High-Temperature Transport Collision Integrals for O ₂ +N Collisions

Abstract

Collision integrals related to transport properties are calculated for O₂+N collisions using quasi-classical trajectory molecular dynamics simulations on high-accuracy ab initio potential energy surfaces for the 2A', 4A', and 6A' electronic states. The influence of O₂ vibrational excitation on collision integrals is investigated within the framework of state-to-state kinetic theory, with inelastic contributions incorporated using the Wang-Chang and Uhlenbeck formulation. Under vibrational nonequilibrium conditions (with vibrational temperatures up to 20,000 K), the thermally averaged diffusion and viscosity collision integrals deviate from their equilibrium values by at most 12 and 17%, respectively. For moderate nonequilibrium (|T - T_v| ≤ 5000 K), deviations remain below 5%, indicating that the equilibrium assumption provides an adequate description. Furthermore, approximating vibrational state-specific collision integrals by those of the vibrational ground state yields results that reproduce the detailed calculations, with only minor errors across the considered temperature range. This approximation provides sufficient accuracy for estimating thermally averaged collision integrals, even when the vibrational distribution function deviates significantly from the Boltzmann distribution, and can substantially simplify state-specific modeling of transport properties in hypersonic flow simulations. For practical implementation, the mean collision integrals are fitted as functions of temperature, and the resulting data are further used to reparameterize widely used collision models.