Vibrational energy transfer of diatomic gases in hypersonic expanding flows

In high temperature flows related to vehicles at hypersonic speeds significant excitation of the vibrational energy modes of the gas can occur. Accurate predictions of the vibrational state of the gas and the rates of vibrational energy transfer are essential to achieve optimum engine performance, for design of heat shields, and for studies of ground based hypersonic test facilities. The Landau-Teller relaxation model is widely used because it has been shown to give accurate predictions in vibrationally heating flows such as behind forebody shocks. However, a number of experiments in nozzles have indicated that it fails to accurately predict the rate of energy transfer in expanding, or cooling, flow regions and fails to predict the distribution of energy in the vibrational quantum levels. The present study examines the range of applicability of the Landau-Teller model in expanding flows and develops techniques which provide accurate predictions in expanding flows.; In the present study, detailed calculations of the vibrational relaxation process of {dollar}Nsb2{dollar} and CO in cooling flows are conducted. A coupled set of vibrational transition rate equations and quasi one-dimensional fluid dynamic equations is solved. Rapid anharmonic Vibration-Translation transition rates and Vibration-Vibration exchange collisions are found to be responsible for vibrational relaxation acceleration in situations of high vibrational temperature and low translational temperature. The predictions of the detailed master equation solver are in excellent agreement with experimental results.; The exact degree of acceleration is cataloged in this study for {dollar}Nsb2{dollar} and is found to be a function of both the translational temperature (T) and the ratio of vibrational to translational temperatures {dollar}(Tsb{lcub}vib{rcub}/T).{dollar} Non-Boltzmann population distributions are observed for values of {dollar}Tsb{lcub}vib{rcub}/T{dollar} as low as 2.0. The local energy transfer rate is shown to be an order of magnitude or more faster than the Landau-Teller model for more extreme cases of thermal non-equilibrium. However these large degrees of local acceleration are difficult to observe in gasdynamic flows because the vibrational energy becomes frozen in rapid expansions. The Landau-Teller model fails to predict non-Boltzmann population distributions for even moderate degrees of thermal non-equilibrium but only fails to accurately predict the overall amount energy in vibration for flows which both have high values of {dollar}Tsb{lcub}vib{rcub}/T{dollar} and are not vibrationally frozen.; A simplified relaxation model is developed which allows both non-Boltzmann population distributions and includes anharmonic transition rates and energy transfer. Although the simplified anharmonic model requires significantly less computational time than the master equation solver it gives good agreement with the detailed solver and with experimental test results.