Date of Award

Spring 2000

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)

Department

Mathematical Sciences

First Advisor

N. Aubry

Second Advisor

Demetrius T. Papageorgiou

Third Advisor

Michael Siegel

Fourth Advisor

Burt S. Tilley

Fifth Advisor

Pushpendra Singh

Abstract

As it is well known, the flow past a cylinder consists of a symmetric recirculation bubble of vortices at small Reynolds numbers. As Reynolds number increases, the bubble becomes unstable and develops into a Karman vortex street of alternating vortices. This instability is responsible for the occurrence of large amplitude oscillations in the lift and an increase in the mean drag. It was previously shown by numerical simulation that the mechanism driving the bubble instability is well mimicked by Foppl's four dimensional potential flow model where the bubble is represented by a saddle point. In this work, we design two active feedback control algorithms for the model based on small perturbations applied to the cylinder in order to control the flow slightly perturbed away from the fixed point. We use the domain perturbation method and asymptotic expansions to derive control algorithms analytically. In the first algorithm, we displace the cylinder by a small vertical distance such that the lift remains zero at all times. We also show by direct numerical simulation of the flow (based on the full N-S equations) that our feedback control system is capable of preventing vortex shedding from occurring in the impulsively started viscous flow at Reynolds number Re = 100. In the second algorithm, we deform the cylinder uniformly so that the drag remains the drag of the steady recirculation bubble.

Included in

Mathematics Commons

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