Numerical Investigation of The Behaviour of Wall Shear Stress in Three-Dimensional Pulsatile Stenotic Flows

This paper presents a numerical study of the behaviour of wall shear stress (WSS) in three-dimensional pulsatile flow through an axisymmetric stenosed artery. A realistic blood flow rate (250 ml min−1 at rest in coronary artery [7]) and cardiac cycle (T=0.84s [5]) are applied in the simulations. The flow is fully three-dimensional, and the fluid is assumed to be Newtonian and incompressible. Direct numerical simulation (DNS) of the Navier-Stokes equations is carried out to investigate how different levels of stenosis (S) affect WSS. It has been found that larger values of S lead to higher WSS in the stenosis region due to the faster flow velocity at the throat (smaller cross-sectional area). Downstream of the stenosis region, WSS decreases due to viscous effects and remains nearly constant for lower stenosis level cases (S=30% and 50%). However, at the highest stenosis case (S=90%), the WSS distribution becomes unsteady downstream of the throat due to the instabilities in the shear layer. Introduction Atherosclerosis, also known as atherosclerotic disease, is the most common form of cardiovascular diseases and the direct cause of heart-attack in the community. It is caused by the formation of plaque on the inner wall that narrows and hardens a specific region in an artery of the human cardiovascular system, which is clinically known as stenosis ([3] and [1]). It was reported by Caro et al [2] that WSS fluctuates rapidly in the vicinity of the stenosis and is relatively steady in other regions of the artery. Since then, various investigations on how the presence of stenosis in the artery affects WSS have been carried out. In these investigations, one common observation has been noted that blood flow characteristics, such as flow velocity, pressure and WSS, of the post-stenotic region are significantly affected and cause the development of flow recirculation and the formation of vortex rings. It was also reported by Ooi et al [4] that the altered blood flow characteristics (velocity, pressure and WSS) downstream of stenosis may further promote the growth of the stenosis or develop a new stenosis region, as well as the blockage of smaller arteries and hence possibility of plaque rupture. Apart from the effects of the stenosis, the pulsatile nature of the cardiac cycle is another important factor that influences the flow characteristics in arteries. Several studies have been undertaken to better understand the flow features in pulsatile flow. [4] reported that some researchers have conducted both experimental and DNS study of a pulsatile flow in a constricted pipe and identified that the flow variables are dependent on the inflow conditions upstream of the stenosis. In [4], 2D simulations were carried out to investigate the effects of different stenosis levels. It was found in [4] that, larger stenosis levels result in higher WSS values. Likewise, the formation and propagation of vortex rings are observed and lower stenosis degrees lead to a closer distance between the two subsequent vortex rings. However, only a few studies have considered the numerical study of WSS in three-dimensional pulsatile flow as the simulations are expensive requiring many grid points to fully resolve all spatial and temporal scales in the calculations. Here, the main purpose is to study how the distribution and behaviour of WSS are affected by varying the stenosis degree in a fully three-dimensional flow field. Specifically, numerical simulations are carried out for an axisymmetric stenosis model with different degrees of stenosis and one pulsatile period. Details of the simulations are described below. Numerical Model In this study, the flow is fully three-dimensional, and the fluid is assumed to be Newtonian and incompressible. Thus, direct numerical simulation (DNS) of the incompressible Navier-Stokes equations is carried out to investigate how different levels of stenosis (S) affect WSS.