Direct Shocks in Vibrationally Nonequilibrium Diatomic Gases at Various Distances from Critical Cross-Section of Nozzle

Abstract

The high-temperature diatomic gas flows are considered in expanding nozzles under the conditions of a disturbance of the equilibrium distribution over vibrational levels of the molecules. The investigation of such flows is bound up with the problem of the inversion of the vibrational populations in the active mediums of molecular lasers. Under diverse values of the pressure overfall on coming out of the nozzle the shock waves can arise at various distances from critical cross-section. Under these conditions the research of the molecular distributions over vibrational levels behind such shocks acquires special significance. Relaxation processes behind a shock-wave front in a vibrationally nonequilibrium gas have been analyzed previously using differential equations for the vibrational populations. In our paper a shock wave is modeled by a thin transient layer between two vibrationally nonequilibrium quasi-stationary states. Generalized conditions of dynamic consistency are derived. The methods of kinetic theory are used. This approach does not allow one to determine the vibrational populations behind a shock wave at various distances from its front. However, it enables one to find the velocity of the gas, the total number of molecules in unit volume, the gas temperature and the temperature, called by Treanor the temperature of the 1st vibrational level, directly behind a shock wave (outside the relaxation zone). The knowledge of these values allows one to determine all parameters of interest using the kinetic theory methods. An advantage of this approach is that the considerably less number of equations is used and the need to know the probabilities of different vibrational transitions is eliminated. Earlier it was shown that the inversion of vibrational populations decreases when the flows pass through a shock wave. In present paper we note two competing factors. The further direct shock is from critical cross-section of the nozzle, the more the nonequilibrium degree of vibrational distributions and the inversion of vibrational populations are. In connection with that the intensity of a shock wave increases. It leads to a decrease of the vibrational nonequilibrium and the inversion of vibrational populations.