Prediction of Vibrational Relaxation in Hypersonic Expanding Flows Part I: Model Development

A number of experiments in nozzles have indicated that the Landau-Teller vibrational relaxation model fails to accurately predict the relaxation process in expanding flows. In the present study vibrational transition rate equations are solved and the detailed calculations are used to develop a simplified relaxation model. The present simplified relaxation model allows both non-BoItzmann population distributions in vibrationally heating and cooling flows. This simplified model also includes the effect of anharmonicity on vibrational transition rates and energy transfer.