There has been a growing interest in implementing state-resolved models for flowfield calculations of high-speed reentry applications that are characterized by regions of strong nonequilibrium. To this end, the present work provides a technique to rigorously compute transport collision integrals for vibrationally excited molecules. Collision dynamics calculations are extended to include state-to-state (StS) effects, and vibrationally resolved transport collisional quantities including scattering angles, cross sections, and collision integrals are computed for the $\mathrm{O}+{\mathrm{O}}_2$ system using potential energy surfaces (PESs) by Varga et al. [J. Chem. Phys. 147, 154312 (2017)]. From the nine surfaces provided by Varga et al., the “surface-averaged” collision integrals are computed for the oxygen system, and Gupta-Yos-style fits to the data are provided. It is found that the StS collision integrals depend not only on the vibrational state of the molecule, but also on the spin and spatial degeneracy associated with the PES that governs the interaction. Comparison of the collision integrals from the Varga et al. surfaces with those generated from the Varandas and Pais PES [Mol. Phys. 65, 843 (1988)] shows significant differences at highly excited vibrational states. The highly attractive nature of the Varandas and Pais surface leads to a monotonic increase in the collision integral values with vibrational excitation of ${\mathrm{O}}_2$, while the surface-averaged state-based collision integral values computed from the comparatively repulsive Varga et al. set of surfaces generally increase with vibrational excitation for temperatures up to 6000 K, and decrease with vibrational excitation at higher temperatures. Additionally, due to this nontrivial dependence of the collision integrals on the vibrational state of ${\mathrm{O}}_2$, simple empirical models are found to be unable to correctly estimate vibrational state-based collision integrals. Differences as high as 80% are obtained between the model predictions and values computed directly from the underlying PES. Evaluation of vibrationally resolved viscosity and translational thermal conductivity for the $\mathrm{O}+{\mathrm{O}}_2$ system under equilibrium conditions indicate that both these transport coefficients depend on the vibrational excitation of ${\mathrm{O}}_2$, with the contribution of the excited vibrational states increasing with rising temperature.

• Received 4 April 2020
• Accepted 14 September 2020

DOI:https://doi.org/10.1103/PhysRevFluids.5.113402