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At least 523 records · Page 29

Recent developments in shock-capturing schemes

The development of the shock capturing methodology is reviewed, paying special attention to the increasing nonlinearity in its design and its relation to interpolation. It is well-known that higher-order approximations to a discontinuous function generate spurious oscillations near the discontinuity (Gibbs phenomenon). Unlike standard finite-difference methods which use a fixed stencil, modern shock capturing schemes use an adaptive stencil which is selected according to the local smoothness of the solution. Near discontinuities this technique automatically switches to one-sided approximations, thus avoiding the use of discontinuous data which brings about spurious oscillations.

Harten, Ami↗

Mixing and non-equilibrium chemical reaction in a compressible mixing layer

The effects of compressibility, chemical reaction exothermicity, and non-equilibrium chemical modeling in a reacting plane mixing layer were investigated by means of two dimensional direct numerical simulations. The chemical reaction was irreversible and second order of the type A + B yields Products + Heat. The general governing fluid equations of a compressible reacting flow field were solved by means of high order finite difference methods. Physical effects were then determined by examining the response of the mixing layer to variation of the relevant non-dimensionalized parameters. The simulations show that increased compressibility generally results in a suppressed mixing, and consequently a reduced chemical reaction conversion rate. Reaction heat release was found to enhance mixing at the initial stages of the layer growth, but had a stabilizing effect at later times. The increased stability manifested itself in the suppression or delay of the formation of large coherent structures within the flow. Calculations were performed for a constant rate chemical kinetics model and an Arrhenius type kinetic prototype. The choice of the model was shown to have an effect on the development of the flow. The Arrhenius model caused a greater temperature increase due to reaction than the constant kinetic model. This had the same effect as increasing the exothermicity of the reaction. Localized flame quenching was also observed when the Zeldovich number was relatively large.

Steinberger, Craig J.↗

Mathematical modeling of the flow field and particle motion in a rotating bioreactor at unit gravity and microgravity

The biotechnology group at NASA Johnson Space Center is developing systems for culturing mammalian cells that stimulate some aspect of microgravity and provide a low shear environment for microgravity-based studies on suspension and anchorage dependent cells. The design of these vessels for culturing cells is based on the need to suspend cells and aggregates of cells and microcarrier beads continually in the culturing medium. The design must also provide sufficient circulation for adequate mass transfer of nutrients to the cells and minimize the total force on the cells. Forces, resulting from sources such as hydrodynamic fluid shear and collisions of cells and walls of the vessels, may damage delicate cells and degrade the formation of three dimensional structures. This study examines one particular design in both unit gravity and microgravity based on two concentric cylinders rotating in the same direction at different speeds to create a Couette flow between them. A numerical simulation for the flow field and the trajectories of particles in the vessel. The flow field for the circulation of the culturing medium is modeled by the Navier-Stokes equations. The forces on a particle are assumed to be drag from the fluid's circulation, buoyancy from the gravitational force and centrifugal force from the rotation of the vessel. The problem requires first solving the system of partial differential equations for the fluid flow by a finite difference method and then solving the system of ordinary differential equations for the trajectories by Gear's stiff method. Results of the study indicate that the trajectories in unit gravity and microgravity are very similar except for small spatial deviations on the fast time scale in unit gravity. The total force per unit cross sectional area on a particle in microgravity, however, is significantly smaller than the corresponding value in unit gravity, which is also smaller than anticipated. Hence, this study indicates that this design for a bioreactor with optimal rates of rotation can provide a good environment for culturing cells in microgravity with adequate circulation and minimal force on the cells.

Boyd, Ernest J.↗

Self-consistent analysis of lattice-matched and pseudomorphic quantum-well emission transistors

A self-consistent analysis of the quantum-well emission transistor (QWET) is presented allowing an exact calculation of the device quantum properties. Poisson's and Schroedinger's equation are solved numerically using a finite-difference method on a self-consistent basis. Pseudomorphic AlGaAs/InGaAs designs with 15-20 percent excess In are suggested for improving the device performance. Design with doping in various parts of the QWET are also studied. This analysis reveals that the device performance is less optimistic than previously predicted by analytic approaches. By introducing the pseudomorphic channel principle, while maintaining a reasonably low Al content for the gate and collector layers, it is, however, possible to obtain satisfactory performance. Optimum pseudomorphic designs showed high current driving capability (200,000 A/sq cm), high transconductance (3S/mm), and small intrinsic delay time (2 ps).

Hong, Kyushik↗

Vapor condensation at the free surface of an axisymmetric liquid mixed by a laminar jet

This paper presents numerical solutions of jet-induced mixing in a partially full cryogenic tank. An axisymmetric laminar jet is discharged from the central part of the tank bottom toward the liquid-vapor interface. Liquid is withdrawn at the same volume flow rate from the outer part of the tank. The jet is at a temperature lower than the interface, which is maintained at a certain saturation temperature. The interface is assumed to be flat and shear free and the condensation-induced velocity is assumed to be negligibly small compared with radial interface velocity. Finite-difference method is used to slove the nondimensional form of steady-state continuity, momentum, and energy equations. Calculations are conducted for jet Reynolds numbers ranging from 150 to 600 and Prandtl numbers ranging from 0.85 to 2.65. The effects of previously stated parameters on the condensation Nusselt and Stanton numbers that characterize the steady-state interface condensation process are investigated. Detailed analysis is performed to gain a better understanding of the fundamentals of fluid mixing and interface condensation.

Lin, Chin-Shun↗

Three-dimensional simulations of large eddies in the compressible mixing layer

Consideration is given to the effect of compressibility on a plane mixing layer that is a prototype free shear layer, amenable to study by numerical simulation and experiment. The full time-dependent compressible Navier-Stokes equations are solved numerically for a temporally evolving mixing layer employing a mixed spectral and high-order finite difference method. Simulations with random initial conditions confirm the prediction of linear stability theory that at high Mach numbers oblique waves grow faster than two-dimensional waves. Simulations are presented of the nonlinear temporal evolution of the most rapidly amplified linear instability waves.

Sandham, N. D.↗

Analysis of the one-dimensional transient compressible vapor flow in heat pipes

The transient compressible one-dimensional vapor flow dynamics in a heat pipe is modeled. The numerical results are obtained by using the implicit non-iterative Beam-Warming finite difference method. The model is tested for simulated heat pipe vapor flow and actual vapor flow in cylindrical heat pipes. A good comparison of the present transient results for the simulated heat pipe vapor flow with the previous results of a two-dimensional numerical model is achieved and the steady state results are in agreement with the existing experimental data. The transient behavior of the vapor flow under subsonic, sonic, and supersonic speeds as well as high mass flow rates are successfully predicted.

Jang, Jong H.↗

Spurious Solutions Of Nonlinear Differential Equations

Report utilizes nonlinear-dynamics approach to investigate possible sources of errors and slow convergence and non-convergence of steady-state numerical solutions when using time-dependent approach for problems containing nonlinear source terms. Emphasizes implications for development of algorithms in CFD and computational sciences in general. Main fundamental conclusion of study is that qualitative features of nonlinear differential equations cannot be adequately represented by finite-difference method and vice versa.

Yee, H. C.↗

A Martian global groundwater model

A global groundwater flow model was constructed for Mars to study hydrologic response under a variety of scenarios, improving and extending earlier simple cross sectional models. The model is capable of treating both steady state and transient flow as well as permeability that is anisotropic in the horizontal dimensions. A single near surface confining layer may be included (representing in these simulations a coherent permafrost layer). Furthermore, in unconfined flow, locations of complete saturation and seepage are determined. The flow model assumes that groundwater gradients are sufficiently low that DuPuit conditions are satisfied and the flow component perpendicular to the ground surface is negligible. The flow equations were solved using a finite difference method employing 10 deg spacing of latitude and longitude.

Howard, Alan D.↗

Fragmentation in stellar collapse

A three dimensional Cartesian code was developed to model molecular cloud collapse and protostellar formation. The basic Eulerian scheme employs spatially second-order accurate, finite difference methods to advance the fluid variables in time. The hydrodynamic equations governing the collapse include the effects of self-gravity, rotation, and radiative transfer. Supplementary equations include Poisson's equation which relates the gravitational potential to the density distribution and a mean intensity equation derived with the Eddington approximation for radiative transfer. The gas pressures and internal energies are determined from equations of state derived for a molecular cloud composed of hydrogen, helium, and heavier elements.

Myhill, E. M.↗

An assessment and application of turbulence models for hypersonic flows

The current approach to the Accurate Computation of Complex high-speed flows is to solve the Reynolds averaged Navier-Stokes equations using finite difference methods. An integral part of this approach consists of development and applications of mathematical turbulence models which are necessary in predicting the aerothermodynamic loads on the vehicle and the performance of the propulsion plant. Computations of several high speed turbulent flows using various turbulence models are described and the models are evaluated by comparing computations with the results of experimental measurements. The cases investigated include flows over insulated and cooled flat plates with Mach numbers ranging from 2 to 8 and wall temperature ratios ranging from 0.2 to 1.0. The turbulence models investigated include zero-equation, two-equation, and Reynolds-stress transport models.

Coakley, T. J.↗

Effect of leading-edge geometry on boundary-layer receptivity to freestream sound

The receptivity to freestream sound of the laminar boundary layer over a semi-infinite flat plate with an elliptic leading edge is simulated numerically. The incompressible flow past the flat plate is computed by solving the full Navier-Stokes equations in general curvilinear coordinates. A finite-difference method which is second-order accurate in space and time is used. Spatial and temporal developments of the Tollmien-Schlichting wave in the boundary layer, due to small-amplitude time-harmonic oscillations of the freestream velocity that closely simulate a sound wave travelling parallel to the plate, are observed. The effect of leading-edge curvature is studied by varying the aspect ratio of the ellipse. The boundary layer over the flat plate with a sharper leading edge is found to be less receptive. The relative contribution of the discontinuity in curvature at the ellipse-flat-plate juncture to receptivity is investigated by smoothing the juncture with a polynomial. Continuous curvature leads to less receptivity. A new geometry of the leading edge, a modified super ellipse, which provides continuous curvature at the juncture with the flat plate, is used to study the effect of continuous curvature and inherent pressure gradient on receptivity.

Lin, Nay↗

Development of an integrated BEM approach for hot fluid structure interaction: BEST-FSI: Boundary Element Solution Technique for Fluid Structure Interaction

As part of the continuing effort at NASA LeRC to improve both the durability and reliability of hot section Earth-to-orbit engine components, significant enhancements must be made in existing finite element and finite difference methods, and advanced techniques, such as the boundary element method (BEM), must be explored. The BEM was chosen as the basic analysis tool because the critical variables (temperature, flux, displacement, and traction) can be very precisely determined with a boundary-based discretization scheme. Additionally, model preparation is considerably simplified compared to the more familiar domain-based methods. Furthermore, the hyperbolic character of high speed flow is captured through the use of an analytical fundamental solution, eliminating the dependence of the solution on the discretization pattern. The price that must be paid in order to realize these advantages is that any BEM formulation requires a considerable amount of analytical work, which is typically absent in the other numerical methods. All of the research accomplishments of a multi-year program aimed toward the development of a boundary element formulation for the study of hot fluid-structure interaction in Earth-to-orbit engine hot section components are detailed. Most of the effort was directed toward the examination of fluid flow, since BEM's for fluids are at a much less developed state. However, significant strides were made, not only in the analysis of thermoviscous fluids, but also in the solution of the fluid-structure interaction problem.

Dargush, G. F.↗

Thermal calibration and analysis of a Bridgman flight furnace

A combination of computer modeling and experimental measurements is proposed which permits the calibration of the temperature profile for a spacecraft flight furnace. The Fluent code based on the finite difference method uses the furnace set-point temperatures as boundary conditions to model a Bridgman directional solidification furnace. Experimental measurements are employed as a comparison for the numerical analysis, and the radial gradients and wall temperatures are selected when the calculated values are sufficiently close to those from measurements. The calculations are found to agree with experimental data, and some results of the modeling are given which relate to specific furnace parameters. The CFD approach facilitates the transposition of furnace calibration to microgravitational operation in addition to providing precise initial radial temperature gradients and furnace-wall temperatures.

Knuteson, D. J.↗

Waveform effects of a metastable olivine tongue in subducting slabs

Velocity models of subducting slabs with a kinetically-depressed olivine to beta- and gamma-spinel transition are constructed, and the effect that such structures would have on teleseismic P waveforms are examined using a full-wave finite-difference method. These 2D calculations yielded waveforms at a range of distances in the downdip direction. The slab models included a wedge-shaped, low-velocity metastable olivine tongue (MOTO) to a depth of 670 km, as well as a plausible thermal anomaly; one model further included a 10-km-thick fast layer on the surface of the slab. The principal effect of MOTO is to produce grazing reflections at wide angles off the phase boundary, generating a secondary arrival 0 to 4 seconds after the initial arrival depending on the take-off angle. The amplitude and timing of this feature vary with the lateral location of the seismic source within the slab cross-section.

Vidale, John E.↗

Numerical models for the collapse and fragmentation of centrally condensed molecular cloud cores

The gravitational collapse and fragmentation of centrally condensed molecular cloud cores are investigated using a new hydrodynamical code. The numerical scheme is second-order accurate and uses explicit finite difference methods to advance the fluid variables on a 3D Cartesian grid. Two initial power-law density profiles, rho varies as r exp -1 and rho varies as r exp -2, are considered, as well as two initial density perturbations in the azimuthal coordinate theta, rho-i - rho(1 + a cos 2theta) where a = 0.1 and 0.5. Fragmentation is found to be possible in these centrally condensed cores if the initial conditions also include differential rotation. Models which collapse with initial uniform rotation do not produce fragments. If molecular cloud cores are indeed centrally condensed, as suggested by observations of star-forming regions and by studies of ambipolar diffusion, then differential rotation may be a mechanism for producing binary protostars during gravitational collapse.

Myhill, Elizabeth A.↗

Convection in superposed fluid and porous layers

Thermal convection due to heating from below in a porous layer underlying a fluid layer has been analyzed using the Navier-Stokes equations for the fluid layers and the extended Darcy equation (including Brinkman and Forchheimer terms) for the porous layer. The flow is assumed to be two-dimensional and periodic in the horizontal direction. The numerical scheme used is a combined Galerkin and finite-difference method, and appropriate boundary conditions are applied at the interface. Results have been obtained for depth ratios of 0, 0.1, 0.2, 0.5, and 1.0, where this ratio is defined as the ratio of the thickness of the fluid layer to that of the porous layer. For the depth ratio of 0.1, the convection is dominated by the porous layer, similar to the situation at onset, even though the Rayleigh number for the fluid layer is well into the supercritical regime.

Chen, Falin↗

Boundary-layer receptivity due to a wall suction and control of Tollmien-Schlichting waves

A numerical study of the generation of Tollmien-Schlichting (T-S) waves due to the interaction between a small free-stream disturbance and a small localized suction slot on an otherwise flat surface was carried out using finite difference methods. The nonlinear steady flow is of the viscous-inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier-Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of T-S waves generated by the interaction between the free-stream disturbance and the suction slot, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T-S waves and the demonstration of the possible active control of the growth of T-S waves.

Bodonyi, R. J.↗