Describing characteristic parameters of turbulence over two-dimensional porous roughness

To describe permeable roughness e ff ects on turbulence statistics, our previously reported PIV (particle image ve-locimetry) experimental data (Shimizu et al., 2019; Okazaki et al., 2020) of turbulent channel flows over two di ff erent permeable roughness types are assessed. The considered roughness elements were porous transverse square ribs and rectangular sectioned short flat plates which were mounted on porous walls with constant spacings. The spacings were controlled to reproduce the so-called k- and d-type roughness geometries. The values of the pore-per-inch of the materials of the roughness elements and the porous wall were the same in each case. Three di ff erent foamed porous materials were considered while their porosities were approximately 0.8. By the assessment of the logarithmic mean velocity profiles of the two roughness cases, it is confirmed that a linear relationship between the zero-plane displacement and the roughness scale exists. The data of the flat porous walls without roughness elements (Suga et al., 2010; 2017) are also confirmed to have the same trend regardless of the porous media. We found an e ff ective displacement parameter which linearly increases as the pore diameter. Using the pore-scale Reynolds number, we then propose a correlation that describes the value of the variable von K´arm´an constant and a simple formula for estimating the equivalent sand grain roughness height for all cases presently assessed.