Non-boltzmann vibrational energy distribution model for shock-heated flows

Dissociation is strongly coupled to the vibrational energy population of the dissociating gas. High-temperature excitation results in the overpopulation of high-energy states which enhances the dissociation rate as high-vibrational energy states are strongly favored to dissociation. Dissociation then results in the depletion of the high-energy population and consequently a balance between excitation and dissociation is reached resulting in quasi-steady state (QSS). QSS is characterized by time invariant non-Boltzmann depleted distributions and therefore reduced dissociation rates relative to the equilibrium estimates. In the kinetics models developed thus far, either the non-Boltzmann effects are ignored or added as pre-factors in an ad-hoc manner to an equilibrium rate constant. Recently, using ab initio potential energy surfaces, direct molecular simulation (DMS) approach has simulated the evolution of air species at the conditions representative of post-shock conditions. Based on the DMS data, a simple physics based model to characterize the non-Boltzmann distributions is developed. The model is compared with zero dimensional DMS simulations for nitrogen and oxygen at constant temperature (isothermal) and constant energy (adiabatic) conditions. The non-Boltzmann distributions are then used in conjunction with state-specific dissociation rate constants to derive a non-equilibrium continuum dissociation model.