Numerical Study of Blood Flow through Symmetry and NonSymmetric Stenosis Artery under Various Flow Rates

Abstract

This study investigated the significance of symmetry and non-symmetry stenosis effects of blood flow and quantifies some of the most relevant non Newtonian characteristics of blood flow in blood vessels. The models studied in this work are the Newtonian and Non-Newtonian (Oldroyd-B) models, as well as their generalized (shear-thinning) modifications. The governing system of equations is based on incompressible Navier-Stokes equations which are generalized to take into account viscoelasticity and shear-thinning properties of blood flow. Finite element method is used for the solution of the governing system of equations. Mathematical tests are performed on an idealized symmetric stenosis and a realistic stenosed carotid bifurcation reconstructed from medical images. Model sensitivity tests are achieved with respect to the characteristic flow rate to evaluate its impact on the observed non-Newtonian effects. The numerical simulation is performed for various flow rates 0.05 to 2 cm 3 /s at Reynold numbers, Re =10 2 and Weissenberg numbers, Wi= 0.6 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. Different effects for these models are presented numerically. Nomenclature  Stress Tensor (Pa)  n Polymer viscosity  v Viscous stress tensor (Pa)  s Solvent viscosity  n Solvent stress tensor (Pa) V / Anti-symmetry velocity gradient L height and the enclosure (m)  Rate of deformation tensor I Identity matrix u, v velocity components (ms-1) Wi Weissenberg number U,V Dimensionless velocity components p pressure (Nm-2) Greek symbols P non-dimensional pressure  Viscosity Re Reynold number  Deformation tensor q Flow rate (m 2 /s) ρ density of the fluid (kgm-3)  x Relaxation time υ kinematic viscosity of the fluid (m 2 s-1)  d Retardation time  s Extra-stress tensor V Symmetry velocity gradient