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.