Direct numerical simulation of turbulent channel flow with permeable walls

Abstract

The main objectives of this study are to suggest a proper boundary condition at the interface between a permeable block and turbulent channel flow and to investigate the characteristics of turbulent channel flow with permeable walls. The boundary condition suggested is an extended version of that applied to laminar channel flow by Beavers & Joseph (1967) and describes the behaviour of slip velocities in the streamwise and spanwise directions at the interface between the permeable block and turbulent channel flow. With the proposed boundary condition, direct numerical simulations of turbulent channel flow that is bounded by the permeable wall are performed and significant skin-friction reductions at the permeable wall are obtained with modification of overall flow structures. The viscous sublayer thickness is decreased and the near-wall vortical structures are significantly weakened by the permeable wall. The permeable wall also reduces the turbulence intensities, Reynolds shear stress, and pressure and vorticity fluctuations throughout the channel except very near the wall. The increase of some turbulence quantities there is due to the slip-velocity fluctuations at the wall. The boundary condition proposed for the permeable wall is validated by comparing solutions with those obtained from a separate direct numerical simulation using both the Brinkman equation for the interior of a permeable block and the Navier–Stokes equation for the main channel bounded by a permeable block.