Velocity transformation for compressible wall-bounded turbulence—An approach through the mixing length hypothesis

In an endeavor to establish a connection between the mean velocity profile in compressible wall-bounded turbulence and its incompressible analogue, a refined version of the Trettel and Larsson’s (TL) transformation is systematically derived and rigorously assessed across diverse flow scenarios. Incorporating the recently proposed intrinsic compressibility effects and modeling the multi-layer structure of mixing lengths, the proposed transformation demonstrates exceptional performance in collapsing 57 canonical flow cases, including cooled channel and pipe flows, channel flows with pseudo heat sources, as well as adiabatic and diabatic boundary layer flows. Furthermore, the transformation seamlessly extends to low Reynolds number cooled channel and pipe flows, achieving a level of accuracy unparalleled by other transformations in the current state-of-the-art.