Direct numerical simulation and PIV measurement of turbulent boundary layer over a rod-roughened wall

Abstract

The effects of surface roughness on a spatially-developing turbulent boundary layer (TBL) were investigated by performing direct numerical simulation (DNS) and particle image velocimetry (PIV) measurements of TBLs over rough and smooth walls. The roughness elements used were periodically arranged two-dimensional spanwise rods, and the roughness height was k/δ=0.05 for DNS and k/δ=0.025 for PIV. Along the streamwise direction, the friction velocity approached a constant value and self-preserving forms of the turbulent Reynolds stress tensors were obtained. Introduction of the roughness elements affected the turbulent stress not only in the roughness sublayer (y<5k) but also in the outer layer (y>5k). Introduction of the roughness elements augmented turbulent stresses in the region of y<4 ~ $5k_s$, where $k_s$ is an effective sand roughness height. This indicates that the effective sand roughness height is a more appropriate length scale for representing the extent of roughness effect rather than the roughness height (k). Despite the roughness-induced increase of the turbulent Reynolds stress tensors in the outer layer, the roughness had only a relatively small effect on the anisotropic Reynolds stress tensor in the outer layer. Inspection of the triple products of the velocity fluctuations revealed that introducing the roughness elements onto the smooth wall had a marked effect on vertical turbulent transport across the whole TBL. By contrast, good surface similarity in the outer layer was obtained for the third-order moments of the velocity fluctuations. The effects of surface roughness on the turbulence structure in the roughness sublayer were examined and compared between DNS and PIV. Iso-contours of the mean velocity and Reynolds stress in the roughness sublayer obtained by PIV were in very good agreement with DNS findings. Vortex structures induced by the rod-roughness and strong sweep events were also examined. Although introduction of roughness elements o...