Turbulent Flow Over and Within a Porous Bed

Abstract

The characteristics of turbulent flow in open channels with a porous bed are studied numerically and experimentally. The “microscopic” approach is followed, by which the Reynolds-averaged Navier-Stokes equations are solved numerically in conjunction with a low-Re κ-e turbulence model above and within the porous bed. The latter is represented by a bundle of cylindrical rods of certain diameter and spacing, resulting in permeability \iK ranging from 5.5490×10\U-7\N to 4.1070×10\U-4\N m² and porosity φ from 0.4404 to 0.8286. Mean velocities and turbulent stresses are measured for φ= 0.8286 using hot-film anemometry. Emphasis is given to the effect of Darcy number Da on the flow properties over and within the porous region. Computed and experimental velocities in the free flow are shown to decrease with increasing Da due to the strong momentum exchange near the porous medium/free flow interface and the corresponding penetration of turbulence into the porous layer for highly permeable beds. Computed discharge indicates the significant reduction of the channel capacity, compared to the situation with an impermeable bed. On the contrary, laminar flow computations, along with analytical solutions and measurements, indicate opposite effects of the porous medium on the free flow.