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

Wall heat-flux effects on turbulence statistics and structures in supersonic turbulent boundary layers with the heated and cooled wall are investigated. To study effects of the semi-local Reynolds number (Re_τ*), we conduct large eddy simulation with constant Re_τ* by imposing a dynamic viscosity proportional to the square root of the density and comparing to flows with a conventional viscosity given by Sutherland's law. For constant Re_τ*, wall heated and cooled cases show collapsed turbulence statistics and structures when scaling with the semi-local length scale. The results suggest that Re_τ* is a similarity parameter of the flows with thermophysical property variations.