Models for direct Monte Carlo simulation of coupled vibration–dissociation

Abstract

Models are developed to permit direct Monte Carlo techniques to simulate coupled vibration–dissociation (CVD) behavior prevalent in high‐temperature gases. This transient thermochemical phenomenon leads to dissociation incubation, reduced quasisteady dissociation rates, and non‐Boltzmann distributions of vibrational energy during both dissociation and recombination. Essential for simulation of rarefied gas dynamics, Monte Carlo methods employ discrete particles to simulate molecular interactions directly, but have traditionally incorporated simplistic reaction models which failed to capture CVD behavior. To identify thermochemical collisions within the gas, a new dissociation selection probability is developed as a function of the extent by which the collision energy exceeds the gap between the dissociation threshold and the molecular vibrational energy of bounded anharmonic oscillators. A free parameter φ in the probability function controls the extent of vibrational favoring in dissociation selection. The new model is modified for application to the unbounded simple harmonic oscillator. Simulation of dissociation‐ and recombination‐dominated thermochemical relaxation of O₂ reservoirs, as well as the dissociation incubation behavior of N₂ behind strong shock waves, demonstrates the ability of the new models to capture CVD behavior. Parameter φ is assessed empirically for O₂ and N₂ dissociation by comparison to experimental data.