(A) study of collision cross-sections and non-equilibrium flow analyses using a molecular collision approach

Abstract

To investigate the non-equilibrium phenomena of bimolecular collisions for hypersonic thermodynamics or rarefied gas dynamics, the cross-section models of elastic and inelastic collisions are needed. The total cross-section is the summation of elastic and inelastic collision cross-sections. The inelastic cross-section is represented by state-to-state cross-section where the state-to-state means that initial rotational and vibrational state of the molecule is transferred to other state by the molecular collision. In the present study, total cross-section model for direct simulation Monte-Carlo calculation, the state-to-state cross-sections and rate coefficients, and non-equilibrium phenomena were investigated. For total cross-sections, modification and expansion of the collision parameters for the general soft-sphere model were made for use in the Direct Simulation Monte-Carlo calculation of hypersonic flows in the temperature range of 300K to 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 total cross-section models. The Direct Simulation Monte-Car...