Radiation coupled chemical nonequilibrium normal shock waves

Abstract

The problem of a normal shock wave in air or other gas with complex chemistry and coupled radiation is considered. Molecular transport properties are neglected and the gas mixture is assumed in translational, rotational, vibrational and electronic equilibrium with the local temperature. Only continuum radiation is included. Solutions are presented for strong shock waves in air, where air is assumed to consist of eleven species, N2, O2, O, NO, NO+, N+, O+, N+2, O+2, and electrons. When the usual methods of integrating ordinary differential equations are applied to the “stiff” equations of chemical nonequilibrium flow, it is found that the maximum step size is very small. Several methods which promise great improvement have appeared in the literature recently. These methods are shown to be special cases of a whole family of approaches, other members of which are superior in many problems. A proof of convergence is given. Solutions are obtained for the comparatively simple optically thin case, and with absorption of radiation behind the shock front. In the latter, the spectrum is broken into regions where the absorption cross section of each species is assumed only a function of temperature. The approximate solution to the radiative transfer equation is obtained by using the first order half moment equations.