Logarithmic laws for compressible turbulent boundary layers

Dimensional similarity arguments proposed by Millikan are used with the Morkovin hypothesis to deduce logarithmic laws for compressible turbulent boundary layers as an alternative to the traditional van Driest analysis. It is shown that an overlap exists between the wall layer and the defect layer, and this leads to logarithmic behavior in the overlap region. The von Karman constant is found to depend parametrically on the Mach number based on the friction velocity, the dimensionless total heat flux, and the specific heat ratio. Even though it remains constant at approximately 0.41 for a freestream Mach number range of 0 to 4.544 with adiabatic wall boundary conditions, it rises sharply as the Mach number increases significantly beyond 4.544. The intercept of the logarithmic law of the wall is found to depend on the Mach number based on the friction velocity, the dimensionless total heat flux, the Prandtl number evaluated at the wall, and the specific heat ratio. On the other hand, the intercept of the logarithmic defect law is parametric in the pressure gradient parameter and all of the aforementioned dimensionless variables except the Prandtl number. A skin friction law is also deduced for compressible boundary layers. The skin friction coefficientmore » is shown to depend on the momentum thickness Reynolds number, the wall temperature ratio, and all of the other parameters already mentioned. 26 refs.« less