EM_levitation

Numerical methods and mathematical models of Elmer
Roland
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EM_levitation

Post by Roland »

Hi,
I would like to set up a transient Electromagnetic levitation model (in 2D Cartesian coordinates in a first step), in which an initial circular liquid metal charge is levitated and deforms thanks to a surrounding high frequency inductor producing the Electromagnetic Lorentz levitation volume force in the liquid charge.
Here attached is the model (half model thanks to the symmetry with respect to the y axis) which has been written by Peter after first discussions with him (many thaks again, Peter, for your efforts!).
The first results are promising but after a few timesteps the shape of the charge which goes upward becomes unregular especially on the top freesurface.
In order to make it easier for the solver's convergence I increased the charge viscosity to a very big value and also neglected the gravity force in a first step.
The model couples the time harmonic electromagnetic solver, the Navier Stokes solver, the mesh update solver for the deformed mesh and the NormalSolver on the free surface on which the ALE (Arbitrarian-Langrangian Eulerian) boundary condition forces the nromal mesh nodes displacement to be equal to the normal Navier Stokes displacement obtained (in the NormalSolver after a modification done by Peter) by a time integration of the normal Navier Stokes velocity.
Here attached is also a result showing the charge at t=0s (initial position) and a result showing the charge at t=2s for which the shape becomes unregular and uncorrect (the real shape should be like a reversed pear in the middle of the inductor after a few vertical oscillations
half_EM_levitation_model.zip
EM_levitation model (no GUI model)
(119.38 KiB) Downloaded 119 times
EM_levitation_at_t_0s.JPG
result at t=0s
(124.84 KiB) Not downloaded yet
EM_levitation_at__t_2s.JPG
result at t=2s
(123.89 KiB) Not downloaded yet
,especially when the viscosity is lowered to a more realistic value).
It would be very kind if somebody could take a look at this model and bring me some help about how to fix this and get a more nice solution!
Thanks in advance!
Best regards
Roland
Rich_B
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Re: EM_levitation

Post by Rich_B »

Hello Roland,

Have you tried running with cylindrical coords, using this keyword command?
Coordinate System = Cylindrical
Using both Axi Symmetric and Cylindric Symmetric set the model dimension to 2, while Cylindrical sets the model dimension to 3. Refer to ModelDescription.F90 under elmerfem/src.

Rich.
raback
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Re: EM_levitation

Post by raback »

Hi

Cylindrical would add a rotational velocity component. Without any rotational force. As there is none in this case I think axissymm. is ok.

The most suspicious step here is the nodal forces applied to n-s. The individual modules have been long used. This coupling not so much.

-Peter
kevinarden
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Re: EM_levitation

Post by kevinarden »

It appears that the elements become highly distorted and causes convergence issues. I attempted several different mesh refinements, more elements, quads, quadratic elements. However the result was the same, high element distortion. I then modified the problem by modeling the liquid metal as a solid mechanical body and used the elastic solver. I modeled the metal with a very small modulus of elasticity as a molten metal would have. The results are much improved.

Models and animations are here

https://github.com/mrkearden/levitation
raback
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Re: EM_levitation

Post by raback »

Hi Kevin,

Looks indeed more cohesive!

A good critical tests could be to solve the problem in transient having just gravity there. Then the sphere should drop as h=-gt^2/2.

For N-S this is:

Code: Select all

  Flow Bodyforce 2 = $-9.81*rho
And for Stress Solver

Code: Select all

  Stress Bodyforce 2 = $-9.81*rho
where $rho is the density.

For StressSolver this has certainly been checked but for FlowSolver there could be something funny as there are no BCs. Will the two fall alike?

I guess the test case needs n-s because the magnetic force causes some internal convection to the molten metal.

The free surface (BC section) is missing the

Code: Select all

  Surface Tension Coefficient = Real 
that could settle down the surface a little for n-s. I don't know what the value should be though...

-Peter
kevinarden
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Re: EM_levitation

Post by kevinarden »

That is a good test suggestion I will look into that.
kevinarden
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Re: EM_levitation

Post by kevinarden »

The sphere as modeled with stress solver drops according to h=-gt^2/2. Calculated value is 0.86
drop.png
(214.63 KiB) Not downloaded yet
raback
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Re: EM_levitation

Post by raback »

Hi

Great! Did you check with FlowSolver? This could be where the problem lies.

-Peter
laurent
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Re: EM_levitation

Post by laurent »

Hi again,
As I (Roland) can no more access my own account since a few days(Again Peter, can you do something so that I can recover my account?) I use the Elmer_forum account of my colleague Laurent...
At first thank you very much for your latest efforts, Kevin and Peter! As you say, Peter, concerning the solid levitation model of Kevin, when levitationg a liquid, there are electromagnetic stirring vortices in the liquid which probably make the things more difficult for the solver's convergence. And you have also to add the ALE relation (which I mentionned in my former posts) as the BC condition for the MeshUpdate solver on the liquid Free surface(which requires the NormalSolver).
I currently try do do all this in a "slohing_tank" model directly inspired from the "FreeSurface_2d_sloshing" example in the Elmer repository (thank you Kevin for this reference!) by adding a surrouding vertical inductor producing the EM forces in the liquid. I think it could be interesting to set up in a first step this model (before the EM_levitation model which requires the NormalSolver recently modified by you, Peter, and is more complex since it must levitate a liquid without any contact with walls...) since in this case the liquid is in a box with side and bottom walls and this allows to use the FreeSurfaceSolver which is available in the GUI. Up to now I have not succeeded in the setting up of this model which couples several physics (Electromagnetics, Navier-Stokes, MeshUpdate Solver and FreeSurface Solver). It would be very kind of you (Kevin, Peter) if you could give me some help about this model which I would like to set up before going back to the EM_levitation model. Tell me if you agree and then I can post the model.
We keep us informed
Best regards and thank you again for your efforts!
Roland
kevinarden
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Re: EM_levitation

Post by kevinarden »

The problem I have with checking flowsolver for the drop solution is that i do not know how to track displacement, displacement is not variable in flowslover.
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