Systematic study of the Reynolds number and streamwise spacing effects in two-dimensional square-bar rough-wall turbulent boundary layers

Turbulent boundary layer experiments above a smooth wall and two-dimensional (2D) rod-roughened walls are conducted to investigate the effects of friction Reynolds numbers Rey and streamwise spacing of the roughness elements on the flow properties. The first study uses the roughness pitch p to height k ratio p/k = 8 and a range of friction Reynolds numbers, 1840 Rey 7500. The result shows that the drag coefficient Cf converges to the fully rough condition (akin to the classic k-type roughness at a fully developed state) with large roughness Reynolds numbers (k+ > 75) when the friction Reynolds number reaches Rey 3900 and the relative roughness height is k/899 0.02, where 899 is the boundary layer thickness. As Rey increases, the premultiplied energy spectra show that the normalized energy of the near-wall cycle decreases, while the large-scale structures become more dominant. The second study uses a wide range of p/k (2 p/k 128) at Rey approximate to 3500. The Cf and the roughness function AU+ results indicate that the increase of streamwise spacing of the roughness elements p/k induces higher Cf and AU+, and it reaches the maximum value at p/k = 8. For p/k > 8, the Cf and AU+ values decrease as p/k increases, indicating a less severe drag increase. The premultiplied energy spectra also show that the highly energetic near-wall cycle of streaks and quasistreamwise vortices decreases as p/k increases (for all cases from p/k = 2-128), and they seem to be transported farther from the wall. The trend is slightly different for the largest-scale structures located around the log region. The result suggests that 2D square-bar roughness can reduce the energy distribution for the largest-scale structure for p/k = 2-128.