Outer turbulent boundary layer similarities for different 2D surface roughnesses at matched Reynolds number

Abstract

The outer layer similarity in zero pressure gradient (ZPG) boundary layers developing over different geometries of 2D roughness elements is assessed, using single hotwire anemometry. Two types of 2D roughness are used: circular rods and sinewave surfaces with two different heights, k = 1.6, and 2.4 mm, and three different streamwise spacings, i.e. sx = 8k, 12k, and 16k. These roughnesses cover a range of ratios of the boundary layer thickness (δ) to the roughness height (k) from δ/k = 21 to 45. As expected, all roughnesses caused a downward shift on the wall-unit normalised streamwise mean velocity profiles compared with smooth wall profiles, with a maximum shift observed for rods with a spacing of sx = 8k, while the minimum shift is noticed for a sinewave surface with a spacing of sx = 16k. The defect velocity profiles collapse entirely for all smooth and rough wall flows when normalised by the friction velocity. It was found that the shape factor, H is a suitable scaling parameter for improving the collapse of the data when using the diagnostic plot. The inner peak of the turbulence intensity profiles for the sinewave roughness is reduced gradually with increasing Reynolds number while the turbulent boundary layer (TBL) develops from a transitionally to a fully rough regime. Meanwhile, this inner peak disappears completely for all rod roughnesses, as the TBL is always in a fully rough regime, and the profiles exhibit only an outer peak, located at a wall-normal location y/δ ≈ 0.06. The results suggest that Townsends similarity hypothesis for 2D surface roughness is relatively well approximated in the outer region of the flow as reflected by the collapse of the distributions of velocity defect, turbulence intensity, skewness, and flatness when scaled with δ.