Drag of a turbulent boundary layer with transverse 2D circular rods on the wall

In this paper, we present the results of a turbulent boundary layer developing over a rod-roughened wall with a spacing of \(\lambda /k = 8\) (\(\lambda\) is the spacing between two adjacent roughness elements, and \(k\) is the rod diameter). Static pressure measurements are taken around a single roughness element to accurately determine the friction velocity, \(U_\tau\) and the error in the origin, \(d_0\), which are the two prominent issues that surround rough-wall boundary layers. In addition, velocity measurements are taken at several streamwise locations using hot-wire anemometry to obtain \(C_\mathrm{f}\) from the momentum integral equation. Results showed that both methods give consistent values for \(U_\tau\), indicating that the contribution of the viscous drag over this rough wall is negligible. This supports the results of Perry et al. (J Fluid Mech 177:437–466, 1969) and Antonia and Luxton (J Fluid Mech 48(04):721–761, 1971) in a boundary layer and of Leonardi et al. (2003) in a channel flow but does not agree with those of Furuya et al. (J Fluids Eng 98(4):635–643, 1976). The results show that both \(U_{\tau }\) and \(d_0\) can be unambiguously measured on this particular rough wall. This paves the way for a proper comparison between the boundary layer developing over this wall and the smooth-wall turbulent boundary layer.