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At least 235 records · Page 13

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NASA NTRS1993

An upwind multigrid method for solving viscous flows on unstructured triangular meshes

A multigrid algorithm is combined with an upwind scheme for solving the two dimensional Reynolds averaged Navier-Stokes equations on triangular meshes resulting in an efficient, accurate code for solving complex flows around multiple bodies. The relaxation scheme uses a backward-Euler time difference and relaxes the resulting linear system using a red-black procedure. Roe's flux-splitting scheme is used to discretize convective and pressure terms, while a central difference is used for the diffusive terms. The multigrid scheme is demonstrated for several flows around single and multi-element airfoils, including inviscid, laminar, and turbulent flows. The results show an appreciable speed up of the scheme for inviscid and laminar flows, and dramatic increases in efficiency for turbulent cases, especially those on increasingly refined grids.

Bonhaus, Daryl Lawrence↗

NASA NTRS2006

Simulations of Sea-Ice Dynamics Using the Material-Point Method

In recent years, the availability of large volumes of recorded ice motion derived from high-resolution SAR data has provided an amazingly detailed look at the deformation of the ice cover. The deformation is dominated by the appearance of linear kinematic features that have been associated with the presence of leads. These remarkable data put us in a position to begin detailed evaluation of current coupled mechanical and thermodynamic models of sea ice. This presentation will describe the material point method (MPM) for solving these model equations. MPM is a numerical method for continuum mechanics that combines the best aspects of Lagrangian and Eulerian discretizations. The material points provide a Lagrangian description of the ice that models convection naturally. Thus, properties such as ice thickness and compactness are computed in a Lagrangian frame and do not suffer from errors associated with Eulerian advection schemes, such as artificial diffusion, dispersion, or oscillations near discontinuities. This desirable property is illustrated by solving transport of ice in uniform, rotational and convergent velocity fields. Moreover, the ice geometry is represented by unconnected material points rather than a grid. This representation facilitates modeling the large deformations observed in the Arctic, as well as localized deformation along leads, and admits a sharp representation of the ice edge. MPM also easily allows the use of any ice constitutive model. The versatility of MPM is demonstrated by using two constitutive models for simulations of wind-driven ice. The first model is a standard viscous-plastic model with two thickness categories. The MPM solution to the viscous-plastic model agrees with previously published results using finite elements. The second model is a new elastic-decohesive model that explicitly represents leads. The model includes a mechanism to initiate leads, and to predict their orientation and width. The elastic-decohesion model can provide similar overall deformation as the viscous-plastic model; however, explicit regions of opening and shear are predicted. Furthermore, the efficiency of MPM with the elastic-decohesive model is competitive with the current best methods for sea ice dynamics. Simulations will also be presented for an area of the Beaufort Sea, where predictions can be validated against satellite observations of the Arctic.

Sulsky, D.↗

NASA NTRS1993

Pickup protons and water ions at Comet Halley - Comparisons with Giotto observations

The cometary ion pickup process along the sun-comet line at Comet Halley is investigated using a quasi-linear diffusion model including both pitch angle and energy diffusion, adiabatic compression, and convective motion with the solar wind flow. The model results are compared with energetic ion distributions observed by instruments on board the Giotto spacecraft. The observed power spectrum index of magnetic turbulence (gamma) is 2-2.5. The present simulation shows that when gamma was 2, the calculated proton distributions were much more isotropic than the observed ones. The numerical solutions of the quasi-linear diffusion equations show that the isotropization of the pickup ion distribution, particularly at the pickup velocity, is not complete even close to the bow shock. Given the observed turbulence level, quasi-linear theory yields pickup ion energy distributions that agree with the observed ones quite well and easily produces energetic ions with energies up to hundreds of keV.

Ye, G.↗

NASA NTRS1977

Atmospheric model development in support of SEASAT. Volume 3: Prediction models

As part of the SEASAT program of NASA, a set of four hemispheric, atmospheric models are developed. The four models use a polar stereographic grid in the horizontal and a sigma coordinate in the vertical. Conservation forms of the difference equations are integrated using either a fifteen or four minute time step on a 381 km or 127 km grid (at 60 deg N) for the 63 x 63 or 187 x 187 models respectively. A nonlinear pressure smoother is used along with momentum and temperature diffusion to help control computational noise. The horizontal boundary conditions are insulated slippery walls. Centered time differencing with time averaging of the pressure gradient force term in the momentum equations is used. Robert time filtering on of the temperature and moisture solutions is used for computational stability. The moisture and heat source/sink terms are modeled. Terms representing evaporation and large scale condensation, sensible heat exchange, parameterized cumulus convection and precipitation, and solar and terrestrial radiation are included. Initialization of the models is based on a pattern conservation technique to obtain objective analysis of the state parameter structure from the surface to 50 mb.

Wellck, R. E.↗

NASA NTRS1982

ADI on staggered mesh - A method for the calculation of compressible convection

An alternating direction implicit (ADI) method has been applied to a staggered grid for the computation of convection in a highly stratified fluid. Since artificial viscosity is not needed, subtle effects like the onset of convection can be studied. These computations compare well with the 2-D results by Graham (1975) and also agree with standard Boussinesq results when taken to that limit. Good efficiency has been achieved with a time step hundreds of times larger than the stability limit imposed by the explicit treatment of diffusion and the Courant number is not restricted to be below 1. The Navier-Stokes equation contains cross spatial derivatives which are treated explicitly in most ADI schemes. The destabilizing effect of such a practice on a 2-D model system with second-order spatial derivative terms only was analyzed and found to be not excessive.

Chan, K. L.↗

NASA NTRS1992

Growth and decay of disturbances in stratified shear flow in a rotating frame

The stability of stratified plane Couette flow in a rotating frame is investigated for a case in which the gravitational force is parallel to the rotation vector. Partial differential equations describing the behavior of disturbances in the linear regime are derived. Unstratified flow is stable as long as the angular momentum gradient is positive. If the gradient is negative, nonaxisymmetric disturbances grow as a power law in time, if the gradient is sufficiently steep. In flow which is unstable to convection, all perturbations asymptotically grow at the rate given by the Brunt-Vaisala frequency. If heat diffusion is included, all nonaxisymmetric perturbations now eventually decay as t exp -2, even if the flow is unstable to convection. If heat diffusion and viscosity are weak, nonaxisymmetric disturbances in convectively unstable flow will undergo a large transient growth before their eventual decay.

Korycansky, D. G.↗

NASA NTRS2015

A Numerical and Experimental Study of Coflow Laminar Diffusion Flames: Effects of Gravity and Inlet Velocity

In this work, the influence of gravity, fuel dilution, and inlet velocity on the structure, stabilization, and sooting behavior of laminar coflow methane-air diffusion flames was investigated both computationally and experimentally. A series of flames measured in the Structure and Liftoff in Combustion Experiment (SLICE) was assessed numerically under microgravity and normal gravity conditions with the fuel stream CH4 mole fraction ranging from 0.4 to 1.0. Computationally, the MC-Smooth vorticity-velocity formulation of the governing equations was employed to describe the reactive gaseous mixture; the soot evolution process was considered as a classical aerosol dynamics problem and was represented by the sectional aerosol equations. Since each flame is axisymmetric, a two-dimensional computational domain was employed, where the grid on the axisymmetric domain was a nonuniform tensor product mesh. The governing equations and boundary conditions were discretized on the mesh by a nine-point finite difference stencil, with the convective terms approximated by a monotonic upwind scheme and all other derivatives approximated by centered differences. The resulting set of fully coupled, strongly nonlinear equations was solved simultaneously using a damped, modified Newton's method and a nested Bi-CGSTAB linear algebra solver. Experimentally, the flame shape, size, lift-off height, and soot temperature were determined by flame emission images recorded by a digital camera, and the soot volume fraction was quantified through an absolute light calibration using a thermocouple. For a broad spectrum of flames in microgravity and normal gravity, the computed and measured flame quantities (e.g., temperature profile, flame shape, lift-off height, and soot volume fraction) were first compared to assess the accuracy of the numerical model. After its validity was established, the influence of gravity, fuel dilution, and inlet velocity on the structure, stabilization, and sooting tendency of laminar coflow methane-air diffusion flames was explored further by examining quantities derived from the computational results.

microgravity↗

NASA NTRS1987

Development and evaluation of improved numerical schemes for recirculating flows

The paper examines the performance of the flux-spline scheme for convection-diffusion. Computations are presented for a number of test cases, both linear and nonlinear. It is shown that in all cases the flux-spline scheme yields results which are superior to those obtained with the lower-order formulations such as hybrid differencing. In order to improve the computational efficiency, the flux-spline scheme has been combined with a direct solution algorithm for the continuity and momentum equations. Such an approach eliminates the need for an equation for pressure or pressure correction and is found to be rapidly convergent.

Patankar, S. V.↗

NASA NTRS1992

An efficient and robust algorithm for time dependent viscous incompressible Navier-Stokes equations

A recently developed finite difference algorithm is presented for steady incompressible Navier-Stokes calculations. The algorithm is extremely robust with respect to Reynolds number, and has been used to directly compute incompressible flows with smoothly resolved streamfunction, kinetic energy and vorticity contours for Reynolds numbers as high as Re = 100,000 without requiring any subscale modelling. The algorithm is second order accurate in both time and space, with Crank-Nicolson differencing for the diffusion terms, with a lagged second order Adams-Basforth differencing for the convection terms, and with central differencing for all space derivatives. The algorithm is extremely efficient with respect to both computing time and physical memory. Solutions are shown for cavity and channel flows at various Reynolds numbers.

Goodrich, John W.↗

NASA NTRS1997

Transport Phenomena During Equiaxed Solidification of Alloys

Recent progress in modeling of transport phenomena during dendritic alloy solidification is reviewed. Starting from the basic theorems of volume averaging, a general multiphase modeling framework is outlined. This framework allows for the incorporation of a variety of microscale phenomena in the macroscopic transport equations. For the case of diffusion dominated solidification, a simplified set of model equations is examined in detail and validated through comparisons with numerous experimental data for both columnar and equiaxed dendritic growth. This provides a critical assessment of the various model assumptions. Models that include melt flow and solid phase transport are also discussed, although their validation is still at an early stage. Several numerical results are presented that illustrate some of the profound effects of convective transport on the final compositional and structural characteristics of a solidified part. Important issues that deserve continuing attention are identified.

Beckermann, C.↗

NASA NTRS1974

Analytic approximations in the study of the solar modulation of electrons

Numerical solutions to the transport equation of galactic cosmic rays in the interplanetary medium have been used to investigate the applicability of commonly used approximate analytic solutions for electrons (10 MeV to 10 GeV). We find that for a given cosmic-ray diffusion coefficient the force-field approximation is in reasonable agreement with the numerical solution at energies above 200 MeV, but deviates significantly at lower energies, depending on the shape of the interstellar electron spectrum. The diffusion-convection approximation agrees generally with the numerical solution within a factor of 2 over the entire energy range.

Cummings, A. C.↗

NASA NTRS1984

On the theory of cosmic-ray-mediated shocks with variable compression ratio

Cosmic-ray-mediated shocks may accelerate enough cosmic rays to high enough energies that they escape the shock, carrying an appreciable amount of energy before being convected to downstream infinity. Under such conditions, it is noted, the overall compression ratio cannot be determined from the conservation equations as in conventional hydrodynamic treatments, and the standard equations for shock acceleration admit arbitrarily high compression ratios. A procedure is outlined for obtaining the structure of high Mach number, cosmic-ray-mediated shocks, including their overall compresion ratio, around a low Mach number viscous subshock. Analytic solutions are obtained by quardrature for an energy-dependent diffusion coefficient in the limit of extreme sensitivity to energy, which, unlike previous solutions, include the finite thermal pressure of the preshock gas.

Eichler, D.↗

NASA NTRS1982

Coupled hydromagnetic wave excitation and ion acceleration upstream of the earth's bow shock

A self-consistent theory is set forth for the excitation of hydromagnetic waves and the acceleration of 'diffuse' ions upstream of the earth's bow shock in the quasi-equilibrium that results when the solar wind velocity and the interplanetary magnetic field are nearly parallel. For the waves, the quasi-equilibrium derives from a balance between excitation by the ions, which stream relative to the solar wind plasma, and convective loss to the magnetosheath. For the diffuse ions, the quasi-equilibrium derives from a balance between injection at the shock front, confinement to the foreshock by pitch angle scattering on the waves, and acceleration by compression at the shock front. It also results from loss to the magnetosheath, loss due to escape upstream of the foreshock, and loss via diffusion perpendicular to the average magnetic field onto field lines that do not connect to the shock front. Diffusion equations describing the ion transport and wave kinetic equations describing the hydromagnetic wave transport are solved self-consistently to give analytical expressions. These describe (1) the differential wave intensity spectrum as a function of frequency and distance from the bow shock and (2) the ion omnidirectional distribution functions and anisotropies as functions of energy and distance from the bow shock.

Lee, M. A.↗

NASA NTRS2011

Stellar Mixing: I. Formalism

In this paper we use the Reynolds stress models (RSM) to derive algebraic expressions for the following variables: a) heat fluxes; b) J.l fluxes; and c) momentum fluxes. These relations, which are fully 3D, include: 1) stable and unstable stratification, represented by the Brunt-Vaislila frequency, N(exp 2) =-g/H(sub p_(del - del(sub ad))(1 - RI(sub mu)); 2) double diffusion, salt-fingers, and semi-convection, represented by the density ratio R(sub mu) = del(sub mu)/(del - del(sub ad)); 3) shear (differential rotation), represented by the mean squared shear Sigma(exp 2) or by the Richardson number, Ri =N(exp 2)Sigma(exp -2); 4) radiative losses represented by a Peclet number, Pe; 5) a complete analytical solution of the ID version of the model. In general, the model requires the solution of two differential equations for the eddy kinetic energy K and its rate of dissipation, epsilon. In the local and stationary cases, when production equals dissipation, the model equations are all algebraic.

Canuto, V .M.↗

NASA NTRS1996

A Computational Fluid Dynamic and Heat Transfer Model for Gaseous Core and Gas Cooled Space Power and Propulsion Reactors

A computational model based on the axisymmetric, thin-layer Navier-Stokes equations is developed to predict the convective, radiation and conductive heat transfer in high temperature space nuclear reactors. An implicit-explicit, finite volume, MacCormack method in conjunction with the Gauss-Seidel line iteration procedure is utilized to solve the thermal and fluid governing equations. Simulation of coolant and propellant flows in these reactors involves the subsonic and supersonic flows of hydrogen, helium and uranium tetrafluoride under variable boundary conditions. An enthalpy-rebalancing scheme is developed and implemented to enhance and accelerate the rate of convergence when a wall heat flux boundary condition is used. The model also incorporated the Baldwin and Lomax two-layer algebraic turbulence scheme for the calculation of the turbulent kinetic energy and eddy diffusivity of energy. The Rosseland diffusion approximation is used to simulate the radiative energy transfer in the optically thick environment of gas core reactors. The computational model is benchmarked with experimental data on flow separation angle and drag force acting on a suspended sphere in a cylindrical tube. The heat transfer is validated by comparing the computed results with the standard heat transfer correlations predictions. The model is used to simulate flow and heat transfer under a variety of design conditions. The effect of internal heat generation on the heat transfer in the gas core reactors is examined for a variety of power densities, 100 W/cc, 500 W/cc and 1000 W/cc. The maximum temperature, corresponding with the heat generation rates, are 2150 K, 2750 K and 3550 K, respectively. This analysis shows that the maximum temperature is strongly dependent on the value of heat generation rate. It also indicates that a heat generation rate higher than 1000 W/cc is necessary to maintain the gas temperature at about 3500 K, which is typical design temperature required to achieve high efficiency in the gas core reactors. The model is also used to predict the convective and radiation heat fluxes for the gas core reactors. The maximum value of heat flux occurs at the exit of the reactor core. Radiation heat flux increases with higher wall temperature. This behavior is due to the fact that the radiative heat flux is strongly dependent on wall temperature. This study also found that at temperature close to 3500 K the radiative heat flux is comparable with the convective heat flux in a uranium fluoride failed gas core reactor.

Anghaie, S.↗

NASA NTRS1975

Numerical solution of the Navier-Stokes equations with topography

A finite difference scheme for solving the equations of fluid motion in a generalized coordinate system has been constructed. The scheme conserves mass and all the first integral moments of the motion. The scheme also advectively 'almost conserves' second moments, in that the magnitude of implicit numerical smoothing is typically about an order smaller than explicit viscosity and diffusion. Calculations with the model support the theoretical conjecture that the difference scheme is stable whenever the analogous Cartesian scheme is stable. The scheme has been used to calculate dry atmospheric convection due to differential heating between top and bottom of mountainous terrain. The general small-scale characteristics of mountain up-slope winds have been simulated. In addition, the results have demonstrated the crucial role played by the eddy diffusivities and the environmental stability, in determining both the quantitative and the qualitative features of the circulation.

Gal-Chen, T.↗

NASA NTRS1988

A fine grid finite element computation of two-dimensional high Reynolds number flows

A velocity-pressure-integrated mixed-interpolation Galerkin finite-element computation of the Navier-Stokes equations using the grids is presented. The velocity variables are interpolated using complete quadratic shape functions, and the pressure was interpolated using linear shape functions defined on a triangular element which is contained inside the quadratic element for velocity variables. Comprehensive computational results for a cavity flow at Reynolds number Re = 400-10,000 and a laminar backward-facing step flow at Re = 100-900 are presented. Many high-Re flows involve convection-dominated motion as well as diffusion-dominated motion in the flow domain. The computational results for both of the fluid motions compared favorably with high-accuracy finite-difference computational results and/or experimental data.

Kim, Sang-Wook↗

NASA NTRS1974

Finite-amplitude thermal convection in a spherical shell

The properties of finite-amplitude thermal convection for a Boussinesq fluid contained in a spherical shell are investigated. All nonlinear terms are retained in the equations, and both axisymmetric and nonaxisymmetric solutions are studied. The velocity is expanded in terms of poloidal and toroidal vectors. Spherical surface harmonics resolve the horizontal structure of the flow, but finite differences are used in the vertical. With a few modifications, the transform method developed by Orszag (1970) is used to calculate the nonlinear terms, while Green's function techniques are applied to the poloidal equation and diffusion terms.

Young, R. E.↗