Exploring the nexus among roughness function, apparent slip velocity and upscaling coefficients for turbulence over porous/textured walls

The interaction between a turbulent flow and a porous boundary is analysed with focus on the sensitivity of the roughness function, to the upscaled coefficients characterizing the wall. The study is aimed at (i) demonstrating that imposing effective velocity boundary conditions at a virtual plane boundary, next to the physical one, can efficiently simplify the direct numerical simulations (DNS); and (ii) pursuing correlations to estimate a priori, once the upscaled coefficients are calculated. The homogenization approach employed incorporates near-interface advection via an Oseen-like linearization, and the macroscopic coefficients thus depend on both the microstructural details of the wall and a slip-velocity-based Reynolds number,. A set of homogenization-simplified DNS is run to study the channel flow over transversely isotropic porous beds, testing values of the grains' pitch within. Reduction of the skin-friction drag is attainable exclusively over streamwise-aligned inclusions for values up to. The drag increase over spanwise-aligned inclusions (or streamwise-aligned ones at large) is accompanied by enhanced turbulence levels, including intensified sweep and ejection events. The root-mean-square of the transpiration velocity fluctuations at the virtual plane, is the key control parameter of; our analysis shows that, provided, then is strongly correlated to a single macroscopic quantity, which comprises the Navier-slip and interface/intrinsic permeability coefficients. Fitting relationships for are proposed, and their applicability is confirmed against reference results for the turbulent flow over impermeable walls roughened with three-dimensional protrusions or different geometries of riblets.