Inelastic processes in state-resolved transport theory: Application to oxygen mixtures

Abstract

The accurate prediction of transport properties in strongly nonequilibrium flows using the State-to-State approach requires reliable state-resolved collision integrals. In the present study, a self-consistent Variable Hard Sphere Statistical Inelastic Cross Section (VHS-SICS) model is constructed to treat elastic and rotationally inelastic collision cross sections within a unified analytical framework, with vibrationally inelastic cross sections incorporated through the forced harmonic oscillator with free rotation model. Two independent sets of VHS parameters are determined by fitting separately to quasiclassical trajectory reference data for the diffusion-type and viscosity-type collision integrals, achieving good agreement over a wide temperature range. The rotationally inelastic contribution to the collision integrals is found to grow significantly with temperature and vibrational excitation, with the Boltzmann-averaged ratio reaching a maximum of ∼1.3, and the effect being notably stronger for O2–O collisions than for O2–O2 collisions. The rotational energy diffusion collision integral Ωcirot,dk(1,1) is evaluated within the VHS-SICS framework for the O2/O system and is found to remain numerically close to the standard diffusion collision integral. The vibrationally inelastic contribution to the collision integrals is negligible throughout the temperature range considered. For the transport coefficients of O2/O mixtures, rotationally inelastic effects lead to reductions in both shear viscosity and thermal conductivity, with the influence growing monotonically with temperature and being most pronounced at an atomic oxygen mole fraction of xO = 50%. The rotational energy diffusion correction is found to have a negligible influence on the thermal conductivity. The present VHS-SICS model provides a reliable and self-consistent framework for the accurate prediction of transport properties in nonequilibrium oxygen-containing flows.