Session QC: Rarefied Gases and Compressible Flows

Importance sampling based direct simulation Monte Carlo method

We propose a novel and efficient approach, termed as importance sampling based direct simulation Monte Carlo (ISDSMC), for prediction of nonequilibrium flows via solution of the Boltzmann equation. Besides leading to a reduction in computational cost, ISDSMC also results in a reduction in statistical scatter compared to conventional direct simulation Monte Carlo (DSMC) and hence appears to be potentially useful for prediction of a variety of flows, especially where the signal to noise ratio is small (e.g. microflows) . In this particle in cell approach, the computational particles are initially assigned weights (or importance) based on constraints on generalized moments of velocity. Solution of the Boltzmann equation is achieved by use of (i) a streaming operator which streams the computational particles and (ii) a collision operator where the representative collision pairs are selected stochastically based on particle weights via an acceptance-rejection algorithm. Performance of ISDSMC approach is evaluated using analysis of three canonical microflows, namely (i) thermal Couette flow, (ii) velocity-slip Couette flow and (iii) Poiseulle flow. Our results based on ISDSMC indicate good agreement with those obtained from conventional DSMC methods. The potential advantages of this (ISDSMC) approach to granular flows will also be demonstrated using simulations of homogeneous relaxation of a granular gas.   

Variance-reduced DSMC simulations of low-signal flows

We present a variance-reduced direct Monte Carlo method for efficient simulation of low-signal kinetic problems. In contrast to previous variance-reduction methods, the method presented here, referred to as VRDSMC, is able to substantially reduce variance with essentially no modification to the standard DSMC algorithm. This is achieved by introducing an auxiliary equilibrium simulation which, via an importance weight formulation, uses the same particle data as the non-equilibrium (DSMC) calculation. The desired hydrodynamic fields are expressed in terms of the difference between the equilibrium and the non-equilibrium results, which yields drastically reduced statistical uncertainty because it exploits the correlation between the two simulations. The resulting formulation is simple to code and provides considerable computational savings for a wide range of problems of practical interest. Sandia National Laboratories is a multi-program laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.   

Improved-Efficiency DSMC Collision-Partner Selection Schemes

The effect of the collision-partner selection scheme on the accuracy and efficiency of the Direct Simulation Monte Carlo (DSMC) method of Bird is investigated. Three schemes to improve the efficiency of the method are proposed in which the standard random collision-partner selection scheme is replaced with a near-neighbor one. These near-neighbor schemes limit the number of selections used to determine the nearest-neighbor by a fixed number, a fixed prescribed discretization error, or the distance traveled by the colliding molecule. These three schemes are evaluated for one-dimensional Fourier flow and two-dimensional hypersonic flow over a biconic. Their convergence characteristics as functions of spatial and temporal discretization and the number of simulators per cell are compared to the convergence characteristics of the sophisticated and standard DSMC algorithms. Improved performance is obtained if the population from which possible collision partners are selected is an appropriate subset of the population of the cell. Sandia National Laboratories is a multi-program laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.   

DSMC Algorithms for Moving-Boundary Problems

Direct Simulation Monte Carlo (DSMC) algorithms for problems with moving boundaries are investigated. The motivation is a microbeam that moves out-of-plane toward and away from a parallel substrate. For implementation and verification purposes, the simpler but analogous one-dimensional situation of a piston moving between two parallel walls is examined. Two moving-boundary algorithms are investigated. In the first algorithm, molecules are reflected rigorously from the moving piston by performing the reflections in the piston reference frame. In the second algorithm, molecules are reflected approximately by moving the piston and subsequently reflecting all molecules from the moving piston at its new or old position. The object moves over the mesh without deforming it in both algorithms. The two algorithms produce essentially identical results (except for noise) for a wide range of piston motions and for both specular and diffuse reflections. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.   

A comparison study of planar Richtmyer-Meshkov instability in Mie-Gr\"{u}neisen fluids and perfect gases

A numerical study of planar Richtmyer-Meshkov instability in fluids with Mie-Gr\"{u}neisen equations of state is presented and compared to similar perfect gas flows to expose the role of the equation of state. Results for single and triple-mode planar Richtmyer-Meshkov instability, when a reflected shock wave occurs, are first given for MORB and Molybdenum. Comparison is drawn to perfect gases with matched non-dimensional pressure jump across the incident shock, post shock Atwood ratio and post shock amplitude to wavelength ratio, which matches the Richtmyer constant linear growth-rate. Differences in start-up time and growth rate oscillations are demonstrated to correlate directly to the oscillation frequency for the transmitted and reflected shocks. Further results are given for single mode Richtmyer-Meshkov instability when a reflected expansion wave is present. Matched perfect gas solutions in such cases yield a higher degree of similarity in start-up time and growth rate oscillations. Additionally, for the reflected expansion case both equations of state are seen to yield incipient weak shock waves in the heavy fluid caused by perturbed-shock driven localized interface oscillations.   

Multidimensional detonation propagation modeled via nonlinear shock wave superposition

Detonation waves in gases are inherently multidimensional due to their cellular structure, and detonations in liquids and heterogeneous solids are often associated with instabilities and stochastic, localized reaction centers (i.e., hot spots). To explore the statistical nature of detonation dynamics in such systems, a simple model that idealizes detonation propagation as an ensemble of interacting blast waves originating from spatially random point sources has been proposed. Prior results using this model exhibited features that have been observed in real detonating systems, such as anomalous scaling between axisymmetric and two-dimensional geometries. However, those efforts used simple linear superposition of the blast waves. The present work uses a model of blast wave superposition developed for multiple-source explosions (the LAMB approximation) that incorporates the nonlinear interaction of shock waves analytically, permitting the effect of a more physical model of blast wave interaction to be explored. The results are suggestive of a universal behavior in systems of spatially randomized energy sources.   

Unsteady numerical simulations over the BLOODHOUND supersonic car

One of the main purposes of the BLOODHOUND SSC project consists on achieving the first 1000 mph record on land. In this study, unsteady flow predictions over the BLOODHOUND supersonic car (http://www.bloodhoundssc.swan.ac.uk/), are shown and discussed with Mach numbers up to 1.4. The governing equations of the flow are solved by implementing a hybrid RANS/LES approach. Close to walls the flow is treated with the RANS-equations and the Menter SST model is considered. In zones with separated flows and significant unsteadiness a subgrid-scale stress model is implemented.   

Shock-initiated Combustion of a Spherical Density Inhomogeneity

A spherical density inhomogeneity is prepared using fuel and oxidizer at a stoichiometric ratio and Xe as a diluent that increases the overall density of the bubble mixture (55$\%$ Xe, 30$\%$ H$_2$, 15$\%$ O$_2$). The experiments are performed in the Wisconsin Shock Tube Laboratory in a 9.2 m vertical shock tube with a $25.4$ cm $\times$ $25.4$ cm square cross-section. An injector is used to generate a 5 cm diameter soap film bubble filled with the combustible mixture. The injector retracts flush into the side of the tube releasing the bubble into a state of free fall. The combustible bubble is accelerated by a planar shock wave in N$_2$ ($2.0 < M < 2.8$). The mismatch of acoustic impedances results in shock-focusing at the downstream pole of the bubble. The shock focusing results in localized temperatures and pressures significantly larger than nominal conditions behind a planar shock wave, resulting in auto-ignition at the focus. Planar Mie scattering and chemiluminescence are used simultaneously to visualize the bubble morphology and combustion characteristics. During the combustion phase, both the span-wise and stream-wise lengths of the bubble are seen to increase compared to the non-combustible scenario. Additionally, smaller instabilities are observed on the upstream surface, which are absent in the non-combustible bubbles.