Incorporating intrinsic compressibility effects in velocity transformations for wall-bounded turbulent flows

A transformation that relates a compressible wall-bounded turbulent flow with non-uniform fluid properties to an equivalent incompressible flow with uniform fluid properties is derived and validated. The transformation accounts for both variable-property and intrinsic compressibility effects, the latter being the key improvement over the current state-of-the-art. The importance of intrinsic compressibility effects contradicts the renowned Morkovin's hypothesis. The proposed transformation is then used for drag and heat transfer prediction in compressible flows. This requires the precise knowledge of the entire velocity and temperature profiles. Current methods typically assume a single velocity scaling law to inverse transform the incompressible reference profile, neglecting the different scaling characteristics of the inner and outer layers. We use distinct velocity transformations for these two regions. In the inner layer, we utilize our proposed scaling law, while the outer layer profile is inverse-transformed with the well-known Van Driest transformation. The result is an analytical expression for the mean shear valid in the entire boundary layer, which combined with a temperature-velocity relationship, provides predictions of mean velocity and temperature profiles at unprecedented accuracy. Using these profiles, drag and heat transfer is evaluated with an accuracy of +/-4% and +/-8%, respectively, for a wide range of compressible turbulent boundary layers up to Mach numbers of 14.