## Open-Loop and Optimal Feedback Control of the Cylinder Wake

### Bartosz Protas , Andrzej Styczek , Jose-Eduardo Wesfreid

#### Abstract

We consider here the control of the plane viscous incompressible wake flow past the circular cylinder at Re=150. The control has the form of the rotary motion of the obstacle. We thoroughly analyze hydrodynamic forces and the related physical mechanisms. We performed several simulations with arbitrarily chosen controls in the form of harmonic oscillations. For certain forcing frequencies significant drag reduction was obtained. It was accompanied by cancellation of the basic Benard-von Karman vortex shedding mode. These flows were investigated from the point of view of the energy budget. Changes in the drag were related to modifications of the mean velocity profiles. Next, an optimal control algorithm was proposed. It allows one to minimize a given functional over a chosen time interval. Sensitivity of the functional to the given type of control is expressed using equations dual to the linearized Navier-Stokes system. They are solved in the velocity-vorticity formulation. In the simulations we obtained substantial drag reduction with a very small control effort. The efficiency of the two control strategies was compared.
 Author Bartosz Protas Bartosz Protas,, - , Andrzej Styczek (FPAE / IAAM) Andrzej Styczek,, - The Institute of Aeronautics and Applied Mechanics , Jose-Eduardo Wesfreid Jose-Eduardo Wesfreid,, - Book , 2000 URL http://adsabs.harvard.edu/abs/2000APS..DFD.DH002P Score (nominal) 3 Citation count*
 Cite