Turbulent boundary layer perturbation by two wall-mounted cylindrical roughness elements arranged in tandem: Effects of spacing and height ratio

Abstract

The perturbation of a turbulent boundary layer by two cylindrical roughness elements in close proximity was experimentally investigated in a water channel using planar particle image velocimetry. The two cylinders were arranged in tandem with center-to-center streamwise spacings of 2d, 4d, and 6d, where d is the diameter of the cylinders. The downstream cylinder had a fixed height 0.2δ, where δ is the incoming boundary layer thickness; the height of the upstream cylinder was varied to achieve upstream to downstream cylinder height ratios of 1, 0.75, and 0.5. The flow measurements were made at Reδ = 56 800 and included measurements over an isolated cylinder as a baseline case. The results highlight the effects of sheltering by an upstream cylinder on the wake of the downstream cylinder. Flow features in the wake, including the downwash, upwash, recirculation zone, velocity deficit, Reynolds shear stress, and turbulent kinetic energy (TKE), are dependent on the degree of sheltering, which is reliant on both the streamwise spacing and height ratio. Overall, sheltering results in a reduction in the downwash and size of the recirculation zone past the downstream cylinder. The magnitude and spatial distribution of the Reynolds shear stress and TKE varied significantly from those past the isolated cylinder. Depending on the streamwise spacing and height ratio, the presence of an upstream cylinder has the potential to enhance or reduce the Reynolds shear stress past the downstream cylinder. For example, the maximum Reynolds shear stress in the near wake was approximately doubled for a spacing of 2d and a height ratio of 0.5 and nearly halved for a spacing of 2d and a height ratio of 1 (relative to that past the isolated cylinder). The variations in these flow features across the 9 considered arrangements suggest changes to the wake and its vortical structures due to the presence of an upstream cylinder. The results highlight the potential of flow control through a pair of roughness elements in close proximity to achieve desired outcomes such as reduced or redistributed Reynolds shear stress and TKE, relative to the isolated cylinder.