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

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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 (0.01⩽Re⩽45) and rotation rates (0⩽α⩽6) were considered for the steady flow regime, where α 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 α varying in the range 0⩽α⩽2. Additionally, the investigations were extended to very high rotation rates (α⩽12) 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 α. 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 α<2. However, for higher α 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 (α⩽2) the flow exhibits the behavior known from the literature, e.g., a linear increase of the mean lift coefficient with increasing α and the suppression of vortex shedding beyond a critical α value of about αL≈1.8. However, for α≈5, 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.