Calculation method of vibrationally relaxing flows in nozzles

The steady expansions of a vibrationally relaxing gas in convergent-divergent nozzles are studied for diatomic homonuclear molecules. An analytical-numerical method is carried out with a relaxation equation which is derived from the Boltzmann equation and which assumes VV collisions to be predominant. The molecular orientation effects are taken into account by choosing an adequate intermolecular potential describing an interaction in which the short-range repulsive effects are preponderant. For the case of nitrogen, the computation is performed with the unsteady Anderson method. The nonequilibrium effects upstream of the throat are evaluated and also the subsequent influence on the flow downstream of the throat. The results obtained in the supersonic section are more satisfying than those of the previous models in view of the experimental data. The relaxation times are 3-6 times shorter than with the model of Schwartz and Herzfeld (1954). Moreover, in the usual shock-tube temperature range, the relaxation time is found to be about six times shorter than the relaxation times measured behind a shock wave. The results are also discussed as functions of geometrical parameters and reservoir conditions, especially to maximize the frozen vibrational energy.