Feedback control of a flow past a cylinder via transverse motion

The instability giving rise to the Karman vortex street in a flow past a circular cylinder is responsible for the occurrence of large amplitude oscillations in the lift. In this work, we seek to control the instability via active feedback control by means of transverse displacements of the solid structure. Our investigation is based on Foppl’s four-dimensional potential flow model of point vortices. A feedback controller capable of manipulating the flow in order to maintain zero lift at all times is derived analytically by using perturbation methods and asymptotic expansions. We then apply the controller to the viscous flow by direct numerical simulation of the flow based on the two-dimensional Navier–Stokes equations and show that our control algorithm is capable of keeping the lift close to zero in the impulsively started viscous flow and, therefore, controlling vortex shedding. Computations are carried out at the Reynolds numbers Re=100 and Re=200.