Characterisation of drag and wake properties of canopy patches immersed in turbulent boundary layers

Abstract

The wakes and the drag forces of canopy patches with different densities, immersed in turbulent boundary layers, are investigated experimentally. The patches are circular (with outer diameter $D$) and are made of several identical circular cylinders (height, $H$, and diameter, $d$). The bulk aspect ratio of all of the patches ($AR=H/D$) was fixed at 1 and the patch density (${\it\phi}=N_{c}d^{2}/D^{2}$, also referred to as the solidity) is altered by varying the number of cylinders ($N_{c}$) in the patch. Drag measurements show that the patch drag coefficient increases with increasing density. However, the drag coefficient of the highest investigated density (${\it\phi}\approx 0.25$) is greater than the drag coefficient of a solid patch (i.e. ${\it\phi}=1$, which is a solid cylinder with $AR=1$). Particle image velocimetry (PIV) measurements were carried out along the streamwise–wall-normal ($x$–$y$) plane along the centreline of patch and in the streamwise–spanwise ($x$–$z$) plane at its mid height (i.e. $y=H/2$). Mean velocity fields show that the porosity of the patch promotes bleeding along all directions. It was observed that bleeding along the vertical/horizontal direction increases/decreases with increasing ${\it\phi}$. Furthermore, it was also observed that bleeding along the lateral direction dictates the point of flow separation along the sides of the patch and makes it independent of ${\it\phi}$. All of these aspects make wakes for porous patches markedly different from their solid counterpart and provide a rational basis to explain the observed trends in the drag coefficient.