Effect of Boundary Layer Thickness on the Estimation of Equivalent Sandgrain Roughness

The equivalent sandgrain roughness, k_s, is routinely extracted from velocity profile data. To obtain k_s, fully rough conditions should exist, and it is recommended that the ratio of the boundary layer thickness, δ, to k_s should be at least 40. In practice, however, k_s is often found for conditions with δ/k_s<40. Experiments were conducted in boundary layers over a surface with uniform stochastic roughness. Profiles of mean velocity and turbulence quantities were acquired at twelve streamwise locations. The ratio of δ to the rms roughness height varied from 55 to 141, and k_s was approximately 4 times the rms height. In the outer region of the boundary layer the mean velocity and turbulence results were found to be invariant with Reynolds number when scaled using δ and the friction velocity, and exhibited similarity with equivalent smooth-wall boundary layer quantities. The k_s values determined from the profiles were found to vary noticeably and inversely with δ when δ/k_s was less than about 40. This suggests a possible need for a modified correlation to account for the δ/k_s dependence. Such a correlation might prove useful for extracting k_s values from low δ/k_s data, and for predicting the effect of roughness on boundary layers with varying δ/k_s.