VIBRATIONAL-RELAXATION AND DISSOCIATION BEHIND SHOCK-WAVES .2. MASTEREQUATION MODELING

This paper addresses the application of the analytical nonperturbative semiclassical vibration-translation and vibration-vibration-translati on forced harmonic oscillator rate models for kinetic modeling calcula tions. Master equation modeling of nonequilibrium dissociating gas flo ws, based on the forced harmonic oscillator multiple-jump rate model, is applied for simulation of vibrational relaxation and dissociation o f N-2 and O-2-Ar mixtures behind strong shock waves. The comparison wi th the first-order rate model (Schwartz, Slawsky, and Herzfeld [SSH] t heory) shows thai the SSH and forced harmonic oscillator theories pred ict strongly different vibrational distribution functions only for tim es less than or equal to the vibrational relaxation time tau(VT). Cons equently, replacing SSH rates by the forced harmonic oscillator rate m odel has very little effect on the calculated dissociation rate, since the dissociation incubation time is tau(inc)similar to tau(VT). The i ncubation time calculated using impulsive and forced harmonic oscillat or dissociation models also agrees well with experimental data. Thus, it is shown that vibrational relaxation, as well as nonequilibrium dis sociation 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 bey ond the applicability of the SSH theory.