A Theoretical and Computational Study on Active Wake Control

Citation

Cortelezzi, Luca (1993) A Theoretical and Computational Study on Active Wake Control. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ZMMS-XA57. https://resolver.caltech.edu/CaltechETD:etd-09302005-111117

Abstract

In the first part of this dissertation a two-dimensional unsteady separated flow past a semi-infinite plate with transverse motion is considered. The flow is assumed incompressible and at high Reynolds number. 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 power-law starting flow is assumed along with a power-law for the transverse motion. The effects of the motion of the plate on the starting vortex circulation and trajectory are presented. A suitable vortex shedding mechanism is introduced and a class of flows involving several vortices is presented. Subsequently, a control strategy able to maintain constant circulation when a vortex is present is derived. An exact solution for the non-linear controller is then obtained. Dynamical system analysis is used to explore the performance of the controlled system. Finally, the control strategy is applied to a class of flows and the results are discussed. In the second part of this dissertation the previous results are extended to the case of a two-dimensional unsteady separated flow past a plate of variable length. Again the rolling-up of the separated shear-layer is modelled by a vortex pair whose time dependent circulation is predicted by an unsteady Kutta condition. A power-law starting flow is assumed while the plate length is kept constant. The results of the simulations are presented and the model validated. A time-dependent scaling which unveils the universality of the phenomenon is discussed. The previous vortex shedding mechanism is implemented and a vortex merging scheme is tested in a class of flows involving several vortices and is shown to be highly accurate. Subsequently, a control strategy able to maintain constant circulation when a vortex pair is present is derived. An exact solution for the non-linear controller is obtained in the form of an ordinary differential equation. Dynamical system analysis is used to explore the performance of the controlled system and the existence of a controllability region is discussed. Finally, the control strategy is applied to two classes of flows and the results are presented.

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