Similar solutions in nonequilibrium nozzle flows

Abstract

The phenomena of thermal and/or chemical nonequilibrium in flowing gases at high temperatures is of fundamental importance in rocket nozzles as well as hypersonic flight simulation facilities. The present state-of-the-art for solving nonequilibrium nozzle flow problems requires complex computer programs with which the flow variables are determined by numerical integration for any given initial and boundary conditions. However, this approach does not provide suitable theoretical comparisons for use by the experimentalist because of many variables involved. Hence, it is apparent that suitable similar solutions, incorporating more general correlating parameters, are highly desirable. Towards this end, Reddy and Daum have analyzed the case of a single diatomic gas undergoing either vibrational relaxation or dissociational relaxation only. In the present work, a more realistic model for nozzle flow of a single diatomic gas like oxygen, undergoing simultaneous relaxation in both vibrational and dissociational modes including coupling between them, is used. The governing equations have been reduced to similar form by applying transformations to both dependent and independent variables. The character and parametric dependence of these similar governing equations are discussed. The near-universal form of these similar governing equations provides exact general correlating parameters. The similar solutions are presented in the form of graphs. Next, the case of a multi-species gas like air, undergoing only chemical nonequilibrium with vibrational mode in equilibrium, is dealt with. Following a similar procedure as used in the case of a single diatomic gas, general correlating parameters for air are obtained and corresponding similar solutions are presented in the form of graphs. For any given initial conditions, the nozzle flow quantities can be read off from the graphs without resorting to complex computer programs.