Comparative study of Reynolds stress budgets of thermally and calorically perfect gases for high-temperature supersonic turbulent channel flow

To study the Reynolds stress budgets, direct numerical simulations of high-temperature supersonic turbulent channel flow for thermally perfect gas and calorically perfect gas are conducted at Mach number 3.0 and Reynolds number 4800 combined with a dimensional wall temperature of 596.30 K. The reliability of the direct numerical simulation data is verified by comparison with previous results (J Fluid Mech 1995, vol. 305, pp.159-183). The effects of variable specific heat are important because the vibrational energy excited degree exceeds 0.1. The viscous diffusion, pressure-velocity gradient correlation, and dissipation terms in the Reynolds stress budgets for TPG, except the streamwise component, are larger than those for calorically perfect gas close to the wall. Compressibility-related term decreases when thermally perfect gas is considered. The major difference for both gas models is mainly due to variations in mean flow properties. Inter-component transfer related to pressure-velocity gradient correlation term can be distinguished into inner and outer regions, whose critical position is approximately 16 for both gas models.