Dynamics of a radiating gas with application to flow over a wavy wall.

Abstract

The spherical-harmonic approximation developed in astrophysics and neutron-Iran sport theory is applied to the radiation-transport equation for a nonscattering, quasi-equilibrium, grey gas. To a first approximation, the exact multidimensional transport equation is replaced by four differential equations. The gasdynamic equations, together with the four approximate transport equations, constitute a determinate set of purely differential equations valid for the complete range of optical thickness. Boundary conditions consistent with such approximations are discussed. Within the framework of linearized theory, the governing equation and the boundary conditions on velocity and on the temperature jump at the wall are obtained in terms of a perturbation velocity potential. To illustrate the special features of two-dimensional flow with radiation, a solution is obtained for steady flow over a sinusoidal wall. The solution is valid throughout the ranges of temperature and optical thickness. It is found that two systems of waves are present, a modified classical wave and a radiationinduced wave. The occurrence of pressure drag at subsonic speeds and the smoothing of the transition from subsonic to supersonic speeds reflect the nonequilibrium character of the radiating-gas flow.