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:
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:
Table 2: Standard mesh characteristics. The mesh consists of tetrahedral and hexahedral elements.
Find below the standard mesh used for this case:
Viscosity model: Newtonian;
\((\nu)\) Kinematic viscosity: 1e-5 \(m²/s\);
\((\rho)\) Density: 1 \(kg/m^3\).
Before defining the boundary conditions, the current nomenclature will be used for the rest of this documentation:
In the table below, the configuration for both velocity and pressure are given at each of the boundaries:
Rotating wall: 0.001 \(rad/s\) around the positive y-axis
Fixed value: 0 (no-slip condition)
Table 3: Summary of the boundary conditions used for all cases
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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