Fluid-conveying elastic-walled tubes arise in many engineering and biomechanical systems. Examples include blood flow in veins and arteries, flow in the airways, and industrial fluid transport and pumping systems.
This PhD project aims to consider such flows using continuum mechanics modelling and a combination of asymptotic and numerical techniques. There will be a particular emphasis on the dynamical interactions and energy transfers between the fluid flow and the material of the surrounding conduit. There are a number of possible areas for investigation, including:
• Examining the energy budget for perturbations to a basic uniform flow, in able to better understand how different instabilities develop.
• Attempting to bridge the gap between the different flows and instability regimes studied previously by different authors, to understand how different physical mechanisms interact in the transition between different regimes.
• Studying and optimising non-peristalitic pumps, where a mean flow is generated along a tube by reversible squeezing of the tube walls.
• Improving elastic models for a tube wall that is subject to a large axial tension (pre-stress), and using such models to improve flow predictions.
These problems will be investigated using a range of appropriate mathematical tools. Continuum mechanics models will be constructed for the fluid flow and wall mechanics, and use will be made of techniques including simplified ODE models, asymptotic analysis, and numerical computations. Successful candidates will already have some experience/knowledge in one or more of these areas, which should be explained their application.
Further background information can be found at http://robert.mathmos.net/research/phd-projects/
A start date prior to October 2019 is possible, but should be discussed with Dr Whittaker in the first instance.
For more information on the supervisor for this project, please go here: https://www.uea.ac.uk/mathematics/people/profile/r-whittaker
Type of programme: PhD
Project start date: October 2019
Mode of study: Full time
Entry requirements: Acceptable first degree - Mathematics, Natural Sciences, Physics, or Engineering;
But a solid grounding in theoretical fluid mechanics, differential equations and advanced mathematical techniques is essential.
The standard minimum entry requirements is 2:1.
i) Jensen and Heil (2003). High-Frequency Self-Excited Oscillations in a Collapsible-Channel Flow, J. Fluid Mech. 481, 235. http://dx.doi.org/10.1017/S002211200300394X
ii) Grotberg and Jensen (2004). Biofluid Mechanics in Flexible Tubes, Ann. Rev. Fluid Mech. 36, 121. http://dx.doi.org/10.1146/annurev.fluid.36.050802.121918
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. http://dx.doi.org/10.1098/rspa.2009.0641
iv) Heil & Hazel (2011) Fluid–Structure Interaction in Internal Physiological Flows, Ann. Rev. Fluid Mech. 43, 141. http://dx.doi.org/10.1146/annurev-fluid-122109-160703
v) Whittaker (2015). A Shear-Relaxation Boundary Layer near the Pinned Ends of a Buckled Elastic-Walled Tube, IMA J Appl. Math. 80 (6), 1932-1967. http://dx.doi.org/10.1093/imamat/hxv022