2D induction cold crucible with impedance boundary conditions

[Roland]

Hi Peter,
As discussed I checked the IBC compared to the No_IBC cold crucible models in cylindrical configuration and it works perfectly as showed in the 2 attached plots. Great progress!
But at this state, as you can see it on the former plots, there is (almost) no magnetic field in the inner area of the cold crucible (say CC) since the current model (either in IBC or without IBC) does not simulate the slits of the sectorized crucible. This means that at this state there is only a current density in the outer (mainly vertical) CC surface, which makes that this non sectorized CC is like a kind of EM shielding with no magnetic field inside it.
When the CC is sectorized (with slits) then the current density (either in IBC or without IBC) loops around each CC sector, which makes that now there will be a current density not only on the outer CC surface but also on the inner CC surface. This makes that there will then appear a non zero magnetic field inside the CC, making it possible to heat (melt, levitate...) a charge set inside it. This is showed in the here attached Comsol model plot.
As these slits don't exist in 2D cylindrical configuration the trick is to add to the current Maxwell equations an additionnal equation (and hence an additionnal variable which is a phi component votage V acting a bit like a Lagrange multiplier) which is an integral constraint which forces the integral of the current density (or surface current density in the IBC model) in the cross section of the CC to be equal to zero.
Do you think that this integral constraint relation (both in the IBC model and also in the No_IBC model) could be added to the existing model? I am very excited to get your opinion about that since, with this add on, it will be then be possible to completely simulate a real cold crucible in 2D, and then to add finaly the crystal growth modeling!
Roland

[raback]

Hi Roland,

I added a new type of linear constraint to the library part of the code. This is applicable to Robin type of BCs where we want to constrain to total flux. For Neumann kind of BCs controlling of total flux is easy since we know what we are putting in. For Robin type of conditions it is more difficult since the flux is part of the solution.

This is still an early version but seems to produce something sensible. The keywords may change still. You should add the following keywords to the IBC model.

Code: Select all

Solver 1  
  Name = "MgdynHarmonic"
  Calculate Loads = True
  Apply Integral BCs = True
  ...

Boundary Condition 2  
   Name = "IBC"
   Flux Integral BC = Logical True
   ...
 

Hope it works!

-Peter

[raback]

Hi,

Attached is a figure of the nodal heating. Many fields look quite similar to the eye. The imaginary part of the vector potential and this though are clearly different. Here you see the heating with just the IBC condition on the left and with the zero-current constraint on the right.

-Peter

[Roland]

Hi Peter,
Thanks a lot for these exciting progresses!
I will check this after installing the latest release and keep you informed.
Thanks again
Roland

[Roland]

Hi Peter,
As discussed I just tried the CC model with your added Integral BC command lines and after having installed the 12_01_2023 latest Elmer version. But there seems to be no difference with before applying the Integral BC command lines, since (see the attached plot) the magnetic field does not go in the inner region (near the symetry axis) of the cold crucible.
I attach also the GUI project (in which I added your command lines by hand editing in the solver 1 since it was not possible to add them in the GUI for the moment).
Perhaps I made a mistake somewhere... Thanks a lot if you could take a look.
We keep us informed.
Roland

[raback]

Hi Roland,

I made some fixes and committed them just. Now at least the net current over the boundary becomes zero.

The main issue was that the constraint matrix related to the lagrange multipliers needed a complex conjugate when doing a transpose. It is related to the inner logic how things are done, so it was not easy to locate.

-Peter

[Roland]

Hi Peter,
Ok, thanks for these good news.
I will reinstall the updated release and see what the model gives with your changes.
I keep you informed.
Thanks again.
Roland

[Roland]

Hi Peter,
I just tried the CC model (with IBC and Integral BC) after installing your latest release, but there is still nothing changed, meaning there is still no magnetic field going in the inner CC region, as you can see on the attached plot.
Thanks if you can take a look and we keep us informed.
Roland

[raback]

Hi Roland,

My figure looks different. Maybe the update was not there early enough. This is from last evening.

IBC-compare.PNG

(342.57 KiB) Not downloaded yet

-Peter

[Roland]

Hi Peter,
I will check this after reinstalling the last update and keep you informed.
Roland