Decomposition of skin-friction and wall heat flux of temporal transition in compressible channel flows with direct numerical and constrained large-eddy simulations

The twofold integral-based decompositions of skin-friction and wall heat flux coefficients are implemented in compressible temporal transitional channel flows with direct numerical simulation and constrained large eddy simulation (CLES) to explore (i) the generations of the skin-friction and wall heat flux coefficients and their overshoot during the transition and (ii) why CLES under-predicts the overshoot phenomenon. The Reynolds shear stress, the mean velocity gradient with respect to time, and the mean velocity convection are dominating terms during the transition process of skin friction coefficient C-f, and the effect of the mean velocity convection becomes stronger as the Mach number (Ma) increases. For the wall heat flux coefficient B-q, the turbulent heat transfer, the mean energy gradients in time, and the viscous stress are significant contributors. The effects of molecular heat transfer and the mean convection on transition are increasingly important to B-q as Ma increases. The overshoot of C-f and B-q at Ma = 1.5 is mainly caused by the significant changes of mean velocity profiles and mean energy profiles with respect to time respectively. At Ma = 3.0, the overshoot of C-f is due to the significant change of mean velocity profiles in time and the mean velocity convection, while the overshoot of B-q is due to the mean energy changes in time and mean energy convection. It is found that the underestimation of the overshoots of C-f and B-q in CLES is primarily caused by the variances of the mean velocity gradient and mean energy gradient, respectively.