Wall temperature effects on scaling law in high-temperature supersonic turbulent channel flows

Direct numerical simulations of temporally evolving high-temperature supersonic turbulent channel flows are performed at Mach number 3 and Reynolds number 4888. Air is assumed to behave as a five-species mixture and chemical equilibrium assumption. Five isothermal wall temperatures are in the range of 1733.2–4100.0 K. The results show that the mixture components undergo strong dissociation and recombination reactions along the channel for all wall temperature conditions. The wall temperature does not alter the original symmetry of fluctuating velocity and equilibrium species. The intermittence of turbulence is insensitive to the wall temperature, and the intermittence of equilibrium species enhances with the wall temperature increased. The scaling law derived and validated for calorically perfect gas still hold or can be generalized for chemical equilibrium assumption. Good linear relationship is observed in the extended self-similarity, which is more obvious than the velocity structure function. The influence of wall temperature on scaling law near the wall is more significant than that at the centerline. As the wall temperature increases, the relative scaling exponents of the generated components near the wall are gradually approaching to the theory proposed by She and Leveque.