An example of active circulation control of the unsteady separated flow past a semi-infinite plate
Active circulation control of the two-dimensional unsteady separated flow past a semiinfinite plate with transverse motion is considered. The rolling-up of the separated shear layer is modelled by a point vortex whose time-dependent circulation is predicted by an unsteady Kutta condition. A suitable vortex shedding mechanism introduced. A control strategy able to maintain constant circulation when a vortex is present is derived. An exact solution for the nonlinear controller is then obtained. Dynamical systems analysis is used to explore the performance of the controlled system. The control strategy is applied to a class of flows and the results are discussed. A procedure to determine the position and the circulation of the vortex, knowing the velocity signature on the plate, is derived. Finally, a physical explanation of the control mechanism is presented.
Copyright © 1994 Cambridge University Press. Reprinteed with permission. (Received 8 July 1992 and in revised form 26 July 1993) The first author is deeply grateful to Dr R. Camassa and Dr D.D. Holm for several valuable discussions and to the Center for Nonlinear Studies at the Los Alamos National Laboratories for the financial support provided during the summer of 1991. This work was supported by the Office for the Naval Research Grants no. N00014-90-5-1589 and no. N00014-89-5-1678 and by Rockwell International.