Mean temperature scalings in compressible wall turbulence

Abstract

We report a new Mach number invariant function for the mean temperature field in compressible wall turbulence. We demonstrate its validation by comparing it with the invariant functions derived in the previous studies, i.e., the semi-local-type and van-Driest-type scalings, case by case. The newly proposed temperature transformations based on the new scaling show an improvement in channel flows over adiabatic walls and supersonic/hypersonic turbulent boundary layers with cold walls. The effects of the generated high-order terms during derivation are also clarified. These findings may be revealing for the development of the near-wall model in high-speed aerodynamics.

Topics & Concepts