The Taylor-Couette flow validation case belongs to fluid dynamics. This test case aims to validate the following parameters:
Rotating wall
Velocity profile
Pressure profile
SimScale’s simulation results were compared to analytical results obtained from methods elucidated in the Scholarpedia article on Taylor-Couette flow\(^1).
The so-called Taylor-Couette flow occurs in the gap between two infinitely long concentric cylinders, when at least one of them is rotating. Therefore, the geometry for this project consists of a slice of an annulus between two cylinders, as seen in Figure 1:
Figure 1: Annulus between two concentric cylinders, used to study the Taylor-Couette flow.
The dimensions of the geometry are given in Table 1:
Mesh and Element Types: The mesh used in this case was created in SimScale with the standard algorithm.
Find in Table 2 an overview of the resulting mesh:
Case
Mesh Type
Cells
Element Type
Taylor-Couette flow
Standard
488457
3D tetrahedral/hexahedral
Table 2: Standard mesh characteristics. The mesh consists of tetrahedral and hexahedral elements.
Find below the standard mesh used for this case:
Figure 2: Standard mesh, with region refinements applied to the area around the inner cylinder wall.
Simulation Setup
Material:
Viscosity model: Newtonian;
\((\nu)\) Kinematic viscosity: 1e-5 \(m²/s\);
\((\rho)\) Density: 1 \(kg/m^3\).
Boundary Conditions:
Before defining the boundary conditions, the current nomenclature will be used for the rest of this documentation:
Figure 3: Nomenclature for the assignment of boundary conditions.
In the table below, the configuration for both velocity and pressure are given at each of the boundaries:
Nomenclature
Boundary Type
Velocity
Pressure
Inner wall
Custom
Fixed value: 0 (no-slip condition)
Zero gradient
Outer wall
Custom
Rotating wall: 0.001 \(rad/s\) around the positive y-axis
Zero gradient
Sides
Custom
Symmetry
Symmetry
Table 3: Summary of the boundary conditions used for all cases
Reference Solution
The analytical solution\(^1\) for Taylor-Couette flow is computed from the simplified Navier-Stokes in cylindrical coordinates. Before calculating the velocity and pressure profiles, we need to calculate two constants, \(A\) and \(B\):
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