Mean flow of turbulent boundary layers over porous substrates

Mean-flow measurements of turbulent boundary layers over porous walls (permeable and rough) with varying pore size (s), permeability (K) and thickness (h) are presented across a wide range of friction Reynolds numbers (Re-tau asymptotic to 2000-18 000) and permeability based Reynolds numbers (Re-K asymptotic to 1.5-60). The mean wall shear stress was determined using a floating element drag balance and the boundary layer profiles were acquired using hot-wire anemometry. Substrate permeability is shown to increase the magnitude of the mean velocity deficit. The use of a modified indicator function, assuming "universal " values for von Karman constant (K = 0.39) supports previous results where a strongly modified logarithmic region was observed. The indicator function was also used to estimate the zero-plane displacement (y(d)), the roughness function (delta U+), and equivalent sandgrain roughness (k(s)). At high Reynolds numbers, the roughness function data collapses on to the Nikuradse's fully rough asymptote. However, at low roughness Reynolds numbers (k(s)(+) < 100), we observe the flow to be transitionally rough, evolving with Nikuradse-type behavior. The equivalent sandgrain roughness k(s) for each substrate appears to include roughness and permeability contributions. These two contributions can be separated using data obtained from the same substrates with different thickness. This may allow us to model the porous wall as a combination of rough and permeable wall.