No abstract

No abstract

No abstract

We numerically investigate spatial and temporal evolution of multiple three-dimensional vortex pairs in a curved artery model under a fully developed pulsatile inflow of a Newtonian blood-analog fluid. We discuss the connection along the axial direction between regions of organized vorticity observed at various cross sections of the model, extending previous two-dimensional analysis. We model a human artery with a simple, rigid 180° curved pipe with circular cross section and constant curvature, neglecting effects of taper, torsion, and elasticity. Numerical results are computed from a discontinuous high-order spectral element flow solver using the flux reconstruction scheme and compared to experimental results obtained using particle image velocimetry. The flow rate used in both the simulation and the experiment is physiological. Vortical structures resulting from secondary flow are observed in various cross sections of the curved pipe, in particular, during the deceleration phase of the physiological waveform. We provide side-by-side comparisons of the numerical and experimental velocity and vorticity fields during acceleration and deceleration, the latter during which multiple vortical structures of both Dean-type and Lyne-type coexist. Correlations and quantitative comparisons of the data at these cross sections are computed along with trajectories of Dean-type vortices. Comparing cross-sectional flow fields and vortices provides a means to validate wall shear stress values computed from these numerical simulations, since the evolution of interior flow structures is heavily dependent upon geometry curvature and inflow and boundary conditions.

Transient, steady and oscillatory flows in a $180^{\circ }$ curved pipe are investigated both numerically and experimentally to understand secondary flow vortex formation and interactions. The results of numerical simulations and particle image velocimetry experiments are highly correlated, with a low error. To enable simulations in a smaller domain with shorter inlet section, an analytical solution for the unsteady Navier–Stokes equation is obtained with non-zero initial conditions to provide physical velocity profiles for the simulations. The vorticity transport equation is studied and its terms are balanced to find the mechanism of vorticity transfer to structures in the curved pipe. Several vortices are identified via various vortex identification (ID) methods and their results are compared. Isosurfaces of the $\unicode[STIX]{x1D706}_{2}$ vortex ID are used to explain the temporal and spatial evolution of vortices in the curved pipe. Eigenvalues and eigenvectors of the velocity gradient tensor are calculated for the swirling strength vortex ID method, which also determines vortex axis orientation. The classical Lyne vortex in oscillatory flow with an inviscid core is also revisited and its results are compared with the transient and steady flows. These in-depth analyses provide a better understanding and characterization of vortical structures in the curved pipe flow. Our findings show that, although there are some 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).