How to calculate the mutual inductance of a coil pair

[millim]

Hi team,

I am completely new to Elmer and my first impression of the tool is impressive having all the great features of (combined) multiphysics solvers.

Before I dig deep into the huge configuration space of Elmer, I am asking the community if the modeling of the mutual inductance of a air coupled coil is feasible with Elmer. So I am about to use the magnetostatic solver for this problem, right?

My question is how I have to setup the boundary conditions, the coil port definitions, the extraction of the H-field, and how I can get the mutual inductance or mutual coupling value out of the simulator?

regards
millim

[millim]

Hello,

this time I have refined my problem. See the attached Zip file.

Regards
millim

[mzenker]

Hi,

I have never used the magnetistatic solver before, but the Models Manual and the tutorial about induction heating may give you more information and a starting point.

HTH,

Matthias

[raback]

Hi Millim

The first problem I see is that you intend to make just the mesh for the conductors. Also the air needs a mesh. See the nice work by "madstamm" for example. See

viewtopic.php?f=3&t=2110&p=6388&hilit=whitney#p6388

The mutual inductance may require a new integral for \Psi_ij. I don't immediately know the best method. The current I would compute with the "Calculate loads" + "boundary sum" method.

-Peter

[millim]

Hi Peter,

thx for the intermediate advices. Meshing the air is somewhat clear to be. But now I am facing a meshing problem of the boundary conditions for applying a constant potential at the coil terminals. First I want to identify a proper tool chain for solving problems including CAD, meshing and FEM. I have evaluated some open source tools and I think FreeCAD, netgen and Elmer could do the job best on Windows.

Now I am very confused with the different formats the tools are supporting and how the best way of transferring data between them should be. Maybe you can give some advice here, too. When I use the *.inp format, I only get two elements and no boundaries when using “elmergrid 5 2 file.inp”. And finally ElmerGUI does not show the mesh; even I think that “mesh.boundary” file is empty?

Attached I have a picture of the boundary condition in red color I want to define (displayed using netgen). How can I transport all 4 coil cross sections to Elmer mesh by using netgen export or ElmerGrid import?

thx

[raback]

Hi

If you're using netgen then why not export the mesh directly in Elmer format. It should be the most trouble free and should open ok in ElmerGUI as well.

-Peter

[millim]

Hi Peter,

sorry I have not mentioned that before. I thought you are aware of that this feature is not available on windows for netgen 4.4 I am using. With 4.9.13 I am able to create the Elmer meshes of both bodies directly with all the surfaces and boundaries. Peter, thx for pointing that out.

So the next step is to model the current density of the primary coil and the static magnetic field in air. Hopefully I can perform the same steps for the air body as mentioned before. On success, I will post some results.

Regards

[millim]

Hi Peter,

by trying to simplify my problem (only one coil generating a magnetic field), I always encounter that the simulation does not converge. I have combined the StatCurrentSolve and StatMagSolve to calculate the magnetic field inside the air cube generated by the coil loop current density without success. Calculation of the current density inside the coil with the surface boundaries set to a desired potential does work, but the field calculation fails. Despairingly, I also have set all remaining boundary conditions for the magnetic potential to zero, but same result. Attached you will find the project files. Probably, I have to stop here..?

[raback]

Hi

Quickly looking at your case there seems to be at least two problems:

1) The coil and the exterior mesh do not seem to conformal (the do not share the interface nodes)

2) You apply the StatMagSolver which, if I remember correctly, works in 3D only under certain assumptions. I would recommend using the Whitney solver (as in the example of madstamm) which fulfills the Coulomb gauge by construction.

-Peter

[millim]

Peter,

oh man, right! The bodies do not have conformal interfaces. I thought that the mesh generator takes care on that. Unfortunately not. So I have to start over again. Netgen does not seem to have a feature to resolve body-in-body problems to interfaces with conformal faces.
In general, this is a fundamental requirement for FEM. My question now, is there an easy way to create conformal interfaces with an open source mesh generator, or do I have to crate the air volume by Boolean difference of coil and air cube in the CAD tool first?

Regards