Impact of the number of upstream sheltering cylinders on the wake of a downstream finite wall-mounted cylinder

The turbulent flow past a roughness element of a finite wall-mounted circular cylinder (FWMCC) geometry was experimentally investigated using planar particle image velocimetry. The FWMCC was subjected to various degrees of upstream sheltering achieved by one to four identical upstream FWMCCs positioned in tandem. Multiple configurations were considered to study the flow at various upstream FWMCCs streamwise spacings and height ratios (defined as the ratio of the upstream cylinders height to the downstream cylinder height). All FWMCCs occupied less than 20% of the incoming turbulent boundary layer thickness, and flow measurements were conducted at a Reynolds number of approximately 60,000, based on the boundary layer thickness and freestream velocity. The investigation focuses on the downstream-most FWMCC wake dependency on upstream sheltering. For each experimental configuration (i.e., each streamwise spacing and height ratio combination), the time-averaged streamwise and wall-normal velocities in the wake exhibit a similar spatial distribution and similar magnitudes for three and four upstream sheltering FWMCCs, suggesting wake independence past three upstream FWMCCs. The in-plane Reynolds shear stress and turbulent kinetic energy evidence a similar independence threshold (i.e., independence after three upstream sheltering FWMCCs). Furthermore, examination of the wake turbulence structure through quadrant analysis and two point correlations suggests a similar independence threshold.