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NASA NTRS1987

Direct simulation of high-vorticity gas flows

The computational limitations associated with the molecular dynamics (MD) method and the direct simulation Monte Carlo (DSMC) method are reviewed in the context of the computation of dilute gas flows with high vorticity. It is concluded that the MD method is generally limited to the dense gas case in which the molecular diameter is one-tenth or more of the mean free path. It is shown that the cell size in DSMC calculations should be small in comparison with the mean free path, and that this may be facilitated by a new subcell procedure for the selection of collision partners.

Bird, G. A.↗

NASA NTRS1988

Thermal and pressure diffusion effects in high altitude flows

An apparently anomalous change in composition adjacent to a non-catalytic surface in an earlier DSMC calculation of a non-reacting gas mixture is shown to have been due to thermal diffusion. Both thermal and pressure diffusion can lead to species separation effects in the flow of gas mixtures, but are not generally included in Navier-Stokes formulations. Additional DSMC calculations are made for blunt-body and plume expansion flows using both a simple gas and an otherwise identical gas mixture. These test calculations indicate that the pressure distribution on the forward face of a blunt body is largely unaffected by the species separation in the stagnation region. The gas density in this region is significantly affected and there is a slight change in the heat transfer to the surface. The pressure distribution around the shoulder of the body is affected. Very large separations occur in the plume expansion of the gas mixtures and there is an order of magnitude increase in density in the backflow region for the mixture.

Bird, G. A.↗

NASA NTRS1988

Rarefied flow past a flat plate at incidence

Results of a numerical study using the direct simulation Monte Carlo (DSMC) method are presented for the transitional flow about a flat plate at 40 deg incidence. The plate has zero thickness and a length of 1.0 m. The flow conditions simulated are those experienced by the Shuttle Orbiter during reentry at 7.5 km/s. The range of freestream conditions are such that the freestream Knudsen number values are between 0.02 and 8.4, i.e., conditions that encompass most of the transitional flow regime. The DSMC simulations show that transitional effects are evident when compared with free molecule results for all cases considered. The calculated results demonstrate clearly the necessity of having a means of identifying the effects of transitional flow when making aerodynamic flight measurements as are currently being made with the Space Shuttle Orbiter vehicles. Previous flight data analyses have relied exclusively on adjustments in the gas-surface interaction models without accounting for the transitional effect which can be comparable in magnitude. The present calculations show that the transitional effect at 175 km would increase the Space Shuttle Orbiter lift-drag ratio by 90 percent over the free molecule value.

Dogra, Virendra K.↗

NASA NTRS1989

Direct simulation Monte Carlo analysis on parallel processors

A method is presented for executing a direct simulation Monte Carlo (DSMC) analysis using parallel processing. The method is based on using domain decomposition to distribute the work load among multiple processors, and the DSMC analysis is performed completely in parallel. Message passing is used to transfer molecules between processors and to provide the synchronization necessary for the correct physical simulation. Benchmark problems are described for testing the method and results are presented which demonstrate the performance on two commercially available multicomputers. The results show that reasonable parallel speedup and efficiency can be obtained if the problem is properly sized to the number of processors. It is projected that with a massively parallel system, performance exceeding that of current supercomputers is possible.

Wilmoth, Richard G.↗

NASA NTRS1989

Computation of rarefied hypersonic flows

Numerical techniques for the simulation of hypersonic flows of rarefied gases are examined in an analytical review. The direct-simulation Monte Carlo (DSMC) method developed to interpret measurement data obtained by the Space Shuttle in the SUMS project is described; the fundamental limitations of the DMSC approach are discussed; and modifications to improve the physical plausibility of DSMC predictions are proposed. Particular attention is given to the use of a double-peaked molecular distribution function for the internal flow in the SUMS probe, a downstream vacuum-reservoir condition as a simplifying assumption, and an explicit forward-time centered-space differencing scheme for the discretization of the SUMS problem. Typical simulation results are presented in extensive graphs and briefly characterized.

Cheng, Sin-I↗

NASA NTRS1990

Direct simulation of reentry flows with ionization

The Direct Simulation Monte Carlo (DSMC) method is applied in this paper to the study of rarefied hypersonic reentry flows. The assumptions and simplifications involved with the treatment of ionization, free electrons and the electric field are investigated. A new method is presented for the calculation of the electric field and handling of charged particles with DSMC. In addition, a two-step model for electron impact ionization is implemented. The flowfield representing a 10 km/sec shock at an altitude of 65 km is calculated. The effects of the new modeling techniques on the calculation results are presented and discussed.

Carlson, Ann B.↗

NASA NTRS1989

Assessment of impingement effects in the isentropic core of a small satellite control thruster plume

Two computational techniques commonly employed in the calculation of rocket and thruster expansion plumes are assessed. These are the method of characteristics (MOC), which is derived from the continuum Euler equations, and the direct simulation Monte Carlo (DSMC) method, which adopts a discrete particle approach. These techniques vary both in the computational expense and in the accuracy and detail of the solutions that they provide, depending upon the regime of application. The assessment is made with reference to the plume expanding from a small monopropellant hydrazine thruster and concentrates on the isentropic core of the jet for the flow regime lying between the continuum and free molecular limits. It is found that the more numerically intensive DSMC method offers the better correspondence to the available experimental data. In addition, large differences in typical impingement effects such as drag force and heat transfer are found at the free molecular limit of the plume expansion for the two predictive techniques. It is concluded that accurate estimation of impingement potential may only be achieved through application of the discrete particle method.

Boyd, I. D.↗

NASA NTRS1989

Rarefied flow past a flat plate at incidence

Dogra, Virendra K.↗

NASA NTRS1990

Numerical simulation of rarefied gas flow through a slit

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas from one reservoir to another through a two-dimensional slit. The cases considered are for hard vacuum downstream pressure, finite pressure ratios, and isobaric pressure with thermal diffusion, which are not well established in spite of the simplicity of the flow field. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, three kinds of collision sampling techniques, the time counter (TC) method, the null collision (NC) method, and the no time counter (NTC) method, are used.

Keith, Theo G., Jr.↗

NASA NTRS1990

A collision-selection rule for a particle simulation method suited to vector computers

A theory is developed for a selection rule governing collisions in a particle simulation of rarefied gas-dynamic flows. The selection rule leads to an algorithmic form highly compatible with fine grain parallel decomposition, allowing for efficient utilization of supercomputers having vector or massively parallel single instruction multiple data architectures. A comparison of shock-wave profiles obtained using both the selection rule and Bird's direct simulation Monte Carlo (DSMC) method show excellent agreement. The equation on which the selection rule is based is shown to be directly related to the time-counter procedure in the DSMC method. The results of several example simulations of representative rarefied flows are presented, for which the number of particles used ranged from 10 to the 6th to 10 to the 7th demonstrating the greatly improved computational efficiency of the method.

Baganoff, D.↗

NASA NTRS1990

Adaptive domain decomposition for Monte Carlo simulations on parallel processors

A method is described for performing direct simulation Monte Carlo (DSMC) calculations on parallel processors using adaptive domain decomposition to distribute the computational work load. The method has been implemented on a commercially available hypercube and benchmark results are presented which show the performance of the method relative to current supercomputers. The problems studied were simulations of equilibrium conditions in a closed, stationary box, a two-dimensional vortex flow, and the hypersonic, rarefield flow in a two-dimensional channel. For these problems, the parallel DSMC method ran 5 to 13 times faster than on a single processor of a Cray-2. The adaptive decomposition method worked well in uniformly distributing the computational work over an arbitrary number of processors and reduced the average computational time by over a factor of two in certain cases.

Wilmoth, Richard G.↗

NASA NTRS1989

Aeroassist flight experiment aerodynamics and aerothermodynamics

The problem is to determine the transitional flow aerodynamics and aerothermodynamics, including the base flow characteristics, of the Aeroassist Flight Experiment (AFE). The justification for the computational fluid dynamic (CFD) Application stems from MSFC's system integration responsibility for the AFE. To insure that the AFE objectives are met, MSFC must understand the limitations and uncertainties of the design data. Perhaps the only method capable of handling the complex physics of the rarefied high energy AFE trajectory is Bird's Direct Simulation Monte Carlo (DSMC) technique. The 3-D code used in this analysis is applicable only to the AFE geometry. It uses the Variable Hard Sphere (VHS) collision model and five specie chemistry model available from Langley Research Center. The code is benchmarked against the AFE flight data and used as an Aeroassisted Space Transfer Vehicle (ASTV) design tool. The code is being used to understand the AFE flow field and verify or modify existing design data. Continued application to lower altitudes is testing the capability of the Numerical Aerodynamic Simulation Facility (NASF) to handle 3-D DSMC and its practicality as an ASTV/AFE design tool.

Brewer, Edwin B.↗

NASA NTRS1990

Analysis of rotational nonequilibrium in standing shock waves of nitrogen

The one-dimensional standing shock wave is the simplest flow in which nonequilibrium effects may be considered. The direct-simulation Monte Carlo method (DSMC) has yielded excellent agreement with results reported for the case of nitrogen flow at Mach 1.7. The DSMC technique is presently used in conjunction with a variable energy transfer probability model in which energy is transferred between the translational and rotational modes via the Borgnakke-Larsen (1975) phenomenological model.

Boyd, Iain D.↗

NASA NTRS1991

Local and overall aerodynamic coefficients for bodies in hypersonic, rarefied flow

A computational method is given for the prediction of local pressure and viscous shear stress on windward surfaces of bluff, convex, axisymmetric or quasi-axisymmetric, hypersonic bodies in the transitional, rarefied flow regime. Overall aerodynamic forces and moments are computed by integration of the local quantities. The method is based upon a correlation of local pressure and shear stress computed by the direct simulation Monte Carlo (DSMC) numerical technique for cold wall, real gas conditions and some supplemental data from low-density, hypersonic wind tunnels. The relative simplicity of the method makes it feasible to do the necessary calculations with a personal computer. Two-dimensional shapes and leeward surfaces are not included in the scope of the method as it is presented here. Results are compared with DSMC computations for both local and overall coefficients. The latter includes sphere and blunt cone drag as well as lift and pitching moment coefficients for the NASA AFE vehicle at various angles of attack. Very satisfactory agreement is shown.

Potter, J. Leith↗

NASA NTRS1990

Vectorization of a particle code used in the simulation of rarefied hypersonic flow

A limitation of the direct simulation Monte Carlo (DSMC) method is that it does not allow efficient use of vector architectures that predominate in current supercomputers. Consequently, the problems that can be handled are limited to those of one- and two-dimensional flows. This work focuses on a reformulation of the DSMC method with the objective of designing a procedure that is optimized to the vector architectures found on machines such as the Cray-2. In addition, it focuses on finding a better balance between algorithmic complexity and the total number of particles employed in a simulation so that the overall performance of a particle simulation scheme can be greatly improved. Simulations of the flow about a 3D blunt body are performed with 10 to the 7th particles and 4 x 10 to the 5th mesh cells. Good statistics are obtained with time averaging over 800 time steps using 4.5 h of Cray-2 single-processor CPU time.

Baganoff, D.↗

NASA NTRS1991

Analysis of vibrational-translational energy transfer using the direct simulation Monte Carlo method

A new model is proposed for energy transfer between the vibrational and translational modes for use in the direct simulation Monte Carlo method (DSMC). The model modifies the Landau-Teller theory for a harmonic oscillator and the rate transition is related to an experimental correlation for the vibrational relaxation time. Assessment of the model is made with respect to three different computations: relaxation in a heat bath, a one-dimensional shock wave, and hypersonic flow over a two-dimensional wedge. These studies verify that the model achieves detailed balance, and excellent agreement with experimental data is obtained in the shock wave calculation. The wedge flow computation reveals that the usual phenomenological method for simulating vibrational nonequilibrium in the DSMC technique predicts much higher vibrational temperatures in the wake region.

Boyd, Iain D.↗

NASA NTRS1991

Energetics of gas-surface interactions in transitional flows at entry velocities

The direct simulation Monte Carlo (DSMC) method has been used to calculate the molecular velocity and energy distributions of molecules striking a surface after traversing a shock layer in hypersonic transitional flow. The calculations were performed for a 1.6-m-diameter sphere at a nominal velocity for re-entry of 7.5 km/s over an altitude range of 130 to 90 km. Real gas effects and chemical reactions were included in the DSMC simulations. Results are presented for these conditions and the need for gas-surface interaction experiments is discussed.

Wilmoth, R. G.↗

NASA NTRS1991

Radiation modeling with direct simulation Monte Carlo

Improvements in the modeling of radiation in low density shock waves with direct simulation Monte Carlo (DSMC) are the subject of this study. A new scheme to determine the relaxation collision numbers for excitation of electronic states is proposed. This scheme attempts to move the DSMC programs toward a more detailed modeling of the physics and more reliance on available experimental data. The new method is compared with the current modeling technique and both techniques are compared with available data. The differences in the results are evaluated. The test case is based on an AVCO-Everett shock tube experiment, a 10-km/s standing shock wave in air at 0.1 Torr. The new method agrees with the available data as well as the results from the earlier scheme and is more easily extrapolated to different flow conditions.

Carlson, Ann B.↗