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Concentric Cylinders-Couette Flow

Couette flow between two circular cylinders is used to investigate the behaviour of velocity boundary condition for complex geometries with q-values. In this flow, the inner cylinder with radius $r_1=0.25/2 m$ rotates with a constant angular velocity $\omega=0.213 rad/s$ and the outer cylinder with radius $r_2=0.5 m$ is kept stationary.

This Couette flow has the following analytical solution $$\begin{equation} u_\theta(r) = \frac{u_0 \beta}{1-\beta^2} \left( \frac{r_2}{r} - \frac{r}{r_2}\right) \end{equation}$$ where $u_0=\omega r_1$ and $\beta=r_1/r_2$.

This analytical solution is provided as the variable vel_analy in the musubi configuration.

The mesh created here is a single level with 32 elements in the inner cylinders diameter (and accordingly 32 elements between inner and outer cylinder).

To decide the convergence, the x axis in the right side of the cylinder is used. This line is defined as the track_line table and used in the abort criteria, a tracking over time and the spatial tracking for the final output. Once the average velocity magnitude over this line doesn't change more than the provided threshold in the abort section anymore or the tmax_phy time is reached, the simulation will stop.

The run.sh runs the complete simulation, from mesh generation to creating an image of the velocity profile over the track_line. You need to set the executable paths there accordingly and have gleaner for it to work.