Date of Award

Spring 2021

Project Type

Dissertation

Program or Major

Mathematics

Degree Name

Doctor of Philosophy

First Advisor

Marianna A Shubov

Second Advisor

Mark Lyon

Third Advisor

John Gibson

Abstract

The present research is devoted to the problem of stability of the fluid flow moving in a channel with flexible walls and interacting with the walls. The walls of the vessel conveying fluid are subject to traveling waves. Experimental data shows that the energy of the flowing fluid can be transferred and consumed by the structure (the walls), which induces “traveling wave flutter.” The problem of stability of fluid-structure interaction splits into two parts: (i) stability of fluid flow in the channel with harmonically moving walls and (ii) stability of solid structure participating in the energy exchange with the flow. Stability of fluid flow is the main focus of the research. It is shown that using the mass conservation and the incompressibility condition one can obtain the initial boundary value problem for the stream function. The boundary conditions reflect the facts that (i) for the axisymmetrical flow, there is no movement in the vertical direction along the axis of symmetry, and (ii) there is no relative movement between the near-boundary flow and the structure (“no-slip” condition). The closed form solution is derived and is represented in the form of an infinite functional series.

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