Flow past finite cylinders of constant curvature

Abstract

Wake visualization experiments were conducted on a finite curved cylinder whose plane of curvature is aligned with the free stream. The stagnation face of the cylinder is oriented concave or convex to the flow at $230\leqslant Re_{D}\leqslant 916$, where $Re_{D}$ is the cylinder Reynolds number and the curvature is constant and ranges from a straight cylinder to a quarter-ring. While the magnitude of the local angle of incidence to the flow is the same for both orientations, the contrast in their wakes demonstrates a violation of a common approximation known as the ‘independence principle’ for curved cylinders. Vortex shedding always occurred for the convex-oriented cylinder for the Reynolds-number range investigated, along most of the cylinder span, at a constant vortex shedding angle. In contrast, a concave-oriented cylinder could exhibit multiple concurrent wake regimes along its span: two shedding regimes (oblique, normal) and two non-shedding regimes. The occurrence of these wake regimes depended on the curvature, aspect ratio and Reynolds number. In some cases, vortex shedding was entirely suppressed, particularly at higher curvatures. In the laminar wake regime, increasing the curvature or decreasing the aspect ratio restricts vortex shedding to smaller regions along the span of the cylinder. Furthermore, the local angle of incidence where vortex shedding occurs is self-similar across cylinders of the same aspect ratio and varying curvature. After the wake transitions to turbulence, the vortex shedding extends along most of the cylinder span. The difference in the wakes between the concave and convex orientations is attributed to the spanwise flow induced by the finite end conditions, which reduces the generation of spanwise vorticity and increases the incidence of non-shedding and obliquely shedding wakes for the concave cylinder.

Wake behind a concave curved cylinder

“…Similar large shedding angles are also reported in Ref. [5], although its experimental research considered different configurations (radius of curvature R/D = 19 and 38, compared to R/D = 12.5 in the present study).…”

“…We therefore conclude that one may need at least a 21D long vertical extension at Re = 200 to get a reliable wake for this configuration. Although a parallel shedding regime is not observed in the VE studies, as proposed in earlier studies [5], we would expect it to appear if the vertical extension is further increased (and the axial velocity disappears). In the present study, we have observed that the axial velocity can be as high as 20% of the free-stream velocity U 0 at z/D = 20, at Re = 200.…”

“…Reference [5] reported a series of experiments of two concave curved cylinders with different curvatures at Reynolds numbers lower than 916 and carefully studied the wakes behind them. While they kept the incoming flow towards the inner face of the curved cylinder, different inflow angles were considered.…”

“…Differently from the experimental study [5], where free ends (and free surface) show up, the previous numerical studies all try to avoid free ends in the simulations and accordingly have special considerations of the boundary conditions. Therefore, straight extensions are usually used in the numerical studies.…”

“…It is worth mentioning that regime 3 in Refs. [5,6] was referred to as "normal shedding regime." We however prefer to call regime 3 in Fig.…”