Investigation of Newtonian and Power-Law Blood Flow Models in a 180° Curved Pipe at Low to Medium Shear Rate

Abstract

The purpose of this brief paper is to obtain quantitative information on mean velocity profile in ideal vasculature (i.e. straight and toroidal pipes) at low to medium shear rates. To shed the light on the significance of considering blood shear-thinning properties, the power-law model is compared to the commonly used Newtonian viscosity hypothesis. Validated CFD models of blood flow were established and parameterized to solve steady incompressible blood flow under Reynolds number of 50~200. The calculations of the Reynolds number and boundary conditions adopted the shear-thinning index of the power-law models to provide physically correct benchmark for the comparison presented herein. Velocity profiles for Newtonian and non-Newtonian fluid flow are described and sketched. Shear rate values had a range of 20~200 s-1 which represents the physiological range found in cerebral vasculature. This study provides the means to estimate the effect of the non-Newtonian properties of the blood on the flow patterns. It is clearly shown that the difference between Newtonian and power-law blood flow models is not significantly affected by Reynolds number for the current range of shear rate. The differences identified in the pressuredrop per unit length and average wall-shear stress were found to be of significant values. The difference between the Newtonian and power-law model (case1) in the pressure drop per unit length for the straight pipe was 386 while for the curved pipe was 371. These differences increased to 538 at Re=200 for the straight pipe and reached 603 for the curved pipe. This research suggests that the non-Newtonian effects of cerebral blood flow should be considered in the respective CFD models.