A Simple New Analysis of Compressible Turbulent Two-Dimensional Skin Friction Under Arbitrary Conditions

Abstract : A new approach is proposed for analyzing the compressible turbulent boundary layer with arbitrary pressure gradient. The new theory generalizes an incompressible study to account for variations in wall temperature and free- stream Mach number and temperature. By properly handling the law-of-the-wall in the integration of momentum and continuity across the boundary layer, one may obtain a single ordinary differential equation for skin friction devoid of integral thicknesses and shape factors. The new differential equation is analyzed for various cases. For flat plate flow, a new relation is derived which is accurate for adiabatic flow and reasonably good for flow with heat transfer. For flow with strong adverse and favorable pressure gradients, the new theory is in good agreement with experiment. The new theory also contains an explicitly criterion for boundary layer flow separation.

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