[Getdp] Non-linear magnetodynamics with a superconducting tape

Wed Oct 28 13:42:25 CET 2015

Good Afternoon,

I had the same reaction as Peter regarding the fact that Frédéric's model is in 3D and the apparent lack of boundary conditions. Yet I also have another question in mind : why is it not necessary to have a cut through the surrounding air region ? It is not simply connected if I am not mistaken. Is it because the basis function used in the air region are BF_GradNode and not BF_Node (I don't think so, otherwise I don't understand this example<http://www.geuz.org/getdp/doc/texinfo/getdp.html#Coupled-spaces>) ? Or is it because the cohomology solver does the same job ?

Anyway, I reworked a lot what I previously sent to the mailing list to use the same H-phi formulation as Christophe and I enclose the latest version of my files with this email. It doesn’t work right know and worse it makes GetDP crash (“Windows has encountered a problem and must close”). The errors takes place during the processing, while executing Generate[System] at the first time step in a TimeLoopTheta[]. It seems that the program can’t generate a ‘_BF_Entity_13’ (GroupOfNodesOf) which is associated with the condition linked to the transport current through the tape. Some information on my hardware that may be relevant : I run GetDP on a Dell Workstation with Intel Xeon E5-2650 v2, 128 Go RAM and a Window 8.1 OS.

Finally, about the usual geometry for HTS ReBCO tapes :

·         The cross section is rectangular

·         Width is usually 4, 6 or 12 mm, it is possible to find 2 mm- or 8 mm-width tape but they are very rare

·         The thickness is around 100 µm and decomposes as follows : first a substrate (Hastelloy / Stainless Steel) of about 60 µm. For a fine study of the tape it would be useful to take the magnetization of the substrate into account (the second benchmark on this page<http://www.htsmodelling.com/?page_id=2>). On top of the substrate are about 1 µm of buffer layers that are very resistive and about 1 µm of ReBCO superconductor. Finally the whole structure is covered with electroplated copper, which adds something like 20 µm on the top, bottom and each sides.

Hoping this may be useful,

Sincerely 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>

-----Message d'origine-----
De : getdp [mailto:getdp-bounces at ace20.montefiore.ulg.ac.be] De la part de Christophe Geuzaine
Envoyé : mercredi 28 octobre 2015 10:42
À : Peter Kis <md2z34 at gmail.com>
Cc : Frederic Trillaud Pighi <ftrillaudp at pumas.iingen.unam.mx>; getdp at geuz.org
Objet : Re: [Getdp] Non-linear magnetodynamics with a superconducting tape

> On 28 Oct 2015, at 08:59, Peter Kis <md2z34 at gmail.com<mailto:md2z34 at gmail.com>> wrote:

>

> Hi,

>

> I checked out Frederic's model and can't understand why it is in 3D. Since it is a straight conductor, it should be modeled in 2D.

> In fact my question is related to this issue. Is this Form1 function

> space suitable for a 2D model? (I think Form1P isn't suitable because

> H is in-plane vector, so it should be Form1.)

I've updated the example on the wiki to also perform 2D calculations: give it a try and let me know. You will see that the formulation does not need to be changed at all - only the geometry.

@Frederic & Peter: do you have "canonical" geometries for superconducting tapes? We could either create a new parametric geometry for those, or maybe just extend "helix.geo" to handle e.g. rectangular (instead of circular) cross-sections.

> Moreover I don't see any boundary condition on the outermost surfaces, where the magnetic field should be set to zero. It is also missing form Christoph's Helix model too. Apparently it works, but why?

>

The "helix" model imposes (weakly) a zero normal magnetic flux density on the boundary of the air box; I think this is more appropriate than imposing (strongly) that the magnetic field vanishes on the boundary. To make it even better we could add a shell transformation to infinity.

Cheers,

Christophe

> Sorry for asking a lot.

>

> Best Regards

>

> Peter

>

>

> On Sun, Oct 25, 2015 at 12:48 AM, Frederic Trillaud Pighi <ftrillaudp at pumas.iingen.unam.mx<mailto:ftrillaudp at pumas.iingen.unam.mx>> wrote:

> Dear Guillaume,

>

> I have completed a run of the code I sent you (I should have checked

> it before sending it!!). Even though it runs, It does not seem to work

> correctly. Indeed, it does not seem to converge. I will look through

> it in my spare time.

>

> Best,

>

> Frederic

>

>

> On Wed, 2015-10-21 at 14:14 +0000, DILASSER Guillaume wrote:

> > 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<mailto:guillaume.dilasser at cea.fr>

> >

> >

> >

> >

> > _______________________________________________

> > getdp mailing list

> > getdp at geuz.org<mailto:getdp at geuz.org>

> > http://www.geuz.org/mailman/listinfo/getdp

>

>

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>

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--

Prof. Christophe Geuzaine

University of Liege, Electrical Engineering and Computer Science http://www.montefiore.ulg.ac.be/~geuzaine

Tetrahedron V, July 4-5 2016: http://tetrahedron.montefiore.ulg.ac.be

Free software: http://gmsh.info | http://getdp.info | http://onelab.info

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