Effects of boundary layer thickness on the estimation of equivalent sandgrain roughness in zero-pressure-gradient boundary layers

Experiments were conducted in zero-pressure-gradient boundary layers over a rough surface. Profiles of mean velocity and turbulence quantities were acquired using laser Doppler velocimetry at twelve streamwise locations for each of three different freestream velocities. Momentum thickness Reynolds numbers ranged from 1550 to 13,650. The roughness was stochastic with positive skewness, and the ratio of the boundary layer thickness, δ, to the root-mean-square roughness height varied from 55 to 141. The equivalent sandgrain roughness height, k_s, was approximately 4 times the rms roughness height. In the outer region of the boundary layer, the mean velocity and turbulence results were found to be invariant with Reynolds number and δ, when scaled using δ and the friction velocity. The outer region quantities exhibited similarity with equivalent smooth-wall boundary layer quantities, in agreement with results from the literature. The equivalent sandgrain roughness was computed from the mean velocity results using a standard correlation, and was found to vary noticeably and inversely with δ when δ/k_s was less than about 40. The possible existence of a modified correlation to account for the δ/k_s dependence was discussed. Such a correlation might prove useful for extracting k_s values from low δ/k_s data and for predicting the effect of roughness with a known k_s on boundary layers with varying δ/k_s.