Generalized Boltzmann solution for non-equilibrium flows and the computation of flowfields of binary gas mixture

Abstract

Hypersonic flows about space vehicles produce flowfields in thermodynamic non-equilibrium with the local Knudsen numbers Kn which may lie in all the three regimes: continuum, transition and rarefied. Continuum flows can be modeled accurately by solving the Navier–Stokes (NS) equations; however, the flows in transition and rarefied regimes require a kinetic approach such as the direct simulation Monte Carlo (DSMC) method or the solution of the Boltzmann equation. The Boltzmann equation and the general solution approach, using the splitting method, will be introduced in this paper. Details of the method used for solving both the classical Boltzmann equation (CBE) and the generalized Boltzmann equation (GBE) are also provided. The gas mixture discussed in this paper may consist of both monoatomic and diatomic gases. In particular, the method is applied to simulate two of the three primary constituents of air (N2, O2, and Ar) in a binary mixture at 1:1 density ratio at Mach 2 and 5, with gases in translational, rotational and vibrational non-equilibrium.

Keywords

• Generalized Boltzmann equation
• Non-equilibrium flow
• Monoatomic gas
• Diatomic gas
• Splitting method