The influence of wall permeability on turbulent channel flow

Abstract

Direct numerical simulations (DNS) have been performed of turbulent flow in a plane channel with a solid top wall and a permeable bottom wall. The permeable wall is a packed bed, which is characterized by the mean particle diameter and the porosity. The main objective is to study the influence of wall permeability on the structure and dynamics of turbulence. The flow inside the permeable wall is described by means of volume-averaged Navier–Stokes equations. Results from four simulations are shown, for which only the wall porosity ($\epsilon_c$) is changed. The Reynolds number based on the thickness of the boundary layer over the permeable wall and the friction velocity varies from $\hbox{\it Re}_{\tau}^p\,{=}\,176$ for $\epsilon_c\,{=}\,0$ to $\hbox{\it Re}_{\tau}^p\,{=}\,498$ for $\epsilon_c\,{=}\,0.95$. The influence of wall permeability can be characterized by the permeability Reynolds number, $\hbox{\it Re}_K$, which represents the ratio of the effective pore diameter to the typical thickness of the viscous sublayers over the individual wall elements. For small $\hbox{\it Re}_K$, the wall behaves like a solid wall. For large $\hbox{\it Re}_K$, the wall is classified as a highly permeable wall near which viscous effects are of minor importance. It is observed that streaks and the associated quasi-streamwise vortices are absent near a highly permeable wall. This is attributed to turbulent transport across the wall interface and the reduction in mean shear due to a weakening of, respectively, the wall-blocking and the wall-induced viscous effect. The absence of streaks is consistent with a decrease in the peak value of the streamwise root mean square (r.m.s.) velocity normalized by the friction velocity at the permeable wall. Despite the increase in the peak values of the spanwise and wall-normal r.m.s. velocities, the peak value of the turbulent kinetic energy is therefore smaller. Turbulence near a highly permeable wall is dominated by relatively large vortical structures, which originate from a Kelvin–Helmholtz type of instability. These structures are responsible for an exchange of momentum between the channel and the permeable wall. This process contributes strongly to the Reynolds-shear stress and thus to a large increase in the skin friction.