VIBRATIONAL-RELAXATION AND DISSOCIATION BEHIND SHOCK-WAVES .2. MASTER EQUATION MODELING

This paper addresses 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 thai 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 tau(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 tau(inc)similar to tau(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.