Magnus effect, a comprehensive CFD Simulation tutorial.





Any object could exhibit the weird effect when traveling at a certain speed in a spin. It is the result of a differential pressure on the spinning object creating a force at a certain angle with the velocity vector.

Magnus effect due to a travelling ball with a spin
Magnus effect due to a traveling ball with a spin

The differential pressure is created due to the motion of air with the spinning direction of the ball on 1 side and against it on the other side.




Geometry

I decided to go for a 2D simulation, the geometry comprised of a 33.3 x 11.3 m rectangle. The domain includes a small perforated box, the perforation is made by a circle of 0.3m in radius. 

Geometry used in the Magnus effect CFD simulation
Geometry used in the Magnus effect CFD simulation

You can download the geometry by clicking here: 2D Model



Mesh

To avoid negative volume cells when enabling the dynamic mesh and 6 DOF method, I applied a tetrahedral mesh all over the fluid domain. In total, the mesh has  83,654 elements. I added a face sizing for the small box with an inflation layer on the circle wall.

Mesh settings
Mesh settings
Face Sizing
Face Sizing

Setup

The CFD simulation is transient and 2 dimensional, therefore, I haven’t added any body forces such as gravitational acceleration. Furthermore, I used the turbulent viscous K-omega SST model due its stability and superiority over the normal K-omega and K-epsilon models.

I selected incompressible air for the fluid domain. Additionally, I created 2 zones for the domain, one internal containing the box and the other external for the rectangular domain. The boundaries comprised the following list:

-The internal domain (internal and external)

-The wall of the circle

-The outlet
As part of the simulation, I interpreted a UDF file which contained information about the mass of the circle and it Mass moment of inertia.
You can download the UDF file here: File




Don’t forget to change the extension of the UDF file from “.txt” to “.C”.
For the next step, I set up the dynamic mesh using the smoothing method and the remeshing:

Dynamic mesh
Dynamic mesh

Once you tick the Six DOF option a new window appears:

  1. Select the circle wall (football) as a rigid body and make sure that the UDF file is attached  to “Six DOF UDF/Properties”
  2. Select the internal domain (inner) as a rigid body and make sure to tick “Passive” under Six DOF panel.



6 DOF settings
6 DOF settings

Initialize your simulation and start with a small time step of 0.0001 s and then run it for as long as you wish!
Magnus effect animation video


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