The effect of entrance flow development on vortex formation and wall shear stress in a curved artery model

Abstract

We numerically investigate the effect of entrance condition on the spatial and temporal evolution of multiple three-dimensional vortex pairs and the wall shear stress distribution in a curved artery model. We perform this study using a Newtonian blood-analog fluid subjected to a pulsatile flow with two inflow conditions. The first flow condition is fully developed while the second condition is undeveloped (i.e., uniform). We discuss the connection along the axial direction between regions of organized vorticity observed at various cross sections of the model and compare results between the different entrance conditions. We model a human artery with a simple, rigid 180° curved pipe with a circular cross section and constant curvature, neglecting the effects of taper, torsion, and elasticity. Numerical results are computed from a discontinuous high-order spectral element flow solver. The flow rate used in this study is physiological. We observe differences in secondary flow patterns, especially during the deceleration phase of the physiological waveform where multiple vortical structures of both Dean-type and Lyne-type coexist. The results indicate that decreased axial velocities under an undeveloped condition produce smaller secondary flows that ultimately inhibit growth of any interior flow vortices. We highlight the effect of the entrance condition on the formation of these structures and subsequent appearance of abnormal inner wall shear stresses, which suggest there may be a lower prevalence of cardiovascular disease in curved arteries where the flow is rather undeveloped—a potentially physiologically significant result to help understand the influence of blood flow development on disease.