Vibrational Relaxation and Dissociation Behind Shock Waves Part 2: Master Equation Modeling

Abstract

We address the application of the analytical nonperturbative semiclassical vibration-translation and vibration-vibration-translation forced harmonic oscillator rate models for kinetic modeling calculations. Master equation modeling of nonequilibrium dissociating gas flows, based on the forced harmonic oscillator multiple-jump rate model, is applied for simulation of vibrational relaxation and dissociation of N 2 and O 2 -Ar mixtures behind strong shock waves. The comparison with the first-order rate model (Schwartz, Slawsky, and Herzfeld [SSH] theory) shows that the SSH and forced harmonic oscillator theories predict strongly different vibrational distribution functions only for times less than or equal to the vibrational relaxation time T vT . Consequently, replacing SSH rates by the forced harmonic oscillator rate model has very little effect on the calculated dissociation rate, since the dissociation incubation time is T lne ∼T VT . The incubation time calculated using impulsive and forced harmonic oscillator dissociation models also agrees well with experimental data. Thus, it is shown that vibrational relaxation, as well as nonequilibrium dissociation at hypersonic temperatures, may be satisfactorily described using the first-order, SSH vibration-vibration-translation rate model, despite the fact that this temperature region is normally clearly beyond the applicability of the SSH theory.