A variable hard sphere-based phenomenological inelastic collision model for rarefied gas flow simulations by the direct simulation Monte Carlo method

Abstract

A modified phenomenological model is constructed for the simulation of rarefied flows of polyatomic non-polar gas molecules by the direct simulation Monte Carlo (DSMC) method. This variable hard sphere-based model employs a constant rotational collision number, but all its collisions are inelastic in nature and at the same time the correct macroscopic relaxation rate is maintained. In equilibrium conditions, there is equi-partition of energy between the rotational and translational modes and it satisfies the principle of reciprocity or detailed balancing. The present model is applicable for moderate temperatures at which the molecules are in their vibrational ground state. For verification, the model is applied to the DSMC simulations of the translational and rotational energy distributions in nitrogen gas at equilibrium and the results are compared with their corresponding Maxwellian distributions. Next, the Couette flow, the temperature jump and the Rayleigh flow are simulated; the viscosity and thermal conductivity coefficients of nitrogen are numerically estimated and compared with experimentally measured values. The model is further applied to the simulation of the rotational relaxation of nitrogen through low- and high-Mach-number normal shock waves in a novel way. In all cases, the results are found to be in good agreement with theoretically expected and experimentally observed values. It is concluded that the inelastic collision of polyatomic molecules can be predicted well by employing the constructed variable hard sphere (VHS)-based collision model.