On kinetics modeling of vibrational energy exchange with application to the nozzle flow problem

The results of a comparison between data and computer modeling for a nonequilibrium expansion are reported. First, three models of vibrational energy exchange are examined by considering requirements imposed by equilibrium and quantized molecular vibration. One model was derived by considering the kinetics of state populations. The other models do not consider the state population kinetics in their derivations, and are often used in multi-temperature computational fluid dynamics programs. It is demonstrated that only the model derived by considering the kinetics of state populations satisfies first principles in the general case of unequal vibrational quanta. Use of the other models outside a singular case of validity may lead to significant misconceptions, especially if integrated in computer codes considering additional energy coupling mechanisms. Second, the model shown to satisfy first principles was used to simulate a nonequilibrium nozzle flow of an admixture approximating air. The results were compared to measurements made using a Raman scattering technique. Perturbations from theoretical or experimental values for V-V collision probabilities reproduced the measured coupling of the vibrational temperatures of N2 and O2. However, the same perturbations did not reproduce other aspects of the data. Further physical modeling may be necessary to account for the remaining discrepancy.