[Getdp] Non-linear magnetodynamics with a superconducting tape
Frederic Trillaud Pighi
ftrillaudp at pumas.iingen.unam.mx
Wed Oct 28 15:11:59 CET 2015
Dear Guillaume and Peter,
The model is 3D because I add a recurring error in the 2D case that I
could not fix to answer quick Guillaume's problem. As Christophe
mentioned, it is not necessary to force the boundary condition in this
case. It should not make much difference as far as I understood (to be
checked). If you impose a Dirichlet condition to zero, I would say ou
need the shell transformation since in reality the magnetic field should
be of the form I/(2*pi*R) at the boundary.
The code I sent turns but there is a problem of convergence to be
solved. I tried the built-in solver and ended up copying Christophe's
model.
For Guillaume:
>why is it not necessary to have a cut through the surrounding air
region?
If you check the model that I sent you, you will see that the air is cut
using the cohomoloy solver (there are two regions: air and
superconductor, no more). In the visibility option you will see
something like "Line" with a name starting with H..., it will show you
the cut (see attached *.png).
Best,
Frederic
On Wed, 2015-10-28 at 12:42 +0000, DILASSER Guillaume wrote:
> 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) ? 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). 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
>
>
>
>
>
>
>
> -----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> 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> 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
>
> > >
>
> > >
>
> > >
>
> > >
>
> > > _______________________________________________
>
> > > getdp mailing list
>
> > > getdp at geuz.org
>
> > > http://www.geuz.org/mailman/listinfo/getdp
>
> >
>
> >
>
> > _______________________________________________
>
> > getdp mailing list
>
> > getdp at geuz.org
>
> > http://www.geuz.org/mailman/listinfo/getdp
>
> >
>
> > _______________________________________________
>
> > getdp mailing list
>
> > getdp at geuz.org
>
> > http://www.geuz.org/mailman/listinfo/getdp
>
>
>
> --
>
> Prof. Christophe Geuzaine
>
> University of Liege, Electrical Engineering and Computer
> Sciencehttp://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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>
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>
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>
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