Consistent post-reaction vibrational energy redistribution in DSMC simulations using TCE model

Abstract

The direct simulation Monte Carlo (DSMC) method has been widely applied to study shockwaves, hypersonic reentry flows, and other nonequilibrium flow phenomena. Although there is currently active research on high-fidelity models based on ab initio data, the total collision energy (TCE) and Larsen-Borgnakke (LB) models remain the most often used chemistry and relaxation models in DSMC simulations, respectively. The conventional implementation of the discrete LB model, however, may not satisfy detailed balance when recombination and exchange reactions play an important role in the flow energy balance. This issue can become even more critical in reacting mixtures involving polyatomic molecules, such as in combustion. In this work, this important shortcoming is addressed and an empirical approach to consistently specify the post-reaction vibrational states close to thermochemical equilibrium conditions is proposed within the TCE framework. Following Bird’s quantum-kinetic (QK) methodology for populating post-reaction states, the new TCE-based approach involves two main steps. The state-specific TCE reaction probabilities for a forward reaction are first pre-computed from equilibrium 0-D simulations. These probabilities are then employed to populate the post-reaction vibrational states of the corresponding reverse reaction. The new approach is illustrated by application to exchange and recombination reactions relevant to H2–O2 combustion processes.