Detailed analysis of vibrational nonequilibrium of molecular oxygen in shock-heated flow

A detailed comparison is made of two different methods for simulating vibrational relaxation behind a strong shock wave in molecular oxygen. The first approach is phenomenological and makes a number of strong assumptions in using an overall vibrational energy relaxation equation. The second approach resolves all of the quantized vibrational energy states using temperature-dependent state-to-state transition rates. Comparisons with experimental measurements indicate that the state-resolved approach is more accurate. The assumptions made in the phenomenological model are assessed in detail by using the state-resolved approach. It is determined that all of the assumptions made in the simpler model are violated directly behind a strong shock wave. A parameter based on the effects of multi-quantum transitions is proposed for predicting when the more detailed modeling approach must be used in compressed non-reacting flows and is found to be effective.