Topological description of near-wall flows around a surface-mounted square cylinder at high Reynolds numbers

Abstract

This study topologically describes near-wall flows around a surface-mounted cylinder at a high Reynolds number ( $Re$ ) of $5\times 10^4$ and in a very thick boundary layer, which were partially measured or technically approximated from the literature. For complete and rational flow construction, we use high-resolution simulations and critical-point theory. The large-scale near-wake vortex is composed of two connected segments rolled up from the sides of the cylinder and from the free end. Another large-scale side vortex clearly roots on two notable foci on the lower side wall. In the junction region, the side vortex moves upwards with a curved trajectory, which induces the formation of nodes on the ground surface. In the free-end region, the side vortex is compressed, which results in a smaller trailing-edge vortex and its downstream movement. Only tip vortices are observed in the far wake. The origin of the tip vortices and their distinction from the near-wake vortex are discussed. Further analyses suggest that $Re$ independence should be treated with high caution when $Re$ increases from 500 to ${O}(10^4)$ . The occurrence of upwash flow behind the cylinder strongly depends on the increase in $Re$ , the mechanism of which is also provided. The separation–reattachment process in the junction region and the trailing-edge vortices are discovered only at a high $Re$ . The former should significantly affect the strength of the side vortex in the junction region and the latter should cause a sharp drop in pressure near the trailing edge.

Direct numerical simulation of the turbulent flow around a Flettner rotor

“…Therefore, gaining a comprehensive understanding of the turbulent H-system is crucial for comprehending, predicting, and controlling the local dynamics in front of cylinders. As also observed by Cao et al 14 , the horseshoe vortex tends to move farther upstream as the turbulent boundary layer gets thicker. Furthermore, as the cylinder starts to rotate, the number of secondary vortices increases substantially since the flow is induced to wrap around the cylinder by the rotation, as shown in Fig.…”

“…High-fidelity numerical or experimental studies that encompass various levels of complexity, such as non-homogeneous inflow or the wall-cylinder interaction, are lacking. A recent study by Cao et al 14 explored a setup similar to ours, involving a square cylinder in a thick boundary layer, without accounting for the rotational effects.…”

Flow separation from polygonal cylinders in an incident flow

“…10) is close to the threshold 36 • in Eq. (12), where the boundary layer on the surface upstream the top PSP is just about to separate (in the time mean sense). Therefore, it appears thicker than well-attached boundary layers in other cases; figure not shown.…”

“…Until recently, studies on flow around polygonal cylinders of N > 4 remained scattered, even though cylinders of N = 3 and 4 (triangular and square cylinders) have been well investigated ( [5][6][7][8][9][10][11][12]). Tian and Li [13] studied a cylinder of N = 24 in a low-speed wind tunnel and found a much lower critical transitional Reynolds number and a 40% lower drag with a lower level of fluctuation compared to a circular cylinder under similar flow conditions.…”

The wake of a rectangular flat plate

“…Studies of the flow around finite cylinders and finite square prisms (e.g. Kindree et al (2018), El Hassan et al (2015, and Cao et al (2022)) have shown that the horseshoe vortex legs have their greatest influence on the near wake of the body (x/W < 2) and that their influence is more pronounced for thicker boundary layers. Farther downstream of the body (such as at x/W = 6), the horseshoe vortex legs will have weakened and spread farther from the wake centreline.…”