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Superconducting wire

Posted Jun 5, 2012, 8:32 a.m. EDT Low-Frequency Electromagnetics, Studies & Solvers Version 4.2a 7 Replies

Shoval Zoran
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Hi,
I was trying to model a tape of superconducting material; its conductivity is dependent on the current going through it.
This creates circular variable dependency, and thus cannot be modeled as easily as I'd like. In the knowledge database there is a model that sort-of deals with that problem:
www.comsol.com/showroom/gallery/689/
Model 689.

In this model, the PDE is solved for the H-field instead of going around with the conductivity.
I have tried to create this model in three dimensions, and I think I succeeded in copying; but I have a few questions about that, and a problem I will add later.

my questions:
1.
How did the equation described in the .PDF file related to the file become in the form of the General Form PDE? where did the Curl go and why is there a div(GAMMA) there?

2.
why is GAMMA defined as it is? if I change one of the values there so that they're both positive/negative, the solution doesn't converge. however if I switch both signs, the solution doesn't change. and in 3D, the third part of gamma doesn't seem to matter at all; if it is 0,0,Ez_sc it's the same as 0,0,234234234.

And now the problem:
I want to have this model eventually coupled with another physics - since I want to add a time dependent magnetic field on the tape. How will I be able to tell the program to do that? to treat my domain with properties that are defined via the PDEs?


I know I'm asking a lot,
Thank you very much for your time,

Shoval
7 Replies Last Post Jun 11, 2012, 10:50 a.m. EDT
Shoval Zoran
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Posted: 1 decade ago Jun 5, 2012, 10:47 a.m. EDT
I attached a model file of the 3D file I created for the case, for you to see. it solved very nicely, in 22 minutes it created a 9.9MB file.
I attached a model file of the 3D file I created for the case, for you to see. it solved very nicely, in 22 minutes it created a 9.9MB file.
Jens Krause
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Posted: 1 decade ago Jun 6, 2012, 3:46 a.m. EDT
Hi Shoval,


do you know Francesco Grilli's (now at KIT in Germany) work? He has published a lot on this.


The Gamma in Comol's implementation correspondes Faraday's equation

curl E = -dB/dt

and it is correct to have the E once with plus and once with minus sign.

div Gamma =

(d/dx) (0 E) (- dE/dy) (0)
(d/dy) (-E 0) = (dE/dx) = curl (0)
(E)


I hope my ASCI art is readable to you.


I cannot check you model because I have no license for CAD and cannot check your equations.

Can you apply the external magnetic fields via boundary conditions.


Regards,

Jens
Hi Shoval, do you know Francesco Grilli's (now at KIT in Germany) work? He has published a lot on this. The Gamma in Comol's implementation correspondes Faraday's equation curl E = -dB/dt and it is correct to have the E once with plus and once with minus sign. div Gamma = (d/dx) (0 E) (- dE/dy) (0) (d/dy) (-E 0) = (dE/dx) = curl (0) (E) I hope my ASCI art is readable to you. I cannot check you model because I have no license for CAD and cannot check your equations. Can you apply the external magnetic fields via boundary conditions. Regards, Jens
Jens Krause
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Posted: 1 decade ago Jun 6, 2012, 3:50 a.m. EDT
my equation are definitly not readable

2nd try

div(gamma)=


(d/dx) (0 E)
(d/dy) (-E 0)

equals

(- dE/dy)
(dE/dx)

which is the curl of a 3-D vector field with only z-coordinate:

curl(0,0,E)


Jens
my equation are definitly not readable 2nd try div(gamma)= (d/dx) (0 E) (d/dy) (-E 0) equals (- dE/dy) (dE/dx) which is the curl of a 3-D vector field with only z-coordinate: curl(0,0,E) Jens
Shoval Zoran
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Posted: 1 decade ago Jun 6, 2012, 8:20 a.m. EDT
Hi Jens,
Thank you very much, you answered completely both of my questions about the Gamma, curl and div.

About the magnetic field - can you elaborate a tad more?
Do you mean that I add magnetic field as BC via the PDE interface? or should I couple it with the MF and only add a magnetic field node over there?

Thank you for your time again,
Shoval
Hi Jens, Thank you very much, you answered completely both of my questions about the Gamma, curl and div. About the magnetic field - can you elaborate a tad more? Do you mean that I add magnetic field as BC via the PDE interface? or should I couple it with the MF and only add a magnetic field node over there? Thank you for your time again, Shoval
Shoval Zoran
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Posted: 1 decade ago Jun 6, 2012, 8:46 a.m. EDT
Hi again,
I have tried to give the magnetic field as a BC inside the PDE interface - I put it in the Dirichlet BC, in addition to what was there, as in:

instead of

H0phi*ephix

I used

H0phi*ephix - (5/(4*pi) ) * 1e5 * cos(omega*t[1/s])

,
The model responded with
"Failed to find consistent initial values.
Last time step is not converged."

It took it maybe 1 minute to get to the error, while running the model without that would be around 10 minutes.
Hi again, I have tried to give the magnetic field as a BC inside the PDE interface - I put it in the Dirichlet BC, in addition to what was there, as in: instead of H0phi*ephix I used H0phi*ephix - (5/(4*pi) ) * 1e5 * cos(omega*t[1/s]) , The model responded with "Failed to find consistent initial values. Last time step is not converged." It took it maybe 1 minute to get to the error, while running the model without that would be around 10 minutes.
Jens Krause
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Posted: 1 decade ago Jun 11, 2012, 5:06 a.m. EDT
Hi Shoval,

try sine instead of cosine.

Explanation, I gues you have Hx=0 and Hy=0 as initial values. Then the
boundary condition must be consitent with the initial state and cosine give
one at zero and sin zero.

Regards

Jens
Hi Shoval, try sine instead of cosine. Explanation, I gues you have Hx=0 and Hy=0 as initial values. Then the boundary condition must be consitent with the initial state and cosine give one at zero and sin zero. Regards Jens
Shoval Zoran
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Posted: 1 decade ago Jun 11, 2012, 10:50 a.m. EDT
Dear Jens,

your advice have worked wonderfully once again, I thank you very much!!

all those tiny little mistakes, spotting them takes some practice indeed.

My model solved nicely and quickly.

Shoval.
Dear Jens, your advice have worked wonderfully once again, I thank you very much!! all those tiny little mistakes, spotting them takes some practice indeed. My model solved nicely and quickly. Shoval.

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