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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Numerical Analysis Seminars: High-Frequency Self-Excited Oscillations in 3D Collapsible Tube Flows

Presented by Robert J. Whittaker , Oxford Centre for Industrial and Applied Mathematics

29 January 2010 14:15 in CM105

Experiments show that steady flow along an elastic-walled tube can become unstable to large-amplitude oscillations involving both the tube wall and the fluid. We consider a 'Starling resistor' setup - a finite length elastic tube attached to rigid end sections, through which an axial flow is driven by either a steady flux at the downstream end or a steady pressure drop between the ends.

I shall describe a theoretical analysis of small-amplitude high-frequency long-wavelength oscillations. We first consider the fluid mechanics (prescribed oscillations) and then the solid mechanics (to derive an appropriate tube law) in isolation. The two strands are then combined to investigate the full fluid--structure interaction problem for self-excited oscillations. We determine the form of the normal modes and obtain expressions for the growth rate and frequency of the oscillations. The predictions from our modelling show good agreement with numerical simulations performed using the oomph-lib C++ library. I shall talk a bit about the library, and some of the numerical difficulties encountered when performing the simulations.

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