Experimental study of flow around polygonal cylinders

The wake of polygonal cylinders with side number N = 2 ∼ ∞ 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 × 10⁴ × 1:0 × 10⁵, 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 θ_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 ξ or St versus ξ for all the tested cases collapse onto a single curve, where the angle ξ is the corrected θ_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.