[Getdp] Non-linear magnetodynamics with a superconducting tape

Frederic Trillaud ftrillaudp at pumas.ii.unam.mx
Wed Oct 28 16:37:11 CET 2015 

Super, thanks a lot.

Best,

Frederic


-----Original Message-----
From: Christophe Geuzaine <cgeuzaine at ulg.ac.be>
To: Peter Kis <md2z34 at gmail.com>
Cc: Frederic Trillaud Pighi <ftrillaudp at pumas.iingen.unam.mx>, DILASSER
Guillaume <Guillaume.DILASSER at cea.fr>, getdp at geuz.org <getdp at geuz.org>
Subject: Re: [Getdp] Non-linear magnetodynamics with a superconducting
tape
Date: Wed, 28 Oct 2015 15:48:45 +0100

Guys,

I've updated the model on http://onelab.info/wiki/Superconducting_wire so that you can define rectangular "filaments". Choosing appropriate dimensions you could definitely validate against the simple tape example available on the HTS website.

Christophe


> On 28 Oct 2015, at 15:33, Peter Kis <md2z34 at gmail.com> wrote:
> 
> Hi there,
> 
> I've just put together something similar in 2D. The solution doesn't seem wrong at a first glance, but the Newton takes one iteration only, which is suspicious. So be careful with this.
> 
> Best Regards
> 
> Peter
> 
> 
> On Wed, Oct 28, 2015 at 3:11 PM, Frederic Trillaud Pighi <ftrillaudp at pumas.iingen.unam.mx> wrote:
> 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
> >
> >
> >
> >
> >
> > _______________________________________________
> >
> > getdp mailing list
> >
> > getdp at geuz.org
> >
> > http://www.geuz.org/mailman/listinfo/getdp
> >
> >
> 
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