Influence of geometry, rheology and compliance on the transition to turbulence in pulsatile pipe flow

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The presence of disturbed flow patterns in the cardiovascular system is thought to trigger diseases. Therefore, in recent years there has been an increasing interest on understanding under what conditions instabilities and turbulence transition occur in the cardiovascular system. Apart from the inherent difficulties of studying transition even in canonical systems, cardiovascular flow includes several additional complexities. Blood flow in the large arteries is pulsatile, the arteries are flexible and exhibit complex geometries, and blood itself is a non-Newtonian fluid. Some of these features have been investigated in the literature, usually separately and in simple setups. The effect of the pulsation has been mostly studied in straight and smooth rigid pipes. Even in this canonical system, transition is greatly affected by the pulsation. Depending on the flow parameters, frequency and shape of the pulsation, the flow can be highly susceptible to the sudden appearance of turbulence during certain phases of the pulsation. This is even more so for flows driven with physiological waveforms, suggesting that turbulence could be more widespread in the cardiovascular system than what was previously thought. The influence of flexible walls and non-Newtonian fluids on pulsatile pipe flow has received little attention in the literature. While both compliance and e.g., shear-thinning rheology usually delay turbulence transition in steady pipe flow, in the pulsatile case their effects remain largely unknown. The goal of this project is to extend the knowledge gained on turbulence transition in pulsatile pipe flows in rigid pipes, and systematically study one additional feature of cardiovascular flow. Three different problems are considered. Firstly, pulsatile flow in straight pipes with flexible walls. Secondly, pulsatile flow of complex fluids in rigid pipes. Thirdly, pulsatile flow in simple geometries which resemble certain sections of the human aorta. The focus will be on determining if each new feature affects the critical mechanism identified for the simple case, or if it even introduces new critical paths to turbulence. In order to do so we will develop numerical tools to perform transient growth analyses, and adapt pre-existing software to perform direct numerical simulations. Direct comparisons to laboratory experiments within the research unit will be performed. The ultimate, long-term goal is to define a complete roadmap to turbulence in the cardiovascular system and model it in a simple way using the experimental and numerical results.