Experimental study of flow around polygonal cylinders

Abstract

The wake of polygonal cylinders with side number $N=2\sim \infty$ is systematically studied based on fluid force, hot-wire, particle image velocimetry and flow visualisation measurements. Each cylinder is examined for two orientations, with a flat surface or a corner leading and facing normally to the free stream. The Reynolds number $Re$ is $1.0\times 10^{4}\sim 1.0\times 10^{5}$, based on the longitudinally projected cylinder width. The time-averaged drag coefficient $C_{D}$ and fluctuating lift coefficient on these cylinders are documented, along with the characteristic properties including the Strouhal number $St$, flow separation point and angle $\unicode[STIX]{x1D703}_{s}$, wake width and critical Reynolds number $Re_{c}$ at which the transition from laminar to turbulent flow occurs. It is found that once $N$ exceeds 12, $Re_{c}$ depends on the difference between the inner diameter (tangent to the faces) and the outer diameter (connecting corners) of a polygon, the relationship being approximately given by the dependence of $Re_{c}$ on the height of the roughness elements for a circular cylinder. It is further found that $C_{D}$ versus $\unicode[STIX]{x1D709}$ or $St$ versus $\unicode[STIX]{x1D709}$ for all the tested cases collapse onto a single curve, where the angle $\unicode[STIX]{x1D709}$ is the corrected $\unicode[STIX]{x1D703}_{s}$ associated with the laterally widest point of the polygon and the separation point. Finally, the empirical correlation between $C_{D}$ and $St$ is discussed.

Scaling of the time-mean characteristics in the polygonal cylinder near-wake

“…Moreover, given for the NF orientation, L r * is approximately equal to L f * for all N, regardless of the occurrence of the transition. In contrast, for the NC orientation L r * appears more sensitive to the transition, which is in line with the variation of C D and St reported in Xu et al (2017); the difference between L f * and L r * is more pronounced as Re increases as the transition influences L r * more than L f * .…”

“…The Strouhal number is defined as St = f s D/U ∞ , where f s was the predominant vortex shedding frequency, extracted from the spectrum of the load cell signal. More information about measurement methods on aerodynamic forces and St can be found in Xu et al (2017).…”

“…The drag on a polygonal cylinder of finite N is in general larger than that on a circular cylinder (N = ∞) in the subcritical flow regime. Given 12 N ≥ , the critical Reynolds number Re c where the transition to turbulence starts to occur in the boundary layer is smaller than, though approaching with increasing N, that of the circular cylinder (Xu et al 2017).…”

“…It has been documented in Xu et al (2017) that the transition from laminar to turbulence occurs in the boundary layer around the cylinders of N = 12 and 16…”

“…The recirculation bubble width Db * is defined to be the maximum distance between the two separation streamlines. Xu et al 2017).…”