Sensitivity to entrance conditions of wall shear stress in a curved vessel

This study aims to numerically investigate the impact of entrance velocity distributions on wall shear stress in a simplified curved vessel model. The flow in a single-curved vessel is simulated with Reynolds numbers adjusted to a Newtonian blood-analog fluid in an external iliac artery (EIA) model. Simulations are conducted assuming a rigid wall and a steady-state flow regime using OpenFOAM (R). Eight entry velocity conditions are implemented, including the effects of flow development, asymmetry, Dean-type secondary flow and rotation. Their influences on hemodynamics features are investigated, focusing on axial wall shear stress (WSS). In the examined configurations of EIA flow, the impact of entrance conditions on WSS distribution is moderate. The maximum WSS is consistently located at the bend exit on the outer wall, except in the case mimicking an upstream curved pipe in the opposite direction of the local curvature. While the entry condition affects the maximum WSS value, this value remains within the same order of magnitude. At Re=560\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Re=560$$\end{document}, the highest WSS value is given by the Poiseuille condition and reaches 4.9 times the value of the laminar straight flow. At Re=1100\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Re=1100$$\end{document}, the maximum value provided by the Dean-type condition, particularly in the case mimicking an upstream curved pipe perpendicular to the local curvature, reaching 7.1 times the laminar straight flow, which exceeds the value of the Poiseuille condition by 17%. The results suggest that, to capture extreme WSS value, opting for Poiseuille flow as the entrance condition is a good choice for further studies on EIA flow. It has to be noted that results presented here tend to confirm the link established between exaggerated WSS and the endofibrosic plaque development.