Suboptimal feedback control of flow over a sphere

In this study, we control unsteady motion in the wake behind a sphere using a suboptimal feedback control method based on the sensing of surface pressure. The cost function to be reduced is the square of the difference between the potential-flow and real pressures at the sphere surface. The actuation velocity (blowing/suction) is obtained from the suboptimal feedback control procedure. The sensing and actuation on the whole surface of the sphere is considered. This is an ideal case but provides a clear understanding of the effect of suboptimal feedback control on the present flow. We choose four different Reynolds numbers, Re = 100, 250, 300, and 425, covering four different flow regimes (steady axisymmetric, steady planar–symmetric, unsteady planar–symmetric, and unsteady asymmetric flows, respectively). With the present control, the vortex shedding disappears for Re = 300 and 425 and the drag is significantly reduced for all the Reynolds numbers considered.