Wall temperature effects of compressible turbulent boundary layers at moderate Reynolds numbers

In this paper, we investigate the influences of wall temperature on compressible turbulent boundary layers at free-stream Mach number 6.0 and moderate Reynolds numbers. The findings demonstrate that turbulent statistics, including the logarithmic scaling of Reynolds stresses in the overlap region, the presence of very-large-scale motions in the outer layer, and their superposition on near-wall turbulence, exhibit qualitative invariance across varying wall temperatures. However, the reduced scale separation between near-wall small-scale motions and outer-layer large-scale motions leads to a contraction in the vertical extent of Reynolds stresses adhering to the logarithmic law. Very-large-scale motions are attenuated in viscous units but intensified in global scalings due to the lower free-stream Reynolds number, following approximately the power law. Their superposition effects on near-wall turbulence, when weighted by density, show only weak dependence on wall temperature. Conversely, the modulation of near-wall velocity and temperature fluctuations by very-large-scale motions diminishes with decreasing wall temperature. Through detailed analysis of spanwise spectra in the outer region, a distinct inertial subrange obeying the classical $-5/3$ scaling law is identified, alongside a universal scaling over the dissipative range. These observations suggest that the mechanisms governing energy cascade processes and the associated small-scale turbulent fluctuations remain independent of wall temperature variations.