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:

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:

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:

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

Rotating wall: 0.001 \(rad/s\) around the positive y-axis

Zero gradient

Outer wall

Custom

Fixed value: 0 (no-slip condition)

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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