Modification and expansion of the generalized soft-sphere model to high temperature based on collision integrals

Abstract

In the present study, modification and expansion of the collision parameters for the general soft-sphere model [J. Fan, Phys. Fluids 12, 4399 (2002)] were made for use in the direct simulation Monte Carlo calculation of hypersonic flows in the temperature range of 300–50 000K. The collision integrals were expressed as a two-term function in a form of the inverse power of temperature, which was cast in terms of the soft-sphere scattering parameters and the four total cross-section parameters. Next, the most recent available data for the diffusion and viscosity collision integrals were collected and fitted into a function of temperature in the same form. By equating these expressions for the diffusion and viscosity collision integrals simultaneously, the five collision parameters were deduced as functions of species combinations. The resulting collision parameters for the general soft-sphere model were tabulated for 191 collision pairs involving 22 species. It was shown that the transport properties calculated by using the present collision parameters are much closer to experiments, theoretical data, and the values obtained by the ab initio calculations from quantum-mechanically derived potential energy surfaces than existing elastic collision models. The direct simulation Monte Carlo calculation of flow around a circular cylinder confirmed that discernible differences exist between the results based on the present study and those of the existing models.