Asymptotic solution for the viscous radiating shock layer.

Abstract

The viscous flow of a transparent radiating gas in a stagnation region is studied by means of matched asymptotic expansions. The boundary-layer equations are taken as the appropriate model of the shock layer. An exact solution is obtained for a special case; by considering asymptotic expansions of this solution in terms of Reynolds number, the interaction of the viscous and in viscid regions is clarified. With this solution as a model, the asymptotic solution for the general case is constructed by the method of matched inner and outer expansions. Owing to the coupling between velocity and enthalpy profiles, the inner expansion is characterized by powers and logarithms of Reynolds number, rather than the usual square root dependence. To first order, the boundary layer is shown to be exactly equivalent to that on a body having larger nose radius and lower flight speed in a nonradiating gas. The asymptotic results are compared with solutions obtained by direct integration using an electronic computer.