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On the formation of vortices under transient and pulsatile inflow conditions in a curved pipe Open Access

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Fluid flow in curved pipes has been the object of many studies due to its relevance in physiological flow and many industrial applications. Moreover, curved pipe flows have complex vortices that interact with each other and are not well understood. In this study, vortices in steady, pulsatile and transient flows are investigated in a 180$^\circ$ curved pipe using both experimental and numerical approaches. Under various flow conditions, multiple vortices are detected in the flow such as Dean, deformed-Dean, split-Dean and Lyne-type vortices. Particle image velocimetry (PIV) was used to obtain planar velocity fields both in cross-sections of the pipe and in axial planes. Numerical simulations were used to simulate the flow which provides three-dimensional, time-resolved data. Our PIV and numerical simulation results agree well with a correlation of 96\% on average and absolute difference of less than 10\%. For the PIV experiments, refractive index (RI)-matched fluids were used to minimize the image distortion. Various working fluids were tested to obtain the best data quality. Sodium iodide (NaI), sodium thiocyanate (NaSCN) and potassium thiocyanate were used to adjust the RI of fluids to that of the test sections and their effects on fluid rheology are also investigated. To achieve better control of the pump to produce unsteady flows with sufficient accuracy, a proportional-integral-derivative (PID) controller algorithm was developed using an Arduino micro-controller. This study is inspired by physiological blood flow in curved arteries. Because blood is a complex fluid, i.e. composed of red and white blood cells, and platelets, it is a non-Newtonian, shear-thinning fluid. Therefore, one of the aims in this study is to investigate the effects of non-Newtonian properties on the morphology of vortices in the curved pipe. A non-Newtonian fluid was fabricated and investigated and results are compared with those of the Newtonian fluid. Moreover, since vessels are compliant and their geometries are not necessarily planar, the effect of vessel compliance and torsion on the flow features are investigated. Our results confirmed that in large diameter vessels when the laminar flow rate is high enough, the effect of non-Newtonian properties on vortices is insignificant. Moreover, the wall compliance in the investigated (physiological) range of elasticity did not have a significant effect on the flow features. However, the flow structures were found to be extremely sensitive to even a slight amount of torsion, especially if the flow is unsteady/pulsatile. Torsion distorts the symmetric secondary flows (which exist in planar curvatures) and can result in the formation of more complex vortical structures. For example, when the split-Dean and Lyne-type vortices with the same sense of rotation (from cross-sectional view) originating from opposite sides of the cross-section tend to merge together in a pulsatile flow. In order to study the formation mechanism of secondary flow vortices and characterize them, several transient flows were studied where the formation of the vortices can be detected. Vorticity transport analysis was performed to assist the characterization of different vortices in the curved pipe and results are compared to purely oscillatory flow where the classical Lyne vortices exist.Our findings show that although there are visual similarities between cross-sectional views of steady/transient flows and oscillatory flows, the structure herein designated as Lyne-type vortex detected in the cross-sections (under steady, transient and pulsatile flows) is not the same as the classical Lyne vortex pair (in oscillatory flows).

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