DNS of turbulent flow along passively permeable walls

Fully developed low-Reynolds-number turbulent flow through straight permeable pipes with circular cross-section is investigated by means of direct numerical simulation. Three different cases of wall permeability are treated and compared with the case of a solid wall. In two of these cases, the wall satisfies the no-slip condition, but allows for the wall normal velocity fluctuations in two different ways. In the third case, the pipe wall has rectangular openings of size (6 Delta z(+) x 10(R Delta phi)(+)), regularly distributed over the whole surface, similar to a chessboard, where the white areas represent the openings and the black ones the solid wall. Velocity boundary conditions in the openings are such that the mean mass flux across the wall is zero and the flow in the openings is stress-free. All flows are driven by the same mean pressure gradient. Consequently, those flows which satisfy the no-slip condition have the same wall shear stress and hence the same turbulence Reynolds number Re-tau = 360. Pipe flow with wall openings exhibits a small, but finite Reynolds shear stress at the wall. If the friction velocity is defined via the total stress at this wall, the flow nominally has the same turbulence Reynolds number. The overall effect of a permeable wall with rectangular openings is a mean axial slip velocity at the wall and reduced viscous stress. In a thin near-wall layer of thickness v/u(tau), the turbulence activity is increased compared to the flow cases, where the velocity components satisfy the no-slip condition. All three rms-velocity fluctuations are non-zero. As a result the structure of the Reynolds stress tensor is modified in this region. This is also reflected in higher order central moments of the velocity fluctuations. A permeable wall with rectangular openings may be viewed as a model for a rough wall with a mean non-dimensional roughness height of 8.3 wall units. Close to such a wall the budgets of the Reynolds stress tensor differ strongly from those for flow along a smooth impermeable wall. (C) 2000 Begell House Inc. Published by Elsevier Science Inc. All rights reserved.