Varied average height and area coverage of rough surfaces on turbulent boundary layers

Turbulent boundary layers (TBL) over various area coverages of rough surfaces were studied in a wind tunnel using hot-wire anemometry. The rough surfaces are built by randomly distributed sand grains with an average of 0.7 and 0.9 mm heights, covering 12%, 25%, 38%, 55%, and 75% of the flat-plate surface area. This paper aims to correlate the average roughness height (k) and roughness area coverage (RAC) with the Hama roughness function ΔU+ and to explore the influence of these roughness characteristics towards the TBL. The correlation between these roughness variables suggests that as the RAC increases, the ΔU+ increases and reaches a peak value at 38% RAC. However, beyond the 38% of RAC, the ΔU+ values decrease and then saturate. The mutual sheltering effect at a certain pitch-to-roughness height ratio is suspected to be the underlying mechanism for this pattern. Another finding in this study is that for surfaces with RAC < 100%, the Hama roughness function does not scale with the roughness effective slope. This finding suggests that the RAC is an important factor for any roughness TBL study, especially for surfaces with RAC < 100%. Finally, this study also correlates the two roughness characteristics (k and RAC) with the fully rough asymptote of Nikuradse (1933) to estimate the associated equivalent sand grain roughness height, ks. The analysis indicates that the majority of the investigated cases are reaching the fully rough condition, and some are in the transitionally rough regime.