Vibrational energy conservation with vibration-dissociation coupling: General theory and numerical studies

The coupling between vibrational relaxation and dissociation in nitrogen is studied. The conservation of vibrational energy equation is derived and the form of the source terms is determined for physically consistent coupling models. Using a computational fluid dynamics method, the results from three current coupling models are compared to existing experimental interferograms for spherical geometries. It is found that the coupling models of Park, Treanor and Marrone, and Macheret and Rich are able to accurately predict the shock standoff distances and reproduce the experimental interference patterns for these conditions. However, there are differences in the vibrational temperature profiles among the coupling models. The experimental interferograms are not sensitive to these differences, though.