Numerical study of the non-Newtonian blood flow in a stenosed artery using two rheological models

Abstract

The numerical simulation of blood flow in arteries using non-Newtonian viscosity model, presents two major difficulties; the first one is the choice of an appropriate constitutive equation, because no one model is universally accepted as a reflection of the true behavior of blood viscosity until now. Another difficulty lies in the numerical convergence of the complex scheme solving the highly non-linear set of equations governing the blood motion. In this paper, the pulsatile blood flow through an arterial stenosis has been numerically modeled to evaluate the flow characteristics and the wall shear stress under physiological conditions. The Navier-Stokes equations governing the fluid motion are solved using the finite element method in unsteady two-dimensional case. The behavior of blood is considered as the Generalized Power-law (Gpl) and Cross models, where the shear-thinning characteristics of the streaming blood are taken into account. Constants in the constitutive equations of previous models have been obtained by fitting experimental viscosity data. The numerical simulations are performed for a wide range of apparent shear rates (10 s-1-750 s-1) with good convergence of the iterative scheme. Results from the blood flow simulations indicate that non-Newtonian behavior has considerable effects on instantaneous flow patterns. However, it seems that the Gpl model will be slightly better for describing the non-Newtonian characteristics of blood than the Cross model.