Three-Dimensional Instabilities in Flow Past a Rotating Cylinder

Flow past a spinning circular cylinder placed in a uniform stream is investigated via three-dimensional computations. A stabilized finite element method is utilized to solve the incompressible Navier-Stokes equations in the primitive variables formulation. The Reynolds number based on the cylinder diameter and freestream speed of the flow is 200. The nondimensional rotation rate, α, (ratio of the surface speed and freestream speed) is 5. It is found that although the two-dimensional flow for $α=5$ is stable, centrifugal instabilities exist along the entire span in a three-dimensional set-up. In addition, a “no-slip” side-wall can result in separation of flow near the cylinder ends. Both these effects lead to a loss in lift and increase in drag. The end conditions and aspect ratio of the cylinder play an important role in the flow past a spinning cylinder. It is shown that the Prandtl’s limit on the maximum lift generated by a spinning cylinder in a uniform flow does not hold.