Rotational and Vibrational Nonequilibrium in a Low Diffusion Particle Method for Continuum Flow Simulation

Abstract

A low diffusion particle method for simulating compressible low Knudsen number gas flows is modified for application to flows involving nonequilibrium distributions in rotational and vibrational energy modes. This method is closely based on the direct simulation Monte Carlo (DSMC) method, and has been developed for use in a strongly coupled hybrid scheme with DSMC. In simulations employing this hybrid scheme, the proposed modifications allow greater consistency with DSMC and reduced information loss along continuum breakdown boundaries when significant internal energy nonequilibrium effects exist within continuum flow regions. Two different approaches for rotational and vibrational nonequilibrium are proposed; the first provides greater efficiency and reduced sensitivity to time step size, while the second utilizes standard DSMC energy exchange procedures and should be easier to implement in an existing DSMC code. Both approaches are evaluated through comparison with DSMC for a set of homogeneous relaxation problems, and capabilities of the hybrid scheme are demonstrated in simulations of a hypersonic flow over a cylinder. I. Introduction wide range of gas flow problems of engineering interest involve regions of continuum flow as well as rarefied regions with strong translational nonequilibrium. These flow problems include gas flows within and around micro-electro-mechanical systems (MEMS), supersonic flows for which the internal structure of shocks is important, flows around reentry vehicles and other hypersonic atmospheric flows, gas venting into a near-vacuum, and rocket exhaust flows at high altitudes. In any of these types of flows, characteristic lines or diffusive quantities may travel in both directions between rarefied and continuum regions, so that two-way coupled information transfer is required during flowfield simulation. Rarefied regions are typically simulated using the direct simulation Monte Carlo (DSMC) method, 1 the dominant method for simulation of high Knudsen number (Kn) gas flows. In a DSMC simulation, a large number of particles – each representing a large collection of atoms or molecules – are tracked through a computational grid. Particle move and collide operations during each simulation time step are consistent with advection and collision terms in the Boltzmann equation (the governing equation for dilute gas flows at any Kn) and macroscopic flow properties are evaluated as cell-based averages of particle quantities. Relative to other simulation techniques for high Kn flows, DSMC tends to provide an excellent balance of computational efficiency, low memory and accuracy. While the underlying assumptions in DSMC are valid in both high and low Kn regimes, the DSMC method can be prohibitively expensive in low Kn regions due to severe restrictions on the cell size and time step interval. More efficient computational fluid dynamics (CFD) methods, typically based on a finite volume solution to the Navier-Stokes (NS) equations, are generally used instead for simulation of low Kn regions where the NS equations are valid.