Scaling turbulence over rib-roughened permeable walls

To clarify the combined effects of wall permeability and surface roughness on turbulence, PIV measurements of turbulent channel flows over porous media with structural surface roughness are conducted. Square porous ribs whose height k is 10% of the channel height are set at regular intervals at w/k=1, 3, 7, 9, 19. Three kinds of porous media applied have the same porosity, 0.9, but different mean pore diameters. The measured bulk Reynolds numbers are from 5000 to 20000. After fitting the mean velocity profiles to the logarithmic law, discussions of the log-law parameters are conducted. It is then confirmed that the zero-plane displacement has a linear relationship with the roughness scale in the case of w/k=1~9 and that the newly determined effective displacement well correlates to the mean pore diameter. Further discussions on the Kármán constant are required to find the universal law of the mean velocity although they generally correlate to the pore Reynolds number.