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Advances in Computational Mathematics

, Volume 45, Issue 4, pp 2047–2063 | Cite as

Numerical modelling of generalized Newtonian fluids in bypass tube

  • Radka KeslerováEmail author
  • Hynek Řezníček
  • Tomáš Padělek
Article
  • 36 Downloads

Abstract

The following paper describes a numerical simulation of a complete bypass of a stenosed human artery. The considered geometry consists of the narrowed host tube and the bypass graft with a 45-degree angle of connection. Different diameters of the narrowing are tested. Blood is the fluid with shear rate–dependent viscosity; therefore, various rheology mathematical models for generalized Newtonian fluids are considered, namely Cross model, modified Cross model, Carreau model, and Carreau-Yasuda model. The fundamental system of equations is based on the system of generalized Navier-Stokes equations. Generalized Newtonian fluids flow in a bypass tube is numerically simulated by using a SIMPLE algorithm included in the open-source CFD tool, OpenFOAM. The aim of this work is to compare the numerical results for the different mathematical models of the viscosity with the changing diameter of the narrowed channel.

Keywords

Generalized Newtonian fluids Generalized Navier-Stokes equations OpenFOAM Bypass 

Mathematics Subject Classification (2010)

65L06 65N08 76A05 76A10 76D05 

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Notes

Funding information

This work was supported by the grant agency of the Czech Technical University in Prague.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Technical MathematicsFME CTU in PraguePraha 2Czech Republic
  2. 2.Department of Transport SystemsFTS CTU in PraguePraha 1Czech Republic

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