State-to-state study of non-equilibrium recombination of oxygen and nitrogen molecules

Rapidly cooled mixtures are of interest for several applications, including hypersonic flows due to the presence of strong cooling temperature gradients in regions such as hypersonic boundary layers and expanding nozzles. There have been very few studies of rapidly cooled mixtures using the high-fidelity rovibrational databases afforded by ab initio potential energy surfaces. This work makes use of existing rovibrational state-specific databases to study rapidly cooled mixtures. In particular, we seek to understand the importance of thermal non-equilibrium in recombining mixtures using both rovibrational and vibrational state-to-state methods for oxygen and nitrogen molecules. We find that although there is significant non-equilibrium during recombination, it is well captured by the vibrational state-specific approach. Finally, we compare the global recombination rate computed based on the state-specific recombination rate coefficients and the global recombination rate computed based on the time local dissociation rate coefficient, which is reversed using the principle of detailed balance. The local dissociation rate coefficient is computed by weighting the state-specific dissociation rate coefficients with the state-specific distribution of energy states. We find a large difference between these rates, highlighting a potential source of errors in hypersonic flow predictions.