Simulations of Frictional Losses in a Turbulent Blood Flow Using Three Rheological Models

Abstract

Blood flow rate is a crucial factor in transporting an oxygen and depends on several parameters like heart pressure, blood properties like density and viscosity, frictional loss and diameter and shape of vein. Frictional loss is a main challenge of current engineering. Therefore, simulation of dependence of blood properties on frictional loss is very important. When blood properties are considered the first step is to find proper rheological model. It is well known that human blood demonstrates a yield shear stress. Therefore, the research is focused on simulating frictional losses in a turbulent flow of human blood, which demonstrates a yield stress. Three arbitrarily chosen rheological models were considered, namely Bingham, Casson and Herschel-Bulkley. Governing equations describing turbulent blood flow were developed to axially symmetrical an aorta. The mathematical model constitutes three partial differential equations, namely momentum equation, kinetic energy of turbulence and its dissipation rate. The main objective of the research is examining influence of the yield shear stress on frictional losses in a human blood in an aorta when flow becomes turbulent. Simulation of blood flow confirmed marginal influence of a yield shear stress on frictional losses when flow becomes turbulent. Results of simulations are discussed and final conclusions are stated.