Large-eddy simulations of turbulent compressible channels with a traveling wavy wall

Large-eddy simulations of turbulent compressible flow over a wavy channel and a channel with a backward traveling wave deforming wall are performed at a subsonic Mach number, M=0.5, and a supersonic Mach number, M=1.5. The Reynolds number (Re) based on the bulk flow velocity (U) and channel half-width (H) is 3000 and the channel walls are adiabatic. The wave steepness and wavelength are 0.07H and 0.5πH, respectively. At both Mach numbers, flow over the stationary wavy wall separates from the downhill of the wave and creates reverse flow near the trough of the wave. Due to the fluid compression in the supersonic channel, shock waves are generated over the peaks of the wave. When the wall undergoes a traveling wave motion with a wave speed of C=0.25πU, flow reattaches and the reverse flow zone is removed, which results in the decrease of the turbulent kinetic energy of the flow near the waves. Furthermore, the shockwaves of the supersonic wavy channel are removed by the traveling waves. The mechanism of shock removal is further investigated by performing simulations of a channel with wave speeds C=0.1πU and C=-0.1πU.