Effects of the semi-local Reynolds number in scaling turbulent statistics for wall heated/cooled supersonic turbulent boundary layers

In supersonic turbulent boundary layers over isothermal walls, we investigate how the wall heat flux affects turbulent statistics and velocity scaling laws. To distinguish local Reynolds number and compressibility effects, we consider a conventional ideal gas with Sutherland's law and a fluid for which the dynamic viscosity is proportional to the square root of density, such that the semi-local Reynolds number is constant in the wall-normal direction. The results clearly indicate that the changes of the semi-local Reynolds number within the boundary layer affect the coherent turbulent structures, which induces the deviation of the viscous stress, Reynolds stress, and semi-local transformed mean velocity between different wall temperature conditions. For the cases with constant semi-local Reynolds number, we observe that the wall heat flux does not affect the turbulent structures and that the velocity profiles perfectly collapse among each other, indicating the importance of the semi-local Reynolds number, rather than the temperature or density themselves, on turbulent statistics and structures. Also, the conditional averaged analysis for the near-wall turbulent phenomena indicates a clear relationship between the turbulent structures and the mean velocity gradients. Additionally, an existing analytical temperature-velocity relation is verified based on the examinations of the applied equilibrium flow assumptions, and the results explain the disagreement between the present data and the analytical solutions in the outer boundary layer region, especially for isothermal wall cases.