Date of Award

Fall 2002

Document Type

Dissertation

Degree Name

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

Department

Mathematical Sciences

First Advisor

N. Aubry

Second Advisor

Denis L. Blackmore

Third Advisor

Demetrius T. Papageorgiou

Fourth Advisor

Pushpendra Singh

Fifth Advisor

Lou Kondic

Abstract

When an incompressible fluid flows past a circular cylinder, vortex shedding occurs as soon as the Reynolds number exceeds about 40. Vortex shedding is usually undesirable, as it generates a significant increase in drag, as well an oscillating lift force on the cylinder leading to cross-stream structural vibrations. Flow control to either delay the appearance of vortex shedding or fully suppress it has attracted much attention during the last decade. The focus of this dissertation is to control vortex shedding from a circular cylinder by applying an external electromagnetic field. As in previous works, the latter is generated by electrodes and magnets alternatively arranged on the cylinder surface. In a weakly conducting fluid such as seawater, this has the effect of creating a Lorentz force tangential to the surface of the cylinder and oriented in the flow direction. A novel analytical expression of the Lorentz force is derived by integrating the Maxwell equations and using series expansions. This expression is then used for the control of vortex shedding in numerical simulations. Specifically, a closed-loop control algorithm is derived utilizing a single point sensor on the cylinder surface and the bilinear searching method in order to determine the appropriate magnitude of the Lorentz force at every time. Numerical simulations based on a two-dimensional Navier-Stokes solver show that vortex shedding is indeed suppressed at the Reynolds number values Re = 100 and 200.

Included in

Mathematics Commons

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