Effect of high rotation rates on the laminar flow around a circular cylinder

A two-dimensional numerical study on the laminar flow past a circular cylinder rotating with a constant angular velocity was carried out. The objectives were to obtain a consistent set of data for the drag and lift coefficients for a wide range of rotation rates not available in the literature and a deeper insight into the flow field and vortex development behind the cylinder. First, a wide range of Reynolds numbers (0.01less than or equal toReless than or equal to45) and rotation rates (0less than or equal toalphaless than or equal to6) were considered for the steady flow regime, where alpha is the circumferential velocity at the cylinder surface normalized by the free-stream velocity. Furthermore, unsteady flow calculations were carried out for one characteristic Reynolds number (Re=100) in the typical two-dimensional (2D) vortex shedding regime with alpha varying in the range 0less than or equal toalphaless than or equal to2. Additionally, the investigations were extended to very high rotation rates (alphaless than or equal to12) for which no data exist in the literature. The numerical investigations were based on a finite-volume flow solver enhanced by multi-grid acceleration and the local grid refinement technique to achieve efficient computations and accurate numerical results. The predictions show that the rotation of the cylinder suppresses the vortex development in both the steady and the unsteady flow regimes and significantly changes the flow field close to the cylinder. For very low Reynolds numbers, the drag force is not affected by rotation and the lift force is a linear function of alpha. For higher Re in the steady flow regime, the drag force decreases with increasing rotational velocities even leading to negative values. The lift force is almost a linear function of the rotational velocity and nearly independent of Re for low rotational speeds of alpha<2. However, for higher alpha values and larger Reynolds numbers (Re>1), a progressive increase in the lift force is observed. A very interesting phenomenon was found in the unsteady flow regime at Re=100. For low rotation rates (alphaless than or equal to2) the flow exhibits the behavior known from the literature, e.g., a linear increase of the mean lift coefficient with increasing alpha and the suppression of vortex shedding beyond a critical alpha value of about alpha(L)approximate to1.8. However, for alphaapproximate to5, an unsteady periodic flow motion was found in the wake which is characterized by a frequency much lower than that known for normal vortex shedding. The change in the flow structure also leads to a distinct change in the mean lift coefficients which exhibits a linear relation of very high rotations rates and asymptotically converges to the values known from the potential flow theory. (C) 2002 American Institute of Physics.