Approximate solutions for compressible turbulent boundary layers in three-dimensional flow.

The governing equations for a compressible turbulent boundary layer in three-dimensional flow are treated in a coordinate system based on the trace of the inviscid streamline on the body. The equation set is simplified by assuming that, within the boundary layer, the component of flow normal to the direction of the inviscid streamline (cross-flow) is small. As a result, the continuity, energy, and streamwise-momentum equations decouple from the cross-flow-momentum equation. An approximate method of solution for the stream wise flow is based on a method given by Sasman and Cresci for two-dimensional flows. The crossflow-momentum equation is then solved, dependent on the streamwise solution. A yawed, infinite-cylinder example is considered in some detail, and analytic heat-transfer results are compared with experiment. Cross-flow solutions provide an indication of the applicability of the small-cross-flow postulate. The cross-flow-velocity profile shape, wall-cooling rate, and streamwise form factor are each shown to have a significant effect on solutions of the cross-flow-momentum equation.