Timothy R. Deschenes

Effects of Rotational Energy Relaxation in a Modular Particle-Continuum Method

Amodular particle-continuum method is extended to include thermal nonequilibrium between translational and rotational energy modes to simulate hypersonic steady-state flows that exhibit small regions of collisional nonequilibrium in a mainly continuum flowfield. This method loosely couples an existing direct-simulation Monte Carlo code to a Navier–Stokes solver (computational fluid dynamics) while allowing both time step and cell size to be completely decoupled between each method. By limiting the size of the direct-simulation Monte Carlo region to only areas in collisional nonequilibrium, the modular particle-continuummethod is able to reproduce full direct-simulationMonte Carlo results for flows with global Knudsen numbers of 0.01 and 0.002 while decreasing the computational time required by factors of 2.94 and 28.1, respectively. The goal of the present study is to include consistent models that separate rotational and translational modes in both flow modules. Inclusion of rotational relaxation decreases the computational cost of the modular particle-continuum method.

Extension of a modular particle-continuum method to vibrationally excited, hypersonic flows

A modular particle-continuum method is extended to include vibrationally excited energy modes to simulate hypersonic steady-state flows that exhibit small regions of translational nonequilibrium in a mainly continuum flowfield. This method loosely couples an existing direct simulation Monte Carlo code to a Navier–Stokes solver (computational fluid dynamics) while allowing both time step and cell size to be completely decoupled between each method. A new information-transfer scheme that controls the inherently large statistical scatter of vibrational energies in low-temperature regions is described and tested. Two vibrational-relaxation models are implemented to test the sensitivity in agreement between direct simulation Monte Carlo and the modular particle-continuum method.By limiting the size of the direct simulationMonteCarlo region to only areas in translational nonequilibrium andmaintaining consistent physicalmodels in both computationalfluid dynamics anddirect simulationMonteCarlo modules, the modular particle-continuummethod is able to reproduce full direct simulationMonte Carlo results for flowwith globalKnudsen number of 0.01while decreasing the computational time required by a factor of about four.

Evaluation of a Hybrid Boltzmann-Continuum Method for High-Speed Nonequilibrium Flows

A series of monatomic gas flows over a cylinder, with a freestream Mach number of 4 and a range of Knudsen numbers, are used to evaluate the unified flow solver (UFS) code. The UFS code combines several compressible gas flow simulation schemes for application to flow problems involving a wide range of Knudsen number (Kn) regimes, and features capabilities for strong coupling between low-Kn and high-Kn schemes along with automatic tree-based grid adaptation. UFS simulation results are compared with results from simulations which employ other codes intended for the same class of problems, and good agreement is generally found. Areas identified for improvement in UFS include calculation of surface quantities and numerical performance of the UFS Boltzmann equation solver.

Incorporating vibrational excitation in a hybrid particle-continuum method

A modular particle-continuum (MPC) method is extended to model vibrational excitation to simulate hypersonic steady-state ows that exhibit regions of collisional nonequilibrium in a mainly continuum ow eld. This method loosely couples a DSMC code to an implicit Navier-Stokes solver. By limiting our study to steady-state ows, both time-step and cell size are decoupled between methods. Control of statistical scatter and information transfer between modules is described. Hypersonic ow over a 2-D cylinder is simulated with di erent physical models. Results from DSMC, CFD, and the MPC method are presented and compared. The agreement in vibrational temperature between DSMC and the MPC method decreases as the size of the continuum domain increases, which may be due to the di erence in macroscopic relaxation rates computed in DSMC and CFD. Other ow variables and surface properties remain in excellent agreement between DSMC and the MPC method. The MPC simulation results are obtained using less than half the computational time compared to full DSMC while also decreasing the memory requirements.

Application of a Modular Particle-Continuum Method to Hypersonic Propulsive Deceleration

A modular particle-continuum (MPC) method is used to quantify the e ect of continuum breakdown on aerodynamic predictions of Mach 12 hypersonic ow over a Mars entry aeroshell with a single-nozzle, sonic propulsive decelerator (PD). The MPC method loosely couples an existing direct simulation Monte Carlo (DSMC) code to a Navier-Stokes solver (CFD). Previous studies have shown that the MPC method can maintain the physical accuracy of DSMC in regions where the Navier-Stokes equations break down, while achieving the computational e ciency of CFD in regions that are considered fully continuum. Due to the very high number density within the jet core, application of the DSMC method across the entire ow eld is computationally expensive, and unnecessary. Comparison of predictions made by full CFD and the MPC method are performed at low and high thrust conditions. It is found that the jet induces an increase in the size of the rare ed region compared to the jet o con guration. Despite the additional mass added by the jet at high thrust, the degree of rarefaction is found to increase due to the intensi cation in ow gradients in the jet expansion region. In addition, it is found that the MPC results predict a larger recirculation region in the jet-shock layer interaction region compared to continuum predictions. The continuum aerodynamic drag coe cients are under predicted by 6% at low thrust con guration and over predicted by a factor of 2:7 at the high thrust condition. However, total axial force predictions made by continuum and hybrid methods are in very good agreement at both thrust conditions.

Application of a Modular Particle‐Continuum Method to Partially Rarefied, Hypersonic Flow

The Modular Particle‐Continuum (MPC) method is used to simulate partially‐rarefied, hypersonic flow over a sting‐mounted planetary probe configuration. This hybrid method uses computational fluid dynamics (CFD) to solve the Navier‐Stokes equations in regions that are continuum, while using direct simulation Monte Carlo (DSMC) in portions of the flow that are rarefied. The MPC method uses state‐based coupling to pass information between the two flow solvers and decouples both time‐step and mesh densities required by each solver. It is parallelized for distributed memory systems using dynamic domain decomposition and internal energy modes can be consistently modeled to be out of equilibrium with the translational mode in both solvers. The MPC results are compared to both full DSMC and CFD predictions and available experimental measurements. By using DSMC in only regions where the flow is nonequilibrium, the MPC method is able to reproduce full DSMC results down to the level of velocity and rotational energy...

Simulation of Near Continuum, Hypersonic Flow Using a Modular Particle-Continuum Method

Modular Parti le-Continuum Method Timothy R. Des henes∗, Iain D. Boyd† Department of Aerospa e Engineering, University of Mi higan, Ann Arbor, MI, 48109 and Thomas E. S hwartzentruber‡ Department of Aerospa e Engineering and Me hani s, University of Minnesota, Minneapolis, MN, 55455 A modular parti leontinuum (MPC) method is used to simulate a low Knudsen number, steady-state hypersoni ow whi h exhibit small regions of ollisional nonequilibrium within a mainly ontinuum ow eld. This method loosely ouples an existing dire t simulation Monte Carlo (DSMC) ode to a Navier-Stokes solver (CFD) while allowing both time-step and ell size to be ompletely de oupled between ea h method. Full thermal nonequilibrium (rotational and vibrational) is implemented in both ow modules with ompatible relaxation models. The goal of the present investigation is to study the e e t of lo ally rare ed regions on the heat transfer along the after body of a planetary probe body. Previous resear h suggests that poor agreement in after body heating ould be due to lo ally rare ed regions along the rear surfa e of blunt bodies in hypersoni ow. Hybrid simulations are ompared to full CFD and experimental measurements for high density, hypersoni ow over a sting-mounted planetary probe on guration. By using a hybrid method, the e e t of rare ed regions an be examined for a very low Knudsen number ase where the omputational expense of performing full DSMC al ulations is very high due to the four order of magnitude variation in hara teristi length and time s ales and unne essary due to the large ontinuum region. Despite an in rease in physi al a ura y in the wake region, the initial MPC results have the same level of agreement with experimental measurements as the full CFD solutions. This ould be due to insu ient transient time for the MPC simulation and will be explored in the future. Nomen lature