[Getdp] Non-linear magnetodynamics with a superconducting tape

Wed Oct 21 16:14:07 CEST 2015

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<http://www.htsmodelling.com/?page_id=2> (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<http://onelab.info/wiki/Superconducting_wire> 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<mailto:guillaume.dilasser at cea.fr>

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