Consistent treatment of transport properties for five-species air direct simulation Monte Carlo/Navier-Stokes applications

Abstract

A general approach for achieving consistency in the transport properties between direct simulation Monte Carlo (DSMC) and Navier-Stokes (CFD) solvers is presented for five-species air. Coefficients of species diffusion, viscosity, and thermal conductivities are considered. The transport coefficients that are modeled in CFD solvers are often obtained by expressions involving sets of collision integrals, which are obtained from more realistic intermolecular potentials (i.e., ab initio calculations). In this work, the self-consistent effective binary diffusion and Gupta et al.–Yos tranport models are considered. The DSMC transport coefficients are approximated from Chapman-Enskog theory in which the collision integrals are computed using either the variable hard sphere (VHS) and variable soft sphere (VSS) (phenomenological) collision cross section models. The VHS and VSS parameters are then used to adjust the DSMC transport coefficients in order to achieve a best-fit to the coefficients computed from more realistic intermolecular potentials over a range of temperatures. The best-fit collision model parameters are determined for both collision-averaged and collision-specific pairing approaches using the Nelder-Mead simplex algorithm. A consistent treatment of the diffusion, viscosity, and thermal conductivities is presented, and recommended sets of best-fit VHS and VSS collision model parameters are provided for a five-species air mixture.