Wake dynamics of finite-aspect-ratio rotating circular cylinders at low Reynolds number

Abstract

We perform direct numerical simulations of flows over finite-aspect-ratio rotating circular cylinders at a Reynolds number of 150 over a range of aspect ratios ($AR=2-12$) and rotation rates ($\alpha=0-5$), aiming at revealing the free-end effects on the wake dynamics and aerodynamic performance. As a direct consequence of lift generation, a pair of counter-rotating tip vortices is formed at the free ends. At low rotation rates, the finite rotating cylinder behaves like a typical bluff body that generates unsteady vortex shedding with three-dimensional modal structures. Such unsteady flows can be stabilized not only by increasing rotation rate that weakens the free shear layer, but also by decreasing aspect ratio which enhances the tip-vortex-induced downwash. A further increase of $\alpha$ triggers the onset of unsteadiness in the tip vortices. At still higher rotation rates, the C-shaped Taylor-like vortices bounded on the cylinder surface emerge from the free ends and propel towards the midspan due to the self-induced velocity by vortex-wall interaction. With increasing $\alpha$, the free-end effects penetrate to the inboard span, leading to reduced lift and elevated drag compared to the two-dimensional flows. The three-dimensional end effects can be effectively suppressed by the addition of end plates, which position the tip vortices away from the cylinder, thereby significantly improving the aerodynamic performance. This study reveals the mechanisms for the formation of three-dimensional wakes under the influence of the free ends of finite rotating cylinders. The insights obtained here can serve as a stepping stone for understanding the complex high-$Re$ flows that are more relevant to industrial applications.