Instabilities in pulsating pipe flow in complex fluids

In large blood vessels Reynolds numbers (Re~4000) considerably exceed transition thresholds of ordinary pipe flow and flows are prone to hydrodynamic instabilities and turbulence. The flows stability however is also influenced by various other factors such as the pulsation frequency, pulsation amplitude, the complex fluid properties, wall compliance and by the frequently complicated geometry (e.g. bends, junctions, constrictions etc.). The occurrence of turbulence and of hydrodynamic instabilities in the circulatory system is often connected to cardiovascular diseases like atherosclerosis or aneurysm formation. Such, for example regular laminar flow with steady wall shear stress levels has been found to upregulate the expression of genes that suppress atherosclerosis in endothelial cells while unstable flows in particular with low wall shear stress intervals lead to the expression of genes that promote inflammation and plaque formation. In order to better understand the causes of instabilities that may be relevant to cardiovascular flows, we here plan to start with the much simpler case of pulsating flow through a straight rigid pipe and to increase the complexity of the problem in steps. In this way we aim to isolate the influence of the different parameters on the flows stability. The main focus here will be on amplitude and frequency values that prevail in large blood vessels and for these parameters we will investigate instabilities that may occur due to local changes in geometry and or due to the fluids complexity. Starting with a purely Newtonian fluid we will investigate the susceptibility of the laminar pulsating flow to different geometrical perturbations such as localized diameter reductions (stenosis) and curved pipe segments. Initial experiments will be carried out for the generic case of a sinusoidal flowrate modulation. The transition threshold will be determined and the flow structures at onset and their variation over the cycle will be closely monitored (using stereoscopic particle image velocimetry, PIV) in order to elucidate the underlying instability mechanism. In the next step the waveform will be altered to that encountered in the aorta, where the much more abrupt acceleration and deceleration is likely to change the transition thresholds and possibly the nature of the transition. Subsequently we will increase the complexity of the fluid by addition of shear thinning polymers. We expect that even moderate amounts of shear thinning (comparable to that of actual blood) will have a significant impact on the flows stability. Finally a comparative study will be carried out with actual blood as the working fluid in order to determine if besides shear thinning other fluid properties alter the transition scenario.

Many flows in nature and applications are driven periodically. A prime example are cardiovascular flows, but also a variety of flows in applications such as fuel injection or peristaltic pumps fall into this category. In all these cases flows transition from laminar to turbulent at sufficiently large flowrates, causing a sharp increase in pressure losses as well as in pumping costs. Moreover, the increased fluctuation levels and wall-shear stresses can have detrimental effects on the blood vessels and can lead to inflammation of their inner lining, the endothelial cell layer. Our study therefore deals with the fundamental question how pulsation influences a flow's stability. In particular, we were able to identify a previously unknown instability that leads to turbulence at unexpectedly low flow velocities. Conditions for which flows were expected to be laminar. We could moreover demonstrate that this instability occurs at slight bends or constrictions (stenosis) of the pipe. At onset the instability takes the form of a helical vortex pattern that grows in amplitude during the deceleration phase and finally turns into turbulence. For acceleration, however, turbulence decays and the flow returns to laminar. Rather than to fully turbulent flow this instability hence leads to the periodic appearance of turbulent bursts. Notably periodic driving has an entirely different influence on the classic route to turbulence, i.e. the instability commonly encountered in steadily-driven pipe flow. This latter transition is typically delayed by flow pulsation. This in itself however does not account for drag reduction. For most of the periodic flowrate modulations tested, the resulting drag was, as expected, larger than that of steadily driven pipe flow. Surprisingly when we chose the same flowrate modulation that occurs in aortic blood flow, the drag was strongly reduced. A parameter study showed that the timing of the accelerating and decelerating phase combined with a rest phase is close to optimal for drag reduction and overall this driving mode was 10% more energy efficient than steady driving, which so far had been assumed optimal. Aside from instabilities due to flow pulsation our investigation was also concerned with flow instabilities caused by complex fluid properties. Many everyday fluids, such as shampoo, blood or solutions of long-chain polymers, have properties that fundamentally differ from ordinary fluids. We were particularly interested in the elastic properties of such complex fluids. These can cause instabilities and a fundamentally different type of turbulence. As our work has shown, turbulence in this case occurs at unexpectedly low speeds or at high viscosity, i.e. conditions where ordinary fluids are laminar. Our experiments could for the first time resolve the spatial structure of this instability and in doing so we confirmed a theoretical prediction concerning the nature of this instability.