Effects of frontal and plan solidities on aerodynamic parameters and the roughness sublayer in turbulent boundary layers

Experiments were conducted in the fully-rough regime on surfaces with large relative roughness height (h/δ ≈ 0.1, where h is the roughness height and δ is the boundary layer thickness). The surfaces were generated by distributed LEGO bricks of uniform height, arranged in different configurations. Measurements were made with both floating-element drag-balance and high-resolution particle image velocimetry on six configurations with different frontal solidity, λF , at fixed plan solidity, λP , and vice versa, for a total of twelve rough-wall cases. Results indicate that the drag reaches a peak value λF ≈ 0.21 or a constant λP = 0.27, whilst it monotonically decreases for increasing values of λP for a fixed λF = 0.15. This is in contrast with previous studies in the literature based on cube roughness that show a peak in drag for both λF and λP variations. The influence of surface morphology on the depth of the roughness sublayer (RSL) is also investigated. Its depth is found to be inversely proportional to the roughness length, y0. A decrease in y0 is usually accompanied by a thickening of the the RSL and vice-versa. Proper orthogonal decomposition analysis was also employed. The shapes of the most energetic modes calculated using the data across the entire boundary layer are found to be selfsimilar across the twelve rough-walls cases, however, when the analysis is restricted to the roughness sublayer, differences that depend on the wall morphology are apparent. Moreover, the energy content of the POD modes within the RSL suggest that the effect of increased frontal solidity is to redistribute the energy towards the larger-scales (i.e. larger portion of energy is within the first few modes) whilst the opposite is found for variation of plan solidity.