A transformation for compressible turbulent boundary layers with air injection

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Abstract
The transformation proposed by Coles for correlating the compressible turbulent boundary layer on a solid surface with a given incompressible layer has been extended to the case of a porous surface with air injection. However, unlike Coles's work, the new transformation does not use the empirical concept of the sublayer to define one of the transformation parameters. Instead this parameter can be defined in terms of the stream function at the wall, and so is directly related to the injection rate. The present paper concerns the transformation for the boundary layer with constant pressure and zero heat transfer, but the possibility of extending the transformation to flows with pressure gradients and heat transfer is mentioned briefly.Comparison with experiments shows that the new transformation successfully relates cf, θ and the fully turbulent part of the velocity profile with their corresponding incompressible values for a wide range of Mach numbers and injection rates.