Dissociation–recombination relaxation behind a normal shock

Abstract

Mathematical methods developed originally for thermal explosion theory are used to study the evolution of a dissociation–recombination process occurring in a compressible gas behind a normal shock. The dissociation–recombination reaction, AB+M■A+B+M, is assumed to have a relatively large dissociation temperature, so that high activation energy perturbation techniques can be used to derive general parameter dependent analytical solutions. Spatial variation of the dependent variables is described in three zones, each of distinct length scale and physical character. Initially, small changes in temperature, concentrations, density, and pressure occur in the relatively high temperature dissociation initiation zone. In the subsequent broader major dissociation region, most of the specie AB is converted to A and B and there are significant variations in all physical variables. In the last and thickest zone, recombination becomes important as the reactive flow evolves to a final equilibrium state. The results provide an analytical counterpart to numerical solutions obtained earlier by Freeman [J. Fluid Mech. 4, 407 (1958)] and Matthews [Phys. Fluids 2, 170 (1959)] for the now classical problem of idealized diatomic gas dissociation.