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A review of the 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. Results obtained using both axisymmetric and 3D codes are included.
The following will outline the methodology and results of validating a coupled Method of Characteristics (MOC) and Direct Simulation Monte Carlo (DSMC) method. This research focused specifically on modeling plume impingement, induced by Reaction Control System (RCS) thrusters that flew on the National Aeronautics and Space Administration’s (NASA’s) space shuttle Discovery. For each simulation, the continuum portion of the RCS thruster was simulated using MOC for solving hyperbolic Partial Differential Equations (PDEs) and computed with the NASA code, Reacting and Multi-phase Program (RAMP). The solution was then implemented as a starting condition into the NASA DSMC code, Direct Simulation and Monte Carlo Analysis Code (DAC). Typically, DSMC models rely on code-to-code validation for fidelity. The significance of this research is in its ability to validate its models against empirical data. Prior to computing solutions for these simulations, the mesh size and structure were optimized and many variants of DSMC input parameters were iterated on in order to acquire a reliable, mesh-independent, fully optimized numerical solution. This research will discuss the mathematical formulation of MOC for nozzle flow and DSMC for rarefied gases. Additionally, it will provide an explanation of how to implement these mathematical concepts into the two solvers: RAMP and DAC. Ultimately, this research will demonstrate that the overall process illustrated produces results in good agreement with empirical data. As a consequence, the methodology presented is granted an increased level of confidence and will greatly contribute to the aerospace industry and its effort in understanding and predicting rarefied flow fields.
The following will outline the methodology and results of validating a coupled Method of Characteristics (MOC) and Direct Simulation Monte Carlo (DSMC) method. This research focused specifically on modeling plume impingement, induced by Reaction Control System (RCS) thrusters that flew on the National Aeronautics and Space Administration’s (NASA’s) space shuttle Discovery. For each simulation, the continuum portion of the RCS thruster was simulated using MOC for solving hyperbolic Partial Differential Equations (PDEs) and computed with the NASA code, Reacting and Multi-phase Program (RAMP). The solution was then implemented as a starting condition into the NASA DSMC code, Direct Simulation and Monte Carlo Analysis Code (DAC). Typically, DSMC models rely on code-to-code validation for fidelity. The significance of this research is in its ability to validate its models against empirical data. Prior to computing solutions for these simulations, the mesh size and structure were optimized and many variants of DSMC input parameters were iterated on in order to acquire a reliable, mesh-independent, fully optimized numerical solution. This research will discuss the mathematical formulation of MOC for nozzle flow and DSMC for rarefied gases. Additionally, it will provide an explanation of how to implement these mathematical concepts into the two solvers: RAMP and DAC. Ultimately, this research will demonstrate that the overall process illustrated produces results in good agreement with empirical data. As a consequence, the methodology presented is granted an increased level of confidence and will greatly contribute to the aerospace industry and its effort in understanding and predicting rarefied flow fields.
An AFRL/NRL team has recently been selected to develop a scalable, parallel, reacting, multidimensional (SUPREM) Direct Simulation Monte Carlo (DSMC) code for the DoD user community under the High Performance Computing Modernization Office (HPCMO) Common High Performance Computing Software Support Initiative (CHSSI). This paper will introduce the JANNAF Exhaust Plume community to this three-year development effort and present the overall goals, schedule, and current status of this new code.
Many of the current direct simulation Monte Carlo (DSMC) codes still employ only simple surface catalysis models. These include only basic mechanisms such as dissociation, recombination, and exchange reactions, without any provision for adsorption and finite rate kinetics. Incorporating finite rate chemistry at the surface is increasingly becoming a necessity for various applications such as high speed re-entry flows over thermal protection systems (TPS), micro-electro-mechanical systems (MEMS), surface catalysis, etc. In the recent years, relatively few works have examined finite-rate surface reaction modeling using the DSMC method.In this work, a generalized finite-rate surface chemistry framework incorporating a comprehensive list of reaction mechanisms is developed and implemented into the DSMC solver SPARTA. The various mechanisms include adsorption, desorption, Langmuir-Hinshelwood (LH), Eley-Rideal (ER), Collision Induced (CI), condensation, sublimation, etc. The approach is to stochastically model the various competing reactions occurring on a set of active sites. Both gas-surface (e.g., ER, CI) and pure-surface (e.g., LH, desorption) reaction mechanisms are incorporated. The reaction mechanisms could also be catalytic or surface altering based on the participation of the bulk-phase species (e.g., bulk carbon atoms). Marschall and MacLean developed a general formulation in which multiple phases and surface sites are used and we adopt a similar convention in the current work. Microscopic parameters of reaction probabilities (for gas-surface reactions) and frequencies (for pure-surface reactions) that are require for DSMC are computed from the surface properties and macroscopic parameters such as rate constants, sticking coefficients, etc. The energy and angular distributions of the products are decided based on the reaction type and input parameters. Thus, the user has the capability to model various surface reactions via user-specified reaction rate constants, surface properties and parameters.
This work describes the direct simulation Monte Carlo (DSMC) investigation of Saturn entry probe scenarios and the influence of non-equilibrium phenomena on Saturn entry conditions. The DSMC simulations coincide with rarefied hypersonic shock tube experiments of a hydrogen-helium mixture performed in the Electric Arc Shock Tube (EAST) at NASA Ames Research Center. The DSMC simulations are post-processed through the NEQAIR line-by-line radiation code to compare directly to the experimental results. Improved collision cross-sections, inelastic collision parameters, and reaction rates are determined for a high temperature DSMC simulation of a 7-species H2-He mixture and an electronic excitation model is implemented in the DSMC code. Simulation results for 27.8 and 27.4 kms shock waves are obtained at 0.2 and 0.1 Torr respectively and compared to measured spectra in the VUV, UV, visible, and IR ranges. These results confirm the persistence of non-equilibrium for several centimeters behind the shock and the diffusion of atomic hydrogen upstream of the shock wave. Although the magnitude of the radiance did not match experiments and an ionization inductance period was not observed in the simulations, the discrepancies indicated where improvements are needed in the DSMC and NEQAIR models.
We derive an adjoint method for the Direct Simulation Monte Carlo (DSMC) method for the spatially homogeneous Boltzmann equation with a general collision law. This generalizes our previous results in Caflisch et al., which was restricted to the case of Maxwell molecules, for which the collision rate is constant. The main difficulty in generalizing the previous results is that a rejection sampling step is required in the DSMC algorithm in order to handle the variable collision rate. We find a new term corresponding to the so-called score function in the adjoint equation and a new adjoint Jacobian matrix capturing the dependence of the collision parameter on the velocities. The new formula works for a much more general class of collision models.
A generalized finite-rate surface chemistry framework incorporating a comprehensive list of reaction mechanisms is developed and implemented into the Direct Simulation Monte Carlo (DSMC) solver SPARTA (Stochastic PArallel Rarefied-gas Time-accurate Analyzer). The various mechanisms include adsorption, desorption, Eley-Rideal (ER), and several types of Langmuir-Hinshelwood (LH) mechanisms. The approach is to stochastically model the various competing reactions occurring on a set of active sites. Both gas-surface (e.g., adsorption, ER) and pure-surface (e.g., desorption) reaction mechanisms are incorporated, and the framework also includes catalytic or surface altering mechanisms involving the participation of the bulk-phase species (e.g., bulk carbon atoms). Marschall and MacLean developed a general formulation in which multiple phases and surface sites are used and a similar convention is adopted in the current work. Expressions for the microscopic parameters of reaction probabilities (for gas-surface reactions) and frequencies (for pure-surface reactions) that are required for DSMC are derived from the surface properties and macroscopic parameters such as rate constants, sticking coefficients, etc. The energy and angular distributions of the products are specified according to the reaction type and input parameters. This framework also presents physically consistent procedures to accurately compute the reaction probabilities and frequencies in the case of multiple reactions. The result is a modeling tool with a wide variety of surface reactions characterized via user-specified reaction rate constants, surface properties and parameters.
Results of direct simulation Monte Carlo (DSMC) solutions are presented for the Japanese Orbital Reentry Experiment (OREX) vehicle, a 50 deg half-angle spherically blunted cone with a nose radius of 1.35 m and a base diameter of 3.4 m. The flow conditions simulated are those for entry into the Earth's atmosphere at a nominal velocity of about 7.4 km/s and zero incidence. Calculations are made for the higher altitude portion of entry, encompassing the transitional flow regime (altitudes of 200 to 80 km). Comparisons with flight measured values are made for axial acceleration, surface pressure, and stagnation point heating.
The direct simulation Monte Carlo (DSMC) method involves the simultaneous computation of the trajectories of thousands of simulated molecules in simulated physical space. Rarefied flow about the double ellipse for test case 6.4.1 has been calculated with the DSMC method of Bird. The gas is assumed to be nonreacting nitrogen flowing at a 30 degree incidence with respect to the body axis, and for the surface boundary conditions, the wall is assumed to be diffuse with full thermal accommodation and at a constant wall temperature of 620 K. A parametric study is presented that considers the effect of variations of computational domain, gas model, cell size, and freestream density on surface quantities.
A comparison of axisymmetric Direct Simulation Monte Carlo (DSMC) Analysis Code (DAC) results to analytic and Computational Fluid Dynamics (CFD) solutions in the near continuum regime and to 3D DAC solutions in the rarefied regime for expansion plumes into a vacuum is performed to investigate the validity of the newest DAC axisymmetric implementation. This new implementation, based on the standard DSMC axisymmetric approach where the representative molecules are allowed to move in all three dimensions but are rotated back to the plane of symmetry by the end of the move step, has been fully integrated into the 3D-based DAC code and therefore retains all of DAC s features, such as being able to compute flow over complex geometries and to model chemistry. Axisymmetric DAC results for a spherically symmetric isentropic expansion are in very good agreement with a source flow analytic solution in the continuum regime and show departure from equilibrium downstream of the estimated breakdown location. Axisymmetric density contours also compare favorably against CFD results for the R1E thruster while temperature contours depart from equilibrium very rapidly away from the estimated breakdown surface. Finally, axisymmetric and 3D DAC results are in very good agreement over the entire plume region and, as expected, this new axisymmetric implementation shows a significant reduction in computer resources required to achieve accurate simulations for this problem over the 3D simulations.
Direct simulation Monte Carlo (DSMC) solutions are presented for the hypersonic flow behind a blunt body in which the wake region is solved in a zonally-decoupled manner. The forebody flow is solved separately using either a DSMC or a Navier-Stokes method, and the forebody exit plane solution is specified as the inflow condition to the decoupled DSMC solution of the wake region. Results are presented for a 70-deg, blunted cone at flow conditions that can be accommodated in existing low-density wind tunnels with the Knudsen number based on base diameter ranging from 0.03 to 0.001. The zonally-decoupled solutions show good agreement with fully-coupled DSMC solutions of the wake flow densities and velocities. The wake closure predicted by the zonally-decoupled solutions is in better agreement with fully-coupled results than that predicted by a fully-coupled Navier-Stokes method indicating the need to account for rarefaction in the wake for the cases considered. The combined use of Navier-Stokes for the forebody with a decoupled DSMC solution for the wake provides an efficient method for solving transitional blunt-body flows where the forebody flow is continuum and the wake is rarefied.
Direct simulation Monte Carlo DSMC simulations are performed for the Apollo capsule in the hypersonic low density transitional flow regime. The focus is on ow conditions similar to that experienced by the Apollo Command Module during the high altitude portion of its reentry Results for aerodynamic forces and moments are presented that demonstrate their sensitivity to rarefaction that is for free molecular to continuum conditions. Also aerodynamic data are presented that shows their sensitivity to a range of reentry velocity encompasing conditions that include reentry from low Earth orbit lunar return and Mars return velocities to km/s. The rarefied results are anchored in the continuum regime with data from Navier Stokes simulations
Various implementations of the direct simulation Monte Carlo (DSMC) method exist in academia, government and industry. By comparing implementations, deficiencies and merits of each can be discovered. This document reports comparisons between DSMC Analysis Code (DAC) and MONACO. DAC is NASA's standard DSMC production code and MONACO is a research DSMC code developed in academia. These codes have various differences; in particular, they employ distinct computational grid definitions. In this study, DAC and MONACO are compared by having each simulate a blunted flat plate wind tunnel test, using an identical volume mesh. Simulation expense and DSMC metrics are compared. In addition, flow results are compared with available laboratory data. Overall, this study revealed that both codes, excluding grid adaptation, performed similarly. For parallel processing, DAC was generally more efficient. As expected, code accuracy was mainly dependent on physical models employed.
Collisional plasma plumes induced by laser irradiation of material targets exhibit large variations in local density as well as ionization and excitation states, making purely hydrodynamic or kinetic simulations inaccurate or infeasible. To address this challenge and capture non-equilibrium effects in laser-induced plasma plumes at arbitrary degrees of ionization, we develop a hybrid computational approach that combines the kinetic direct simulation Monte Carlo (DSMC) method with a collisional-radiative model (CRM). This ℓDSMC-CRM approach utilizes a lumped particle method to represent minor fractions of excited ions in particle-based simulations and a special coarse-graining technique for atomic spectra and photoionization rates, ensuring numerical convergence at reduced computational cost. The hybrid approach is applied to simulate spatially homogeneous relaxation as well as one- and two-dimensional expansions of plasma plumes induced by irradiation of a copper target by a nanosecond laser pulse in a vacuum or background gas. The comparison with an equilibrium model, where local Saha-Boltzmann equilibrium is enforced, shows that the non-equilibrium effects play a dominant role. The equilibrium model can fail to predict the flow structure and strongly underestimate the degree of absorption of laser radiation by the plume. The ℓDSMC-CRM approach is validated against experimental data demonstrating reasonable agreement with the experimental electron density and temperature, while the equilibrium model is found to dramatically underestimate electron density and temperature. The flexibility of the ℓDSMC-CRM approach allows for its seamless integration into existing DSMC frameworks, making it a valuable tool for high-fidelity plasma modeling in laser-material interactions, laser-based manufacturing, and beyond.
This work describes the direct simulation Monte Carlo (DSMC) investigation of Saturn entry probe scenarios and the influence of non-equilibrium phenomena on Saturn entry conditions. The DSMC simulations coincide with rarefied hypersonic shock tube experiments of a hydrogen-helium mixture performed in the Electric Arc Shock Tube (EAST) at NASA Ames Research Center. To directly compare to the experimental results, the DSMC simulations are post-processed through the NEQAIR line-by-line radiation code. Improved collision cross-sections, inelastic collision parameters, and reaction rates are determined for a high temperature DSMC simulation of a 7-species H2-He mixture and an electronic excitation model is implemented in the DSMC code. Simulation results for 27.8 and 27.4 kms shock waves are obtained at 0.2 and 0.1 Torr respectively and compared to measured spectra in the VUV, UV, visible, and IR ranges. These results confirm the persistence of non-equilibrium for several centimeters behind the shock and the diffusion of atomic hydrogen upstream of the shock wave. Although the magnitude of the radiance did not match experiments and an ionization inductance period was not observed in the simulations, the discrepancies indicated where improvements are needed in the DSMC and NEQAIR models.
This work describes the direct simulation Monte Carlo (DSMC) investigation of Saturn entry probe scenarios and the influence of non-equilibrium phenomena on Saturn entry conditions. The DSMC simulations coincide with rarefied hypersonic shock tube experiments of a hydrogen-helium mixture performed in the Electric Arc Shock Tube (EAST) at the NASA Ames Research Center. The DSMC simulations are post-processed through the NEQAIR line-by-line radiation code to compare directly to the experimental results. Improved collision cross-sections, inelastic collision parameters, and reaction rates are determined for a high temperature DSMC simulation of a 7-species H2-He mixture and an electronic excitation model is implemented in the DSMC code. Simulation results for 27.8 and 27.4 km/s shock waves are obtained at 0.2 and 0.1 Torr, respectively, and compared to measured spectra in the VUV, UV, visible, and IR ranges. These results confirm the persistence of non-equilibrium for several centimeters behind the shock and the diffusion of atomic hydrogen upstream of the shock wave. Although the magnitude of the radiance did not match experiments and an ionization inductance period was not observed in the simulations, the discrepancies indicated where improvements are needed in the DSMC and NEQAIR models.
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 rarefield 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.