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Aorta, Non-Newtonian pulsating blood flow, ANSYS Fluent Simulation Training

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In this study, a non-Newtonian pulsating blood flow in Aorta has been studied.

This product includes Geometry & Mesh file and a comprehensive Training Movie.

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Description

Project Description

In this study, a non-Newtonian pulsating blood flow in Aorta has been studied. UDF defines the pulsatile inlet velocity. A non-Newtonian fluid is a fluid that does not follow Newton’s law of viscosity, i.e., constant viscosity independent of stress. In non-Newtonian fluids, viscosity can change when under force to either more liquid or more solid.

Assumption:

The assumptions that we used in this study are listed below:

  • The flow is unsteady
  • The flow is Turbulent
  • The density is constant and equals 1060 kg/m3
  • The working fluid (Blood) is non-Newtonian
  • No-slip condition for the inner surface of the vessel wall

Aorta Geometry & Mesh

The geometry is a *.stl file that should be repaired before generating the mesh. Some powerful tools can assist us in fixing the geometry, such as Spaceclaim, ICEM CFD, and Design Modeler. In this study, we used ICEM CFD to fix the geometry and generating mesh. First, the mesh was generated using the octree method and with 5 layers of prism meshes with a ratio of 1.2. Second, the Delaunay method has been used to improve the quality of the existing mesh. The final number of mesh is 457864 cells.

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Model Setup

Table 1 shows all the settings which are used in this study.

Table 1. Model setup and boundary conditions

General Settings
Gravity 9.81 (Z-Direction)
Solver type Pressure-Based
Time Transient
Models
Viscous
k-omega
Viscosity (Non-Newtonian) Carreau Model
Density (Blood) 1060 (kg/m3)
Boundary Conditions
Inlet UDF (Appendix)
Outlet Pressure Outlet
Wall No-Slip
Solution Methods
Coupling of Pressure-Velocity SIMPLE
Spatial Discretization 2nd order for Pressure and Momentum

Non-Newtonian CARREAU Model

In the Carreau Model, like the Power Law Fluid Model, viscosity depends upon the shear rate. Pierre Carreau first proposed the model. Blood is a non-Newtonian fluid whose behavior follows this model. This model works based on both the shear model and temperature. In this study, there is no energy equation. Therefore, the temperature was ignored. The following equation shows the viscosity relation with the shear model.

Aorta

Where µ0, µ∞, n, and λ are zero shear viscosity, infinite shear viscosity, power index, and relaxation time, respectively. The values of the Carreau Model’s parameters are set in the table below.

Parameter Value
zero shear viscosity (kg/m-s) 0.022
infinite shear viscosity (kg/m-s) 0.0022
power index 0.392
relaxation time (s) 0.11

Aorta Results

The following figures illustrate inlet velocity and pressure drop, respectively. As the figures show, the maximum velocity is at the Time of 0.15 (s).

According to the contours, the WSS (wall shear stress) has the maximum value in the Aorta sections whose diameter is less than others. Also, the contours of static pressure show, at the beginning of the pumping blood, at the entrance of the branches, the pressure is maximum. When the suction occurs at the Time of 0.4 s, it has the most significant impact on the inlet section of the Aorta. To see the pluses and better understand the flow condition, animation files of pressure and shear stress have been attached to this report.

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Appendix

Here we provide you with the UDF that was used to define pulsating inlet velocity to that Aorta. The equation of the UDF is:

aorta

You can obtain Geometry & Mesh file, and a comprehensive Training Movie which presents how to solve the problem and extract all desired results.

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