A numerical study of flow past a rotating circular cylinder using a hybrid vortex scheme

Abstract

The vortex shedding and wake development of a two-dimensional viscous incompressible flow generated by a circular cylinder which begins its rotation and translation impulsively in a stationary fluid is investigated by a hybrid vortex scheme at a Reynolds number of 1000. The rotational to translational speed ratio α varies from 0 to 6. The method used to calculate the flow can be considered as a combination of the diffusion-vortex method and the vortex-in-cell method. More specifically, the full flow field is divided into two regions: near the body surface the diffusion-vortex method is used to solve the Navier–Stokes equations, while the vortex-in-cell method is used in the exterior inviscid domain. Being more efficient, the present computation scheme is capable of extending the computation to a much larger dimensionless time than those reported in the literature.The time-dependent pressure, shear stress and velocity distributions, the Strouhal number of vortex shedding as well as the mean lift, drag, moment and power coefficients are determined together with the streamline and vorticity flow patterns. When comparison is possible, the present computations are found to compare favourably with published experimental and numerical results. The present results seem to indicate the existence of a critical α value of about 2 when a closed streamline circulating around the cylinder begins to appear. Below this critical α, Kármán vortex shedding exists, separation points can be found, the mean lift and drag coefficients and Strouhal number increase almost linearly with α. Above α ≈ 2, the region enclosed by the dividing closed streamline grows in size, Kármán vortex shedding ceases, the flow structure, pressure and shear stress distributions around the cylinder tend towards self-similarity with increase α, and lift and drag coefficients approach asymptotic values. The optimum lift to drag ratio occurs at α ≈ 2. The present investigation confirms Prandtl's postulation of the presence of limiting lift force at high α, and thus the usefulness of the Magnus effect in lift generation is limited.The results show that the present method can be used to calculate not only the global characteristics of the separated flow, but also the precise evolution with time of the fine structure of the flow field.