Lagrangian mixing of pulsatile flows in constricted tubes

Abstract

Several Lagrangian methods were used to analyze the mixing processes in an experimental model of a constricted artery under a pulsatile flow. Upstream Reynolds number Re was changed between 1187 and 1999, while the pulsatile period T was fixed at 0.96 s. Velocity fields were acquired using Digital Particle Image Velocimetry for a region of interest (ROI) located downstream of the constriction. The flow is composed of a central jet and a recirculation region near the wall where the vortex forms and sheds. To study the mixing processes, finite-time Lyapunov exponents (FTLE) fields and concentration maps were computed. Two Lagrangian coherent structures (LCS) responsible for mixing fluid were found from FTLE ridges. A first LCS delimits the trailing edge of the vortex, separating the flow that enters the ROI between successive periods. A second LCS delimits the leading edge of the vortex. This LCS concentrates the highest particle agglomeration, as verified by the concentration maps. Moreover, from particle residence time maps, the probability of a fluid particle leaving the ROI before one cycle was measured. As Re increases, the probability of leaving the ROI increases from 0.6 to 0.95. Final position maps rf were introduced to evaluate the flow mixing between different subregions of the ROI. These maps allowed us to compute an exchange index between subregions, EI¯, which shows the main region responsible for the mixing increase with Re. Finally, by integrating the results of the different Lagrangian methods, a comprehensive description of the mixing and transport of the flow was provided.