has been shown for some usual numerical tests. The final goal, which is beyond the scope of this paper, is to consider a network including several pipelines connected at junctions, as those employed for natural gas transport.
Asynchronous, macrotasked relaxation strategies for the solution of viscous, hypersonic flows
NASA Technical Reports Server (NTRS)
Gnoffo, Peter A.
1991-01-01
A point-implicit, asynchronous macrotasked relaxation of the steady, thin-layer, Navier-Stokes equations is presented. The method employs multidirectional, single-level storage Gauss-Seidel relaxation sweeps, which effectively communicate perturbations across the entire domain in 2n sweeps, where n is the dimension of the domain. In order to enhance convergence the application of relaxation factors to specific components of the Jacobian is examined using a stability analysis of the advection and diffusion equations. Attention is also given to the complications associated with asynchronous multitasking. Solutions are generated for hypersonic flows over blunt bodies in two and three dimensions with chemical reactions, utilizing single-tasked and multitasked relaxation strategies.
Cascade-probabilistic methods and solution of Boltzman type of equations for particle flow
NASA Astrophysics Data System (ADS)
Kupchishin, A. I.; Kupchishin, A. A.; Voronova, N. A.
2016-02-01
A new method for calculating the spatial and temporal distributions of secondary particles and passing through a substance called cascade-probabilistic (HF) was proposed, developed and described. Original problems in the application of the original CP-technique in radiation physics, cosmic ray and positron physics was resolved. The general expression for the Boltzmann equation for the steady and unsteady cases was recorded based on an analysis of all the studies. In case of one-dimensional and three-dimensional (coordinate and angles θ and φ) Boltzmann equations solution goes into the previously obtained expressions for Nm. In addition, all previously derived analytical expressions for flow of different particles: protons, neutrons, electrons, concentration of defects, etc. are obtained after simplifying. At the same calculations give satisfactory agreement with experimental data.
Numerical solution of the Navier-Stokes equations for blunt nosed bodies in supersonic flows
NASA Technical Reports Server (NTRS)
Warsi, Z. U. A.; Devarayalu, K.; Thompson, J. F.
1978-01-01
A time dependent, two dimensional Navier-Stokes code employing the method of body fitted coordinate technique was developed for supersonic flows past blunt bodies of arbitrary shapes. The bow shock ahead of the body is obtained as part of the solution, viz., by shock capturing. A first attempt at mesh refinement in the shock region was made by using the forcing function in the coordinate generating equations as a linear function of the density gradients. The technique displaces a few lines from the neighboring region into the shock region. Numerical calculations for Mach numbers 2 and 4.6 and Reynolds numbers from 320 to 10,000 were performed for a circular cylinder with and without a fairing. Results of Mach number 4.6 and Reynolds number 10,000 for an isothermal wall temperature of 556 K are presented in detail.
NASA Astrophysics Data System (ADS)
Lavery, N.; Taylor, C.
1999-07-01
Multigrid and iterative methods are used to reduce the solution time of the matrix equations which arise from the finite element (FE) discretisation of the time-independent equations of motion of the incompressible fluid in turbulent motion. Incompressible flow is solved by using the method of reduce interpolation for the pressure to satisfy the Brezzi-Babuska condition. The k-l model is used to complete the turbulence closure problem. The non-symmetric iterative matrix methods examined are the methods of least squares conjugate gradient (LSCG), biconjugate gradient (BCG), conjugate gradient squared (CGS), and the biconjugate gradient squared stabilised (BCGSTAB). The multigrid algorithm applied is based on the FAS algorithm of Brandt, and uses two and three levels of grids with a V-cycling schedule. These methods are all compared to the non-symmetric frontal solver. Copyright
The Two-Phase Hell-Shaw Flow: Construction of an Exact Solution
NASA Astrophysics Data System (ADS)
Malaikah, K. R.
2013-03-01
We consider a two-phase Hele-Shaw cell whether or not the gap thickness is time-dependent. We construct an exact solution in terms of the Schwarz function of the interface for the two-phase Hele-Shaw flow. The derivation is based upon the single-valued complex velocity potential instead of the multiple-valued complex potential. As a result, the construction is applicable to the case of the time-dependent gap. In addition, there is no need to introduce branch cuts in the computational domain. Furthermore, the interface evolution in a two-phase problem is closely linked to its counterpart in a one-phase problem
NASA Astrophysics Data System (ADS)
Mach, Patryk; Malec, Edward; Karkowski, Janusz
2013-10-01
We investigate spherical, isothermal and polytropic steady accretion models in the presence of the cosmological constant. Exact solutions are found for three classes of isothermal fluids, assuming the test gas approximation. The cosmological constant damps the mass accretion rate and—above a certain limit—completely stops the steady accretion onto black holes. A “homoclinic-type” accretion flow of polytropic gas has been discovered in anti-de Sitter spacetimes in the test-gas limit. These results can have cosmological connotation, through the Einstein-Straus vacuole model of embedding local structures into Friedman-Lemaitre-Robertson-Walker spacetimes. In particular, one infers that steady accretion would not exist in the late phases of Penrose’s scenario of the evolution of the Universe, known as the Weyl curvature hypothesis.
Wilson, Derek J; Konermann, Lars
2005-11-01
The adverse effects of nonvolatile salts on the electrospray (ESI) mass spectra of proteins and other biological analytes are a major obstacle for a wide range of applications. Numerous sample cleanup approaches have been devised to facilitate ESI-MS analyses. Recently developed microdialysis techniques can shorten desalting times down to several minutes, the bottleneck being diffusion of the contaminant through a semipermeable membrane. This work introduces an approach that allows the on-line desalting of macromolecule solutions within tens of milliseconds. The device does not employ a membrane; instead, it uses a two-layered laminar flow geometry that exploits the differential diffusion of macromolecular analytes and low molecular weight contaminants. To maximize desalting efficiency, diffusive exchange between the flow layers is permitted only for such a time as to allow full exchange of salt, while incurring minimal macromolecule exchange. Computer simulations and optical studies show that the device can reduce the salt concentration by roughly 1 order of magnitude, while retaining approximately 70% of the original protein concentration. Application of this approach to the on-line purification of salt-contaminated protein solutions in ESI-MS results in dramatic improvements of both the signal-to-noise ratio and the absolute signal intensity. However, efficient desalting requires the diffusion coefficients of salt and analyte to differ by roughly 1 order of magnitude or more. This technique has potential to facilitate high-throughput analyses of biological macromolecules directly from complex matrixes. In addition, it may become a valuable tool for process monitoring and for on-line kinetic studies on biological systems.
Development of iterative techniques for the solution of unsteady compressible viscous flows
NASA Technical Reports Server (NTRS)
Hixon, Duane; Sankar, L. N.
1993-01-01
During the past two decades, there has been significant progress in the field of numerical simulation of unsteady compressible viscous flows. At present, a variety of solution techniques exist such as the transonic small disturbance analyses (TSD), transonic full potential equation-based methods, unsteady Euler solvers, and unsteady Navier-Stokes solvers. These advances have been made possible by developments in three areas: (1) improved numerical algorithms; (2) automation of body-fitted grid generation schemes; and (3) advanced computer architectures with vector processing and massively parallel processing features. In this work, the GMRES scheme has been considered as a candidate for acceleration of a Newton iteration time marching scheme for unsteady 2-D and 3-D compressible viscous flow calculation; from preliminary calculations, this will provide up to a 65 percent reduction in the computer time requirements over the existing class of explicit and implicit time marching schemes. The proposed method has ben tested on structured grids, but is flexible enough for extension to unstructured grids. The described scheme has been tested only on the current generation of vector processor architecture of the Cray Y/MP class, but should be suitable for adaptation to massively parallel machines.
Development of a pressure based multigrid solution method for complex fluid flows
NASA Technical Reports Server (NTRS)
Shyy, Wei
1991-01-01
In order to reduce the computational difficulty associated with a single grid (SG) solution procedure, the multigrid (MG) technique was identified as a useful means for improving the convergence rate of iterative methods. A full MG full approximation storage (FMG/FAS) algorithm is used to solve the incompressible recirculating flow problems in complex geometries. The algorithm is implemented in conjunction with a pressure correction staggered grid type of technique using the curvilinear coordinates. In order to show the performance of the method, two flow configurations, one a square cavity and the other a channel, are used as test problems. Comparisons are made between the iterations, equivalent work units, and CPU time. Besides showing that the MG method can yield substantial speed-up with wide variations in Reynolds number, grid distributions, and geometry, issues such as the convergence characteristics of different grid levels, the choice of convection schemes, and the effectiveness of the basic iteration smoothers are studied. An adaptive grid scheme is also combined with the MG procedure to explore the effects of grid resolution on the MG convergence rate as well as the numerical accuracy.
Navier-Stokes Solutions of Rotor and Rotor-Body Flows
NASA Technical Reports Server (NTRS)
Srinivasan, G. R.; Holst, Terry L. (Technical Monitor)
1994-01-01
This paper will review the advances made recently in the Navier-Stokes CFD methods to simulate aerodynamics and aeroacoustics of helicopter rotors and rotor-body flows. Although a complete flowfield simulation of full helicopter is currently not feasible with these methods, impressive gains have been made in analyzing individual components of this complex problem in a very detailed manner. The use of the state-of-the-art numerical algorithms in solution methods, in conjunction with powerful supercomputers, like the Cray-2, have enabled noticeable progress to be made in modeling viscous-inviscid interactions, blade-vortex interactions, tip-vortex: simulation and wake effects, as well as high speed impulsive noise in hover and forward flight for isolated rotor blades. This paper will critically evaluate the presently available Euler and Navier-Stokes methods, both finite-difference and finite volume methods using structured and unstructured grids for helicopter applications for accuracy, suitability, and computational efficiency. The review will also include the recent progress made using overset grids to model rotor-body flows. All the material for this review will be drawn from the published material shown below.
Lorber, A.A.; Carey, G.F.; Bova, S.W.; Harle, C.H.
1996-12-31
The connection between the solution of linear systems of equations by iterative methods and explicit time stepping techniques is used to accelerate to steady state the solution of ODE systems arising from discretized PDEs which may involve either physical or artificial transient terms. Specifically, a class of Runge-Kutta (RK) time integration schemes with extended stability domains has been used to develop recursion formulas which lead to accelerated iterative performance. The coefficients for the RK schemes are chosen based on the theory of Chebyshev iteration polynomials in conjunction with a local linear stability analysis. We refer to these schemes as Chebyshev Parameterized Runge Kutta (CPRK) methods. CPRK methods of one to four stages are derived as functions of the parameters which describe an ellipse {Epsilon} which the stability domain of the methods is known to contain. Of particular interest are two-stage, first-order CPRK and four-stage, first-order methods. It is found that the former method can be identified with any two-stage RK method through the correct choice of parameters. The latter method is found to have a wide range of stability domains, with a maximum extension of 32 along the real axis. Recursion performance results are presented below for a model linear convection-diffusion problem as well as non-linear fluid flow problems discretized by both finite-difference and finite-element methods.
Hermosilla, Laura; Prampolini, Giacomo; Calle, Paloma; García de la Vega, José Manuel; Brancato, Giuseppe; Barone, Vincenzo
2015-01-01
A computational strategy that combines both time-dependent and time-independent approaches is exploited to accurately model molecular dynamics and solvent effects on the isotropic hyperfine coupling constants of the DMPO-H nitroxide. Our recent general force field for nitroxides derived from AMBER ff99SB is further extended to systems involving hydrogen atoms in β-positions with respect to NO. The resulting force-field has been employed in a series of classical molecular dynamics simulations, comparing the computed EPR parameters from selected molecular configurations to the corresponding experimental data in different solvents. The effect of vibrational averaging on the spectroscopic parameters is also taken into account, by second order vibrational perturbation theory involving semi-diagonal third energy derivatives together first and second property derivatives. PMID:26584116
NASA Astrophysics Data System (ADS)
de Rooij, G. H.; Hogervorst, F. A.; Bloem, E.; Stagnitti, F.; Cirpka, O. A.
2007-12-01
Water flow and solute transport in soils are invariably affected by heterogeneity and often by preferential flow, both typically occurring within 1 square meter. Paradoxically, we need to understand flow and transport at this small scale to quantify them at the field and regional scales. This paradox arises from the geometry of soils: the scale in the direction of the flow is orders of magnitude smaller than the scales perpendicular to it. We present a coherent package of experimental and theoretical tools to observe and analyze small-scale variations (within 0.1- 1 square meter) of water and solute fluxes. Multicompartment samplers can measure small-scale water and solute movement in space and time, particularly in temperate climates. The latest generation of samplers allows repeated extraction of percolate samples in situ under controlled suction to minimize disturbance of the unsaturated flow field. After discussing the general principle of such samplers, a method will be presented to estimate the required total sampling area of a sampler from the degree of flow convergence in a soil. In recent years, we improved our ability to analyze the data produced by multicompartment samplers. The spatial solute distribution curve as the spatial equivalent of the travel time distribution was parameterized and physically interpreted. Both distributions were unified in the leaching surface, which has tremendous potential for detailed interpretation and model evaluation. Multicompartment samplers can also help identify the nature of the solute transport process. Recently, we expanded the theory of solute dilution to make it applicable to multicompartment sampler data. We will demonstrate how dilution theory can be used to determine the predominance of a convective-dispersive or a stochastic-convective transport regime during a tracer experiment.
NASA Technical Reports Server (NTRS)
Ratkiewicz, Romana E.; Scherer, Klaus; Fahr, Hans J.; Cuzzi, Jeffrey N. (Technical Monitor)
1994-01-01
The solar system is in relative motion with respect to the ambient interstellar medium. The supersonic solar wind is expected to pass through the termination shock, thus the solar wind plasma eventually has to enter into an asymptotic outflow geometry appropriately adopted to this counterflow situation. Many attempts have been done to simulate the interaction between the solar wind and the LISM numerically. In this paper we generalize a Parker type analytical solution of the counterflow. The idea is to introduce a special kind of compressibility of the solar wind flow. With the assumption that only a transversal component of the density gradient normal to the flow lines exists we are able to calculate a full set of hydrodynamical quantities describing the circumsolar flow field of a Sun moving through the LISM. The equations governing the velocity and density fields lead to analytical solutions which can be taken as good approximations to the more general case of compressible plasma flows.
Machado, Anaïs; Bodiguel, Hugues; Beaumont, Julien; Clisson, Gérald; Colin, Annie
2016-07-01
We study flows of hydrolized polyacrylamide solutions in two dimensional porous media made using microfluidics, for which elastic effects are dominant. We focus on semi-dilute solutions (0.1%-0.4%) which exhibit a strong shear thinning behavior. We systematically measure the pressure drop and find that the effective permeability is dramatically higher than predicted when the Weissenberg number is greater than about 10. Observations of the streamlines of the flow reveal that this effect coincides with the onset of elastic instabilities. Moreover, and importantly for applications, we show using local measurements that the mean flow is modified: it appears to be more uniform at high Weissenberg number than for Newtonian fluids. These observations are compared and discussed using pore network simulations, which account for the effect of disorder and shear thinning on the flow properties. PMID:27478522