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 ( c ) is changed. The Reynolds number based on the thickness of the boundary layer over the permeable wall and the friction velocity varies from Re p τ = 176 for c = 0 to Re p τ = 498 for c = 0.95. The influence of wall permeability can be characterized by the permeability Reynolds number, 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 Re K , the wall behaves like a solid wall. For large 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.

Turbulence structure of open channel flows over permeable and impermeable beds: A comparative study

“…Recently, Breugem et al 3 presented Direct Numerical Simulations ͑DNS͒ of the volume-averaged Navier-Stokes equations for a channel flow bounded by a smooth wall at the top and a permeable wall at the bottom. The volume averaging procedure was applied to a flow region big enough to smooth inhomogeneities at the pore scale but also small enough to resolve the flow dynamics of interest at larger scales.…”

“…This approach, besides being computationally less demanding than a standard DNS proved to be reliable for the description of flow statistics above and within the permeable wall. Breugem et al 3 point out that permeable walls are also unavoidably rough. The effect of surface roughness on the turbulent flow depends on the roughness Reynolds number defined as Re d = du ‫ء‬ / , where d is the characteristic diameter of the particle composing the bed.…”

“…For large values of Re K eddies are able to penetrate the permeable wall and the effects of permeability are significant, whereas for Re K Ӷ 1 the wall can be considered impermeable. Breugem et al 3 aimed at studying the effects of permeability exclusively; therefore a small particle diameter was imposed in the simulations in order to have a small Re d and high Re K . This guaranteed that the effects of permeability were enhanced and those of roughness minimized.…”

“…[4][5][6][7][8][9][10][11][12] In contrast, due to technical difficulties and heavy computational costs, the number of experiments and numerical simulations explicitly designed for investigating the transition layer between a turbulent boundary layer and a porous medium region is much more limited. [13][14][15]3 Ruff and Gelhar 13 performed velocity measurements in pipe flows where the porous medium was composed of foam. Velocities were measured by means of hot-wire anemometry.…”

“…Although the main focus of the numerical work by Breugem et al 3 was investigating the effects of permeability on the surface flow, plenty of results are also presented about the flow within the permeable wall. The simulations of Breu- gem et al 3 confirmed the exponential decay of turbulence intensities, pressure fluctuations, and mean velocities within the permeable bed.…”