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At least 289 records · Page 16

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NASA NTRS1995

Numerical simulations of small amplitude acoustic wave propagation in a converging-diverging nozzle

Numerical simulations of the small amplitude acoustic wave propagation in a converging-diverging nozzle proposed in Category 5 are performed and presented here. The quasi 1-D unsteady flow equations in conservative form are discretized by the DRP scheme with the artificial damping developed by Tam and Webb. Characteristic boundary conditions are used at both the inlet and outlet of the nozzle. The effect of different numerical implementations of the subsonic inflow boundary conditions on the convergence of the solution to the steady state is studied. In the case of a subsonic outflow in which a shock is formed in the nozzle, the interaction between acoustics and the shock is also investigated.

Dong, Thomas Z.↗

NASA NTRS1995

Overview of techniques for mitigation of fading and shadowing in the direct broadcast satellite radio environment

The DBS radio propagation environment is divided into three sub-environments, indoor, rural-suburban mobile and urban mobile. Indoor propagation effects are in a large part determined by construction material. Non-metallic materials afford direct, albeit attenuated penetration of the satellite signal with a minimum of multipath signal scattering. Signal penetration into structures using significant metallic materials is often indirect, through openings such as doors and windows and propagation will involve significant multipath components. Even so, delay spread in many situations is on the order of 10's of nanoseconds resulting in relatively flat fading. Thus frequency diversity techniques such as Orthogonal Frequency Division Multiplex (OFDM) and Code Division Multiple Access (CDMA) or equalization techniques do not realize their intended performance enhancement. Antenna diversity, directivity and placement are key mitigation techniques for the indoor environment. In the Rural-Suburban mobile environment with elevation angles greater than 20 deg, multipath components from the satellite signal are 15-20 dB below the line-of-sight signal level and often originate from nearby reflectors. Thus shadowing is the dominant signal impairment and fading effects are again found to be relatively flat for a large fading margin. Because receiver motion induces rapid variations in the signal level, temporal diversity techniques such as interleaving, channel coding and retransmission can be used to combat short intermittent fading events. Antenna diversity and directivity techniques are again useful in this environment. Finally, in the Urban mobile environment, slower vehicle speeds and blockage by buildings causes signal fades that are too long and too deep to combat with signal margin or time diversity. Land-based signal boosters are needed to fill in the coverage gaps of the satellite only broadcast scheme. On frequency boosters are suggested to conserve bandwidth yet these produce long delay multipath and create a frequency selective fading environment. Enter now OFDM, spread spectrum, equalization and other techniques that are capable of deconvolving the channel effects and effecting significant performance improvements by extracting the frequency diversity or time diversity components comprising the received signal.

Bell, David↗

NASA NTRS2004

Numerical Modeling of Conjugate Heat Transfer in Fluid Network

Fluid network modeling with conjugate heat transfer has many applications in Aerospace engineering. In modeling unsteady flow with heat transfer, it is important to know the variation of wall temperature in time and space to calculate heat transfer between solid to fluid. Since wall temperature is a function of flow, a coupled analysis of temperature of solid and fluid is necessary. In cryogenic applications, modeling of conjugate heat transfer is of great importance to correctly predict boil-off rate in propellant tanks and chill down of transfer lines. In TFAWS 2003, the present author delivered a paper to describe a general-purpose computer program, GFSSP (Generalized Fluid System Simulation Program). GFSSP calculates flow distribution in complex flow circuit for compressible/incompressible, with or without heat transfer or phase change in all real fluids or mixtures. The flow circuit constitutes of fluid nodes and branches. The mass, energy and specie conservation equations are solved at the nodes where as momentum conservation equations are solved at the branches. The proposed paper describes the extension of GFSSP to model conjugate heat transfer. The network also includes solid nodes and conductors in addition to fluid nodes and branches. The energy conservation equations for solid nodes solves to determine the temperatures of the solid nodes simultaneously with all conservation equations governing fluid flow. The numerical scheme accounts for conduction, convection and radiation heat transfer. The paper will also describe the applications of the code to predict chill down of cryogenic transfer line and boil-off rate of cryogenic propellant storage tank.

Majumdar, Alok↗

NASA NTRS2006

Newly-Developed 3D GRMHD Code and its Application to Jet Formation

We have developed a new three-dimensional general relativistic magnetohydrodynamic code by using a conservative, high-resolution shock-capturing scheme. The numerical fluxes are calculated using the HLL approximate Riemann solver scheme. The flux-interpolated constrained transport scheme is used to maintain a divergence-free magnetic field. We have performed various 1-dimensional test problems in both special and general relativity by using several reconstruction methods and found that the new 3D GRMHD code shows substantial improvements over our previous model. The . preliminary results show the jet formations from a geometrically thin accretion disk near a non-rotating and a rotating black hole. We will discuss the jet properties depended on the rotation of a black hole and the magnetic field strength.

Mizuno, Y.↗

NASA NTRS2006

GRMHD Simulations of Jet Formation with a New Code

Mizuno, Y.↗

NASA NTRS2006

GRMHD Simulations of Jet Formation with a Newly-Developed GRMHD Code

We have developed a new three-dimensional general relativistic magnetohydrodynamic code by using a conservative, high-resolution shock-capturing scheme. The numerical fluxes are calculated using the HLL approximate Riemann solver scheme. The flux-CT scheme is used to maintain a divergence-free magnetic field. Various 1-dimensional test problems show significant improvements over our previous GRMHD code. We have performed simulations of jet formations from a geometrically thin accretion disk near a non-rotating and a rotating black hole. The new simulation results show that the jet is formed by the same manner as in previous works and propagates outward. As the magnetic field strength becomes weaker, larger amount of matter launches with the jet. On the other hand when the magnetic field strength becomes stronger, the jet has less-matter and becomes poynting flux dominated. We will also discuss how the jet properties depend on the rotation of a black hole.

Mizuno, Y.↗

NASA NTRS2007

GRMHD and GRPIC Simulations

We have developed a new three-dimensional general relativistic magnetohydrodynamic (GRMHD) code by using a conservative, high-resolution shock-capturing scheme. The numerical fluxes are calculated using the HLL approximate Riemann solver scheme. The flux-interpolated constrained transport scheme is used to maintain a divergence-free magnetic field. We have performed various 1-dimensional test problems in both special and general relativity by using several reconstruction methods and found that the new 3D GRMHD code shows substantial improvements over our previous code. The simulation results show the jet formations from a geometrically thin accretion disk near a nonrotating and a rotating black hole. We will discuss the jet properties depended on the rotation of a black hole and the magnetic field configuration including issues for future research. A General Relativistic Particle-in-Cell Code (GRPIC) has been developed using the Kerr-Schild metric. The code includes kinetic effects, and is in accordance with GRMHD code. Since the gravitational force acting on particles is extreme near black holes, there are some difficulties in numerically describing these processes. The preliminary code consists of an accretion disk and free-falling corona. Results indicate that particles are ejected from the black hole. These results are consistent with other GRMHD simulations. The GRPIC simulation results will be presented, along with some remarks and future improvements. The emission is calculated from relativistic flows in black hole systems using a fully general relativistic radiative transfer formulation, with flow structures obtained by GRMHD simulations considering thermal free-free emission and thermal synchrotron emission. Bright filament-like features protrude (visually) from the accretion disk surface, which are enhancements of synchrotron emission where the magnetic field roughly aligns with the line-of-sight in the co-moving frame. The features move back and forth as the accretion flow evolves, but their visibility and morphology are robust. We would like to extend this research using GRPIC simulations and examine a possible new mechanism for certain X-ray quasi-periodic oscillations (QPOs) observed in blackhole X-ray binaries.

Nishikawa, K.-I.↗

NASA NTRS1981

Numerical approximation of boundary conditions with applications to inviscid equations of gas dynamics

A comprehensive overview of the state of the art of well-posedness and stability analysis of difference approximations for initial boundary value problems of the hyperbolic type is presented. The applicability of recent theoretical development to practical calculations for nonlinear gas dynamics is examined. The one dimensional inviscid gas dynamics equations in conservation law form are selected for numerical experiments. The class of implicit schemes developed from linear multistep methods in ordinary differential equations is chosen and the use of linear extrapolation as an explicit or implicit boundary scheme is emphasized. Specification of boundary data in the primitive variables and computation in terms of the conservative variables in the interior is discussed. Some numerical examples for the quasi-one-dimensional nozzle are given.

Yee, H. C.↗

NASA NTRS1997

The Implicit and Explicit alpha-mu Schemes

Artificial numerical dissipation is an important issue in large Reynolds number computations. In such computations, the artificial dissipation inherent in traditional numerical schemes can overwhelm the physical dissipation and yield inaccurate results on meshes of practical size. In the present work, the space-time conservation element and solution element method is used to construct new and accurate numerical schemes such that artificial numerical dissipation will not overwhelm physical dissipation. Specifically, these schemes have the property that numerical dissipation vanishes when the physical viscosity goes to zero. These new schemes therefore accurately model the physical dissipation even when it is extremely small. The method of space-time conservation element and solution element, currently under development, is a nontraditional numerical method for solving conservation laws. The method is developed on the basis of local and global flux conservation in a space-time domain, in which space and time are treated in a unified manner. Explicit solvers for model and fluid dynamic conservation laws have previously been investigated. In this paper, we introduce a new concept in the design of implicit schemes, and use it to construct two highly accurate solvers for a convection-diffusion equation. The two schemes become identical in the pure convection case, and in the pure diffusion case. The implicit schemes are applicable over the whole Reynolds number range, from purely diffusive equations to purely inviscid (convective) equations. The stability and consistency of the schemes are analyzed, and some numerical results are presented. It is shown that, in the inviscid case, the new schemes become explicit and their amplification factors are identical to those of the Leapfrog scheme. On the other hand, in the pure diffusion case, their principal amplification factor becomes the amplification factor of the Crank-Nicolson scheme. We also construct an explicit solver with the treatment of diffusion being based on that in the implicit solvers. The explicit solver has only a CFL stability limitation on the Courant number, yet it retains the second-order spatial accuracy of the implicit schemes.

Chang, Sin-Chung↗

NASA NTRS1975

Calculation of shock-separated turbulent boundary layers

Numerical solutions of the complete, time-averaged conservation equations using several eddy-viscosity models for the Reynolds shear stress to close the equations are compared with experimental measurements in a compressible, turbulent separated flow. An efficient time-splitting, explicit difference scheme was used to solve the two-dimensional conservation equations. The experiment used for comparison was a turbulent boundary layer that was separated by an incident shock wave in a Mach 2.93 flow with a unit Reynolds number of 5.7 x 10 to the seventh power m. Comparisons of predicted and experimental values of surface pressure, shear stress along the wall, and velocity profiles are shown. One of the tested eddy-viscosity models which allows the shear stress to be out of equilibrium with the mean flow produces substantially better agreement with the experimental measurements than the simpler models. A tool is thereby provided for inferring additional information about the flow, such as static pressures in the stream, which might not be directly obtainable from experiments.

Baldwin, B. S.↗

NASA NTRS1994

A flux splitting scheme with high-resolution and robustness for discontinuities

A flux splitting scheme is proposed for the general nonequilibrium flow equations with an aim at removing numerical dissipation of Van-Leer-type flux-vector splittings on a contact discontinuity. The scheme obtained is also recognized as an improved Advection Upwind Splitting Method (AUSM) where a slight numerical overshoot immediately behind the shock is eliminated. The proposed scheme has favorable properties: high-resolution for contact discontinuities; conservation of enthalpy for steady flows; numerical efficiency; applicability to chemically reacting flows. In fact, for a single contact discontinuity, even if it is moving, this scheme gives the numerical flux of the exact solution of the Riemann problem. Various numerical experiments including that of a thermo-chemical nonequilibrium flow were performed, which indicate no oscillation and robustness of the scheme for shock/expansion waves. A cure for carbuncle phenomenon is discussed as well.

Wada, Yasuhiro↗

NASA NTRS1981

Stable boundary approximations for a class of implicit schemes for the one-dimensional inviscid equations of gas dynamics

The applicability to practical calculations of recent theoretical developments in the stability analysis of difference approximations for initial-boundary-value problems of the hyperbolic type. For the numerical experiments, select the one-dimensional inviscid gas-dynamic equations in conservation-law form is selected. A class of implicit schemes based on linear multistep methods for ordinary differential equations is chosen and the use of space or space-time extrapolations as implicit or explicit boundary schemes is emphasized. Some numerical examples with various inflow-outflow conditions highlight the commonly discussed issues: explicit versus implicit boundary schemes, unconditionally stable schemes, and underspecification or overspecification of boundary conditions.

Yee, H. C.↗

NASA NTRS1989

Improved vortex methods for three-dimensional flows

Robust numerical methods are developed for three-dimensional incompressible vortical flows, using Lagrangian vortex elements. A successful scheme must be able to handle regions of intense vortex stretching and vortex reconnection with reasonable accuracy (without diverging). Here, consideration is given to vortex particles, also commonly called vortons or vortex sticks. The following issues are discussed: (1) use of delta-function elements and weak solutions of the vorticity equation; (2) use of smoothed elements and the choice of the smoothing function; (3) representation of viscous effects and the redistribution of element strength; and (4) conservation laws (are they satisfied?). The various proposed schemes have been tested on flows involving a strong interaction between two vortex rings.

Winckelmans, G.↗

NASA NTRS2002

Entropy Splitting for High Order Numerical Simulation of Compressible Turbulence

A stable high-order numerical scheme for direct numerical simulation (DNS) of shock-free compressible turbulence is presented. The method is applicable to general geometries. It contains no upwinding, artificial dissipation, or filtering. Instead the method relies on the stabilizing mechanisms of an appropriate conditioning of the governing equations and the use of compatible spatial difference operators for the interior points (interior scheme) as well as the boundary points (boundary scheme). An entropy-splitting approach splits the inviscid flux derivatives into conservative and nonconservative portions. The spatial difference operators satisfy a summation-by-parts condition, leading to a stable scheme (combined interior and boundary schemes) for the initial boundary value problem using a generalized energy estimate. A Laplacian formulation of the viscous and heat conduction terms on the right hand side of the Navier–Stokes equations is used to ensure that any tendency to odd–even decoupling associated with central schemes can be countered by the fluid viscosity. The resulting methods are able to minimize the spurious high-frequency oscillations associated with pure central schemes, especially for long time integration applications such as DNS. For validation purposes, the methods are tested in a DNS of compressible turbulent plane channel flow at low values of friction Mach number, where reference turbulence data bases exist. It is demonstrated that the methods are robust in terms of grid resolution, and in good agreement with published channel data. Accurate turbulence statistics can be obtained with moderate grid sizes. Stability limits on the range of the splitting parameter are determined from numerical tests.

N.D. Sandham↗

NASA NTRS1992

Numerical simulation of conservation laws

A new numerical framework for solving conservation laws is being developed. This new approach differs substantially from the well established methods, i.e., finite difference, finite volume, finite element and spectral methods, in both concept and methodology. The key features of the current scheme include: (1) direct discretization of the integral forms of conservation laws, (2) treating space and time on the same footing, (3) flux conservation in space and time, and (4) unified treatment of the convection and diffusion fluxes. The model equation considered in the initial study is the standard one dimensional unsteady constant-coefficient convection-diffusion equation. In a stability study, it is shown that the principal and spurious amplification factors of the current scheme, respectively, are structurally similar to those of the leapfrog/DuFort-Frankel scheme. As a result, the current scheme has no numerical diffusion in the special case of pure convection and is unconditionally stable in the special case of pure diffusion. Assuming smooth initial data, it will be shown theoretically and numerically that, by using an easily determined optimal time step, the accuracy of the current scheme may reach a level which is several orders of magnitude higher than that of the MacCormack scheme, with virtually identical operation count.

Chang, Sin-Chung↗

NASA NTRS1993

High resolution numerical simulation of the linearized Euler equations in conservation law form

A linearized Euler solver based on a high resolution numerical scheme is presented. The approach is to linearize the flux vector as opposed to carrying through the complete linearization analysis with the dependent variable vector written as a sum of the mean and the perturbed flow. This allows the linearized equations to be maintained in conservation law form. The linearized equations are used to compute unsteady flows in turbomachinery blade rows arising due to blade vibrations. Numerical solutions are compared to theoretical results (where available) and to numerical solutions of the nonlinear Euler equations.

Sreenivas, Kidambi↗

NASA NTRS1981

Numerical method for gas dynamics combining characteristic and conservation concepts

An efficient implicit numerical method that solves the compressible Navier-Stokes equations in arbitrary curvilinear coordinates by the finite-volume technique is presented. An intrinsically dissipative difference scheme and a fully implicit treatment of boundary conditions, based on characteristic and conservation concepts, are used to improve stability and accuracy. Efficiency is achieved by using a diagonal form of the implicit algorithm and spatially varying time-steps. Comparisons of various schemes and methods are presented for one- and two-dimensional flows, including transonic separated flow past a thick circular-arc airfoil in a channel. The new method is equal to or better than a version of MacCormack's hybrid method in accuracy and it converges to a steady state up to an order of magnitude faster.

Coakley, T. J.↗

NASA NTRS1987

Modification of the Osher upwind scheme for use in three dimensions

The Osher upwind scheme, a shock-capturing algorithm based on an approximate Riemann solver, which has been developed for the solution of hyperbolic conservation laws, is briefly described, and the need for modification of the scheme for use in three dimensions is demonstrated. Two forms of a scheme modification for use on a three-dimensional arbitrary grid are then presented.

Hessenius, Kristin A.↗