A Coupled Vibration-Dissociation Model for Nitrogen from Direct Molecular Simulation

Abstract

A new two-temperature model for use in computational fluid dynamics (CFD) simulations for coupled internal energy transfer and dissociation in nitrogen is constructed based on ab-initio data from Direct Molecular Simulation (DMS). The DMS method imbeds trajectory calculations, where molecular collisions are integrated using an ab-initio potential energy surface, within a direct simulation Monte Carlo calculation. As a result, the DMS method is able to directly simulate rovibrational excitation and dissociation processes, including the evolution of non-Boltzmann internal energy distribution functions and coupling to dissociation. Guided by recent DMS results for a full nitrogen system (both N-N 2 and N 2 -N 2 collisions), a simple model based on surprisal analysis is found to accurately predict both the overpopulation of high v-level states during rapid excitation and the depletion of high v-level states due to dissociation. Furthermore, both DMS and quasi-classical-trajectory (QCT) results can be used to determine the dissociation probability for molecules in a certain vibrational energy level (v). A simple probability model that is a function of v-level is shown to accurately reproduce DMS data. Combined, the probability expression can be integrated over the surprisal model, which accounts for non-Boltzmann vibrational energy distributions. The result, is a two-temperature (T , T v ) dissociation model that accurately reproduces a range of coupled vibration-dissociation phenomena found in previous studies and in the current DMS results. The new two-temperature model is suitable for large scale CFD simulations.