Numerical study of anharmonic diatomic relaxation rates in shock waves and nozzles

The vibrational master equation, including dissociation, for a system of anharmonic oscillator molecules in a heat bath and in flows behind a normal shock and along a nozzle is numerically integrated. From these solutions the vibrational excitation, dissociation, vibrational de-excitation and recombination rates are found. The effect of vibration to vibration energy exchange (V-V) on the relaxation rates is shown to cause the induction time for dissociation to be longer; to suggest a failure of the linear rate law for H2 and Ar mixtures; to give an acceleration of vibrational excitation as equilibrium is approached; to cause the vibrational 'temperature' in a nozzle to be lower, for vibrational de-excitation only, and higher, for recombination included, than if no V-V exchanges were permitted. The magnitudes of the relaxation rates are in reasonable agreement with experiment. The use of conventional nozzle flow programs, with shock-tube-determined dissociation and vibrational excitation rates, appears to be valid for the cases examined.