Vibrational state-specific model for dissociation and recombination of the O( Σ )+O( P) system in DSMC.

A vibrational state-specific model for dissociation and recombination reactions within the direct simulation Monte Carlo method is introduced to study the energy level dynamics of the O + O system. The state-resolved cross sections for vibrational relaxation and dissociation reactions are obtained from a rotationally averaged quasi-classical trajectory database based on the Varandas and Pais O(  Σ )+O(  P) potential energy surface. A two-step binary collision framework is outlined to characterize the vibrational state-resolved recombination probabilities, which are constrained by detailed balance for orbiting pair formation, and microscopic reversibility applied to the dissociation cross sections for orbiting pair stabilization. The vibrational state-to-state (STS) model is compared to the phenomenological total collision energy (TCE) and quantum kinetic (QK) models through a series of 0-d non-equilibrium relaxation calculations. A quasi-steady state (QSS) region is established in the vibrational temperature profiles of the TCE, QK, and STS models under non-equilibrium heating. This QSS region is a result of the competition between vibrational relaxation by vibrational-translational (VT) transitions and O dissociation. The duration of QSS predicted by the STS model is approximately ten and four times that of the TCE and QK model predictions, respectively, and the total time to reach equilibrium is approximately 3.5 times that of the TCE model and 1.5 times that of the QK model. A distinct QSS region is not observed in the non-equilibrium cooling case. This is attributed to the relatively rapid VT transitions that work to equilibrate the vibrational energy distribution upon recombination, which is comparatively slow. The total time to reach equilibrium by the STS model in the non-equilibrium cooling case is five times and three times greater than those of the QK and TCE models, respectively.