Static and dynamic characteristics of parallel-grooved seals

NASA Technical Reports Server (NTRS)

Iwatsubo, Takuzo; Yang, Bo-Suk; Ibaraki, Ryuji

1987-01-01

Presented is an analytical method to determine static and dynamic characteristics of annular parallel-grooved seals. The governing equations were derived by using the turbulent lubrication theory based on the law of fluid friction. Linear zero- and first-order perturbation equations of the governing equations were developed, and these equations were analytically investigated to obtain the reaction force of the seals. An analysis is presented that calculates the leakage flow rate, the torque loss, and the rotordynamic coefficients for parallel-grooved seals. To demonstrate this analysis, we show the effect of changing number of stages, land and groove width, and inlet swirl on stability of the boiler feed water pump seals. Generally, as the number of stages increased or the grooves became wider, the leakage flow rate and rotor-dynamic coefficients decreased and the torque loss increased.

Residual-based Methods for Controlling Discretization Error in CFD

DTIC Science & Technology

2015-08-24

discrete equations uh into Equation (3), then subtracting the original (continuous) governing equation 0)~( uL gives 0)()~()(  hhh uuLuL  . If...error from Equation (1) results in )()( hhh uL   (4) which for Burgers’ equation becomes  4 2 4 42 3 3 2 2 126 xO x dx udx dx ud u dx d dx d u...GTEE given in Equation (3) gives the continuous residual )()( hhh uuL  (8) which is analogous to the finite element residual (Ainsworth and

Development of Spatially-Based Emission Factors from Real-Time Measurements of Gaseous Pollutants Using Cermet Sensors

DTIC Science & Technology

2005-03-01

produce a current-limited steady state output potential that follows the Nernst equation (Fraden 1993): E = Eo + ((RT)/nF)ln(CO/CR) (2) CO...temperature, EO: electrode potential at standard state. Nernst equation governs many half-cell reactions in electrochemical cells. The cell...voltammetric cell, the analytes react (oxidize or reduce) at very characteristic potentials according to the following simplified equation (Smyth

Coupling of Coastal Wave Transformation and Computational Fluid Dynamics Models for Seakeeping Analysis

DTIC Science & Technology

2017-04-03

setup in terms of temporal and spatial discretization . The second component was an extension of existing depth-integrated wave models to describe...equations (Abbott, 1976). Discretization schemes involve numerical dispersion and dissipation that distort the true character of the governing equations...represent a leading-order approximation of the Boussinesq-type equations. Tam and Webb (1993) proposed a wavenumber-based discretization scheme to preserve

From the paddle to the beach - A Boussinesq shallow water numerical wave tank based on Madsen and Sørensen's equations

NASA Astrophysics Data System (ADS)

Orszaghova, Jana; Borthwick, Alistair G. L.; Taylor, Paul H.

2012-01-01

This article describes a one-dimensional numerical model of a shallow-water flume with an in-built piston paddle moving boundary wavemaker. The model is based on a set of enhanced Boussinesq equations and the nonlinear shallow water equations. Wave breaking is described approximately, by locally switching to the nonlinear shallow water equations when a critical wave steepness is reached. The moving shoreline is calculated as part of the solution. The piston paddle wavemaker operates on a movable grid, which is Lagrangian on the paddle face and Eulerian away from the paddle. The governing equations are, however, evolved on a fixed mapped grid, and the newly calculated solution is transformed back onto the moving grid via a domain mapping technique. Validation test results are compared against analytical solutions, confirming correct discretisation of the governing equations, wave generation via the numerical paddle, and movement of the wet/dry front. Simulations are presented that reproduce laboratory experiments of wave runup on a plane beach and wave overtopping of a laboratory seawall, involving solitary waves and compact wave groups. In practice, the numerical model is suitable for simulating the propagation of weakly dispersive waves and can additionally model any associated inundation, overtopping or inland flooding within the same simulation.

Determination of constant-volume balloon capabilities for aeronautical research. [specifically measurement of atmospheric phenomena

NASA Technical Reports Server (NTRS)

Tatom, F. B.; King, R. L.

1977-01-01

The proper application of constant-volume balloons (CVB) for measurement of atmospheric phenomena was determined. And with the proper interpretation of the resulting data. A literature survey covering 176 references is included. the governing equations describing the three-dimensional motion of a CVB immersed in a flow field are developed. The flowfield model is periodic, three-dimensional, and nonhomogeneous, with mean translational motion. The balloon motion and flow field equations are cast into dimensionless form for greater generality, and certain significant dimensionless groups are identified. An alternate treatment of the balloon motion, based on first-order perturbation analysis, is also presented. A description of the digital computer program, BALLOON, used for numerically integrating the governing equations is provided.

On the Representation of Aquifer Compressibility in General Subsurface Flow Codes: How an Alternate Definition of Aquifer Compressibility Matches Results from the Groundwater Flow Equation

NASA Astrophysics Data System (ADS)

Birdsell, D.; Karra, S.; Rajaram, H.

2016-12-01

The governing equations for subsurface flow codes in deformable porous media are derived from the fluid mass balance equation. One class of these codes, which we call general subsurface flow (GSF) codes, does not explicitly track the motion of the solid porous media but does accept general constitutive relations for porosity, density, and fluid flux. Examples of GSF codes include PFLOTRAN, FEHM, STOMP, and TOUGH2. Meanwhile, analytical and numerical solutions based on the groundwater flow equation have assumed forms for porosity, density, and fluid flux. We review the derivation of the groundwater flow equation, which uses the form of Darcy's equation that accounts for the velocity of fluids with respect to solids and defines the soil matrix compressibility accordingly. We then show how GSF codes have a different governing equation if they use the form of Darcy's equation that is written only in terms of fluid velocity. The difference is seen in the porosity change, which is part of the specific storage term in the groundwater flow equation. We propose an alternative definition of soil matrix compressibility to correct for the untracked solid velocity. Simulation results show significantly less error for our new compressibility definition than the traditional compressibility when compared to analytical solutions from the groundwater literature. For example, the error in one calculation for a pumped sandstone aquifer goes from 940 to <70 Pa when the new compressibility is used. Code users and developers need to be aware of assumptions in the governing equations and constitutive relations in subsurface flow codes, and our newly-proposed compressibility function should be incorporated into GSF codes.

On the Representation of Aquifer Compressibility in General Subsurface Flow Codes: How an Alternate Definition of Aquifer Compressibility Matches Results from the Groundwater Flow Equation

NASA Astrophysics Data System (ADS)

Birdsell, D.; Karra, S.; Rajaram, H.

2017-12-01

The governing equations for subsurface flow codes in deformable porous media are derived from the fluid mass balance equation. One class of these codes, which we call general subsurface flow (GSF) codes, does not explicitly track the motion of the solid porous media but does accept general constitutive relations for porosity, density, and fluid flux. Examples of GSF codes include PFLOTRAN, FEHM, STOMP, and TOUGH2. Meanwhile, analytical and numerical solutions based on the groundwater flow equation have assumed forms for porosity, density, and fluid flux. We review the derivation of the groundwater flow equation, which uses the form of Darcy's equation that accounts for the velocity of fluids with respect to solids and defines the soil matrix compressibility accordingly. We then show how GSF codes have a different governing equation if they use the form of Darcy's equation that is written only in terms of fluid velocity. The difference is seen in the porosity change, which is part of the specific storage term in the groundwater flow equation. We propose an alternative definition of soil matrix compressibility to correct for the untracked solid velocity. Simulation results show significantly less error for our new compressibility definition than the traditional compressibility when compared to analytical solutions from the groundwater literature. For example, the error in one calculation for a pumped sandstone aquifer goes from 940 to <70 Pa when the new compressibility is used. Code users and developers need to be aware of assumptions in the governing equations and constitutive relations in subsurface flow codes, and our newly-proposed compressibility function should be incorporated into GSF codes.

Formulation and closure of compressible turbulence equations in the light of kinetic theory

NASA Technical Reports Server (NTRS)

Tsuge, S.; Sagara, K.

1976-01-01

Fluid-dynamic moment equations, based on a kinetic hierarchy system, are derived governing the interaction between turbulent and thermal fluctuations. The kinetic theory is shown to reduce the inherent complexity of the conventional formalism of compressible turbulence theory and to minimize arbitrariness in formulating the closure condition.

Thermal-Interaction Matrix For Resistive Test Structure

NASA Technical Reports Server (NTRS)

Buehler, Martin G.; Dhiman, Jaipal K.; Zamani, Nasser

1990-01-01

Linear mathematical model predicts increase in temperature in each segment of 15-segment resistive structure used to test electromigration. Assumption of linearity based on fact: equations that govern flow of heat are linear and coefficients in equations (heat conductivities and capacities) depend only weakly on temperature and considered constant over limited range of temperature.

Vibration analysis of partially cracked plate submerged in fluid

NASA Astrophysics Data System (ADS)

Soni, Shashank; Jain, N. K.; Joshi, P. V.

2018-01-01

The present work proposes an analytical model for vibration analysis of partially cracked rectangular plates coupled with fluid medium. The governing equation of motion for the isotropic plate based on the classical plate theory is modified to accommodate a part through continuous line crack according to simplified line spring model. The influence of surrounding fluid medium is incorporated in the governing equation in the form of inertia effects based on velocity potential function and Bernoulli's equations. Both partially and totally submerged plate configurations are considered. The governing equation also considers the in-plane stretching due to lateral deflection in the form of in-plane forces which introduces geometric non-linearity into the system. The fundamental frequencies are evaluated by expressing the lateral deflection in terms of modal functions. The assessment of the present results is carried out for intact submerged plate as to the best of the author's knowledge the literature lacks in analytical results for submerged cracked plates. New results for fundamental frequencies are presented as affected by crack length, fluid level, fluid density and immersed depth of plate. By employing the method of multiple scales, the frequency response and peak amplitude of the cracked structure is analyzed. The non-linear frequency response curves show the phenomenon of bending hardening or softening and the effect of fluid dynamic pressure on the response of the cracked plate.

Nonlinear (time domain) and linearized (time and frequency domain) solutions to the compressible Euler equations in conservation law form

NASA Technical Reports Server (NTRS)

Sreenivas, Kidambi; Whitfield, David L.

1995-01-01

Two linearized solvers (time and frequency domain) based on a high resolution numerical scheme are presented. The basic approach is to linearize the flux vector by expressing it as a sum of a mean and a perturbation. This allows the governing equations to be maintained in conservation law form. A key difference between the time and frequency domain computations is that the frequency domain computations require only one grid block irrespective of the interblade phase angle for which the flow is being computed. As a result of this and due to the fact that the governing equations for this case are steady, frequency domain computations are substantially faster than the corresponding time domain computations. The linearized equations are used to compute flows in turbomachinery blade rows (cascades) arising due to blade vibrations. Numerical solutions are compared to linear theory (where available) and to numerical solutions of the nonlinear Euler equations.

Finite-volume method with lattice Boltzmann flux scheme for incompressible porous media flow at the representative-elementary-volume scale.

PubMed

Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong

2016-02-01

Based on the Darcy-Brinkman-Forchheimer equation, a finite-volume computational model with lattice Boltzmann flux scheme is proposed for incompressible porous media flow in this paper. The fluxes across the cell interface are calculated by reconstructing the local solution of the generalized lattice Boltzmann equation for porous media flow. The time-scaled midpoint integration rule is adopted to discretize the governing equation, which makes the time step become limited by the Courant-Friedricks-Lewy condition. The force term which evaluates the effect of the porous medium is added to the discretized governing equation directly. The numerical simulations of the steady Poiseuille flow, the unsteady Womersley flow, the circular Couette flow, and the lid-driven flow are carried out to verify the present computational model. The obtained results show good agreement with the analytical, finite-difference, and/or previously published solutions.

Two-dimensional coupled mathematical modeling of fluvial processes with intense sediment transport and rapid bed evolution

NASA Astrophysics Data System (ADS)

Yue, Zhiyuan; Cao, Zhixian; Li, Xin; Che, Tao

2008-09-01

Alluvial rivers may experience intense sediment transport and rapid bed evolution under a high flow regime, for which traditional decoupled mathematical river models based on simplified conservation equations are not applicable. A two-dimensional coupled mathematical model is presented, which is generally applicable to the fluvial processes with either intense or weak sediment transport. The governing equations of the model comprise the complete shallow water hydrodynamic equations closed with Manning roughness for boundary resistance and empirical relationships for sediment exchange with the erodible bed. The second-order Total-Variation-Diminishing version of the Weighted-Average-Flux method, along with the HLLC approximate Riemann Solver, is adapted to solve the governing equations, which can properly resolve shock waves and contact discontinuities. The model is applied to the pilot study of the flooding due to a sudden outburst of a real glacial-lake.

Morphing Continuum Theory: A First Order Approximation to the Balance Laws

NASA Astrophysics Data System (ADS)

Wonnell, Louis; Cheikh, Mohamad Ibrahim; Chen, James

2017-11-01

Morphing Continuum Theory is constructed under the framework of Rational Continuum Mechanics (RCM) for fluid flows with inner structure. This multiscale theory has been successfully emplyed to model turbulent flows. The framework of RCM ensures the mathematical rigor of MCT, but contains new material constants related to the inner structure. The physical meanings of these material constants have yet to be determined. Here, a linear deviation from the zeroth-order Boltzmann-Curtiss distribution function is derived. When applied to the Boltzmann-Curtiss equation, a first-order approximation of the MCT governing equations is obtained. The integral equations are then related to the appropriate material constants found in the heat flux, Cauchy stress, and moment stress terms in the governing equations. These new material properties associated with the inner structure of the fluid are compared with the corresponding integrals, and a clearer physical interpretation of these coefficients emerges. The physical meanings of these material properties is determined by analyzing previous results obtained from numerical simulations of MCT for compressible and incompressible flows. The implications for the physics underlying the MCT governing equations will also be discussed. This material is based upon work supported by the Air Force Office of Scientific Research under Award Number FA9550-17-1-0154.

Parametrically excited non-linear multidegree-of-freedom systems with repeated natural frequencies

NASA Astrophysics Data System (ADS)

Tezak, E. G.; Nayfeh, A. H.; Mook, D. T.

1982-12-01

A method for analyzing multidegree-of-freedom systems having a repeated natural frequency subjected to a parametric excitation is presented. Attention is given to the ordering of the various terms (linear and non-linear) in the governing equations. The analysis is based on the method of multiple scales. As a numerical example involving a parametric resonance, panel flutter is discussed in detail in order to illustrate the type of results one can expect to obtain with this analysis. Some of the analytical results are verified by a numerical integration of the governing equations.

Thermal-stress analysis for a wood composite blade

NASA Technical Reports Server (NTRS)

Fu, K. C.; Harb, A.

1984-01-01

A thermal-stress analysis of a wind turbine blade made of wood composite material is reported. First, the governing partial differential equation on heat conduction is derived, then, a finite element procedure using variational approach is developed for the solution of the governing equation. Thus, the temperature distribution throughout the blade is determined. Next, based on the temperature distribution, a finite element procedure using potential energy approach is applied to determine the thermal-stress distribution. A set of results is obtained through the use of a computer, which is considered to be satisfactory. All computer programs are contained in the report.

Direct modeling for computational fluid dynamics

NASA Astrophysics Data System (ADS)

Xu, Kun

2015-06-01

All fluid dynamic equations are valid under their modeling scales, such as the particle mean free path and mean collision time scale of the Boltzmann equation and the hydrodynamic scale of the Navier-Stokes (NS) equations. The current computational fluid dynamics (CFD) focuses on the numerical solution of partial differential equations (PDEs), and its aim is to get the accurate solution of these governing equations. Under such a CFD practice, it is hard to develop a unified scheme that covers flow physics from kinetic to hydrodynamic scales continuously because there is no such governing equation which could make a smooth transition from the Boltzmann to the NS modeling. The study of fluid dynamics needs to go beyond the traditional numerical partial differential equations. The emerging engineering applications, such as air-vehicle design for near-space flight and flow and heat transfer in micro-devices, do require further expansion of the concept of gas dynamics to a larger domain of physical reality, rather than the traditional distinguishable governing equations. At the current stage, the non-equilibrium flow physics has not yet been well explored or clearly understood due to the lack of appropriate tools. Unfortunately, under the current numerical PDE approach, it is hard to develop such a meaningful tool due to the absence of valid PDEs. In order to construct multiscale and multiphysics simulation methods similar to the modeling process of constructing the Boltzmann or the NS governing equations, the development of a numerical algorithm should be based on the first principle of physical modeling. In this paper, instead of following the traditional numerical PDE path, we introduce direct modeling as a principle for CFD algorithm development. Since all computations are conducted in a discretized space with limited cell resolution, the flow physics to be modeled has to be done in the mesh size and time step scales. Here, the CFD is more or less a direct construction of discrete numerical evolution equations, where the mesh size and time step will play dynamic roles in the modeling process. With the variation of the ratio between mesh size and local particle mean free path, the scheme will capture flow physics from the kinetic particle transport and collision to the hydrodynamic wave propagation. Based on the direct modeling, a continuous dynamics of flow motion will be captured in the unified gas-kinetic scheme. This scheme can be faithfully used to study the unexplored non-equilibrium flow physics in the transition regime.

Differential Geometry Based Multiscale Models

PubMed Central

Wei, Guo-Wei

2010-01-01

Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atom-istic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier–Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson–Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson–Nernst–Planck equations that are coupled to generalized Navier–Stokes equations for fluid dynamics, Newton's equation for molecular dynamics, and potential and surface driving geometric flows for the micro-macro interface. For excessively large aqueous macromolecular complexes in chemistry and biology, we further develop differential geometry based multiscale fluid-electro-elastic models to replace the expensive molecular dynamics description with an alternative elasticity formulation. PMID:20169418

A High-Resolution Godunov Method for Compressible Multi-Material Flow on Overlapping Grids

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

Banks, J W; Schwendeman, D W; Kapila, A K

2006-02-13

A numerical method is described for inviscid, compressible, multi-material flow in two space dimensions. The flow is governed by the multi-material Euler equations with a general mixture equation of state. Composite overlapping grids are used to handle complex flow geometry and block-structured adaptive mesh refinement (AMR) is used to locally increase grid resolution near shocks and material interfaces. The discretization of the governing equations is based on a high-resolution Godunov method, but includes an energy correction designed to suppress numerical errors that develop near a material interface for standard, conservative shock-capturing schemes. The energy correction is constructed based on amore » uniform pressure-velocity flow and is significant only near the captured interface. A variety of two-material flows are presented to verify the accuracy of the numerical approach and to illustrate its use. These flows assume an equation of state for the mixture based on Jones-Wilkins-Lee (JWL) forms for the components. This equation of state includes a mixture of ideal gases as a special case. Flow problems considered include unsteady one-dimensional shock-interface collision, steady interaction of an planar interface and an oblique shock, planar shock interaction with a collection of gas-filled cylindrical inhomogeneities, and the impulsive motion of the two-component mixture in a rigid cylindrical vessel.« less

Direct Logistic Fuel JP-8 Conversion in a Liquid Tin Anode Solid Oxide Fuel Cell (LTA-SOFC)

DTIC Science & Technology

2008-04-09

GeSnOOSn sgl [1] As governed by the Nernst equation Open Circuit Voltage (OCV) is inversely proportional to temperature. The OCV of...inherently stable at 1,000°C. The LTA-SOFC electrochemical reaction is based on the following thermodynamic equation . C1000T kJ 311 42 o)(2... equation 1 is 0.8V at 1000°C, using an oxygen partial pressure of one. This equation gives the OCV for a LTA–SOFC functioning as a battery. The tin oxide

Schrödinger equation revisited

PubMed Central

Schleich, Wolfgang P.; Greenberger, Daniel M.; Kobe, Donald H.; Scully, Marlan O.

2013-01-01

The time-dependent Schrödinger equation is a cornerstone of quantum physics and governs all phenomena of the microscopic world. However, despite its importance, its origin is still not widely appreciated and properly understood. We obtain the Schrödinger equation from a mathematical identity by a slight generalization of the formulation of classical statistical mechanics based on the Hamilton–Jacobi equation. This approach brings out most clearly the fact that the linearity of quantum mechanics is intimately connected to the strong coupling between the amplitude and phase of a quantum wave. PMID:23509260

Theoretical study on a Miniature Joule-Thomson & Bernoulli Cryocooler

NASA Astrophysics Data System (ADS)

Xiong, L. Y.; Kaiser, G.; Binneberg, A.

2004-11-01

In this paper, a microchannel-based cryocooler consisting of a compressor, a recuperator and a cold heat exchanger has been developed to study the feasibility of cryogenic cooling by the use of Joule-Thomson effect and Bernoulli effect. A set of governing equations including Bernoulli equations and energy equations are introduced and the performance of the cooler is calculated. The influences of some working conditions and structure parameters on the performance of coolers are discussed in details.

Experimental Investigation of Hydrodynamic Self-Acting Gas Bearings at High Knudsen Numbers.

DTIC Science & Technology

1980-07-01

Reynolds equation. Two finite - difference algorithms were used to solve the equation. Numerical results - the predicted load and pitch angle - from the two...that should be used. The majority of the numerical solution are still based on the finite difference approximation of the governing equation. But in... finite difference method. Reddi and Chu [26) also noted that it is very difficult to compare the two techniques on the same level since the solution

Force and moment rotordynamic coefficients for pump-impeller shroud surfaces

NASA Technical Reports Server (NTRS)

Childs, Dara W.

1987-01-01

Governing equations of motion are derived for a bulk-flow model of the leakage path between an impeller shroud and a pump housing. The governing equations consist of a path-momentum, a circumferential - momentum, and a continuity equation. The fluid annulus between the impeller shroud and pump housing is assumed to be circumferentially symmetric when the impeller is centered; i.e., the clearance can vary along the pump axis but does not vary in the circumferential direction. A perturbation expansion of the governing equations in the eccentricity ratio yields a set of zeroth and first-order governing equations. The zeroth-order equations define the leaking rate and the circumferential and path velocity distributions and pressure distributions for a centered impeller position. The first-order equations define the perturbations in the velocity and pressure distributions due to either a radial-displacement perturbation or a tilt perturbation of the impeller. Integration of the perturbed pressure and shear-stress distribution acting on the rotor yields the reaction forces and moments acting on the impeller face.

Modelling vortex-induced fluid-structure interaction.

PubMed

Benaroya, Haym; Gabbai, Rene D

2008-04-13

The principal goal of this research is developing physics-based, reduced-order, analytical models of nonlinear fluid-structure interactions associated with offshore structures. Our primary focus is to generalize the Hamilton's variational framework so that systems of flow-oscillator equations can be derived from first principles. This is an extension of earlier work that led to a single energy equation describing the fluid-structure interaction. It is demonstrated here that flow-oscillator models are a subclass of the general, physical-based framework. A flow-oscillator model is a reduced-order mechanical model, generally comprising two mechanical oscillators, one modelling the structural oscillation and the other a nonlinear oscillator representing the fluid behaviour coupled to the structural motion.Reduced-order analytical model development continues to be carried out using a Hamilton's principle-based variational approach. This provides flexibility in the long run for generalizing the modelling paradigm to complex, three-dimensional problems with multiple degrees of freedom, although such extension is very difficult. As both experimental and analytical capabilities advance, the critical research path to developing and implementing fluid-structure interaction models entails-formulating generalized equations of motion, as a superset of the flow-oscillator models; and-developing experimentally derived, semi-analytical functions to describe key terms in the governing equations of motion. The developed variational approach yields a system of governing equations. This will allow modelling of multiple d.f. systems. The extensions derived generalize the Hamilton's variational formulation for such problems. The Navier-Stokes equations are derived and coupled to the structural oscillator. This general model has been shown to be a superset of the flow-oscillator model. Based on different assumptions, one can derive a variety of flow-oscillator models.

Jet Engine Noise Reduction

DTIC Science & Technology

2009-04-01

greatest attention. 4 Excessive noise can cause temporary or permanent hearing loss or tinnitus , a constant ringing in the ear. In addition...industry effort focused on a ten-fold improvement in turbine engine affordable capability by the year 2017. This is following the model of the...exhibit a mix of chaotic and deterministic behavior . Although the governing equations describing fluid flows, the Navier Stokes equations, are based

Proper Orthogonal Decomposition in Optimal Control of Fluids

NASA Technical Reports Server (NTRS)

Ravindran, S. S.

1999-01-01

In this article, we present a reduced order modeling approach suitable for active control of fluid dynamical systems based on proper orthogonal decomposition (POD). The rationale behind the reduced order modeling is that numerical simulation of Navier-Stokes equations is still too costly for the purpose of optimization and control of unsteady flows. We examine the possibility of obtaining reduced order models that reduce computational complexity associated with the Navier-Stokes equations while capturing the essential dynamics by using the POD. The POD allows extraction of certain optimal set of basis functions, perhaps few, from a computational or experimental data-base through an eigenvalue analysis. The solution is then obtained as a linear combination of these optimal set of basis functions by means of Galerkin projection. This makes it attractive for optimal control and estimation of systems governed by partial differential equations. We here use it in active control of fluid flows governed by the Navier-Stokes equations. We show that the resulting reduced order model can be very efficient for the computations of optimization and control problems in unsteady flows. Finally, implementational issues and numerical experiments are presented for simulations and optimal control of fluid flow through channels.

Unsteady boundary layer flow over a sphere in a porous medium

NASA Astrophysics Data System (ADS)

Mohammad, Nurul Farahain; Waini, Iskandar; Kasim, Abdul Rahman Mohd; Majid, Nurazleen Abdul

2017-08-01

This study focuses on the problem of unsteady boundary layer flow over a sphere in a porous medium. The governing equations which consists of a system of dimensional partial differential equations is applied with dimensionless parameter in order to attain non-dimensional partial differential equations. Later, the similarity transformation is performed in order to attain nonsimilar governing equations. Afterwards, the nonsimilar governing equations are solved numerically by using the Keller-Box method in Octave programme. The effect of porosity parameter is examined on separation time, velocity profile and skin friction of the unsteady flow. The results attained are presented in the form of table and graph.

Investigation of supersonic jet plumes using an improved two-equation turbulence model

NASA Technical Reports Server (NTRS)

Lakshmanan, B.; Abdol-Hamid, Khaled S.

1994-01-01

Supersonic jet plumes were studied using a two-equation turbulence model employing corrections for compressible dissipation and pressure-dilatation. A space-marching procedure based on an upwind numerical scheme was used to solve the governing equations and turbulence transport equations. The computed results indicate that two-equation models employing corrections for compressible dissipation and pressure-dilatation yield improved agreement with the experimental data. In addition, the numerical study demonstrates that the computed results are sensitive to the effect of grid refinement and insensitive to the type of velocity profiles used at the inflow boundary for the cases considered in the present study.

FINITE ELEMENT MODEL FOR TIDES AND CURRENTS WITH FIELD APPLICATIONS.

USGS Publications Warehouse

Walters, Roy A.

1988-01-01

A finite element model, based upon the shallow water equations, is used to calculate tidal amplitudes and currents for two field-scale test problems. Because tides are characterized by line spectra, the governing equations are subjected to harmonic decomposition. Thus the solution variables are the real and imaginary parts of the amplitude of sea level and velocity rather than a time series of these variables. The time series is recovered through synthesis. This scheme, coupled with a modified form of the governing equations, leads to high computational efficiency and freedom from excessive numerical noise. Two test-cases are presented. The first is a solution for eleven tidal constituents in the English Channel and southern North Sea, and three constituents are discussed. The second is an analysis of the frequency response and tidal harmonics for south San Francisco Bay.

Mathematical Model of Two Phase Flow in Natural Draft Wet-Cooling Tower Including Flue Gas Injection

NASA Astrophysics Data System (ADS)

Hyhlík, Tomáš

2016-03-01

The previously developed model of natural draft wet-cooling tower flow, heat and mass transfer is extended to be able to take into account the flow of supersaturated moist air. The two phase flow model is based on void fraction of gas phase which is included in the governing equations. Homogeneous equilibrium model, where the two phases are well mixed and have the same velocity, is used. The effect of flue gas injection is included into the developed mathematical model by using source terms in governing equations and by using momentum flux coefficient and kinetic energy flux coefficient. Heat and mass transfer in the fill zone is described by the system of ordinary differential equations, where the mass transfer is represented by measured fill Merkel number and heat transfer is calculated using prescribed Lewis factor.

Semi-analytical solutions of the Schnakenberg model of a reaction-diffusion cell with feedback

NASA Astrophysics Data System (ADS)

Al Noufaey, K. S.

2018-06-01

This paper considers the application of a semi-analytical method to the Schnakenberg model of a reaction-diffusion cell. The semi-analytical method is based on the Galerkin method which approximates the original governing partial differential equations as a system of ordinary differential equations. Steady-state curves, bifurcation diagrams and the region of parameter space in which Hopf bifurcations occur are presented for semi-analytical solutions and the numerical solution. The effect of feedback control, via altering various concentrations in the boundary reservoirs in response to concentrations in the cell centre, is examined. It is shown that increasing the magnitude of feedback leads to destabilization of the system, whereas decreasing this parameter to negative values of large magnitude stabilizes the system. The semi-analytical solutions agree well with numerical solutions of the governing equations.

A general method to determine the stability of compressible flows

NASA Technical Reports Server (NTRS)

Guenther, R. A.; Chang, I. D.

1982-01-01

Several problems were studied using two completely different approaches. The initial method was to use the standard linearized perturbation theory by finding the value of the individual small disturbance quantities based on the equations of motion. These were serially eliminated from the equations of motion to derive a single equation that governs the stability of fluid dynamic system. These equations could not be reduced unless the steady state variable depends only on one coordinate. The stability equation based on one dependent variable was found and was examined to determine the stability of a compressible swirling jet. The second method applied a Lagrangian approach to the problem. Since the equations developed were based on different assumptions, the condition of stability was compared only for the Rayleigh problem of a swirling flow, both examples reduce to the Rayleigh criterion. This technique allows including the viscous shear terms which is not possible in the first method. The same problem was then examined to see what effect shear has on stability.

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

NASA Astrophysics Data System (ADS)

Adem, Abdullahi Rashid; Moawad, Salah M.

2018-05-01

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

The Ffowcs Williams-Hawkings equation - Fifteen years of research

NASA Technical Reports Server (NTRS)

Farassat, F.

1986-01-01

The Ffowcs Williams-Hawkings equation governs the generation of sound in fluids in the presence of solid boundaries in motion. This equation is reviewed for situations where the linearization of the governing equations is allowed. In addition, research on the application of this equation to problems of aeroacoustic is briefly surveyed. Particular attention is given to the formulation of supersonic sources moving in uniform propeller-like motion.

Test particle propagation in magnetostatic turbulence. 2: The local approximation method

NASA Technical Reports Server (NTRS)

Klimas, A. J.; Sandri, G.; Scudder, J. D.; Howell, D. R.

1976-01-01

An approximation method for statistical mechanics is presented and applied to a class of problems which contains a test particle propagation problem. All of the available basic equations used in statistical mechanics are cast in the form of a single equation which is integrodifferential in time and which is then used as the starting point for the construction of the local approximation method. Simplification of the integrodifferential equation is achieved through approximation to the Laplace transform of its kernel. The approximation is valid near the origin in the Laplace space and is based on the assumption of small Laplace variable. No other small parameter is necessary for the construction of this approximation method. The n'th level of approximation is constructed formally, and the first five levels of approximation are calculated explicitly. It is shown that each level of approximation is governed by an inhomogeneous partial differential equation in time with time independent operator coefficients. The order in time of these partial differential equations is found to increase as n does. At n = 0 the most local first order partial differential equation which governs the Markovian limit is regained.

Helmholtz-Smoluchowski velocity for viscoelastic electroosmotic flows.

PubMed

Park, H M; Lee, W M

2008-01-15

Many biofluids such as blood and DNA solutions are viscoelastic and exhibit extraordinary flow behaviors, not existing in Newtonian fluids. Adopting appropriate constitutive equations these exotic flow behaviors can be modeled and predicted reasonably using various numerical methods. However, the governing equations for viscoelastic flows are not easily solvable, especially for electroosmotic flows where the streamwise velocity varies rapidly from zero at the wall to a nearly uniform velocity at the outside of the very thin electric double layer. In the present investigation, we have devised a simple method to find the volumetric flow rate of viscoelastic electroosmotic flows through microchannels. It is based on the concept of the Helmholtz-Smoluchowski velocity which is widely adopted in the electroosmotic flows of Newtonian fluids. It is shown that the Helmholtz-Smoluchowski velocity for viscoelastic fluids can be found by solving a simple cubic algebraic equation. The volumetric flow rate obtained using this Helmholtz-Smoluchowski velocity is found to be almost the same as that obtained by solving the governing partial differential equations for various viscoelastic fluids.

Soliton evolution and radiation loss for the sine-Gordon equation.

PubMed

Smyth, N F; Worthy, A L

1999-08-01

An approximate method for describing the evolution of solitonlike initial conditions to solitons for the sine-Gordon equation is developed. This method is based on using a solitonlike pulse with variable parameters in an averaged Lagrangian for the sine-Gordon equation. This averaged Lagrangian is then used to determine ordinary differential equations governing the evolution of the pulse parameters. The pulse evolves to a steady soliton by shedding dispersive radiation. The effect of this radiation is determined by examining the linearized sine-Gordon equation and loss terms are added to the variational equations derived from the averaged Lagrangian by using the momentum and energy conservation equations for the sine-Gordon equation. Solutions of the resulting approximate equations, which include loss, are found to be in good agreement with full numerical solutions of the sine-Gordon equation.

Control-Volume Analysis Of Thrust-Augmenting Ejectors

NASA Technical Reports Server (NTRS)

Drummond, Colin K.

1990-01-01

New method of analysis of transient flow in thrust-augmenting ejector based on control-volume formulation of governing equations. Considered as potential elements of propulsion subsystems of short-takeoff/vertical-landing airplanes.

Measurement-based perturbation theory and differential equation parameter estimation with applications to satellite gravimetry

NASA Astrophysics Data System (ADS)

Xu, Peiliang

2018-06-01

The numerical integration method has been routinely used by major institutions worldwide, for example, NASA Goddard Space Flight Center and German Research Center for Geosciences (GFZ), to produce global gravitational models from satellite tracking measurements of CHAMP and/or GRACE types. Such Earth's gravitational products have found widest possible multidisciplinary applications in Earth Sciences. The method is essentially implemented by solving the differential equations of the partial derivatives of the orbit of a satellite with respect to the unknown harmonic coefficients under the conditions of zero initial values. From the mathematical and statistical point of view, satellite gravimetry from satellite tracking is essentially the problem of estimating unknown parameters in the Newton's nonlinear differential equations from satellite tracking measurements. We prove that zero initial values for the partial derivatives are incorrect mathematically and not permitted physically. The numerical integration method, as currently implemented and used in mathematics and statistics, chemistry and physics, and satellite gravimetry, is groundless, mathematically and physically. Given the Newton's nonlinear governing differential equations of satellite motion with unknown equation parameters and unknown initial conditions, we develop three methods to derive new local solutions around a nominal reference orbit, which are linked to measurements to estimate the unknown corrections to approximate values of the unknown parameters and the unknown initial conditions. Bearing in mind that satellite orbits can now be tracked almost continuously at unprecedented accuracy, we propose the measurement-based perturbation theory and derive global uniformly convergent solutions to the Newton's nonlinear governing differential equations of satellite motion for the next generation of global gravitational models. Since the solutions are global uniformly convergent, theoretically speaking, they are able to extract smallest possible gravitational signals from modern and future satellite tracking measurements, leading to the production of global high-precision, high-resolution gravitational models. By directly turning the nonlinear differential equations of satellite motion into the nonlinear integral equations, and recognizing the fact that satellite orbits are measured with random errors, we further reformulate the links between satellite tracking measurements and the global uniformly convergent solutions to the Newton's governing differential equations as a condition adjustment model with unknown parameters, or equivalently, the weighted least squares estimation of unknown differential equation parameters with equality constraints, for the reconstruction of global high-precision, high-resolution gravitational models from modern (and future) satellite tracking measurements.

Numerical solutions of Navier-Stokes equations for a Butler wing

NASA Technical Reports Server (NTRS)

Abolhassani, J. S.; Tiwari, S. N.

1985-01-01

The flow field is simulated on the surface of a given delta wing (Butler wing) at zero incident in a uniform stream. The simulation is done by integrating a set of flow field equations. This set of equations governs the unsteady, viscous, compressible, heat conducting flow of an ideal gas. The equations are written in curvilinear coordinates so that the wing surface is represented accurately. These equations are solved by the finite difference method, and results obtained for high-speed freestream conditions are compared with theoretical and experimental results. In this study, the Navier-Stokes equations are solved numerically. These equations are unsteady, compressible, viscous, and three-dimensional without neglecting any terms. The time dependency of the governing equations allows the solution to progress naturally for an arbitrary initial initial guess to an asymptotic steady state, if one exists. The equations are transformed from physical coordinates to the computational coordinates, allowing the solution of the governing equations in a rectangular parallel-piped domain. The equations are solved by the MacCormack time-split technique which is vectorized and programmed to run on the CDC VPS 32 computer.

Development of linear projecting in studies of non-linear flow. Acoustic heating induced by non-periodic sound

NASA Astrophysics Data System (ADS)

Perelomova, Anna

2006-08-01

The equation of energy balance is subdivided into two dynamics equations, one describing evolution of the dominative sound, and the second one responsible for acoustic heating. The first one is the famous KZK equation, and the second one is a novel equation governing acoustic heating. The novel dynamic equation considers both periodic and non-periodic sound. Quasi-plane geometry of flow is supposed. Subdividing is provided on the base of specific links of every mode. Media with arbitrary thermic T(p,ρ) and caloric e(p,ρ) equations of state are considered. Individual roles of thermal conductivity and viscosity in the heating induced by aperiodic sound in the ideal gases and media different from ideal gases are discussed.

A paradigm for modeling and computation of gas dynamics

NASA Astrophysics Data System (ADS)

Xu, Kun; Liu, Chang

2017-02-01

In the continuum flow regime, the Navier-Stokes (NS) equations are usually used for the description of gas dynamics. On the other hand, the Boltzmann equation is applied for the rarefied flow. These two equations are based on distinguishable modeling scales for flow physics. Fortunately, due to the scale separation, i.e., the hydrodynamic and kinetic ones, both the Navier-Stokes equations and the Boltzmann equation are applicable in their respective domains. However, in real science and engineering applications, they may not have such a distinctive scale separation. For example, around a hypersonic flying vehicle, the flow physics at different regions may correspond to different regimes, where the local Knudsen number can be changed significantly in several orders of magnitude. With a variation of flow physics, theoretically a continuous governing equation from the kinetic Boltzmann modeling to the hydrodynamic Navier-Stokes dynamics should be used for its efficient description. However, due to the difficulties of a direct modeling of flow physics in the scale between the kinetic and hydrodynamic ones, there is basically no reliable theory or valid governing equations to cover the whole transition regime, except resolving flow physics always down to the mean free path scale, such as the direct Boltzmann solver and the Direct Simulation Monte Carlo (DSMC) method. In fact, it is an unresolved problem about the exact scale for the validity of the NS equations, especially in the small Reynolds number cases. The computational fluid dynamics (CFD) is usually based on the numerical solution of partial differential equations (PDEs), and it targets on the recovering of the exact solution of the PDEs as mesh size and time step converging to zero. This methodology can be hardly applied to solve the multiple scale problem efficiently because there is no such a complete PDE for flow physics through a continuous variation of scales. For the non-equilibrium flow study, the direct modeling methods, such as DSMC, particle in cell, and smooth particle hydrodynamics, play a dominant role to incorporate the flow physics into the algorithm construction directly. It is fully legitimate to combine the modeling and computation together without going through the process of constructing PDEs. In other words, the CFD research is not only to obtain the numerical solution of governing equations but to model flow dynamics as well. This methodology leads to the unified gas-kinetic scheme (UGKS) for flow simulation in all flow regimes. Based on UGKS, the boundary for the validation of the Navier-Stokes equations can be quantitatively evaluated. The combination of modeling and computation provides a paradigm for the description of multiscale transport process.

Role of Turbulent Prandtl Number on Heat Flux at Hypersonic Mach Numbers

NASA Technical Reports Server (NTRS)

Xiao, X.; Edwards, J. R.; Hassan, H. A.; Gaffney, R. L., Jr.

2007-01-01

A new turbulence model suited for calculating the turbulent Prandtl number as part of the solution is presented. The model is based on a set of two equations: one governing the variance of the enthalpy and the other governing its dissipation rate. These equations were derived from the exact energy equation and thus take into consideration compressibility and dissipation terms. The model is used to study two cases involving shock wave/boundary layer interaction at Mach 9.22 and Mach 5.0. In general, heat transfer prediction showed great improvement over traditional turbulence models where the turbulent Prandtl number is assumed constant. It is concluded that using a model that calculates the turbulent Prandtl number as part of the solution is the key to bridging the gap between theory and experiment for flows dominated by shock wave/boundary layer interactions.

Supersonic wing and wing-body shape optimization using an adjoint formulation

NASA Technical Reports Server (NTRS)

Reuther, James; Jameson, Antony

1995-01-01

This paper describes the implementation of optimization techniques based on control theory for wing and wing-body design of supersonic configurations. The work represents an extension of our earlier research in which control theory is used to devise a design procedure that significantly reduces the computational cost by employing an adjoint equation. In previous studies it was shown that control theory could be used toeviseransonic design methods for airfoils and wings in which the shape and the surrounding body-fitted mesh are both generated analytically, and the control is the mapping function. The method has also been implemented for both transonic potential flows and transonic flows governed by the Euler equations using an alternative formulation which employs numerically generated grids, so that it can treat more general configurations. Here results are presented for three-dimensional design cases subject to supersonic flows governed by the Euler equation.

Role of Turbulent Prandtl Number on Heat Flux at Hypersonic Mach Numbers

NASA Technical Reports Server (NTRS)

Gaffney, R. L., Jr.; Xiao, X.; Edwards, J. R.; Hassan, H. A.

2005-01-01

A new turbulence model suited for calculating the turbulent Prandtl number as part of the solution is presented. The model is based on a set of two equations: one governing the variance of the enthalpy and the other governing its dissipation rate. These equations were derived from the exact energy equation and thus take into consideration compressibility and dissipation terms. The model is used to study two cases involving shock wave/boundary layer interaction at Mach 9.22 and Mach 5.0. In general, heat transfer prediction showed great improvement over traditional turbulence models where the turbulent Prandtl number is assumed constant. It is concluded that using a model that calculates the turbulent Prandtl number as part of the solution is the key to bridging the gap between theory and experiment for flows dominated by shock wave/boundary layer interactions.

Two-dimensional integrating matrices on rectangular grids. [solving differential equations associated with rotating structures

NASA Technical Reports Server (NTRS)

Lakin, W. D.

1981-01-01

The use of integrating matrices in solving differential equations associated with rotating beam configurations is examined. In vibration problems, by expressing the equations of motion of the beam in matrix notation, utilizing the integrating matrix as an operator, and applying the boundary conditions, the spatial dependence is removed from the governing partial differential equations and the resulting ordinary differential equations can be cast into standard eigenvalue form. Integrating matrices are derived based on two dimensional rectangular grids with arbitrary grid spacings allowed in one direction. The derivation of higher dimensional integrating matrices is the initial step in the generalization of the integrating matrix methodology to vibration and stability problems involving plates and shells.

Nonlinear analysis of 0-3 polarized PLZT microplate based on the new modified couple stress theory

NASA Astrophysics Data System (ADS)

Wang, Liming; Zheng, Shijie

2018-02-01

In this study, based on the new modified couple stress theory, the size- dependent model for nonlinear bending analysis of a pure 0-3 polarized PLZT plate is developed for the first time. The equilibrium equations are derived from a variational formulation based on the potential energy principle and the new modified couple stress theory. The Galerkin method is adopted to derive the nonlinear algebraic equations from governing differential equations. And then the nonlinear algebraic equations are solved by using Newton-Raphson method. After simplification, the new model includes only a material length scale parameter. In addition, numerical examples are carried out to study the effect of material length scale parameter on the nonlinear bending of a simply supported pure 0-3 polarized PLZT plate subjected to light illumination and uniform distributed load. The results indicate the new model is able to capture the size effect and geometric nonlinearity.

Analysis of eccentric annular incompressible seals. II - Effects of eccentricity on rotordynamic coefficients

NASA Technical Reports Server (NTRS)

Nelson, C. C.; Nguyen, D. T.

1987-01-01

A new analysis procedure has been presented which solves for the flow variables of an annular pressure seal in which the rotor has a large static displacement (eccentricity) from the centered position. The present paper incorporates the solutions to investigate the effect of eccentricity on the rotordynamic coefficients. The analysis begins with a set of governing equations based on a turbulent bulk-flow model and Moody's friction factor equation. Perturbations of the flow variables yields a set of zeroth- and first-order equations. After integration of the zeroth-order equations, the resulting zeroth-order flow variables are used as input in the solution of the first-order equations. Further integration of the first order pressures yields the eccentric rotordynamic coefficients. The results from this procedure compare well with available experimental and theoretical data, with accuracy just as good or slightly better than the predictions based on a finite-element model.

The Approach to Equilibrium: Detailed Balance and the Master Equation

ERIC Educational Resources Information Center

Alexander, Millard H.; Hall, Gregory E.; Dagdigian, Paul J.

2011-01-01

The approach to the equilibrium (Boltzmann) distribution of populations of internal states of a molecule is governed by inelastic collisions in the gas phase and with surfaces. The set of differential equations governing the time evolution of the internal state populations is commonly called the master equation. An analytic solution to the master…

Nonlinear Viscoelastic Mechanics of Cross-linked Rubbers

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Leonov, Arkady I.; Gray, Hugh R. (Technical Monitor)

2002-01-01

The paper develops a general theory for finite rubber viscoelasticity, and specifies it in the form, convenient for solving problems important for rubber, tire and space industries. Based on the quasi-linear approach of non-equilibrium thermodynamics, a general nonlinear theory has been developed for arbitrary nonisothermal deformations of viscoelastic solids. In this theory, the constitutive equations are presented as the sum of known equilibrium (rubber elastic) and non-equilibrium (liquid polymer viscoelastic) terms. These equations are then simplified using several modeling arguments. Stability constraints for the proposed constitutive equations are also discussed. It is shown that only strong ellipticity criteria are applicable for assessing stability of the equations governing viscoelastic solids.

Modeling and vibration control of the flapping-wing robotic aircraft with output constraint

NASA Astrophysics Data System (ADS)

He, Wei; Mu, Xinxing; Chen, Yunan; He, Xiuyu; Yu, Yao

2018-06-01

In this paper, we propose the boundary control for undesired vibrations suppression with output constraint of the flapping-wing robotic aircraft (FWRA). We also present the dynamics of the flexible wing of FWRA with governing equations and boundary conditions, which are partial differential equations (PDEs) and ordinary differential equations (ODEs), respectively. An energy-based barrier Lyapunov function is introduced to analyze the system stability and prevent violation of output constraint. With the effect of the proposed boundary controller, distributed states of the system remain in the constrained spaces. Then the IBLF-based boundary controls are proposed to assess the stability of the FWRA in the presence of output constraint.

Effect of liquid droplets on turbulence in a round gaseous jet

NASA Technical Reports Server (NTRS)

Mostafa, A. A.; Elghobashi, S. E.

1986-01-01

The main objective of this investigation is to develop a two-equation turbulence model for dilute vaporizing sprays or in general for dispersed two-phase flows including the effects of phase changes. The model that accounts for the interaction between the two phases is based on rigorously derived equations for turbulence kinetic energy (K) and its dissipation rate epsilon of the carrier phase using the momentum equation of that phase. Closure is achieved by modeling the turbulent correlations, up to third order, in the equations of the mean motion, concentration of the vapor in the carrier phase, and the kinetic energy of turbulence and its dissipation rate for the carrier phase. The governing equations are presented in both the exact and the modeled formes. The governing equations are solved numerically using a finite-difference procedure to test the presented model for the flow of a turbulent axisymmetric gaseous jet laden with either evaporating liquid droplets or solid particles. The predictions include the distribution of the mean velocity, volume fractions of the different phases, concentration of the evaporated material in the carrier phase, turbulence intensity and shear stress of the carrier phase, droplet diameter distribution, and the jet spreading rate. The predictions are in good agreement with the experimental data.

Flight in low-level wind shear

NASA Technical Reports Server (NTRS)

Frost, W.

1983-01-01

Results of studies of wind shear hazard to aircraft operation are summarized. Existing wind shear profiles currently used in computer and flight simulator studies are reviewed. The governing equations of motion for an aircraft are derived incorporating the variable wind effects. Quantitative discussions of the effects of wind shear on aircraft performance are presented. These are followed by a review of mathematical solutions to both the linear and nonlinear forms of the governing equations. Solutions with and without control laws are presented. The application of detailed analysis to develop warning and detection systems based on Doppler radar measuring wind speed along the flight path is given. A number of flight path deterioration parameters are defined and evaluated. Comparison of computer-predicted flight paths with those measured in a manned flight simulator is made. Some proposed airborne and ground-based wind shear hazard warning and detection systems are reviewed. The advantages and disadvantages of both types of systems are discussed.

Structural vibration-based damage classification of delaminated smart composite laminates

NASA Astrophysics Data System (ADS)

Khan, Asif; Kim, Heung Soo; Sohn, Jung Woo

2018-03-01

Separation along the interfaces of layers (delamination) is a principal mode of failure in laminated composites and its detection is of prime importance for structural integrity of composite materials. In this work, structural vibration response is employed to detect and classify delaminations in piezo-bonded laminated composites. Improved layerwise theory and finite element method are adopted to develop the electromechanically coupled governing equation of a smart composite laminate with and without delaminations. Transient responses of the healthy and damaged structures are obtained through a surface bonded piezoelectric sensor by solving the governing equation in the time domain. Wavelet packet transform (WPT) and linear discriminant analysis (LDA) are employed to extract discriminative features from the structural vibration response of the healthy and delaminated structures. Dendrogram-based support vector machine (DSVM) is used to classify the discriminative features. The confusion matrix of the classification algorithm provided physically consistent results.

Growth, Quantitative Growth Analysis, and Applications of Graphene on γ-Al2O3 catalysts

PubMed Central

Park, Jaehyun; Lee, Joohwi; Choi, Jung-Hae; Hwang, Do Kyung; Song, Yong-Won

2015-01-01

The possibilities offered by catalytic γ-Al2O3 substrates are explored, and the mechanism governing graphene formation thereon is elucidated using both numerical simulations and experiments. The growth scheme offers metal-free synthesis at low temperature, grain-size customization, large-area uniformity of electrical properties, single-step preparation of graphene/dielectric structures, and readily detachable graphene. We quantify based on thermodynamic principles the activation energies associated with graphene nucleation/growth on γ-Al2O3, verifying the low physical and chemical barriers. Importantly, we derive a universal equation governing the adsorption-based synthesis of graphene over a wide range of temperatures in both catalytic and spontaneous growth regimes. Experimental results support the equation, highlighting the catalytic function of γ-Al2O3 at low temperatures. The synthesized graphene is manually incorporated as a ‘graphene sticker’ into an ultrafast mode-locked laser. PMID:26137994

Scaling and scale invariance of conservation laws in Reynolds transport theorem framework

NASA Astrophysics Data System (ADS)

Haltas, Ismail; Ulusoy, Suleyman

2015-07-01

Scale invariance is the case where the solution of a physical process at a specified time-space scale can be linearly related to the solution of the processes at another time-space scale. Recent studies investigated the scale invariance conditions of hydrodynamic processes by applying the one-parameter Lie scaling transformations to the governing equations of the processes. Scale invariance of a physical process is usually achieved under certain conditions on the scaling ratios of the variables and parameters involved in the process. The foundational axioms of hydrodynamics are the conservation laws, namely, conservation of mass, conservation of linear momentum, and conservation of energy from continuum mechanics. They are formulated using the Reynolds transport theorem. Conventionally, Reynolds transport theorem formulates the conservation equations in integral form. Yet, differential form of the conservation equations can also be derived for an infinitesimal control volume. In the formulation of the governing equation of a process, one or more than one of the conservation laws and, some times, a constitutive relation are combined together. Differential forms of the conservation equations are used in the governing partial differential equation of the processes. Therefore, differential conservation equations constitute the fundamentals of the governing equations of the hydrodynamic processes. Applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework instead of applying to the governing partial differential equations may lead to more fundamental conclusions on the scaling and scale invariance of the hydrodynamic processes. This study will investigate the scaling behavior and scale invariance conditions of the hydrodynamic processes by applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework.

A Multiscale Model for Virus Capsid Dynamics

PubMed Central

Chen, Changjun; Saxena, Rishu; Wei, Guo-Wei

2010-01-01

Viruses are infectious agents that can cause epidemics and pandemics. The understanding of virus formation, evolution, stability, and interaction with host cells is of great importance to the scientific community and public health. Typically, a virus complex in association with its aquatic environment poses a fabulous challenge to theoretical description and prediction. In this work, we propose a differential geometry-based multiscale paradigm to model complex biomolecule systems. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum domain of the fluid mechanical description of the aquatic environment from the microscopic discrete domain of the atomistic description of the biomolecule. A multiscale action functional is constructed as a unified framework to derive the governing equations for the dynamics of different scales. We show that the classical Navier-Stokes equation for the fluid dynamics and Newton's equation for the molecular dynamics can be derived from the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. PMID:20224756

Mixed finite-difference scheme for analysis of simply supported thick plates.

NASA Technical Reports Server (NTRS)

Noor, A. K.

1973-01-01

A mixed finite-difference scheme is presented for the stress and free vibration analysis of simply supported nonhomogeneous and layered orthotropic thick plates. The analytical formulation is based on the linear, three-dimensional theory of orthotropic elasticity and a Fourier approach is used to reduce the governing equations to six first-order ordinary differential equations in the thickness coordinate. The governing equations possess a symmetric coefficient matrix and are free of derivatives of the elastic characteristics of the plate. In the finite difference discretization two interlacing grids are used for the different fundamental unknowns in such a way as to reduce both the local discretization error and the bandwidth of the resulting finite-difference field equations. Numerical studies are presented for the effects of reducing the interior and boundary discretization errors and of mesh refinement on the accuracy and convergence of solutions. It is shown that the proposed scheme, in addition to a number of other advantages, leads to highly accurate results, even when a small number of finite difference intervals is used.

Creep rupture analysis of a beam resting on high temperature foundation

NASA Technical Reports Server (NTRS)

Gu, Randy J.; Cozzarelli, Francis A.

1988-01-01

A simplified uniaxial strain controlled creep damage law is deduced with the use of experimental observation from a more complex strain dependent law. This creep damage law correlates the creep damage, which is interpreted as the density variation in the material, directly with the accumulated creep strain. Based on the deduced uniaxial strain controlled creep damage law, a continuum mechanical creep rupture analysis is carried out for a beam resting on a high temperature elastic (Winkler) foundation. The analysis includes the determination of the nondimensional time for initial rupture, the propagation of the rupture front with the associated thinning of the beam, and the influence of creep damage on the deflection of the beam. Creep damage starts accumulating in the beam as soon as the load is applied, and a creep rupture front develops at and propagates from the point at which the creep damage first reaches its critical value. By introducing a series of fundamental assumptions within the framework of technical Euler-Bernoulli type beam theory, a governing set of integro-differential equations is derived in terms of the nondimensional bending moment and the deflection. These governing equations are subjected to a set of interface conditions at the propagating rupture front. A numerical technique is developed to solve the governing equations together with the interface equations, and the computed results are presented and discussed in detail.

Universal solution for the characteristic time and the degree of settlement in nonlinear soil consolidation scenarios. A deduction based on nondimensionalization

NASA Astrophysics Data System (ADS)

Alhama Manteca, Iván; García-Ros, Gonzalo; Alhama López, Francisco

2018-04-01

Using the mathematical-physical process of nondimensionalization of governing equations, the problem of nonlinear soil consolidation based on the Cornetti and Battaglio model removing some of the restrictive hypotheses assumed by these authors is studied for the search of the dimensionless groups that govern the characteristic time and the average degree of settlement. The derived groups, once verified by numerical simulations, allow the universal representation of the aforementioned unknowns for the wide range of properties of real soils.

Variational theorems for superimposed motions in elasticity, with application to beams

NASA Technical Reports Server (NTRS)

Doekmeci, M. C.

1976-01-01

Variational theorems are presented for a theory of small motions superimposed on large static deformations and governing equations for prestressed beams on the basis of 3-D theory of elastodynamics. First, the principle of virtual work is modified through Friedrichs's transformation so as to describe the initial stress problem of elastodynamics. Next, the modified principle together with a chosen displacement field is used to derive a set of 1-D macroscopic governing equations of prestressed beams. The resulting equations describe all the types of superimposed motions in elastic beams, and they include all the effects of transverse shear and normal strains, and the rotatory inertia. The instability of the governing equations is discussed briefly.

Numerical solution of equations governing longitudinal suspension line wave motion during the parachute unfurling process. Ph.D. Thesis - George Washington Univ., Washington, D. C.

NASA Technical Reports Server (NTRS)

Poole, L. R.

1973-01-01

Equations are presented which govern the dynamics of the lines-first parachute unfurling process, including wave motion in the parachute suspension lines. Techniques are developed for obtaining numerical solutions to the governing equations. Histories of tension at test data, and generally good agreement is observed. Errors in computed results are attributed to several areas of uncertainty, the most significant being a poorly defined boundary condition on the wave motion at the vehicle-suspension line boundary.

Probabilistic Simulation for Nanocomposite Characterization

NASA Technical Reports Server (NTRS)

Chamis, Christos C.; Coroneos, Rula M.

2007-01-01

A unique probabilistic theory is described to predict the properties of nanocomposites. The simulation is based on composite micromechanics with progressive substructuring down to a nanoscale slice of a nanofiber where all the governing equations are formulated. These equations have been programmed in a computer code. That computer code is used to simulate uniaxial strengths properties of a mononanofiber laminate. The results are presented graphically and discussed with respect to their practical significance. These results show smooth distributions.

Role of Turbulent Prandtl Number on Heat Flux at Hypersonic Mach Number

NASA Technical Reports Server (NTRS)

Xiao, X.; Edwards, J. R.; Hassan, H. A.

2004-01-01

Present simulation of turbulent flows involving shock wave/boundary layer interaction invariably overestimates heat flux by almost a factor of two. One possible reason for such a performance is a result of the fact that the turbulence models employed make use of Morkovin's hypothesis. This hypothesis is valid for non-hypersonic Mach numbers and moderate rates of heat transfer. At hypersonic Mach numbers, high rates of heat transfer exist in regions where shock wave/boundary layer interactions are important. As a result, one should not expect traditional turbulence models to yield accurate results. The goal of this investigation is to explore the role of a variable Prandtl number formulation in predicting heat flux in flows dominated by strong shock wave/boundary layer interactions. The intended applications involve external flows in the absence of combustion such as those encountered in supersonic inlets. This can be achieved by adding equations for the temperature variance and its dissipation rate. Such equations can be derived from the exact Navier-Stokes equations. Traditionally, modeled equations are based on the low speed energy equation where the pressure gradient term and the term responsible for energy dissipation are ignored. It is clear that such assumptions are not valid for hypersonic flows. The approach used here is based on the procedure used in deriving the k-zeta model, in which the exact equations that governed k, the variance of velocity, and zeta, the variance of vorticity, were derived and modeled. For the variable turbulent Prandtl number, the exact equations that govern the temperature variance and its dissipation rate are derived and modeled term by term. The resulting set of equations are free of damping and wall functions and are coordinate-system independent. Moreover, modeled correlations are tensorially consistent and invariant under Galilean transformation. The final set of equations will be given in the paper.

On order and chaos in the mergers of galaxies

NASA Astrophysics Data System (ADS)

Vandervoort, Peter O.

2018-03-01

This paper describes a low-dimensional model of the merger of two galaxies. The governing equations are the complete sets of moment equations of the first and second orders derived from the collisionless Boltzmann equations representing the galaxies. The moment equations reduce to an equation governing the relative motion of the galaxies, tensor virial equations, and equations governing the kinetic energy tensors. We represent the galaxies as heterogeneous ellipsoids with Gaussian stratifications of their densities, and we represent the mean stellar motions in terms of velocity fields that sustain those densities consistently with the equation of continuity. We reduce and solve the governing equations for a head-on encounter of a dwarf galaxy with a giant galaxy. That reduction includes the effect of dynamical friction on the relative motion of the galaxies. Our criterion for chaotic behaviour is sensitivity of the motion to small changes in the initial conditions. In a survey of encounters and mergers of a dwarf galaxy with a giant galaxy, chaotic behaviour arises mainly in non-linear oscillations of the dwarf galaxy. The encounter disrupts the dwarf, excites chaotic oscillations of the dwarf, or excites regular oscillations. Dynamical friction can drive a merger to completion within a Hubble time only if the dwarf is sufficiently massive. The survey of encounters and mergers is the basis for a simple model of the evolution of a `Local Group' consisting of a giant galaxy and a population of dwarf galaxies bound to the giant as satellites on radial orbits.

Direct numerical simulations of fluid flow, heat transfer and phase changes

NASA Technical Reports Server (NTRS)

Juric, D.; Tryggvason, G.; Han, J.

1997-01-01

Direct numerical simulations of fluid flow, heat transfer, and phase changes are presented. The simulations are made possible by a recently developed finite difference/front tracking method based on the one-field formulation of the governing equations where a single set of conservation equations is written for all the phases involved. The conservation equations are solved on a fixed rectangular grid, but the phase boundaries are kept sharp by tracking them explicitly by a moving grid of lower dimension. The method is discussed and applications to boiling heat transfer and the solidification of drops colliding with a wall are shown.

Discrete Kalman filtering equations of second-order form for control-structure interaction simulations

NASA Technical Reports Server (NTRS)

Park, K. C.; Alvin, K. F.; Belvin, W. Keith

1991-01-01

A second-order form of discrete Kalman filtering equations is proposed as a candidate state estimator for efficient simulations of control-structure interactions in coupled physical coordinate configurations as opposed to decoupled modal coordinates. The resulting matrix equation of the present state estimator consists of the same symmetric, sparse N x N coupled matrices of the governing structural dynamics equations as opposed to unsymmetric 2N x 2N state space-based estimators. Thus, in addition to substantial computational efficiency improvement, the present estimator can be applied to control-structure design optimization for which the physical coordinates associated with the mass, damping and stiffness matrices of the structure are needed instead of modal coordinates.

Vibration analysis of a rotating functionally graded tapered microbeam based on the modified couple stress theory by DQEM

NASA Astrophysics Data System (ADS)

Ghadiri, Majid; Shafiei, Navvab; Alireza Mousavi, S.

2016-09-01

Due to having difficulty in solving governing nonlinear differential equations of a non-uniform microbeam, a few numbers of authors have studied such fields. In the present study, for the first time, the size-dependent vibration behavior of a rotating functionally graded (FG) tapered microbeam based on the modified couple stress theory is investigated using differential quadrature element method (DQEM). It is assumed that physical and mechanical properties of the FG microbeam are varying along the thickness that will be defined as a power law equation. The governing equations are determined using Hamilton's principle, and DQEM is presented to obtain the results for cantilever and propped cantilever boundary conditions. The accuracy and validity of the results are shown in several numerical examples. In order to display the influence of size on the first two natural frequencies and consequently changing of some important microbeam parameters such as material length scale, rate of cross section, angular velocity and gradient index of the FG material, several diagrams and tables are represented. The results of this article can be used in designing and optimizing elastic and rotary-type micro-electro-mechanical systems like micro-motors and micro-robots including rotating parts.

Computational physical oceanography -- A comprehensive approach based on generalized CFD/grid techniques for planetary scale simulations of oceanic flows. Final report, September 1, 1995--August 31, 1996

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

Beddhu, M.; Jiang, M.Y.; Whitfield, D.L.

The original intention for this work was to impart the technology that was developed in the field of computational aeronautics to the field of computational physical oceanography. This technology transfer involved grid generation techniques and solution procedures to solve the governing equations over the grids thus generated. Specifically, boundary fitting non-orthogonal grids would be generated over a sphere taking into account the topography of the ocean floor and the topography of the continents. The solution methodology to be employed involved the application of an upwind, finite volume discretization procedure that uses higher order numerical fluxes at the cell faces tomore » discretize the governing equations and an implicit Newton relaxation technique to solve the discretized equations. This report summarizes the efforts put forth during the past three years to achieve these goals and indicates the future direction of this work as it is still an ongoing effort.« less

Fractional Brownian motion and motion governed by the fractional Langevin equation in confined geometries.

PubMed

Jeon, Jae-Hyung; Metzler, Ralf

2010-02-01

Motivated by subdiffusive motion of biomolecules observed in living cells, we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and restricted to a finite domain. We investigate by analytic calculations and simulations how time-averaged observables (e.g., the time-averaged mean-squared displacement and displacement correlation) are affected by spatial confinement and dimensionality. In particular, we study the degree of weak ergodicity breaking and scatter between different single trajectories for this confined motion in the subdiffusive domain. The general trend is that deviations from ergodicity are decreased with decreasing size of the movement volume and with increasing dimensionality. We define the displacement correlation function and find that this quantity shows distinct features for fractional Brownian motion, fractional Langevin equation, and continuous time subdiffusion, such that it appears an efficient measure to distinguish these different processes based on single-particle trajectory data.

Radiation boundary condition and anisotropy correction for finite difference solutions of the Helmholtz equation

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.; Webb, Jay C.

1994-01-01

In this paper finite-difference solutions of the Helmholtz equation in an open domain are considered. By using a second-order central difference scheme and the Bayliss-Turkel radiation boundary condition, reasonably accurate solutions can be obtained when the number of grid points per acoustic wavelength used is large. However, when a smaller number of grid points per wavelength is used excessive reflections occur which tend to overwhelm the computed solutions. Excessive reflections are due to the incompability between the governing finite difference equation and the Bayliss-Turkel radiation boundary condition. The Bayliss-Turkel radiation boundary condition was developed from the asymptotic solution of the partial differential equation. To obtain compatibility, the radiation boundary condition should be constructed from the asymptotic solution of the finite difference equation instead. Examples are provided using the improved radiation boundary condition based on the asymptotic solution of the governing finite difference equation. The computed results are free of reflections even when only five grid points per wavelength are used. The improved radiation boundary condition has also been tested for problems with complex acoustic sources and sources embedded in a uniform mean flow. The present method of developing a radiation boundary condition is also applicable to higher order finite difference schemes. In all these cases no reflected waves could be detected. The use of finite difference approximation inevita bly introduces anisotropy into the governing field equation. The effect of anisotropy is to distort the directional distribution of the amplitude and phase of the computed solution. It can be quite large when the number of grid points per wavelength used in the computation is small. A way to correct this effect is proposed. The correction factor developed from the asymptotic solutions is source independent and, hence, can be determined once and for all. The effectiveness of the correction factor in providing improvements to the computed solution is demonstrated in this paper.

Textbook Multigrid Efficiency for Computational Fluid Dynamics Simulations

NASA Technical Reports Server (NTRS)

Brandt, Achi; Thomas, James L.; Diskin, Boris

2001-01-01

Considerable progress over the past thirty years has been made in the development of large-scale computational fluid dynamics (CFD) solvers for the Euler and Navier-Stokes equations. Computations are used routinely to design the cruise shapes of transport aircraft through complex-geometry simulations involving the solution of 25-100 million equations; in this arena the number of wind-tunnel tests for a new design has been substantially reduced. However, simulations of the entire flight envelope of the vehicle, including maximum lift, buffet onset, flutter, and control effectiveness have not been as successful in eliminating the reliance on wind-tunnel testing. These simulations involve unsteady flows with more separation and stronger shock waves than at cruise. The main reasons limiting further inroads of CFD into the design process are: (1) the reliability of turbulence models; and (2) the time and expense of the numerical simulation. Because of the prohibitive resolution requirements of direct simulations at high Reynolds numbers, transition and turbulence modeling is expected to remain an issue for the near term. The focus of this paper addresses the latter problem by attempting to attain optimal efficiencies in solving the governing equations. Typically current CFD codes based on the use of multigrid acceleration techniques and multistage Runge-Kutta time-stepping schemes are able to converge lift and drag values for cruise configurations within approximately 1000 residual evaluations. An optimally convergent method is defined as having textbook multigrid efficiency (TME), meaning the solutions to the governing system of equations are attained in a computational work which is a small (less than 10) multiple of the operation count in the discretized system of equations (residual equations). In this paper, a distributed relaxation approach to achieving TME for Reynolds-averaged Navier-Stokes (RNAS) equations are discussed along with the foundations that form the basis of this approach. Because the governing equations are a set of coupled nonlinear conservation equations with discontinuities (shocks, slip lines, etc.) and singularities (flow- or grid-induced), the difficulties are many. This paper summarizes recent progress towards the attainment of TME in basic CFD simulations.

Toward Better Modeling of Supercritical Turbulent Mixing

NASA Technical Reports Server (NTRS)

Selle, Laurent; Okongo'o, Nora; Bellan, Josette; Harstad, Kenneth

2008-01-01

study was done as part of an effort to develop computational models representing turbulent mixing under thermodynamic supercritical (here, high pressure) conditions. The question was whether the large-eddy simulation (LES) approach, developed previously for atmospheric-pressure compressible-perfect-gas and incompressible flows, can be extended to real-gas non-ideal (including supercritical) fluid mixtures. [In LES, the governing equations are approximated such that the flow field is spatially filtered and subgrid-scale (SGS) phenomena are represented by models.] The study included analyses of results from direct numerical simulation (DNS) of several such mixing layers based on the Navier-Stokes, total-energy, and conservation- of-chemical-species governing equations. Comparison of LES and DNS results revealed the need to augment the atmospheric- pressure LES equations with additional SGS momentum and energy terms. These new terms are the direct result of high-density-gradient-magnitude regions found in the DNS and observed experimentally under fully turbulent flow conditions. A model has been derived for the new term in the momentum equation and was found to perform well at small filter size but to deteriorate with increasing filter size. Several alternative models were derived for the new SGS term in the energy equation that would need further investigations to determine if they are too computationally intensive in LES.

Analysis of Three-Dimensional, Nonlinear Development of Wave-Like Structure in a Compressible Round Jet

NASA Technical Reports Server (NTRS)

Dahl, Milo D.; Mankbadi, Reda R.

2002-01-01

An analysis of the nonlinear development of the large-scale structures or instability waves in compressible round jets was conducted using the integral energy method. The equations of motion were decomposed into two sets of equations; one set governing the mean flow motion and the other set governing the large-scale structure motion. The equations in each set were then combined to derive kinetic energy equations that were integrated in the radial direction across the jet after the boundary-layer approximations were applied. Following the application of further assumptions regarding the radial shape of the mean flow and the large structures, equations were derived that govern the nonlinear, streamwise development of the large structures. Using numerically generated mean flows, calculations show the energy exchanges and the effects of the initial amplitude on the coherent structure development in the jet.

Numerical Modeling of a Vortex Stabilized Arcjet. Ph.D. Thesis, 1991 Final Report

NASA Technical Reports Server (NTRS)

Pawlas, Gary E.

1992-01-01

Arcjet thrusters are being actively considered for use in Earth orbit maneuvering applications. Experimental studies are currently the chief means of determining an optimal thruster configuration. Earlier numerical studies have failed to include all of the effects found in typical arcjets including complex geometries, viscosity, and swirling flow. Arcjet geometries are large area ratio converging nozzles with centerbodies in the subsonic portion of the nozzle. The nozzle walls serve as the anode while the centerbody functions as the cathode. Viscous effects are important because the Reynolds number, based on the throat radius, is typically less than 1,000. Experimental studies have shown that a swirl or circumferential velocity component stabilizes a constricted arc. This dissertation describes the equations governing flow through a constricted arcjet thruster. An assumption that the flowfield is in local thermodynamic equilibrium leads to a single fluid plasma temperature model. An order of magnitude analysis reveals the governing fluid mechanics equations are uncoupled from the electromagnetic field equations. A numerical method is developed to solve the governing fluid mechanics equations, the Thin Layer Navier-Stokes equations. A coordinate transformation is employed in deriving the governing equations to simplify the application of boundary conditions in complex geometries. An axisymmetric formulation is employed to include the swirl velocity component as well as the axial and radial velocity components. The numerical method is an implicit finite-volume technique and allows for large time steps to reach a converged steady-state solution. The inviscid fluxes are flux-split, and Gauss-Seidel line relaxation is used to accelerate convergence. Converging-diverging nozzles with exit-to-throat area ratios up to 100:1 and annular nozzles were examined. Quantities examined included Mach number and static wall pressure distributions, and oblique shock structures. As the level of swirl and viscosity in the flowfield increased the mass flow rate and thrust decreased. The technique was used to predict the flow through a typical arcjet thruster geometry. Results indicate swirl and viscosity play an important role in the complex geometry of an arcjet.

Numerical modeling of a vortex stabilized arcjet

NASA Astrophysics Data System (ADS)

Pawlas, Gary E.

1992-11-01

Arcjet thrusters are being actively considered for use in Earth orbit maneuvering applications. Experimental studies are currently the chief means of determining an optimal thruster configuration. Earlier numerical studies have failed to include all of the effects found in typical arcjets including complex geometries, viscosity, and swirling flow. Arcjet geometries are large area ratio converging nozzles with centerbodies in the subsonic portion of the nozzle. The nozzle walls serve as the anode while the centerbody functions as the cathode. Viscous effects are important because the Reynolds number, based on the throat radius, is typically less than 1,000. Experimental studies have shown that a swirl or circumferential velocity component stabilizes a constricted arc. This dissertation describes the equations governing flow through a constricted arcjet thruster. An assumption that the flowfield is in local thermodynamic equilibrium leads to a single fluid plasma temperature model. An order of magnitude analysis reveals the governing fluid mechanics equations are uncoupled from the electromagnetic field equations. A numerical method is developed to solve the governing fluid mechanics equations, the Thin Layer Navier-Stokes equations. A coordinate transformation is employed in deriving the governing equations to simplify the application of boundary conditions in complex geometries. An axisymmetric formulation is employed to include the swirl velocity component as well as the axial and radial velocity components. The numerical method is an implicit finite-volume technique and allows for large time steps to reach a converged steady-state solution. The inviscid fluxes are flux-split, and Gauss-Seidel line relaxation is used to accelerate convergence. Converging-diverging nozzles with exit-to-throat area ratios up to 100:1 and annular nozzles were examined. Quantities examined included Mach number and static wall pressure distributions, and oblique shock structures. As the level of swirl and viscosity in the flowfield increased the mass flow rate and thrust decreased.

Saturation behavior: a general relationship described by a simple second-order differential equation.

PubMed

Kepner, Gordon R

2010-04-13

The numerous natural phenomena that exhibit saturation behavior, e.g., ligand binding and enzyme kinetics, have been approached, to date, via empirical and particular analyses. This paper presents a mechanism-free, and assumption-free, second-order differential equation, designed only to describe a typical relationship between the variables governing these phenomena. It develops a mathematical model for this relation, based solely on the analysis of the typical experimental data plot and its saturation characteristics. Its utility complements the traditional empirical approaches. For the general saturation curve, described in terms of its independent (x) and dependent (y) variables, a second-order differential equation is obtained that applies to any saturation phenomena. It shows that the driving factor for the basic saturation behavior is the probability of the interactive site being free, which is described quantitatively. Solving the equation relates the variables in terms of the two empirical constants common to all these phenomena, the initial slope of the data plot and the limiting value at saturation. A first-order differential equation for the slope emerged that led to the concept of the effective binding rate at the active site and its dependence on the calculable probability the interactive site is free. These results are illustrated using specific cases, including ligand binding and enzyme kinetics. This leads to a revised understanding of how to interpret the empirical constants, in terms of the variables pertinent to the phenomenon under study. The second-order differential equation revealed the basic underlying relations that describe these saturation phenomena, and the basic mathematical properties of the standard experimental data plot. It was shown how to integrate this differential equation, and define the common basic properties of these phenomena. The results regarding the importance of the slope and the new perspectives on the empirical constants governing the behavior of these phenomena led to an alternative perspective on saturation behavior kinetics. Their essential commonality was revealed by this analysis, based on the second-order differential equation.

Data-driven discovery of partial differential equations.

PubMed

Rudy, Samuel H; Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan

2017-04-01

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg-de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable.

Finite elements and finite differences for transonic flow calculations

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Murman, E. M.; Wellford, L. C.

1978-01-01

The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.

Variable viscosity on unsteady dissipative Carreau fluid over a truncated cone filled with titanium alloy nanoparticles

NASA Astrophysics Data System (ADS)

Raju, C. S. K.; Sekhar, K. R.; Ibrahim, S. M.; Lorenzini, G.; Viswanatha Reddy, G.; Lorenzini, E.

2017-05-01

In this study, we proposed a theoretical investigation on the temperature-dependent viscosity effect on magnetohydrodynamic dissipative nanofluid over a truncated cone with heat source/sink. The involving set of nonlinear partial differential equations is transforming to set of nonlinear ordinary differential equations by using self-similarity solutions. The transformed governing equations are solved numerically using Runge-Kutta-based Newton's technique. The effects of various dimensionless parameters on the skin friction coefficient and the local Nusselt number profiles are discussed and presented with the support of graphs. We also obtained the validation of the current solutions with existing solution under some special cases. The water-based titanium alloy has a lesser friction factor coefficient as compared with kerosene-based titanium alloy, whereas the rate of heat transfer is higher in water-based titanium alloy compared with kerosene-based titanium alloy. From this we can highlight that depending on the industrial needs cooling/heating chooses the water- or kerosene-based titanium alloys.

A two-phase model of plantar tissue: a step toward prediction of diabetic foot ulceration.

PubMed

Sciumè, G; Boso, D P; Gray, W G; Cobelli, C; Schrefler, B A

2014-11-01

A new computational model, based on the thermodynamically constrained averaging theory, has been recently proposed to predict tumor initiation and proliferation. A similar mathematical approach is proposed here as an aid in diabetic ulcer prevention. The common aspects at the continuum level are the macroscopic balance equations governing the flow of the fluid phase, diffusion of chemical species, tissue mechanics, and some of the constitutive equations. The soft plantar tissue is modeled as a two-phase system: a solid phase consisting of the tissue cells and their extracellular matrix, and a fluid one (interstitial fluid and dissolved chemical species). The solid phase may become necrotic depending on the stress level and on the oxygen availability in the tissue. Actually, in diabetic patients, peripheral vascular disease impacts tissue necrosis; this is considered in the model via the introduction of an effective diffusion coefficient that governs transport of nutrients within the microvasculature. The governing equations of the mathematical model are discretized in space by the finite element method and in time domain using the θ-Wilson Method. While the full mathematical model is developed in this paper, the example is limited to the simulation of several gait cycles of a healthy foot. Copyright © 2014 John Wiley & Sons, Ltd.

An Analytical Comparison of the Acoustic Analogy and Kirchhoff Formulation for Moving Surfaces

NASA Technical Reports Server (NTRS)

Brentner, Kenneth S.; Farassat, F.

1997-01-01

The Lighthill acoustic analogy, as embodied in the Ffowcs Williams-Hawkings (FW-H) equation, is compared with the Kirchhoff formulation for moving surfaces. A comparison of the two governing equations reveals that the main Kirchhoff advantage (namely nonlinear flow effects are included in the surface integration) is also available to the FW-H method if the integration surface used in the FW-H equation is not assumed impenetrable. The FW-H equation is analytically superior for aeroacoustics because it is based upon the conservation laws of fluid mechanics rather than the wave equation. This means that the FW-H equation is valid even if the integration surface is in the nonlinear region. This is demonstrated numerically in the paper. The Kirchhoff approach can lead to substantial errors if the integration surface is not positioned in the linear region. These errors may be hard to identify. Finally, new metrics based on the Sobolev norm are introduced which may be used to compare input data for both quadrupole noise calculations and Kirchhoff noise predictions.

Calculation of Water Entry Problem for Free-falling Bodies Using a Developed Cartesian Cut Cell Mesh

NASA Astrophysics Data System (ADS)

Wenhua, Wang; Yanying, Wang

2010-05-01

This paper describes the development of free surface capturing method on Cartesian cut cell mesh to water entry problem for free-falling bodies with body-fluid interaction. The incompressible Euler equations for a variable density fluid system are presented as governing equations and the free surface is treated as a contact discontinuity by using free surface capturing method. In order to be convenient for dealing with the problem with moving body boundary, the Cartesian cut cell technique is adopted for generating the boundary-fitted mesh around body edge by cutting solid regions out of a background Cartesian mesh. Based on this mesh system, governing equations are discretized by finite volume method, and at each cell edge inviscid flux is evaluated by means of Roe's approximate Riemann solver. Furthermore, for unsteady calculation in time domain, a time accurate solution is achieved by a dual time-stepping technique with artificial compressibility method. For the body-fluid interaction, the projection method of momentum equations and exact Riemann solution are applied in the calculation of fluid pressure on the solid boundary. Finally, the method is validated by test case of water entry for free-falling bodies.

Scalar/Vector potential formulation for compressible viscous unsteady flows

NASA Technical Reports Server (NTRS)

Morino, L.

1985-01-01

A scalar/vector potential formulation for unsteady viscous compressible flows is presented. The scalar/vector potential formulation is based on the classical Helmholtz decomposition of any vector field into the sum of an irrotational and a solenoidal field. The formulation is derived from fundamental principles of mechanics and thermodynamics. The governing equations for the scalar potential and vector potential are obtained, without restrictive assumptions on either the equation of state or the constitutive relations or the stress tensor and the heat flux vector.

Blood flow problem in the presence of magnetic particles through a circular cylinder using Caputo-Fabrizio fractional derivative

NASA Astrophysics Data System (ADS)

Uddin, Salah; Mohamad, Mahathir; Khalid, Kamil; Abdulhammed, Mohammed; Saifullah Rusiman, Mohd; Che – Him, Norziha; Roslan, Rozaini

2018-04-01

In this paper, the flow of blood mixed with magnetic particles subjected to uniform transverse magnetic field and pressure gradient in an axisymmetric circular cylinder is studied by using a new trend of fractional derivative without singular kernel. The governing equations are fractional partial differential equations derived based on the Caputo-Fabrizio time-fractional derivatives NFDt. The current result agrees considerably well with that of the previous Caputo fractional derivatives UFDt.

Three-dimensional marginal separation

NASA Technical Reports Server (NTRS)

Duck, Peter W.

1988-01-01

The three dimensional marginal separation of a boundary layer along a line of symmetry is considered. The key equation governing the displacement function is derived, and found to be a nonlinear integral equation in two space variables. This is solved iteratively using a pseudo-spectral approach, based partly in double Fourier space, and partly in physical space. Qualitatively, the results are similar to previously reported two dimensional results (which are also computed to test the accuracy of the numerical scheme); however quantitatively the three dimensional results are much different.

Probabilistic Simulation for Nanocomposite Fracture

NASA Technical Reports Server (NTRS)

Chamis, Christos C.

2010-01-01

A unique probabilistic theory is described to predict the uniaxial strengths and fracture properties of nanocomposites. The simulation is based on composite micromechanics with progressive substructuring down to a nanoscale slice of a nanofiber where all the governing equations are formulated. These equations have been programmed in a computer code. That computer code is used to simulate uniaxial strengths and fracture of a nanofiber laminate. The results are presented graphically and discussed with respect to their practical significance. These results show smooth distributions from low probability to high.

A MATHEMATICAL MODEL FOR CALCULATING ELECTRICAL CONDITIONS IN WIRE-DUCT ELECTROSTATIC PRECIPITATION DEVICES

EPA Science Inventory

The article reports the development of a new method of calculating electrical conditions in wire-duct electrostatic precipitation devices. The method, based on a numerical solution to the governing differential equations under a suitable choice of boundary conditions, accounts fo...

Thermal Marangoni convection in two-phase flow of dusty Casson fluid

NASA Astrophysics Data System (ADS)

Mahanthesh, B.; Gireesha, B. J.

2018-03-01

This paper deals with the thermal Marangoni convection effects in magneto-Casson liquid flow through suspension of dust particles. The transpiration cooling aspect is accounted. The surface tension is assumed to be fluctuating linearly with temperature. The fluid and dust particle's temperature of the interface is chosen as a quadratic function of interface arc length. The governing problem is modelled by conservation laws of mass, momentum and energy for fluid and dust particle phase. Stretching transformation technique is utilized to form ordinary differential equations from the partial differential equations. Later, the numerical solutions based on Runge-Kutta-Fehlberg method are established. The momentum and heat transport distributions are focused on the outcome of distinct governing parameters. The results of Nusselt number is also presented and discussed. It is established that the heat transfer rate is higher in the case of dusty non-Newtonian fluid than dusty Newtonian fluid. The rate of heat transfer can be enhanced by suspending dust particles in a base liquid.

The Equations of Oceanic Motions

NASA Astrophysics Data System (ADS)

Müller, Peter

2006-10-01

Modeling and prediction of oceanographic phenomena and climate is based on the integration of dynamic equations. The Equations of Oceanic Motions derives and systematically classifies the most common dynamic equations used in physical oceanography, from large scale thermohaline circulations to those governing small scale motions and turbulence. After establishing the basic dynamical equations that describe all oceanic motions, M|ller then derives approximate equations, emphasizing the assumptions made and physical processes eliminated. He distinguishes between geometric, thermodynamic and dynamic approximations and between the acoustic, gravity, vortical and temperature-salinity modes of motion. Basic concepts and formulae of equilibrium thermodynamics, vector and tensor calculus, curvilinear coordinate systems, and the kinematics of fluid motion and wave propagation are covered in appendices. Providing the basic theoretical background for graduate students and researchers of physical oceanography and climate science, this book will serve as both a comprehensive text and an essential reference.

A thermodynamic equation of jamming

NASA Astrophysics Data System (ADS)

Lu, Kevin; Pirouz Kavehpour, H.

2008-03-01

Materials ranging from sand to fire-retardant to toothpaste are considered fragile, able to exhibit both solid and fluid-like properties across the jamming transition. Guided by granular flow experiments, our equation of jammed states is path-dependent, definable at different athermal equilibrium states. The non-equilibrium thermodynamics based on a structural temperature incorporate physical ageing to address the non-exponential, non-Arrhenious relaxation of granular flows. In short, jamming is simply viewed as a thermodynamic transition that occurs to preserve a positive configurational entropy above absolute zero. Without any free parameters, the proposed equation-of-state governs the mechanism of shear-banding and the associated features of shear-softening and thickness-invariance.

Chaotic Motion of Relativistic Electrons Driven by Whistler Waves

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Telnikhin, A. A.; Kronberg, Tatiana K.

2007-01-01

Canonical equations governing an electron motion in electromagnetic field of the whistler mode waves propagating along the direction of an ambient magnetic field are derived. The physical processes on which the equations of motion are based .are identified. It is shown that relativistic electrons interacting with these fields demonstrate chaotic motion, which is accompanied by the particle stochastic heating and significant pitch angle diffusion. Evolution of distribution functions is described by the Fokker-Planck-Kolmogorov equations. It is shown that the whistler mode waves could provide a viable mechanism for stochastic energization of electrons with energies up to 50 MeV in the Jovian magnetosphere.

The stagnation-point flow towards a shrinking sheet with homogeneous - heterogeneous reactions effects: A stability analysis

NASA Astrophysics Data System (ADS)

Ismail, Nurul Syuhada; Arifin, Norihan Md.; Bachok, Norfifah; Mahiddin, Norhasimah

2017-01-01

A numerical study is performed to evaluate the problem of stagnation - point flow towards a shrinking sheet with homogeneous - heterogeneous reaction effects. By using non-similar transformation, the governing equations be able to reduced to an ordinary differential equation. Then, results of the equations can be obtained numerically by shooting method with maple implementation. Based on the numerical results obtained, the velocity ratio parameter λ< 0, the dual solutions do exist. Then, the stability analysis is carried out to determine which solution is more stable between both of the solutions by bvp4c solver in Matlab.

Empirical prediction of peak pressure levels in anthropogenic impulsive noise. Part I: Airgun arrays signals.

PubMed

Galindo-Romero, Marta; Lippert, Tristan; Gavrilov, Alexander

2015-12-01

This paper presents an empirical linear equation to predict peak pressure level of anthropogenic impulsive signals based on its correlation with the sound exposure level. The regression coefficients are shown to be weakly dependent on the environmental characteristics but governed by the source type and parameters. The equation can be applied to values of the sound exposure level predicted with a numerical model, which provides a significant improvement in the prediction of the peak pressure level. Part I presents the analysis for airgun arrays signals, and Part II considers the application of the empirical equation to offshore impact piling noise.

A fully vectorized numerical solution of the incompressible Navier-Stokes equations. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Patel, N.

1983-01-01

A vectorizable algorithm is presented for the implicit finite difference solution of the incompressible Navier-Stokes equations in general curvilinear coordinates. The unsteady Reynolds averaged Navier-Stokes equations solved are in two dimension and non-conservative primitive variable form. A two-layer algebraic eddy viscosity turbulence model is used to incorporate the effects of turbulence. Two momentum equations and a Poisson pressure equation, which is obtained by taking the divergence of the momentum equations and satisfying the continuity equation, are solved simultaneously at each time step. An elliptic grid generation approach is used to generate a boundary conforming coordinate system about an airfoil. The governing equations are expressed in terms of the curvilinear coordinates and are solved on a uniform rectangular computational domain. A checkerboard SOR, which can effectively utilize the computer architectural concept of vector processing, is used for iterative solution of the governing equations.

Numerical solutions of 3-dimensional Navier-Stokes equations for closed bluff-bodies

NASA Technical Reports Server (NTRS)

Abolhassani, J. S.; Tiwari, S. N.

1985-01-01

The Navier-Stokes equations are solved numerically. These equations are unsteady, compressible, viscous, and three-dimensional without neglecting any terms. The time dependency of the governing equations allows the solution to progress naturally for an arbitrary initial guess to an asymptotic steady state, if one exists. The equations are transformed from physical coordinates to the computational coordinates, allowing the solution of the governing equations in a rectangular parallelepiped domain. The equations are solved by the MacCormack time-split technique which is vectorized and programmed to run on the CDc VPS 32 computer. The codes are written in 32-bit (half word) FORTRAN, which provides an approximate factor of two decreasing in computational time and doubles the memory size compared to the 54-bit word size.

Discovering governing equations from data by sparse identification of nonlinear dynamical systems

PubMed Central

Brunton, Steven L.; Proctor, Joshua L.; Kutz, J. Nathan

2016-01-01

Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing. PMID:27035946

Discovering governing equations from data by sparse identification of nonlinear dynamical systems.

PubMed

Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan

2016-04-12

Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing.

The calculation of transport phenomena in electromagnetically levitated metal droplets

NASA Technical Reports Server (NTRS)

El-Kaddah, N.; Szekely, J.

1982-01-01

A mathematical representation has been developed for the electromagnetic force field, fluid flow field, and solute concentration field of levitation-melted metal specimens. The governing equations consist of the conventional transport equations combined with the appropriate expressions for the electromagnetic force field. The predictions obtained by solving the governing equations numerically on a digital computer are in good agreement with lifting force and average temperature measurements reported in the literature.

A comparative study of two codes with an improved two-equation turbulence model for predicting jet plumes

NASA Technical Reports Server (NTRS)

Balakrishnan, L.; Abdol-Hamid, Khaled S.

1992-01-01

Compressible jet plumes were studied using a two-equation turbulence model. A space marching procedure based on an upwind numerical scheme was used to solve the governing equations and turbulence transport equations. The computed results indicate that extending the space marching procedure for solving supersonic/subsonic mixing problems can be stable, efficient and accurate. Moreover, a newly developed correction for compressible dissipation has been verified in fully expanded and underexpanded jet plumes. For a sonic jet plume, no improvement in results over the standard two-equation model was seen. However for a supersonic jet plume, the correction due to compressible dissipation successfully predicted the reduced spreading rate of the jet compared to the sonic case. The computed results were generally in good agreement with the experimental data.

Biconvection flow of Carreau fluid over an upper paraboloid surface: A computational study

NASA Astrophysics Data System (ADS)

Khan, Mair; Hussain, Arif; Malik, M. Y.; Salahuddin, T.

Present article explored the physical characteristics of biconvection effects on the MHD flow of Carreau nanofluid over upper horizontal surface of paraboloid revolution along with chemical reaction. The concept of the Carreau nanofluid was introduced the new parameterization achieve the momentum governing equation. Using similarity transformed, the governing partial differential equations are converted into the ordinary differential equations. The obtained governing equations are solved computationally by using implicit finite difference method known as the Keller box technique. The numerical solutions are obtained for the velocity, temperature, concentration, friction factor, local heat and mass transfer coefficients by varying controlling parameters i.e. Biconvection parameter, fluid parameter, Weissenberg number, Hartmann number, Prandtl number, Brownian motion parameter, thermophoresis parameter, Lewis number and chemical reaction parameter. The obtained results are discussed via graphs and tables.

Torsional vibration of a pipe pile in transversely isotropic saturated soil

NASA Astrophysics Data System (ADS)

Zheng, Changjie; Hua, Jianmin; Ding, Xuanming

2016-09-01

This study considers the torsional vibration of a pipe pile in a transversely isotropic saturated soil layer. Based on Biot's poroelastic theory and the constitutive relations of the transversely isotropic medium, the dynamic governing equations of the outer and inner transversely isotropic saturated soil layers are derived. The Laplace transform is used to solve the governing equations of the outer and inner soil layers. The dynamic torsional response of the pipe pile in the frequency domain is derived utilizing 1D elastic theory and the continuous conditions at the interfaces between the pipe pile and the soils. The time domain solution is obtained by Fourier inverse transform. A parametric study is conducted to demonstrate the influence of the anisotropies of the outer and inner soil on the torsional dynamic response of the pipe pile.

Data-driven discovery of partial differential equations

PubMed Central

Rudy, Samuel H.; Brunton, Steven L.; Proctor, Joshua L.; Kutz, J. Nathan

2017-01-01

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg–de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable. PMID:28508044

Closed-form solution for static pull-in voltage of electrostatically actuated clamped-clamped micro/nano beams under the effect of fringing field and van der Waals force

NASA Astrophysics Data System (ADS)

Bhojawala, V. M.; Vakharia, D. P.

2017-12-01

This investigation provides an accurate prediction of static pull-in voltage for clamped-clamped micro/nano beams based on distributed model. The Euler-Bernoulli beam theory is used adapting geometric non-linearity of beam, internal (residual) stress, van der Waals force, distributed electrostatic force and fringing field effects for deriving governing differential equation. The Galerkin discretisation method is used to make reduced-order model of the governing differential equation. A regime plot is presented in the current work for determining the number of modes required in reduced-order model to obtain completely converged pull-in voltage for micro/nano beams. A closed-form relation is developed based on the relationship obtained from curve fitting of pull-in instability plots and subsequent non-linear regression for the proposed relation. The output of regression analysis provides Chi-square (χ 2) tolerance value equals to 1  ×  10-9, adjusted R-square value equals to 0.999 29 and P-value equals to zero, these statistical parameters indicate the convergence of non-linear fit, accuracy of fitted data and significance of the proposed model respectively. The closed-form equation is validated using available data of experimental and numerical results. The relative maximum error of 4.08% in comparison to several available experimental and numerical data proves the reliability of the proposed closed-form equation.

Introduction to Physical Intelligence

NASA Technical Reports Server (NTRS)

Zak, Michail

2011-01-01

A slight deviation from Newtonian dynamics can lead to new effects associated with the concept of physical intelligence. Non-Newtonian effects such as deviation from classical thermodynamic as well as quantum-like properties have been analyzed. A self-supervised (intelligent) particle that can escape from Brownian motion autonomously is introduced. Such a capability is due to a coupling of the particle governing equation with its own Liouville equation via an appropriate feedback. As a result, the governing equation is self-stabilized, and random oscillations are suppressed, while the Liouville equation takes the form of the Fokker-Planck equation with negative diffusion. Non- Newtonian properties of such a dynamical system as well as thermodynamical implications have been evaluated.

Brine flow in heated geologic salt.

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

Kuhlman, Kristopher L.; Malama, Bwalya

This report is a summary of the physical processes, primary governing equations, solution approaches, and historic testing related to brine migration in geologic salt. Although most information presented in this report is not new, we synthesize a large amount of material scattered across dozens of laboratory reports, journal papers, conference proceedings, and textbooks. We present a mathematical description of the governing brine flow mechanisms in geologic salt. We outline the general coupled thermal, multi-phase hydrologic, and mechanical processes. We derive these processes governing equations, which can be used to predict brine flow. These equations are valid under a wide varietymore » of conditions applicable to radioactive waste disposal in rooms and boreholes excavated into geologic salt.« less

Theoretical and computational analyses of LNG evaporator

NASA Astrophysics Data System (ADS)

Chidambaram, Palani Kumar; Jo, Yang Myung; Kim, Heuy Dong

2017-04-01

Theoretical and numerical analysis on the fluid flow and heat transfer inside a LNG evaporator is conducted in this work. Methane is used instead of LNG as the operating fluid. This is because; methane constitutes over 80% of natural gas. The analytical calculations are performed using simple mass and energy balance equations. The analytical calculations are made to assess the pressure and temperature variations in the steam tube. Multiphase numerical simulations are performed by solving the governing equations (basic flow equations of continuity, momentum and energy equations) in a portion of the evaporator domain consisting of a single steam pipe. The flow equations are solved along with equations of species transport. Multiphase modeling is incorporated using VOF method. Liquid methane is the primary phase. It vaporizes into the secondary phase gaseous methane. Steam is another secondary phase which flows through the heating coils. Turbulence is modeled by a two equation turbulence model. Both the theoretical and numerical predictions are seen to match well with each other. Further parametric studies are planned based on the current research.

Movement of Landslide Triggered by Bedrock Exfiltration with Nonuniform Pore Pressure Distribution

NASA Astrophysics Data System (ADS)

Jan, C. D.; Jian, Z. K.

2014-12-01

Landslides are common phenomena of sediment movement in mountain areas and usually pose severe risks to people and infrastructure around those areas. The occurrence of landslides is influenced by groundwater dynamics and bedrock characteristics as well as by rainfall and soil-mass properties. The bedrock may drain or contribute to groundwater in the overlying soil mass, depending on the hydraulic conductivity, degree of fracturing, saturation, and hydraulic head. Our study here is based on the model proposed by Iverson (2005). The model describes the relation between landslide displacement and the shear-zone dilation/contraction of pore water pressure. To study landslide initiation and movement, a block soil mass sliding down an inclined beck-rock plane is governed by Newton's equation of motion, while both the bedrock exfiltration and excess pore pressure induced by dilatation or contraction of basal shear zone are described by diffusion equations. The Chebyshev collocation method was used to transform the governing equations to a system of first-order ordinary differential equations, without the need of iteration. Then a fourth-order Runge-Kutta scheme was used to solve these ordinary differential equations. The effects of nonuniform bedrock exfiltration pressure distributions, such as the delayed peak, central peak, and advanced peak distributions, on the time of landslide initiation and the speed of landslide movement were compared and discussed.

REVIEW OF THE GOVERNING EQUATIONS, COMPUTATIONAL ALGORITHMS, AND OTHER COMPONENTS OF THE MODELS-3 COMMUNITY MULTISCALE AIR QUALITY (CMAQ) MODELING SYSTEM

EPA Science Inventory

This article describes the governing equations, computational algorithms, and other components entering into the Community Multiscale Air Quality (CMAQ) modeling system. This system has been designed to approach air quality as a whole by including state-of-the-science capabiliti...

On a nonlinear model for tumour growth with drug application

NASA Astrophysics Data System (ADS)

Donatelli, Donatella; Trivisa, Konstantina

2015-05-01

We investigate the dynamics of a nonlinear system modelling tumour growth with drug application. The tumour is viewed as a mixture consisting of proliferating, quiescent and dead cells as well as a nutrient in the presence of a drug. The system is given by a multi-phase flow model: the densities of the different cells are governed by a set of transport equations, the density of the nutrient and the density of the drug are governed by rather general diffusion equations, while the velocity of the tumour is given by Brinkman's equation. The domain occupied by the tumour in this setting is a growing continuum Ω with boundary ∂Ω both of which evolve in time. Global-in-time weak solutions are obtained using an approach based on penalization of the boundary behaviour, diffusion and viscosity in the weak formulation. Both the solutions and the domain are rather general, no symmetry assumption is required and the result holds for large initial data. This article is part of a research programme whose aim is the investigation of the effect of drug application in tumour growth.

Thermochemical nonequilibrium in atomic hydrogen at elevated temperatures

NASA Technical Reports Server (NTRS)

Scott, R. K.

1972-01-01

A numerical study of the nonequilibrium flow of atomic hydrogen in a cascade arc was performed to obtain insight into the physics of the hydrogen cascade arc. A rigorous mathematical model of the flow problem was formulated, incorporating the important nonequilibrium transport phenomena and atomic processes which occur in atomic hydrogen. Realistic boundary conditions, including consideration of the wall electrostatic sheath phenomenon, were included in the model. The governing equations of the asymptotic region of the cascade arc were obtained by writing conservation of mass and energy equations for the electron subgas, an energy conservation equation for heavy particles and an equation of state. Finite-difference operators for variable grid spacing were applied to the governing equations and the resulting system of strongly coupled, stiff equations were solved numerically by the Newton-Raphson method.

Topology optimisation for natural convection problems

NASA Astrophysics Data System (ADS)

Alexandersen, Joe; Aage, Niels; Andreasen, Casper Schousboe; Sigmund, Ole

2014-12-01

This paper demonstrates the application of the density-based topology optimisation approach for the design of heat sinks and micropumps based on natural convection effects. The problems are modelled under the assumptions of steady-state laminar flow using the incompressible Navier-Stokes equations coupled to the convection-diffusion equation through the Boussinesq approximation. In order to facilitate topology optimisation, the Brinkman approach is taken to penalise velocities inside the solid domain and the effective thermal conductivity is interpolated in order to accommodate differences in thermal conductivity of the solid and fluid phases. The governing equations are discretised using stabilised finite elements and topology optimisation is performed for two different problems using discrete adjoint sensitivity analysis. The study shows that topology optimisation is a viable approach for designing heat sink geometries cooled by natural convection and micropumps powered by natural convection.

A calculation procedure for viscous flow in turbomachines, volume 3. [computer programs

NASA Technical Reports Server (NTRS)

Khalil, I.; Sheoran, Y.; Tabakoff, W.

1980-01-01

A method for analyzing the nonadiabatic viscous flow through turbomachine blade passages was developed. The field analysis is based upon the numerical integration of the full incompressible Navier-Stokes equations, together with the energy equation on the blade-to-blade surface. A FORTRAN IV computer program was written based on this method. The numerical code used to solve the governing equations employs a nonorthogonal boundary fitted coordinate system. The flow may be axial, radial or mixed and there may be a change in stream channel thickness in the through-flow direction. The inputs required for two FORTRAN IV programs are presented. The first program considers laminar flows and the second can handle turbulent flows. Numerical examples are included to illustrate the use of the program, and to show the results that are obtained.

Local-in-Time Adjoint-Based Method for Optimal Control/Design Optimization of Unsteady Compressible Flows

NASA Technical Reports Server (NTRS)

Yamaleev, N. K.; Diskin, B.; Nielsen, E. J.

2009-01-01

.We study local-in-time adjoint-based methods for minimization of ow matching functionals subject to the 2-D unsteady compressible Euler equations. The key idea of the local-in-time method is to construct a very accurate approximation of the global-in-time adjoint equations and the corresponding sensitivity derivative by using only local information available on each time subinterval. In contrast to conventional time-dependent adjoint-based optimization methods which require backward-in-time integration of the adjoint equations over the entire time interval, the local-in-time method solves local adjoint equations sequentially over each time subinterval. Since each subinterval contains relatively few time steps, the storage cost of the local-in-time method is much lower than that of the global adjoint formulation, thus making the time-dependent optimization feasible for practical applications. The paper presents a detailed comparison of the local- and global-in-time adjoint-based methods for minimization of a tracking functional governed by the Euler equations describing the ow around a circular bump. Our numerical results show that the local-in-time method converges to the same optimal solution obtained with the global counterpart, while drastically reducing the memory cost as compared to the global-in-time adjoint formulation.

Output Feedback-Based Boundary Control of Uncertain Coupled Semilinear Parabolic PDE Using Neurodynamic Programming.

PubMed

Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

2018-04-01

In this paper, neurodynamic programming-based output feedback boundary control of distributed parameter systems governed by uncertain coupled semilinear parabolic partial differential equations (PDEs) under Neumann or Dirichlet boundary control conditions is introduced. First, Hamilton-Jacobi-Bellman (HJB) equation is formulated in the original PDE domain and the optimal control policy is derived using the value functional as the solution of the HJB equation. Subsequently, a novel observer is developed to estimate the system states given the uncertain nonlinearity in PDE dynamics and measured outputs. Consequently, the suboptimal boundary control policy is obtained by forward-in-time estimation of the value functional using a neural network (NN)-based online approximator and estimated state vector obtained from the NN observer. Novel adaptive tuning laws in continuous time are proposed for learning the value functional online to satisfy the HJB equation along system trajectories while ensuring the closed-loop stability. Local uniformly ultimate boundedness of the closed-loop system is verified by using Lyapunov theory. The performance of the proposed controller is verified via simulation on an unstable coupled diffusion reaction process.

Robust iterative method for nonlinear Helmholtz equation

NASA Astrophysics Data System (ADS)

Yuan, Lijun; Lu, Ya Yan

2017-08-01

A new iterative method is developed for solving the two-dimensional nonlinear Helmholtz equation which governs polarized light in media with the optical Kerr nonlinearity. In the strongly nonlinear regime, the nonlinear Helmholtz equation could have multiple solutions related to phenomena such as optical bistability and symmetry breaking. The new method exhibits a much more robust convergence behavior than existing iterative methods, such as frozen-nonlinearity iteration, Newton's method and damped Newton's method, and it can be used to find solutions when good initial guesses are unavailable. Numerical results are presented for the scattering of light by a nonlinear circular cylinder based on the exact nonlocal boundary condition and a pseudospectral method in the polar coordinate system.

A semi-analytical solution for elastic analysis of rotating thick cylindrical shells with variable thickness using disk form multilayers.

PubMed

Zamani Nejad, Mohammad; Jabbari, Mehdi; Ghannad, Mehdi

2014-01-01

Using disk form multilayers, a semi-analytical solution has been derived for determination of displacements and stresses in a rotating cylindrical shell with variable thickness under uniform pressure. The thick cylinder is divided into disk form layers form with their thickness corresponding to the thickness of the cylinder. Due to the existence of shear stress in the thick cylindrical shell with variable thickness, the equations governing disk layers are obtained based on first-order shear deformation theory (FSDT). These equations are in the form of a set of general differential equations. Given that the cylinder is divided into n disks, n sets of differential equations are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. A numerical solution using finite element method (FEM) is also presented and good agreement was found.

A Semi-Analytical Solution for Elastic Analysis of Rotating Thick Cylindrical Shells with Variable Thickness Using Disk Form Multilayers

PubMed Central

Zamani Nejad, Mohammad; Jabbari, Mehdi; Ghannad, Mehdi

2014-01-01

Using disk form multilayers, a semi-analytical solution has been derived for determination of displacements and stresses in a rotating cylindrical shell with variable thickness under uniform pressure. The thick cylinder is divided into disk form layers form with their thickness corresponding to the thickness of the cylinder. Due to the existence of shear stress in the thick cylindrical shell with variable thickness, the equations governing disk layers are obtained based on first-order shear deformation theory (FSDT). These equations are in the form of a set of general differential equations. Given that the cylinder is divided into n disks, n sets of differential equations are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. A numerical solution using finite element method (FEM) is also presented and good agreement was found. PMID:24719582

Numerical modeling of a vortex stabilized arcjet

NASA Astrophysics Data System (ADS)

Pawlas, Gary Edward

Arcjet thrusters are being actively considered for use in Earth orbit maneuvering applications. Satellite station-keeping is an example of a maneuvering application requiring the low thrust, high specific impulse of an arcjet. Experimental studies are currently the chief means of determining an optimal thruster configuration. Earlier numerical studies have failed to include all of the effects found in typical arcjets including complex geometries, viscosity and swirling flow. Arcjet geometries are large area ratio converging-diverging nozzles with centerbodies in the subsonic portion of the nozzle. The nozzle walls serve as the anode while the centerbody functions as the cathode. Viscous effects are important because the Reynolds number, based on the throat radius, is typically less than 1,000. Experimental studies have shown a swirl or circumferential velocity component stabilizes a constricted arc. The equations are described which governs the flow through a constricted arcjet thruster. An assumption that the flowfield is in local thermodynamic equilibrium leads to a single fluid plasma temperature model. An order of magnitude analysis reveals the governing fluid mechanics equations are uncoupled from the electromagnetic field equations. A numerical method is developed to solve the governing fluid mechanics equations, the Thin Layer Navier-Stokes equations. A coordinate transformation is used in deriving the governing equations to simplify the application of boundary conditions in complex geometries. An axisymmetric formulation is employed to include the swirl velocity component as well as the axial and redial velocity components. The numerical method is an implicit finite-volume technique and allows for large time steps to reach a converged steady-state solution. The inviscid fluxes are flux-split and Gauss-Seidel line relaxation is used to accelerate convergence. 'Converging diverging' nozzles with exit-to-throat area ratios up to 100:1 and annual nozzles were examined. Comparisons with experimental data and previous numerical results were in excellent agreement. Quantities examined included Mach number and static wall pressure distributions, and oblique shock structures.

A finite-difference method for the variable coefficient Poisson equation on hierarchical Cartesian meshes

NASA Astrophysics Data System (ADS)

Raeli, Alice; Bergmann, Michel; Iollo, Angelo

2018-02-01

We consider problems governed by a linear elliptic equation with varying coefficients across internal interfaces. The solution and its normal derivative can undergo significant variations through these internal boundaries. We present a compact finite-difference scheme on a tree-based adaptive grid that can be efficiently solved using a natively parallel data structure. The main idea is to optimize the truncation error of the discretization scheme as a function of the local grid configuration to achieve second-order accuracy. Numerical illustrations are presented in two and three-dimensional configurations.

Computer-aided design of bevel gear tooth surfaces

NASA Technical Reports Server (NTRS)

Shuo, Hung Chang; Huston, Ronald L.; Coy, John J.

1989-01-01

This paper presents a computer-aided design procedure for generating bevel gears. The development is based on examining a perfectly plastic, cone-shaped gear blank rolling over a cutting tooth on a plane crown rack. The resulting impression on the plastic gear blank is the envelope of the cutting tooth. This impression and envelope thus form a conjugate tooth surface. Equations are presented for the locus of points on the tooth surface. The same procedures are then extended to simulate the generation of a spiral bevel gear. The corresponding governing equations are presented.

Computer aided design of bevel gear tooth surfaces

NASA Technical Reports Server (NTRS)

Chang, S. H.; Huston, R. L.; Coy, J. J.

1989-01-01

This paper presents a computer-aided design procedure for generating bevel gears. The development is based on examining a perfectly plastic, cone-shaped gear blank rolling over a cutting tooth on a plane crown rack. The resulting impression on the plastic gear blank is the envelope of the cutting tooth. This impression and envelope thus form a conjugate tooth surface. Equations are presented for the locus of points on the tooth surface. The same procedures are then extended to simulate the generation of a spiral bevel gear. The corresponding governing equations are presented.

Complexity reduction of rate-equations models for two-choice decision-making.

PubMed

Carrillo, José Antonio; Cordier, Stéphane; Deco, Gustavo; Mancini, Simona

2013-01-01

We are concerned with the complexity reduction of a stochastic system of differential equations governing the dynamics of a neuronal circuit describing a decision-making task. This reduction is based on the slow-fast behavior of the problem and holds on the whole phase space and not only locally around the spontaneous state. Macroscopic quantities, such as performance and reaction times, computed applying this reduction are in agreement with previous works in which the complexity reduction is locally performed at the spontaneous point by means of a Taylor expansion.

Sharpness of interference pattern of the 3-pole wiggler

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

Dejus, Roger J., E-mail: dejus@aps.anl.gov; Kim, Kwang-Je

2016-07-27

Due to the small emittance, radiation from neighboring poles of a strong wiggler in future multi-bend achromat-based storage rings can exhibit sharp interference patterns. The spectral-angular distributions of the 3-pole wiggler for the proposed Advanced Photon Source (APS) upgrade were computed and prominent interference patterns were found. In this paper we provide an understanding of such interference patterns. The equations governing the interference pattern are described and computed spectral-angular distributions of a modeled 3-pole wiggler magnetic field using these equations are presented.

Sharpness of Interference Pattern of the 3-Pole Wiggler

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

Dejus, Roger J.; Kim, Kwang-Je

2016-07-02

Due to the small emittance, radiation from neighboring poles of a strong wiggler in future multi-bend achromat-based storage rings can exhibit sharp interference patterns. The spectral-angular distributions of the 3-pole wiggler for the proposed Advanced Photon Source (APS) upgrade were computed and prominent interference patterns were found. In this paper we provide an understanding of such interference patterns. The equations governing the interference pattern are described and computed spectral-angular distributions of a modeled 3-pole wiggler magnetic field using these equations are presented.

Aerodynamic Shape Optimization of Complex Aircraft Configurations via an Adjoint Formulation

NASA Technical Reports Server (NTRS)

Reuther, James; Jameson, Antony; Farmer, James; Martinelli, Luigi; Saunders, David

1996-01-01

This work describes the implementation of optimization techniques based on control theory for complex aircraft configurations. Here control theory is employed to derive the adjoint differential equations, the solution of which allows for a drastic reduction in computational costs over previous design methods (13, 12, 43, 38). In our earlier studies (19, 20, 22, 23, 39, 25, 40, 41, 42) it was shown that this method could be used to devise effective optimization procedures for airfoils, wings and wing-bodies subject to either analytic or arbitrary meshes. Design formulations for both potential flows and flows governed by the Euler equations have been demonstrated, showing that such methods can be devised for various governing equations (39, 25). In our most recent works (40, 42) the method was extended to treat wing-body configurations with a large number of mesh points, verifying that significant computational savings can be gained for practical design problems. In this paper the method is extended for the Euler equations to treat complete aircraft configurations via a new multiblock implementation. New elements include a multiblock-multigrid flow solver, a multiblock-multigrid adjoint solver, and a multiblock mesh perturbation scheme. Two design examples are presented in which the new method is used for the wing redesign of a transonic business jet.

A homogenization approach for characterization of the fluid-solid coupling parameters in Biot's equations for acoustic poroelastic materials

NASA Astrophysics Data System (ADS)

Gao, K.; van Dommelen, J. A. W.; Göransson, P.; Geers, M. G. D.

2015-09-01

In this paper, a homogenization method is proposed to obtain the parameters of Biot's poroelastic theory from a multiscale perspective. It is assumed that the behavior of a macroscopic material point can be captured through the response of a microscopic Representative Volume Element (RVE) consisting of both a solid skeleton and a gaseous fluid. The macroscopic governing equations are assumed to be Biot's poroelastic equations and the RVE is governed by the conservation of linear momentum and the adopted linear constitutive laws under the isothermal condition. With boundary conditions relying on the macroscopic solid displacement and fluid pressure, the homogenized solid stress and fluid displacement are obtained based on energy consistency. This homogenization framework offers an approach to obtain Biot's parameters directly through the response of the RVE in the regime of Darcy's flow where the pressure gradient is dominating. A numerical experiment is performed in the form of a sound absorption test on a porous material with an idealized partially open microstructure that is described by Biot's equations where the parameters are obtained through the proposed homogenization approach. The result is evaluated by comparison with Direct Numerical Simulations (DNS), showing a superior performance of this approach compared to an alternative semi-phenomenological model for estimating Biot's parameters of the studied porous material.

General equations for optimal selection of diagnostic image acquisition parameters in clinical X-ray imaging.

PubMed

Zheng, Xiaoming

2017-12-01

The purpose of this work was to examine the effects of relationship functions between diagnostic image quality and radiation dose on the governing equations for image acquisition parameter variations in X-ray imaging. Various equations were derived for the optimal selection of peak kilovoltage (kVp) and exposure parameter (milliAmpere second, mAs) in computed tomography (CT), computed radiography (CR), and direct digital radiography. Logistic, logarithmic, and linear functions were employed to establish the relationship between radiation dose and diagnostic image quality. The radiation dose to the patient, as a function of image acquisition parameters (kVp, mAs) and patient size (d), was used in radiation dose and image quality optimization. Both logistic and logarithmic functions resulted in the same governing equation for optimal selection of image acquisition parameters using a dose efficiency index. For image quality as a linear function of radiation dose, the same governing equation was derived from the linear relationship. The general equations should be used in guiding clinical X-ray imaging through optimal selection of image acquisition parameters. The radiation dose to the patient could be reduced from current levels in medical X-ray imaging.

Pseudo-time methods for constrained optimization problems governed by PDE

NASA Technical Reports Server (NTRS)

Taasan, Shlomo

1995-01-01

In this paper we present a novel method for solving optimization problems governed by partial differential equations. Existing methods are gradient information in marching toward the minimum, where the constrained PDE is solved once (sometimes only approximately) per each optimization step. Such methods can be viewed as a marching techniques on the intersection of the state and costate hypersurfaces while improving the residuals of the design equations per each iteration. In contrast, the method presented here march on the design hypersurface and at each iteration improve the residuals of the state and costate equations. The new method is usually much less expensive per iteration step since, in most problems of practical interest, the design equation involves much less unknowns that that of either the state or costate equations. Convergence is shown using energy estimates for the evolution equations governing the iterative process. Numerical tests show that the new method allows the solution of the optimization problem in a cost of solving the analysis problems just a few times, independent of the number of design parameters. The method can be applied using single grid iterations as well as with multigrid solvers.

FRACTIONAL PEARSON DIFFUSIONS.

PubMed

Leonenko, Nikolai N; Meerschaert, Mark M; Sikorskii, Alla

2013-07-15

Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are useful for modeling sub-diffusive phenomena, caused by particle sticking and trapping. This paper provides explicit strong solutions for fractional Pearson diffusions, using spectral methods. It also presents stochastic solutions, using a non-Markovian inverse stable time change.

2.5-D poroelastic wave modelling in double porosity media

NASA Astrophysics Data System (ADS)

Liu, Xu; Greenhalgh, Stewart; Wang, Yanghua

2011-09-01

To approximate seismic wave propagation in double porosity media, the 2.5-D governing equations of poroelastic waves are developed and numerically solved. The equations are obtained by taking a Fourier transform in the strike or medium-invariant direction over all of the field quantities in the 3-D governing equations. The new memory variables from the Zener model are suggested as a way to represent the sum of the convolution integrals for both the solid particle velocity and the macroscopic fluid flux in the governing equations. By application of the memory equations, the field quantities at every time step need not be stored. However, this approximation allows just two Zener relaxation times to represent the very complex double porosity and dual permeability attenuation mechanism, and thus reduce the difficulty. The 2.5-D governing equations are numerically solved by a time-splitting method for the non-stiff parts and an explicit fourth-order Runge-Kutta method for the time integration and a Fourier pseudospectral staggered-grid for handling the spatial derivative terms. The 2.5-D solution has the advantage of producing a 3-D wavefield (point source) for a 2-D model but is much more computationally efficient than the full 3-D solution. As an illustrative example, we firstly show the computed 2.5-D wavefields in a homogeneous single porosity model for which we reformulated an analytic solution. Results for a two-layer, water-saturated double porosity model and a laterally heterogeneous double porosity structure are also presented.

Imperfection Sensitivity of Nonlinear Vibration of Curved Single-Walled Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory

PubMed Central

Eshraghi, Iman; Jalali, Seyed K.; Pugno, Nicola Maria

2016-01-01

Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs) is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ) method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of amplitude and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency for various boundary conditions are investigated. The results show that the geometric imperfection and non-locality play a significant role in the nonlinear vibration characteristics of curved SWCNTs. PMID:28773911

A theoretical model for investigating the effect of vacuum fluctuations on the electromechanical stability of nanotweezers

NASA Astrophysics Data System (ADS)

Farrokhabadi, A.; Mokhtari, J.; Koochi, A.; Abadyan, M.

2015-06-01

In this paper, the impact of the Casimir attraction on the electromechanical stability of nanowire-fabricated nanotweezers is investigated using a theoretical continuum mechanics model. The Dirichlet mode is considered and an asymptotic solution, based on path integral approach, is applied to consider the effect of vacuum fluctuations in the model. The Euler-Bernoulli beam theory is employed to derive the nonlinear governing equation of the nanotweezers. The governing equations are solved by three different approaches, i.e. the modified variation iteration method, generalized differential quadrature method and using a lumped parameter model. Various perspectives of the problem, including the comparison with the van der Waals force regime, the variation of instability parameters and effects of geometry are addressed in present paper. The proposed approach is beneficial for the precise determination of the electrostatic response of the nanotweezers in the presence of Casimir force.

In-plane free vibration analysis of cable arch structure

NASA Astrophysics Data System (ADS)

Zhao, Yueyu; Kang, Houjun

2008-05-01

Cable-stayed arch bridge is a new type of composite bridge, which utilizes the mechanical characters of cable and arch. Based on the supporting members of cable-stayed arch bridge and of erection of arch bridge using of the cantilever construction method with tiebacks, we propose a novel mechanical model of cable-arch structure. In this model, the equations governing vibrations of the cable-arch are derived according to Hamilton's principle for dynamic problems in elastic body under equilibrium state. Then, the program of solving the dynamic governing equations is ultimately established by the transfer matrix method for free vibration of uniform and variable cross-section, and the internal characteristics of the cable-arch are investigated. After analyzing step by step, the research results approve that the program is accurate; meanwhile, the mechanical model and method are both valuable and significant not only in theoretical research and calculation but also in design of engineering.

Simulations of Fluvial Landscapes

NASA Astrophysics Data System (ADS)

Cattan, D.; Birnir, B.

2013-12-01

The Smith-Bretherton-Birnir (SBB) model for fluvial landsurfaces consists of a pair of partial differential equations, one governing water flow and one governing the sediment flow. Numerical solutions of these equations have been shown to provide realistic models in the evolution of fluvial landscapes. Further analysis of these equations shows that they possess scaling laws (Hack's Law) that are known to exist in nature. However, the simulations are highly dependent on the numerical methods used; with implicit methods exhibiting the correct scaling laws, but the explicit methods fail to do so. These equations, and the resulting models, help to bridge the gap between the deterministic and the stochastic theories of landscape evolution. Slight modifications of the SBB equations make the results of the model more realistic. By modifying the sediment flow equation, the model obtains more pronounced meandering rivers. Typical landsurface with rivers.

A Numerical Model for Trickle Bed Reactors

NASA Astrophysics Data System (ADS)

Propp, Richard M.; Colella, Phillip; Crutchfield, William Y.; Day, Marcus S.

2000-12-01

Trickle bed reactors are governed by equations of flow in porous media such as Darcy's law and the conservation of mass. Our numerical method for solving these equations is based on a total-velocity splitting, sequential formulation which leads to an implicit pressure equation and a semi-implicit mass conservation equation. We use high-resolution finite-difference methods to discretize these equations. Our solution scheme extends previous work in modeling porous media flows in two ways. First, we incorporate physical effects due to capillary pressure, a nonlinear inlet boundary condition, spatial porosity variations, and inertial effects on phase mobilities. In particular, capillary forces introduce a parabolic component into the recast evolution equation, and the inertial effects give rise to hyperbolic nonconvexity. Second, we introduce a modification of the slope-limiting algorithm to prevent our numerical method from producing spurious shocks. We present a numerical algorithm for accommodating these difficulties, show the algorithm is second-order accurate, and demonstrate its performance on a number of simplified problems relevant to trickle bed reactor modeling.

Three-dimensional time-dependent computer modeling of the electrothermal atomizers for analytical spectrometry

NASA Astrophysics Data System (ADS)

Tsivilskiy, I. V.; Nagulin, K. Yu.; Gilmutdinov, A. Kh.

2016-02-01

A full three-dimensional nonstationary numerical model of graphite electrothermal atomizers of various types is developed. The model is based on solution of a heat equation within solid walls of the atomizer with a radiative heat transfer and numerical solution of a full set of Navier-Stokes equations with an energy equation for a gas. Governing equations for the behavior of a discrete phase, i.e., atomic particles suspended in a gas (including gas-phase processes of evaporation and condensation), are derived from the formal equations molecular kinetics by numerical solution of the Hertz-Langmuir equation. The following atomizers test the model: a Varian standard heated electrothermal vaporizer (ETV), a Perkin Elmer standard THGA transversely heated graphite tube with integrated platform (THGA), and the original double-stage tube-helix atomizer (DSTHA). The experimental verification of computer calculations is carried out by a method of shadow spectral visualization of the spatial distributions of atomic and molecular vapors in an analytical space of an atomizer.

A formulation of rotor-airframe coupling for design analysis of vibrations of helicopter airframes

NASA Technical Reports Server (NTRS)

Kvaternik, R. G.; Walton, W. C., Jr.

1982-01-01

A linear formulation of rotor airframe coupling intended for vibration analysis in airframe structural design is presented. The airframe is represented by a finite element analysis model; the rotor is represented by a general set of linear differential equations with periodic coefficients; and the connections between the rotor and airframe are specified through general linear equations of constraint. Coupling equations are applied to the rotor and airframe equations to produce one set of linear differential equations governing vibrations of the combined rotor airframe system. These equations are solved by the harmonic balance method for the system steady state vibrations. A feature of the solution process is the representation of the airframe in terms of forced responses calculated at the rotor harmonics of interest. A method based on matrix partitioning is worked out for quick recalculations of vibrations in design studies when only relatively few airframe members are varied. All relations are presented in forms suitable for direct computer implementation.

Scaling analysis for the direct reactor auxiliary cooling system for FHRs

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

Lv, Q.; Kim, I. H.; Sun, X.

2015-04-01

The Direct Reactor Auxiliary Cooling System (DRACS) is a passive residual heat removal system proposed for the Fluoride-salt-cooled High-temperature Reactor (FHR) that combines the coated particle fuel and graphite moderator with a liquid fluoride salt as the coolant. The DRACS features three natural circulation/convection loops that rely on buoyancy as the driving force and are coupled via two heat exchangers, namely, the DRACS heat exchanger and the natural draft heat exchanger. A fluidic diode is employed to minimize the parasitic flow into the DRACS primary loop and correspondingly the heat loss to the DRACS during reactor normal operation, and tomore » activate the DRACS in accidents when the reactor is shut down. While the DRACS concept has been proposed, there are no actual prototypic DRACS systems for FHRs built or tested in the literature. In this paper, a detailed scaling analysis for the DRACS is performed, which will provide guidance for the design of scaled-down DRACS test facilities. Based on the Boussinesq assumption and one-dimensional flow formulation, the governing equations are non-dimensionalized by introducing appropriate dimensionless parameters. The key dimensionless numbers that characterize the DRACS system are obtained from the non-dimensional governing equations. Based on the dimensionless numbers and non-dimensional governing equations, similarity laws are proposed. In addition, a scaling methodology has been developed, which consists of a core scaling and a loop scaling. The consistency between the core and loop scaling is examined via the reference volume ratio, which can be obtained from both the core and loop scaling processes. The scaling methodology and similarity laws have been applied to obtain a scientific design of a scaled-down high-temperature DRACS test facility.« less

Vertically Integrated Models for Carbon Storage Modeling in Heterogeneous Domains

NASA Astrophysics Data System (ADS)

Bandilla, K.; Celia, M. A.

2017-12-01

Numerical modeling is an essential tool for studying the impacts of geologic carbon storage (GCS). Injection of carbon dioxide (CO2) into deep saline aquifers leads to multi-phase flow (injected CO2 and resident brine), which can be described by a set of three-dimensional governing equations, including mass-balance equation, volumetric flux equations (modified Darcy), and constitutive equations. This is the modeling approach on which commonly used reservoir simulators such as TOUGH2 are based. Due to the large density difference between CO2 and brine, GCS models can often be simplified by assuming buoyant segregation and integrating the three-dimensional governing equations in the vertical direction. The integration leads to a set of two-dimensional equations coupled with reconstruction operators for vertical profiles of saturation and pressure. Vertically-integrated approaches have been shown to give results of comparable quality as three-dimensional reservoir simulators when applied to realistic CO2 injection sites such as the upper sand wedge at the Sleipner site. However, vertically-integrated approaches usually rely on homogeneous properties over the thickness of a geologic layer. Here, we investigate the impact of general (vertical and horizontal) heterogeneity in intrinsic permeability, relative permeability functions, and capillary pressure functions. We consider formations involving complex fluvial deposition environments and compare the performance of vertically-integrated models to full three-dimensional models for a set of hypothetical test cases consisting of high permeability channels (streams) embedded in a low permeability background (floodplains). The domains are randomly generated assuming that stream channels can be represented by sinusoidal waves in the plan-view and by parabolas for the streams' cross-sections. Stream parameters such as width, thickness and wavelength are based on values found at the Ketzin site in Germany. Results from the vertically-integrated approach are compared to results using TOUGH2, both in terms of depth-averaged saturation and vertical saturation profiles.

Unified approach for incompressible flows

NASA Astrophysics Data System (ADS)

Chang, Tyne-Hsien

1995-07-01

A unified approach for solving incompressible flows has been investigated in this study. The numerical CTVD (Centered Total Variation Diminishing) scheme used in this study was successfully developed by Sanders and Li for compressible flows, especially for the high speed. The CTVD scheme possesses better mathematical properties to damp out the spurious oscillations while providing high-order accuracy for high speed flows. It leads us to believe that the CTVD scheme can equally well apply to solve incompressible flows. Because of the mathematical difference between the governing equations for incompressible and compressible flows, the scheme can not directly apply to the incompressible flows. However, if one can modify the continuity equation for incompressible flows by introducing pseudo-compressibility, the governing equations for incompressible flows would have the same mathematical characters as compressible flows. The application of the algorithm to incompressible flows thus becomes feasible. In this study, the governing equations for incompressible flows comprise continuity equation and momentum equations. The continuity equation is modified by adding a time-derivative of the pressure term containing the artificial compressibility. The modified continuity equation together with the unsteady momentum equations forms a hyperbolic-parabolic type of time-dependent system of equations. Thus, the CTVD schemes can be implemented. In addition, the physical and numerical boundary conditions are properly implemented by the characteristic boundary conditions. Accordingly, a CFD code has been developed for this research and is currently under testing. Flow past a circular cylinder was chosen for numerical experiments to determine the accuracy and efficiency of the code. The code has shown some promising results.

Unified approach for incompressible flows

NASA Technical Reports Server (NTRS)

Chang, Tyne-Hsien

1995-01-01

A unified approach for solving incompressible flows has been investigated in this study. The numerical CTVD (Centered Total Variation Diminishing) scheme used in this study was successfully developed by Sanders and Li for compressible flows, especially for the high speed. The CTVD scheme possesses better mathematical properties to damp out the spurious oscillations while providing high-order accuracy for high speed flows. It leads us to believe that the CTVD scheme can equally well apply to solve incompressible flows. Because of the mathematical difference between the governing equations for incompressible and compressible flows, the scheme can not directly apply to the incompressible flows. However, if one can modify the continuity equation for incompressible flows by introducing pseudo-compressibility, the governing equations for incompressible flows would have the same mathematical characters as compressible flows. The application of the algorithm to incompressible flows thus becomes feasible. In this study, the governing equations for incompressible flows comprise continuity equation and momentum equations. The continuity equation is modified by adding a time-derivative of the pressure term containing the artificial compressibility. The modified continuity equation together with the unsteady momentum equations forms a hyperbolic-parabolic type of time-dependent system of equations. Thus, the CTVD schemes can be implemented. In addition, the physical and numerical boundary conditions are properly implemented by the characteristic boundary conditions. Accordingly, a CFD code has been developed for this research and is currently under testing. Flow past a circular cylinder was chosen for numerical experiments to determine the accuracy and efficiency of the code. The code has shown some promising results.

SCREENING MODEL FOR NONAQUEOUS PHASE-LIQUID TRANSPORT IN THE VADOSE ZONE USING GREEN-AMPT AND KINEMATIC WAVE THEORY

EPA Science Inventory

In this paper, a screening model for flow of a nonaqueous phase liquid (NAPL) and associated chemical transport in the vadose zone is developed. he model is based on kinematic approximation of the governing equations for both the NAPL and a partitionable chemical constituent. he ...

A New Hope? Overcoming the Limitations of Effects-Based Operations

DTIC Science & Technology

2007-05-10

sway. Nor does the equation of a “Warlord” to a Junta government apply because often the “Warlord” is the head of a tribe through heredity or has...operations. More communities without power give rise to a greater disenfranchised population. In considering power plants as a target to 12

Calculation of the bending stresses in helicopter rotor blades

NASA Technical Reports Server (NTRS)

De Guillenchmidt, P

1951-01-01

A comparatively rapid method is presented for determining theoretically the bending stresses of helicopter rotor blades in forward flight. The method is based on the analysis of the properties of a vibrating beam, and its uniqueness lies in the simple solution of the differential equation which governs the motion of the bent blades.

A survey of numerical models for wind prediction

NASA Technical Reports Server (NTRS)

Schonfeld, D.

1980-01-01

A literature review is presented of the work done in the numerical modeling of wind flows. Pertinent computational techniques are described, as well as the necessary assumptions used to simplify the governing equations. A steady state model is outlined, based on the data obtained at the Deep Space Communications complex at Goldstone, California.

Damping mathematical modelling and dynamic responses for FRP laminated composite plates with polymer matrix

NASA Astrophysics Data System (ADS)

Liu, Qimao

2018-02-01

This paper proposes an assumption that the fibre is elastic material and polymer matrix is viscoelastic material so that the energy dissipation depends only on the polymer matrix in dynamic response process. The damping force vectors in frequency and time domains, of FRP (Fibre-Reinforced Polymer matrix) laminated composite plates, are derived based on this assumption. The governing equations of FRP laminated composite plates are formulated in both frequency and time domains. The direct inversion method and direct time integration method for nonviscously damped systems are employed to solve the governing equations and achieve the dynamic responses in frequency and time domains, respectively. The computational procedure is given in detail. Finally, dynamic responses (frequency responses with nonzero and zero initial conditions, free vibration, forced vibrations with nonzero and zero initial conditions) of a FRP laminated composite plate are computed using the proposed methodology. The proposed methodology in this paper is easy to be inserted into the commercial finite element analysis software. The proposed assumption, based on the theory of material mechanics, needs to be further proved by experiment technique in the future.

Vibration analysis of rotating functionally graded Timoshenko microbeam based on modified couple stress theory under different temperature distributions

NASA Astrophysics Data System (ADS)

Ghadiri, Majid; Shafiei, Navvab

2016-04-01

In this study, thermal vibration of rotary functionally graded Timoshenko microbeam has been analyzed based on modified couple stress theory considering temperature change in four types of temperature distribution on thermal environment. Material properties of FG microbeam are supposed to be temperature dependent and vary continuously along the thickness according to the power-law form. The axial forces are also included in the model as the thermal and true spatial variation due to the rotation. Governing equations and boundary conditions have been derived by employing Hamiltonian's principle. The differential quadrature method is employed to solve the governing equations for cantilever and propped cantilever boundary conditions. Validations are done by comparing available literatures and obtained results which indicate accuracy of applied method. Results represent effects of temperature changes, different boundary conditions, nondimensional angular velocity, length scale parameter, different boundary conditions, FG index and beam thickness on fundamental, second and third nondimensional frequencies. Results determine critical values of temperature changes and other essential parameters which can be applicable to design micromachines like micromotor and microturbine.

A cumulative energy demand indicator (CED), life cycle based, for industrial waste management decision making.

PubMed

Puig, Rita; Fullana-I-Palmer, Pere; Baquero, Grau; Riba, Jordi-Roger; Bala, Alba

2013-12-01

Life cycle thinking is a good approach to be used for environmental decision-support, although the complexity of the Life Cycle Assessment (LCA) studies sometimes prevents their wide use. The purpose of this paper is to show how LCA methodology can be simplified to be more useful for certain applications. In order to improve waste management in Catalonia (Spain), a Cumulative Energy Demand indicator (LCA-based) has been used to obtain four mathematical models to help the government in the decision of preventing or allowing a specific waste from going out of the borders. The conceptual equations and all the subsequent developments and assumptions made to obtain the simplified models are presented. One of the four models is discussed in detail, presenting the final simplified equation to be subsequently used by the government in decision making. The resulting model has been found to be scientifically robust, simple to implement and, above all, fulfilling its purpose: the limitation of waste transport out of Catalonia unless the waste recovery operations are significantly better and justify this transport. Copyright © 2013. Published by Elsevier Ltd.

All-optical differential equation solver with constant-coefficient tunable based on a single microring resonator.

PubMed

Yang, Ting; Dong, Jianji; Lu, Liangjun; Zhou, Linjie; Zheng, Aoling; Zhang, Xinliang; Chen, Jianping

2014-07-04

Photonic integrated circuits for photonic computing open up the possibility for the realization of ultrahigh-speed and ultra wide-band signal processing with compact size and low power consumption. Differential equations model and govern fundamental physical phenomena and engineering systems in virtually any field of science and engineering, such as temperature diffusion processes, physical problems of motion subject to acceleration inputs and frictional forces, and the response of different resistor-capacitor circuits, etc. In this study, we experimentally demonstrate a feasible integrated scheme to solve first-order linear ordinary differential equation with constant-coefficient tunable based on a single silicon microring resonator. Besides, we analyze the impact of the chirp and pulse-width of input signals on the computing deviation. This device can be compatible with the electronic technology (typically complementary metal-oxide semiconductor technology), which may motivate the development of integrated photonic circuits for optical computing.

All-optical differential equation solver with constant-coefficient tunable based on a single microring resonator

PubMed Central

Yang, Ting; Dong, Jianji; Lu, Liangjun; Zhou, Linjie; Zheng, Aoling; Zhang, Xinliang; Chen, Jianping

2014-01-01

Photonic integrated circuits for photonic computing open up the possibility for the realization of ultrahigh-speed and ultra wide-band signal processing with compact size and low power consumption. Differential equations model and govern fundamental physical phenomena and engineering systems in virtually any field of science and engineering, such as temperature diffusion processes, physical problems of motion subject to acceleration inputs and frictional forces, and the response of different resistor-capacitor circuits, etc. In this study, we experimentally demonstrate a feasible integrated scheme to solve first-order linear ordinary differential equation with constant-coefficient tunable based on a single silicon microring resonator. Besides, we analyze the impact of the chirp and pulse-width of input signals on the computing deviation. This device can be compatible with the electronic technology (typically complementary metal-oxide semiconductor technology), which may motivate the development of integrated photonic circuits for optical computing. PMID:24993440

An approach for modeling thermal destruction of hazardous wastes in circulating fluidized bed incinerator.

PubMed

Patil, M P; Sonolikar, R L

2008-10-01

This paper presents a detailed computational fluid dynamics (CFD) based approach for modeling thermal destruction of hazardous wastes in a circulating fluidized bed (CFB) incinerator. The model is based on Eular - Lagrangian approach in which gas phase (continuous phase) is treated in a Eularian reference frame, whereas the waste particulate (dispersed phase) is treated in a Lagrangian reference frame. The reaction chemistry hasbeen modeled through a mixture fraction/ PDF approach. The conservation equations for mass, momentum, energy, mixture fraction and other closure equations have been solved using a general purpose CFD code FLUENT4.5. Afinite volume method on a structured grid has been used for solution of governing equations. The model provides detailed information on the hydrodynamics (gas velocity, particulate trajectories), gas composition (CO, CO2, O2) and temperature inside the riser. The model also allows different operating scenarios to be examined in an efficient manner.

An unstructured grid, three-dimensional model based on the shallow water equations

USGS Publications Warehouse

Casulli, V.; Walters, R.A.

2000-01-01

A semi-implicit finite difference model based on the three-dimensional shallow water equations is modified to use unstructured grids. There are obvious advantages in using unstructured grids in problems with a complicated geometry. In this development, the concept of unstructured orthogonal grids is introduced and applied to this model. The governing differential equations are discretized by means of a semi-implicit algorithm that is robust, stable and very efficient. The resulting model is relatively simple, conserves mass, can fit complicated boundaries and yet is sufficiently flexible to permit local mesh refinements in areas of interest. Moreover, the simulation of the flooding and drying is included in a natural and straightforward manner. These features are illustrated by a test case for studies of convergence rates and by examples of flooding on a river plain and flow in a shallow estuary. Copyright ?? 2000 John Wiley & Sons, Ltd.

Data-based adjoint and H2 optimal control of the Ginzburg-Landau equation

NASA Astrophysics Data System (ADS)

Banks, Michael; Bodony, Daniel

2017-11-01

Equation-free, reduced-order methods of control are desirable when the governing system of interest is of very high dimension or the control is to be applied to a physical experiment. Two-phase flow optimal control problems, our target application, fit these criteria. Dynamic Mode Decomposition (DMD) is a data-driven method for model reduction that can be used to resolve the dynamics of very high dimensional systems and project the dynamics onto a smaller, more manageable basis. We evaluate the effectiveness of DMD-based forward and adjoint operator estimation when applied to H2 optimal control approaches applied to the linear and nonlinear Ginzburg-Landau equation. Perspectives on applying the data-driven adjoint to two phase flow control will be given. Office of Naval Research (ONR) as part of the Multidisciplinary University Research Initiatives (MURI) Program, under Grant Number N00014-16-1-2617.

Modeling Sound Propagation Through Non-Axisymmetric Jets

NASA Technical Reports Server (NTRS)

Leib, Stewart J.

2014-01-01

A method for computing the far-field adjoint Green's function of the generalized acoustic analogy equations under a locally parallel mean flow approximation is presented. The method is based on expanding the mean-flow-dependent coefficients in the governing equation and the scalar Green's function in truncated Fourier series in the azimuthal direction and a finite difference approximation in the radial direction in circular cylindrical coordinates. The combined spectral/finite difference method yields a highly banded system of algebraic equations that can be efficiently solved using a standard sparse system solver. The method is applied to test cases, with mean flow specified by analytical functions, corresponding to two noise reduction concepts of current interest: the offset jet and the fluid shield. Sample results for the Green's function are given for these two test cases and recommendations made as to the use of the method as part of a RANS-based jet noise prediction code.

Numerical study of entropy generation in MHD water-based carbon nanotubes along an inclined permeable surface

NASA Astrophysics Data System (ADS)

Soomro, Feroz Ahmed; Rizwan-ul-Haq; Khan, Z. H.; Zhang, Qiang

2017-10-01

Main theme of the article is to examine the entropy generation analysis for the magneto-hydrodynamic mixed convection flow of water functionalized carbon nanotubes along an inclined stretching surface. Thermophysical properties of both particles and working fluid are incorporated in the system of governing partial differential equations. Rehabilitation of nonlinear system of equations is obtained via similarity transformations. Moreover, solutions of these equations are further utilized to determine the volumetric entropy and characteristic entropy generation. Solutions of governing boundary layer equations are obtained numerically using the finite difference method. Effects of two types of carbon nanotubes, namely, single-wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs) with water as base fluid have been analyzed over the physical quantities of interest, namely, surface skin friction, heat transfer rate and entropy generation coefficients. Influential results of velocities, temperature, entropy generation and isotherms are plotted against the emerging parameter, namely, nanoparticle fraction 0≤φ ≤ 0.2, thermal convective parameter 0≤ λ ≤ 5, Hartmann number 0≤ M≤ 2, suction/injection parameter -1≤ S≤ 1, and Eckert number 0≤ Ec ≤ 2. It is finally concluded that skin friction increases due to the increase in the magnetic parameter, suction/injection and nanoparticle volume fraction, whereas the Nusselt number shows an increasing trend due to the increase in the suction parameter, mixed convection parameter and nanoparticle volume fraction. Similarly, entropy generation shows an opposite behavior for the Hartmann number and mixed convection parameter for both single-wall and multi-wall carbon nanotubes.

Fractional Diffusion Analysis of the Electromagnetic Field In Fractured Media Part II: 2.5-D Approach

NASA Astrophysics Data System (ADS)

Ge, J.; Everett, M. E.; Weiss, C. J.

2012-12-01

A 2.5D finite difference (FD) frequency-domain modeling algorithm based on the theory of fractional diffusion of electromagnetic (EM) fields generated by a loop source lying above a fractured geological medium is addressed in this paper. The presence of fractures in the subsurface, usually containing highly conductive pore fluids, gives rise to spatially hierarchical flow paths of induced EM eddy currents. The diffusion of EM eddy currents in such formations is anomalous, generalizing the classical Gaussian process described by the conventional Maxwell equations. Based on the continuous time random walk (CTRW) theory, the diffusion of EM eddy currents in a rough medium is governed by the fractional Maxwell equations. Here, we model the EM response of a 2D subsurface containing fractured zones, with a 3D loop source, which results the so-called 2.5D model geometry. The governing equation in the frequency domain is converted using Fourier transform into k domain along the strike direction (along which the model conductivity doesn't vary). The resulting equation system is solved by the multifrontal massively parallel solver (MUMPS). The data obtained is then converted back to spatial domain and the time domain. We find excellent agreement between the FD and analytic solutions for a rough halfspace model. Then FD solutions are calculated for a 2D fault zone model with variable conductivity and roughness. We compare the results with responses from several classical models and explore the relationship between the roughness and the spatial density of the fracture distribution.

Reactive solute transport in streams: 1. Development of an equilibrium- based model

USGS Publications Warehouse

Runkel, Robert L.; Bencala, Kenneth E.; Broshears, Robert E.; Chapra, Steven C.

1996-01-01

An equilibrium-based solute transport model is developed for the simulation of trace metal fate and transport in streams. The model is formed by coupling a solute transport model with a chemical equilibrium submodel based on MINTEQ. The solute transport model considers the physical processes of advection, dispersion, lateral inflow, and transient storage, while the equilibrium submodel considers the speciation and complexation of aqueous species, precipitation/dissolution and sorption. Within the model, reactions in the water column may result in the formation of solid phases (precipitates and sorbed species) that are subject to downstream transport and settling processes. Solid phases on the streambed may also interact with the water column through dissolution and sorption/desorption reactions. Consideration of both mobile (water-borne) and immobile (streambed) solid phases requires a unique set of governing differential equations and solution techniques that are developed herein. The partial differential equations describing physical transport and the algebraic equations describing chemical equilibria are coupled using the sequential iteration approach.

A model for tides and currents in the English Channel and southern North Sea

USGS Publications Warehouse

Walters, Roy A.

1987-01-01

The amplitude and phase of 11 tidal constituents for the English Channel and southern North Sea are calculated using a frequency domain, finite element model. The governing equations - the shallow water equations - are modifed such that sea level is calculated using an elliptic equation of the Helmholz type followed by a back-calculation of velocity using the primitive momentum equations. Triangular elements with linear basis functions are used. The modified form of the governing equations provides stable solutions with little numerical noise. In this field-scale test problem, the model was able to produce the details of the structure of 11 tidal constituents including O1, K1, M2, S2, N2, K2, M4, MS4, MN4, M6, and 2MS6.

Diffusion of Charged Species in Liquids

NASA Astrophysics Data System (ADS)

Del Río, J. A.; Whitaker, S.

2016-11-01

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases.

Diffusion of Charged Species in Liquids.

PubMed

Del Río, J A; Whitaker, S

2016-11-04

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases.

Diffusion of Charged Species in Liquids

PubMed Central

del Río, J. A.; Whitaker, S.

2016-01-01

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases. PMID:27811959

Exact finite elements for conduction and convection

NASA Technical Reports Server (NTRS)

Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.

1981-01-01

An approach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions.

Development and Verification of the Charring Ablating Thermal Protection Implicit System Solver

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Calvert, Nathan D.; Kirk, Benjamin S.

2010-01-01

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method with first and second order implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton's method, while the fully implicit linear system is solved with the Generalized Minimal Residual method. Verification results from exact solutions and the Method of Manufactured Solutions are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

Development and Verification of the Charring, Ablating Thermal Protection Implicit System Simulator

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Calvert, Nathan; Kirk, Benjamin S.

2011-01-01

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver (CATPISS) is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method (FEM) with first and second order fully implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton s method, while the linear system is solved via the Generalized Minimum Residual method (GMRES). Verification results from exact solutions and Method of Manufactured Solutions (MMS) are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

Numerical techniques in radiative heat transfer for general, scattering, plane-parallel media

NASA Technical Reports Server (NTRS)

Sharma, A.; Cogley, A. C.

1982-01-01

The study of radiative heat transfer with scattering usually leads to the solution of singular Fredholm integral equations. The present paper presents an accurate and efficient numerical method to solve certain integral equations that govern radiative equilibrium problems in plane-parallel geometry for both grey and nongrey, anisotropically scattering media. In particular, the nongrey problem is represented by a spectral integral of a system of nonlinear integral equations in space, which has not been solved previously. The numerical technique is constructed to handle this unique nongrey governing equation as well as the difficulties caused by singular kernels. Example problems are solved and the method's accuracy and computational speed are analyzed.

Application of the method of lines for solutions of the Navier-Stokes equations using a nonuniform grid distribution

NASA Technical Reports Server (NTRS)

Abolhassani, J. S.; Tiwari, S. N.

1983-01-01

The feasibility of the method of lines for solutions of physical problems requiring nonuniform grid distributions is investigated. To attain this, it is also necessary to investigate the stiffness characteristics of the pertinent equations. For specific applications, the governing equations considered are those for viscous, incompressible, two dimensional and axisymmetric flows. These equations are transformed from the physical domain having a variable mesh to a computational domain with a uniform mesh. The two governing partial differential equations are the vorticity and stream function equations. The method of lines is used to solve the vorticity equation and the successive over relaxation technique is used to solve the stream function equation. The method is applied to three laminar flow problems: the flow in ducts, curved-wall diffusers, and a driven cavity. Results obtained for different flow conditions are in good agreement with available analytical and numerical solutions. The viability and validity of the method of lines are demonstrated by its application to Navier-Stokes equations in the physical domain having a variable mesh.

Parallel iterative solution for h and p approximations of the shallow water equations

USGS Publications Warehouse

Barragy, E.J.; Walters, R.A.

1998-01-01

A p finite element scheme and parallel iterative solver are introduced for a modified form of the shallow water equations. The governing equations are the three-dimensional shallow water equations. After a harmonic decomposition in time and rearrangement, the resulting equations are a complex Helmholz problem for surface elevation, and a complex momentum equation for the horizontal velocity. Both equations are nonlinear and the resulting system is solved using the Picard iteration combined with a preconditioned biconjugate gradient (PBCG) method for the linearized subproblems. A subdomain-based parallel preconditioner is developed which uses incomplete LU factorization with thresholding (ILUT) methods within subdomains, overlapping ILUT factorizations for subdomain boundaries and under-relaxed iteration for the resulting block system. The method builds on techniques successfully applied to linear elements by introducing ordering and condensation techniques to handle uniform p refinement. The combined methods show good performance for a range of p (element order), h (element size), and N (number of processors). Performance and scalability results are presented for a field scale problem where up to 512 processors are used. ?? 1998 Elsevier Science Ltd. All rights reserved.

Optimum wall impedance for spinning modes: A correlation with mode cut-off ratio

NASA Technical Reports Server (NTRS)

Rice, E. J.

1978-01-01

A correlating equation relating the optimum acoustic impedance for the wall lining of a circular duct to the acoustic mode cut-off ratio, is presented. The optimum impedance was correlated with cut-off ratio because the cut-off ratio appears to be the fundamental parameter governing the propagation of sound in the duct. Modes with similar cut-off ratios respond in a similar way to the acoustic liner. The correlation is a semi-empirical expression developed from an empirical modification of an equation originally derived from sound propagation theory in a thin boundary layer. This correlating equation represents a part of a simplified liner design method, based upon modal cut-off ratio, for multimodal noise propagation.

A Shock-Adaptive Godunov Scheme Based on the Generalised Lagrangian Formulation

NASA Astrophysics Data System (ADS)

Lepage, C. Y.; Hui, W. H.

1995-12-01

Application of the Godunov scheme to the Euler equations of gas dynamics based on the Eulerian formulation of flow smears discontinuities, sliplines especially, over several computational cells, while the accuracy in the smooth flow region is of the order O( h), where h is the cell width. Based on the generalised Lagrangian formulation (GLF) of Hui et al., the Godunov scheme yields superior accuracy. By the use of coordinate streamlines in the GLF, the slipline—itself a streamline—is resolved crisply. Infinite shock resolution is achieved through the splitting of shock-cells. An improved entropy-conservation formulation of the governing equations is also proposed for computations in smooth flow regions. Finally, the use of the GLF substantially simplifies the programming logic resulting in a very robust, accurate, and efficient scheme.

A nonlocal continuum model for the biaxial buckling analysis of composite nanoplates with shape memory alloy nanowires

NASA Astrophysics Data System (ADS)

Farajpour, M. R.; Shahidi, A. R.; Farajpour, A.

2018-03-01

In this study, the buckling behavior of a three-layered composite nanoplate reinforced with shape memory alloy (SMA) nanowires is examined. Whereas the upper and lower layers are reinforced with typical nanowires, SMA nanoscale wires are used to strengthen the middle layer of the system. The composite nanoplate is assumed to be under the action of biaxial compressive loading. A scale-dependent mathematical model is presented with the consideration of size effects within the context of the Eringen’s nonlocal continuum mechanics. Using the one-dimensional Brinson’s theory and the Kirchhoff theory of plates, the governing partial differential equations of SMA nanowire-reinforced hybrid nanoplates are derived. Both lateral and longitudinal deflections are taken into consideration in the theoretical formulation and method of solution. In order to reduce the governing differential equations to their corresponding algebraic equations, a discretization approach based on the differential quadrature method is employed. The critical buckling loads of the hybrid nanosystem with various boundary conditions are obtained with the use of a standard eigenvalue solver. It is found that the stability response of SMA composite nanoplates is strongly sensitive to the small scale effect.

On an application of Tikhonov's fixed point theorem to a nonlocal Cahn-Hilliard type system modeling phase separation

NASA Astrophysics Data System (ADS)

Colli, Pierluigi; Gilardi, Gianni; Sprekels, Jürgen

2016-06-01

This paper investigates a nonlocal version of a model for phase separation on an atomic lattice that was introduced by P. Podio-Guidugli (2006) [36]. The model consists of an initial-boundary value problem for a nonlinearly coupled system of two partial differential equations governing the evolution of an order parameter ρ and the chemical potential μ. Singular contributions to the local free energy in the form of logarithmic or double-obstacle potentials are admitted. In contrast to the local model, which was studied by P. Podio-Guidugli and the present authors in a series of recent publications, in the nonlocal case the equation governing the evolution of the order parameter contains in place of the Laplacian a nonlocal expression that originates from nonlocal contributions to the free energy and accounts for possible long-range interactions between the atoms. It is shown that just as in the local case the model equations are well posed, where the technique of proving existence is entirely different: it is based on an application of Tikhonov's fixed point theorem in a rather unusual separable and reflexive Banach space.

On the sensitivity of complex, internally coupled systems

NASA Technical Reports Server (NTRS)

Sobieszczanskisobieski, Jaroslaw

1988-01-01

A method is presented for computing sensitivity derivatives with respect to independent (input) variables for complex, internally coupled systems, while avoiding the cost and inaccuracy of finite differencing performed on the entire system analysis. The method entails two alternative algorithms: the first is based on the classical implicit function theorem formulated on residuals of governing equations, and the second develops the system sensitivity equations in a new form using the partial (local) sensitivity derivatives of the output with respect to the input of each part of the system. A few application examples are presented to illustrate the discussion.

Composite Nanomechanics: A Mechanistic Properties Prediction

NASA Technical Reports Server (NTRS)

Chamis, Christos C.; Handler, Louis M.; Manderscheid, Jane M.

2007-01-01

A unique mechanistic theory is described to predict the properties of nanocomposites. The theory is based on composite micromechanics with progressive substructuring down to a nanoscale slice of a nanofiber where all the governing equations are formulated. These equations hav e been programmed in a computer code. That computer code is used to predict 25 properties of a mononanofiber laminate. The results are pr esented graphically and discussed with respect to their practical sig nificance. Most of the results show smooth distributions. Results for matrix-dependent properties show bimodal through-the-thickness distr ibution with discontinuous changes from mode to mode.

The spectrum of density perturbations in an expanding universe

NASA Technical Reports Server (NTRS)

Silk, J.

1974-01-01

The basic dynamic equations that govern the evolution of perturbations in a Friedmann-Lemaitre universe are derived. General solutions describing the evolution of adiabatic perturbations in the density of matter are obtained, and the choice of the appropriate initial conditions is examined. The various perturbation modes are compared, and the effects of decoupling on the perturbation spectrum are studied. The scheme used to follow the evolution of density perturbations through decoupling is based on an extension of the Eddington approximation to the radiative transfer equation, and is strictly valid in both optically thick and thin limits.

The Application of a Boundary Integral Equation Method to the Prediction of Ducted Fan Engine Noise

NASA Technical Reports Server (NTRS)

Dunn, M. H.; Tweed, J.; Farassat, F.

1999-01-01

The prediction of ducted fan engine noise using a boundary integral equation method (BIEM) is considered. Governing equations for the BIEM are based on linearized acoustics and describe the scattering of incident sound by a thin, finite-length cylindrical duct in the presence of a uniform axial inflow. A classical boundary value problem (BVP) is derived that includes an axisymmetric, locally reacting liner on the duct interior. Using potential theory, the BVP is recast as a system of hypersingular boundary integral equations with subsidiary conditions. We describe the integral equation derivation and solution procedure in detail. The development of the computationally efficient ducted fan noise prediction program TBIEM3D, which implements the BIEM, and its utility in conducting parametric noise reduction studies are discussed. Unlike prediction methods based on spinning mode eigenfunction expansions, the BIEM does not require the decomposition of the interior acoustic field into its radial and axial components which, for the liner case, avoids the solution of a difficult complex eigenvalue problem. Numerical spectral studies are presented to illustrate the nexus between the eigenfunction expansion representation and BIEM results. We demonstrate BIEM liner capability by examining radiation patterns for several cases of practical interest.

A Finite-Volume approach for compressible single- and two-phase flows in flexible pipelines with fluid-structure interaction

NASA Astrophysics Data System (ADS)

Daude, F.; Galon, P.

2018-06-01

A Finite-Volume scheme for the numerical computations of compressible single- and two-phase flows in flexible pipelines is proposed based on an approximate Godunov-type approach. The spatial discretization is here obtained using the HLLC scheme. In addition, the numerical treatment of abrupt changes in area and network including several pipelines connected at junctions is also considered. The proposed approach is based on the integral form of the governing equations making it possible to tackle general equations of state. A coupled approach for the resolution of fluid-structure interaction of compressible fluid flowing in flexible pipes is considered. The structural problem is solved using Euler-Bernoulli beam finite elements. The present Finite-Volume method is applied to ideal gas and two-phase steam-water based on the Homogeneous Equilibrium Model (HEM) in conjunction with a tabulated equation of state in order to demonstrate its ability to tackle general equations of state. The extensive application of the scheme for both shock tube and other transient flow problems demonstrates its capability to resolve such problems accurately and robustly. Finally, the proposed 1-D fluid-structure interaction model appears to be computationally efficient.

SCREENING MODEL FOR NONAQUEOUS PHASE LIQUID TRANS- PORT IN THE VADOSE ZONE USING GREEN-AMPT AND KINEMATIC WAVE THEORY

EPA Science Inventory

In this paper, a screening model for flow of a nonaqueous phase liquid (NAPL) and associated chemical transport in the vadose zone is developed. The model is based on kinematic approximation of the governing equations for both the NAPL and a partitionable chemical constituent. Th...

Finite stretching of a circular plate of neo-Hookean material.

NASA Technical Reports Server (NTRS)

Biricikoglu, V.

1971-01-01

The analytical solution presented is based on the assumption that the deformed thickness of the plate is approximately constant. The nonlinear equations governing finite axisymmetric deformations of a circular plate made of neo-Hookean material are used in the analysis. The variation of circumferential extension ratio and the variation of deformed thickness are shown in graphs.

Spacecraft detumbling through energy dissipation

NASA Technical Reports Server (NTRS)

Fitz-Coy, Norman; Chatterjee, Anindya

1993-01-01

The attitude motion of a tumbling, rigid, axisymmetric spacecraft is considered. A methodology for detumbling the spacecraft through energy dissipation is presented. The differential equations governing this motion are stiff, and therefore an approximate solution, based on the variation of constants method, is developed and utilized in the analysis of the detumbling strategy. Stability of the detumbling process is also addressed.

Rebuilding Organizational Capacity in Turnaround Schools: Insights from the Corporate, Government, and Non-Profit Sectors

ERIC Educational Resources Information Center

Murphy, Joseph; Meyers, Coby V.

2009-01-01

In this article, we provide a grounded narrative of capacity building in the turnaround equation by exploring the turnaround literature outside of education and applying it to troubled schools. Our analysis is based upon reviews of: (1) 14 comprehensive, historical volumes that examine the turnaround phenomenon; (2) 16 book-length analyses of…

A model for tides and currents in the English Channel and southern North Sea

NASA Astrophysics Data System (ADS)

Walters, Roy. A.

The amplitude and phase of 11 tidal constituents for the English Channel and southern North Sea are calculated using a frequency domain, finite element model. The governing equations — the shallow water equations — are modifed such that sea level is calculated using an elliptic equation of the Helmholz type followed by a back-calculation of velocity using the primitive momentum equations. Triangular elements with linear basis functions are used. The modified form of the governing equations provides stable solutions with little numerical noise. In this field-scale test problem, the model was able to produce the details of the structure of 11 tidal constituents including O 1, K 1, M 2, S 2, N 2, K 2, M 4, MS 4, MN 4, M 6, and 2MS 6.

The changing power equation in hospitals.

PubMed

Rayburn, J M; Rayburn, L G

1997-01-01

This research traces the origins, development, and reasons for change in the power equation in the U.S. hospitals between physicians, administrators and accountants. The paper contains three major sections: a review of the literature concerning authority, power, influence, and institutional theory; a review of the development of the power of professions, especially physicians, accounting and healthcare administrators, and the power equilibrium of a hospital; and, a discussion of the social policy implications of the power struggle. The basis for physicians' power derives from their legal ability to act on which others are dependent, such as choosing which hospital to admit patients, order tests and procedures for their patients. The Federal Government's prospective payment system and the hospitals' related case-mix accounting systems appear to influence the power structure in hospitals by redistributing that power. The basis of the accountants' power base is control of financial information. Accountants have a definite potential for influencing which departments receive financial resources and for what purpose. This moves hospital accountants into the power equation. The basis of the hospital administrators' power is their formal authority in the organization. Regardless of what actions federal government agencies, hospital accountants, or hospital administrators take, physicians are expected to remain the dominant factor in the power equation. Without major environmental changes to gain control of physician services, only insignificant results in cost containment will occur.

Computer modeling of heat pipe performance

NASA Technical Reports Server (NTRS)

Peterson, G. P.

1983-01-01

A parametric study of the defining equations which govern the steady state operational characteristics of the Grumman monogroove dual passage heat pipe is presented. These defining equations are combined to develop a mathematical model which describes and predicts the operational and performance capabilities of a specific heat pipe given the necessary physical characteristics and working fluid. Included is a brief review of the current literature, a discussion of the governing equations, and a description of both the mathematical and computer model. Final results of preliminary test runs of the model are presented and compared with experimental tests on actual prototypes.

Heavy-tailed fractional Pearson diffusions.

PubMed

Leonenko, N N; Papić, I; Sikorskii, A; Šuvak, N

2017-11-01

We define heavy-tailed fractional reciprocal gamma and Fisher-Snedecor diffusions by a non-Markovian time change in the corresponding Pearson diffusions. Pearson diffusions are governed by the backward Kolmogorov equations with space-varying polynomial coefficients and are widely used in applications. The corresponding fractional reciprocal gamma and Fisher-Snedecor diffusions are governed by the fractional backward Kolmogorov equations and have heavy-tailed marginal distributions in the steady state. We derive the explicit expressions for the transition densities of the fractional reciprocal gamma and Fisher-Snedecor diffusions and strong solutions of the associated Cauchy problems for the fractional backward Kolmogorov equation.

LETTER TO THE EDITOR: Gravitational instantons

NASA Astrophysics Data System (ADS)

Nutku, Y.; Sheftel', M. B.; Malykh, A. A.

1997-03-01

New instanton solutions of the Einstein field equations are presented. These solutions are obtained from a reduction of the complex Monge - Ampère equation governing metrics with anti-self-dual curvature to an interesting two-dimensional real Monge - Ampère equation.

a Speculative Study on Negative-Dimensional Potential and Wave Problems by Implicit Calculus Modeling Approach

NASA Astrophysics Data System (ADS)

Chen, Wen; Wang, Fajie

Based on the implicit calculus equation modeling approach, this paper proposes a speculative concept of the potential and wave operators on negative dimensionality. Unlike the standard partial differential equation (PDE) modeling, the implicit calculus modeling approach does not require the explicit expression of the PDE governing equation. Instead the fundamental solution of physical problem is used to implicitly define the differential operator and to implement simulation in conjunction with the appropriate boundary conditions. In this study, we conjecture an extension of the fundamental solution of the standard Laplace and Helmholtz equations to negative dimensionality. And then by using the singular boundary method, a recent boundary discretization technique, we investigate the potential and wave problems using the fundamental solution on negative dimensionality. Numerical experiments reveal that the physics behaviors on negative dimensionality may differ on positive dimensionality. This speculative study might open an unexplored territory in research.

Multigrid Method for Modeling Multi-Dimensional Combustion with Detailed Chemistry

NASA Technical Reports Server (NTRS)

Zheng, Xiaoqing; Liu, Chaoqun; Liao, Changming; Liu, Zhining; McCormick, Steve

1996-01-01

A highly accurate and efficient numerical method is developed for modeling 3-D reacting flows with detailed chemistry. A contravariant velocity-based governing system is developed for general curvilinear coordinates to maintain simplicity of the continuity equation and compactness of the discretization stencil. A fully-implicit backward Euler technique and a third-order monotone upwind-biased scheme on a staggered grid are used for the respective temporal and spatial terms. An efficient semi-coarsening multigrid method based on line-distributive relaxation is used as the flow solver. The species equations are solved in a fully coupled way and the chemical reaction source terms are treated implicitly. Example results are shown for a 3-D gas turbine combustor with strong swirling inflows.

Statics of wrinkling films

NASA Technical Reports Server (NTRS)

Zak, M.

1982-01-01

An analytical investigation of the equilibrium of wrinkling films is conducted. Zak (1979) has shown that wrinkling occurs in connection with the instability of a smooth film having no resistance to bending in the case of compression. The governing equation for the equilibrium of a film with possible regions of wrinkling is considered. The introduction of fictitious stress reduces the governing equation to a form which formally coincides with the governing equation for a string. Equilibrium conditions in the case of an absence of external forces are explored, taking into account the stretching of a semispherical film, the torsion of a convex film of revolution, and stress singularities. A study is conducted of the equilibrium under conditions in which external forces normal to the surface of a film are present. Attention is also given to the equilibrium in a potential field.

Chronology of DIC technique based on the fundamental mathematical modeling and dehydration impact.

PubMed

Alias, Norma; Saipol, Hafizah Farhah Saipan; Ghani, Asnida Che Abd

2014-12-01

A chronology of mathematical models for heat and mass transfer equation is proposed for the prediction of moisture and temperature behavior during drying using DIC (Détente Instantanée Contrôlée) or instant controlled pressure drop technique. DIC technique has the potential as most commonly used dehydration method for high impact food value including the nutrition maintenance and the best possible quality for food storage. The model is governed by the regression model, followed by 2D Fick's and Fourier's parabolic equation and 2D elliptic-parabolic equation in a rectangular slice. The models neglect the effect of shrinkage and radiation effects. The simulations of heat and mass transfer equations with parabolic and elliptic-parabolic types through some numerical methods based on finite difference method (FDM) have been illustrated. Intel®Core™2Duo processors with Linux operating system and C programming language have been considered as a computational platform for the simulation. Qualitative and quantitative differences between DIC technique and the conventional drying methods have been shown as a comparative.

On the slow dynamics of near-field acoustically levitated objects under High excitation frequencies

NASA Astrophysics Data System (ADS)

Ilssar, Dotan; Bucher, Izhak

2015-10-01

This paper introduces a simplified analytical model describing the governing dynamics of near-field acoustically levitated objects. The simplification converts the equation of motion coupled with the partial differential equation of a compressible fluid, into a compact, second order ordinary differential equation, where the local stiffness and damping are transparent. The simplified model allows one to more easily analyse and design near-field acoustic levitation based systems, and it also helps to devise closed-loop controller algorithms for such systems. Near-field acoustic levitation employs fast ultrasonic vibrations of a driving surface and exploits the viscosity and the compressibility of a gaseous medium to achieve average, load carrying pressure. It is demonstrated that the slow dynamics dominates the transient behaviour, while the time-scale associated with the fast, ultrasonic excitation has a small presence in the oscillations of the levitated object. Indeed, the present paper formulates the slow dynamics under an ultrasonic excitation without the need to explicitly consider the latter. The simplified model is compared with a numerical scheme based on Reynolds equation and with experiments, both showing reasonably good results.

Progress Toward Improving Jet Noise Predictions in Hot Jets

NASA Technical Reports Server (NTRS)

Khavaran, Abbas; Kenzakowski, Donald C.

2007-01-01

An acoustic analogy methodology for improving noise predictions in hot round jets is presented. Past approaches have often neglected the impact of temperature fluctuations on the predicted sound spectral density, which could be significant for heated jets, and this has yielded noticeable acoustic under-predictions in such cases. The governing acoustic equations adopted here are a set of linearized, inhomogeneous Euler equations. These equations are combined into a single third order linear wave operator when the base flow is considered as a locally parallel mean flow. The remaining second-order fluctuations are regarded as the equivalent sources of sound and are modeled. It is shown that the hot jet effect may be introduced primarily through a fluctuating velocity/enthalpy term. Modeling this additional source requires specialized inputs from a RANS-based flowfield simulation. The information is supplied using an extension to a baseline two equation turbulence model that predicts total enthalpy variance in addition to the standard parameters. Preliminary application of this model to a series of unheated and heated subsonic jets shows significant improvement in the acoustic predictions at the 90 degree observer angle.

Existence and stability of dispersive solutions to the Kadomtsev-Petviashvili equation in the presence of dispersion effect

NASA Astrophysics Data System (ADS)

Das, Amiya; Ganguly, Asish

2017-07-01

The paper deals with Kadomtsev-Petviashvili (KP) equation in presence of a small dispersion effect. The nature of solutions are examined under the dispersion effect by using Lyapunov function and dynamical system theory. We prove that when dispersion is added to the KP equation, in certain regions, yet there exist bounded traveling wave solutions in the form of solitary waves, periodic and elliptic functions. The general solution of the equation with or without the dispersion effect are obtained in terms of Weirstrass ℘ functions and Jacobi elliptic functions. New form of kink-type solutions are established by exploring a new technique based on factorization method, use of functional transformation and the Abel's first order nonlinear equation. Furthermore, the stability analysis of the dispersive solutions are examined which shows that the traveling wave velocity is a bifurcation parameter which governs between different classes of waves. We use the phase plane analysis and show that at a critical velocity, the solution has a transcritical bifurcation.

Arbitrarily Curved and Twisted Space Beams. Ph.D. Thesis - Va. Polytech. Inst. and State Univ.; [Elastic Deformation, Stress Analysis

NASA Technical Reports Server (NTRS)

Hunter, W. F.

1974-01-01

A derivation of the equations which govern the deformation of an arbitrarily curved and twisted space beam is presented. These equations differ from those of the classical theory in that (1) extensional effects are included; (2) the strain-displacement relations are derived; and (3) the expressions for the stress resultants are developed from the strain displacement relations. It is shown that the torsional stress resultant obtained by the classical approach is basically incorrect except when the cross-section is circular. The governing equations are given in the form of first-order differential equations. A numerical algorithm is given for obtaining the natural vibration characteristics and example problems are presented.

Fractional calculus in hydrologic modeling: A numerical perspective

PubMed Central

Benson, David A.; Meerschaert, Mark M.; Revielle, Jordan

2013-01-01

Fractional derivatives can be viewed either as handy extensions of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Lévy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Lévy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus. PMID:23524449

Application of the control volume mixed finite element method to a triangular discretization

USGS Publications Warehouse

Naff, R.L.

2012-01-01

A two-dimensional control volume mixed finite element method is applied to the elliptic equation. Discretization of the computational domain is based in triangular elements. Shape functions and test functions are formulated on the basis of an equilateral reference triangle with unit edges. A pressure support based on the linear interpolation of elemental edge pressures is used in this formulation. Comparisons are made between results from the standard mixed finite element method and this control volume mixed finite element method. Published 2011. This article is a US Government work and is in the public domain in the USA. ?? 2012 John Wiley & Sons, Ltd. This article is a US Government work and is in the public domain in the USA.

Application of the Finite Element Method to Rotary Wing Aeroelasticity

NASA Technical Reports Server (NTRS)

Straub, F. K.; Friedmann, P. P.

1982-01-01

A finite element method for the spatial discretization of the dynamic equations of equilibrium governing rotary-wing aeroelastic problems is presented. Formulation of the finite element equations is based on weighted Galerkin residuals. This Galerkin finite element method reduces algebraic manipulative labor significantly, when compared to the application of the global Galerkin method in similar problems. The coupled flap-lag aeroelastic stability boundaries of hingeless helicopter rotor blades in hover are calculated. The linearized dynamic equations are reduced to the standard eigenvalue problem from which the aeroelastic stability boundaries are obtained. The convergence properties of the Galerkin finite element method are studied numerically by refining the discretization process. Results indicate that four or five elements suffice to capture the dynamics of the blade with the same accuracy as the global Galerkin method.

Modern gyrokinetic formulation of collisional and turbulent transport in toroidally rotating plasmas

NASA Astrophysics Data System (ADS)

Sugama, H.

2017-12-01

Collisional and turbulent transport processes in toroidal plasmas with large toroidal flows on the order of the ion thermal velocity are formulated based on the modern gyrokinetic theory. Governing equations for background and turbulent electromagnetic fields and gyrocenter distribution functions are derived from the Lagrangian variational principle with effects of collisions and external sources taken into account. Noether's theorem modified for collisional systems and the collision operator given in terms of Poisson brackets are applied to derivation of the particle, energy, and toroidal momentum balance equations in the conservative forms which are desirable properties for long-time global transport simulation. The resultant balance equations are shown to include the classical, neoclassical, and turbulent transport fluxes which agree with those obtained from the conventional recursive formulations.

Numerical investigation of shock induced bubble collapse in water

NASA Astrophysics Data System (ADS)

Apazidis, N.

2016-04-01

A semi-conservative, stable, interphase-capturing numerical scheme for shock propagation in heterogeneous systems is applied to the problem of shock propagation in liquid-gas systems. The scheme is based on the volume-fraction formulation of the equations of motion for liquid and gas phases with separate equations of state. The semi-conservative formulation of the governing equations ensures the absence of spurious pressure oscillations at the material interphases between liquid and gas. Interaction of a planar shock in water with a single spherical bubble as well as twin adjacent bubbles is investigated. Several stages of the interaction process are considered, including focusing of the transmitted shock within the deformed bubble, creation of a water-hammer shock as well as generation of high-speed liquid jet in the later stages of the process.

Energy-optimal path planning by stochastic dynamically orthogonal level-set optimization

NASA Astrophysics Data System (ADS)

Subramani, Deepak N.; Lermusiaux, Pierre F. J.

2016-04-01

A stochastic optimization methodology is formulated for computing energy-optimal paths from among time-optimal paths of autonomous vehicles navigating in a dynamic flow field. Based on partial differential equations, the methodology rigorously leverages the level-set equation that governs time-optimal reachability fronts for a given relative vehicle-speed function. To set up the energy optimization, the relative vehicle-speed and headings are considered to be stochastic and new stochastic Dynamically Orthogonal (DO) level-set equations are derived. Their solution provides the distribution of time-optimal reachability fronts and corresponding distribution of time-optimal paths. An optimization is then performed on the vehicle's energy-time joint distribution to select the energy-optimal paths for each arrival time, among all stochastic time-optimal paths for that arrival time. Numerical schemes to solve the reduced stochastic DO level-set equations are obtained, and accuracy and efficiency considerations are discussed. These reduced equations are first shown to be efficient at solving the governing stochastic level-sets, in part by comparisons with direct Monte Carlo simulations. To validate the methodology and illustrate its accuracy, comparisons with semi-analytical energy-optimal path solutions are then completed. In particular, we consider the energy-optimal crossing of a canonical steady front and set up its semi-analytical solution using a energy-time nested nonlinear double-optimization scheme. We then showcase the inner workings and nuances of the energy-optimal path planning, considering different mission scenarios. Finally, we study and discuss results of energy-optimal missions in a wind-driven barotropic quasi-geostrophic double-gyre ocean circulation.

On an Acoustic Wave Equation Arising in Non-Equilibrium Gasdynamics. Classroom Notes

ERIC Educational Resources Information Center

Chandran, Pallath

2004-01-01

The sixth-order wave equation governing the propagation of one-dimensional acoustic waves in a viscous, heat conducting gaseous medium subject to relaxation effects has been considered. It has been reduced to a system of lower order equations corresponding to the finite speeds occurring in the equation, following a method due to Whitham. The lower…

Green function of the double-fractional Fokker-Planck equation: path integral and stochastic differential equations.

PubMed

Kleinert, H; Zatloukal, V

2013-11-01

The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.

Effects of Classroom Instruction on Students' Understanding of Quadratic Equations

ERIC Educational Resources Information Center

Vaiyavutjamai, Pongchawee; Clements, M. A.

2006-01-01

Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of…

Theoretical and experimental investigations on the dynamic and thermodynamic characteristics of the linear compressor for the pulse tube cryocooler

NASA Astrophysics Data System (ADS)

Zhang, L.; Dang, H. Z.; Tan, J.; Bao, D.; Zhao, Y. B.; Qian, G. Z.

2015-12-01

Theoretical and experimental investigations on the dynamic and thermodynamic characteristics of a linear compressor incorporating the thermodynamic characteristics of the inertance tube pulse tube cold finger have been made. Both the compressor and cold finger are assumed as a one-dimensional thermodynamic model. The governing equations of the thermodynamic characteristics of the working gas are summarized, and the effects of the cooling performance on the working gas in the compression space are discussed. Based on the analysis of the working gas, the governing equations of the dynamic and thermodynamic characteristics of the compressor are deduced, and then the principles of achieving the optimal performance of the compressor are discussed in detail. Systematic experimental investigations are conducted on a developed moving-coil linear compressor which drives a pulse tube cold finger, which indicate the general agreement with the simulated results, and thus verify the rationality of the theoretical model and analyses.

A general numerical model for wave rotor analysis

NASA Technical Reports Server (NTRS)

Paxson, Daniel W.

1992-01-01

Wave rotors represent one of the promising technologies for achieving very high core temperatures and pressures in future gas turbine engines. Their operation depends upon unsteady gas dynamics and as such, their analysis is quite difficult. This report describes a numerical model which has been developed to perform such an analysis. Following a brief introduction, a summary of the wave rotor concept is given. The governing equations are then presented, along with a summary of the assumptions used to obtain them. Next, the numerical integration technique is described. This is an explicit finite volume technique based on the method of Roe. The discussion then focuses on the implementation of appropriate boundary conditions. Following this, some results are presented which first compare the numerical approximation to the governing differential equations and then compare the overall model to an actual wave rotor experiment. Finally, some concluding remarks are presented concerning the limitations of the simplifying assumptions and areas where the model may be improved.

Process Simulation of Cold Pressing and Sintering of Armstrong CP-Ti Powders

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

Gorti, Sarma B; Sabau, Adrian S; Peter, William H

A computational methodology is presented for the process simulation of cold pressing and sintering of Armstrong CP-Ti powders. Since the powder consolidation is governed by specific pressure-dependent constitutive equations, solution algorithms were developed for the ABAQUS user material subroutine, UMAT, for computing the plastic strain increments based on an implicit integration of the nonlinear yield function, flow rule, and hardening equations. Sintering was simulated using a model based on diffusional creep using the user subroutine CREEP. The initial mesh, stress, and density for the simulation of sintering were obtained from the results of the cold pressing simulation, minimizing the errorsmore » from decoupling the cold pressing and sintering simulations. Numerical simulation results are presented for the cold compaction followed by a sintering step of the Ti powders. The numerical simulation results for the relative density were compared to those measured from experiments before and after sintering, showing that the relative density can be accurately predicted. Notice: This manuscript has been authored by UT-Battelle, LLC, under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. ACKNOWLEDGEMENTS This research was sponsored by the U.S. DOE, and carried out at ORNL, under Contract DE-AC05-00OR22725 with UT-Battelle, LLC. This research was sponsored by the U.S. DOE, EERE Industrial Technology Program Office under CPS Agreement # 17881.« less

An Exact Integration Scheme for Radiative Cooling in Hydrodynamical Simulations

NASA Astrophysics Data System (ADS)

Townsend, R. H. D.

2009-04-01

A new scheme for incorporating radiative cooling in hydrodynamical codes is presented, centered around exact integration of the governing semidiscrete cooling equation. Using benchmark calculations based on the cooling downstream of a radiative shock, I demonstrate that the new scheme outperforms traditional explicit and implicit approaches in terms of accuracy, while remaining competitive in terms of execution speed.

Application of a new multiphase multicomponent volcanic conduit model with magma degassing and crystallization to Stromboli volcano.

NASA Astrophysics Data System (ADS)

La Spina, Giuseppe; Burton, Mike; de'Michieli Vitturi, Mattia

2014-05-01

Volcanoes exhibit a wide range of eruption styles, from relatively slow effusive eruptions, generating lava flows and lava domes, to explosive eruptions, in which very large volumes of fragmented magma and volcanic gas are ejected high into the atmosphere. During an eruption, much information regarding the magma ascent dynamics can be gathered: melt and exsolved gas composition, crystal content, mass flow rate and ballistic velocities, to name just a few. Due to the lack of direct observations of the conduit itself, mathematical models for magma ascent provide invaluable tools for a better comprehension of the system. The complexity of the multiphase multicomponent gas-magma-solid system is reflected in the corresponding mathematical model; a set of non-linear hyperbolic partial differential and constitutive equations, which describe the physical system, has to be formulated and solved. The standard approach to derive governing equations for two-phase flow is based on averaging procedures, which leads to a system of governing equations in the form of mass, momentum and energy balance laws for each phase coupled with algebraic and differential source terms which represent phase interactions. For this work, we used the model presented by de' Michieli Vitturi et al. (EGU General Assembly Conference Abstracts, 2013), where a different approach based on the theory of thermodynamically compatible systems has been adopted to write the governing multiphase equations for two-phase compressible flow (with two velocities and two pressures) in the form of a conservative hyperbolic system of partial differential equations, coupled with non-differential source terms. Here, in order to better describe the multicomponent nature of the system, we extended the model adding several transport equations to the system for different crystal components and different gas species, and implementing appropriate equations of state. The constitutive equations of the model are chosen to reproduce both effusive and explosive eruptive activities at Stromboli volcano. Three different crystal components (olivine, pyroxene and feldspar) and two different gas species (water and carbon dioxide) are taken into account. The equilibrium profiles of crystallization as function of pressure, temperature and water content are modeled using the numerical codes AlphaMELTS and DAKOTA. The equilibrium of dissolved gas content, instead, is obtained using a non-linear fitting of data computed using VolatileCALC. With these data, we simulate numerically the lava effusion that occurred at Stromboli between 27 February and 2 April 2007, and find good agreement with the observed data (vesicularity, exsolved gas composition, crystal content and mass flow rate) at the vent. We find that the model is highly sensitive to input magma temperature, going from effusive to explosive eruption with temperature changes by just 20 °C. We thoroughly investigated through a sensitivity analysis the control of the temperature of magma chamber and of the radius of the conduit on the mass flow rate, obtaining also a set of admissible temperatures and conduit radii that produce results in agreement with the real observations.

Theory and modeling of atmospheric turbulence, part 1

NASA Technical Reports Server (NTRS)

1984-01-01

The cascade transfer which is the only function to describe the mode coupling as the result of the nonlinear hydrodynamic state of turbulence is discussed. A kinetic theory combined with a scaling procedure was developed. The transfer function governs the non-linear mode coupling in strong turbulence. The master equation is consistent with the hydrodynamical system that describes the microdynamic state of turbulence and has the advantages to be homogeneous and have fewer nonlinear terms. The modes are scaled into groups to decipher the governing transport processes and statistical characteristics. An equation of vorticity transport describes the microdynamic state of two dimensional, isotropic and homogeneous, geostrophic turbulence. The equation of evolution of the macrovorticity is derived from group scaling in the form of the Fokker-Planck equation with memory. The microdynamic state of turbulence is transformed into the Liouville equation to derive the kinetic equation of the singlet distribution in turbulence. The collision integral contains a memory, which is analyzed with pair collision and the multiple collision. Two other kinetic equations are developed in parallel for the propagator and the transition probability for the interaction among the groups.

Transformed Fourier and Fick equations for the control of heat and mass diffusion

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

Guenneau, S.; Petiteau, D.; Zerrad, M.

We review recent advances in the control of diffusion processes in thermodynamics and life sciences through geometric transforms in the Fourier and Fick equations, which govern heat and mass diffusion, respectively. We propose to further encompass transport properties in the transformed equations, whereby the temperature is governed by a three-dimensional, time-dependent, anisotropic heterogeneous convection-diffusion equation, which is a parabolic partial differential equation combining the diffusion equation and the advection equation. We perform two dimensional finite element computations for cloaks, concentrators and rotators of a complex shape in the transient regime. We precise that in contrast to invisibility cloaks for waves,more » the temperature (or mass concentration) inside a diffusion cloak crucially depends upon time, its distance from the source, and the diffusivity of the invisibility region. However, heat (or mass) diffusion outside cloaks, concentrators and rotators is unaffected by their presence, whatever their shape or position. Finally, we propose simplified designs of layered cylindrical and spherical diffusion cloaks that might foster experimental efforts in thermal and biochemical metamaterials.« less

An approximate Riemann solver for real gas parabolized Navier-Stokes equations

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

Urbano, Annafederica, E-mail: annafederica.urbano@uniroma1.it; Nasuti, Francesco, E-mail: francesco.nasuti@uniroma1.it

2013-01-15

Under specific assumptions, parabolized Navier-Stokes equations are a suitable mean to study channel flows. A special case is that of high pressure flow of real gases in cooling channels where large crosswise gradients of thermophysical properties occur. To solve the parabolized Navier-Stokes equations by a space marching approach, the hyperbolicity of the system of governing equations is obtained, even for very low Mach number flow, by recasting equations such that the streamwise pressure gradient is considered as a source term. For this system of equations an approximate Roe's Riemann solver is developed as the core of a Godunov type finitemore » volume algorithm. The properties of the approximated Riemann solver, which is a modification of Roe's Riemann solver for the parabolized Navier-Stokes equations, are presented and discussed with emphasis given to its original features introduced to handle fluids governed by a generic real gas EoS. Sample solutions are obtained for low Mach number high compressible flows of transcritical methane, heated in straight long channels, to prove the solver ability to describe flows dominated by complex thermodynamic phenomena.« less

Exact finite elements for conduction and convection

NASA Technical Reports Server (NTRS)

Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.

1981-01-01

An appproach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions. Previously announced in STAR as N81-31507

Development of a three-dimensional supersonic inlet flow analysis

NASA Technical Reports Server (NTRS)

Buggeln, R. C.; Mcdonald, H.; Levy, R.; Kreskovsky, J. P.

1980-01-01

A method for computing three dimensional flow in supersonic inlets is described. An approximate set of governing equations is given for viscous flows which have a primary flow direction. The governing equations are written in general orthogonal coordinates. These equations are modified in the subsonic region of the flow to prevent the phenomenon of branching. Results are presented for the two sample cases: a Mach number equals 2.5 flow in a square duct, and a Mach number equals 3.0 flow in a research jet engine inlet. In the latter case the computed results are compared with the experimental data. A users' manual is included.

Dynamic sealing principles

NASA Technical Reports Server (NTRS)

Zuk, J.

1976-01-01

The fundamental principles governing dynamic sealing operation are discussed. Different seals are described in terms of these principles. Despite the large variety of detailed construction, there appear to be some basic principles, or combinations of basic principles, by which all seals function, these are presented and discussed. Theoretical and practical considerations in the application of these principles are discussed. Advantages, disadvantages, limitations, and application examples of various conventional and special seals are presented. Fundamental equations governing liquid and gas flows in thin film seals, which enable leakage calculations to be made, are also presented. Concept of flow functions, application of Reynolds lubrication equation, and nonlubrication equation flow, friction and wear; and seal lubrication regimes are explained.

Incremental analysis of large elastic deformation of a rotating cylinder

NASA Technical Reports Server (NTRS)

Buchanan, G. R.

1976-01-01

The effect of finite deformation upon a rotating, orthotropic cylinder was investigated using a general incremental theory. The incremental equations of motion are developed using the variational principle. The governing equations are derived using the principle of virtual work for a body with initial stress. The governing equations are reduced to those for the title problem and a numerical solution is obtained using finite difference approximations. Since the problem is defined in terms of one independent space coordinate, the finite difference grid can be modified as the incremental deformation occurs without serious numerical difficulties. The nonlinear problem is solved incrementally by totaling a series of linear solutions.

Continuum mechanics and thermodynamics in the Hamilton and the Godunov-type formulations

NASA Astrophysics Data System (ADS)

Peshkov, Ilya; Pavelka, Michal; Romenski, Evgeniy; Grmela, Miroslav

2018-01-01

Continuum mechanics with dislocations, with the Cattaneo-type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov-type system of the first-order, symmetric hyperbolic partial differential equations (SHTC equations). The compatibility with thermodynamics of the time reversible part of the governing equations is mathematically expressed in the former formulation as degeneracy of the Hamiltonian structure and in the latter formulation as the existence of a companion conservation law. In both formulations the time irreversible part represents gradient dynamics. The Godunov-type formulation brings the mathematical rigor (the local well posedness of the Cauchy initial value problem) and the possibility to discretize while keeping the physical content of the governing equations (the Godunov finite volume discretization).

Solving the Fluid Pressure Poisson Equation Using Multigrid-Evaluation and Improvements.

PubMed

Dick, Christian; Rogowsky, Marcus; Westermann, Rudiger

2016-11-01

In many numerical simulations of fluids governed by the incompressible Navier-Stokes equations, the pressure Poisson equation needs to be solved to enforce mass conservation. Multigrid solvers show excellent convergence in simple scenarios, yet they can converge slowly in domains where physically separated regions are combined at coarser scales. Moreover, existing multigrid solvers are tailored to specific discretizations of the pressure Poisson equation, and they cannot easily be adapted to other discretizations. In this paper we analyze the convergence properties of existing multigrid solvers for the pressure Poisson equation in different simulation domains, and we show how to further improve the multigrid convergence rate by using a graph-based extension to determine the coarse grid hierarchy. The proposed multigrid solver is generic in that it can be applied to different kinds of discretizations of the pressure Poisson equation, by using solely the specification of the simulation domain and pre-assembled computational stencils. We analyze the proposed solver in combination with finite difference and finite volume discretizations of the pressure Poisson equation. Our evaluations show that, despite the common assumption, multigrid schemes can exploit their potential even in the most complicated simulation scenarios, yet this behavior is obtained at the price of higher memory consumption.

Development of advanced Navier-Stokes solver

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan

1994-01-01

The objective of research was to develop and validate new computational algorithms for solving the steady and unsteady Euler and Navier-Stokes equations. The end-products are new three-dimensional Euler and Navier-Stokes codes that are faster, more reliable, more accurate, and easier to use. The three-dimensional Euler and full/thin-layer Reynolds-averaged Navier-Stokes equations for compressible/incompressible flows are solved on structured hexahedral grids. The Baldwin-Lomax algebraic turbulence model is used for closure. The space discretization is based on a cell-centered finite-volume method augmented by a variety of numerical dissipation models with optional total variation diminishing limiters. The governing equations are integrated in time by an implicit method based on lower-upper factorization and symmetric Gauss-Seidel relaxation. The algorithm is vectorized on diagonal planes of sweep using two-dimensional indices in three dimensions. Convergence rates and the robustness of the codes are enhanced by the use of an implicit full approximation storage multigrid method.

Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes

NASA Astrophysics Data System (ADS)

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2016-05-01

A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

Numerical Modeling of Unsteady Thermofluid Dynamics in Cryogenic Systems

NASA Technical Reports Server (NTRS)

Majumdar, Alok

2003-01-01

A finite volume based network analysis procedure has been applied to model unsteady flow without and with heat transfer. Liquid has been modeled as compressible fluid where the compressibility factor is computed from the equation of state for a real fluid. The modeling approach recognizes that the pressure oscillation is linked with the variation of the compressibility factor; therefore, the speed of sound does not explicitly appear in the governing equations. The numerical results of chilldown process also suggest that the flow and heat transfer are strongly coupled. This is evident by observing that the mass flow rate during 90-second chilldown process increases by factor of ten.

Three-Loop Automatic of Control System the Landfill of Household Solid Waste

NASA Astrophysics Data System (ADS)

Sereda, T. G.; Kostarev, S. N.

2017-05-01

The analysis of models of governance ground municipal solid waste (MSW). Considered a distributed circuit (spatio-temporal) ground control model. Developed a dynamic model of multicontour control landfill. Adjustable parameters are defined (the ratio of CH4 CO2 emission/fluxes, concentrations of heavy metals ions) and control (purging array, irrigation, adding reagents). Based on laboratory studies carried out with the analysis of equity flows and procedures developed by the transferring matrix that takes into account the relationship control loops. A system of differential equations in the frequency and time domains. Given the numerical approaches solving systems of differential equations in finite differential form.

Full-Scale Direct Numerical Simulation of Two- and Three-Dimensional Instabilities and Rivulet Formulation in Heated Falling Films

NASA Technical Reports Server (NTRS)

Krishnamoorthy, S.; Ramaswamy, B.; Joo, S. W.

1995-01-01

A thin film draining on an inclined plate has been studied numerically using finite element method. Three-dimensional governing equations of continuity, momentum and energy with a moving boundary are integrated in an arbitrary Lagrangian Eulerian frame of reference. Kinematic equation is solved to precisely update interface location. Rivulet formation based on instability mechanism has been simulated using full-scale computation. Comparisons with long-wave theory are made to validate the numerical scheme. Detailed analysis of two- and three-dimensional nonlinear wave formation and spontaneous rupture forming rivulets under the influence of combined thermocapillary and surface-wave instabilities is performed.

Ablative Thermal Response Analysis Using the Finite Element Method

NASA Technical Reports Server (NTRS)

Dec John A.; Braun, Robert D.

2009-01-01

A review of the classic techniques used to solve ablative thermal response problems is presented. The advantages and disadvantages of both the finite element and finite difference methods are described. As a first step in developing a three dimensional finite element based ablative thermal response capability, a one dimensional computer tool has been developed. The finite element method is used to discretize the governing differential equations and Galerkin's method of weighted residuals is used to derive the element equations. A code to code comparison between the current 1-D tool and the 1-D Fully Implicit Ablation and Thermal Response Program (FIAT) has been performed.

Analytical Characterization on Pulse Propagation in a Semiconductor Optical Amplifier Based on Homotopy Analysis Method

NASA Astrophysics Data System (ADS)

Jia, Xiaofei

2018-06-01

Starting from the basic equations describing the evolution of the carriers and photons inside a semiconductor optical amplifier (SOA), the equation governing pulse propagation in the SOA is derived. By employing homotopy analysis method (HAM), a series solution for the output pulse by the SOA is obtained, which can effectively characterize the temporal features of the nonlinear process during the pulse propagation inside the SOA. Moreover, the analytical solution is compared with numerical simulations with a good agreement. The theoretical results will benefit the future analysis of other problems related to the pulse propagation in the SOA.

Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators

NASA Technical Reports Server (NTRS)

Burns, John A.; Marrekchi, Hamadi

1993-01-01

The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.

Combined effects of heat and mass transfer to magneto hydrodynamics oscillatory dusty fluid flow in a porous channel

NASA Astrophysics Data System (ADS)

Govindarajan, A.; Vijayalakshmi, R.; Ramamurthy, V.

2018-04-01

The main aim of this article is to study the combined effects of heat and mass transfer to radiative Magneto Hydro Dynamics (MHD) oscillatory optically thin dusty fluid in a saturated porous medium channel. Based on certain assumptions, the momentum, energy, concentration equations are obtained.The governing equations are non-dimensionalised, simplified and solved analytically. The closed analytical form solutions for velocity, temperature, concentration profiles are obtained. Numerical computations are presented graphically to show the salient features of various physical parameters. The shear stress, the rate of heat transfer and the rate of mass transfer are also presented graphically.

Hamiltonian structure of the Lotka-Volterra equations

NASA Astrophysics Data System (ADS)

Nutku, Y.

1990-03-01

The Lotka-Volterra equations governing predator-prey relations are shown to admit Hamiltonian structure with respect to a generalized Poisson bracket. These equations provide an example of a system for which the naive criterion for the existence of Hamiltonian structure fails. We show further that there is a three-component generalization of the Lotka-Volterra equations which is a bi-Hamiltonian system.

Direct simulation of groundwater age

USGS Publications Warehouse

Goode, Daniel J.

1996-01-01

A new method is proposed to simulate groundwater age directly, by use of an advection-dispersion transport equation with a distributed zero-order source of unit (1) strength, corresponding to the rate of aging. The dependent variable in the governing equation is the mean age, a mass-weighted average age. The governing equation is derived from residence-time-distribution concepts for the case of steady flow. For the more general case of transient flow, a transient governing equation for age is derived from mass-conservation principles applied to conceptual “age mass.” The age mass is the product of the water mass and its age, and age mass is assumed to be conserved during mixing. Boundary conditions include zero age mass flux across all noflow and inflow boundaries and no age mass dispersive flux across outflow boundaries. For transient-flow conditions, the initial distribution of age must be known. The solution of the governing transport equation yields the spatial distribution of the mean groundwater age and includes diffusion, dispersion, mixing, and exchange processes that typically are considered only through tracer-specific solute transport simulation. Traditional methods have relied on advective transport to predict point values of groundwater travel time and age. The proposed method retains the simplicity and tracer-independence of advection-only models, but incorporates the effects of dispersion and mixing on volume-averaged age. Example simulations of age in two idealized regional aquifer systems, one homogeneous and the other layered, demonstrate the agreement between the proposed method and traditional particle-tracking approaches and illustrate use of the proposed method to determine the effects of diffusion, dispersion, and mixing on groundwater age.

Structure-preserving operators for thermal-nonequilibrium hydrodynamics

NASA Astrophysics Data System (ADS)

Shiroto, Takashi; Kawai, Soshi; Ohnishi, Naofumi

2018-07-01

Radiation hydrodynamics simulations based on a single fluid two-temperature model may violate the law of energy conservation, because the governing equations are expressed in a nonconservative formulation. In this study, we maintain the important physical requirements by employing a strategy based on the key concept that mathematical structures associated with conservative and nonconservative equations are preserved, even at the discrete level. To this end, we discretize the conservation laws and transform them using exact algebraic operations. The proposed scheme maintains global conservation errors within the round-off level. In addition, a numerical experiment concerning the shock tube problem suggests that the proposed scheme agrees well with the jump conditions at the discontinuities regulated by the Rankine-Hugoniot relationship. The generalized derivation allows us to employ arbitrary central difference, artificial dissipation, and Runge-Kutta methods.

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

McHugh, P.R.; Ramshaw, J.D.

MAGMA is a FORTRAN computer code designed to viscous flow in in situ vitrification melt pools. It models three-dimensional, incompressible, viscous flow and heat transfer. The momentum equation is coupled to the temperature field through the buoyancy force terms arising from the Boussinesq approximation. All fluid properties, except density, are assumed variable. Density is assumed constant except in the buoyancy force terms in the momentum equation. A simple melting model based on the enthalpy method allows the study of the melt front progression and latent heat effects. An indirect addressing scheme used in the numerical solution of the momentum equationmore » voids unnecessary calculations in cells devoid of liquid. Two-dimensional calculations can be performed using either rectangular or cylindrical coordinates, while three-dimensional calculations use rectangular coordinates. All derivatives are approximated by finite differences. The incompressible Navier-Stokes equations are solved using a new fully implicit iterative technique, while the energy equation is differenced explicitly in time. Spatial derivatives are written in conservative form using a uniform, rectangular, staggered mesh based on the marker and cell placement of variables. Convective terms are differenced using a weighted average of centered and donor cell differencing to ensure numerical stability. Complete descriptions of MAGMA governing equations, numerics, code structure, and code verification are provided. 14 refs.« less

Discovering governing equations from data by sparse identification of nonlinear dynamics

NASA Astrophysics Data System (ADS)

Brunton, Steven

The ability to discover physical laws and governing equations from data is one of humankind's greatest intellectual achievements. A quantitative understanding of dynamic constraints and balances in nature has facilitated rapid development of knowledge and enabled advanced technology, including aircraft, combustion engines, satellites, and electrical power. There are many more critical data-driven problems, such as understanding cognition from neural recordings, inferring patterns in climate, determining stability of financial markets, predicting and suppressing the spread of disease, and controlling turbulence for greener transportation and energy. With abundant data and elusive laws, data-driven discovery of dynamics will continue to play an increasingly important role in these efforts. This work develops a general framework to discover the governing equations underlying a dynamical system simply from data measurements, leveraging advances in sparsity-promoting techniques and machine learning. The resulting models are parsimonious, balancing model complexity with descriptive ability while avoiding overfitting. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions. This perspective, combining dynamical systems with machine learning and sparse sensing, is explored with the overarching goal of real-time closed-loop feedback control of complex systems. This is joint work with Joshua L. Proctor and J. Nathan Kutz. Video Abstract: https://www.youtube.com/watch?v=gSCa78TIldg

The nonlinear evolution of modes on unstable stratified shear layers

NASA Technical Reports Server (NTRS)

Blackaby, Nicholas; Dando, Andrew; Hall, Philip

1993-01-01

The nonlinear development of disturbances in stratified shear flows (having a local Richardson number of value less than one quarter) is considered. Such modes are initially fast growing but, like related studies, we assume that the viscous, non-parallel spreading of the shear layer results in them evolving in a linear fashion until they reach a position where their amplitudes are large enough and their growth rates have diminished sufficiently so that amplitude equations can be derived using weakly nonlinear and non-equilibrium critical-layer theories. Four different basic integro-differential amplitude equations are possible, including one due to a novel mechanism; the relevant choice of amplitude equation, at a particular instance, being dependent on the relative sizes of the disturbance amplitude, the growth rate of the disturbance, its wavenumber, and the viscosity of the fluid. This richness of choice of possible nonlinearities arises mathematically from the indicial Frobenius roots of the governing linear inviscid equation (the Taylor-Goldstein equation) not, in general, differing by an integer. The initial nonlinear evolution of a mode will be governed by an integro-differential amplitude equations with a cubic nonlinearity but the resulting significant increase in the size of the disturbance's amplitude leads on to the next stage of the evolution process where the evolution of the mode is governed by an integro-differential amplitude equations with a quintic nonlinearity. Continued growth of the disturbance amplitude is expected during this stage, resulting in the effects of nonlinearity spreading to outside the critical level, by which time the flow has become fully nonlinear.

On the Representation of the Porosity-Pressure Relationship in General Subsurface Flow Codes

DOE PAGES

Birdsell, Daniel Traver; Karra, Satish; Rajaram, Harihar

2018-01-11

The governing equations for subsurface flow codes in a deformable porous media are derived from the balance of fluid mass and Darcy's equation. One class of these codes, which we call general subsurface flow codes (GSFs), allow for more general constitutive relations for material properties such as porosity, permeability and density. Examples of GSFs include PFLOTRAN, FEHM, TOUGH2, STOMP, and some reservoir simulators such as BOAST. Depending on the constitutive relations used in GSFs, an inconsistency arises between the standard groundwater flow equation and the governing equation of GSFs, and we clarify that the reason for this inconsistency is becausemore » the Darcy's equation used in the GSFs should account for the velocity of fluid with respect to solid. Due to lack of awareness of this inconsistency, users of the GSFs tend to use a porosity-pressure relationship that comes from the standard groundwater flow equation and assumes that the relative velocity is already accounted for. For the Theis problem, we show that using this traditional relationship in the GSFs leads to significantly large errors. We propose an alternate porosity-pressure relationship that is consistent with the derivation of the governing equations in the GSFs where the solid velocity is not tracked, and show that, with this relationship, the results are more accurate for the Theis problem. In conclusion, the purpose of this note is to make the users and developers of these GSFs aware of this inconsistency and to advocate that the alternate porosity model derived here should be incorporated in GSFs.« less

On the Representation of the Porosity-Pressure Relationship in General Subsurface Flow Codes

NASA Astrophysics Data System (ADS)

Birdsell, Daniel T.; Karra, Satish; Rajaram, Harihar

2018-02-01

The governing equations for subsurface flow codes in a deformable porous media are derived from the balance of fluid mass and Darcy's equation. One class of these codes, which we call general subsurface flow codes (GSFs), allow for more general constitutive relations for material properties such as porosity, permeability and density. Examples of GSFs include PFLOTRAN, FEHM, TOUGH2, STOMP, and some reservoir simulators such as BOAST. Depending on the constitutive relations used in GSFs, an inconsistency arises between the standard groundwater flow equation and the governing equation of GSFs, and we clarify that the reason for this inconsistency is because the Darcy's equation used in the GSFs should account for the velocity of fluid with respect to solid. Due to lack of awareness of this inconsistency, users of the GSFs tend to use a porosity-pressure relationship that comes from the standard groundwater flow equation and assumes that the relative velocity is already accounted for. For the Theis problem, we show that using this traditional relationship in the GSFs leads to significantly large errors. We propose an alternate porosity-pressure relationship that is consistent with the derivation of the governing equations in the GSFs where the solid velocity is not tracked, and show that, with this relationship, the results are more accurate for the Theis problem. The purpose of this note is to make the users and developers of these GSFs aware of this inconsistency and to advocate that the alternate porosity model derived here should be incorporated in GSFs.

On the Representation of the Porosity-Pressure Relationship in General Subsurface Flow Codes

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

Birdsell, Daniel Traver; Karra, Satish; Rajaram, Harihar

The governing equations for subsurface flow codes in a deformable porous media are derived from the balance of fluid mass and Darcy's equation. One class of these codes, which we call general subsurface flow codes (GSFs), allow for more general constitutive relations for material properties such as porosity, permeability and density. Examples of GSFs include PFLOTRAN, FEHM, TOUGH2, STOMP, and some reservoir simulators such as BOAST. Depending on the constitutive relations used in GSFs, an inconsistency arises between the standard groundwater flow equation and the governing equation of GSFs, and we clarify that the reason for this inconsistency is becausemore » the Darcy's equation used in the GSFs should account for the velocity of fluid with respect to solid. Due to lack of awareness of this inconsistency, users of the GSFs tend to use a porosity-pressure relationship that comes from the standard groundwater flow equation and assumes that the relative velocity is already accounted for. For the Theis problem, we show that using this traditional relationship in the GSFs leads to significantly large errors. We propose an alternate porosity-pressure relationship that is consistent with the derivation of the governing equations in the GSFs where the solid velocity is not tracked, and show that, with this relationship, the results are more accurate for the Theis problem. In conclusion, the purpose of this note is to make the users and developers of these GSFs aware of this inconsistency and to advocate that the alternate porosity model derived here should be incorporated in GSFs.« less

Coupled rotor and fuselage equations of motion

NASA Technical Reports Server (NTRS)

Warmbrodt, W.

1979-01-01

The governing equations of motion of a helicopter rotor coupled to a rigid body fuselage are derived. A consistent formulation is used to derive nonlinear periodic coefficient equations of motion which are used to study coupled rotor/fuselage dynamics in forward flight. Rotor/fuselage coupling is documented and the importance of an ordering scheme in deriving nonlinear equations of motion is reviewed. The nature of the final equations and the use of multiblade coordinates are discussed.

Fluid flow and heat transfer of carbon nanotubes along a flat plate with Navier slip boundary

NASA Astrophysics Data System (ADS)

Khan, W. A.; Khan, Z. H.; Rahi, M.

2014-06-01

Homogeneous flow model is used to study the flow and heat transfer of carbon nanotubes (CNTs) along a flat plate subjected to Navier slip and uniform heat flux boundary conditions. This is the first paper on the flow and heat transfer of CNTs along a flat plate. Two types of CNTs, namely, single- and multi-wall CNTs are used with water, kerosene or engine oil as base fluids. The empirical correlations are used for the thermophysical properties of CNTs in terms of the solid volume fraction of CNTs. For the effective thermal conductivity of CNTs, Xue (Phys B Condens Matter 368:302-307, 2005) model has been used and the results are compared with the existing theoretical models. The governing partial differential equations and boundary conditions are converted into a set of nonlinear ordinary differential equations using suitable similarity transformations. These equations are solved numerically using a very efficient finite difference method with shooting scheme. The effects of the governing parameters on the dimensionless velocity, temperature, skin friction, and Nusselt numbers are investigated and presented in graphical and tabular forms. The numerical results of skin friction and Nusselt numbers are compared with the available data for special cases and are found in good agreement.

Investigation of a Parabolic Iterative Solver for Three-dimensional Configurations

NASA Technical Reports Server (NTRS)

Nark, Douglas M.; Watson, Willie R.; Mani, Ramani

2007-01-01

A parabolic iterative solution procedure is investigated that seeks to extend the parabolic approximation used within the internal propagation module of the duct noise propagation and radiation code CDUCT-LaRC. The governing convected Helmholtz equation is split into a set of coupled equations governing propagation in the positive and negative directions. The proposed method utilizes an iterative procedure to solve the coupled equations in an attempt to account for possible reflections from internal bifurcations, impedance discontinuities, and duct terminations. A geometry consistent with the NASA Langley Curved Duct Test Rig is considered and the effects of acoustic treatment and non-anechoic termination are included. Two numerical implementations are studied and preliminary results indicate that improved accuracy in predicted amplitude and phase can be obtained for modes at a cut-off ratio of 1.7. Further predictions for modes at a cut-off ratio of 1.1 show improvement in predicted phase at the expense of increased amplitude error. Possible methods of improvement are suggested based on analytic and numerical analysis. It is hoped that coupling the parabolic iterative approach with less efficient, high fidelity finite element approaches will ultimately provide the capability to perform efficient, higher fidelity acoustic calculations within complex 3-D geometries for impedance eduction and noise propagation and radiation predictions.

The prediction of the noise of supersonic propellers in time domain - New theoretical results

NASA Technical Reports Server (NTRS)

Farassat, F.

1983-01-01

In this paper, a new formula for the prediction of the noise of supersonic propellers is derived in the time domain which is superior to the previous formulations in several respects. The governing equation is based on the Ffowcs Williams-Hawkings (FW-H) equation with the thickness source term replaced by an equivalent loading source term derived by Isom (1975). Using some results of generalized function theory and simple four-dimensional space-time geometry, the formal solution of the governing equation is manipulated to a form requiring only the knowledge of blade surface pressure data and geometry. The final form of the main result of this paper consists of some surface and line integrals. The surface integrals depend on the surface pressure, time rate of change of surface pressure, and surface pressure gradient. These integrals also involve blade surface curvatures. The line integrals which depend on local surface pressure are along the trailing edge, the shock traces on the blade, and the perimeter of the airfoil section at the inner radius of the blade. The new formulation is for the full blade surface and does not involve any numerical observer time differentiation. The method of implementation on a computer for numerical work is also discussed.

Application of discontinuous Galerkin method for solving a compressible five-equation two-phase flow model

NASA Astrophysics Data System (ADS)

Saleem, M. Rehan; Ali, Ishtiaq; Qamar, Shamsul

2018-03-01

In this article, a reduced five-equation two-phase flow model is numerically investigated. The formulation of the model is based on the conservation and energy exchange laws. The model is non-conservative and the governing equations contain two equations for the mass conservation, one for the over all momentum and one for the total energy. The fifth equation is the energy equation for one of the two phases that includes a source term on the right hand side for incorporating energy exchange between the two fluids in the form of mechanical and thermodynamical works. A Runge-Kutta discontinuous Galerkin finite element method is applied to solve the model equations. The main attractive features of the proposed method include its formal higher order accuracy, its nonlinear stability, its ability to handle complicated geometries, and its ability to capture sharp discontinuities or strong gradients in the solutions without producing spurious oscillations. The proposed method is robust and well suited for large-scale time-dependent computational problems. Several case studies of two-phase flows are presented. For validation and comparison of the results, the same model equations are also solved by using a staggered central scheme. It was found that discontinuous Galerkin scheme produces better results as compared to the staggered central scheme.

Analysis of composite ablators using massively parallel computation

NASA Technical Reports Server (NTRS)

Shia, David

1995-01-01

In this work, the feasibility of using massively parallel computation to study the response of ablative materials is investigated. Explicit and implicit finite difference methods are used on a massively parallel computer, the Thinking Machines CM-5. The governing equations are a set of nonlinear partial differential equations. The governing equations are developed for three sample problems: (1) transpiration cooling, (2) ablative composite plate, and (3) restrained thermal growth testing. The transpiration cooling problem is solved using a solution scheme based solely on the explicit finite difference method. The results are compared with available analytical steady-state through-thickness temperature and pressure distributions and good agreement between the numerical and analytical solutions is found. It is also found that a solution scheme based on the explicit finite difference method has the following advantages: incorporates complex physics easily, results in a simple algorithm, and is easily parallelizable. However, a solution scheme of this kind needs very small time steps to maintain stability. A solution scheme based on the implicit finite difference method has the advantage that it does not require very small times steps to maintain stability. However, this kind of solution scheme has the disadvantages that complex physics cannot be easily incorporated into the algorithm and that the solution scheme is difficult to parallelize. A hybrid solution scheme is then developed to combine the strengths of the explicit and implicit finite difference methods and minimize their weaknesses. This is achieved by identifying the critical time scale associated with the governing equations and applying the appropriate finite difference method according to this critical time scale. The hybrid solution scheme is then applied to the ablative composite plate and restrained thermal growth problems. The gas storage term is included in the explicit pressure calculation of both problems. Results from ablative composite plate problems are compared with previous numerical results which did not include the gas storage term. It is found that the through-thickness temperature distribution is not affected much by the gas storage term. However, the through-thickness pressure and stress distributions, and the extent of chemical reactions are different from the previous numerical results. Two types of chemical reaction models are used in the restrained thermal growth testing problem: (1) pressure-independent Arrhenius type rate equations and (2) pressure-dependent Arrhenius type rate equations. The numerical results are compared to experimental results and the pressure-dependent model is able to capture the trend better than the pressure-independent one. Finally, a performance study is done on the hybrid algorithm using the ablative composite plate problem. It is found that there is a good speedup of performance on the CM-5. For 32 CPU's, the speedup of performance is 20. The efficiency of the algorithm is found to be a function of the size and execution time of a given problem and the effective parallelization of the algorithm. It also seems that there is an optimum number of CPU's to use for a given problem.

Wavelet-based spectral finite element dynamic analysis for an axially moving Timoshenko beam

NASA Astrophysics Data System (ADS)

Mokhtari, Ali; Mirdamadi, Hamid Reza; Ghayour, Mostafa

2017-08-01

In this article, wavelet-based spectral finite element (WSFE) model is formulated for time domain and wave domain dynamic analysis of an axially moving Timoshenko beam subjected to axial pretension. The formulation is similar to conventional FFT-based spectral finite element (SFE) model except that Daubechies wavelet basis functions are used for temporal discretization of the governing partial differential equations into a set of ordinary differential equations. The localized nature of Daubechies wavelet basis functions helps to rule out problems of SFE model due to periodicity assumption, especially during inverse Fourier transformation and back to time domain. The high accuracy of WSFE model is then evaluated by comparing its results with those of conventional finite element and SFE results. The effects of moving beam speed and axial tensile force on vibration and wave characteristics, and static and dynamic stabilities of moving beam are investigated.

Laminar flow effects in the coil planet centrifuge

NASA Technical Reports Server (NTRS)

Herrmann, F. T.

1984-01-01

The coil planet centrifuge designed by Ito employs flow of a single liquid phase, through a rotating coiled tube in a centrifugal force field, to provide a separation of particles based on sedimentation rates. Mathematical solutions are derived for the linear differential equations governing particle behavior in the coil planet centrifuge device. These solutions are then applied as the basis of a model for optimizing particle separations.

Stochastic Representation of Chaos Using Terminal Attractors

NASA Technical Reports Server (NTRS)

Zak, Michail

2006-01-01

A nonlinear version of the Liouville equation based on terminal attractors is part of a mathematical formalism for describing postinstability motions of dynamical systems characterized by exponential divergences of trajectories leading to chaos (including turbulence as a form of chaos). The formalism can be applied to both conservative systems (e.g., multibody systems in celestial mechanics) and dissipative systems (e.g., viscous fluids). The development of the present formalism was undertaken in an effort to remove positive Lyapunov exponents. The means chosen to accomplish this is coupling of the governing dynamical equations with the corresponding Liouville equation that describes the evolution of the flow of error probability. The underlying idea is to suppress the divergences of different trajectories that correspond to different initial conditions, without affecting a target trajectory, which is one that starts with prescribed initial conditions.

Toward the automated analysis of plasma physics problems

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

Mynick, H.E.

1989-04-01

A program (CALC) is described, which carries out nontrivial plasma physics calculations, in a manner intended to emulate the approach of a human theorist. This includes the initial process of gathering the relevant equations from a plasma knowledge base, and then determining how to solve them. Solution of the sets of equations governing physics problems, which in general have a nonuniform,irregular structure, not amenable to solution by standardized algorithmic procedures, is facilitated by an analysis of the structure of the equations and the relations among them. This often permits decompositions of the full problem into subproblems, and other simplifications inmore » form, which renders the resultant subsystems soluble by more standardized tools. CALC's operation is illustrated by a detailed description of its treatment of a sample plasma calculation. 5 refs., 3 figs.« less

Physics, stability, and dynamics of supply networks

NASA Astrophysics Data System (ADS)

Helbing, Dirk; Lämmer, Stefan; Seidel, Thomas; Šeba, Pétr; Płatkowski, Tadeusz

2004-12-01

We show how to treat supply networks as physical transport problems governed by balance equations and equations for the adaptation of production speeds. Although the nonlinear behavior is different, the linearized set of coupled differential equations is formally related to those of mechanical or electrical oscillator networks. Supply networks possess interesting features due to their complex topology and directed links. We derive analytical conditions for absolute and convective instabilities. The empirically observed “bullwhip effect” in supply chains is explained as a form of convective instability based on resonance effects. Moreover, it is generalized to arbitrary supply networks. Their related eigenvalues are usually complex, depending on the network structure (even without loops). Therefore, their generic behavior is characterized by damped or growing oscillations. We also show that regular distribution networks possess two negative eigenvalues only, but perturbations generate a spectrum of complex eigenvalues.

Well-posed Euler model of shock-induced two-phase flow in bubbly liquid

NASA Astrophysics Data System (ADS)

Tukhvatullina, R. R.; Frolov, S. M.

2018-03-01

A well-posed mathematical model of non-isothermal two-phase two-velocity flow of bubbly liquid is proposed. The model is based on the two-phase Euler equations with the introduction of an additional pressure at the gas bubble surface, which ensures the well-posedness of the Cauchy problem for a system of governing equations with homogeneous initial conditions, and the Rayleigh-Plesset equation for radial pulsations of gas bubbles. The applicability conditions of the model are formulated. The model is validated by comparing one-dimensional calculations of shock wave propagation in liquids with gas bubbles with a gas volume fraction of 0.005-0.3 with experimental data. The model is shown to provide satisfactory results for the shock propagation velocity, pressure profiles, and the shock-induced motion of the bubbly liquid column.

Large eddy simulation of cavitating flows

NASA Astrophysics Data System (ADS)

Gnanaskandan, Aswin; Mahesh, Krishnan

2014-11-01

Large eddy simulation on unstructured grids is used to study hydrodynamic cavitation. The multiphase medium is represented using a homogeneous equilibrium model that assumes thermal equilibrium between the liquid and the vapor phase. Surface tension effects are ignored and the governing equations are the compressible Navier Stokes equations for the liquid/vapor mixture along with a transport equation for the vapor mass fraction. A characteristic-based filtering scheme is developed to handle shocks and material discontinuities in non-ideal gases and mixtures. A TVD filter is applied as a corrector step in a predictor-corrector approach with the predictor scheme being non-dissipative and symmetric. The method is validated for canonical one dimensional flows and leading edge cavitation over a hydrofoil, and applied to study sheet to cloud cavitation over a wedge. This work is supported by the Office of Naval Research.

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.

Numerical study of supersonic combustion using a finite rate chemistry model

NASA Technical Reports Server (NTRS)

Chitsomboon, T.; Tiwari, S. N.; Kumar, A.; Drummond, J. P.

1986-01-01

The governing equations of two-dimensional chemically reacting flows are presented together with a global two-step chemistry model for H2-air combustion. The explicit unsplit MacCormack finite difference algorithm is used to advance the discrete system of the governing equations in time until convergence is attained. The source terms in the species equations are evaluated implicitly to alleviate stiffness associated with fast reactions. With implicit source terms, the species equations give rise to a block-diagonal system which can be solved very efficiently on vector-processing computers. A supersonic reacting flow in an inlet-combustor configuration is calculated for the case where H2 is injected into the flow from the side walls and the strut. Results of the calculation are compared against the results obtained by using a complete reaction model.

Basic governing equations for the flight regimes of aeroassisted orbital transfer vehicles

NASA Technical Reports Server (NTRS)

Lee, J.-H.

1984-01-01

The basic governing equations for the low-density, high-enthalpy flow regimes expected in the shock layers over the heat shields of the proposed aeroassisted orbital transfer vehicles are derived by combining and extending existing theories. The conservation equations are derived from gas kinetic principles for a four-component ionized gas consisting of neutral molecules, neutral atoms, singly ionized ions, and electrons, assuming a continuum flow. The differences among translational-rotational, vibrational, and electron temperatures are accounted for, as well as chemical nonequilibrium and electric-charge separation. Expressions for convective and viscous fluxes, transport properties, and the terms representing interactions among various energy modes are given explicitly. The expressions for the rate of electron-vibration energy transfer, which violates the Landau-Teller conditions, is derived by solving the system of master equations accounting for the multiple-level transitions.

Basic Governing Equations for the Flight Regimes of Aeroassisted Orbital Transfer Vehicles

NASA Technical Reports Server (NTRS)

Lee, Jong-Hun

1985-01-01

The basic governing equations for the low-density, high-enthalpy flow regimes expected in the shock layers over the heat shields of the proposed aeroassisted orbital transfer vehicles are derived by combining and extending existing theories. The conservation equations are derived from gas kinetic principles for a four-component ionized gas consisting of neutral molecules, neutral atoms, singly ionized ions, and electrons, assuming a continuum flow. The differences among translational-rotational, vibrational, and electron temperatures are accounted for, as well as chemical nonequilibrium and electric-charge separation. Expressions for convective and viscous fluxes, transport properties, and the terms representing interactions among various energy modes are explicitly given. The expressions for the rate of electron-vibration energy transfer, which violates the Landau-Teller conditions, are derived by solving the system of master equations accounting for the multiple-level transitions.

Integral equation methods for vesicle electrohydrodynamics in three dimensions

NASA Astrophysics Data System (ADS)

Veerapaneni, Shravan

2016-12-01

In this paper, we develop a new boundary integral equation formulation that describes the coupled electro- and hydro-dynamics of a vesicle suspended in a viscous fluid and subjected to external flow and electric fields. The dynamics of the vesicle are characterized by a competition between the elastic, electric and viscous forces on its membrane. The classical Taylor-Melcher leaky-dielectric model is employed for the electric response of the vesicle and the Helfrich energy model combined with local inextensibility is employed for its elastic response. The coupled governing equations for the vesicle position and its transmembrane electric potential are solved using a numerical method that is spectrally accurate in space and first-order in time. The method uses a semi-implicit time-stepping scheme to overcome the numerical stiffness associated with the governing equations.

Large amplitude flexural vibration of thin elastic flat plates and shells

NASA Technical Reports Server (NTRS)

Pandalia, K. A. V.

1972-01-01

The general equations governing the large amplitude flexural vibration of any thin elastic shell using curvilinear orthogonal coordinates are derived and consist of two coupled, nonlinear, partial differential equations in the normal displacement w and the stress function F. From these equations, the governing equations for the case of shells of revolution or flat plates can be readily obtained as special cases. The material of the shell or plate is isotropic and homogeneous and Hooke's law for the two-dimensional case is valid. It is suggested that the difference between the hardening type of nonlinearity in the case of flat plates and straight beams and the softening type of nonlinearity in the case of shells and rings can, in general, be traced to the amount of curvature present in the underformed median surface of the structure concerned.

Expectation-Based Control of Noise and Chaos

NASA Technical Reports Server (NTRS)

Zak, Michael

2006-01-01

A proposed approach to control of noise and chaos in dynamic systems would supplement conventional methods. The approach is based on fictitious forces composed of expectations governed by Fokker-Planck or Liouville equations that describe the evolution of the probability densities of the controlled parameters. These forces would be utilized as feedback control forces that would suppress the undesired diffusion of the controlled parameters. Examples of dynamic systems in which the approach is expected to prove beneficial include spacecraft, electronic systems, and coupled lasers.

Analysis of pulse thermography using similarities between wave and diffusion propagation

NASA Astrophysics Data System (ADS)

Gershenson, M.

2017-05-01

Pulse thermography or thermal wave imaging are commonly used as nondestructive evaluation (NDE) method. While the technical aspect has evolve with time, theoretical interpretation is lagging. Interpretation is still using curved fitting on a log log scale. A new approach based directly on the governing differential equation is introduced. By using relationships between wave propagation and the diffusive propagation of thermal excitation, it is shown that one can transform from solutions in one type of propagation to the other. The method is based on the similarities between the Laplace transforms of the diffusion equation and the wave equation. For diffusive propagation we have the Laplace variable s to the first power, while for the wave propagation similar equations occur with s2. For discrete time the transformation between the domains is performed by multiplying the temperature data vector by a matrix. The transform is local. The performance of the techniques is tested on synthetic data. The application of common back projection techniques used in the processing of wave data is also demonstrated. The combined use of the transform and back projection makes it possible to improve both depth and lateral resolution of transient thermography.

Helical localized wave solutions of the scalar wave equation.

PubMed

Overfelt, P L

2001-08-01

A right-handed helical nonorthogonal coordinate system is used to determine helical localized wave solutions of the homogeneous scalar wave equation. Introducing the characteristic variables in the helical system, i.e., u = zeta - ct and v = zeta + ct, where zeta is the coordinate along the helical axis, we can use the bidirectional traveling plane wave representation and obtain sets of elementary bidirectional helical solutions to the wave equation. Not only are these sets bidirectional, i.e., based on a product of plane waves, but they may also be broken up into right-handed and left-handed solutions. The elementary helical solutions may in turn be used to create general superpositions, both Fourier and bidirectional, from which new solutions to the wave equation may be synthesized. These new solutions, based on the helical bidirectional superposition, are members of the class of localized waves. Examples of these new solutions are a helical fundamental Gaussian focus wave mode, a helical Bessel-Gauss pulse, and a helical acoustic directed energy pulse train. Some of these solutions have the interesting feature that their shape and localization properties depend not only on the wave number governing propagation along the longitudinal axis but also on the normalized helical pitch.

Multi-Hamiltonian structure of equations of hydrodynamic type

NASA Astrophysics Data System (ADS)

Gümral, H.; Nutku, Y.

1990-11-01

The discussion of the Hamiltonian structure of two-component equations of hydrodynamic type is completed by presenting the Hamiltonian operators for Euler's equation governing the motion of plane sound waves of finite amplitude and another quasilinear second-order wave equation. There exists a doubly infinite family of conserved Hamiltonians for the equations of gas dynamics that degenerate into one, namely, the Benney sequence, for shallow-water waves. Infinite sequences of conserved quantities for these equations are also presented. In the case of multicomponent equations of hydrodynamic type, it is shown, that Kodama's generalization of the shallow-water equations admits bi-Hamiltonian structure.

Partial slip effect on non-aligned stagnation point nanofluid over a stretching convective surface

NASA Astrophysics Data System (ADS)

Nadeem, S.; Rashid, Mehmood; Noreen Sher, Akbar

2015-01-01

The present study inspects the non-aligned stagnation point nano fluid over a convective surface in the presence of partial slip.Two types of base fluids namely water and kerosene are selected with Cu nanoparticles. The governing physical problem is presented and transformed into a system of coupled nonlinear differential equations using suitable similarity transformations. These equations are then solved numerically using midpoint integration scheme along with Richardson extrapolation via Maple. Impact of relevant physical parameters on the dimensionless velocity and temperature profiles are portrayed through graphs. Physical quantities such as local skin frictions co-efficient and Nusselt numbers are tabularized. It is detected from numerical computations that kerosene-based nano fluids have better heat transfer capability compared with water-based nanofluids. Moreover it is found that water-based nanofluids offer less resistance in terms of skin friction than kerosene-based fluid. In order to authenticate our present study, the calculated results are compared with the prevailing literature and a considerable agreement is perceived for the limiting case.

Modeling tracer transport in randomly heterogeneous porous media by nonlocal moment equations: Anomalous transport

NASA Astrophysics Data System (ADS)

Morales-Casique, E.; Lezama-Campos, J. L.; Guadagnini, A.; Neuman, S. P.

2013-05-01

Modeling tracer transport in geologic porous media suffers from the corrupt characterization of the spatial distribution of hydrogeologic properties of the system and the incomplete knowledge of processes governing transport at multiple scales. Representations of transport dynamics based on a Fickian model of the kind considered in the advection-dispersion equation (ADE) fail to capture (a) the temporal variation associated with the rate of spreading of a tracer, and (b) the distribution of early and late arrival times which are often observed in field and/or laboratory scenarios and are considered as the signature of anomalous transport. Elsewhere we have presented exact stochastic moment equations to model tracer transport in randomly heterogeneous aquifers. We have also developed a closure scheme which enables one to provide numerical solutions of such moment equations at different orders of approximations. The resulting (ensemble) average and variance of concentration fields were found to display a good agreement against Monte Carlo - based simulation results for mildly heterogeneous (or well-conditioned strongly heterogeneous) media. Here we explore the ability of the moment equations approach to describe the distribution of early arrival times and late time tailing effects which can be observed in Monte-Carlo based breakthrough curves (BTCs) of the (ensemble) mean concentration. We show that BTCs of mean resident concentration calculated at a fixed space location through higher-order approximations of moment equations display long tailing features of the kind which is typically associated with anomalous transport behavior and are not represented by an ADE model with constant dispersive parameter, such as the zero-order approximation.

Analogy between the Navier-Stokes equations and Maxwell's equations: Application to turbulence

NASA Astrophysics Data System (ADS)

Marmanis, Haralambos

1998-06-01

A new theory of turbulence is initiated, based on the analogy between electromagnetism and turbulent hydrodynamics, for the purpose of describing the dynamical behavior of averaged flow quantities in incompressible fluid flows of high Reynolds numbers. The starting point is the recognition that the vorticity (w=∇×u) and the Lamb vector (l=w×u) should be taken as the kernel of a dynamical theory of turbulence. The governing equations for these fields can be obtained by the Navier-Stokes equations, which underlie the whole evolution. Then whatever parts are not explicitly expressed as a function of w or l only are gathered and treated as source terms. This is done by introducing the concepts of turbulent charge and turbulent current. Thus we are led to a closed set of linear equations for the averaged field quantities. The premise is that the earlier introduced sources will be apt for modeling, in the sense that their distribution will depend only on the geometry and the total energetics of the flow. The dynamics described in the preceding manner is what we call the metafluid dynamics.

Analysis of cavitation bubble dynamics in a liquid

NASA Technical Reports Server (NTRS)

Fontenot, L. L.; Lee, Y. C.

1971-01-01

General differential equations governing the dynamics of the cavitation bubbles in a liquid were derived. With the assumption of spherical symmetry the governing equations were simplified. Closed form solutions were obtained for simple cases, and numerical solutions were calculated for complicated ones. The growth and the collapse of the bubble were analyzed, oscillations of the bubbles were studied, and the stability of the cavitation bubbles were investigated. The results show that the cavitation bubbles are unstable, and the oscillation is not sinusoidal.

Loss-less propagation, elastic and inelastic interaction of electromagnetic soliton in an anisotropic ferromagnetic nanowire

NASA Astrophysics Data System (ADS)

Senthil Kumar, V.; Kavitha, L.; Boopathy, C.; Gopi, D.

2017-10-01

Nonlinear interaction of electromagnetic solitons leads to a plethora of interesting physical phenomena in the diverse area of science that include magneto-optics based data storage industry. We investigate the nonlinear magnetization dynamics of a one-dimensional anisotropic ferromagnetic nanowire. The famous Landau-Lifshitz-Gilbert equation (LLG) describes the magnetization dynamics of the ferromagnetic nanowire and the Maxwell's equations govern the propagation dynamics of electromagnetic wave passing through the axis of the nanowire. We perform a uniform expansion of magnetization and magnetic field along the direction of propagation of electromagnetic wave in the framework of reductive perturbation method. The excitation of magnetization of the nanowire is restricted to the normal plane at the lowest order of perturbation and goes out of plane for higher orders. The dynamics of the ferromagnetic nanowire is governed by the modified Korteweg-de Vries (mKdV) equation and the perturbed modified Korteweg-de Vries (pmKdV) equation for the lower and higher values of damping respectively. We invoke the Hirota bilinearization procedure to mKdV and pmKdV equation to construct the multi-soliton solutions, and explicitly analyze the nature of collision phenomena of the co-propagating EM solitons for the above mentioned lower and higher values of Gilbert-damping due to the precessional motion of the ferromagnetic spin. The EM solitons appearing in the higher damping regime exhibit elastic collision thus yielding the fascinating state restoration property, whereas those of lower damping regime exhibit inelastic collision yielding the solitons of suppressed intensity profiles. The propagation of EM soliton in the nanoscale magnetic wire has potential technological applications in optimizing the magnetic storage devices and magneto-electronics.

Development of monitoring system of helium leakage from canister

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

Toriu, D.; Ushijima, S.; Takeda, H.

2013-07-01

This paper presents a computational method for the helium leakage from a canister. The governing equations for compressible fluids consist of mass conservation equation in Eulerian description, momentum equations and energy equation. The numerical procedures are divided into three phases, advection, diffusion and acoustic phases, and the equations of compressible fluids are discretized with a finite volume method. Thus, the mass conservation law is sufficiently satisfied in the calculation region. In particular, our computational method enables us to predict the change of the temperature distributions around the canister boundaries by calculating the governing equations for the compressible gas flows, whichmore » are leaked out from a slight crack on the canister boundary. In order to confirm the validity of our method, it was applied to the basic problem, 2-dimensional natural convection flows in a rectangular cavity. As a result, it was shown that the naturally convected flows can be reasonably simulated by our method. Furthermore, numerical experiments were conducted for the helium leakage from canister and we derived a close relationship between the inner pressure and the boundary temperature distributions.« less

Characterization of Defects in Scaled Mis Dielectrics with Variable Frequency Charge Pumping

NASA Astrophysics Data System (ADS)

Paulsen, Ronald Eugene

1995-01-01

Historically, the interface trap has been extensively investigated to determine the effects on device performance. Recently, much attention has been paid to trapping in near-interface oxide traps. Performance of high precision analog circuitry is affected by charge trapping in near-interface oxide traps which produces hysteresis, charge redistribution errors, and dielectric relaxation effects. In addition, the performance of low power digital circuitry, with reduced noise margins, may be drastically affected by the threshold voltage shifts associated with charge trapping in near -interface oxide traps. Since near-interface oxide traps may substantially alter the performance of devices, complete characterization of these defects is necessary. In this dissertation a new characterization technique, variable frequency charge pumping, is introduced which allows charge trapped at the interface to be distinguished from the charge trapped within the oxide. The new experimental technique is an extension of the charge pumping technique to low frequencies such that tunneling may occur from interface traps to near-interface oxide traps. A generalized charge pumping model, based on Shockley-Read-Hall statistics and trap-to-trap tunneling theory, has been developed which allows a more complete characterization of near-interface oxide traps. A pair of coupled differential equations governing the rate of change of occupied interface and near-interface oxide traps have been developed. Due to the experimental conditions in the charge pumping technique the equations may be decoupled, leading to an equation governing the rate of change of occupied interface traps and an equation governing the rate of change of occcupied near-interface oxide traps. Solving the interface trap equation and applying non-steady state charge dynamics leads to an interface trap component of the charge pumping current. In addition, solution to the near-interface oxide trap equation leads to an additional oxide trap component to the charge pumping current. Numerical simulations have been performed to support the analytical development of the generalized charge pumping model. By varying the frequency of the applied charge pumping waveform and monitoring the charge recombined per cycle, the contributions from interface traps may be separated from the contributions of the near-interface oxide traps. The generalized charge pumping model allows characterization of the density and spatial distribution of near-interface oxide traps from this variable frequency charge pumping technique. Characterization of interface and near-interface oxide trap generation has been performed on devices exposed to ionizing radiation, hot electron injection, and high -field/Fowler-Nordheim stressing. Finally, using SONOS nonvolatile memory devices, a framework has been established for experimentally determining not only the spatial distribution of near-interface oxide traps, but also the energetic distribution. An experimental approach, based on tri-level charge pumping, is discussed which allows the energetic distribution of near-interface oxide traps to be determined.

Flow model for open-channel reach or network

USGS Publications Warehouse

Schaffranek, R.W.

1987-01-01

Formulation of a one-dimensional model for simulating unsteady flow in a single open-channel reach or in a network of interconnected channels is presented. The model is both general and flexible in that it can be used to simulate a wide range of flow conditions for various channel configurations. It is based on a four-point (box), implicit, finite-difference approximation of the governing nonlinear flow equations with user-definable weighting coefficients to permit varying the solution scheme from box-centered to fully forward. Unique transformation equations are formulated that permit correlation of the unknowns at the extremities of the channels, thereby reducing coefficient matrix and execution time requirements. Discharges and water-surface elevations computed at intermediate locations within a channel are determined following solution of the transformation equations. The matrix of transformation and boundary-condition equations is solved by Gauss elimination using maximum pivot strategy. Two diverse applications of the model are presented to illustrate its broad utility. (USGS)

Planar dynamics of a uniform beam with rigid bodies affixed to the ends

NASA Technical Reports Server (NTRS)

Storch, J.; Gates, S.

1983-01-01

The planar dynamics of a uniform elastic beam subject to a variety of geometric and natural boundary conditions and external excitations were analyzed. The beams are inextensible and capable of small transverse bending deformations only. Classical beam vibration eigenvalue problems for a cantilever with tip mass, a cantilever with tip body and an unconstrained beam with rigid bodies at each are examined. The characteristic equations, eigenfunctions and orthogonality relations for each are derived. The forced vibration of a cantilever with tip body subject to base acceleration is analyzed. The exact solution of the governing nonhomogeneous partial differential equation with time dependent boundary conditions is presented and compared with a Rayleigh-Ritz approximate solution. The arbitrary planar motion of an elastic beam with rigid bodies at the ends is addressed. Equations of motion are derived for two modal expansions of the beam deflection. The motion equations are cast in a first order form suitable for numerical integration. Selected FORTRAN programs are provided.

A study of the viscous and nonadiabatic flow in radial turbines

NASA Technical Reports Server (NTRS)

Khalil, I.; Tabakoff, W.

1981-01-01

A method for analyzing the viscous nonadiabatic flow within turbomachine rotors is presented. The field analysis is based upon the numerical integration of the incompressible Navier-Stokes equations together with the energy equation over the rotors blade-to-blade stream channels. The numerical code used to solve the governing equations employs a nonorthogonal boundary fitted coordinate system that suits the most complicated blade geometries. Effects of turbulence are modeled with two equations; one expressing the development of the turbulence kinetic energy and the other its dissipation rate. The method of analysis is applied to a radial inflow turbine. The solution obtained indicates the severity of the complex interaction mechanism that occurs between different flow regimes (i.e., boundary layers, recirculating eddies, separation zones, etc.). Comparison with nonviscous flow solutions tend to justify strongly the inadequacy of using the latter with standard boundary layer techniques to obtain viscous flow details within turbomachine rotors. Capabilities and limitations of the present method of analysis are discussed.

An efficient model for coupling structural vibrations with acoustic radiation

NASA Technical Reports Server (NTRS)

Frendi, Abdelkader; Maestrello, Lucio; Ting, LU

1993-01-01

The scattering of an incident wave by a flexible panel is studied. The panel vibration is governed by the nonlinear plate equations while the loading on the panel, which is the pressure difference across the panel, depends on the reflected and transmitted waves. Two models are used to calculate this structural-acoustic interaction problem. One solves the three dimensional nonlinear Euler equations for the flow-field coupled with the plate equations (the fully coupled model). The second uses the linear wave equation for the acoustic field and expresses the load as a double integral involving the panel oscillation (the decoupled model). The panel oscillation governed by a system of integro-differential equations is solved numerically and the acoustic field is then defined by an explicit formula. Numerical results are obtained using the two models for linear and nonlinear panel vibrations. The predictions given by these two models are in good agreement but the computational time needed for the 'fully coupled model' is 60 times longer than that for 'the decoupled model'.

Emergence and analysis of Kuramoto-Sakaguchi-like models as an effective description for the dynamics of coupled Wien-bridge oscillators.

PubMed

English, L Q; Mertens, David; Abdoulkary, Saidou; Fritz, C B; Skowronski, K; Kevrekidis, P G

2016-12-01

We derive the Kuramoto-Sakaguchi model from the basic circuit equations governing two coupled Wien-bridge oscillators. A Wien-bridge oscillator is a particular realization of a tunable autonomous oscillator that makes use of frequency filtering (via an RC bandpass filter) and positive feedback (via an operational amplifier). In the past few years, such oscillators have started to be utilized in synchronization studies. We first show that the Wien-bridge circuit equations can be cast in the form of a coupled pair of van der Pol equations. Subsequently, by applying the method of multiple time scales, we derive the differential equations that govern the slow evolution of the oscillator phases and amplitudes. These equations are directly reminiscent of the Kuramoto-Sakaguchi-type models for the study of synchronization. We analyze the resulting system in terms of the existence and stability of various coupled oscillator solutions and explain on that basis how their synchronization emerges. The phase-amplitude equations are also compared numerically to the original circuit equations and good agreement is found. Finally, we report on experimental measurements of two coupled Wien-bridge oscillators and relate the results to the theoretical predictions.

Manning’s equation and two-dimensional flow analogs

NASA Astrophysics Data System (ADS)

Hromadka, T. V., II; Whitley, R. J.; Jordan, N.; Meyer, T.

2010-07-01

SummaryTwo-dimensional (2D) flow models based on the well-known governing 2D flow equations are applied to floodplain analysis purposes. These 2D models numerically solve the governing flow equations simultaneously or explicitly on a discretization of the floodplain using grid tiles or similar tile cell geometry, called "elements". By use of automated information systems such as digital terrain modeling, digital elevation models, and GIS, large-scale topographic floodplain maps can be readily discretized into thousands of elements that densely cover the floodplain in an edge-to-edge form. However, the assumed principal flow directions of the flow model analog, as applied across an array of elements, typically do not align with the floodplain flow streamlines. This paper examines the mathematical underpinnings of a four-direction flow analog using an array of square elements with respect to floodplain flow streamlines that are not in alignment with the analog's principal flow directions. It is determined that application of Manning's equation to estimate the friction slope terms of the governing flow equations, in directions that are not coincident with the flow streamlines, may introduce a bias in modeling results, in the form of slight underestimation of flow depths. It is also determined that the maximum theoretical bias, occurs when a single square element is rotated by about 13°, and not 45° as would be intuitively thought. The bias as a function of rotation angle for an array of square elements follows approximately the bias for a single square element. For both the theoretical single square element and an array of square elements, the bias as a function of alignment angle follows a relatively constant value from about 5° to about 85°, centered at about 45°. This bias was first noted about a decade prior to the present paper, and the magnitude of this bias was estimated then to be about 20% at about 10° misalignment. An adjustment of Manning's n is investigated based on a considered steady state uniform flow problem, but the magnitude of the adjustment (about 20%) is on the order of the magnitude of the accepted ranges of friction factors. For usual cases where random streamline trajectory variability within the floodplain flow is greater than a few degrees from perfect alignment, the apparent bias appears to be implicitly included in the Manning's n values. It can be concluded that the array of square elements may be applied over the digital terrain model without respect to topographic flow directions.

Sub-optimal control of unsteady boundary layer separation and optimal control of Saltzman-Lorenz model

NASA Astrophysics Data System (ADS)

Sardesai, Chetan R.

The primary objective of this research is to explore the application of optimal control theory in nonlinear, unsteady, fluid dynamical settings. Two problems are considered: (1) control of unsteady boundary-layer separation, and (2) control of the Saltzman-Lorenz model. The unsteady boundary-layer equations are nonlinear partial differential equations that govern the eruptive events that arise when an adverse pressure gradient acts on a boundary layer at high Reynolds numbers. The Saltzman-Lorenz model consists of a coupled set of three nonlinear ordinary differential equations that govern the time-dependent coefficients in truncated Fourier expansions of Rayleigh-Renard convection and exhibit deterministic chaos. Variational methods are used to derive the nonlinear optimal control formulations based on cost functionals that define the control objective through a performance measure and a penalty function that penalizes the cost of control. The resulting formulation consists of the nonlinear state equations, which must be integrated forward in time, and the nonlinear control (adjoint) equations, which are integrated backward in time. Such coupled forward-backward time integrations are computationally demanding; therefore, the full optimal control problem for the Saltzman-Lorenz model is carried out, while the more complex unsteady boundary-layer case is solved using a sub-optimal approach. The latter is a quasi-steady technique in which the unsteady boundary-layer equations are integrated forward in time, and the steady control equation is solved at each time step. Both sub-optimal control of the unsteady boundary-layer equations and optimal control of the Saltzman-Lorenz model are found to be successful in meeting the control objectives for each problem. In the case of boundary-layer separation, the control results indicate that it is necessary to eliminate the recirculation region that is a precursor to the unsteady boundary-layer eruptions. In the case of the Saltzman-Lorenz model, it is possible to control the system about either of the two unstable equilibrium points representing clockwise and counterclockwise rotation of the convection roles in a parameter regime for which the uncontrolled solution would exhibit deterministic chaos.

Diffuse-Interface Capturing Methods for Compressible Two-Phase Flows

NASA Astrophysics Data System (ADS)

Saurel, Richard; Pantano, Carlos

2018-01-01

Simulation of compressible flows became a routine activity with the appearance of shock-/contact-capturing methods. These methods can determine all waves, particularly discontinuous ones. However, additional difficulties may appear in two-phase and multimaterial flows due to the abrupt variation of thermodynamic properties across the interfacial region, with discontinuous thermodynamical representations at the interfaces. To overcome this difficulty, researchers have developed augmented systems of governing equations to extend the capturing strategy. These extended systems, reviewed here, are termed diffuse-interface models, because they are designed to compute flow variables correctly in numerically diffused zones surrounding interfaces. In particular, they facilitate coupling the dynamics on both sides of the (diffuse) interfaces and tend to the proper pure fluid-governing equations far from the interfaces. This strategy has become efficient for contact interfaces separating fluids that are governed by different equations of state, in the presence or absence of capillary effects, and with phase change. More sophisticated materials than fluids (e.g., elastic-plastic materials) have been considered as well.

Steady-state configuration and tension calculations of marine cables under complex currents via separated particle swarm optimization

NASA Astrophysics Data System (ADS)

Xu, Xue-song

2014-12-01

Under complex currents, the motion governing equations of marine cables are complex and nonlinear, and the calculations of cable configuration and tension become difficult compared with those under the uniform or simple currents. To obtain the numerical results, the usual Newton-Raphson iteration is often adopted, but its stability depends on the initial guessed solution to the governing equations. To improve the stability of numerical calculation, this paper proposed separated the particle swarm optimization, in which the variables are separated into several groups, and the dimension of search space is reduced to facilitate the particle swarm optimization. Via the separated particle swarm optimization, these governing nonlinear equations can be solved successfully with any initial solution, and the process of numerical calculation is very stable. For the calculations of cable configuration and tension of marine cables under complex currents, the proposed separated swarm particle optimization is more effective than the other particle swarm optimizations.

Receiving sensitivity and transmitting voltage response of a fluid loaded spherical piezoelectric transducer with an elastic coating.

PubMed

George, Jineesh; Ebenezer, D D; Bhattacharyya, S K

2010-10-01

A method is presented to determine the response of a spherical acoustic transducer that consists of a fluid-filled piezoelectric sphere with an elastic coating embedded in infinite fluid to electrical and plane-wave acoustic excitations. The exact spherically symmetric, linear, differential, governing equations are used for the interior and exterior fluids, and elastic and piezoelectric materials. Under acoustic excitation and open circuit boundary condition, the equation governing the piezoelectric sphere is homogeneous and the solution is expressed in terms of Bessel functions. Under electrical excitation, the equation governing the piezoelectric sphere is inhomogeneous and the complementary solution is expressed in terms of Bessel functions and the particular integral is expressed in terms of a power series. Numerical results are presented to illustrate the effect of dimensions of the piezoelectric sphere, fluid loading, elastic coating and internal material losses on the open-circuit receiving sensitivity and transmitting voltage response of the transducer.

The Shock and Vibration Digest. Volume 16, Number 11

DTIC Science & Technology

1984-11-01

wave [19], a secular equation for Rayleigh waves on ing, seismic risk, and related problems are discussed. the surface of an anisotropic half-space...waves in an !so- tive equation of an elastic-plastic rack medium was....... tropic linear elastic half-space with plane material used; the coefficient...pair of semi-linear hyperbolic partial differential -- " Conditions under which the equations of motion equations governing slow variations in amplitude

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 1: Analysis description

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. The governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models are described in detail.

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 1: Analysis description

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 3D has been developed to solve the three dimensional, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort has been to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation have been emphasized. The governing equations are solved in generalized non-orthogonal body-fitted coordinates by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. It describes in detail the governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models.

Near-wall modelling of compressible turbulent flows

NASA Technical Reports Server (NTRS)

So, Ronald M. C.

1990-01-01

Work was carried out to formulate near-wall models for the equations governing the transport of the temperature-variance and its dissipation rate. With these equations properly modeled, a foundation is laid for their extension together with the heat-flux equations to compressible flows. This extension is carried out in a manner similar to that used to extend the incompressible near-wall Reynolds-stress models to compressible flows. The methodology used to accomplish the extension of the near-wall Reynolds-stress models is examined and the actual extension of the models for the Reynolds-stress equations and the near-wall dissipation-rate equation to compressible flows is given. Then the formulation of the near-wall models for the equations governing the transport of the temperature variance and its dissipation rate is discussed. Finally, a sample calculation of a flat plate compressible turbulent boundary-layer flow with adiabatic wall boundary condition and a free-stream Mach number of 2.5 using a two-equation near-wall closure is presented. The results show that the near-wall two-equation closure formulated for compressible flows is quite valid and the calculated properties are in good agreement with measurements. Furthermore, the near-wall behavior of the turbulence statistics and structure parameters is consistent with that found in incompressible flows.

Exact vibration analysis of a double-nanobeam-systems embedded in an elastic medium by a Hamiltonian-based method

NASA Astrophysics Data System (ADS)

Zhou, Zhenhuan; Li, Yuejie; Fan, Junhai; Rong, Dalun; Sui, Guohao; Xu, Chenghui

2018-05-01

A new Hamiltonian-based approach is presented for finding exact solutions for transverse vibrations of double-nanobeam-systems embedded in an elastic medium. The continuum model is established within the frameworks of the symplectic methodology and the nonlocal Euler-Bernoulli and Timoshenko beam beams. The symplectic eigenfunctions are obtained after expressing the governing equations in a Hamiltonian form. Exact frequency equations, vibration modes and displacement amplitudes are obtained by using symplectic eigenfunctions and end conditions. Comparisons with previously published work are presented to illustrate the accuracy and reliability of the proposed method. The comprehensive results for arbitrary boundary conditions could serve as benchmark results for verifying numerically obtained solutions. In addition, a study on the difference between the nonlocal beam and the nonlocal plate is also included.

Meshless Solution of the Problem on the Static Behavior of Thin and Thick Laminated Composite Beams

NASA Astrophysics Data System (ADS)

Xiang, S.; Kang, G. W.

2018-03-01

For the first time, the static behavior of laminated composite beams is analyzed using the meshless collocation method based on a thin-plate-spline radial basis function. In the approximation of a partial differential equation by using a radial basis function, the shape parameter has an important role in ensuring the numerical accuracy. The choice of a shape parameter in the thin plate spline radial basis function is easier than in other radial basis functions. The governing differential equations are derived based on Reddy's third-order shear deformation theory. Numerical results are obtained for symmetric cross-ply laminated composite beams with simple-simple and cantilever boundary conditions under a uniform load. The results found are compared with available published ones and demonstrate the accuracy of the present method.

A split finite element algorithm for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Baker, A. J.

1979-01-01

An accurate and efficient numerical solution algorithm is established for solution of the high Reynolds number limit of the Navier-Stokes equations governing the multidimensional flow of a compressible essentially inviscid fluid. Finite element interpolation theory is used within a dissipative formulation established using Galerkin criteria within the Method of Weighted Residuals. An implicit iterative solution algorithm is developed, employing tensor product bases within a fractional steps integration procedure, that significantly enhances solution economy concurrent with sharply reduced computer hardware demands. The algorithm is evaluated for resolution of steep field gradients and coarse grid accuracy using both linear and quadratic tensor product interpolation bases. Numerical solutions for linear and nonlinear, one, two and three dimensional examples confirm and extend the linearized theoretical analyses, and results are compared to competitive finite difference derived algorithms.

Methods for the calculation of axial wave numbers in lined ducts with mean flow

NASA Technical Reports Server (NTRS)

Eversman, W.

1981-01-01

A survey is made of the methods available for the calculation of axial wave numbers in lined ducts. Rectangular and circular ducts with both uniform and non-uniform flow are considered as are ducts with peripherally varying liners. A historical perspective is provided by a discussion of the classical methods for computing attenuation when no mean flow is present. When flow is present these techniques become either impractical or impossible. A number of direct eigenvalue determination schemes which have been used when flow is present are discussed. Methods described are extensions of the classical no-flow technique, perturbation methods based on the no-flow technique, direct integration methods for solution of the eigenvalue equation, an integration-iteration method based on the governing differential equation for acoustic transmission, Galerkin methods, finite difference methods, and finite element methods.

Dynamic field theory and equations of motion in cosmology

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

Kopeikin, Sergei M., E-mail: kopeikins@missouri.edu; Petrov, Alexander N., E-mail: alex.petrov55@gmail.com

2014-11-15

We discuss a field-theoretical approach based on general-relativistic variational principle to derive the covariant field equations and hydrodynamic equations of motion of baryonic matter governed by cosmological perturbations of dark matter and dark energy. The action depends on the gravitational and matter Lagrangian. The gravitational Lagrangian depends on the metric tensor and its first and second derivatives. The matter Lagrangian includes dark matter, dark energy and the ordinary baryonic matter which plays the role of a bare perturbation. The total Lagrangian is expanded in an asymptotic Taylor series around the background cosmological manifold defined as a solution of Einstein’s equationsmore » in the form of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric tensor. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the series expansion is gauge-invariant and all of them together form a basis for the successive post-Friedmannian approximations around the background metric. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Friedmannian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background FLRW metric. The temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large scale inhomogeneities in these two components as those generated by the primordial cosmological perturbations with an effective matter density contrast δρ/ρ≤1. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations of the background manifold that admits δρ/ρ≫1. Mathematically, the large scale perturbations are given by the homogeneous solution of the linearized field equations while the small scale perturbations are described by a particular solution of these equations with the bare stress–energy tensor of the baryonic matter. We explicitly work out the covariant field equations of the successive post-Friedmannian approximations of Einstein’s equations in cosmology and derive equations of motion of large and small scale inhomogeneities of dark matter and dark energy. We apply these equations to derive the post-Friedmannian equations of motion of baryonic matter comprising stars, galaxies and their clusters.« less

SToRM: A numerical model for environmental surface flows

USGS Publications Warehouse

Simoes, Francisco J.

2009-01-01

SToRM (System for Transport and River Modeling) is a numerical model developed to simulate free surface flows in complex environmental domains. It is based on the depth-averaged St. Venant equations, which are discretized using unstructured upwind finite volume methods, and contains both steady and unsteady solution techniques. This article provides a brief description of the numerical approach selected to discretize the governing equations in space and time, including important aspects of solving natural environmental flows, such as the wetting and drying algorithm. The presentation is illustrated with several application examples, covering both laboratory and natural river flow cases, which show the model’s ability to solve complex flow phenomena.

Stability of Capillary Surfaces in Rectangular Containers: The Right Square Cylinder

NASA Technical Reports Server (NTRS)

Weislogel, M. M.; Hsieh, K. C.

1998-01-01

The linearized governing equations for an ideal fluid are presented for numerical analysis for the stability of free capillary surfaces in rectangular containers against unfavorable disturbances (accelerations,i.e. Rayleigh-Taylor instability). The equations are solved for the case of the right square cylinder. The results are expressed graphically in term of a critical Bond number as a function of system contact angle. A critical wetting phenomena in the corners is shown to significantly alter the region of stability for such containers in contrast to simpler geometries such as the right circular cylinder or the infinite rectangular slot. Such computational results provide additional constraints for the design of fluids systems for space-based applications.

A computer program for calculating laminar and turbulent boundary layers for two-dimensional time-dependent flows

NASA Technical Reports Server (NTRS)

Cebeci, T.; Carr, L. W.

1978-01-01

A computer program is described which provides solutions of two dimensional equations appropriate to laminar and turbulent boundary layers for boundary conditions with an external flow which fluctuates in magnitude. The program is based on the numerical solution of the governing boundary layer equations by an efficient two point finite difference method. An eddy viscosity formulation was used to model the Reynolds shear stress term. The main features of the method are briefly described and instructions for the computer program with a listing are provided. Sample calculations to demonstrate its usage and capabilities for laminar and turbulent unsteady boundary layers with an external flow which fluctuated in magnitude are presented.

Numerical analysis of flow about a total temperature sensor

NASA Technical Reports Server (NTRS)

Von Lavante, Ernst; Bruns, Russell L., Jr.; Sanetrik, Mark D.; Lam, Tim

1989-01-01

The unsteady flowfield about an airfoil-shaped inlet temperature sensor has been investigated using the thin-layer and full Navier-Stokes equations. A finite-volume formulation of the governing equations was used in conjunction with a Runge-Kutta time stepping scheme to analyze the flow about the sensor. Flow characteristics for this configuration were established at Mach numbers of 0.5 and 0.8 for different Reynolds numbers. The results were obtained for configurations of increasing complexity; important physical phenomena such as shock formation, boundary-layer separation, and unsteady wake formation were noted. Based on the computational results, recommendations for further study and refinement of the inlet temperature sensor were made.

The application of the least squares finite element method to Abel's integral equation. [with application to glow discharge problem

NASA Technical Reports Server (NTRS)

Balasubramanian, R.; Norrie, D. H.; De Vries, G.

1979-01-01

Abel's integral equation is the governing equation for certain problems in physics and engineering, such as radiation from distributed sources. The finite element method for the solution of this non-linear equation is presented for problems with cylindrical symmetry and the extension to more general integral equations is indicated. The technique was applied to an axisymmetric glow discharge problem and the results show excellent agreement with previously obtained solutions

The Boundary Layer Flows of a Rivlin-Ericksen Fluid

NASA Astrophysics Data System (ADS)

Sadeghy, K.; Khabazi, N.; Taghavi, S. M.

The present work deals with the two-dimensional incompressible, laminar, steady-state boundary layer equations. First, we determine a family of velocity distributions outside the boundary layer such that these problems may have similarity solutions. We study the Falkner-Skan flow of a viscoelastic fluid governed by second order model, as the Reynolds number Re→ ∞. We obtain an ordinary forth order differential equation to obtain the stream function, velocity profile and the stress. The stream function is then governed by a generalized Falkner-Skan equation. In comparison with Newtonian Falkner-Skan equation that has two coefficients this new one has four coefficients that two of them represent elastic properties of the fluid. The effects of the elastic parameter on the velocity filed have been discussed. As it is shown in the figure there is a good agreement between numerical results and previous special cases confirm the validity of the presented algorithm.

Fluid-structure interaction in Taylor-Couette flow

NASA Astrophysics Data System (ADS)

Kempf, Martin Horst Willi

1998-10-01

The linear stability of a viscous fluid between two concentric, rotating cylinders is considered. The inner cylinder is a rigid boundary and the outer cylinder has an elastic layer exposed to the fluid. The subject is motivated by flow between two adjoining rollers in a printing press. The governing equations of the fluid layer are the incompressible Navier-Stokes equations, and the governing equations of the elastic layer are Navier's equations. A narrow gap, neutral stability, and axisymmetric disturbances are assumed. The solution involves a novel technique for treating two layer stability problems, where an exact solution in the elastic layer is used to isolate the problem in the fluid layer. The results show that the presence of the elastic layer has only a slight effect on the critical Taylor numbers for the elastic parameters of modern printing presses. However, there are parameter values where the critical Taylor number is dramatically different than the classical Taylor-Couette problem.

Finite element computation of a viscous compressible free shear flow governed by the time dependent Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Cooke, C. H.; Blanchard, D. K.

1975-01-01

A finite element algorithm for solution of fluid flow problems characterized by the two-dimensional compressible Navier-Stokes equations was developed. The program is intended for viscous compressible high speed flow; hence, primitive variables are utilized. The physical solution was approximated by trial functions which at a fixed time are piecewise cubic on triangular elements. The Galerkin technique was employed to determine the finite-element model equations. A leapfrog time integration is used for marching asymptotically from initial to steady state, with iterated integrals evaluated by numerical quadratures. The nonsymmetric linear systems of equations governing time transition from step-to-step are solved using a rather economical block iterative triangular decomposition scheme. The concept was applied to the numerical computation of a free shear flow. Numerical results of the finite-element method are in excellent agreement with those obtained from a finite difference solution of the same problem.

An implicit semianalytic numerical method for the solution of nonequilibrium chemistry problems

NASA Technical Reports Server (NTRS)

Graves, R. A., Jr.; Gnoffo, P. A.; Boughner, R. E.

1974-01-01

The first order differential equation form systems of equations. They are solved by a simple and relatively accurate implicit semianalytic technique which is derived from a quadrature solution of the governing equation. This method is mathematically simpler than most implicit methods and has the exponential nature of the problem embedded in the solution.

Thermoelastic-plastic flow equations in general coordinates

DOE PAGES

Blaschke, Daniel N.; Preston, Dean L.

2018-03-28

The equations governing the thermoelastic-plastic flow of isotropic solids in the Prandtl- Reuss and small anisotropy approximations in Cartesian coordinates are generalized to arbitrary coordinate systems. In applications the choice of coordinates is dictated by the symmetry of the solid flow. The generally invariant equations are evaluated in spherical, cylindrical (including uniaxial), and both prolate and oblate spheroidal coordinates.

Thermoelastic-plastic flow equations in general coordinates

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

Blaschke, Daniel N.; Preston, Dean L.

The equations governing the thermoelastic-plastic flow of isotropic solids in the Prandtl- Reuss and small anisotropy approximations in Cartesian coordinates are generalized to arbitrary coordinate systems. In applications the choice of coordinates is dictated by the symmetry of the solid flow. The generally invariant equations are evaluated in spherical, cylindrical (including uniaxial), and both prolate and oblate spheroidal coordinates.

(2 + 1)-dimensional bright optical solitons in metamaterials with Kerr, power and parabolic law nonlinearities

NASA Astrophysics Data System (ADS)

Boubir, Badreddine

2018-06-01

In this paper, we investigate the dynamics of bright optical solitons in nonlinear metamaterials governed by a (2 + 1)-dimensional nonlinear Schrödinger equation. Three types of nonlinearities have been considered, Kerr law, power law and parabolic law. We based on the solitary wave ansatz method to find these optical soliton solutions. All necessary parametric conditions for their existence are driven.

High-Maneuverability Airframe: Initial Investigation of Configuration’s Aft End for Increased Stability, Range, and Maneuverability

DTIC Science & Technology

2013-09-01

including the interaction effects between the fins and canards. 2. Solution Technique 2.1 Computational Aerodynamics The double-precision solver of a...and overset grids (unified-grid). • Total variation diminishing discretization based on a new multidimensional interpolation framework. • Riemann ... solvers to provide proper signal propagation physics including versions for preconditioned forms of the governing equations. • Consistent and

Computational Implementation of a Thermodynamically Based Work Potential Model For Progressive Microdamage and Transverse Cracking in Fiber-Reinforced Laminates

NASA Technical Reports Server (NTRS)

Pineda, Evan J.; Waas, Anthony M.; Bednarcyk, Brett A.; Collier, Craig S.

2012-01-01

A continuum-level, dual internal state variable, thermodynamically based, work potential model, Schapery Theory, is used capture the effects of two matrix damage mechanisms in a fiber-reinforced laminated composite: microdamage and transverse cracking. Matrix microdamage accrues primarily in the form of shear microcracks between the fibers of the composite. Whereas, larger transverse matrix cracks typically span the thickness of a lamina and run parallel to the fibers. Schapery Theory uses the energy potential required to advance structural changes, associated with the damage mechanisms, to govern damage growth through a set of internal state variables. These state variables are used to quantify the stiffness degradation resulting from damage growth. The transverse and shear stiffness of the lamina are related to the internal state variables through a set of measurable damage functions. Additionally, the damage variables for a given strain state can be calculated from a set of evolution equations. These evolution equations and damage functions are implemented into the finite element method and used to govern the constitutive response of the material points in the model. Additionally, an axial failure criterion is included in the model. The response of a center-notched, buffer strip-stiffened panel subjected to uniaxial tension is investigated and results are compared to experiment.

Thermodynamic analysis of biofuels as fuels for high temperature fuel cells

NASA Astrophysics Data System (ADS)

Milewski, Jarosław; Bujalski, Wojciech; Lewandowski, Janusz

2011-11-01

Based on mathematical modeling and numerical simulations, applicativity of various biofuels on high temperature fuel cell performance are presented. Governing equations of high temperature fuel cell modeling are given. Adequate simulators of both solid oxide fuel cell (SOFC) and molten carbonate fuel cell (MCFC) have been done and described. Performance of these fuel cells with different biofuels is shown. Some characteristics are given and described. Advantages and disadvantages of various biofuels from the system performance point of view are pointed out. An analysis of various biofuels as potential fuels for SOFC and MCFC is presented. The results are compared with both methane and hydrogen as the reference fuels. The biofuels are characterized by both lower efficiency and lower fuel utilization factors compared with methane. The presented results are based on a 0D mathematical model in the design point calculation. The governing equations of the model are also presented. Technical and financial analysis of high temperature fuel cells (SOFC and MCFC) are shown. High temperature fuel cells can be fed by biofuels like: biogas, bioethanol, and biomethanol. Operational costs and possible incomes of those installation types were estimated and analyzed. A comparison against classic power generation units is shown. A basic indicator net present value (NPV) for projects was estimated and commented.

Thermodynamic analysis of biofuels as fuels for high temperature fuel cells

NASA Astrophysics Data System (ADS)

Milewski, Jarosław; Bujalski, Wojciech; Lewandowski, Janusz

2013-02-01

Based on mathematical modeling and numerical simulations, applicativity of various biofuels on high temperature fuel cell performance are presented. Governing equations of high temperature fuel cell modeling are given. Adequate simulators of both solid oxide fuel cell (SOFC) and molten carbonate fuel cell (MCFC) have been done and described. Performance of these fuel cells with different biofuels is shown. Some characteristics are given and described. Advantages and disadvantages of various biofuels from the system performance point of view are pointed out. An analysis of various biofuels as potential fuels for SOFC and MCFC is presented. The results are compared with both methane and hydrogen as the reference fuels. The biofuels are characterized by both lower efficiency and lower fuel utilization factors compared with methane. The presented results are based on a 0D mathematical model in the design point calculation. The governing equations of the model are also presented. Technical and financial analysis of high temperature fuel cells (SOFC and MCFC) are shown. High temperature fuel cells can be fed by biofuels like: biogas, bioethanol, and biomethanol. Operational costs and possible incomes of those installation types were estimated and analyzed. A comparison against classic power generation units is shown. A basic indicator net present value (NPV) for projects was estimated and commented.

Nonlinear effects on electrophoresis of a charged dielectric nanoparticle in a charged hydrogel medium

NASA Astrophysics Data System (ADS)

Bhattacharyya, S.; De, Simanta

2016-09-01

The impact of the solid polarization of a charged dielectric particle in gel electrophoresis is studied without imposing a weak-field or a thin Debye length assumption. The electric polarization of a dielectric particle due to an external electric field creates a non-uniform surface charge density, which in turn creates a non-uniform Debye layer at the solid-gel interface. The solid polarization of the particle, the polarization of the double layer, and the electro-osmosis of mobile ions within the hydrogel medium create a nonlinear effect on the electrophoresis. We have incorporated those nonlinear effects by considering the electrokinetics governed by the Stokes-Brinkman-Nernst-Planck-Poisson equations. We have computed the governing nonlinear coupled set of equations numerically by adopting a finite volume based iterative algorithm. Our numerical method is tested for accuracy by comparing with several existing results on free-solution electrophoresis as well as results based on the Debye-Hückel approximation. Our computed result shows that the electrophoretic velocity decreases with the rise of the particle dielectric permittivity constant and attains a saturation limit at large values of permittivity. A significant impact of the solid polarization is found in gel electrophoresis compared to the free-solution electrophoresis.

Laminar and turbulent flow computations of Type 4 shock-shock interference aerothermal loads using unstructured grids

NASA Technical Reports Server (NTRS)

Vemaganti, Gururaja R.

1994-01-01

This report presents computations for the Type 4 shock-shock interference flow under laminar and turbulent conditions using unstructured grids. Mesh adaptation was accomplished by remeshing, refinement, and mesh movement. Two two-equation turbulence models were used to analyze turbulent flows. The mean flow governing equations and the turbulence governing equations are solved in a coupled manner. The solution algorithm and the details pertaining to its implementation on unstructured grids are described. Computations were performed at two different freestream Reynolds numbers at a freestream Mach number of 11. Effects of the variation in the impinging shock location are studied. The comparison of the results in terms of wall heat flux and wall pressure distributions is presented.

Description of Jet Breakup

NASA Technical Reports Server (NTRS)

Papageorgiou, Demetrios T.

1996-01-01

In this article we review recent results on the breakup of cylindrical jets of a Newtonian fluid. Capillary forces provide the main driving mechanism and our interest is in the description of the flow as the jet pinches to form drops. The approach is to describe such topological singularities by constructing local (in time and space) similarity solutions from the governing equations. This is described for breakup according to the Euler, Stokes or Navier-Stokes equations. It is found that slender jet theories can be applied when viscosity is present, but for inviscid jets the local shape of the jet at breakup is most likely of a non-slender geometry. Systems of one-dimensional models of the governing equations are solved numerically in order to illustrate these differences.

Numerical simulations of three-dimensional laminar flow over a backward facing step; flow near side walls

NASA Technical Reports Server (NTRS)

Steinthorsson, Erlendur; Liou, Meng-Sing; Povinelli, Louis A.; Arnone, Andrea

1993-01-01

This paper reports the results of numerical simulations of steady, laminar flow over a backward-facing step. The governing equations used in the simulations are the full 'compressible' Navier-Stokes equations, solutions to which were computed by using a cell-centered, finite volume discretization. The convection terms of the governing equations were discretized by using the Advection Upwind Splitting Method (AUSM), whereas the diffusion terms were discretized using central differencing formulas. The validity and accuracy of the numerical solutions were verified by comparing the results to existing experimental data for flow at identical Reynolds numbers in the same back step geometry. The paper focuses attention on the details of the flow field near the side wall of the geometry.

Flight test evaluation of a method to determine the level flight performance of a propeller-driven aircraft

NASA Technical Reports Server (NTRS)

Bridges, P. G.; Cross, E. J., Jr.; Boatwright, D. W.

1977-01-01

The overall drag of the aircraft is expressed in terms of the measured increment of power required to overcome a corresponding known increment of drag, which is generated by a towed drogue. The simplest form of the governing equations, D = delta D SHP/delta SHP, is such that all of the parameters on the right side of the equation can be measured in flight. An evaluation of the governing equations has been performed using data generated by flight test of a Beechcraft T-34B. The simplicity of this technique and its proven applicability to sailplanes and small aircraft is well known. However, the method fails to account for airframe-propulsion system.

Magnetohydrodynamics Nanofluid Flow Containing Gyrotactic Microorganisms Propagating Over a Stretching Surface by Successive Taylor Series Linearization Method

NASA Astrophysics Data System (ADS)

Shahid, A.; Zhou, Z.; Bhatti, M. M.; Tripathi, D.

2018-03-01

Nanofluid dynamics with magnetohydrodynamics has tremendously contributed in industrial applications recently since presence of nanoparticle in base fluids enhances the specific chemical and physical properties. Owing to the relevance of nanofluid dynamics, we analyze the nanofluid flow in the presence of gyrotactic microorganism and magnetohydrodynamics through a stretching/shrinking plate. The impacts of chemical reaction and thermal radiation on flow characteristics are also studied. To simplify the governing equations of microorganisms, velocity, concentration and temperature, the similarity transformations are employed. The couple governing equations are numerically solved using Successive Taylor Series Linearization Method (STSLM). The velocity profile, motile microorganism density profile, concentration profile, temperature profile as well as Nusselt number, skin friction coefficient, Sherwood number and density number of motile microorganisms are discussed using tables and graphs against all the sundry parameters. A numerical comparison is also given for Nusselt number, Sherwood number, skin friction, and density number of motile microorganisms with previously published results to validate the present model. The results show that Nusselt number, Sherwood number and density number diminish with increasing the magnetic field effects.

The open prototype for educational NanoSats: Fixing the other side of the small satellite cost equation

NASA Astrophysics Data System (ADS)

Berk, Josh; Straub, Jeremy; Whalen, David

Government supported nano-satellite launch programs and emerging commercial small satellite launch services are reducing the cost of access to space for educational and other CubeSat projects. The cost and complexity of designing and building these satellites remains a vexing complication for many would be CubeSat aspirants. The Open Prototype for Educational NanoSats (OPEN), a proposed nano-satellite development platform, is described in this paper. OPEN endeavors to reduce the costs and risks associated with educational, government and commercial nano-satellite development. OPEN provides free and publicly available plans for building, testing and operating a versatile, low-cost satellite, based on the standardized CubeSat form-factor. OPEN consists of public-domain educational reference plans, complete with engineering schematics, CAD files, construction and test instructions as well as ancillary reference materials relevant to satellite building and operation. By making the plan, to produce a small but capable spacecraft freely available, OPEN seeks to lower the barriers to access on the other side (non-launch costs) of the satellite cost equation.

Towards an orientation-distribution-based multi-scale approach for remodelling biological tissues.

PubMed

Menzel, A; Harrysson, M; Ristinmaa, M

2008-10-01

The mechanical behaviour of soft biological tissues is governed by phenomena occurring on different scales of observation. From the computational modelling point of view, a vital aspect consists of the appropriate incorporation of micromechanical effects into macroscopic constitutive equations. In this work, particular emphasis is placed on the simulation of soft fibrous tissues with the orientation of the underlying fibres being determined by distribution functions. A straightforward but convenient Taylor-type homogenisation approach links the micro- or rather meso-level of fibres to the overall macro-level and allows to reflect macroscopically orthotropic response. As a key aspect of this work, evolution equations for the fibre orientations are accounted for so that physiological effects like turnover or rather remodelling are captured. Concerning numerical applications, the derived set of equations can be embedded into a nonlinear finite element context so that first elementary simulations are finally addressed.

A purely Lagrangian method for simulating the shallow water equations on a sphere using smooth particle hydrodynamics

NASA Astrophysics Data System (ADS)

Capecelatro, Jesse

2018-03-01

It has long been suggested that a purely Lagrangian solution to global-scale atmospheric/oceanic flows can potentially outperform tradition Eulerian schemes. Meanwhile, a demonstration of a scalable and practical framework remains elusive. Motivated by recent progress in particle-based methods when applied to convection dominated flows, this work presents a fully Lagrangian method for solving the inviscid shallow water equations on a rotating sphere in a smooth particle hydrodynamics framework. To avoid singularities at the poles, the governing equations are solved in Cartesian coordinates, augmented with a Lagrange multiplier to ensure that fluid particles are constrained to the surface of the sphere. An underlying grid in spherical coordinates is used to facilitate efficient neighbor detection and parallelization. The method is applied to a suite of canonical test cases, and conservation, accuracy, and parallel performance are assessed.

Four-fluid MHD Simulations of the Plasma and Neutral Gas Environment of Comet Churyumov-Gerasimenko Near Perihelion

NASA Astrophysics Data System (ADS)

Huang, Z.; Toth, G.; Gombosi, T.; Jia, X.; Rubin, M.; Fougere, N.; Tenishev, V.; Combi, M.; Bieler, A.; Hansen, K.; Shou, Y.; Altwegg, K.

2015-10-01

We develop a 3-D four fluid model to study the plasma environment of comet Churyumov- Gerasimenko (CG), which is the target of the Rosetta mission. Our model is based on BATS-R-US within the SWMF (Space Weather Modeling Framework) that solves the governing multifluid MHD equations and and the Euler equations for the neutral gas fluid. These equations describe the behavior and interactions of the cometary heavy ions, the solar wind protons, the electrons, and the neutrals. This model incorporates mass loading processes, including photo and electron impact ionization, furthermore taken into account are charge exchange, dissociative ion-electron recombination, as well as collisional interactions between different fluids. We simulate the near nucleus plasma and neutral gas environment with a realistic shape model of CG near perihelion and compare our simulation results with Rosetta observations.

Four-fluid MHD Simulations of the Plasma and Neutral Gas Environment of Comet Churyumov-Gerasimenko Near Perihelio

NASA Astrophysics Data System (ADS)

Huang, Z.; Toth, G.; Gombosi, T. I.; Jia, X.; Rubin, M.; Hansen, K. C.; Fougere, N.; Bieler, A. M.; Shou, Y.; Altwegg, K.; Combi, M. R.; Tenishev, V.

2015-12-01

The neutral and plasma environment is critical in understanding the interaction of comet Churyumov-Gerasimenko (CG), the target of the Rosetta mission, and the solar wind. To serve this need and support the Rosetta mission, we develop a 3-D four fluid model, which is based on BATS-R-US within the SWMF (Space Weather Modeling Framework) that solves the governing multi-fluid MHD equations and the Euler equations for the neutral gas fluid. These equations describe the behavior and interactions of the cometary heavy ions, the solar wind protons, the electrons, and the neutrals. This model incorporates different mass loading processes, including photo and electron impact ionization, charge exchange, dissociative ion-electron recombination, and collisional interactions between different fluids. We simulate the near nucleus plasma and neutral gas environment near perihelion with a realistic shape model of CG and compare our simulation results with Rosetta observations.

Numerical solutions of Navier-Stokes equations for compressible turbulent two/three dimensional flows in terminal shock region of an inlet/diffuser

NASA Technical Reports Server (NTRS)

Liu, N. S.; Shamroth, S. J.; Mcdonald, H.

1983-01-01

The multidimensional ensemble averaged compressible time dependent Navier Stokes equations in conjunction with mixing length turbulence model and shock capturing technique were used to study the terminal shock type of flows in various flight regimes occurring in a diffuser/inlet model. The numerical scheme for solving the governing equations is based on a linearized block implicit approach and the following high Reynolds number calculations were carried out: (1) 2 D, steady, subsonic; (2) 2 D, steady, transonic with normal shock; (3) 2 D, steady, supersonic with terminal shock; (4) 2 D, transient process of shock development and (5) 3 D, steady, transonic with normal shock. The numerical results obtained for the 2 D and 3 D transonic shocked flows were compared with corresponding experimental data; the calculated wall static pressure distributions agree well with the measured data.

Similarity transformation for equilibrium boundary layers, including effects of blowing and suction

NASA Astrophysics Data System (ADS)

Chen, Xi; Hussain, Fazle

2017-03-01

We present a similarity transformation for the mean velocity profiles in sink flow turbulent boundary layers, including effects of blowing and suction. It is based on symmetry analysis which transforms the governing partial differential equations (for mean mass and momentum) into an ordinary differential equation and yields a new result including an exact, linear relation between the mean normal (V ) and streamwise (U ) velocities. A characteristic length function is further introduced which, under a first order expansion (whose coefficient is η ) in wall blowing and suction velocity, leads to the similarity transformation for U with the value of η ≈-1 /9 . This transformation is shown to be a group invariant and maps different U profiles under different blowing and suction conditions into a (universal) profile for no blowing or suction. Its inverse transformation enables predictions of all mean quantities in the mean mass and momentum equations, in good agreement with DNS data.

The generalized DMPK equation revisited: towards a systematic derivation

NASA Astrophysics Data System (ADS)

Douglas, Andrew; Markoš, Peter; Muttalib, K. A.

2014-03-01

The generalized Dorokov-Mello-Pereyra-Kumar (DMPK) equation has recently been used to obtain a family of very broad and highly asymmetric conductance distributions for three-dimensional disordered conductors. However, there are two major criticisms of the derivation of the generalized DMPK equation: (1) certain eigenvector correlations were neglected based on qualitative arguments that cannot be valid for all strengths of disorder, and (2) the repulsion between two closely spaced eigenvalues were not rigorously governed by symmetry considerations. In this work we show that it is possible to address both criticisms by including the eigenvalue and eigenvector correlations in a systematic and controlled way. It turns out that the added correlations determine the evolution of the Jacobian, without affecting the evaluation of the conductance distributions. They also guarantee the symmetry requirements. In addition, we obtain an exact relationship between the eigenvectors and the Lyapunov exponents leading to a sum rule for the latter at all disorder strengths.

Entropy Analysis in Mixed Convection MHD flow of Nanofluid over a Non-linear Stretching Sheet

NASA Astrophysics Data System (ADS)

Matin, Meisam Habibi; Nobari, Mohammad Reza Heirani; Jahangiri, Pouyan

This article deals with a numerical study of entropy analysis in mixed convection MHD flow of nanofluid over a non-linear stretching sheet taking into account the effects of viscous dissipation and variable magnetic field. The nanofluid is made of such nano particles as SiO2 with pure water as a base fluid. To analyze the problem, at first the boundary layer equations are transformed into non-linear ordinary equations using a similarity transformation. The resultant equations are then solved numerically using the Keller-Box scheme based on the implicit finite-difference method. The effects of different non-dimensional governing parameters such as magnetic parameter, nanoparticles volume fraction, Nusselt, Richardson, Eckert, Hartman, Brinkman, Reynolds and entropy generation numbers are investigated in details. The results indicate that increasing the nano particles to the base fluids causes the reduction in shear forces and a decrease in stretching sheet heat transfer coefficient. Also, decreasing the magnetic parameter and increasing the Eckert number result in improves heat transfer rate. Furthermore, the surface acts as a strong source of irreversibility due to the higher entropy generation number near the surface.

An Extended Trajectory Mechanics Approach for Calculating the Path of a Pressure Transient: Derivation and Illustration

NASA Astrophysics Data System (ADS)

Vasco, D. W.

2018-04-01

Following an approach used in quantum dynamics, an exponential representation of the hydraulic head transforms the diffusion equation governing pressure propagation into an equivalent set of ordinary differential equations. Using a reservoir simulator to determine one set of dependent variables leaves a reduced set of equations for the path of a pressure transient. Unlike the current approach for computing the path of a transient, based on a high-frequency asymptotic solution, the trajectories resulting from this new formulation are valid for arbitrary spatial variations in aquifer properties. For a medium containing interfaces and layers with sharp boundaries, the trajectory mechanics approach produces paths that are compatible with travel time fields produced by a numerical simulator, while the asymptotic solution produces paths that bend too strongly into high permeability regions. The breakdown of the conventional asymptotic solution, due to the presence of sharp boundaries, has implications for model parameter sensitivity calculations and the solution of the inverse problem. For example, near an abrupt boundary, trajectories based on the asymptotic approach deviate significantly from regions of high sensitivity observed in numerical computations. In contrast, paths based on the new trajectory mechanics approach coincide with regions of maximum sensitivity to permeability changes.

Viscous Driven-Cavity Solver: User's Manual

NASA Technical Reports Server (NTRS)

Wood, William A.

1997-01-01

The viscous driven-cavity problem is solved using a stream-function and vorticity formulation for the incompressible Navier-Stokes equations. This report provides the user's manual and FORTRAN code for the set of governing equations presented in NASA TM-110262.

An algorithm for solving the perturbed gas dynamic equations

NASA Technical Reports Server (NTRS)

Davis, Sanford

1993-01-01

The present application of a compact, higher-order central-difference approximation to the linearized Euler equations illustrates the multimodal character of these equations by means of computations for acoustic, vortical, and entropy waves. Such dissipationless central-difference methods are shown to propagate waves exhibiting excellent phase and amplitude resolution on the basis of relatively large time-steps; they can be applied to wave problems governed by systems of first-order partial differential equations.

A conservative fully implicit algorithm for predicting slug flows

NASA Astrophysics Data System (ADS)

Krasnopolsky, Boris I.; Lukyanov, Alexander A.

2018-02-01

An accurate and predictive modelling of slug flows is required by many industries (e.g., oil and gas, nuclear engineering, chemical engineering) to prevent undesired events potentially leading to serious environmental accidents. For example, the hydrodynamic and terrain-induced slugging leads to unwanted unsteady flow conditions. This demands the development of fast and robust numerical techniques for predicting slug flows. The presented in this paper study proposes a multi-fluid model and its implementation method accounting for phase appearance and disappearance. The numerical modelling of phase appearance and disappearance presents a complex numerical challenge for all multi-component and multi-fluid models. Numerical challenges arise from the singular systems of equations when some phases are absent and from the solution discontinuity when some phases appear or disappear. This paper provides a flexible and robust solution to these issues. A fully implicit formulation described in this work enables to efficiently solve governing fluid flow equations. The proposed numerical method provides a modelling capability of phase appearance and disappearance processes, which is based on switching procedure between various sets of governing equations. These sets of equations are constructed using information about the number of phases present in the computational domain. The proposed scheme does not require an explicit truncation of solutions leading to a conservative scheme for mass and linear momentum. A transient two-fluid model is used to verify and validate the proposed algorithm for conditions of hydrodynamic and terrain-induced slug flow regimes. The developed modelling capabilities allow to predict all the major features of the experimental data, and are in a good quantitative agreement with them.

Mathematical modeling of impact of two metal plates using two-fluid approach

NASA Astrophysics Data System (ADS)

Utkin, P. S.; Fortova, S. V.

2018-01-01

The paper is devoted to the development of the two-fluid mathematical model and the computational algorithm for the modeling of two metal plates impact. In one-dimensional case the governing system of equations comprises seven equations: three conservation laws for each fluid and transfer equation for the volume fraction of one of the fluids. Both fluids are considered to be compressible and equilibrium on velocities. Pressures equilibrium is used as fluids interface condition. The system has hyperbolic type but could not be written in the conservative form because of nozzling terms in the right-hand side of the equations. The algorithm is based on the Harten-Lax-van Leer numerical flux function. The robust computation in the presence of the interface boundary is carried out due to the special pressure relaxation procedure. The problem is solved using stiffened gas equations of state for each fluid. The parameters in the equations of state are calibrated using the results of computations using wide-range equations of state for the metals. In simulations of metal plates impact we get two shocks after the initial impact that propagate to the free surfaces of the samples. The characteristics of shock waves are close (maximum relative error in characteristics of shocks is not greater than 7%) to the data from the wide-range equations of states computations.

Numerical study of viscous dissipation during single drop impact on wetted surfaces

NASA Astrophysics Data System (ADS)

An, Yi; Yang, Shihao; Liu, Qingquan

2017-11-01

The splashing crown by the impact of a drop on a liquid film has been studied extensively since Yarin and Weiss (JFM 1995). The motion of the crown base is believed to be kinematic which results in the equation R =(2/3H)1/4(T-T0)1/2. This equation is believed to overestimate the crown size by about 15%. While Trojillo and Lee (PoF 2001) find the influence of the Re not notable. Considering the dissipation in the initial stage of the impact, Gao and Li (PRE, 2015) obtained a well-validated equation. However, how to estimate the dissipation is still worth some detailed discussion. We carried out a series of VOF simulations with special focusing on the influence of viscosity. The simulation is based on the Basilisk code to utilize adaptive mesh refinement. We found that the role of dissipation could be divided into three stages. When T> 1, the commonly used shallow water equation provides a good approximation while the initial condition should be considered properly. Between this two stages, the viscous dissipation is the governing factor and thus causes inaccurate estimation of the crown base motion in the third stage. This work was financially supported by the National Natural Science Foundation of China (No. 11672310, No. 11372326).

Econometric Model of Rice Policy Based On Presidential Instruction

NASA Astrophysics Data System (ADS)

Abadi Sembiring, Surya; Hutauruk, Julia

2018-01-01

The objective of research is to build an econometric model based on Presidential Instruction rice policy. The data was monthly time series from March 2005 to September 2009. Rice policy model specification using simultaneous equation, consisting of 14 structural equations and four identity equation, which was estimated using Two Stages Least Squares (2SLS) method. The results show that: (1) an increase of government purchasing price of dried harvest paddy has a positive impact on to increase in total rice production and community rice stock, (2) an increase community rice stock lead to decrease the rice imports, (3) an increase of the realization of the distribution of subsidized ZA fertilizers and the realization of the distribution of subsidized NPK fertilizers has a positive impact on to increase in total rice production and community rice stock and to reduce rice imports, (4) the price of the dried harvest paddy is highly responsive to the water content of dried harvest paddy both the short run and long run, (5) the quantity of rice imported is highly responsive to the imported rice price, both short run and long run.

Differential geometry based solvation model. III. Quantum formulation

PubMed Central

Chen, Zhan; Wei, Guo-Wei

2011-01-01

Solvation is of fundamental importance to biomolecular systems. Implicit solvent models, particularly those based on the Poisson-Boltzmann equation for electrostatic analysis, are established approaches for solvation analysis. However, ad hoc solvent-solute interfaces are commonly used in the implicit solvent theory. Recently, we have introduced differential geometry based solvation models which allow the solvent-solute interface to be determined by the variation of a total free energy functional. Atomic fixed partial charges (point charges) are used in our earlier models, which depends on existing molecular mechanical force field software packages for partial charge assignments. As most force field models are parameterized for a certain class of molecules or materials, the use of partial charges limits the accuracy and applicability of our earlier models. Moreover, fixed partial charges do not account for the charge rearrangement during the solvation process. The present work proposes a differential geometry based multiscale solvation model which makes use of the electron density computed directly from the quantum mechanical principle. To this end, we construct a new multiscale total energy functional which consists of not only polar and nonpolar solvation contributions, but also the electronic kinetic and potential energies. By using the Euler-Lagrange variation, we derive a system of three coupled governing equations, i.e., the generalized Poisson-Boltzmann equation for the electrostatic potential, the generalized Laplace-Beltrami equation for the solvent-solute boundary, and the Kohn-Sham equations for the electronic structure. We develop an iterative procedure to solve three coupled equations and to minimize the solvation free energy. The present multiscale model is numerically validated for its stability, consistency and accuracy, and is applied to a few sets of molecules, including a case which is difficult for existing solvation models. Comparison is made to many other classic and quantum models. By using experimental data, we show that the present quantum formulation of our differential geometry based multiscale solvation model improves the prediction of our earlier models, and outperforms some explicit solvation model. PMID:22112067

Analytical and experimental comparisons of electromechanical vibration response of a piezoelectric bimorph beam for power harvesting

NASA Astrophysics Data System (ADS)

Lumentut, M. F.; Howard, I. M.

2013-03-01

Power harvesters that extract energy from vibrating systems via piezoelectric transduction show strong potential for powering smart wireless sensor devices in applications of health condition monitoring of rotating machinery and structures. This paper presents an analytical method for modelling an electromechanical piezoelectric bimorph beam with tip mass under two input base transverse and longitudinal excitations. The Euler-Bernoulli beam equations were used to model the piezoelectric bimorph beam. The polarity-electric field of the piezoelectric element is excited by the strain field caused by base input excitation, resulting in electrical charge. The governing electromechanical dynamic equations were derived analytically using the weak form of the Hamiltonian principle to obtain the constitutive equations. Three constitutive electromechanical dynamic equations based on independent coefficients of virtual displacement vectors were formulated and then further modelled using the normalised Ritz eigenfunction series. The electromechanical formulations include both the series and parallel connections of the piezoelectric bimorph. The multi-mode frequency response functions (FRFs) under varying electrical load resistance were formulated using Laplace transformation for the multi-input mechanical vibrations to provide the multi-output dynamic displacement, velocity, voltage, current and power. The experimental and theoretical validations reduced for the single mode system were shown to provide reasonable predictions. The model results from polar base excitation for off-axis input motions were validated with experimental results showing the change to the electrical power frequency response amplitude as a function of excitation angle, with relevance for practical implementation.

Efficient stabilization and acceleration of numerical simulation of fluid flows by residual recombination

NASA Astrophysics Data System (ADS)

Citro, V.; Luchini, P.; Giannetti, F.; Auteri, F.

2017-09-01

The study of the stability of a dynamical system described by a set of partial differential equations (PDEs) requires the computation of unstable states as the control parameter exceeds its critical threshold. Unfortunately, the discretization of the governing equations, especially for fluid dynamic applications, often leads to very large discrete systems. As a consequence, matrix based methods, like for example the Newton-Raphson algorithm coupled with a direct inversion of the Jacobian matrix, lead to computational costs too large in terms of both memory and execution time. We present a novel iterative algorithm, inspired by Krylov-subspace methods, which is able to compute unstable steady states and/or accelerate the convergence to stable configurations. Our new algorithm is based on the minimization of the residual norm at each iteration step with a projection basis updated at each iteration rather than at periodic restarts like in the classical GMRES method. The algorithm is able to stabilize any dynamical system without increasing the computational time of the original numerical procedure used to solve the governing equations. Moreover, it can be easily inserted into a pre-existing relaxation (integration) procedure with a call to a single black-box subroutine. The procedure is discussed for problems of different sizes, ranging from a small two-dimensional system to a large three-dimensional problem involving the Navier-Stokes equations. We show that the proposed algorithm is able to improve the convergence of existing iterative schemes. In particular, the procedure is applied to the subcritical flow inside a lid-driven cavity. We also discuss the application of Boostconv to compute the unstable steady flow past a fixed circular cylinder (2D) and boundary-layer flow over a hemispherical roughness element (3D) for supercritical values of the Reynolds number. We show that Boostconv can be used effectively with any spatial discretization, be it a finite-difference, finite-volume, finite-element or spectral method.

Flash flood warning based on fully dynamic hydrology modelling

NASA Astrophysics Data System (ADS)

Pejanovic, Goran; Petkovic, Slavko; Cvetkovic, Bojan; Nickovic, Slobodan

2016-04-01

Numerical hydrologic modeling has achieved limited success in the past due to, inter alia, lack of adequate input data. Over the last decade, data availability has improved substantially. For modelling purposes, high-resolution data on topography, river routing, and land cover and soil features have meanwhile become available, as well as the observations such as radar precipitation information. In our study, we have implemented the HYPROM model (Hydrology Prognostic Model) to predict a flash flood event at a smaller-scale basin in Southern Serbia. HYPROM is based on the full set of governing equations for surface hydrological dynamics, in which momentum components, along with the equation of mass continuity, are used as full prognostic equations. HYPROM also includes a river routing module serving as a collector for the extra surface water. Such approach permits appropriate representation of different hydrology scales ranging from flash floods to flows of large and slow river basins. The use of full governing equations, if not appropriately parameterized, may lead to numerical instability systems when the surface water in a model is vanishing. To resolve these modelling problems, an unconditionally stable numerical scheme and a method for height redistribution avoiding shortwave height noise have been developed in HYPROM, which achieve numerical convergence of u, v and h when surface water disappears. We have applied HYPROM, driven by radar-estimated precipitation, to predict flash flooding occurred over smaller and medium-size river basins. Two torrential rainfall cases have been simulated to check the accuracy of the model: the exceptional flooding of May 2014 in Western Serbia, and the convective flash flood of January 2015 in Southern Serbia. The second episode has been successfully predicted by HYPROM in terms of timing and intensity six hours before the event occurred. Such flash flood warning system is in preparation to be operationally implemented in the Republic Hydrometeorological Service of Serbia.

A computer program for the geometrically nonlinear static and dynamic analysis of arbitrarily loaded shells of revolution, theory and users manual

NASA Technical Reports Server (NTRS)

Ball, R. E.

1972-01-01

A digital computer program known as SATANS (static and transient analysis, nonlinear, shells) for the geometrically nonlinear static and dynamic response of arbitrarily loaded shells of revolution is presented. Instructions for the preparation of the input data cards and other information necessary for the operation of the program are described in detail and two sample problems are included. The governing partial differential equations are based upon Sanders' nonlinear thin shell theory for the conditions of small strains and moderately small rotations. The governing equations are reduced to uncoupled sets of four linear, second order, partial differential equations in the meridional and time coordinates by expanding the dependent variables in a Fourier sine or cosine series in the circumferential coordinate and treating the nonlinear modal coupling terms as pseudo loads. The derivatives with respect to the meridional coordinate are approximated by central finite differences, and the displacement accelerations are approximated by the implicit Houbolt backward difference scheme with a constant time interval. The boundaries of the shell may be closed, free, fixed, or elastically restrained. The program is coded in the FORTRAN 4 language and is dimensioned to allow a maximum of 10 arbitrary Fourier harmonics and a maximum product of the total number of meridional stations and the total number of Fourier harmonics of 200. The program requires 155,000 bytes of core storage.

An explicit dissipation-preserving method for Riesz space-fractional nonlinear wave equations in multiple dimensions

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

2018-06-01

In this work, we investigate numerically a model governed by a multidimensional nonlinear wave equation with damping and fractional diffusion. The governing partial differential equation considers the presence of Riesz space-fractional derivatives of orders in (1, 2], and homogeneous Dirichlet boundary data are imposed on a closed and bounded spatial domain. The model under investigation possesses an energy function which is preserved in the undamped regime. In the damped case, we establish the property of energy dissipation of the model using arguments from functional analysis. Motivated by these results, we propose an explicit finite-difference discretization of our fractional model based on the use of fractional centered differences. Associated to our discrete model, we also propose discretizations of the energy quantities. We establish that the discrete energy is conserved in the undamped regime, and that it dissipates in the damped scenario. Among the most important numerical features of our scheme, we show that the method has a consistency of second order, that it is stable and that it has a quadratic order of convergence. Some one- and two-dimensional simulations are shown in this work to illustrate the fact that the technique is capable of preserving the discrete energy in the undamped regime. For the sake of convenience, we provide a Matlab implementation of our method for the one-dimensional scenario.

Semiannual Report October 1, 1999 through March 31, 2000

DTIC Science & Technology

2000-04-01

Mark Carpenter (NASA Langley). Textbook Multigrid Efficiency for the Navier-Stokes Equations Boris Diskin A typical modern Reynolds-Averaged...defined as textbook multigrid efficiency (TME), meaning the solutions to the governing system of equations are attained in a computational work...basic elements of the barriers to be overcome in extending textbook efficiencies to the compressible RANS equations, namely entering flows, far wake

Numerical study of hydrogen-air supersonic combustion by using elliptic and parabolized equations

NASA Technical Reports Server (NTRS)

Chitsomboon, T.; Tiwari, S. N.

1986-01-01

The two-dimensional Navier-Stokes and species continuity equations are used to investigate supersonic chemically reacting flow problems which are related to scramjet-engine configurations. A global two-step finite-rate chemistry model is employed to represent the hydrogen-air combustion in the flow. An algebraic turbulent model is adopted for turbulent flow calculations. The explicit unsplit MacCormack finite-difference algorithm is used to develop a computer program suitable for a vector processing computer. The computer program developed is then used to integrate the system of the governing equations in time until convergence is attained. The chemistry source terms in the species continuity equations are evaluated implicitly to alleviate stiffness associated with fast chemical reactions. The problems solved by the elliptic code are re-investigated by using a set of two-dimensional parabolized Navier-Stokes and species equations. A linearized fully-coupled fully-implicit finite difference algorithm is used to develop a second computer code which solves the governing equations by marching in spce rather than time, resulting in a considerable saving in computer resources. Results obtained by using the parabolized formulation are compared with the results obtained by using the fully-elliptic equations. The comparisons indicate fairly good agreement of the results of the two formulations.

A Textbook for a First Course in Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Zingg, D. W.; Pulliam, T. H.; Nixon, David (Technical Monitor)

1999-01-01

This paper describes and discusses the textbook, Fundamentals of Computational Fluid Dynamics by Lomax, Pulliam, and Zingg, which is intended for a graduate level first course in computational fluid dynamics. This textbook emphasizes fundamental concepts in developing, analyzing, and understanding numerical methods for the partial differential equations governing the physics of fluid flow. Its underlying philosophy is that the theory of linear algebra and the attendant eigenanalysis of linear systems provides a mathematical framework to describe and unify most numerical methods in common use in the field of fluid dynamics. Two linear model equations, the linear convection and diffusion equations, are used to illustrate concepts throughout. Emphasis is on the semi-discrete approach, in which the governing partial differential equations (PDE's) are reduced to systems of ordinary differential equations (ODE's) through a discretization of the spatial derivatives. The ordinary differential equations are then reduced to ordinary difference equations (O(Delta)E's) using a time-marching method. This methodology, using the progression from PDE through ODE's to O(Delta)E's, together with the use of the eigensystems of tridiagonal matrices and the theory of O(Delta)E's, gives the book its distinctiveness and provides a sound basis for a deep understanding of fundamental concepts in computational fluid dynamics.

A distributed parameter electromechanical model for bimorph piezoelectric energy harvesters based on the refined zigzag theory

NASA Astrophysics Data System (ADS)

Chen, Chung-De

2018-04-01

In this paper, a distributed parameter electromechanical model for bimorph piezoelectric energy harvesters based on the refined zigzag theory (RZT) is developed. In this model, the zigzag function is incorporated into the axial displacement, and the zigzag distribution of the displacement between the adjacent layers of the bimorph structure can be considered. The governing equations, including three equations of motions and one equation of circuit, are derived using Hamilton’s principle. The natural frequency, its corresponding modal function and the steady state response of the base excitation motion are given in exact forms. The presented results are benchmarked with the finite element method and two beam theories, the first-order shear deformation theory and the classical beam theory. Comparing examples shows that the RZT provides predictions of output voltage and generated power at high accuracy, especially for the case of a soft middle layer. Variation of the parameters, such as the beam thickness, excitation frequencies and the external electrical loads, is investigated and its effects on the performance of the energy harvesters are studied by using the RZT developed in this paper. Based on this refined theory, analysts and engineers can capture more details on the electromechanical behavior of piezoelectric harvesters.

Performance of a parallel algebraic multilevel preconditioner for stabilized finite element semiconductor device modeling

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

Lin, Paul T.; Shadid, John N.; Sala, Marzio

In this study results are presented for the large-scale parallel performance of an algebraic multilevel preconditioner for solution of the drift-diffusion model for semiconductor devices. The preconditioner is the key numerical procedure determining the robustness, efficiency and scalability of the fully-coupled Newton-Krylov based, nonlinear solution method that is employed for this system of equations. The coupled system is comprised of a source term dominated Poisson equation for the electric potential, and two convection-diffusion-reaction type equations for the electron and hole concentration. The governing PDEs are discretized in space by a stabilized finite element method. Solution of the discrete system ismore » obtained through a fully-implicit time integrator, a fully-coupled Newton-based nonlinear solver, and a restarted GMRES Krylov linear system solver. The algebraic multilevel preconditioner is based on an aggressive coarsening graph partitioning of the nonzero block structure of the Jacobian matrix. Representative performance results are presented for various choices of multigrid V-cycles and W-cycles and parameter variations for smoothers based on incomplete factorizations. Parallel scalability results are presented for solution of up to 10{sup 8} unknowns on 4096 processors of a Cray XT3/4 and an IBM POWER eServer system.« less

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

NASA Astrophysics Data System (ADS)

Gnaneswara Reddy, Machireddy

2017-12-01

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

Protostellar hydrodynamics: Constructing and testing a spacially and temporally second-order accurate method. 2: Cartesian coordinates

NASA Technical Reports Server (NTRS)

Myhill, Elizabeth A.; Boss, Alan P.

1993-01-01

In Boss & Myhill (1992) we described the derivation and testing of a spherical coordinate-based scheme for solving the hydrodynamic equations governing the gravitational collapse of nonisothermal, nonmagnetic, inviscid, radiative, three-dimensional protostellar clouds. Here we discuss a Cartesian coordinate-based scheme based on the same set of hydrodynamic equations. As with the spherical coorrdinate-based code, the Cartesian coordinate-based scheme employs explicit Eulerian methods which are both spatially and temporally second-order accurate. We begin by describing the hydrodynamic equations in Cartesian coordinates and the numerical methods used in this particular code. Following Finn & Hawley (1989), we pay special attention to the proper implementations of high-order accuracy, finite difference methods. We evaluate the ability of the Cartesian scheme to handle shock propagation problems, and through convergence testing, we show that the code is indeed second-order accurate. To compare the Cartesian scheme discussed here with the spherical coordinate-based scheme discussed in Boss & Myhill (1992), the two codes are used to calculate the standard isothermal collapse test case described by Bodenheimer & Boss (1981). We find that with the improved codes, the intermediate bar-configuration found previously disappears, and the cloud fragments directly into a binary protostellar system. Finally, we present the results from both codes of a new test for nonisothermal protostellar collapse.

Analytic solutions for Long's equation and its generalization

NASA Astrophysics Data System (ADS)

Humi, Mayer

2017-12-01

Two-dimensional, steady-state, stratified, isothermal atmospheric flow over topography is governed by Long's equation. Numerical solutions of this equation were derived and used by several authors. In particular, these solutions were applied extensively to analyze the experimental observations of gravity waves. In the first part of this paper we derive an extension of this equation to non-isothermal flows. Then we devise a transformation that simplifies this equation. We show that this simplified equation admits solitonic-type solutions in addition to regular gravity waves. These new analytical solutions provide new insights into the propagation and amplitude of gravity waves over topography.

Unified approach for incompressible flows

NASA Astrophysics Data System (ADS)

Chang, Tyne-Hsien

1993-12-01

An unified approach for solving both compressible and incompressible flows was investigated in this study. The difference in CFD code development between incompressible and compressible flows is due to the mathematical characteristics. However, if one can modify the continuity equation for incompressible flows by introducing pseudocompressibility, the governing equations for incompressible flows would have the same mathematical characters as compressible flows. The application of a compressible flow code to solve incompressible flows becomes feasible. Among numerical algorithms developed for compressible flows, the Centered Total Variation Diminishing (CTVD) schemes possess better mathematical properties to damp out the spurious oscillations while providing high-order accuracy for high speed flows. It leads us to believe that CTVD schemes can equally well solve incompressible flows. In this study, the governing equations for incompressible flows include the continuity equation and momentum equations. The continuity equation is modified by adding a time-derivative of the pressure term containing the artificial compressibility. The modified continuity equation together with the unsteady momentum equations forms a hyperbolic-parabolic type of time-dependent system of equations. The continuity equation is modified by adding a time-derivative of the pressure term containing the artificial compressibility. The modified continuity equation together with the unsteady momentum equations forms a hyperbolic-parabolic type of time-dependent system of equations. Thus, the CTVD schemes can be implemented. In addition, the boundary conditions including physical and numerical boundary conditions must be properly specified to obtain accurate solution. The CFD code for this research is currently in progress. Flow past a circular cylinder will be used for numerical experiments to determine the accuracy and efficiency of the code before applying this code to more specific applications.

Wave theory in rotating systems: Schrödinger equations bridge the gaps between the equatorial β-plane and the spherical earth

NASA Astrophysics Data System (ADS)

Paldor, N.

2017-12-01

The concise and elegant wave theory developed on the equatorial β-plane by Matsuno (1966, M66 hereafter) is based on the formulation of a Schrödinger equation associated with the governing Linear Rotating Shallow Water Equations (LRSWE). The theory yields explicit expressions for the dispersion relations and meridional amplitude structures of all zonally propagating waves - Rossby, Inertia-Gravity, Kelvin and Yanai. In contrast, the spherical wave theory of Longuet-Higgins (1968) is a collection of asymptotic expansions in many sub-ranges e.g. large, small (and even negative) Lamb Number; high and low frequency; low-latitudes, etc. that rests upon extensive numerical solutions of several Ordinary Differential Equations. The difference between the two theories is highlighted by their lengths. The essential elements of the former planar study are completely revealed in just 3-4 pages including the derivation of explicit formulae for the phase speeds and amplitude meridional structures. In comtrast, the latter spherical theory contains 97 pages and the results of the numerical calculations are summarized in 30 pages of tables filled with numerical values and about 31 figures, each of which containing many separate curves! In my talk I will re-visit the wave problem on a sphere by developing several Schrödinger equations that approximate the governing eigenvalue equation associated with zonally propagating waves. Each of the Schrödinger equations approximates the original second order Ordinary Differential Equation in a different range of the 3 parameters: Lamb-Number, frequency and zonal wavenumber. As in M66, each of the Schrödinger equations yields explicit expressions for the dispersion relations and meridional amplitude structure of Rossby and Inertia-Gravity waves. In addition, the analysis shows that Yanai wave exists on a sphere even tough the zonal velocity is regular everywhere there (in contrast to the β-plane where the zonal velocity is singular everywhere) and that Kelvin waves do not exist as a separate mode (but the eastward propagating n=0 Inertia-Gravity is nearly non-dispersive). References Longuet-Higgins, M. S. Phil. Trans. Roy. Soc. London; 262, 511-607; 1968 Matsuno, T.; J. Met. Soc. Japan. 44(1), 25-43; 1966

Coupled out of plane vibrations of spiral beams for micro-scale applications

NASA Astrophysics Data System (ADS)

Amin Karami, M.; Yardimoglu, Bulent; Inman, Daniel J.

2010-12-01

An analytical method is proposed to calculate the natural frequencies and the corresponding mode shape functions of an Archimedean spiral beam. The deflection of the beam is due to both bending and torsion, which makes the problem coupled in nature. The governing partial differential equations and the boundary conditions are derived using Hamilton's principle. Two factors make the vibrations of spirals different from oscillations of constant radius arcs. The first is the presence of terms with derivatives of the radius in the governing equations of spirals and the second is the fact that variations of radius of the beam causes the coefficients of the differential equations to be variable. It is demonstrated, using perturbation techniques that the derivative of the radius terms have negligible effect on structure's dynamics. The spiral is then approximated with many merging constant-radius curved sections joined together to approximate the slow change of radius along the spiral. The equations of motion are formulated in non-dimensional form and the effect of all the key parameters on natural frequencies is presented. Non-dimensional curves are used to summarize the results for clarity. We also solve the governing equations using Rayleigh's approximate method. The fundamental frequency results of the exact and Rayleigh's method are in close agreement. This to some extent verifies the exact solutions. The results show that the vibration of spirals is mostly torsional which complicates using the spiral beam as a host for a sensor or energy harvesting device.

Guiding-center equations for electrons in ultraintense laser fields

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

Moore, J.E.; Fisch, N.J.

1994-01-01

The guiding-center equations are derived for electrons in arbitrarily intense laser fields also subject to external fields and ponderomotive forces. Exhibiting the relativistic mass increase of the oscillating electrons, a simple frame-invariant equation is shown to govern the behavior of the electrons for sufficiently weak background fields and ponderomotive forces. The parameter regime for which such a formulation is valid is made precise, and some predictions of the equation are checked by numerical simulation.

Contact interaction of thin-walled elements with an elastic layer and an infinite circular cylinder under torsion

NASA Astrophysics Data System (ADS)

Kanetsyan, E. G.; Mkrtchyan, M. S.; Mkhitaryan, S. M.

2018-04-01

We consider a class of contact torsion problems on interaction of thin-walled elements shaped as an elastic thin washer – a flat circular plate of small height – with an elastic layer, in particular, with a half-space, and on interaction of thin cylindrical shells with a solid elastic cylinder, infinite in both directions. The governing equations of the physical models of elastic thin washers and thin circular cylindrical shells under torsion are derived from the exact equations of mathematical theory of elasticity using the Hankel and Fourier transforms. Within the framework of the accepted physical models, the solution of the contact problem between an elastic washer and an elastic layer is reduced to solving the Fredholm integral equation of the first kind with a kernel representable as a sum of the Weber–Sonin integral and some integral regular kernel, while solving the contact problem between a cylindrical shell and solid cylinder is reduced to a singular integral equation (SIE). An effective method for solving the governing integral equations of these problems are specified.

Radiating dispersive shock waves in non-local optical media

PubMed Central

El, Gennady A.

2016-01-01

We consider the step Riemann problem for the system of equations describing the propagation of a coherent light beam in nematic liquid crystals, which is a general system describing nonlinear wave propagation in a number of different physical applications. While the equation governing the light beam is of defocusing nonlinear Schrödinger (NLS) equation type, the dispersive shock wave (DSW) generated from this initial condition has major differences from the standard DSW solution of the defocusing NLS equation. In particular, it is found that the DSW has positive polarity and generates resonant radiation which propagates ahead of it. Remarkably, the velocity of the lead soliton of the DSW is determined by the classical shock velocity. The solution for the radiative wavetrain is obtained using the Wentzel–Kramers–Brillouin approximation. It is shown that for sufficiently small initial jumps the nematic DSW is asymptotically governed by a Korteweg–de Vries equation with the fifth-order dispersion, which explicitly shows the resonance generating the radiation ahead of the DSW. The constructed asymptotic theory is shown to be in good agreement with the results of direct numerical simulations. PMID:27118911

Investigation of Heat and Mass Transfer and Irreversibility Phenomena Within a Three-Dimensional Tilted Enclosure for Different Shapes

NASA Astrophysics Data System (ADS)

Oueslati, F.; Ben-Beya, B.

2018-01-01

Three-dimensional thermosolutal natural convection and entropy generation within an inclined enclosure is investigated in the current study. A numerical method based on the finite volume method and a full multigrid technique is implemented to solve the governing equations. Effects of various parameters, namely, the aspect ratio, buoyancy ratio, and tilt angle on the flow patterns and entropy generation are predicted and discussed.

On whole Abelian model dynamics

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

Chauca, J.; Doria, R.; Aprendanet, Petropolis, 25600

2012-09-24

Physics challenge is to determine the objects dynamics. However, there are two ways for deciphering the part. The first one is to search for the ultimate constituents; the second one is to understand its behaviour in whole terms. Therefore, the parts can be defined either from elementary constituents or as whole functions. Historically, science has been moving through the first aspect, however, quarks confinement and complexity are interrupting this usual approach. These relevant facts are supporting for a systemic vision be introduced. Our effort here is to study on the whole meaning through gauge theory. Consider a systemic dynamics orientedmore » through the U(1) - systemic gauge parameter which function is to collect a fields set {l_brace}A{sub {mu}I}{r_brace}. Derive the corresponding whole gauge invariant Lagrangian, equations of motion, Bianchi identities, Noether relationships, charges and Ward-Takahashi equations. Whole Lorentz force and BRST symmetry are also studied. These expressions bring new interpretations further than the usual abelian model. They are generating a systemic system governed by 2N+ 10 classical equations plus Ward-Takahashi identities. A whole dynamics based on the notions of directive and circumstance is producing a set determinism where the parts dynamics are inserted in the whole evolution. A dynamics based on state, collective and individual equations with a systemic interdependence.« less

Comparison of finite-difference schemes for analysis of shells of revolution. [stress and free vibration analysis

NASA Technical Reports Server (NTRS)

Noor, A. K.; Stephens, W. B.

1973-01-01

Several finite difference schemes are applied to the stress and free vibration analysis of homogeneous isotropic and layered orthotropic shells of revolution. The study is based on a form of the Sanders-Budiansky first-approximation linear shell theory modified such that the effects of shear deformation and rotary inertia are included. A Fourier approach is used in which all the shell stress resultants and displacements are expanded in a Fourier series in the circumferential direction, and the governing equations reduce to ordinary differential equations in the meridional direction. While primary attention is given to finite difference schemes used in conjunction with first order differential equation formulation, comparison is made with finite difference schemes used with other formulations. These finite difference discretization models are compared with respect to simplicity of application, convergence characteristics, and computational efficiency. Numerical studies are presented for the effects of variations in shell geometry and lamination parameters on the accuracy and convergence of the solutions obtained by the different finite difference schemes. On the basis of the present study it is shown that the mixed finite difference scheme based on the first order differential equation formulation and two interlacing grids for the different fundamental unknowns combines a number of advantages over other finite difference schemes previously reported in the literature.

A Nonlinear Programming Perspective on Sensitivity Calculations for Systems Governed by State Equations

NASA Technical Reports Server (NTRS)

Lewis, Robert Michael

1997-01-01

This paper discusses the calculation of sensitivities. or derivatives, for optimization problems involving systems governed by differential equations and other state relations. The subject is examined from the point of view of nonlinear programming, beginning with the analytical structure of the first and second derivatives associated with such problems and the relation of these derivatives to implicit differentiation and equality constrained optimization. We also outline an error analysis of the analytical formulae and compare the results with similar results for finite-difference estimates of derivatives. We then attend to an investigation of the nature of the adjoint method and the adjoint equations and their relation to directions of steepest descent. We illustrate the points discussed with an optimization problem in which the variables are the coefficients in a differential operator.

A Numerical Study of Coupled Non-Linear Equations of Thermo-Viscous Fluid Flow in Cylindrical Geometry

NASA Astrophysics Data System (ADS)

Pothanna, N.; Aparna, P.; Gorla, R. S. R.

2017-12-01

In this paper we present numerical solutions to coupled non-linear governing equations of thermo-viscous fluid flow in cylindrical geometry using MATHEMATICA software solver. The numerical results are presented in terms of velocity, temperature and pressure distribution for various values of the material parameters such as the thermo-mechanical stress coefficient, thermal conductivity coefficient, Reiner Rivlin cross viscosity coefficient and the Prandtl number in the form of tables and graphs. Also, the solutions to governing equations for slow steady motion of a fluid have been obtained numerically and compared with the existing analytical results and are found to be in excellent agreement. The results of the present study will hopefully enable a better understanding applications of the flow under consideration.

Modelling the Projectile Motion of a Cricket Ball.

ERIC Educational Resources Information Center

Coutis, Peter

1998-01-01

Presents the equations of motion governing the trajectory of a cricket ball subject to a linear drag force. Uses a perturbation expansion technique to solve the resulting trajectory equation for the range of a cricket ball struck into the outfield. (Author/ASK)

Bending analysis of agglomerated carbon nanotube-reinforced beam resting on two parameters modified Vlasov model foundation

NASA Astrophysics Data System (ADS)

Ghorbanpour Arani, A.; Zamani, M. H.

2018-06-01

The present work deals with bending behavior of nanocomposite beam resting on two parameters modified Vlasov model foundation (MVMF), with consideration of agglomeration and distribution of carbon nanotubes (CNTs) in beam matrix. Equivalent fiber based on Eshelby-Mori-Tanaka approach is employed to determine influence of CNTs aggregation on elastic properties of CNT-reinforced beam. The governing equations are deduced using the principle of minimum potential energy under assumption of the Euler-Bernoulli beam theory. The MVMF required the estimation of γ parameter; to this purpose, unique iterative technique based on variational principles is utilized to compute value of the γ and subsequently fourth-order differential equation is solved analytically. Eventually, the transverse displacements and bending stresses are obtained and compared for different agglomeration parameters, various boundary conditions simultaneously and variant elastic foundation without requirement to instate values for foundation parameters.

Bifurcation Analysis of an Electrostatically Actuated Nano-Beam Based on Modified Couple Stress Theory

NASA Astrophysics Data System (ADS)

Rezaei Kivi, Araz; Azizi, Saber; Norouzi, Peyman

2017-12-01

In this paper, the nonlinear size-dependent static and dynamic behavior of an electrostatically actuated nano-beam is investigated. A fully clamped nano-beam is considered for the modeling of the deformable electrode of the NEMS. The governing differential equation of the motion is derived using Hamiltonian principle based on couple stress theory; a non-classical theory for considering length scale effects. The nonlinear partial differential equation of the motion is discretized to a nonlinear Duffing type ODE's using Galerkin method. Static and dynamic pull-in instabilities obtained by both classical theory and MCST are compared. At the second stage of analysis, shooting technique is utilized to obtain the frequency response curve, and to capture the periodic solutions of the motion; the stability of the periodic solutions are gained by Floquet theory. The nonlinear dynamic behavior of the deformable electrode due to the AC harmonic accompanied with size dependency is investigated.

Computational fluid dynamics: Transition to design applications

NASA Technical Reports Server (NTRS)

Bradley, R. G.; Bhateley, I. C.; Howell, G. A.

1987-01-01

The development of aerospace vehicles, over the years, was an evolutionary process in which engineering progress in the aerospace community was based, generally, on prior experience and data bases obtained through wind tunnel and flight testing. Advances in the fundamental understanding of flow physics, wind tunnel and flight test capability, and mathematical insights into the governing flow equations were translated into improved air vehicle design. The modern day field of Computational Fluid Dynamics (CFD) is a continuation of the growth in analytical capability and the digital mathematics needed to solve the more rigorous form of the flow equations. Some of the technical and managerial challenges that result from rapidly developing CFD capabilites, some of the steps being taken by the Fort Worth Division of General Dynamics to meet these challenges, and some of the specific areas of application for high performance air vehicles are presented.

Transonic flow of steam with non-equilibrium and homogenous condensation

NASA Astrophysics Data System (ADS)

Virk, Akashdeep Singh; Rusak, Zvi

2017-11-01

A small-disturbance model for studying the physical behavior of a steady transonic flow of steam with non-equilibrium and homogeneous condensation around a thin airfoil is derived. The steam thermodynamic behavior is described by van der Waals equation of state. The water condensation rate is calculated according to classical nucleation and droplet growth models. The current study is based on an asymptotic analysis of the fluid flow and condensation equations and boundary conditions in terms of the small thickness of the airfoil, small angle of attack, closeness of upstream flow Mach number to unity and small amount of condensate. The asymptotic analysis gives the similarity parameters that govern the problem. The flow field may be described by a non-homogeneous transonic small-disturbance equation coupled with a set of four ordinary differential equations for the calculation of the condensate mass fraction. An iterative numerical scheme which combines Murman & Cole's (1971) method with Simpson's integration rule is applied to solve the coupled system of equations. The model is used to study the effects of energy release from condensation on the aerodynamic performance of airfoils operating at high pressures and temperatures and near the vapor-liquid saturation conditions.

A frequency-duty cycle equation for the ACGIH hand activity level.

PubMed

Radwin, Robert G; Azari, David P; Lindstrom, Mary J; Ulin, Sheryl S; Armstrong, Thomas J; Rempel, David

2015-01-01

A new equation for predicting the hand activity level (HAL) used in the American Conference for Government Industrial Hygienists threshold limit value®(TLV®) was based on exertion frequency (F) and percentage duty cycle (D). The TLV® includes a table for estimating HAL from F and D originating from data in Latko et al. (Latko WA, Armstrong TJ, Foulke JA, Herrin GD, Rabourn RA, Ulin SS, Development and evaluation of an observational method for assessing repetition in hand tasks. American Industrial Hygiene Association Journal, 58(4):278-285, 1997) and post hoc adjustments that include extrapolations outside of the data range. Multimedia video task analysis determined D for two additional jobs from Latko's study not in the original data-set, and a new nonlinear regression equation was developed to better fit the data and create a more accurate table. The equation, HAL = 6:56 ln D[F(1:31) /1+3:18 F(1:31), generally matches the TLV® HAL lookup table, and is a substantial improvement over the linear model, particularly for F>1.25 Hz and D>60% jobs. The equation more closely fits the data and applies the TLV® using a continuous function.

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

NASA Astrophysics Data System (ADS)

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

2013-04-01

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

Wave propagation through a flexoelectric piezoelectric slab sandwiched by two piezoelectric half-spaces.

PubMed

Jiao, Fengyu; Wei, Peijun; Li, Yueqiu

2018-01-01

Reflection and transmission of plane waves through a flexoelectric piezoelectric slab sandwiched by two piezoelectric half-spaces are studied in this paper. The secular equations in the flexoelectric piezoelectric material are first derived from the general governing equation. Different from the classical piezoelectric medium, there are five kinds of coupled elastic waves in the piezoelectric material with the microstructure effects taken into consideration. The state vectors are obtained by the summation of contributions from all possible partial waves. The state transfer equation of flexoelectric piezoelectric slab is derived from the motion equation by the reduction of order, and the transfer matrix of flexoelectric piezoelectric slab is obtained by solving the state transfer equation. By using the continuous conditions at the interface and the approach of partition matrix, we get the resultant algebraic equations in term of the transfer matrix from which the reflection and transmission coefficients can be calculated. The amplitude ratios and further the energy flux ratios of various waves are evaluated numerically. The numerical results are shown graphically and are validated by the energy conservation law. Based on these numerical results, the influences of two characteristic lengths of microstructure and the flexoelectric coefficients on the wave propagation are discussed. Copyright © 2017 Elsevier B.V. All rights reserved.

Effect of multiple slip on a chemically reactive MHD non-Newtonian nanofluid power law fluid flow over a stretching sheet with microorganism

NASA Astrophysics Data System (ADS)

Basir, Mohammad Faisal Mohd; Ismail, Fazreen Amira; Amirsom, Nur Ardiana; Latiff, Nur Amalina Abdul; Ismail, Ahmad Izani Md.

2017-04-01

The effect of multiple slip on a chemically reactive magnetohydrodynamic (MHD) non-Newtonian power law fluid flow over a stretching sheet with microorganism was numerically investigated. The governing partial differential equations were transformed into nonlinear ordinary differential equations using the similarity transformations developed by Lie group analysis. The reduced governing nonlinear ordinary differential equations were then numerically solved using the Runge-Kutta-Fehlberg fourth-fifth order method. Good agreement was found between the present numerical solutions with the existing published results to support the validity and the accuracy of the numerical computations. The influences of the velocity, thermal, mass and microorganism slips, the magnetic field parameter and the chemical reaction parameter on the dimensionless velocity, temperature, nanoparticle volume fraction, microorganism concentration, the distribution of the density of motile microorganisms have been illustrated graphically. The effects of the governing parameters on the physical quantities, namely, the local heat transfer rate, the local mass transfer rate and the local microorganism transfer rate were analyzed and discussed.

On the optimal systems of subalgebras for the equations of hydrodynamic stability analysis of smooth shear flows and their group-invariant solutions

NASA Astrophysics Data System (ADS)

Hau, Jan-Niklas; Oberlack, Martin; Chagelishvili, George

2017-04-01

We present a unifying solution framework for the linearized compressible equations for two-dimensional linearly sheared unbounded flows using the Lie symmetry analysis. The full set of symmetries that are admitted by the underlying system of equations is employed to systematically derive the one- and two-dimensional optimal systems of subalgebras, whose connected group reductions lead to three distinct invariant ansatz functions for the governing sets of partial differential equations (PDEs). The purpose of this analysis is threefold and explicitly we show that (i) there are three invariant solutions that stem from the optimal system. These include a general ansatz function with two free parameters, as well as the ansatz functions of the Kelvin mode and the modal approach. Specifically, the first approach unifies these well-known ansatz functions. By considering two limiting cases of the free parameters and related algebraic transformations, the general ansatz function is reduced to either of them. This fact also proves the existence of a link between the Kelvin mode and modal ansatz functions, as these appear to be the limiting cases of the general one. (ii) The Lie algebra associated with the Lie group admitted by the PDEs governing the compressible dynamics is a subalgebra associated with the group admitted by the equations governing the incompressible dynamics, which allows an additional (scaling) symmetry. Hence, any consequences drawn from the compressible case equally hold for the incompressible counterpart. (iii) In any of the systems of ordinary differential equations, derived by the three ansatz functions in the compressible case, the linearized potential vorticity is a conserved quantity that allows us to analyze vortex and wave mode perturbations separately.

Wave propagation in embedded inhomogeneous nanoscale plates incorporating thermal effects

NASA Astrophysics Data System (ADS)

Ebrahimi, Farzad; Barati, Mohammad Reza; Dabbagh, Ali

2018-04-01

In this article, an analytical approach is developed to study the effects of thermal loading on the wave propagation characteristics of an embedded functionally graded (FG) nanoplate based on refined four-variable plate theory. The heat conduction equation is solved to derive the nonlinear temperature distribution across the thickness. Temperature-dependent material properties of nanoplate are graded using Mori-Tanaka model. The nonlocal elasticity theory of Eringen is introduced to consider small-scale effects. The governing equations are derived by the means of Hamilton's principle. Obtained frequencies are validated with those of previously published works. Effects of different parameters such as temperature distribution, foundation parameters, nonlocal parameter, and gradient index on the wave propagation response of size-dependent FG nanoplates have been investigated.

Flowfield computation of entry vehicles

NASA Technical Reports Server (NTRS)

Prabhu, Dinesh K.

1990-01-01

The equations governing the multidimensional flow of a reacting mixture of thermally perfect gasses were derived. The modeling procedures for the various terms of the conservation laws are discussed. A numerical algorithm, based on the finite-volume approach, to solve these conservation equations was developed. The advantages and disadvantages of the present numerical scheme are discussed from the point of view of accuracy, computer time, and memory requirements. A simple one-dimensional model problem was solved to prove the feasibility and accuracy of the algorithm. A computer code implementing the above algorithm was developed and is presently being applied to simple geometries and conditions. Once the code is completely debugged and validated, it will be used to compute the complete unsteady flow field around the Aeroassist Flight Experiment (AFE) body.

A numerical algorithm for optimal feedback gains in high dimensional linear quadratic regulator problems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Ito, K.

1991-01-01

A hybrid method for computing the feedback gains in linear quadratic regulator problem is proposed. The method, which combines use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite-dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantages of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed, and numerical evidence of the efficacy of these ideas is presented.

A numerical algorithm for optimal feedback gains in high dimensional LQR problems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Ito, K.

1986-01-01

A hybrid method for computing the feedback gains in linear quadratic regulator problems is proposed. The method, which combines the use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated so as to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantage of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed and numerical evidence of the efficacy of our ideas presented.

On shifted Jacobi spectral method for high-order multi-point boundary value problems

NASA Astrophysics Data System (ADS)

Doha, E. H.; Bhrawy, A. H.; Hafez, R. M.

2012-10-01

This paper reports a spectral tau method for numerically solving multi-point boundary value problems (BVPs) of linear high-order ordinary differential equations. The construction of the shifted Jacobi tau approximation is based on conventional differentiation. This use of differentiation allows the imposition of the governing equation at the whole set of grid points and the straight forward implementation of multiple boundary conditions. Extension of the tau method for high-order multi-point BVPs with variable coefficients is treated using the shifted Jacobi Gauss-Lobatto quadrature. Shifted Jacobi collocation method is developed for solving nonlinear high-order multi-point BVPs. The performance of the proposed methods is investigated by considering several examples. Accurate results and high convergence rates are achieved.

Morphing continuum theory for turbulence: Theory, computation, and visualization.

PubMed

Chen, James

2017-10-01

A high order morphing continuum theory (MCT) is introduced to model highly compressible turbulence. The theory is formulated under the rigorous framework of rational continuum mechanics. A set of linear constitutive equations and balance laws are deduced and presented from the Coleman-Noll procedure and Onsager's reciprocal relations. The governing equations are then arranged in conservation form and solved through the finite volume method with a second-order Lax-Friedrichs scheme for shock preservation. A numerical example of transonic flow over a three-dimensional bump is presented using MCT and the finite volume method. The comparison shows that MCT-based direct numerical simulation (DNS) provides a better prediction than Navier-Stokes (NS)-based DNS with less than 10% of the mesh number when compared with experiments. A MCT-based and frame-indifferent Q criterion is also derived to show the coherent eddy structure of the downstream turbulence in the numerical example. It should be emphasized that unlike the NS-based Q criterion, the MCT-based Q criterion is objective without the limitation of Galilean invariance.

A Novel Blast-mitigation Concept for Light Tactical Vehicles

DTIC Science & Technology

2013-01-01

analysis which utilizes the mass and energy (but not linear momentum ) conservation equations is provided. It should be noted that the identical final...results could be obtained using an analogous analysis which combines the mass and the linear momentum conservation equations. For a calorically...governing mass, linear momentum and energy conservation and heat conduction equations are solved within ABAQUS/ Explicit with a second-order accurate

Hidden Statistics of Schroedinger Equation

NASA Technical Reports Server (NTRS)

Zak, Michail

2011-01-01

Work was carried out in determination of the mathematical origin of randomness in quantum mechanics and creating a hidden statistics of Schr dinger equation; i.e., to expose the transitional stochastic process as a "bridge" to the quantum world. The governing equations of hidden statistics would preserve such properties of quantum physics as superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods.

Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics

NASA Technical Reports Server (NTRS)

Pratt, D. T.

1984-01-01

Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.

A second-order shock-adaptive Godunov scheme based on the generalized Lagrangian formulation

NASA Astrophysics Data System (ADS)

Lepage, Claude

Application of the Godunov scheme to the Euler equations of gas dynamics, based on the Eulerian formulation of flow, smears discontinuities (especially sliplines) over several computational cells, while the accuracy in the smooth flow regions is of the order of a function of the cell width. Based on the generalized Lagrangian formulation (GLF), the Godunov scheme yields far superior results. By the use of coordinate streamlines in the GLF, the slipline (itself a streamline) is resolved crisply. Infinite shock resolution is achieved through the splitting of shock cells, while the accuracy in the smooth flow regions is improved using a nonconservative formulation of the governing equations coupled to a second order extension of the Godunov scheme. Furthermore, GLF requires no grid generation for boundary value problems and the simple structure of the solution to the Riemann problem in the GLF is exploited in the numerical implementation of the shock adaptive scheme. Numerical experiments reveal high efficiency and unprecedented resolution of shock and slipline discontinuities.

On the linear stability of blood flow through model capillary networks.

PubMed

Davis, Jeffrey M

2014-12-01

Under the approximation that blood behaves as a continuum, a numerical implementation is presented to analyze the linear stability of capillary blood flow through model tree and honeycomb networks that are based on the microvascular structures of biological tissues. The tree network is comprised of a cascade of diverging bifurcations, in which a parent vessel bifurcates into two descendent vessels, while the honeycomb network also contains converging bifurcations, in which two parent vessels merge into one descendent vessel. At diverging bifurcations, a cell partitioning law is required to account for the nonuniform distribution of red blood cells as a function of the flow rate of blood into each descendent vessel. A linearization of the governing equations produces a system of delay differential equations involving the discharge hematocrit entering each network vessel and leads to a nonlinear eigenvalue problem. All eigenvalues in a specified region of the complex plane are captured using a transformation based on contour integrals to construct a linear eigenvalue problem with identical eigenvalues, which are then determined using a standard QR algorithm. The predicted value of the dimensionless exponent in the cell partitioning law at the instability threshold corresponds to a supercritical Hopf bifurcation in numerical simulations of the equations governing unsteady blood flow. Excellent agreement is found between the predictions of the linear stability analysis and nonlinear simulations. The relaxation of the assumption of plug flow made in previous stability analyses typically has a small, quantitative effect on the stability results that depends on the specific network structure. This implementation of the stability analysis can be applied to large networks with arbitrary structure provided only that the connectivity among the network segments is known.

On geodynamo integrations conserving momentum flux

NASA Astrophysics Data System (ADS)

Wu, C.; Roberts, P. H.

2012-12-01

The equations governing the geodynamo are most often integrated by representing the magnetic field and fluid velocity by toroidal and poloidal scalars (for example, MAG code [1]). This procedure does not automatically conserve the momentum flux. The results can, particularly for flows with large shear, introduce significant errors, unless the viscosity is artificially increased. We describe a method that evades this difficulty, by solving the momentum equation directly while properly conserving momentum. It finds pressure by FFT and cyclic reduction, and integrates the governing equations on overlapping grids so avoiding the pole problem. The number of operations per time step is proportional to N3 where N is proportional to the number of grid points in each direction. This contrasts with the order N4 operations of standard spectral transform methods. The method is easily parallelized. It can also be easily adapted to schemes such as the Weighted Essentially Non-Oscillatory (WENO) method [2], a flux based procedure based on upwinding that is numerically stable even for zero explicit viscosity. The method has been successfully used to investigate the generation of magnetic fields by flows confined to spheroidal containers and driven by precessional and librational forcing [3, 4]. For spherical systems it satisfies dynamo benchmarks [5]. [1] MAG, http://www.geodynamics.org/cig/software/mag [2] Liu, XD, Osher, S and Chan, T, Weighted Essentially Nonoscillatory Schemes, J. Computational Physics, 115, 200-212, 1994. [3] Wu, CC and Roberts, PH, On a dynamo driven by topographic precession, Geophysical & Astrophysical Fluid Dynamics, 103, 467-501, (DOI: 10.1080/03091920903311788), 2009. [4] Wu, CC and Roberts, PH, On a dynamo driven topographically by longitudinal libration, Geophysical & Astrophysical Fluid Dynamics, DOI:10.1080/03091929.2012.682990, 2012. [5] Christensen, U, et al., A numerical dynamo benchmark, Phys. Earth Planet Int., 128, 25-34, 2001.

Magnetic field effect on Poiseuille flow and heat transfer of carbon nanotubes along a vertical channel filled with Casson fluid

NASA Astrophysics Data System (ADS)

Aman, Sidra; Khan, Ilyas; Ismail, Zulkhibri; Salleh, Mohd Zuki; Alshomrani, Ali Saleh; Alghamdi, Metib Said

2017-01-01

Applications of carbon nanotubes, single walls carbon nanotubes (SWCNTs) and multiple walls carbon nanotubes (MWCNTs) in thermal engineering have recently attracted significant attention. However, most of the studies on CNTs are either experimental or numerical and the lack of analytical studies limits further developments in CNTs research particularly in channel flows. In this work, an analytical investigation is performed on heat transfer analysis of SWCNTs and MWCNTs for mixed convection Poiseuille flow of a Casson fluid along a vertical channel. These CNTs are suspended in three different types of base fluids (Water, Kerosene and engine Oil). Xue [Phys. B Condens. Matter 368, 302-307 (2005)] model has been used for effective thermal conductivity of CNTs. A uniform magnetic field is applied in a transverse direction to the flow as magnetic field induces enhancement in the thermal conductivity of nanofluid. The problem is modelled by using the constitutive equations of Casson fluid in order to characterize the non-Newtonian fluid behavior. Using appropriate non-dimensional variables, the governing equations are transformed into the non-dimensional form, and the perturbation method is utilized to solve the governing equations with some physical conditions. Velocity and temperature solutions are obtained and discussed graphically. Expressions for skin friction and Nusselt number are also evaluated in tabular form. Effects of different parameters such as Casson parameter, radiation parameter and volume fraction are observed on the velocity and temperature profiles. It is found that velocity is reduced under influence of the exterior magnetic field. The temperature of single wall CNTs is found greater than MWCNTs for all the three base fluids. Increase in volume fraction leads to a decrease in velocity of the fluid as the nanofluid become more viscous by adding CNTs.

Conformal field theory as microscopic dynamics of incompressible Euler and Navier-Stokes equations.

PubMed

Fouxon, Itzhak; Oz, Yaron

2008-12-31

We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the nonrelativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the nonrelativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them.

A Heuristic Fast Method to Solve the Nonlinear Schroedinger Equation in Fiber Bragg Gratings with Arbitrary Shape Input Pulse

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

Emami, F.; Hatami, M.; Keshavarz, A. R.

2009-08-13

Using a combination of Runge-Kutta and Jacobi iterative method, we could solve the nonlinear Schroedinger equation describing the pulse propagation in FBGs. By decomposing the electric field to forward and backward components in fiber Bragg grating and utilizing the Fourier series analysis technique, the boundary value problem of a set of coupled equations governing the pulse propagation in FBG changes to an initial condition coupled equations which can be solved by simple Runge-Kutta method.

An exact solution for the solidification of a liquid slab of binary mixture

NASA Technical Reports Server (NTRS)

Antar, B. N.; Collins, F. G.; Aumalia, A. E.

1986-01-01

The time dependent temperature and concentration profiles of a one dimensional finite slab of a binary liquid alloy is investigated during solidification. The governing equations are reduced to a set of coupled, nonlinear initial value problems using the method outlined by Meyer. Two methods will be used to solve these equations. The first method uses a Runge-Kutta-Fehlberg integrator to solve the equations numerically. The second method comprises of finding closed form solutions of the equations.

Some More Solutions of Burgers' Equation

NASA Astrophysics Data System (ADS)

Kumar, Mukesh; Kumar, Raj

2015-01-01

In this work, similarity solutions of viscous one-dimensional Burgers' equation are attained by using Lie group theory. The symmetry generators are used for constructing Lie symmetries with commuting infinitesimal operators which lead the governing partial differential equation (PDE) to ordinary differential equation (ODE). Most of the constructed solutions are found in terms of Bessel functions which are new as far as authors are aware. Effect of various parameters in the evolutional profile of the solutions are shown graphically and discussed them physically.

Effect of breathing-hole size on the electrochemical species in a free-breathing cathode of a DMFC

NASA Astrophysics Data System (ADS)

Hwang, J. J.; Wu, S. D.; Lai, L. K.; Chen, C. K.; Lai, D. Y.

A three-dimensional numerical model is developed to study the electrochemical species characteristics in a free-breathing cathode of a direct methanol fuel cell (DMFC). A perforated current collector is attached to the porous cathode that breathes the fresh air through an array of orifices. The radius of the orifice is varied to examine its effect on the electrochemical performance. Gas flow in the porous cathode is governed by the Darcy equation with constant porosity and permeability. The multi-species diffusive transports in the porous cathode are described using the Stefan-Maxwell equation. Electrochemical reaction on the surfaces of the porous matrices is depicted via the Butler-Volmer equation. The charge transports in the porous matrices are dealt with by Ohm's law. The coupled equations are solved by a finite-element-based CFD technique. Detailed distributions of electrochemical species characteristics such as flow velocities, species mass fractions, species fluxes, and current densities are presented. The optimal breathing-hole radius is derived from the current drawn out of the porous cathode under a fixed overpotential.

Towards a unified theory for morphomechanics

PubMed Central

Taber, Larry A.

2009-01-01

Mechanical forces are closely involved in the construction of an embryo. Experiments have suggested that mechanical feedback plays a role in regulating these forces, but the nature of this feedback is poorly understood. Here, we propose a general principle for the mechanics of morphogenesis, as governed by a pair of evolution equations based on feedback from tissue stress. In one equation, the rate of growth (or contraction) depends on the difference between the current tissue stress and a target (homeostatic) stress. In the other equation, the target stress changes at a rate that depends on the same stress difference. The parameters in these morphomechanical laws are assumed to depend on stress rate. Computational models are used to illustrate how these equations can capture a relatively wide range of behaviours observed in developing embryos, as well as show the limitations of this theory. Specific applications include growth of pressure vessels (e.g. the heart, arteries and brain), wound healing and sea urchin gastrulation. Understanding the fundamental principles of tissue construction can help engineers design new strategies for creating replacement tissues and organs in vitro. PMID:19657011

Non-Markovian electron dynamics in nanostructures coupled to dissipative contacts

NASA Astrophysics Data System (ADS)

Novakovic, B.; Knezevic, I.

2013-02-01

In quasiballistic semiconductor nanostructures, carrier exchange between the active region and dissipative contacts is the mechanism that governs relaxation. In this paper, we present a theoretical treatment of transient quantum transport in quasiballistic semiconductor nanostructures, which is based on the open system theory and valid on timescales much longer than the characteristic relaxation time in the contacts. The approach relies on a model interaction between the current-limiting active region and the contacts, given in the scattering-state basis. We derive a non-Markovian master equation for the irreversible evolution of the active region's many-body statistical operator by coarse-graining the exact dynamical map over the contact relaxation time. In order to obtain the response quantities of a nanostructure under bias, such as the potential and the charge and current densities, the non-Markovian master equation must be solved numerically together with the Schr\\"{o}dinger, Poisson, and continuity equations. We discuss how to numerically solve this coupled system of equations and illustrate the approach on the example of a silicon nin diode.

Numerical simulation of advective-dispersive multisolute transport with sorption, ion exchange and equilibrium chemistry

USGS Publications Warehouse

Lewis, F.M.; Voss, C.I.; Rubin, Jacob

1986-01-01

A model was developed that can simulate the effect of certain chemical and sorption reactions simultaneously among solutes involved in advective-dispersive transport through porous media. The model is based on a methodology that utilizes physical-chemical relationships in the development of the basic solute mass-balance equations; however, the form of these equations allows their solution to be obtained by methods that do not depend on the chemical processes. The chemical environment is governed by the condition of local chemical equilibrium, and may be defined either by the linear sorption of a single species and two soluble complexation reactions which also involve that species, or binary ion exchange and one complexation reaction involving a common ion. Partial differential equations that describe solute mass balance entirely in the liquid phase are developed for each tenad (a chemical entity whose total mass is independent of the reaction process) in terms of their total dissolved concentration. These equations are solved numerically in two dimensions through the modification of an existing groundwater flow/transport computer code. (Author 's abstract)

Integrated force method versus displacement method for finite element analysis

NASA Technical Reports Server (NTRS)

Patnaik, S. N.; Berke, L.; Gallagher, R. H.

1991-01-01

A novel formulation termed the integrated force method (IFM) has been developed in recent years for analyzing structures. In this method all the internal forces are taken as independent variables, and the system equilibrium equations (EEs) are integrated with the global compatibility conditions (CCs) to form the governing set of equations. In IFM the CCs are obtained from the strain formulation of St. Venant, and no choices of redundant load systems have to be made, in constrast to the standard force method (SFM). This property of IFM allows the generation of the governing equation to be automated straightforwardly, as it is in the popular stiffness method (SM). In this report IFM and SM are compared relative to the structure of their respective equations, their conditioning, required solution methods, overall computational requirements, and convergence properties as these factors influence the accuracy of the results. Overall, this new version of the force method produces more accurate results than the stiffness method for comparable computational cost.

Integrated force method versus displacement method for finite element analysis

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Berke, Laszlo; Gallagher, Richard H.

1990-01-01

A novel formulation termed the integrated force method (IFM) has been developed in recent years for analyzing structures. In this method all the internal forces are taken as independent variables, and the system equilibrium equations (EE's) are integrated with the global compatibility conditions (CC's) to form the governing set of equations. In IFM the CC's are obtained from the strain formulation of St. Venant, and no choices of redundant load systems have to be made, in constrast to the standard force method (SFM). This property of IFM allows the generation of the governing equation to be automated straightforwardly, as it is in the popular stiffness method (SM). In this report IFM and SM are compared relative to the structure of their respective equations, their conditioning, required solution methods, overall computational requirements, and convergence properties as these factors influence the accuracy of the results. Overall, this new version of the force method produces more accurate results than the stiffness method for comparable computational cost.

Differential geometry-based solvation and electrolyte transport models for biomolecular modeling: a review

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

Wei, Guowei; Baker, Nathan A.

2016-11-11

This chapter reviews the differential geometry-based solvation and electrolyte transport for biomolecular solvation that have been developed over the past decade. A key component of these methods is the differential geometry of surfaces theory, as applied to the solvent-solute boundary. In these approaches, the solvent-solute boundary is determined by a variational principle that determines the major physical observables of interest, for example, biomolecular surface area, enclosed volume, electrostatic potential, ion density, electron density, etc. Recently, differential geometry theory has been used to define the surfaces that separate the microscopic (solute) domains for biomolecules from the macroscopic (solvent) domains. In thesemore » approaches, the microscopic domains are modeled with atomistic or quantum mechanical descriptions, while continuum mechanics models (including fluid mechanics, elastic mechanics, and continuum electrostatics) are applied to the macroscopic domains. This multiphysics description is integrated through an energy functional formalism and the resulting Euler-Lagrange equation is employed to derive a variety of governing partial differential equations for different solvation and transport processes; e.g., the Laplace-Beltrami equation for the solvent-solute interface, Poisson or Poisson-Boltzmann equations for electrostatic potentials, the Nernst-Planck equation for ion densities, and the Kohn-Sham equation for solute electron density. Extensive validation of these models has been carried out over hundreds of molecules, including proteins and ion channels, and the experimental data have been compared in terms of solvation energies, voltage-current curves, and density distributions. We also propose a new quantum model for electrolyte transport.« less

The dissolution or growth of a sphere

NASA Technical Reports Server (NTRS)

Shankar, N.; Wiltshire, Timothy J.; Subramanian, R. Shankar

1984-01-01

The problem of the dissolution or growth of an isolated stationary sphere in a large fluid body is analyzed. The motion of the boundary as well as the the resulting motion in the liquid are properly taken into account. The governing equations are solved using a recently developed technique (Subramanian and Weinberg, 1981) which employs an asymptotic expansion in time. Results for the radius of the sphere as a function of time are calculated. The range of utility of the present solution is established by comparison with a numerical solution of the governing equations obtained by the method of finite differences.

Computation of steady nozzle flow by a time-dependent method

NASA Technical Reports Server (NTRS)

Cline, M. C.

1974-01-01

The equations of motion governing steady, inviscid flow are of a mixed type, that is, hyperbolic in the supersonic region and elliptic in the subsonic region. These mathematical difficulties may be removed by using the so-called time-dependent method, where the governing equations become hyperbolic everywhere. The steady-state solution may be obtained as the asymptotic solution for large time. The object of this research was to develop a production type computer program capable of solving converging, converging-diverging, and plug two-dimensional nozzle flows in computational times of 1 min or less on a CDC 6600 computer.

Cooperative Factors, Cooperative Innovation Effect and Innovation Performance for Chinese Firms: an Empirical Study

NASA Astrophysics Data System (ADS)

Xie, Xuemei

Based on a survey to 1206 Chinese firms, this paper empirically explores the factors impacting cooperative innovation effect of firms, and seeks to explore the relationship between cooperative innovation effect (CIE) and innovation performance using the technique of Structural Equation Modeling (SEM). The study finds there are significant positive relationships between basic sustaining factors, factors of government and policy, factors of cooperation mechanism and social network, and cooperative innovation effect. However, the result reveals that factors of government and policy demonstrate little impact on the CIE of firms compared with other factors. It is hoped that the findings can pave the way for future studies in improving cooperative innovation capacity for firms in emerging countries.

Green's function solution to heat transfer of a transparent gas through a tube

NASA Technical Reports Server (NTRS)

Frankel, J. I.

1989-01-01

A heat transfer analysis of a transparent gas flowing through a circular tube of finite thickness is presented. This study includes the effects of wall conduction, internal radiative exchange, and convective heat transfer. The natural mathematical formulation produces a nonlinear, integrodifferential equation governing the wall temperature and an ordinary differential equation describing the gas temperature. This investigation proposes to convert the original system of equations into an equivalent system of integral equations. The Green's function method permits the conversion of an integrodifferential equation into a pure integral equation. The proposed integral formulation and subsequent computational procedure are shown to be stable and accurate.

Towards Perfectly Absorbing Boundary Conditions for Euler Equations

NASA Technical Reports Server (NTRS)

Hayder, M. Ehtesham; Hu, Fang Q.; Hussaini, M. Yousuff

1997-01-01

In this paper, we examine the effectiveness of absorbing layers as non-reflecting computational boundaries for the Euler equations. The absorbing-layer equations are simply obtained by splitting the governing equations in the coordinate directions and introducing absorption coefficients in each split equation. This methodology is similar to that used by Berenger for the numerical solutions of Maxwell's equations. Specifically, we apply this methodology to three physical problems shock-vortex interactions, a plane free shear flow and an axisymmetric jet- with emphasis on acoustic wave propagation. Our numerical results indicate that the use of absorbing layers effectively minimizes numerical reflection in all three problems considered.

Spurious Behavior of Shock-Capturing Methods: Problems Containing Stiff Source Terms and Discontinuities

NASA Technical Reports Server (NTRS)

Yee, Helen M. C.; Kotov, D. V.; Wang, Wei; Shu, Chi-Wang

2013-01-01

The goal of this paper is to relate numerical dissipations that are inherited in high order shock-capturing schemes with the onset of wrong propagation speed of discontinuities. For pointwise evaluation of the source term, previous studies indicated that the phenomenon of wrong propagation speed of discontinuities is connected with the smearing of the discontinuity caused by the discretization of the advection term. The smearing introduces a nonequilibrium state into the calculation. Thus as soon as a nonequilibrium value is introduced in this manner, the source term turns on and immediately restores equilibrium, while at the same time shifting the discontinuity to a cell boundary. The present study is to show that the degree of wrong propagation speed of discontinuities is highly dependent on the accuracy of the numerical method. The manner in which the smearing of discontinuities is contained by the numerical method and the overall amount of numerical dissipation being employed play major roles. Moreover, employing finite time steps and grid spacings that are below the standard Courant-Friedrich-Levy (CFL) limit on shockcapturing methods for compressible Euler and Navier-Stokes equations containing stiff reacting source terms and discontinuities reveals surprising counter-intuitive results. Unlike non-reacting flows, for stiff reactions with discontinuities, employing a time step and grid spacing that are below the CFL limit (based on the homogeneous part or non-reacting part of the governing equations) does not guarantee a correct solution of the chosen governing equations. Instead, depending on the numerical method, time step and grid spacing, the numerical simulation may lead to (a) the correct solution (within the truncation error of the scheme), (b) a divergent solution, (c) a wrong propagation speed of discontinuities solution or (d) other spurious solutions that are solutions of the discretized counterparts but are not solutions of the governing equations. The present investigation for three very different stiff system cases confirms some of the findings of Lafon & Yee (1996) and LeVeque & Yee (1990) for a model scalar PDE. The findings might shed some light on the reported difficulties in numerical combustion and problems with stiff nonlinear (homogeneous) source terms and discontinuities in general.

Basic lubrication equations

NASA Technical Reports Server (NTRS)

Hamrock, B. J.; Dowson, D.

1981-01-01

Lubricants, usually Newtonian fluids, are assumed to experience laminar flow. The basic equations used to describe the flow are the Navier-Stokes equation of motion. The study of hydrodynamic lubrication is, from a mathematical standpoint, the application of a reduced form of these Navier-Stokes equations in association with the continuity equation. The Reynolds equation can also be derived from first principles, provided of course that the same basic assumptions are adopted in each case. Both methods are used in deriving the Reynolds equation, and the assumptions inherent in reducing the Navier-Stokes equations are specified. Because the Reynolds equation contains viscosity and density terms and these properties depend on temperature and pressure, it is often necessary to couple the Reynolds with energy equation. The lubricant properties and the energy equation are presented. Film thickness, a parameter of the Reynolds equation, is a function of the elastic behavior of the bearing surface. The governing elasticity equation is therefore presented.

Symbolic generation of elastic rotor blade equations using a FORTRAN processor and numerical study on dynamic inflow effects on the stability of helicopter rotors

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.

1986-01-01

The process of performing an automated stability analysis for an elastic-bladed helicopter rotor is discussed. A symbolic manipulation program, written in FORTRAN, is used to aid in the derivation of the governing equations of motion for the rotor. The blades undergo coupled bending and torsional deformations. Two-dimensional quasi-steady aerodynamics below stall are used. Although reversed flow effects are neglected, unsteady effects, modeled as dynamic inflow are included. Using a Lagrangian approach, the governing equations are derived in generalized coordinates using the symbolic program. The program generates the steady and perturbed equations and writes into subroutines to be called by numerical routines. The symbolic program can operate on both expressions and matrices. For the case of hovering flight, the blade and dynamic inflow equations are converted to equations in a multiblade coordinate system by rearranging the coefficients of the equations. For the case of forward flight, the multiblade equations are obtained through the symbolic program. The final multiblade equations are capable of accommodating any number of elastic blade modes. The computer implementation of this procedure consists of three stages: (1) the symbolic derivation of equations; (2) the coding of the equations into subroutines; and (3) the numerical study after identifying mass, damping, and stiffness coefficients. Damping results are presented in hover and in forward flight with and without dynamic inflow effects for various rotor blade models, including rigid blade lag-flap, elastic flap-lag, flap-lag-torsion, and quasi-static torsion. Results from dynamic inflow effects which are obtained from a lift deficiency function for a quasi-static inflow model in hover are also presented.

MULTISCALE MODELS OF TAXIS-DRIVEN PATTERNING IN BACTERIAL POPULATIONS

PubMed Central

XUE, CHUAN; OTHMER, HANS G.

2009-01-01

Spatially-distributed populations of various types of bacteria often display intricate spatial patterns that are thought to result from the cellular response to gradients of nutrients or other attractants. In the past decade a great deal has been learned about signal transduction, metabolism and movement in E. coli and other bacteria, but translating the individual-level behavior into population-level dynamics is still a challenging problem. However, this is a necessary step because it is computationally impractical to use a strictly cell-based model to understand patterning in growing populations, since the total number of cells may reach 1012 - 1014 in some experiments. In the past phenomenological equations such as the Patlak-Keller-Segel equations have been used in modeling the cell movement that is involved in the formation of such patterns, but the question remains as to how the microscopic behavior can be correctly described by a macroscopic equation. Significant progress has been made for bacterial species that employ a “run-and-tumble” strategy of movement, in that macroscopic equations based on simplified schemes for signal transduction and turning behavior have been derived [14, 15]. Here we extend previous work in a number of directions: (i) we allow for time-dependent signals, which extends the applicability of the equations to natural environments, (ii) we use a more general turning rate function that better describes the biological behavior, and (iii) we incorporate the effect of hydrodynamic forces that arise when cells swim in close proximity to a surface. We also develop a new approach to solving the moment equations derived from the transport equation that does not involve closure assumptions. Numerical examples show that the solution of the lowest-order macroscopic equation agrees well with the solution obtained from a Monte Carlo simulation of cell movement under a variety of temporal protocols for the signal. We also apply the method to derive equations of chemotactic movement that are governed by multiple chemotactic signals. PMID:19784399

Storm time global thermosphere: A driven-dissipative thermodynamic system

NASA Astrophysics Data System (ADS)

Burke, W. J.; Lin, C. S.; Hagan, M. P.; Huang, C. Y.; Weimer, D. R.; Wise, J. O.; Gentile, L. C.; Marcos, F. A.

2009-06-01

Orbit-averaged mass densities $\\overline{\\rho and exospheric temperatures $\\overline{T ∞ inferred from measurements by accelerometers on the Gravity Recovery and Climate Experiment (GRACE) satellites are used to investigate global energy Eth and power Πth inputs to the thermosphere during two complex magnetic storms. Measurements show $\\overline{\\rho, $\\overline{T ∞, and Eth rising from and returning to prevailing baselines as the magnetospheric electric field $\\varepsilon$ VS and the Dst index wax and wane. Observed responses of Eth and $\\overline{T ∞ to $\\varepsilon$ VS driving suggest that the storm time thermosphere evolves as a driven-but-dissipative thermodynamic system, described by a first-order differential equation that is identical in form to that governing the behavior of Dst. Coupling and relaxation coefficients of the Eth, $\\overline{T ∞, and Dst equations are established empirically. Numerical solutions of the equations for $\\overline{T ∞ and Eth are shown to agree with GRACE data during large magnetic storms. Since $\\overline{T ∞ and Dst have the same $\\varepsilon$ VS driver, it is possible to combine their governing equations to obtain estimates of storm time thermospheric parameters, even when lacking information about interplanetary conditions. This approach has the potential for significantly improving the performance of operational models used to calculate trajectories of satellites and space debris and is also useful for developing forensic reconstructions of past magnetic storms. The essential correctness of the approach is supported by agreement between thermospheric power inputs calculated from both GRACE-based estimates of Eth and the Weimer Poynting flux model originally derived from electric and magnetic field measurements acquired by the Dynamics Explorer 2 satellite.

Effect of tumor shape, size, and tissue transport properties on drug delivery to solid tumors

PubMed Central

2014-01-01

Background The computational methods provide condition for investigation related to the process of drug delivery, such as convection and diffusion of drug in extracellular matrices, drug extravasation from microvessels or to lymphatic vessels. The information of this process clarifies the mechanisms of drug delivery from the injection site to absorption by a solid tumor. In this study, an advanced numerical method is used to solve fluid flow and solute transport equations simultaneously to investigate the effect of tumor shape and size on drug delivery to solid tumor. Methods The advanced mathematical model used in our previous work is further developed by adding solute transport equation to the governing equations. After applying appropriate boundary and initial conditions on tumor and surrounding tissue geometry, the element-based finite volume method is used for solving governing equations of drug delivery in solid tumor. Also, the effects of size and shape of tumor and some of tissue transport parameters such as effective pressure and hydraulic conductivity on interstitial fluid flow and drug delivery are investigated. Results Sensitivity analysis shows that drug delivery in prolate shape is significantly better than other tumor shapes. Considering size effect, increasing tumor size decreases drug concentration in interstitial fluid. This study shows that dependency of drug concentration in interstitial fluid to osmotic and intravascular pressure is negligible. Conclusions This study shows that among diffusion and convection mechanisms of drug transport, diffusion is dominant in most different tumor shapes and sizes. In tumors in which the convection has considerable effect, the drug concentration is larger than that of other tumors at the same time post injection. PMID:24987457

New Finite Difference Methods Based on IIM for Inextensible Interfaces in Incompressible Flows

PubMed Central

Li, Zhilin; Lai, Ming-Chih

2012-01-01

In this paper, new finite difference methods based on the augmented immersed interface method (IIM) are proposed for simulating an inextensible moving interface in an incompressible two-dimensional flow. The mathematical models arise from studying the deformation of red blood cells in mathematical biology. The governing equations are incompressible Stokes or Navier-Stokes equations with an unknown surface tension, which should be determined in such a way that the surface divergence of the velocity is zero along the interface. Thus, the area enclosed by the interface and the total length of the interface should be conserved during the evolution process. Because of the nonlinear and coupling nature of the problem, direct discretization by applying the immersed boundary or immersed interface method yields complex nonlinear systems to be solved. In our new methods, we treat the unknown surface tension as an augmented variable so that the augmented IIM can be applied. Since finding the unknown surface tension is essentially an inverse problem that is sensitive to perturbations, our regularization strategy is to introduce a controlled tangential force along the interface, which leads to a least squares problem. For Stokes equations, the forward solver at one time level involves solving three Poisson equations with an interface. For Navier-Stokes equations, we propose a modified projection method that can enforce the pressure jump condition corresponding directly to the unknown surface tension. Several numerical experiments show good agreement with other results in the literature and reveal some interesting phenomena. PMID:23795308

Dispersion relations of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with initial stresses.

PubMed

Guo, Xiao; Wei, Peijun

2016-03-01

The dispersion relations of elastic waves in a one-dimensional phononic crystal formed by periodically repeating of a pre-stressed piezoelectric slab and a pre-stressed piezomagnetic slab are studied in this paper. The influences of initial stress on the dispersive relation are considered based on the incremental stress theory. First, the incremental stress theory of elastic solid is extended to the magneto-electro-elasto solid. The governing equations, constitutive equations, and boundary conditions of the incremental stresses in a magneto-electro-elasto solid are derived with consideration of the existence of initial stresses. Then, the transfer matrices of a pre-stressed piezoelectric slab and a pre-stressed piezomagnetic slab are formulated, respectively. The total transfer matrix of a single cell in the phononic crystal is obtained by the multiplication of two transfer matrixes related with two adjacent slabs. Furthermore, the Bloch theorem is used to obtain the dispersive equations of in-plane and anti-plane Bloch waves. The dispersive equations are solved numerically and the numerical results are shown graphically. The oblique propagation and the normal propagation situations are both considered. In the case of normal propagation of elastic waves, the analytical expressions of the dispersion equation are derived and compared with other literatures. The influences of initial stresses, including the normal initial stresses and shear initial stresses, on the dispersive relations are both discussed based on the numerical results. Copyright © 2015 Elsevier B.V. All rights reserved.

Dynamic adaptive chemistry with operator splitting schemes for reactive flow simulations

NASA Astrophysics Data System (ADS)

Ren, Zhuyin; Xu, Chao; Lu, Tianfeng; Singer, Michael A.

2014-04-01

A numerical technique that uses dynamic adaptive chemistry (DAC) with operator splitting schemes to solve the equations governing reactive flows is developed and demonstrated. Strang-based splitting schemes are used to separate the governing equations into transport fractional substeps and chemical reaction fractional substeps. The DAC method expedites the numerical integration of reaction fractional substeps by using locally valid skeletal mechanisms that are obtained using the directed relation graph (DRG) reduction method to eliminate unimportant species and reactions from the full mechanism. Second-order temporal accuracy of the Strang-based splitting schemes with DAC is demonstrated on one-dimensional, unsteady, freely-propagating, premixed methane/air laminar flames with detailed chemical kinetics and realistic transport. The use of DAC dramatically reduces the CPU time required to perform the simulation, and there is minimal impact on solution accuracy. It is shown that with DAC the starting species and resulting skeletal mechanisms strongly depend on the local composition in the flames. In addition, the number of retained species may be significant only near the flame front region where chemical reactions are significant. For the one-dimensional methane/air flame considered, speed-up factors of three and five are achieved over the entire simulation for GRI-Mech 3.0 and USC-Mech II, respectively. Greater speed-up factors are expected for larger chemical kinetics mechanisms.

Influence of heat conducting substrates on explosive crystallization in thin layers

NASA Astrophysics Data System (ADS)

Schneider, Wilhelm

2017-09-01

Crystallization in a thin, initially amorphous layer is considered. The layer is in thermal contact with a substrate of very large dimensions. The energy equation of the layer contains source and sink terms. The source term is due to liberation of latent heat in the crystallization process, while the sink term is due to conduction of heat into the substrate. To determine the latter, the heat diffusion equation for the substrate is solved by applying Duhamel's integral. Thus, the energy equation of the layer becomes a heat diffusion equation with a time integral as an additional term. The latter term indicates that the heat loss due to the substrate depends on the history of the process. To complete the set of equations, the crystallization process is described by a rate equation for the degree of crystallization. The governing equations are then transformed to a moving co-ordinate system in order to analyze crystallization waves that propagate with invariant properties. Dual solutions are found by an asymptotic expansion for large activation energies of molecular diffusion. By introducing suitable variables, the results can be presented in a universal form that comprises the influence of all non-dimensional parameters that govern the process. Of particular interest for applications is the prediction of a critical heat loss parameter for the existence of crystallization waves with invariant properties.

BMS3 invariant fluid dynamics at null infinity

NASA Astrophysics Data System (ADS)

Penna, Robert F.

2018-02-01

We revisit the boundary dynamics of asymptotically flat, three dimensional gravity. The boundary is governed by a momentum conservation equation and an energy conservation equation, which we interpret as fluid equations, following the membrane paradigm. We reformulate the boundary’s equations of motion as Hamiltonian flow on the dual of an infinite-dimensional, semi-direct product Lie algebra equipped with a Lie–Poisson bracket. This gives the analogue for boundary fluid dynamics of the Marsden–Ratiu–Weinstein formulation of the compressible Euler equations on a manifold, M, as Hamiltonian flow on the dual of the Lie algebra of \

A note on the solutions of some nonlinear equations arising in third-grade fluid flows: an exact approach.

PubMed

Aziz, Taha; Mahomed, F M

2014-01-01

In this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. We obtain some simple closed-form steady-state solutions of these reduced equations. Our solutions are valid for the whole domain [0,∞) and also satisfy the physical boundary conditions. We also present the numerical solutions for some of the underlying equations. The graphs corresponding to the essential physical parameters of the flow are presented and discussed.

A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach

PubMed Central

Mahomed, F. M.

2014-01-01

In this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. We obtain some simple closed-form steady-state solutions of these reduced equations. Our solutions are valid for the whole domain [0,∞) and also satisfy the physical boundary conditions. We also present the numerical solutions for some of the underlying equations. The graphs corresponding to the essential physical parameters of the flow are presented and discussed. PMID:25143962

A Numerical Analysis of the Transient Response of an Ablation System Including Effects of Thermal Nonequilibrium, Mass Transfer and Chemical Kinetics. Ph.D Thesis - Virginia Polytechnic Inst. and State Univ.

NASA Technical Reports Server (NTRS)

Clark, R. K.

1972-01-01

The differential equations governing the transient response of a one-dimensional ablative thermal protection system undergoing stagnation ablation are derived. These equations are for thermal nonequilibrium effects between the pyrolysis gases and the char layer and kinetically controlled chemical reactions and mass transfer between the pyrolysis gases and the char layer. The boundary conditions are written for the particular case of stagnation heating with surface removal by oxidation or sublimation and pyrolysis of the uncharred layer occurring in a plane. The governing equations and boundary conditions are solved numerically using the modified implicit method (Crank-Nicolson method). Numerical results are compared with exact solutions for a number of simplified cases. The comparison is favorable in each instance.

The effect of convective boundary condition on MHD mixed convection boundary layer flow over an exponentially stretching vertical sheet

NASA Astrophysics Data System (ADS)

Isa, Siti Suzilliana Putri Mohamed; Arifin, Norihan Md.; Nazar, Roslinda; Bachok, Norfifah; Ali, Fadzilah Md

2017-12-01

A theoretical study that describes the magnetohydrodynamic mixed convection boundary layer flow with heat transfer over an exponentially stretching sheet with an exponential temperature distribution has been presented herein. This study is conducted in the presence of convective heat exchange at the surface and its surroundings. The system is controlled by viscous dissipation and internal heat generation effects. The governing nonlinear partial differential equations are converted into ordinary differential equations by a similarity transformation. The converted equations are then solved numerically using the shooting method. The results related to skin friction coefficient, local Nusselt number, velocity and temperature profiles are presented for several sets of values of the parameters. The effects of the governing parameters on the features of the flow and heat transfer are examined in detail in this study.

Adaptive Grid Generation for Numerical Solution of Partial Differential Equations.

DTIC Science & Technology

1983-12-01

numerical solution of fluid dynamics problems is presented. However, the method is applicable to the numer- ical evaluation of any partial differential...emphasis is being placed on numerical solution of the governing differential equations by finite difference methods . In the past two decades, considerable...original equations presented in that paper. The solution of the second problem is more difficult. 2 The method of Thompson et al. provides control for

The Shock and Vibration Digest. Volume 15. Number 2

DTIC Science & Technology

1983-02-01

plates - other analyses. Asymptotic solu- tions of the general three-dimensional elasticity equations for an anisotropic beam have been used by Sayir...34Operatorsand Fractional Deriva- tives for Viscoelastic Constitutive Equations " (Submitted to J. Rheology, Apr 1982). 53. Bagley, R.L and Torvik, P.J... equations governing free, undamped vibration modes, the hull is specified by sectional quaruties. They are: hull stiffness, as represented by bending

Convergence of the flow of a chemically reacting gaseous mixture to incompressible Euler equations in a unbounded domain

NASA Astrophysics Data System (ADS)

Kwon, Young-Sam

2017-12-01

The flow of chemically reacting gaseous mixture is associated with a variety of phenomena and processes. We study the combined quasineutral and inviscid limit from the flow of chemically reacting gaseous mixture governed by Poisson equation to incompressible Euler equations with the ill-prepared initial data in the unbounded domain R^2× T. Furthermore, the convergence rates are obtained.

On a new class of completely integrable nonlinear wave equations. II. Multi-Hamiltonian structure

NASA Astrophysics Data System (ADS)

Nutku, Y.

1987-11-01

The multi-Hamiltonian structure of a class of nonlinear wave equations governing the propagation of finite amplitude waves is discussed. Infinitely many conservation laws had earlier been obtained for these equations. Starting from a (primary) Hamiltonian formulation of these equations the necessary and sufficient conditions for the existence of bi-Hamiltonian structure are obtained and it is shown that the second Hamiltonian operator can be constructed solely through a knowledge of the first Hamiltonian function. The recursion operator which first appears at the level of bi-Hamiltonian structure gives rise to an infinite sequence of conserved Hamiltonians. It is found that in general there exist two different infinite sequences of conserved quantities for these equations. The recursion relation defining higher Hamiltonian structures enables one to obtain the necessary and sufficient conditions for the existence of the (k+1)st Hamiltonian operator which depends on the kth Hamiltonian function. The infinite sequence of conserved Hamiltonians are common to all the higher Hamiltonian structures. The equations of gas dynamics are discussed as an illustration of this formalism and it is shown that in general they admit tri-Hamiltonian structure with two distinct infinite sets of conserved quantities. The isothermal case of γ=1 is an exceptional one that requires separate treatment. This corresponds to a specialization of the equations governing the expansion of plasma into vacuum which will be shown to be equivalent to Poisson's equation in nonlinear acoustics.

Differential equations governing slip-induced pore-pressure fluctuations in a water-saturated granular medium

USGS Publications Warehouse

Iverson, R.M.

1993-01-01

Macroscopic frictional slip in water-saturated granular media occurs commonly during landsliding, surface faulting, and intense bedload transport. A mathematical model of dynamic pore-pressure fluctuations that accompany and influence such sliding is derived here by both inductive and deductive methods. The inductive derivation shows how the governing differential equations represent the physics of the steadily sliding array of cylindrical fiberglass rods investigated experimentally by Iverson and LaHusen (1989). The deductive derivation shows how the same equations result from a novel application of Biot's (1956) dynamic mixture theory to macroscopic deformation. The model consists of two linear differential equations and five initial and boundary conditions that govern solid displacements and pore-water pressures. Solid displacements and water pressures are strongly coupled, in part through a boundary condition that ensures mass conservation during irreversible pore deformation that occurs along the bumpy slip surface. Feedback between this deformation and the pore-pressure field may yield complex system responses. The dual derivations of the model help explicate key assumptions. For example, the model requires that the dimensionless parameter B, defined here through normalization of Biot's equations, is much larger than one. This indicates that solid-fluid coupling forces are dominated by viscous rather than inertial effects. A tabulation of physical and kinematic variables for the rod-array experiments of Iverson and LaHusen and for various geologic phenomena shows that the model assumptions commonly are satisfied. A subsequent paper will describe model tests against experimental data. ?? 1993 International Association for Mathematical Geology.

Meshless Method with Operator Splitting Technique for Transient Nonlinear Bioheat Transfer in Two-Dimensional Skin Tissues

PubMed Central

Zhang, Ze-Wei; Wang, Hui; Qin, Qing-Hua

2015-01-01

A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (2D) skin tissues. In the numerical scheme, the nonlinearity caused by linear and exponential relationships of temperature-dependent blood perfusion rate (TDBPR) is taken into consideration. In the analysis, the OSM is used first to separate the Laplacian operator and the nonlinear source term, and then the second-order time-stepping schemes are employed for approximating two splitting operators to convert the original governing equation into a linear nonhomogeneous Helmholtz-type governing equation (NHGE) at each time step. Subsequently, the RBF interpolation and the MFS involving the fundamental solution of the Laplace equation are respectively employed to obtain approximated particular and homogeneous solutions of the nonhomogeneous Helmholtz-type governing equation. Finally, the full fields consisting of the particular and homogeneous solutions are enforced to fit the NHGE at interpolation points and the boundary conditions at boundary collocations for determining unknowns at each time step. The proposed method is verified by comparison of other methods. Furthermore, the sensitivity of the coefficients in the cases of a linear and an exponential relationship of TDBPR is investigated to reveal their bioheat effect on the skin tissue. PMID:25603180

Meshless method with operator splitting technique for transient nonlinear bioheat transfer in two-dimensional skin tissues.

PubMed

Zhang, Ze-Wei; Wang, Hui; Qin, Qing-Hua

2015-01-16

A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (2D) skin tissues. In the numerical scheme, the nonlinearity caused by linear and exponential relationships of temperature-dependent blood perfusion rate (TDBPR) is taken into consideration. In the analysis, the OSM is used first to separate the Laplacian operator and the nonlinear source term, and then the second-order time-stepping schemes are employed for approximating two splitting operators to convert the original governing equation into a linear nonhomogeneous Helmholtz-type governing equation (NHGE) at each time step. Subsequently, the RBF interpolation and the MFS involving the fundamental solution of the Laplace equation are respectively employed to obtain approximated particular and homogeneous solutions of the nonhomogeneous Helmholtz-type governing equation. Finally, the full fields consisting of the particular and homogeneous solutions are enforced to fit the NHGE at interpolation points and the boundary conditions at boundary collocations for determining unknowns at each time step. The proposed method is verified by comparison of other methods. Furthermore, the sensitivity of the coefficients in the cases of a linear and an exponential relationship of TDBPR is investigated to reveal their bioheat effect on the skin tissue.

Albany/FELIX: A parallel, scalable and robust, finite element, first-order Stokes approximation ice sheet solver built for advanced analysis

DOE PAGES

Tezaur, I. K.; Perego, M.; Salinger, A. G.; ...

2015-04-27

This paper describes a new parallel, scalable and robust finite element based solver for the first-order Stokes momentum balance equations for ice flow. The solver, known as Albany/FELIX, is constructed using the component-based approach to building application codes, in which mature, modular libraries developed as a part of the Trilinos project are combined using abstract interfaces and template-based generic programming, resulting in a final code with access to dozens of algorithmic and advanced analysis capabilities. Following an overview of the relevant partial differential equations and boundary conditions, the numerical methods chosen to discretize the ice flow equations are described, alongmore » with their implementation. The results of several verification studies of the model accuracy are presented using (1) new test cases for simplified two-dimensional (2-D) versions of the governing equations derived using the method of manufactured solutions, and (2) canonical ice sheet modeling benchmarks. Model accuracy and convergence with respect to mesh resolution are then studied on problems involving a realistic Greenland ice sheet geometry discretized using hexahedral and tetrahedral meshes. Also explored as a part of this study is the effect of vertical mesh resolution on the solution accuracy and solver performance. The robustness and scalability of our solver on these problems is demonstrated. Lastly, we show that good scalability can be achieved by preconditioning the iterative linear solver using a new algebraic multilevel preconditioner, constructed based on the idea of semi-coarsening.« less

Surface self-organization in multilayer film coatings

NASA Astrophysics Data System (ADS)

Shuvalov, Gleb M.; Kostyrko, Sergey A.

2017-12-01

It is a recognized fact that during film deposition and subsequent thermal processing the film surface evolves into an undulating profile. Surface roughness affects many important aspects in the engineering application of thin film materials such as wetting, heat transfer, mechanical, electromagnetic and optical properties. To accurately control the morphological surface modifications at the micro- and nanoscale and improve manufacturing techniques, we design a mathematical model of the surface self-organization process in multilayer film materials. In this paper, we consider a solid film coating with an arbitrary number of layers under plane strain conditions. The film surface has a small initial perturbation described by a periodic function. It is assumed that the evolution of the surface relief is governed by surface and volume diffusion. Based on Gibbs thermodynamics and linear theory of elasticity, we present a procedure for constructing a governing equation that gives the amplitude change of the surface perturbation with time. A parametric study of the evolution equation leads to the definition of a critical undulation wavelength that stabilizes the surface. As a numerical result, the influence of geometrical and physical parameters on the morphological stability of an isotropic two-layered film coating is analyzed.

Thermoviscoplastic analysis of fibrous periodic composites using triangular subvolumes

NASA Technical Reports Server (NTRS)

Walker, Kevin P.; Freed, Alan D.; Jordan, Eric H.

1993-01-01

The nonlinear viscoplastic behavior of fibrous periodic composites is analyzed by discretizing the unit cell into triangular subvolumes. A set of these subvolumes can be configured by the analyst to construct a representation for the unit cell of a periodic composite. In each step of the loading history, the total strain increment at any point is governed by an integral equation which applies to the entire composite. A Fourier series approximation allows the incremental stresses and strains to be determined within a unit cell of the periodic lattice. The nonlinearity arising from the viscoplastic behavior of the constituent materials comprising the composite is treated as fictitious body force in the governing integral equation. Specific numerical examples showing the stress distributions in the unit cell of a fibrous tungsten/copper metal matrix composite under viscoplastic loading conditions are given. The stress distribution resulting in the unit cell when the composite material is subjected to an overall transverse stress loading history perpendicular to the fibers is found to be highly heterogeneous, and typical homogenization techniques based on treating the stress and strain distributions within the constituent phases as homogeneous result in large errors under inelastic loading conditions.

Thermoviscoplastic analysis of fibrous periodic composites by the use of triangular subvolumes

NASA Technical Reports Server (NTRS)

Walker, Kevin P.; Freed, Alan D.; Jordan, Eric H.

1994-01-01

The non-linear viscoplastic behavior of fibrous periodic composites is analyzed by discretizing the unit cell into triangular subvolumes. A set of these subvolumes can be configured by the analyst to construct a representation for the unit cell of a periodic composite. In each step of the loading history the total strain increment at any point is governed by an integral equation which applies to the entire composite. A Fourier series approximation allows the incremental stresses and strains to be determined within a unit cell of the periodic lattice. The non-linearity arising from the viscoplastic behavior of the constituent materials comprising the composite is treated as a fictitious body force in the governing integral equation. Specific numerical examples showing the stress distributions in the unit cell of a fibrous tungsten/copper metal-matrix composite under viscoplastic loading conditions are given. The stress distribution resulting in the unit cell when the composite material is subjected to an overall transverse stress loading history perpendicular to the fibers is found to be highly heterogeneous, and typical homogenization techniques based on treating the stress and strain distributions within the constituent phases as homogeneous result in large errors under inelastic loading conditions.

System identification principles in studies of forest dynamics.

Treesearch

Rolfe A. Leary

1970-01-01

Shows how it is possible to obtain governing equation parameter estimates on the basis of observed system states. The approach used represents a constructive alternative to regression techniques for models expressed as differential equations. This approach allows scientists to more completely quantify knowledge of forest development processes, to express theories in...

Nonlinear coherent structures of Alfvén wave in a collisional plasma

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

Jana, Sayanee; Chakrabarti, Nikhil; Ghosh, Samiran

2016-07-15

The Alfvén wave dynamics is investigated in the framework of two-fluid approach in a compressible collisional magnetized plasma. In the finite amplitude limit, the dynamics of the nonlinear Alfvén wave is found to be governed by a modified Korteweg-de Vries Burgers equation (mKdVB). In this mKdVB equation, the electron inertia is found to act as a source of dispersion, and the electron-ion collision serves as a dissipation. The collisional dissipation is eventually responsible for the Burgers term in mKdVB equation. In the long wavelength limit, this weakly nonlinear Alfvén wave is shown to be governed by a damped nonlinear Schrödingermore » equation. Furthermore, these nonlinear equations are analyzed by means of analytical calculation and numerical simulation to elucidate the various aspects of the phase-space dynamics of the nonlinear wave. Results reveal that nonlinear Alfvén wave exhibits the dissipation mediated shock, envelope, and breather like structures. Numerical simulations also predict the formation of dissipative Alfvénic rogue wave, giant breathers, and rogue wave holes. These results are discussed in the context of the space plasma.« less

Enhanced simulation software for rocket turbopump, turbulent, annular liquid seals

NASA Technical Reports Server (NTRS)

Padavala, Satya; Palazzolo, Alan

1994-01-01

One of the main objectives of this work is to develop a new dynamic analysis for liquid annular seals with arbitrary profile and to analyze a general distorted interstage seal of the space shuttle main engine high pressure oxygen turbopump (SSME-ATD-HPOTP). The dynamic analysis developed is based on a method originally proposed by Nelson and Nguyen. A simpler scheme based on cubic splines is found to be computationally more efficient and has better convergence properties at higher eccentricities. The first order solution of the original analysis is modified by including a more exact solution that takes into account the variation of perturbed variables along the circumference. A new set of equations for dynamic analysis are derived based on this more general model. A unified solution procedure that is valid for both Moody's and Hirs' friction models is presented. Dynamic analysis is developed for three different models: constant properties, variable properties, and thermal effects with variable properties. Arbitrarily varying seal profiles in both axial and circumferential directions are considered. An example case of an elliptical seal with varying degrees of axial curvature is analyzed in detail. A case study based on predicted clearances of an interstage seal of the SSME-ATD-HPOTP is presented. Dynamic coefficients based on external specified load are introduced to analyze seals that support a preload. The other objective of this work is to study the effect of large rotor displacements of SSME-ATD-HPOTP on the dynamics of the annular seal and the resulting transient motion. One task is to identify the magnitude of motion of the rotor about the centered position and establish limits of effectiveness of using current linear models. This task is accomplished by solving the bulk flow model seal governing equations directly for transient seal forces for any given type of motion, including motion with large eccentricities. Based on the above study, an equivalence is established between linearized coefficients based transient motion and the same motion as predicted by the original governing equations. An innovative method is developed to model nonlinearities in an annular seal based on dynamic coefficients computed at various static eccentricities. This method is thoroughly tested for various types of transient motion using bulk flow model results as a benchmark.

Testing for nonlinear dependence in financial markets.

PubMed

Dore, Mohammed; Matilla-Garcia, Mariano; Marin, Manuel Ruiz

2011-07-01

This article addresses the question of improving the detection of nonlinear dependence by means of recently developed nonparametric tests. To this end a generalized version of BDS test and a new test based on symbolic dynamics are used on realizations from a well-known artificial market for which the dynamic equation governing the market is known. Comparisons with other tests for detecting nonlinearity are also provided. We show that the test based on symbolic dynamics outperforms other tests with the advantage that it depends only on one free parameter, namely the embedding dimension. This does not hold for other tests for nonlinearity.

Computing rates of Markov models of voltage-gated ion channels by inverting partial differential equations governing the probability density functions of the conducting and non-conducting states.

PubMed

Tveito, Aslak; Lines, Glenn T; Edwards, Andrew G; McCulloch, Andrew

2016-07-01

Markov models are ubiquitously used to represent the function of single ion channels. However, solving the inverse problem to construct a Markov model of single channel dynamics from bilayer or patch-clamp recordings remains challenging, particularly for channels involving complex gating processes. Methods for solving the inverse problem are generally based on data from voltage clamp measurements. Here, we describe an alternative approach to this problem based on measurements of voltage traces. The voltage traces define probability density functions of the functional states of an ion channel. These probability density functions can also be computed by solving a deterministic system of partial differential equations. The inversion is based on tuning the rates of the Markov models used in the deterministic system of partial differential equations such that the solution mimics the properties of the probability density function gathered from (pseudo) experimental data as well as possible. The optimization is done by defining a cost function to measure the difference between the deterministic solution and the solution based on experimental data. By evoking the properties of this function, it is possible to infer whether the rates of the Markov model are identifiable by our method. We present applications to Markov model well-known from the literature. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

Streaming current magnetic fields in a charged nanopore.

PubMed

Mansouri, Abraham; Taheri, Peyman; Kostiuk, Larry W

2016-11-11

Magnetic fields induced by currents created in pressure driven flows inside a solid-state charged nanopore were modeled by numerically solving a system of steady state continuum partial differential equations, i.e., Poisson, Nernst-Planck, Ampere and Navier-Stokes equations (PNPANS). This analysis was based on non-dimensional transport governing equations that were scaled using Debye length as the characteristic length scale, and applied to a finite length cylindrical nano-channel. The comparison of numerical and analytical studies shows an excellent agreement and verified the magnetic fields density both inside and outside the nanopore. The radially non-uniform currents resulted in highly non-uniform magnetic fields within the nanopore that decay as 1/r outside the nanopore. It is worth noting that for either streaming currents or streaming potential cases, the maximum magnetic field occurred inside the pore in the vicinity of nanopore wall, as opposed to a cylindrical conductor that carries a steady electric current where the maximum magnetic fields occur at the perimeter of conductor. Based on these results, it is suggested and envisaged that non-invasive external magnetic fields readouts generated by streaming/ionic currents may be viewed as secondary electronic signatures of biomolecules to complement and enhance current DNA nanopore sequencing techniques.

A finite element based method for solution of optimal control problems

NASA Technical Reports Server (NTRS)

Bless, Robert R.; Hodges, Dewey H.; Calise, Anthony J.

1989-01-01

A temporal finite element based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables that are expanded in terms of elemental values and simple shape functions. Unlike other variational approaches to optimal control problems, however, time derivatives of the states and costates do not appear in the governing variational equation. Instead, the only quantities whose time derivatives appear therein are virtual states and virtual costates. Also noteworthy among characteristics of the finite element formulation is the fact that in the algebraic equations which contain costates, they appear linearly. Thus, the remaining equations can be solved iteratively without initial guesses for the costates; this reduces the size of the problem by about a factor of two. Numerical results are presented herein for an elementary trajectory optimization problem which show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The goal is to evaluate the feasibility of this approach for real-time guidance applications. To this end, a simplified two-stage, four-state model for an advanced launch vehicle application is presented which is suitable for finite element solution.

Streaming current magnetic fields in a charged nanopore

NASA Astrophysics Data System (ADS)

Mansouri, Abraham; Taheri, Peyman; Kostiuk, Larry W.

2016-11-01

Magnetic fields induced by currents created in pressure driven flows inside a solid-state charged nanopore were modeled by numerically solving a system of steady state continuum partial differential equations, i.e., Poisson, Nernst-Planck, Ampere and Navier-Stokes equations (PNPANS). This analysis was based on non-dimensional transport governing equations that were scaled using Debye length as the characteristic length scale, and applied to a finite length cylindrical nano-channel. The comparison of numerical and analytical studies shows an excellent agreement and verified the magnetic fields density both inside and outside the nanopore. The radially non-uniform currents resulted in highly non-uniform magnetic fields within the nanopore that decay as 1/r outside the nanopore. It is worth noting that for either streaming currents or streaming potential cases, the maximum magnetic field occurred inside the pore in the vicinity of nanopore wall, as opposed to a cylindrical conductor that carries a steady electric current where the maximum magnetic fields occur at the perimeter of conductor. Based on these results, it is suggested and envisaged that non-invasive external magnetic fields readouts generated by streaming/ionic currents may be viewed as secondary electronic signatures of biomolecules to complement and enhance current DNA nanopore sequencing techniques.

Computing aerodynamic sound using advanced statistical turbulence theories

NASA Technical Reports Server (NTRS)

Hecht, A. M.; Teske, M. E.; Bilanin, A. J.

1981-01-01

It is noted that the calculation of turbulence-generated aerodynamic sound requires knowledge of the spatial and temporal variation of Q sub ij (xi sub k, tau), the two-point, two-time turbulent velocity correlations. A technique is presented to obtain an approximate form of these correlations based on closure of the Reynolds stress equations by modeling of higher order terms. The governing equations for Q sub ij are first developed for a general flow. The case of homogeneous, stationary turbulence in a unidirectional constant shear mean flow is then assumed. The required closure form for Q sub ij is selected which is capable of qualitatively reproducing experimentally observed behavior. This form contains separation time dependent scale factors as parameters and depends explicitly on spatial separation. The approximate forms of Q sub ij are used in the differential equations and integral moments are taken over the spatial domain. The velocity correlations are used in the Lighthill theory of aerodynamic sound by assuming normal joint probability.

A numerical spectral approach to solve the dislocation density transport equation

NASA Astrophysics Data System (ADS)

Djaka, K. S.; Taupin, V.; Berbenni, S.; Fressengeas, C.

2015-09-01

A numerical spectral approach is developed to solve in a fast, stable and accurate fashion, the quasi-linear hyperbolic transport equation governing the spatio-temporal evolution of the dislocation density tensor in the mechanics of dislocation fields. The approach relies on using the Fast Fourier Transform algorithm. Low-pass spectral filters are employed to control both the high frequency Gibbs oscillations inherent to the Fourier method and the fast-growing numerical instabilities resulting from the hyperbolic nature of the transport equation. The numerical scheme is validated by comparison with an exact solution in the 1D case corresponding to dislocation dipole annihilation. The expansion and annihilation of dislocation loops in 2D and 3D settings are also produced and compared with finite element approximations. The spectral solutions are shown to be stable, more accurate for low Courant numbers and much less computation time-consuming than the finite element technique based on an explicit Galerkin-least squares scheme.

Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media

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

Mohamed, M. Shadi, E-mail: m.s.mohamed@durham.ac.uk; Seaid, Mohammed; Trevelyan, Jon

2013-10-15

We investigate the effectiveness of the partition-of-unity finite element method for transient conduction–radiation problems in diffusive grey media. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary diffusion approximation to the radiation in grey media. The coupled equations are integrated in time using a semi-implicit method in the finite element framework. We show that for the considered problems, a combination of hyperbolic and exponential enrichment functions based on an approximation of the boundary layer leads to improved accuracy compared to the conventional finite element method. It is illustrated that this approach canmore » be more efficient than using h adaptivity to increase the accuracy of the finite element method near the boundary walls. The performance of the proposed partition-of-unity method is analyzed on several test examples for transient conduction–radiation problems in two space dimensions.« less

Four-fluid MHD Simulations of the Plasma and Neutral Gas Environment of Comet 67P/Churyumov-Gerasimenko Near Perihelion

NASA Astrophysics Data System (ADS)

Huang, Zhenguang; Toth, Gabor; Gombosi, Tamas; Jia, Xianzhe; Rubin, Martin; Fougere, Nicolas; Tenishev, Valeriy; Combi, Michael; Bieler, Andre; Hansen, Kenneth; Shou, Yinsi; Altwegg, Kathrin

2016-04-01

The neutral and plasma environment is critical in understanding the interaction of the solar wind and comet 67P/Churyumov-Gerasimenko (CG), the target of the European Space Agency's Rosetta mission. In this study, we have developed a 3-D four-fluid model, which is based on BATS-R-US (Block-Adaptive Tree Solarwind Roe-type Upwind Scheme) within SWMF (Space Weather Modeling Framework) that solves the governing multi-fluid MHD equations and the Euler equations for the neutral gas fluid. These equations describe the behavior and interactions of the cometary heavy ions, the solar wind protons, the electrons, and the neutrals. We simulated the plasma and neutral gas environment of comet CG with SHAP5 model near perihelion and we showed that the plasma environment in the inner coma region have some new features: magnetic reconnection in the tail region, a magnetic pile-up region on the nightside, and nucleus directed plasma flow inside the nightside reconnection region.

Design and control of rotating soil-like substrate plant-growing facility based on plant water requirement and computational fluid dynamics simulation

NASA Astrophysics Data System (ADS)

Hu, Dawei; Li, Leyuan; Liu, Hui; Zhang, Houkai; Fu, Yuming; Sun, Yi; Li, Liang

It is necessary to process inedible plant biomass into soil-like substrate (SLS) by bio-compost to realize biological resource sustainable utilization. Although similar to natural soil in structure and function, SLS often has uneven water distribution adversely affecting the plant growth due to unsatisfactory porosity, permeability and gravity distribution. In this article, SLS plant-growing facility (SLS-PGF) were therefore rotated properly for cultivating lettuce, and the Brinkman equations coupled with laminar flow equations were taken as governing equations, and boundary conditions were specified by actual operating characteristics of rotating SLS-PGF. Optimal open-control law of the angular and inflow velocity was determined by lettuce water requirement and CFD simulations. The experimental result clearly showed that water content was more uniformly distributed in SLS under the action of centrifugal and Coriolis force, rotating SLS-PGF with the optimal open-control law could meet lettuce water requirement at every growth stage and achieve precise irrigation.

Vibration of initially stressed carbon nanotubes under magneto-thermal environment for nanoparticle delivery via higher-order nonlocal strain gradient theory

NASA Astrophysics Data System (ADS)

Farajpour, M. R.; Shahidi, A. R.; Tabataba'i-Nasab, F.; Farajpour, A.

2018-06-01

In this paper, the forced vibration of a single-walled carbon nanotube (SWCNT) under a moving nanoparticle is investigated based on the higher-order nonlocal strain gradient theory. The SWCNT is subjected to thermo-mechanical stresses and an external longitudinal magnetic field. The influences of higher-order stress gradients in conjunction with the strain gradient nonlocality are taken into account. Using Hamilton's principle and Maxwell's equations, the higher-order differential equations of motion are derived. An analytical solution is obtained for the dynamic deflection of SWCNTs using the Galerkin method. Furthermore, the governing differential equation is solved numerically using the precise integration method. The results of the two solution procedures are compared and an excellent agreement is found between them. Finally, the influences of various scale parameters, the velocity of the moving nanoparticle, the initial axial stress, the temperature change and longitudinal magnetic field on the dynamic response of SWCNTs are investigated.

On the various forms of the energy equation for a dilute, monatomic mixture of nonreacting gases

NASA Technical Reports Server (NTRS)

Kennedy, Christopher A.

1994-01-01

In the case of gas mixtures, the governing equations become rather formidable and a complete listing of the equations in their various forms and methods to evaluate the transport coefficients is difficult to find. This paper seeks to compile common, as well as less well known, results in a single document. Various relationships between equations describing conservation of energy for a dilute, monatomic, nonreacting gas in local equilibrium are provided. The gas is treated as nonrelativistic, not subject to magnetic or electric fields, or radiative effects.

Defocusing complex short-pulse equation and its multi-dark-soliton solution.

PubMed

Feng, Bao-Feng; Ling, Liming; Zhu, Zuonong

2016-05-01

In this paper, we propose a complex short-pulse equation of both focusing and defocusing types, which governs the propagation of ultrashort pulses in nonlinear optical fibers. It can be viewed as an analog of the nonlinear Schrödinger (NLS) equation in the ultrashort-pulse regime. Furthermore, we construct the multi-dark-soliton solution for the defocusing complex short-pulse equation through the Darboux transformation and reciprocal (hodograph) transformation. One- and two-dark-soliton solutions are given explicitly, whose properties and dynamics are analyzed and illustrated.

The Role of Thermal Properties in Periodic Time-Varying Phenomena

ERIC Educational Resources Information Center

Marin, E.

2007-01-01

The role played by physical parameters governing the transport of heat in periodical time-varying phenomena within solids is discussed. Starting with a brief look at the conduction heat transport mechanism, the equations governing heat conduction under static, stationary and non-stationary conditions, and the physical parameters involved, are…

Electrokinetics Models for Micro and Nano Fluidic Impedance Sensors

DTIC Science & Technology

2010-11-01

primitive Differential-Algebraic Equations (DAEs), used to process and interpret the experimentally measured electrical impedance data (Sun and Morgan...field, and species respectively. A second-order scheme was used to calculate the ionic species distribution. The linearized algebraic equations were...is governed by the Poisson equation 2 0 0 r i i i F z cε ε φ∇ + =∑ where ε0 and εr are, respectively, the electrical permittivity in the vacuum

Invariant Clustering Using Scattering Matrices.

DTIC Science & Technology

1983-02-23

general three-dimensional elasticity a discontinuous fiber, however. equations for an anisotropic beam have been used by Sayir [19] to show that shear...34 Exptl. tives for Viscoelastic Constitutive Equations " Tech.,6(2), pp 10-14 (Apr 1982). (Submitted to J. Rheology, Apr 1982). 63. Gibson, R.F., Yau, A...vibration modes up to about nine nodes [4], Added mass of water. The frequency range relevant In the Timoshenko beam equations governing free, for ship

CLASSICAL AREAS OF PHENOMENOLOGY: Material parameter equation for rotating elliptical spherical cloaks

NASA Astrophysics Data System (ADS)

Ma, Hua; Qu, Shao-Bo; Xu, Zhuo; Zhang, Jie-Qiu; Wang, Jia-Fu

2009-01-01

By using the coordinate transformation method, we have deduced the material parameter equation for rotating elliptical spherical cloaks and carried out simulation as well. The results indicate that the rotating elliptical spherical cloaking shell, which is made of meta-materials whose permittivity and permeability are governed by the equation deduced in this paper, can achieve perfect invisibility by excluding electromagnetic fields from the internal region without disturbing any external field.

Traveling wave solutions and conservation laws for nonlinear evolution equation

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa

2018-02-01

In this work, the Riccati-Bernoulli sub-ordinary differential equation and modified tanh-coth methods are used to reach soliton solutions of the nonlinear evolution equation. We acquire new types of traveling wave solutions for the governing equation. We show that the equation is nonlinear self-adjoint by obtaining suitable substitution. Therefore, we construct conservation laws for the equation using new conservation theorem. The obtained solutions in this work may be used to explain and understand the physical nature of the wave spreads in the most dispersive medium. The constraint condition for the existence of solitons is stated. Some three dimensional figures for some of the acquired results are illustrated.

A model for closing the inviscid form of the average-passage equation system

NASA Technical Reports Server (NTRS)

Adamczyk, J. J.; Mulac, R. A.; Celestina, M. L.

1985-01-01

A mathematical model is proposed for closing or mathematically completing the system of equations which describes the time average flow field through the blade passages of multistage turbomachinery. These equations referred to as the average passage equation system govern a conceptual model which has proven useful in turbomachinery aerodynamic design and analysis. The closure model is developed so as to insure a consistency between these equations and the axisymmetric through flow equations. The closure model was incorporated into a computer code for use in simulating the flow field about a high speed counter rotating propeller and a high speed fan stage. Results from these simulations are presented.

A Short Review of Ablative-Material Response Models and Simulation Tools

NASA Technical Reports Server (NTRS)

Lachaud, Jean; Magin, Thierry E.; Cozmuta, Ioana; Mansour, Nagi N.

2011-01-01

A review of the governing equations and boundary conditions used to model the response of ablative materials submitted to a high-enthalpy flow is proposed. The heritage of model-development efforts undertaken in the 1960s is extremely clear: the bases of the models used in the community are mathematically equivalent. Most of the material-response codes implement a single model in which the equation parameters may be modified to model different materials or conditions. The level of fidelity of the models implemented in design tools only slightly varies. Research and development codes are generally more advanced but often not as robust. The capabilities of each of these codes are summarized in a color-coded table along with research and development efforts currently in progress.

Unsteady seepage flow over sloping beds in response to multiple localized recharge

NASA Astrophysics Data System (ADS)

Bansal, Rajeev K.

2017-05-01

New generalized solutions of linearized Boussinesq equation are derived to approximate the dynamic behavior of subsurface seepage flow induced by multiple localized time-varying recharges over sloping ditch-drain aquifer system. The mathematical model is based on extended Dupuit-Forchheimer assumption and treats the spatial location of recharge basins as additional parameter. Closed form analytic expressions for spatio-temporal variations in water head distribution and discharge rate into the drains are obtained by solving the governing flow equation using eigenvalue-eigenfunction method. Downward and zero-sloping aquifers are treated as special cases of main results. A numerical example is used for illustration of combined effects of various parameters such as spatial coordinates of the recharge basin, aquifer's bed slope, and recharge rate on the dynamic profiles of phreatic surface.

Numerical simulation and experimental investigation about internal and external flows†

NASA Astrophysics Data System (ADS)

Wang, Tao; Yang, Guowei; Huang, Guojun; Zhou, Liandi

2006-06-01

In this paper, TASCflow3D is used to solve inner and outer 3D viscous incompressible turbulent flow (Re=5.6×106) around axisymmetric body with duct. The governing equation is a RANS equation with standard k ɛ turbulence model. The discrete method used is a finite volume method based on the finite element approach. In this method, the description of geometry is very flexible and at the same time important conservative properties are retained. The multi-block and algebraic multi-grid techniques are used for the convergence acceleration. Agreement between experimental results and calculation is good. It indicates that this novel approach can be used to simulate complex flow such as the interaction between rotor and stator or propulsion systems containing tip clearance and cavitation.

Modern aspects of homogeneous-heterogeneous reactions and variable thickness in nanofluids through carbon nanotubes

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Ahmed, Sohail; Muhammad, Taseer; Alsaedi, Ahmed

2017-10-01

This article examines homogeneous-heterogeneous reactions and internal heat generation in Darcy-Forchheimer flow of nanofluids with different base fluids. Flow is generated due to a nonlinear stretchable surface of variable thickness. The characteristics of nanofluid are explored using CNTs (single and multi walled carbon nanotubes). Equal diffusion coefficients are considered for both reactants and auto catalyst. The conversion of partial differential equations (PDEs) to ordinary differential equations (ODEs) is done via appropriate transformations. Optimal homotopy approach is implemented for solutions development of governing problems. Averaged square residual errors are computed. The optimal solution expressions of velocity, temperature and concentration are explored through plots by using several values of physical parameters. Further the coefficient of skin friction and local Nusselt number are examined through graphs.

Three-Dimensional Incompressible Navier-Stokes Flow Computations about Complete Configurations Using a Multiblock Unstructured Grid Approach

NASA Technical Reports Server (NTRS)

Sheng, Chunhua; Hyams, Daniel G.; Sreenivas, Kidambi; Gaither, J. Adam; Marcum, David L.; Whitfield, David L.

2000-01-01

A multiblock unstructured grid approach is presented for solving three-dimensional incompressible inviscid and viscous turbulent flows about complete configurations. The artificial compressibility form of the governing equations is solved by a node-based, finite volume implicit scheme which uses a backward Euler time discretization. Point Gauss-Seidel relaxations are used to solve the linear system of equations at each time step. This work employs a multiblock strategy to the solution procedure, which greatly improves the efficiency of the algorithm by significantly reducing the memory requirements by a factor of 5 over the single-grid algorithm while maintaining a similar convergence behavior. The numerical accuracy of solutions is assessed by comparing with the experimental data for a submarine with stem appendages and a high-lift configuration.

Coolant side heat transfer with rotation: User manual for 3D-TEACH with rotation

NASA Technical Reports Server (NTRS)

Syed, S. A.; James, R. H.

1989-01-01

This program solves the governing transport equations in Reynolds average form for the flow of a 3-D, steady state, viscous, heat conducting, multiple species, single phase, Newtonian fluid with combustion. The governing partial differential equations are solved in physical variables in either a Cartesian or cylindrical coordinate system. The effects of rotation on the momentum and enthalpy calculations modeled in Cartesian coordinates are examined. The flow of the fluid should be confined and subsonic with a maximum Mach number no larger than 0.5. This manual describes the operating procedures and input details for executing a 3D-TEACH computation.

Heat transfer characteristics of an emergent strand

NASA Technical Reports Server (NTRS)

Simon, W. E.; Witte, L. C.; Hedgcoxe, P. G.

1974-01-01

A mathematical model was developed to describe the heat transfer characteristics of a hot strand emerging into a surrounding coolant. A stable strand of constant efflux velocity is analyzed, with a constant (average) heat transfer coefficient on the sides and leading surface of the strand. After developing a suitable governing equation to provide an adequate description of the physical system, the dimensionless governing equation is solved with Laplace transform methods. The solution yields the temperature within the strand as a function of axial distance and time. Generalized results for a wide range of parameters are presented, and the relationship of the results and experimental observations is discussed.

Numerical Simulation for the Unsteady MHD Flow and Heat Transfer of Couple Stress Fluid over a Rotating Disk

PubMed Central

2014-01-01

The present work is devoted to study the numerical simulation for unsteady MHD flow and heat transfer of a couple stress fluid over a rotating disk. A similarity transformation is employed to reduce the time dependent system of nonlinear partial differential equations (PDEs) to ordinary differential equations (ODEs). The Runge-Kutta method and shooting technique are employed for finding the numerical solution of the governing system. The influences of governing parameters viz. unsteadiness parameter, couple stress and various physical parameters on velocity, temperature and pressure profiles are analyzed graphically and discussed in detail. PMID:24835274

A well-posed and stable stochastic Galerkin formulation of the incompressible Navier–Stokes equations with random data

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

Pettersson, Per, E-mail: per.pettersson@uib.no; Nordström, Jan, E-mail: jan.nordstrom@liu.se; Doostan, Alireza, E-mail: alireza.doostan@colorado.edu

2016-02-01

We present a well-posed stochastic Galerkin formulation of the incompressible Navier–Stokes equations with uncertainty in model parameters or the initial and boundary conditions. The stochastic Galerkin method involves representation of the solution through generalized polynomial chaos expansion and projection of the governing equations onto stochastic basis functions, resulting in an extended system of equations. A relatively low-order generalized polynomial chaos expansion is sufficient to capture the stochastic solution for the problem considered. We derive boundary conditions for the continuous form of the stochastic Galerkin formulation of the velocity and pressure equations. The resulting problem formulation leads to an energy estimatemore » for the divergence. With suitable boundary data on the pressure and velocity, the energy estimate implies zero divergence of the velocity field. Based on the analysis of the continuous equations, we present a semi-discretized system where the spatial derivatives are approximated using finite difference operators with a summation-by-parts property. With a suitable choice of dissipative boundary conditions imposed weakly through penalty terms, the semi-discrete scheme is shown to be stable. Numerical experiments in the laminar flow regime corroborate the theoretical results and we obtain high-order accurate results for the solution variables and the velocity divergence converges to zero as the mesh is refined.« less

Simultaneous computation of jet turbulence and noise

NASA Technical Reports Server (NTRS)

Berman, C. H.; Ramos, J. I.

1989-01-01

The existing flow computation methods, wave computation techniques, and theories based on noise source models are reviewed in order to assess the capabilities of numerical techniques to compute jet turbulence noise and understand the physical mechanisms governing it over a range of subsonic and supersonic nozzle exit conditions. In particular, attention is given to (1) methods for extrapolating near field information, obtained from flow computations, to the acoustic far field and (2) the numerical solution of the time-dependent Lilley equation.

Applications and theory of electrokinetic enrichment in micro-nanofluidic chips.

PubMed

Chen, Xueye; Zhang, Shuai; Zhang, Lei; Yao, Zhen; Chen, Xiaodong; Zheng, Yue; Liu, Yanlin

2017-09-01

This review reports the progress on the recent development of electrokinetic enrichment in micro-nanofluidic chips. The governing equations of electrokinetic enrichment in micro-nanofluidic chips are given. Various enrichment applications including protein analysis, DNA analysis, bacteria analysis, viruses analysis and cell analysis are illustrated and discussed. The advantages and difficulties of each enrichment method are expatiated. This paper will provide a particularly convenient and valuable reference to those who intend to research the electrokinetic enrichment based on micro-nanofluidic chips.

Global conservation model for a mushy region over a moving substrate

NASA Astrophysics Data System (ADS)

Kyselica, J.; Šimkanin, J.

2018-03-01

We study solidification over a cool substrate moving with a relative velocity with respect to the rest of the fluid. A mathematical model based on global conservation of solute is presented. The explicit solutions of the governing equations are found and analysed via the asymptotic methods. The assessment of how the boundary-layer flow influences the physical characteristics of the mushy region is given, together with the discussion of a possible connection with the solidification at the inner core boundary.

Effects of spacecraft motions on fluids experiments

NASA Technical Reports Server (NTRS)

Gans, R. F.

1981-01-01

The equations of motion governing an incompressible fluid contained in an orbiting laboratory were examined to isolate various fictitious forces and their relative influence on the fluid. The forces are divided into those arising from the orbital motions and those arising from small local motions of the spacecraft about its center of mass. The latter dominate the nonrotating experiments. Both are important for rotating experiments. A brief discussion of the onset of time-dependence and violent instability in earth-based rotating and processing systems is given.

Effects of Contact Load on the Fretting Fatigue Behavior of IN-100 at Elevated Temperature

DTIC Science & Technology

2009-03-01

initiated crack. The bulk stress dominates the third stage as the crack continues to propagate further. The fourth and final stage occurs when either the...two contacting bodies . The following equation governs the contact region: )()(1)( * 1 xqd x p x xh A βς ς ς πδ δ − − = ∫ (2.1) where )()()( 21...two contact bodies respectively. The determination of the Young’s modulus for this experimental setup is discussed in Appendix C. Based on the

Dynamic response of a riser under excitation of internal waves

NASA Astrophysics Data System (ADS)

Lou, Min; Yu, Chenglong; Chen, Peng

2015-12-01

In this paper, the dynamic response of a marine riser under excitation of internal waves is studied. With the linear approximation, the governing equation of internal waves is given. Based on the rigid-lid boundary condition assumption, the equation is solved by Thompson-Haskell method. Thus the velocity field of internal waves is obtained by the continuity equation. Combined with the modified Morison formula, using finite element method, the motion equation of riser is solved in time domain with Newmark-β method. The computation programs are compiled to solve the differential equations in time domain. Then we get the numerical results, including riser displacement and transfiguration. It is observed that the internal wave will result in circular shear flow, and the first two modes have a dominant effect on dynamic response of the marine riser. In the high mode, the response diminishes rapidly. In different modes of internal waves, the deformation of riser has different shapes, and the location of maximum displacement shifts. Studies on wave parameters indicate that the wave amplitude plays a considerable role in response displacement of riser, while the wave frequency contributes little. Nevertheless, the internal waves of high wave frequency will lead to a high-frequency oscillation of riser; it possibly gives rise to fatigue crack extension and partial fatigue failure.

Human body surface area: a theoretical approach.

PubMed

Wang, Jianfeng; Hihara, Eiji

2004-04-01

Knowledge of the human body surface area has important applications in medical practice, garment design, and other engineering sizing. Therefore, it is not surprising that several expressions correlating body surface area with direct measurements of body mass and length have been reported in the literature. In the present study, based on the assumption that the exterior shape of the human body is the result of convex and concave deformations from a basic cylinder, we derive a theoretical equation minimizing body surface area (BSA) at a fixed volume (V): BSA=(9pi VL)(0.5), where L is the reference length of the body. Assuming a body density value of 1,000 kg.m(-3), the equation becomes BSA=(BM.BH/35.37)(0.5), where BSA is in square meters, BM is the body mass in kilograms, and BH is the body height in meters. BSA values calculated by means of this equation fall within +/-7% of the values obtained by means of the equations available in the literature, in the range of BSA from children to adults. It is also suggested that the above equation, which is obtained by minimizing the outer body surface at a fixed volume, implies a fundamental relation set by the geometrical constraints governing the growth and the development of the human body.

Simulation of hot spots formation and evolution in HMX

NASA Astrophysics Data System (ADS)

Wang, Cheng; Yang, Tonghui

2017-06-01

In order to study the formation and evolution of hot spots under shock loading, HMX explosives were selected as the object of study for the two-dimensional finite difference numerical simulation. A fifth order finite difference weighted essentially non-oscillatory (WENO) scheme and a third order TVD Runge-Kutta method are utilized for the spatial discretization and the time advance, respectively. The governing equations are based on the fluid elasto-plastic control equations. The Mie-Gruneisen equation of state and the ideal gas equation of state are selected to use in the state equation of the solid explosives and gas material. In order to simplify the calculation of the model, the reaction can be considered to complete in one step. The calculated area is [ 3.0 ×10-5 m ] × [ 3.0 ×10-5 m ] . The radius is 0.6 ×10-5 m, and the internal gas is not involved in the reaction. The calculation area is divided into 300×300 grids and 10 grids are selected from the bottom of each column to give the particle velocity u as the initial condition. In the selected grid, different initial velocity 100m/s and 200m/s are loaded respectively to study the influence of hot spot formation and evolution in different impact intensity.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Convection Heat and Mass Transfer in a Power Law Fluid with Non Constant Relaxation Time Past a Vertical Porous Plate in the Presence of Thermo and Thermal Diffusion

NASA Astrophysics Data System (ADS)

Olajuwon, B. I.; Oyelakin, I. S.

2012-12-01

The paper investigates convection heat and mass transfer in power law fluid flow with non relaxation time past a vertical porous plate in presence of a chemical reaction, heat generation, thermo diffu- sion and thermal diffusion. The non - linear partial differential equations governing the flow are transformed into ordinary differential equations using the usual similarity method. The resulting similarity equations are solved numerically using Runge-Kutta shooting method. The results are presented as velocity, temperature and concentration profiles for pseudo plastic fluids and for different values of parameters governing the prob- lem. The skin friction, heat transfer and mass transfer rates are presented numerically in tabular form. The results show that these parameters have significant effects on the flow, heat transfer and mass transfer.

Transport equations in an enzymatic glucose fuel cell

NASA Astrophysics Data System (ADS)

Jariwala, Soham; Krishnamurthy, Balaji

2018-01-01

A mathematical model is developed to study the effects of convective flux and operating temperature on the performance of an enzymatic glucose fuel cell with a membrane. The model assumes isothermal operating conditions and constant feed rate of glucose. The glucose fuel cell domain is divided into five sections, with governing equations describing transport characteristics in each region, namely - anode diffusion layer, anode catalyst layer (enzyme layer), membrane, cathode catalyst layer and cathode diffusion layer. The mass transport is assumed to be one-dimensional and the governing equations are solved numerically. The effects flow rate of glucose feed on the performance of the fuel cell are studied as it contributes significantly to the convective flux. The effects of operating temperature on the performance of a glucose fuel cell are also modeled. The cell performances are compared using cell polarization curves, which were found compliant with experimental observations.

Preliminary study of the effects of a reversible chemical reaction on gas bubble dissolution. [for space glass refining

NASA Technical Reports Server (NTRS)

Weinberg, M. C.

1982-01-01

A preliminary investigation is carried out of the effects of a reversible chemical reaction on the dissolution of an isolated, stationary gas bubble in a glass melt. The exact governing equations for the model system are formulated and analyzed. The approximate quasi-steady-state version of these equations is solved analytically, and a calculation is made of bubble dissolution rates. The results are then compared with numerical solutions obtained from the finite difference form of the exact governing equations. It is pointed out that in the microgravity condition of space, the buoyant rise of a gas bubble in a glass melt will be negligible on the time scale of most experiments. For this reason, a determination of the behavior of a stationary gas bubble in a melt is relevant for an understanding of glass refining in space.

Wind-US User's Guide, Version 2.0

NASA Technical Reports Server (NTRS)

Towne, Charles E.

2009-01-01

Wind-US is a computational platform which may be used to numerically solve various sets of equations governing physical phenomena. Currently, the code supports the solution of the Euler and Navier-Stokes equations of fluid mechanics, along with supporting equation sets governing turbulent and chemically reacting flows. Wind-US is a product of the NPARC Alliance, a partnership between the NASA Glenn Research Center (GRC) and the Arnold Engineering Development Center (AEDC) dedicated to the establishment of a national, applications-oriented flow simulation capability. The Boeing Company has also been closely associated with the Alliance since its inception, and represents the interests of the NPARC User's Association. The "Wind-US User's Guide" describes the operation and use of Wind-US, including: a basic tutorial; the physical and numerical models that are used; the boundary conditions; monitoring convergence; the files that are read and/or written; parallel execution; and a complete list of input keywords and test options.

Mixed convection boundary layer flow over a moving vertical flat plate in an external fluid flow with viscous dissipation effect.

PubMed

Bachok, Norfifah; Ishak, Anuar; Pop, Ioan

2013-01-01

The steady boundary layer flow of a viscous and incompressible fluid over a moving vertical flat plate in an external moving fluid with viscous dissipation is theoretically investigated. Using appropriate similarity variables, the governing system of partial differential equations is transformed into a system of ordinary (similarity) differential equations, which is then solved numerically using a Maple software. Results for the skin friction or shear stress coefficient, local Nusselt number, velocity and temperature profiles are presented for different values of the governing parameters. It is found that the set of the similarity equations has unique solutions, dual solutions or no solutions, depending on the values of the mixed convection parameter, the velocity ratio parameter and the Eckert number. The Eckert number significantly affects the surface shear stress as well as the heat transfer rate at the surface.

Modeling of outgassing and matrix decomposition in carbon-phenolic composites

NASA Technical Reports Server (NTRS)

Mcmanus, Hugh L.

1994-01-01

Work done in the period Jan. - June 1994 is summarized. Two threads of research have been followed. First, the thermodynamics approach was used to model the chemical and mechanical responses of composites exposed to high temperatures. The thermodynamics approach lends itself easily to the usage of variational principles. This thermodynamic-variational approach has been applied to the transpiration cooling problem. The second thread is the development of a better algorithm to solve the governing equations resulting from the modeling. Explicit finite difference method is explored for solving the governing nonlinear, partial differential equations. The method allows detailed material models to be included and solution on massively parallel supercomputers. To demonstrate the feasibility of the explicit scheme in solving nonlinear partial differential equations, a transpiration cooling problem was solved. Some interesting transient behaviors were captured such as stress waves and small spatial oscillations of transient pressure distribution.

The terminal area simulation system. Volume 1: Theoretical formulation

NASA Technical Reports Server (NTRS)

Proctor, F. H.

1987-01-01

A three-dimensional numerical cloud model was developed for the general purpose of studying convective phenomena. The model utilizes a time splitting integration procedure in the numerical solution of the compressible nonhydrostatic primitive equations. Turbulence closure is achieved by a conventional first-order diagnostic approximation. Open lateral boundaries are incorporated which minimize wave reflection and which do not induce domain-wide mass trends. Microphysical processes are governed by prognostic equations for potential temperature water vapor, cloud droplets, ice crystals, rain, snow, and hail. Microphysical interactions are computed by numerous Orville-type parameterizations. A diagnostic surface boundary layer is parameterized assuming Monin-Obukhov similarity theory. The governing equation set is approximated on a staggered three-dimensional grid with quadratic-conservative central space differencing. Time differencing is approximated by the second-order Adams-Bashforth method. The vertical grid spacing may be either linear or stretched. The model domain may translate along with a convective cell, even at variable speeds.

The development of a three-dimensional partially elliptic flow computer program for combustor research

NASA Technical Reports Server (NTRS)

Pan, Y. S.

1978-01-01

A three dimensional, partially elliptic, computer program was developed. Without requiring three dimensional computer storage locations for all flow variables, the partially elliptic program is capable of predicting three dimensional combustor flow fields with large downstream effects. The program requires only slight increase of computer storage over the parabolic flow program from which it was developed. A finite difference formulation for a three dimensional, fully elliptic, turbulent, reacting, flow field was derived. Because of the negligible diffusion effects in the main flow direction in a supersonic combustor, the set of finite-difference equations can be reduced to a partially elliptic form. Only the pressure field was governed by an elliptic equation and requires three dimensional storage; all other dependent variables are governed by parabolic equations. A numerical procedure which combines a marching integration scheme with an iterative scheme for solving the elliptic pressure was adopted.

Elliptic Euler-Poisson-Darboux equation, critical points and integrable systems

NASA Astrophysics Data System (ADS)

Konopelchenko, B. G.; Ortenzi, G.

2013-12-01

The structure and properties of families of critical points for classes of functions W(z,{\\overline{z}}) obeying the elliptic Euler-Poisson-Darboux equation E(1/2, 1/2) are studied. General variational and differential equations governing the dependence of critical points in variational (deformation) parameters are found. Explicit examples of the corresponding integrable quasi-linear differential systems and hierarchies are presented. There are the extended dispersionless Toda/nonlinear Schrödinger hierarchies, the ‘inverse’ hierarchy and equations associated with the real-analytic Eisenstein series E(\\beta ,{\\overline{\\beta }};1/2) among them. The specific bi-Hamiltonian structure of these equations is also discussed.

Admitting the Inadmissible: Adjoint Formulation for Incomplete Cost Functionals in Aerodynamic Optimization

NASA Technical Reports Server (NTRS)

Arian, Eyal; Salas, Manuel D.

1997-01-01

We derive the adjoint equations for problems in aerodynamic optimization which are improperly considered as "inadmissible." For example, a cost functional which depends on the density, rather than on the pressure, is considered "inadmissible" for an optimization problem governed by the Euler equations. We show that for such problems additional terms should be included in the Lagrangian functional when deriving the adjoint equations. These terms are obtained from the restriction of the interior PDE to the control surface. Demonstrations of the explicit derivation of the adjoint equations for "inadmissible" cost functionals are given for the potential, Euler, and Navier-Stokes equations.

Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Anderson, W. Kyle

1998-01-01

A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompressible solvers are differentiated and the accuracy of the sensitivity derivatives is verified by comparing with gradients obtained using finite differences. Several simplifying approximations to the complete linearization of the residual are also presented, and the resulting accuracy of the derivatives is examined. Demonstration optimizations for both compressible and incompressible flows are given.

Statistical properties of Charney-Hasegawa-Mima zonal flows

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

Anderson, Johan, E-mail: anderson.johan@gmail.com; Botha, G. J. J.

2015-05-15

A theoretical interpretation of numerically generated probability density functions (PDFs) of intermittent plasma transport events in unforced zonal flows is provided within the Charney-Hasegawa-Mima (CHM) model. The governing equation is solved numerically with various prescribed density gradients that are designed to produce different configurations of parallel and anti-parallel streams. Long-lasting vortices form whose flow is governed by the zonal streams. It is found that the numerically generated PDFs can be matched with analytical predictions of PDFs based on the instanton method by removing the autocorrelations from the time series. In many instances, the statistics generated by the CHM dynamics relaxesmore » to Gaussian distributions for both the electrostatic and vorticity perturbations, whereas in areas with strong nonlinear interactions it is found that the PDFs are exponentially distributed.« less

Simplified analysis and optimization of space base and space shuttle heat rejection systems

NASA Technical Reports Server (NTRS)

Wulff, W.

1972-01-01

A simplified radiator system analysis was performed to predict steady state radiator system performance. The system performance was found to be describable in terms of five non-dimensional system parameters. The governing differential equations are integrated numerically to yield the enthalpy rejection for the coolant fluid. The simplified analysis was extended to produce the derivatives of the coolant exit temperature with respect to the governing system parameters. A procedure was developed to find the optimum set of system parameters which yields the lowest possible coolant exit temperature for either a given projected area or a given total mass. The process can be inverted to yield either the minimum area or the minimum mass, together with the optimum geometry, for a specified heat rejection rate.

Non-linear instability analysis of the two-dimensional Navier-Stokes equation: The Taylor-Green vortex problem

NASA Astrophysics Data System (ADS)

Sengupta, Tapan K.; Sharma, Nidhi; Sengupta, Aditi

2018-05-01

An enstrophy-based non-linear instability analysis of the Navier-Stokes equation for two-dimensional (2D) flows is presented here, using the Taylor-Green vortex (TGV) problem as an example. This problem admits a time-dependent analytical solution as the base flow, whose instability is traced here. The numerical study of the evolution of the Taylor-Green vortices shows that the flow becomes turbulent, but an explanation for this transition has not been advanced so far. The deviation of the numerical solution from the analytical solution is studied here using a high accuracy compact scheme on a non-uniform grid (NUC6), with the fourth-order Runge-Kutta method. The stream function-vorticity (ψ, ω) formulation of the governing equations is solved here in a periodic square domain with four vortices at t = 0. Simulations performed at different Reynolds numbers reveal that numerical errors in computations induce a breakdown of symmetry and simultaneous fragmentation of vortices. It is shown that the actual physical instability is triggered by the growth of disturbances and is explained by the evolution of disturbance mechanical energy and enstrophy. The disturbance evolution equations have been traced by looking at (a) disturbance mechanical energy of the Navier-Stokes equation, as described in the work of Sengupta et al., "Vortex-induced instability of an incompressible wall-bounded shear layer," J. Fluid Mech. 493, 277-286 (2003), and (b) the creation of rotationality via the enstrophy transport equation in the work of Sengupta et al., "Diffusion in inhomogeneous flows: Unique equilibrium state in an internal flow," Comput. Fluids 88, 440-451 (2013).

'Butterfly effect' in porous Bénard convection heated from below

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

Siri, Z.; Liew, K. Y.; Ibrahim, R. I.

2014-07-10

Transition from steady to chaos for the onset of Bénard convection in porous medium was analyzed. The governing equation is reduced to ordinary differential equation and solved using built in MATLAB ODE45. The transition from steady to chaos take over from a limit cycle followed by homoclinic explosion.

Constraint elimination in dynamical systems

NASA Technical Reports Server (NTRS)

Singh, R. P.; Likins, P. W.

1989-01-01

Large space structures (LSSs) and other dynamical systems of current interest are often extremely complex assemblies of rigid and flexible bodies subjected to kinematical constraints. A formulation is presented for the governing equations of constrained multibody systems via the application of singular value decomposition (SVD). The resulting equations of motion are shown to be of minimum dimension.

Creeping gaseous flows through elastic tube and annulus micro-configurations

NASA Astrophysics Data System (ADS)

Elbaz, Shai; Jacob, Hila; Gat, Amir

2016-11-01

Gaseous flows in elastic micro-configurations is relevant to biological systems (e.g. alveolar ducts in the lungs) as well as to applications such as gas actuated soft micro-robots. We here examine the effect of low-Mach-number compressibility on creeping gaseous axial flows through linearly elastic tube and annulus micro-configurations. For steady flows, the leading-order effects of elasticity on the pressure distribution and mass-flux are obtained. For transient flow in a tube with small deformations, elastic effects are shown to be negligible in leading order due to compressibility. We then examine transient flows in annular configurations where the deformation is significant compared with the gap between the inner and outer cylinders defining the annulus. Both compressibility and elasticity are obtained as dominant terms interacting with viscosity. For a sudden flux impulse, the governing non-linear leading order diffusion equation is initially approximated by a porous-medium-equation of order 2.5 for the pressure square. However, as the fluid expand and the pressure decreases, the governing equation degenerates to a porous-medium-equation of order 2 for the pressure.

Diffusion of chemically reactive species in MHD oscillatory flow with thermal radiation in the presence of constant suction and injection

NASA Astrophysics Data System (ADS)

Sasikumar, J.; Bhuvaneshwari, S.; Govindarajan, A.

2018-04-01

In this project, it is proposed to investigate the effect of suction/injection on the unsteady oscillatory flow of an incompressible viscous electrically conducting fluid through a channel filled with porous medium and non-uniform wall temperature. The fluid is subjected to a uniform magnetic field normal to the channel and the velocity slip at the cold plate is taken into consideration. With the assumption of magnetic Reynolds number to be very small, the induced magnetic field is neglected. Assuming pressure gradient to be oscillatory across the ends of the channel, resulting flow as unsteady oscillatory flow. Under the usual Bousinessq approximation, a mathematical model representing this fluid flow consisting of governing equations with boundary conditions will be developed. Closed form solutions of the dimensionless governing equations of the fluid flow, namely momentum equation, energy equation and species concentration can be obtained . The effects of heat radiation and chemical reaction with suction and injection on temperature, velocity and species concentration profiles will be analysed with tables and graphs.

Numerical Analysis of the Heat Transfer Characteristics within an Evaporating Meniscus

NASA Astrophysics Data System (ADS)

Ball, Gregory

A numerical analysis was performed as to investigate the heat transfer characteristics of an evaporating thin-film meniscus. A mathematical model was used in the formulation of a third order ordinary differential equation. This equation governs the evaporating thin-film through use of continuity, momentum, energy equations and the Kelvin-Clapeyron model. This governing equation was treated as an initial value problem and was solved numerically using a Runge-Kutta technique. The numerical model uses varying thermophysical properties and boundary conditions such as channel width, applied superheat, accommodation coefficient and working fluid which can be tailored by the user. This work focused mainly on the effects of altering accommodation coefficient and applied superheat. A unified solution is also presented which models the meniscus to half channel width. The model was validated through comparison to literature values. In varying input values the following was determined; increasing superheat was found to shorten the film thickness and greatly increase the interfacial curvature overshoot values. The effect of decreasing accommodation coefficient lengthened the thin-film and retarded the evaporative effects.

Dispersion in tidally averaged transport equation

USGS Publications Warehouse

Cheng, R.T.; Casulli, V.

1992-01-01

A general governing inter-tidal transport equation for conservative solutes has been derived without invoking the weakly nonlinear approximation. The governing inter-tidal transport equation is a convection-dispersion equation in which the convective velocity is a mean Lagrangian residual current, and the inter-tidal dispersion coefficient is defined by a dispersion patch. When the weakly nonlinear condition is violated, the physical significance of the Stokes' drift, as used in tidal dynamics, becomes questionable. For nonlinear problems, analytical solutions for the mean Lagrangian residual current and for the inter-tidal dispersion coefficient do not exist, they must be determined numerically. A rectangular tidal inlet with a constriction is used in the first example. The solutions of the residual currents and the computed properties of the inter-tidal dispersion coefficient are used to illuminate the mechanisms of the inter-tidal transport processes. Then, the present formulation is tested in a geometrically complex tidal estuary – San Francisco Bay, California. The computed inter-tidal dispersion coefficients are in the range between 5×104 and 5×106 cm2/sec., which are consistent with the values reported in the literature

The Principle of Energetic Consistency: Application to the Shallow-Water Equations

NASA Technical Reports Server (NTRS)

Cohn, Stephen E.

2009-01-01

If the complete state of the earth's atmosphere (e.g., pressure, temperature, winds and humidity, everywhere throughout the atmosphere) were known at any particular initial time, then solving the equations that govern the dynamical behavior of the atmosphere would give the complete state at all subsequent times. Part of the difficulty of weather prediction is that the governing equations can only be solved approximately, which is what weather prediction models do. But weather forecasts would still be far from perfect even if the equations could be solved exactly, because the atmospheric state is not and cannot be known completely at any initial forecast time. Rather, the initial state for a weather forecast can only be estimated from incomplete observations taken near the initial time, through a process known as data assimilation. Weather prediction models carry out their computations on a grid of points covering the earth's atmosphere. The formulation of these models is guided by a mathematical convergence theory which guarantees that, given the exact initial state, the model solution approaches the exact solution of the governing equations as the computational grid is made more fine. For the data assimilation process, however, there does not yet exist a convergence theory. This book chapter represents an effort to begin establishing a convergence theory for data assimilation methods. The main result, which is called the principle of energetic consistency, provides a necessary condition that a convergent method must satisfy. Current methods violate this principle, as shown in earlier work of the author, and therefore are not convergent. The principle is illustrated by showing how to apply it as a simple test of convergence for proposed methods.

Macroscopic constitutive equations of thermo-poroviscoelasticity derived using eigenstrains

NASA Astrophysics Data System (ADS)

Suvorov, A. P.; Selvadurai, A. P. S.

2010-10-01

Macroscopic constitutive equations for thermo-viscoelastic processes in a fully saturated porous medium are re-derived from basic principles of micromechanics applicable to solid multi-phase materials such as composites. Simple derivations of the constitutive relations and the void occupancy relationship are presented. The derivations use the notion of eigenstrain or, equivalently, eigenstress applied to the separate phases of a porous medium. Governing coupled equations for the displacement components and the fluid pressure are also obtained.

The application of MINIQUASI to thermal program boundary and initial value problems

NASA Technical Reports Server (NTRS)

1974-01-01

The feasibility of applying the solution techniques of Miniquasi to the set of equations which govern a thermoregulatory model is investigated. For solving nonlinear equations and/or boundary conditions, a Taylor Series expansion is required for linearization of both equations and boundary conditions. The solutions are iterative and in each iteration, a problem like the linear case is solved. It is shown that Miniquasi cannot be applied to the thermoregulatory model as originally planned.

Analytic approach to photoelectron transport.

NASA Technical Reports Server (NTRS)

Stolarski, R. S.

1972-01-01

The equation governing the transport of photoelectrons in the ionosphere is shown to be equivalent to the equation of radiative transfer. In the single-energy approximation this equation is solved in closed form by the method of discrete ordinates for isotropic scattering and for a single-constituent atmosphere. The results include prediction of the angular distribution of photoelectrons at all altitudes and, in particular, the angular distribution of the escape flux. The implications of these solutions in real atmosphere calculations are discussed.

Another look at North Sea pole tide dynamics

NASA Technical Reports Server (NTRS)

Dickman, S. R.; Preisig, J. R.

1986-01-01

The mechanism proposed by Wunsch (1974) to explain pole tide observations in the North Sea is evaluated. Wunsch's equations governing pole tide in the North Sea are presented, and solutions for correcting the depth, stream function, and deviation of the tidal height from the equilibrium values are described. The similarity between the Stokes paradox and the tidal equations of the North Sea, and the need for inclusion of inertial terms in the tidal equations are discussed.

Perturbed soliton excitations of Rao-dust Alfvén waves in magnetized dusty plasmas

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

Kavitha, L., E-mail: louiskavitha@yahoo.co.in; The Abdus Salam International Centre for Theoretical Physics, Trieste; Lavanya, C.

We investigate the propagation dynamics of the perturbed soliton excitations in a three component fully ionized dusty magnetoplasma consisting of electrons, ions, and heavy charged dust particulates. We derive the governing equation of motion for the two dimensional Rao-dust magnetohydrodynamic (R-D-MHD) wave by employing the inertialess electron equation of motion, inertial ion equation of motion, the continuity equations in a plasma with immobile charged dust grains, together with the Maxwell's equations, by assuming quasi neutrality and neglecting the displacement current in Ampere's law. Furthermore, we assume the massive dust particles are practically immobile since we are interested in timescales muchmore » shorter than the dusty plasma period, thereby neglecting any damping of the modes due to the grain charge fluctuations. We invoke the reductive perturbation method to represent the governing dynamics by a perturbed cubic nonlinear Schrödinger (pCNLS) equation. We solve the pCNLS, along the lines of Kodama-Ablowitz multiple scale nonlinear perturbation technique and explored the R-D-MHD waves as solitary wave excitations in a magnetized dusty plasma. Since Alfvén waves play an important role in energy transport in driving field-aligned currents, particle acceleration and heating, solar flares, and the solar wind, this representation of R-D-MHD waves as soliton excitations may have extensive applications to study the lower part of the earth's ionosphere.« less