Turbulent boundary layers over sparsely-spaced rod-roughened walls

Abstract

Direct numerical simulations (DNSs) of spatially developing turbulent boundary layers (TBLs) over sparsely-spaced two-dimensional (2D) rod-roughened walls were performed. The rod elements were periodically arranged along the streamwise direction with pitches of p(x)/k = 8, 16, 32, 64 and 128, where p(x) is the streamwise spacing of the rods, and k is the roughness height. The Reynolds number based on the momentum thickness was varied from Re-0 = 300-1400, and the height of the roughness element was k = 1.5 theta(in), where theta(in), is the momentum thickness at the inlet. The characteristics of the TBLs, such as the friction velocity, mean velocity, and Reynolds stresses over the rod-roughened walls, were examined by varying the spacing of the roughness features (8 <= p(x)/k <= 128). The outer-layer similarity between the rough and smooth walls was established for the sparsely-distributed rough walls (p(x)/k >= 32) based on the profiles of the Reynolds stresses, whereas those are not for p(x)/k = 8 and 16. Inspection of the interaction between outer-layer large-scale motions and near-wall small-scale motions using two-point amplitude modulation (AM) covariance showed that modulation effect of large-scale motions on near-wall small-scale motions was strongly disturbed over the rough wall for p(x)/k = 8 and 16. For p(x)/k >= 32, the flow that passed through the upstream roughness element transitioned to a smooth wall flow between the consecutive rods. The strong influence of the surface roughness in the outer layer for p(x)/k = 8 and 16 was attributed to large-scale erupting motions by the surface roughness, creating both upward shift of the near-wall turbulent energy and active energy production in the outer layer with little influence on the near-wall region.