Pulsatile Non-Newtonian Laminar Blood Flows through Arterial Double Stenoses

The paper presents a numerical investigation of non-Newtonian modeling effects on unsteady periodic flows in a two-dimensional (2D) pipe with two idealized stenoses of 75% and 50% degrees, respectively. The governing Navier-Stokes equations have been modified using the Cartesian curvilinear coordinates to handle complex geometries. The investigation has been carried out to characterize four different non-Newtonian constitutive equations of blood, namely, the (i) Carreau, (ii) Cross, (iii) Modified Casson, and (iv) Quemada models. The Newtonian model has also been analyzed to study the physics of fluid and the results are compared with the non-Newtonian viscosity models. The numerical results are represented in terms of streamwise velocity, pressure distribution, and wall shear stress (WSS) as well as the vorticity, streamlines, and vector plots indicating recirculation zones at the poststenotic region. The results of this study demonstrate a lower risk of thrombogenesis at the downstream of stenoses and inadequate blood supply to different organs of human body in the Newtonian model compared to the non-Newtonian ones. 1. Introduction Stenosis is characterized by localized arterial narrowing that is initiated due to deposition of lipid, cholesterol, and some other substances on the endothelium and is of major concern to most of the Western world. Atherosclerotic lesions preferentially occur in arteries and arterioles in regions of high curvature or bifurcations and junctions causing major changes in flow structure and consequently large changes in fluid loading on vessel walls [1]. Such plaques or arterial constrictions usually disturb normal blood flow through the artery and there is considerable evidence that hydrodynamic factors can play a significant role in the development and progression of these lesions. It has been established that once a mild stenosis is developed inside the arterial lumen, the resulting flow disorder further influences the development of the disease and the arterial deformability to some extent, which eventually changes the regional blood rheology as well [2]. The rheological behavior of blood can be identified by non-Newtonian viscosity. Halder [3] demonstrated that the rheology of blood and the fluid dynamical properties of blood flow can play an important role in the basic understanding, diagnosis, and treatment of many cardiovascular and arterial diseases. Now, stenosis not only develops in one position of artery but also it may develop at more than one location of the cardiovascular system. However, in many medical