AN ASYMPTOTIC 2-LAYER MODEL FOR SUPERSONIC TURBULENT BOUNDARY-LAYERS

An asymptotic analysis of the compressible turbulent boundary-layer eq uations is carried out for large Reynolds numbers and mainstream Mach numbers of O(1). A self-consistent two-layer asymptotic structure is d escribed wherein the time-mean velocity and total enthalpy are logarit hmic within the overlap zone but in terms of the Howarth-Dorodnitsyn v ariable; the proposed structure leads to a compressible law of the wal l for high-speed turbulent flows with surface heat transfer. Simple ou ter-region algebraic turbulence models are formulated to reflect the e ffects of compressibility. To test the proposed asymptotic structure a nd turbulence models, a set of self-similar outer-region profiles for velocity and total enthalpy is obtained for constant-pressure flow and for constant wall temperature; these are combined with wall-layer pro files to form a set of composite profiles valid across the entire boun dary layer. A direct comparison with experimental data shows good agre ement over a wide range of conditions for flows with and without surfa ce heat transfer.