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NASA NTRS1981

Numerical simulation of reentry flow around the Shuttle Orbiter including real gas effects

The flight environment of a reentry vehicle is predicted from the numerical solution of fluid dynamics equations for the region between the blunt nose and the swept wings. The inviscid portion of the shock layer is modeled by the Euler equations, but the laminar viscous flow adjacent to the wall is modeled by the approximate parabolic Navier-Stokes equations. The approximations made to the axial gradients of pressure and diffusive fluxes enable the coupled inviscid and viscous equations to be solved efficiently along the body axis. The equilibrium air aftbody code contains significant improvements over its predecessor which only considers a perfect gas model and noncircular configurations. The inclusion of numerical damping either explicitly or implicitly has extended its capabilities for predicting flow field around a winged configuration at higher Machs and greater angles of attack. The results are obtained on the cylindrical coordinates and satisfactory for the Shuttle Orbiter at a free-stream Mach number of 22 and an angle of attack of 40 deg. Also discussed are the inviscid formulation and its application for wind-tunnel conditions.

Li, C. P.↗

NASA NTRS1984

Thermal evaporation of spherical clouds - Effects of viscous stresses

The thermal evaporation of a cold spherical cloud embedded in hot gas is analyzed, including the effects of viscous stresses as well as 'saturation' of the conductive heat flux, for the case of equal electron and ion temperatures. The relevant transport properties for an H-He plasma are discussed, including the modification of these transport coefficients when temperature or velocity gradients become large. The fluid-dynamical equations for steady spherical evaporation are given and cast into dimensinless form. Numerical integration of these equations and the results are discussed, emphasizing the novel features of the viscous solutions, astrophysical implications, and uncertainties in the physics.

Giuliani, J. L., Jr.↗

NASA NTRS1985

A 3-dimensional Navier-Stokes-Euler code for blunt-body flow computations

The shock-layer flowfield is obtained with or without viscous and heat-conducting dissipations from the conservative laws of fluid dynamics equations using a shock-fitting implicity finite-difference technique. The governing equations are cast in curvilinear-orthogonal coordinates and transformed to the domain between the shock and the body. Another set of equations is used for the singular coordinate axis, which, together with a cone generator away from the stagnation point, encloses the computation domain. A time-dependent alternating direction implicit factorization technique is applied to integrate the equations with local-time increment until a steady solution is reached. The shock location is updated after the flowfield computation, but the wall conditions are implemented into the implicit procedure. Innovative procedures are introduced to define the initial flowfield, to treat both perfect and equilibrium gases, to advance the solution on a coarse-to-fine grid sequence, and to start viscous flow computations from their corresponding inviscid solutions. The results are obtained from a grid no greater than 28 by 18 by 7 and converged within 300 integration steps. They are of sufficient accuracy to start parabolized Navier-Stokes or Euler calculations beyond the nose region, to compare with flight and wind-tunnel data, and to evaluate conceptual designs of reentry spacecraft.

Li, C. P.↗

NASA NTRS1985

Dynamic response characteristics of a circulation control rotor model pneumatic system

Numerical and experimental simulation of unsteady airflow through the control valve and slotted air duct of a circulation control rotor is described. The numerical analysis involves the solution of the quasi-one-dimensional compressible fluid-dynamic equations in the blade air duct together with the coupled isentropic flow equations for flow into the blade through the valve and out of the blade through the Coanda slot. Numerical solutions are compared with basic experimental results obtained for a mockup of a circulation control rotor and its pneumatic valving system. The pneumodynamic phenomena that were observed are discussed with particular emphasis on the characteristic system time lags associated with the response of the flow variables to transient and periodic control valve inputs.

Watkins, C. B.↗

NASA NTRS1986

Geostrophic adjustment in a shallow-water numerical model as it relates to thermospheric dynamics

The theory of geostrophic adjustment and its application to the dynamics of the high latitude thermosphere have been discussed in previous papers based on a linearized treatment of the fluid dynamical equations. However, a linearized treatment is only valid for small Rossby numbers given by Ro = V/fL, where V is the wind speed, f is the local value of the Coriolis parameter, and L is a characteristic horizontal scale for the flow. For typical values in the auroral zone, the approximation is not reasonable for wind speeds greater than 25 m/s or so. A shallow-water (one layer) model was developed that includes the spherical geometry and full nonlinear dynamics in the momentum equations in order to isolate the effects of the nonlinearities on the adjustment process. A belt of accelerated winds between 60 deg and 70 deg latitude was used as the initial condition. The adjustment process was found to proceed as expected from the linear formulation, but that an asymmetry between the response for an eastward and westward flow results from the nonlineawr curvature (centrifugal) terms. In general, the amplitude of an eastward flowing wind will be less after adjustment than a westward wind. For instance, if the initial wind velocity is 300 m/s, the linearized theory predicts a final wind speed of 240 m/s, regardless of the flow direction. However, the nonlinear curvature terms modify the response and produce a final wind speed of only 200 m/s for an initial eastward wind and a final wind speed of almost 300 m/s for an initial westward flow direction. Also, less gravity wave energy is produced by the adjustment of the westward flow than by the adjustment of the eastward flow. The implications are that the response of the thermosphere should be significantly different on the dawn and dusk sides of the auroral oval. Larger flow velocities would be expected on the dusk side since the plasma will accelerate the flow in a westward direction in that sector.

Larsen, M. F.↗

NASA NTRS1986

A model of Comet P/Giacobini-Zinner

A computer model of Comet P/Giacobini-Zinner is presented which contains photoprocesses, gas-phase chemical kinetics, energy balance, multifluid hydrodynamics with a transition to free molecular flow, and solar wind interaction. Recently the physics for electrons in the model has been improved by including electron impact ionization and dissociation and separately accounting for electron energetics. Electron heating and cooling mechanisms include photoprocesses, recombination processes, inelastic and elastic collisions with heavy molecules, and expansion cooling. The model incorporates an internally consistent interaction of the solar wind with the coma gas using the axisymmetric ideal fluid dynamic equations. The nuclear size and composition have been chosen to make the calculations relevant to the September 11, 1985 International Cometary Explorer (ICE) encounter with Comet P/Giacobini-Zinner. Model profiles of the temperature, velocity, and number density of the electrons are in good agreement with measurements along ICE's trajectory. The results indicate the probe passed through a region of the coma at the onset of the plasma tail.

Boice, D. C.↗

NASA NTRS1988

Adaptive computational methods for aerothermal heating analysis

The development of adaptive gridding techniques for finite-element analysis of fluid dynamics equations is described. The developmental work was done with the Euler equations with concentration on shock and inviscid flow field capturing. Ultimately this methodology is to be applied to a viscous analysis for the purpose of predicting accurate aerothermal loads on complex shapes subjected to high speed flow environments. The development of local error estimate strategies as a basis for refinement strategies is discussed, as well as the refinement strategies themselves. The application of the strategies to triangular elements and a finite-element flux-corrected-transport numerical scheme are presented. The implementation of these strategies in the GIM/PAGE code for 2-D and 3-D applications is documented and demonstrated.

Price, John M.↗

NASA NTRS1988

Improving the accuracy of central difference schemes

General difference approximations to the fluid dynamic equations require an artificial viscosity in order to converge to a steady state. This artificial viscosity serves two purposes. One is to suppress high frequency noise which is not damped by the central differences. The second purpose is to introduce an entropy-like condition so that shocks can be captured. These viscosities need a coefficient to measure the amount of viscosity to be added. In the standard scheme, a scalar coefficient is used based on the spectral radius of the Jacobian of the convective flux. However, this can add too much viscosity to the slower waves. Hence, it is suggested that a matrix viscosity be used. This gives an appropriate viscosity for each wave component. With this matrix valued coefficient, the central difference scheme becomes closer to upwind biased methods.

Turkel, Eli↗

NASA NTRS1988

Modeling of combustion processes of stick propellants via combined Eulerian-Lagrangian approach

This research is motivated by the improved ballistic performance of large-caliber guns using stick propellant charges. A comprehensive theoretical model for predicting the flame spreading, combustion, and grain deformation phenomena of long, unslotted stick propellants is presented. The formulation is based upon a combined Eulerian-Lagrangian approach to simulate special characteristics of the two phase combustion process in a cartridge loaded with a bundle of sticks. The model considers five separate regions consisting of the internal perforation, the solid phase, the external interstitial gas phase, and two lumped parameter regions at either end of the stick bundle. For the external gas phase region, a set of transient one-dimensional fluid-dynamic equations using the Eulerian approach is obtained; governing equations for the stick propellants are formulated using the Lagrangian approach. The motion of a representative stick is derived by considering the forces acting on the entire propellant stick. The instantaneous temperature and stress fields in the stick propellant are modeled by considering the transient axisymmetric heat conduction equation and dynamic structural analysis.

Kuo, K. K.↗

NASA NTRS1988

Hypersonic research at Stanford University

The status of the hypersonic research program at Stanford University is discussed and recent results are highlighted. The main areas of interest in the program are the numerical simulation of radiating, reacting and thermally excited flows, the investigation and numerical solution of hypersonic shock wave physics, the extension of the continuum fluid dynamic equations to the transition regime between continuum and free-molecule flow, and the development of novel numerical algorithms for efficient particulate simulations of flowfields.

Candler, Graham↗

NASA NTRS1989

Application of a self-adaptive grid method to complex flows

A directional-split, modular, user-friendly grid point distribution code is applied to several test problems. The code is self-adaptive in the sense that grid point spacing is determined by user-specified constants denoting maximum and minimum grid spacings and constants relating the relative influence of smoothness and orthogonality. Estimates of truncation error, in terms of flow-field gradients and/or geometric features, are used to determine the point distribution. Points are redistributed along grid lines in a specified direction in an elliptic manner over a user-specified subdomain, while orthogonality and smoothness are controlled in a parabolic (marching) manner in the remaining directions. Multidirectional adaption is achieved by sequential application of the method in each coordinate direction. The flow-field solution is redistributed onto the newly distributed grid points after each unidirectional adaption by a simple one-dimensional interpolation scheme. For time-accurate schemes such interpolation is not necessary and time-dependent metrics are carried in the fluid dynamic equations to account for grid movement.

Deiwert, G. S.↗

NASA NTRS1990

Effect of artificial viscosity on three-dimensional flow solutions

Artificial viscosity is added either implicitly or explicitly in practically every numerical scheme for suppressing spurious oscillations in the solution of fluid dynamics equations. In the present central-difference scheme, artificial viscosity is added explicitly for suppressing high frequency oscillations and achieving good convergence properties. The amount of artificial viscosity added is controlled through the use of pre-selected coefficients. In the standard scheme, scalar coefficients based on the spectral radii of the Jacobian of convective fluxes are used. However, this can add too much viscosity to the slower waves. Hence, use the matrix-valued coefficients, which give appropriate viscosity for each wave component is suggested. With the matrix-valued coefficients, the central-difference scheme produces more accurate solutions on a given grid, particularly in the vicinity of shocks, while still maintaining good convergence properties.

Turkel, Eli↗

NASA NTRS1992

A numerical method for systems of conservation laws of mixed type admitting hyperbolic flux splitting

The present treatment of elliptic regions via hyperbolic flux-splitting and high order methods proposes a flux splitting in which the corresponding Jacobians have real and positive/negative eigenvalues. While resembling the flux splitting used in hyperbolic systems, the present generalization of such splitting to elliptic regions allows the handling of mixed-type systems in a unified and heuristically stable fashion. The van der Waals fluid-dynamics equation is used. Convergence with good resolution to weak solutions for various Riemann problems are observed.

Shu, Chi-Wang↗

NASA NTRS1994

Effect of artificial viscosity on three-dimensional flow solutions

Artificial viscosity is added either implicity or explicitly in practically every numerical scheme for suppressing spurious oscillations in the solution of fluid-dynamics equations. In the present central-difference scheme, artificial viscosity is added explicitly for suppressing high-frequency oscillations and achieving good convergence properties. The amount of artificial viscosity added is controlled through the use of preselected coefficients. In the standard scheme, scalar coefficients based on the spectral radii of the Jacobian of the convective fluxes are used. However, this can add too much viscosity to the slower waves. Hence, the use of matrix-valued coefficients, which give appropriate viscosity for each wave component, is suggested. With the matrix-valued coefficients, the central-difference scheme produces more accurate solutions on a given grid, particularly in the vicinity of shocks and boundary layers, while still maintaining good convergence properties.

Turkel, Eli↗

NASA NTRS1998

Pulsing Inertial Oscillation, Supercell Storms, and Surface Mesonetwork Data

The pulsing inertial oscillation (PIO) model is a nonlinear, time-dependent, translating vortex solution of the inviscid, compressible fluid dynamic equations in the middle troposphere. The translation of this vortex during a pulse is strikingly similar to that of a supercell storm -- a rotating thunderstorm that can generate tornadoes and hail. Two studies were performed to test the hypothesis that some supercell storms are manifestations of a PIO pulse. The first study applied the model to an intense interior draft whose buoyancy was bounded by a temperature excess of +/- 12 K. The peak updraft speed achieved was 41.5 m/ s and the peak Rossby number was 92.9. The study also pointed to an advanced concept for attaining higher values. The second study applied the PIO model to a supercell storm as a whole and succeeded in replicating its bulk properties, such as mesocyclonic circulation, net mass and moisture influxes, and time track. This study also identified a critical feature of the PIO model that could be tested against storm data: The average vertical draft is downward before the turn in the storm track and upward afterwards. In the conventional theory, the average vertical draft is upward from storm inception until dissipation. These differing draft predictions were compared with the best available data, which are surface mesonetwork data. These data were found to support the PIO model. However, surface data alone are not conclusive, and further measurements are warranted.

Costen, R. C.↗

NASA NTRS1988

Optical matrix-vector processing for computational fluid dynamics

An optical processor to solve partial differential equations for computational fluid dynamics applications is considered. This application is new and original for optical processors. The algorithms that are used are optical realizations of the Newton-Raphson method for nonlinear equations and a new optical LU direct decomposition and Gauss-Seidel iterative solution to the resultant linear algebraic equations. These algorithms are used to solve Burger's equation (a specific form of the momentum equation in fluid dynamics). The nonlinear equations provide 1-D velocity data at each time step. Simulation results of optical processing with these algorithms on computational fluid dynamics data is included.

Perlee, Caroline J.↗

NASA NTRS2012

Sonic Boom Mitigation Through Aircraft Design and Adjoint Methodology

This paper presents a novel approach to design of the supersonic aircraft outer mold line (OML) by optimizing the A-weighted loudness of sonic boom signature predicted on the ground. The optimization process uses the sensitivity information obtained by coupling the discrete adjoint formulations for the augmented Burgers Equation and Computational Fluid Dynamics (CFD) equations. This coupled formulation links the loudness of the ground boom signature to the aircraft geometry thus allowing efficient shape optimization for the purpose of minimizing the impact of loudness. The accuracy of the adjoint-based sensitivities is verified against sensitivities obtained using an independent complex-variable approach. The adjoint based optimization methodology is applied to a configuration previously optimized using alternative state of the art optimization methods and produces additional loudness reduction. The results of the optimizations are reported and discussed.

Rallabhandi, Siriam K.↗

DOE OSTI2025

Foundations of magnetohydrodynamics

In this tutorial, a derivation of magnetohydrodynamics (MHD) valid beyond the usual ideal gas approximation is presented. Non-equilibrium thermodynamics is used to obtain conservation equations and linear constitutive relations. When coupled with Maxwell's equations, this provides closed fluid equations in terms of material properties of the plasma, described by the equation of state and transport coefficients. These properties are connected to microscopic dynamics using the Irving–Kirkwood procedure and Green–Kubo relations. Symmetry arguments and the Onsager–Casimir relations allow one to vastly simplify the number of independent coefficients. Importantly, expressions for current density, heat flux, and stress (conventionally Ohm's law, Fourier's law, and Newton's law) take different forms in systems with a non-ideal equation of state. The traditional form of the MHD equations, which is usually obtained from a Chapman–Enskog solution of the Boltzmann equation, corresponds to the ideal gas limit of the general equations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗