Compressible Boundary Layer Velocity Transformation Based on a Generalized Form of the Total Stress

We demonstrate that density and viscosity fluctuations have a significant impact on the near-wall stress balance of compressible boundary layers. Utilizing a DNS simulation dataset of wall-bounded hypersonic flow cases with wall-cooling, semi-local Reynolds numbering ranging from 800 to 34000 and Mach number up to 12, fluctuating viscosity and density-related terms were seen to consistently exceed 5% of the wall shear stress for all cases. In some cases, these terms exceeded 30% of the wall shear stress. The growth in the Morkovin-scaled turbulent stress peak is seen to increase with the semi-local Reynolds number, Re*. By retaining terms to account for density and viscosity fluctuations, the near wall momentum balance expected from the incompressible wall bounded turbulence is restored in a generalized form and used to identify two key properties: (1) the near-wall momentum balance for the generalized total stress and (2) the relative contributions from the viscous and turbulent stresses to the total stress, which are found to be approximately Mach-invariant. Utilizing these properties, we propose a mean velocity transformation for compressible wall bounded hypersonic flows that builds upon the recent transform proposed by Griffin, Fu and Moin (2021) to produce a tighter collapse of log-layer intercept and slope and that closely matches that observed for incompressible flows.