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 di erent 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 the patches (AR = H D) was xed at 1 and the patch density (φ = Ncd 2 D 2 , also referred to as solidity) is altered by varying the number of cylinders (Nc) in the patch. Drag measurements show that the patch drag coe cient increases with increasing density. However, the drag coe cient of the highest investigated density (φ ≈ 0.25) is greater than the drag coe cient of a solid patch (i.e. φ = 1, which is a solid cylinder with AR = 1). PIV measurements were carried out along 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 elds 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 φ. Furthermore, it was also observed that bleeding along the lateral direction dictates the point of ow separation along the sides of the patch and makes it independent of φ. All these aspects make wakes for porous patches markedly di erent from their solid counterpart and provide a rational basis to explain the observed trends in the drag coe cient.

The effect of permeability on the flow past permeable disks at low Reynolds numbers

“…6(a) has been found in previous experimental and numerical studies, 3,4,11 but what causes this increase remains unclear. To understand what causes this increase, consider the case of a highly permeable disk (far to the right of regime III); in this case, the velocity is constant and axial, the pressure field is antisymmetric across the disk, and according to Eq.…”

“…6(a)], which is consistent with the experimental results for permeable spheres, cylinders, and other permeable bodies. 3,4,11 The peak in C D occurs at higher Da for decreasing Re, and the peak value significantly exceeds the drag on an impervious disk of the same dimensions C D,s for moderate values of Re. This finding is consistent with the numerical simulations and experiments on the flow past permeable cylinders, 4 where increases were found for moderate-Re flow past a permeable cylinder compared with an impervious one.…”

“…4 There is an emerging literature on the study of the flow past arrays, or patches, of obstacles. 11 Interestingly, the drag coefficient measured for sparse arrays is found to increase with decreasing permeability, reaching a maximum for some finite permeability. This maximum is higher than that found for an equivalent impervious obstacle, in agreement with experiments on permeable spheres 3 and permeable cylinders.…”

“…The solution in regime II does not yield to an asymptotic analysis and must be explored by solving the original equations numerically, and we show that our results are consistent with previous studies on permeable bodies. 3,4,11,22 The paper is structured as follows: in Sec. II, the governing equations are written down and non-dimensionalized (Sec.…”

“…These wings supply 90% of the force produced by an impervious wing but weigh about 10% of such a wing. 10 The drag force experienced by permeable bodies such as permeable spheres 3 and permeable cylinders 4,11 can also exceed that of an equivalent impervious body.…”