Three-dimensional vortical structures and wall shear stress in a curved artery model

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.