[Getdp] Non-linear magnetodynamics with a superconducting tape

[Frederic Trillaud]

Guillaume,

J'ai implémenté le cas que tu viens de décrire. Je suis encore entrain
de résoudre les petits problèmes (détail du "Cohomology solver"). Comme
Je suis débordé en ce moment, je suis relativement lent. J’espère avoir
le code qui fonctionne la semaine qui vient.

Cordialement,

Frederic


-----Original Message-----
From: DILASSER Guillaume <Guillaume.DILASSER at cea.fr>
To: getdp at geuz.org <getdp at geuz.org>
Subject: [Getdp] Non-linear magnetodynamics with a superconducting tape
Date: Wed, 21 Oct 2015 14:14:07 +0000

Good evening,

 

I am writing this Email to hopefully get some advice on how to implement
in GetDP a non-linear material law corresponding to the behavior of a
HTS superconductor. I have recently started to use GetDP with the aim of
simulating superconducting electromagnets but for now I am still
learning how to use the software. I chose to work first on an example
available here (HTS modelling workgroup website, it is example 1 at the
top of the page) to be able to compare my results to those of the
community. The scenario implies a simple strand of superconductor with a
rectangular cross-section to which is applied an AC current, everything
is then surrounded by air. For the benchmark, the aim is mostly to
compute the AC losses in the material during the current cycle.

 

Since I have much to learn, I tackled the problem step by step by first
considering a linear case in which I have resistive material in place of
the superconductor. I enclose the files I have been working on for those
who want to have a look at them (sadly it is mostly written in French…).
The outline of what I tried is following : I considered the 2D case to
resolve the problem in the cross-section but did not implement yet the
use of symmetries. I wrote the A-Phi formulation with constant
parameters nu and sigma. The resolution of the magnetodynamic problem is
fairly trivial as everything is linear. I guess the solution shown in
the enclosed files is about to be correct yet I still have some
unanswered questions :

·        Is the way I implemented the shell-to-infinite-domain
transformation correct ? I had some error like “the Jacobian x is not in
the range [a,b]” which I did not understand when messing with the
VolSphShell Jacobian, is there a specific documentation on the topic ? 

·        When I try to drop the thickness of the tape down to about 1 µm
(the width of the tape is about 4 mm), Gmsh gives an error as “some
points are coincident”. I tried the solutions to prevent that, namely
decrease the size of the mesh elements in the conductor and/or increase
the mesh.RandomFactor but without success. What did I miss ?

·        I tried to compute the AC losses in the material in the
post-process but unfortunately I must have done something wrong as I
always find 0… Where does it come from ?

 

Those were the issues I still have with my first (resistive) scenario
but to switch now to the original example I need to add the E-J material
law for the superconductor. My plan is to begin with a simple non-linear
power law E = e0 * (|J|/jc)^N * (J/jc), e0 = 10-4 V/m, jc = 108 A/m², N
about 10. For the A-Phi formulation I have to implement a sigma(E) =
sigma(dA/dt + gradPhi) relation in the equations but what is precisely
to do remains unclear.

·        The helix.pro example gave me an idea of what I could do even
if it is not the same formulation. However, if I am unsure on how I can
linearize the expressions involving sigma. If I understood well, it is
forbidden to write a term such as [ DtDof[ sigma[Dof[{a}],{v}] *
Dof[{a}], {a} ].

·        Or, is this possible to use some of the Built-in functions like
IterativeLoop[] with non-linear term like the one above ?

I would really appreciate your advice on how I can (and should)
implement this material power-law behavior. I realize that A-Phi was
probably not the best formulation to work with as the sigma appears a
lot in the equation and is a function of two variables… 

 

Faithfully yours,

 

Guillaume DILASSER

Doctorant SACM / LEAS

CEA - Centre de Saclay - Bât.123 - PC 319c

91191 Gif sur Yvette Cedex - France -

 

guillaume.dilasser at cea.fr

 


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