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

Abstract

Experiments were conducted in the fully rough regime on surfaces with large relative roughness height ($h/{\it\delta}\approx 0.1$, where $h$ is the roughness height and ${\it\delta}$ 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 solidities, ${\it\lambda}_{F}$, at fixed plan solidity, ${\it\lambda}_{P}$, and vice versa, for a total of twelve rough-wall cases. The results indicated that the drag reaches a peak value ${\it\lambda}_{F}\approx 0.21$ for a constant ${\it\lambda}_{P}=0.27$, while it monotonically decreases for increasing values of ${\it\lambda}_{P}$ for a fixed ${\it\lambda}_{F}=0.15$. This is in contrast to previous studies in the literature based on cube roughness which show a peak in drag for both ${\it\lambda}_{F}$ and ${\it\lambda}_{P}$ variations. The influence of surface morphology on the depth of the roughness sublayer (RSL) was also investigated. Its depth was found to be inversely proportional to the roughness length, $y_{0}$. A decrease in $y_{0}$ was usually accompanied by a thickening of the RSL and vice versa. Proper orthogonal decomposition (POD) analysis was also employed. The shapes of the most energetic modes calculated using the data across the entire boundary layer were found to be self-similar across the twelve rough-wall cases. However, when the analysis was restricted to the roughness sublayer, differences that depended on the wall morphology were apparent. Moreover, the energy content of the POD modes within the RSL suggested that the effect of increased frontal solidity was to redistribute the energy towards the larger scales (i.e. a larger portion of the energy was within the first few modes), while the opposite was found for variation of plan solidity.