A new equivalent sand grain roughness relation for two-dimensional rough wall turbulent boundary layers

Abstract

The effects of different geometries of two-dimensional (2-D) roughness elements in a zero pressure gradient (ZPG) turbulent boundary layer (TBL) on turbulence statistics and drag coefficient are assessed using single hot-wire anemometry. Three kinds of 2-D roughness are used: (i) circular rods with two different heights, k = 1.6 and 2.4 mm, and five different streamwise spacing of sx = 6k to 24k, (ii) three-dimensional (3-D) printed triangular ribs with heights of k = 1.6 mm and spacing of sx = 8k and (iii) computerized numerical control (CNC) machined sinewave surfaces with two different heights, k = 1.6 and 2.4 mm, and spacing of sx = 8k. These roughnesses cover a wide range of ratios of the boundary layer thickness to the roughness height (23 < δ/k < 41), where δ is the boundary layer thickness. All roughnesses cause a downward shift on the wall-unit normalised streamwise mean velocity profile when compared with the smooth wall profiles agreeing with the literature, with a maximum downward shift observed for sx = 8k. In the fully rough regime, the drag coefficient becomes independent of the Reynolds number. Changing the roughness height while maintaining the same spacing ratio sx/k exhibits little influence on the drag coefficient in the fully rough regime. On the other hand, the effective slope (ES) and the height skewness (ksk) appear to be major surface roughness parameters that affect the drag coefficient. These parameters are used in a new expression for ks, the equivalent sand grain roughness, developed for 2-D uniformly distributed roughness in the fully rough regime.