Lagrangian analysis of fluid transport in pulsatile post-stenotic flows

A comprehensive experimental study was performed to characterize the fluid transportation processes in pulsatile post-stenotic flows. This study aims to understand the effect of pulsatility on the transportation dynamics of post-stenotic flows and to establish a non-dimensional number to quantify transportation effectiveness in these flows. Two-dimensional particle tracking velocimetry measurements were conducted in a close flow loop with a symmetric stenosis model. A pathline extension algorithm is then applied to the obtained Lagrangian data, such that fluid parcels are continuously tracked as they flow through the region of interest. Pulsatile flows at Reynolds numbers ${\mathrm{Re}}_m=1000,2000,4000$, Strouhal number $\mathrm{St}=0.05,0.1,0.15$ and amplitude ratio $\lambda =0.4$ and 0.8 are systematically investigated to understand the influence of pulsatility on the transport and mixing dynamics. The flow structures, such as the formation and evaluation of vortex rings, Kelvin-Helmoltz instabilities, jet meandering and breakdown, are clearly revealed by the lifespan parcel trajectories and the particle residence time (PRT). These structures are closely related to the transportation behaviours of the post-stenotic flows. Using the obtained Lagrangian results, the transportation effectiveness of the post-stenotic flows is further quantified by the depletion efficiency. The results demonstrate that while post-stenotic flows transport most residual fluids under a higher amplitude ratio, the depletion efficiency itself is insensitive to the amplitude ratio. The flow system operates more efficiently with high pulsatile frequencies ($\mathrm{St}=0.8$). Additionally, a transportation effectiveness parameter, $\mathrm{Te}$, is defined to evaluate the transport performance by comparing the transportation efficiency to the pressure drop. The $\mathrm{Te}$ value is optimized at a high pulsatile frequency ($\mathrm{St}=0.8$) and a low amplitude ratio ($\lambda =0.4$), with $\mathrm{Te}$ being up to twice as high as its counterpart in the steady flow.