Oscillations in Flow Through an Elastic-Walled Tube (WHITTAKERU16SCI)
Flow-induced oscillations of 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 e.g. 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.
This PhD project is offered on a self-funding basis. It is open to applicants with funding or those applying to funding sources.
A bench fee is also payable on top of the tuition fee to cover specialist equipment or laboratory costs required for the research. The amount charged annually will vary considerably depending on the nature of the project and applicants should contact the primary supervisor for further information about the fee associated with the project.
i) Jensen and Heil (2003). High-Frequency Self-Excited Oscillations in a Collapsible-Channel Flow, J. Fluid Mech. 481, 235.
ii) Grotberg and Jensen (2004). Biofluid Mechanics in Flexible Tubes, Ann. Rev. Fluid Mech. 36, 121.
iii) Whittaker et al. (2010) Predicting the Onset of High-Frequency Self-Excited Oscillations in Elastic-Walled Tubes, Proc. Roy. Soc. A 466 (2124), 3635.
iv) Heil & Hazel (2011) Fluid–Structure Interaction in Internal Physiological Flows, Ann. Rev. Fluid Mech. 43, 141.
v) Whittaker (2015). A Shear-Relaxation Boundary Layer near the Pinned Ends of a Buckled Elastic-Walled Tube, IMA J Appl. Math. advance online access.