Non-Newtonian Flow: Pulsatile Blood in a Vein

Non-Newtonian Blood Pulsatile Flow in a Vein — ANSYS Fluent CFD Simulation Training

This project simulates non-Newtonian, pulsatile blood flow through a vein using ANSYS Fluent, with the full case analyzed through CFD post-processing.

The working fluid is blood, a non-Newtonian fluid. Non-Newtonian fluids are those whose viscosity changes with shear rate, meaning they have no single fixed viscosity. In such fluids the relationship between shear stress and applied strain rate is nonlinear, so no constant viscosity coefficient applies. The simulation is run as transient over 0.5 s, and a User-Defined Function (UDF) is applied to model the pulsing of the blood flow. Because blood flow is not steady but pulsed, the velocity is prescribed as a periodic function through the UDF code.

The geometry was created in Gambit. The model consists of a main cylindrical vessel and two smaller branch vessels of reduced size and diameter — one branching at a 90-degree angle and the other with a 45-degree curvature. It has one inlet section and two outlet sections.

Meshing was performed in ANSYS Meshing using an unstructured grid, for a total of 397,388 cells.

Methodology

The working fluid is blood, with a density of 1050 kg/m³. Because blood is non-Newtonian, its viscosity is described using the Carreau model with appropriate parameters.

Newtonian fluids maintain a constant viscosity under applied force, whereas non-Newtonian fluids exhibit variable viscosity, of which there are several types. Time-dependent non-Newtonian fluids fall into two categories: rheopectic fluids, such as printer ink and cream, whose viscosity increases over time under load, and thixotropic fluids, such as honey, whose viscosity decreases as force is applied. Time-independent non-Newtonian fluids divide into three groups: dilatants, such as starch and clay, whose viscosity depends only on the magnitude of the applied force; pseudoplastics, such as greases, paints, soaps, and ketchup, whose viscosity is inversely related to the applied force; and Bingham fluids, such as toothpaste and silica nanocomposites, which require a threshold stress before they begin to flow.

In this simulation, blood is treated as a pseudoplastic non-Newtonian fluid defined by the Carreau model. This model spans a wide range of fluid behavior by fitting a curve that matches both Newtonian and shear-thinning (pseudoplastic) responses.

Results

After the solution is complete, contours of pressure and wall shear stress are obtained at several time instants. The results confirm that the flow inside the vessel is fully pulsatile, since the pressure varies over time. They also show that pressure and wall shear stress are correlated: as the pressure inside the vessel rises, the wall shear stress increases accordingly.