[Getdp] Non-linear magnetodynamics with a superconducting tape

Christophe Geuzaine cgeuzaine at ulg.ac.be
Wed Oct 28 10:42:26 CET 2015 

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

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