Mathematical modelling of the influence of yield shear stress on blood friction in a turbulent flow

Abstract

Measurements of blood rheology indicate that human blood has a yield shear stress. Transport of oxygen in the aorta or a vein depends on blood flow rate. Therefore, it is interesting to find out how blood yield shear stress affects blood transportation if flow is turbulent. The majority of mathematical approaches deal with laminar flow of human blood, which is rather simple compared to turbulent flow modelling. This paper presents a mathematical model of fully developed turbulent flow of human blood in the aorta. The physical model assumes that blood is a non-Newtonian liquid that demonstrates yield shear tress. The main objective of the research is to examine the influence of human blood yield shear stress on turbulent properties, like friction factor, in the aorta. Available blood rheology experimental data for various concentrations of haematocrit were used in order to fit the rheological model. The rheological model together with the momentum equation and the two-equation turbulence model constitute a mathematical model of turbulent flow of human blood. Results of simulations are discussed and presented as figures and conclusions.