Comparison of Three Radiative Formulations for Interactions in Three-Dimensional Boundary Layers

Abstract

This paper presents a comparison of analyses using three radiative interaction formulations to evaluate the effects of an external source of thermal radiation on the three-dimensional hypersonic turbulent boundary layer on a sharp cone at an angle of attack. The three radiative formulations considered are: 1) optically thin limit approximation, 2) optically thick limit approximation for the optical thickness of the medium, and 3) approximation for the wavelength-dependent properties of the medium. For each of these formulations, interactions between radiation from an external source and the hypersonic boundary layer on a cone at an angle of attack are determined by solving numerically the three-dimensional compressible turbulent boundary-layer equations together with the energy equation modified to include thermal radiation. Turbulence is accounted for by making use of Prandtl's mixing length hypothesis with van Driest's modification for the wall region. Local nonsimilarity in the axial direction has been used to facilitate the numerical solution. Velocity and temperature fields, heat-transfer rates, and axial and normal aerodynamic coefficients have been compared for the three formulations at different Reynolds and Mach numbers. Even though the band approximation model is in general the most accurate of the three formulations considered, the results indicate that because of the extensive CPU time needed for this model it is not recommended for application to the problem under study.