Experimental study of flow around polygonal cylinders

S. J. Xu, W. G. Zhang, L. Gan, M. G. Li, Y. Zhou
2016 Journal of Fluid Mechanics  
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
more » ... ficient 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.
doi:10.1017/jfm.2016.801 fatcat:krfrnuipxfchfduhexlhj6wbge