Mean Velocity Profiles over Streamwise-Aligned Permeable Ridges

Abstract

To understand the effects of permeable roughness on logarithmic velocity profiles, discussions of the PIV measurement data of turbulent channel flows over rib-roughened porous media are carried out. By fitting the measured mean velocity profiles to the logarithmic law, parameters: the zero-plane displacement d, the equivalent roughness scale h and the von Kármán constant $\kappa$ are obtained. It is found that the parameters normalized by the mean pore diameter $d/D_p, h/D_p$ become almost constant regardless of the roughness geometry and the permeability. Moreover the zero-plane displacement has a linear relationship with the roughness scale as $d/h\simeq 2.5$. The von Kármán constant $\kappa$ for permeable roughness case is smaller than that for impermeable case. The equivalent sand grain roughness height $k_s^+$ has an almost linear relationship with $h^+$ as $k_s^+=8h^+$. This implies that the von Kármán constant for the present cases is $\kappa \simeq 0.25$. Although it was reported that $h^+$ for flat porous wall cases correlated to the permeability Reynolds number Re$_K$ regardless of the wall permeability, that for permeable roughness cases does not show the same tendency.