Numerical Solution of Two-Dimensional Compressible Radiating Flowfields

A two-dimensional numerical model for flows with coupled radiation from an emitting, absorbing, and scattering fluid is developed. The continuity, momentum, and energy equations are approximated by a finite-difference method, and the radiative transfer equation is discretized by the product-integration method in which the shape function is taken to be piecewise-constant. The numerical grid for the radiation field is matched with the flowfield grid, and the continuity, momentum, and energy equations are coupled with the radiative transfer equation to obtain steady-state solutions. The model is verified by comparison with existing solutions for a laminar Poiseuille flow. Some sample calculations of inviscid supersonic flow of an ideal gas through a two-dimensional diffuser are presented to show the effect of radiation on the temperature field in the diffuser.