PhD Studentship: Mathematical Modelling of High-Frequency Self-Excited Oscillations in Fluid Conveying Elastic Walled Tubes (WHITTAKERR_U18SCI)

University of East Anglia - Mathematics

Start Date: October 2018

Supervisor: Dr Robert Whittaker

Project description: Flow-induced oscillations in fluid-conveying elastic-walled tubes arise in many engineering and biomechanical systems. Examples include pipe flutter, wheezing during forced expiration from the pulmonary airways, and the development of Korotkoff sounds during blood pressure measurement by sphygmomanometry.

Experimental studies of flow in collapsible tubes are typically performed with a Starling resistor. A finite-length elastic tube is mounted between two rigid tubes and flow is driven through the system.  The collapsible segment is contained inside a pressure chamber which allows the external pressure acting on the elastic tube to be controlled. If the external pressure is sufficiently large, the tube will buckle non-axisymmetrically. Experiments show that in this buckled state, the elastic tube segment has a propensity to develop large-amplitude self-excited oscillations of great complexity when the flow rate is increased beyond a certain value.

This PhD project aims to further our understanding of some of the mechanisms that can lead to this instability. The fluid flow will be described by the Navier-Stokes equations, and an appropriate elastic model will be used for the tube wall. Whittaker et al (2010) developed a relatively simple model for small-amplitude long-wavelength high-frequency oscillations in an elliptical tube. This project will start by working to relax some of these assumptions by, for example, adding nonlinear effects and allowing for different cross-sectional shapes. The project will likely focus on developing reduced analytic models (which may need to be solved analytically or numerically) and there is also scope for conducting full-scale numerical simulations.

Further background information can be found at

Interviews will be held w/c 22 January 2018.

Person specification: Acceptable first degree: Mathematics. The standard minimum entry requirement is 2:1.

Funding notes: This PhD project is in a Faculty of Science competition for funded studentships. These studentships are funded for 3 years and comprise home/EU fees, an annual stipend of £14,553, and £1,000 per annum to support research training. Overseas applicants may apply but they are required to fund the difference between home/EU and overseas tuition fees (in 2017/18 the difference is £13,805 for the Schools of CHE, PHA, & MTH (Engineering) and £10,605 for CMP & MTH, but fees are subject to an annual increase).

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