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.

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

“…[39][40][41][42][43][44][45][46] Details on the current flow solver are provided in Cox et al [47][48][49] and Cox. 50 A grid spacing h and polynomial p convergence study was performed 12 where we found that a mesh containing a total of 69 888 hexahedral elements and a p = 4 Lagrange polynomial used to approximate the solution in each element provide ample spatial resolution (∼8.7M degrees of freedom) to converge the L 2 -norm of the error in the wall shear stress to within 0.78% and the velocity magnitude to within 0.25%. We use the free 3-D finite element mesh generator GMSH 51 to create all computational domains.…”

“…The numerical solver requires that a velocity field u be specified at the inlet boundary to the computational domain. Under WEC, this velocity field is extracted from PIV data captured upstream of the curvature 12 in the straight section of the pipe where the flow is fully developed pulsatile flow, where the only non-zero component of the velocity field is the streamwise velocity. These PIV data were obtained over a discretized set of 100 phases over the entire waveform period.…”

“…The development of secondary flow creates vortical structures that affect wall shear stress patterns, which may play a significant role in the progression of cardiovascular disease. 12 The mechanism of secondary flow in a curved pipe under fully developed steady flow conditions was originally put forth by Dean, 13,14 who found that fluid motion is dependent upon a parameter κ referred to thereafter as the Dean number 1 In curved pipes, the primary flow is defined to be parallel to the pipe axis whereas the secondary flow is superimposed on and perpendicular to the primary flow. and defined as 15…”

“…Despite the vast amount of research in the 20th century on flow through curved conduits, the appearance of vortical structures under pulsatile developing flow and their role in vascular flows still warrants further investigation. Recent research by Cox et al 12 characterized the spatial and temporal evolution of three-dimensional vortical structures under pulsatile flow through a curved artery model, specifically capturing both Dean-type and Lyne-type vortices throughout the deceleration phase of the physiologically relevant flow rate. From these results, the authors discussed the connection along the axial direction between vortical structures observed at various cross sections of the model, supplementing previously limited two-dimensional analysis.…”

High-Strouhal-number pulsatile flow in a curved pipe

“…Einstein (1926) also noted the influence of secondary flows in the accumulation of tea leaves swept into the centre of a cup after stirring has ceased. The enhanced shear stress induced by a secondary flow also has implications for hemodynamics in cardiovascular systems (Siggers & Waters 2008; Cox, Najjari & Plesniak 2019), hence the vast body of research associated with this area. The mixing in the heat exchanger and particle erosion/deposition (Inthavong 2019) in a curved pipe arising from secondary flow has a substantial impact on power loss in the industrial piping system.…”