A new supersonic rough-wall RANS model towards accurate drag and heat flux prediction

The effects of Mach number (Ma_∞) and wall-to-recovery temperature ratio (T_w/T_aw) on supersonic rough-wall turbulent boundary layers are investigated using Direct Numerical Simulation (DNS). DNS results indicate that both drag and heat flux increments induced by roughness increase as Ma_∞ increases and decrease as T_w/T_aw decreases, with the heat flux increment smaller than the drag increment. The classical roughness function, originally developed for incompressible flows, is inadequate for supersonic flows, as the downward shift of velocity profile is influenced by T_w/T_aw. A new supersonic roughness function is proposed to account for this effect. Additionally, Wilcox’s rough-wall k-ω model is evaluated for supersonic flows, revealing maximum prediction errors of 29.3 % for drag and 81.4 % for heat flux. A new supersonic rough-wall Reynolds-Averaged Navier-Stokes (RANS) model is proposed by utilizing the supersonic roughness function and adding a compressible correction factor α to the ω boundary. The drag prediction error is reduced to <4 %. Besides, heat flux decomposition analysis suggests that both turbulent heat transport and Reynolds stress work terms in RANS energy equation need modification to improve heat flux prediction. By reducing these two terms by a factor of β_r, heat flux prediction error is reduced from 81.4 % to 7.7 %.