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Enhancements and applications of DSMC for hypersonic rarefied flows

A review of the direct simulation Monte Carlo (DSMC) method of Bird is presented. The DSMC method provides the capability of simulating real gas flows in the rarefied flow regime. Recent developments and applications of the method for hypersonic flows are reported for both ground-based tests and during entry. The flows considered were three-dimensional, and both an existing general code and a new code under development were used.

Moss, James N.↗

Hypersonic blunt body wake computations using DSMC and Navier-Stokes solvers

Numerical results obtained with direct simulation Monte Carlo (DSMC) and Navier-Stokes methods are presented for Mach 20 nitrogen flow about a 70-deg blunted cone. The flow conditions simulated are those that can be obtained in existing low-density hypersonic wind tunnels. Three sets of flow conditions are considered with freestream Knudsen numbers ranging from 0.03 to 0.001. The focus is on the wake structure: how does the wake structure change as a function of rarefaction, what are the afterbody levels of heating, and to what limits are continuum models realistic as rarefaction in the wake is progressively increased. Calculations are made with and without an afterbody sting. Results for the afterbody sting are emphasized in anticipation of an experimental study for the current flow conditions and model configuration. The Navier-Stokes calculations were made with and without slip boundary conditions. Comparisons of the results obtained with the two simulation methodologies are made for both flowfield structure and surface quantities.

Moss, James N.↗

Rarefaction effects on Galileo probe aerodynamics

Solutions of aerodynamic characteristics are presented for the Galileo Probe entering Jupiter's hydrogen-helium atmosphere at a nominal relative velocity of 47.4 km/s. Focus is on predicting the aerodynamic drag coefficient during the transitional flow regime using the direct simulation Monte Carlo (DSMC) method. Accuracy of the probe's drag coefficient directly impacts the inferred atmospheric properties that are being extracted from the deceleration measurements made by onboard accelerometers as part of the Atmospheric Structure Experiment. The range of rarefaction considered in the present study extends from the free molecular limit to continuum conditions. Comparisons made with previous calculations and experimental measurements show the present results for drag to merge well with Navier-Stokes and experimental results for the least rarefied conditions considered.

Moss, James N.↗

DSMC simulation of the interaction between rarefied free jets

This paper presents a direct simulation Monte Carlo (DSMC) calculation of two interacting free jets exhausting into vacuum. The computed flow field is compared against available experimental data and shows excellent agreement everywhere except in the very near field (less than one orifice diameter downstream of the jet exhaust plane). The lack of agreement in this region is attributed to having assumed an inviscid boundary condition for the orifice lip. The results serve both to validate the DSMC code for a very complex, three dimensional non-equilibrium flow field, and to provide some insight as to the complicated nature of this flow.

Dagum, Leonardo↗

An efficient DSMC algorithm applied to a delta wing

A new algorithm for 3D direct simulation Monte Carlo (DSMC) is tested and numerical results are compared with wind tunnel data and results obtained earlier with a more traditional DSMC code. The test case is the flowfield around a delta wing at incidence at Knudsen number of 0.016 and Mach number of 20.2. The results are shown to compare favorably with both experimental and earlier numerical results. The new algorithm is described with special emphasis placed on its distinctive features: Cartesian/unstructured combination grid, special body surface definition, discretization in physical space.

Rault, D. F. G.↗

Application of a parallel DSMC method to hypersonic rarefied flows

This paper describes a method for doing direct simulation Monte Carlo (DSMC) calculations using parallel processing and presents some results of applying the method to several hypersonic, rarefied flow problems. The performance and efficiency of the parallel method are discussed. The applications described are the flow in a channel and the flow about a flat plate at incidence. The results show significant advantages of parallel processing over conventional scalar processing and demonstrate the scalability of the method to large problems.

Wilmoth, Richard G.↗

DSMC calculations for the delta wing

Results are reported from three-dimensional direct simulation Monte Carlo (DSMC) computations, using a variable-hard-sphere molecular model, of hypersonic flow on a delta wing. The body-fitted grid is made up of deformed hexahedral cells divided into six tetrahedral subcells with well defined triangular faces; the simulation is carried out for 9000 time steps using 150,000 molecules. The uniform freestream conditions include M = 20.2, T = 13.32 K, rho = 0.00001729 kg/cu m, and T(wall) = 620 K, corresponding to lambda = 0.00153 m and Re = 14,000. The results are presented in graphs and briefly discussed. It is found that, as the flow expands supersonically around the leading edge, an attached leeside flow develops around the wing, and the near-surface density distribution has a maximum downstream from the stagnation point. Coefficients calculated include C(H) = 0.067, C(DP) = 0.178, C(DF) = 0.110, C(L) = 0.714, and C(D) = 1.089. The calculations required 56 h of CPU time on the NASA Langley Voyager CRAY-2 supercomputer.

Celenligil, M. Cevdet↗

Comparisons of the Maxwell and CLL Gas/Surface Interaction Models Using DSMC

Two contrasting models of gas-surface interactions are studied using the Direct Simulation Monte Carlo (DSMC) method. The DSMC calculations examine differences in predictions of aerodynamic forces and heat transfer between the Maxwell and Cercignani-Lampis-Lord (CLL) models for flat plate configurations at freestream conditions corresponding to a 140 km orbit around Venus. The size of the flat plate is that of one of the solar panels on the Magellan spacecraft, and the freestream conditions are one of those experienced during aerobraking maneuvers. Results are presented for both a single flat plate and a two-plate configuration as a function of angle of attack and gas-surface accommodation coefficients. The two plate system is not representative of the Magellan geometry, but is studied to explore possible experiments that might be used to differentiate between the two gas surface interaction models.

Hedahl, Marc O.↗

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.↗

DSMC Simulations of Hypersonic Flows and Comparison With Experiments

This paper presents computational results obtained with the direct simulation Monte Carlo (DSMC) method for several biconic test cases in which shock interactions and flow separation-reattachment are key features of the flow. Recent ground-based experiments have been performed for several biconic configurations, and surface heating rate and pressure measurements have been proposed for code validation studies. The present focus is to expand on the current validating activities for a relatively new DSMC code called DS2V that Bird (second author) has developed. Comparisons with experiments and other computations help clarify the agreement currently being achieved between computations and experiments and to identify the range of measurement variability of the proposed validation data when benchmarked with respect to the current computations. For the test cases with significant vibrational nonequilibrium, the effect of the vibrational energy surface accommodation on heating and other quantities is demonstrated.

Moss, James N.↗

DSMC Simulations of Ballute Aerothermodynamics Under Hypersonic Rarefied Conditions

This paper presents computational results obtained with the direct simulation Monte Carlo (DSMC) method for towed ballute applications. A ballute is an inflatable drag device that can be used to create a large amount of drag at high altitudes. Consequently, ballutes provide a potential technology for achieving aerocapture when the primary spacecraft velocity reduction (ΔV) is achieved at much higher altitudes than with the conventional rigid aeroshell. Since the ΔV is achieved at relatively high altitudes, rarefaction can be significant and is the motivation for the current study with the DSMC method. Computed surface and flow-field results are presented for a toroidal ballute, isolated tethers when exposed to free-stream flow conditions, and the flow interactions resulting from a toroidal ballute when towed by a six meter diameter Mars Pathfinder shaped (without tethers) spacecraft. All results presented are for Earth entry at velocities of 14 to 7 km/s (primary focus is at 8.55 km/s, same as some previous Titan aerocapture studies) and altitudes of 200 to 100 km. Variations of drag and heating coefficients as a function of rarefaction are presented. A description of the flow structure is provided and also an explanation of how it is affected by shock interactions produced solely by the ballute and those resulting from the two body combination of towed ballute and spacecraft is also given.

James N Moss↗

Grids for DSMC computation of two and three-dimensional flows

Contemporary grid schemes for use in Direct Simulation Monte Carlo (DSMC) method of computing two- and three-dimensional flows are briefly surveyed. The grids described include: (1) simple, constant area cells defined by a rectangular grid; (2) multilevel rectangular grids; (3) adaptive rectangular cells; (4) 'point reference' scheme; (5) body-fitted 'analytical' cells; (6) 'general' schemes; (7) 'general' schemes with subcells; (8) orthogonal transformation to rectangular grid; (9) structural tetrahedral grids; (10) rectangular multilevel subcells with adaptive body-fitted cells.

Bird, G. A.↗

DSMC and continuum analyses of low-density nozzle flow

Two different approaches, the direct-simulation Monte Carlo (DSMC) method based on molecular gas dynamics and a finite-volume approximation of the Navier-Stokes equations, which are based on continuum gas dynamics, are employed in the analysis of a low-density gas flow in a small converging-diverging nozzle. The fluid experiences various kinds of flow regimes including continuum, slip, transition, and free-molecular. Results from the two numerical methods are compared with Rothe's experimental dam, in which density and rotational temperature variations along the centerline and at various locations inside a low density nozzle were measured by the electron-beam fluorescence technique. The continuum approach showed good agreement with the experimental data as far as density is concerned. The results from the DSMC method showed good agreement with the experimental data both in the density and the rotational temperature. It is also shown that the simulation parameters, such as the gas/surface interaction model, the energy exchange model between rotational and translational modes, and the viscosity temperature exponent, have substantial effects on the results of the DSMC method.

Chung, Chan-Hong↗

Recommended DSMC Collision Model Parameters for Planetary Entry

Hybrid simulation frameworks combining Computational Fluid Dynamics (CFD) and Direct Simulation Monte Carlo (DSMC) are frequently employed to efficiently perform high-fidelity simulations of environments consisting of both continuum and rarified flow. DSMC is a stochastic, particle-based method which solves the fundamental Boltzmann equation and is therefore necessary for high-Knudsen flow where continuum-based assumptions governing CFD break down. However, the DSMC methodology is generally computationally inefficient to model the continuum regime. In a CFD/DSMC hybrid approach, obtaining an accurate, high-fidelity solution hinges on the consistent treatment of transport properties and the thermo-chemical models employed within the two solvers. In principle, in regions where CFD and DSMC are both employed, the same gas mixture under the same conditions should have the same properties, regardless of simulation type. Observed differences should be due to non-equilibrium processes, rather than differences in physical models. The goal of this work is to provide a comprehensive DSMC transport database encompassing the vast majority of known gas species encountered during Earth or other planetary atmospheric entry. This goal is largely possible due to recently performed ab initio quantum chemistry calculations. Combined with other high-fidelity data, the planned database will consist of collision integral data for over 200 neutral and ionized species and over 20000 binary collisions. From these collision integrals, Nelder-Mead optimization is used to compute collision-specific Variable Soft Sphere (VSS) collision model parameters, fitted from 300 K to 20000 K. Initial comparisons of transport properties of relevant equilibrium gas mixtures show great agreement between CFD and DSMC-derived results. The completed database can be readily applied to model binary collisions of any gas mixture containing the included species over the specified temperature range, making it a valuable tool for future planetary probe modeling efforts. An example is shown below in Fig. 1. Equilibrium mixture transport properties for a 35-species mixture composed originally of 10% air and 90% pyrolysis species of a carbon-phenolic ablator material [4] are computed using both fitted VSS Parameters and the original CFD collision integral values. Deviations in computed properties between the two approaches are less than 5% for the entire temperature range.

M. R. Gosma↗

DSMC Simulations of Hypersonic Flows With Shock Interactions and Validation With Experiments

The capabilities of a relatively new direct simulation Monte Carlo (DSMC) code are examined for the problem of hypersonic laminar shock/shock and shock/boundary layer interactions, where boundary layer separation is an important feature of the flow. Flow about two model configurations is considered, where both configurations (a biconic and a hollow cylinder-flare) have recent published experimental measurements. The computations are made by using the DS2V code of Bird, a general two-dimensional/axisymmetric time accurate code that incorporates many of the advances in DSMC over the past decade. The current focus is on flows produced in ground-based facilities at Mach 12 and 16 test conditions with nitrogen as the test gas and the test models at zero incidence. Results presented highlight the sensitivity of the calculations to grid resolution, sensitivity to physical modeling parameters, and comparison with experimental measurements. Information is provided concerning the flow structure and surface results for the extent of separation, heating, pressure, and skin friction.

Moss, James N.↗

DSMC Simulations of Hypersonic Flows With Shock Interactions and Validation With Experiments

The capabilities of a relatively new direct simulation Monte Carlo (DSMC) code are examined for the problem of hypersonic laminar shock/shock and shock/boundary layer interactions, where boundary layer separation is an important feature of the flow. Flow about two model configurations is considered, where both configurations (a biconic and a hollow cylinder-flare) have recent published experimental measurements. The computations are made by using the DS2V code of Bird, a general two-dimensional/axisymmetric time accurate code that incorporates many of the advances in DSMC over the past decade. The current focus is on flows produced in ground-based facilities at Mach 12 and 16 test conditions with nitrogen as the test gas and the test models at zero incidence. Results presented highlight the sensitivity of the calculations to grid resolutions, sensitivity to physical modeling parameters, and comparison with experimental measurements. Information is provided concerning the flow structure and surface results for the extent of separation, heating, pressure, and skin friction.

Moss, James N.↗

Comparisons of the Maxwell and CLL gas/surface interaction models using DSMC

The behavior of two different models of gas-surface interactions is studied using the Direct Simulation Monte Carlo (DSMC) method. The DSMC calculations examine differences in predictions of aerodynamic forces and heat transfer between the Maxwell and the Cercignani-Lampis-Lord (CLL) models for flat plate configurations at freestream conditions corresponding to a 140 km orbit around Venus. The size of the flat plate represents one of the solar panels on the Magellan spacecraft, and the freestream conditions correspond to those experienced during aerobraking maneuvers. Results are presented for both a single flat plate and a two-plate configuration as a function of angle of attack and gas-surface accommodation coefficients. The two-plate system is not representative of the Magellan geometry but is studied to explore possible experiments that might be used to differentiate between the two gas-surface interaction models. The Maxwell and CLL models produce qualitatively similar results for the aerodynamic forces and heat transfer on a single flat plate. However, the flow fields produced with the two models are qualitatively different for both the single-plate and two-plate calculations. These differences in the flowfield lead to predictions of the angle of attack for maximum heat transfer in a two plate configuration that are distinctly different for the two gas-surface interactions models.

Hedahl, Marc O.↗

A Holistic DSMC Transport Database for Re-Entry and Ablation Modeling

Hybrid simulation frameworks combining Computational Fluid Dynamics (CFD) and Direct Simulation Monte Carlo (DSMC) are frequently employed to efficiently perform high-fidelity solutions of environments containing combined continuum/rarified flow. The use of DSMC, a stochastic, particle-based method, is necessary for high-Knudsen flow where continuum-based assumptions governing CFD break down. However, the DSMC methodology is generally very computationally inefficient to model the continuum regime. In a CFD/DSMC hybrid approach, obtaining an accurate, high-fidelity solution hinges on the consistent treatment of transport properties and the used thermo-chemical models employed within the two solvers. In principle, in regions where CFD and DSMC are both employed, the same gas mixture under the same conditions should have the same properties, regardless of simulation type. Observed differences should be due to non-equilibrium processes, rather than differences in physical models. While the transport models governing CFD and DSMC simulations are starkly different, they can effectively be linked via their use of reduced Chapman-Enskog collision integrals. In CFD, these integrals are typically stored as fitted polynomial expressions and used to directly compute gas transport properties via mixing rules or the full Chapman-Enskog formulation. In DSMC, they can be used to derive the collision parameters needed for the phenomenological collision cross-section models that govern particle interactions, via a Nelder-Mead optimization scheme. The goal of this work is to provide a unified DSMC transport database encompassing the vast majority of known gas species encountered during atmospheric entry, on Earth or any other Solar body. This goal is largely possible due to recently performed ab-initio quantum chemistry calculations. Combined with other high-fidelity literature sources, the planned database will consist of collision integral data for over 200 neutral and ionized species and over 17000 binary collisions. From these collision integrals, Nelder-Mead optimization is used to compute Variable Soft Sphere (VSS) collision model parameters for DSMC, fitted from 300 K to 20000 K. Initial comparisons of transport properties of relevant equilibrium gas mixtures show great agreement between CFD and DSMC-derived results. The completed database will be able to be readily applied to model binary collisions of any gas mixture containing the included species over the specified temperature range, making it a valuable tool for future planetary probe modeling efforts. An example is shown below. Equilibrium mixture transport properties for a 19-species Titan atmospheric model [4] are computed using both fitted VSS parameters and the original CFD collision integral values. Deviations in computed properties between the two approaches is less than 5% for the entire temperature range.

M R Gosma↗