Vortex shedding from a circular cylinder of finite length at low Reynolds numbers

Abstract

Flow past a circular cylinder of finite span-length with two free ends is investigated based on direct numerical solutions of the three-dimensional unsteady incompressible Navier-Stokes equations. Special attention is paid to the effect of length-to-diameter ratio L/D on vortex shedding from the cylinder into its wake, where L is the span-length and D is the diameter of the cylinder. The length-to-diameter ratio L/D is prescribed in the range of 0.5≥ L/D≥100, and the Reynolds number Re which is based on D is 40≥Re≥300. Results show that vortex shedding from, and thus wake pattern behind, the cylinder changes drastically depending on both L/D and Re. Five basic patterns of vortex shedding are found to exist: (i) Periodic oblique vortex shedding at relatively large L/D and at Re beyond a critical Reynolds number, (ii) quasiperiodic oblique vortex shedding also at relatively large L/D but at Re below the critical Reynolds number, (iii) periodic shedding of hairpin-shaped vortices that occurs when L/D is moderate, (iv) steady two counter-rotating vortex pairs that appear when both L/D and Re are small, and (v) alternate shedding of a counter-rotating vortex pair from two flat ends, which occurs when L/D is small but Re is high. Transition processes between the basic patterns are also examined. Three-dimensional vortical structures in the wake are clarified in some detail. © 2008 American Institute of Physics.