Effects of porous walls on near-wall supersonic turbulence

We have investigated the effects of the wall permeability on the isothermal-wall supersonic channel flow turbulence. The study is conducted via large-eddy simulations (LES) based on the sub-grid-scale closure proposed by Vreman [Phys. Fluids 16, 3670 (2004)]. The effects of the wall porosity are modeled via the application of a time-domain impedance boundary condition (TDIBC), which accurately imposes the complex acoustic wall impedance. Bulk Mach numbers of M-b = 1.50 and 3.50 are selected, with bulk Reynolds numbers chosen to ensure the same semilocal friction Reynolds number of Re-tau* approximate to 220. A three-parameter impedance model is used with resonating frequency tuned to the time scales of the energy containing eddies, with wall acoustic resistances R = 0.50, 1.00, infinity, ranging from the most permeable to impermeable, respectively. It is found that only cases with R = 0.50 yield significant changes in the near-wall turbulence structures, which include a deviation from the linear relation of mean velocity and normalized wall distance in viscous sublayer, and increase in the mean wall-shear stress, as well as a strong increase in both turbulent kinetic energy (TKE) production and dissipation near the wall primarily due to large contribution coming from the instability waves triggered by the permeability. Such waves are found to be confined in the first 10% of the channel half-height near the impedance boundary, creating local circulation zones separated by regions of flow entrainment. It is found that for a given R, the waves are more confined as the Mach number increases. For pressure-related terms, the complex impedance wall effects changes the role of pressure diffusion term in the budget the most, making it responsible for the transport toward the wall, opposite to what is observed in impermeable wall cases. The confined waves also enhance the sink/source effect of the pressure strain term in budget of Reynolds normal stresses, leading to a redistribution of normal stresses.