Cylinders model after magnetization.

Life-HTSLiège university Finite Element models for High-Temperature Superconductors

This project contains template and model files for modeling systems containing high-temperature superconductors (HTS) with GetDP as a finite element solver and Gmsh as mesh generator.


Files are available here

Several finite element formulations are implemented together with various linearization methods and iterative procedures. Simple models are proposed for practical applications (bulk and tapes HTS, coupling with ferromagnets...)

These models are developed at the University of Liège.

Features

  • Power law model for HTS.
  • Simple anhysteretic model for soft ferromagnetic materials (FM).
  • Two dual formulations for nonlinear equations in 1D, 2D and 3D. h-conform (h or h-phi) and b-conform (a or a-v).
  • Coupled formulations for nonlinear systems with HTS and FM (2D-3D; h-a, h-phi-a, h-b, a-j).
  • A t-a-formulation with global variables inside the formulation (for voltage coupling for example) (2D-3D).

Models

  • Cylinder: Bulk cylindrical HTS subjected to an external field parallel to its axis (2D axisymmetric). In particular, the magnetization curve and the current density distribution are interesting outputs.
  • Tape: Thin HTS tape with imposed current intensity (2D). Simple model for AC loss calculation. This model also features the t-a-formulation.
  • Cube: Bulk cube HTS subjected to an external field along a principal direction (3D). This model illustrates the benefit of using the b-conform formulation with large time steps.
  • Cylinders: Stacked bulk cylinders: HTS with ferromagnetic materials on top of it, subjected to an external field parallel to their symmetry axis (2D axisymmetric). This model is a simple example for the coupled formulation.
  • HTS-Motor: A simple HTS motor (2D), with torque computation and rotating mesh.
  • Magnet: HTS bulk magnet (3D), bulk magnetization with an inducting coil (imposed current via a generalized source field in h-formulation). The bulk is on top of a FM. Handling both HTS and FM is most efficiently done with a coupled h-a-formulation (with scalar potential in air "h-phi"). See reference below.

Magnet model. Left: geometry. Right: current density at two time instants (up: during first flux penetration, down: during pulse relaxation) (left: x-component of the current density, right: current density in three planes).

Quick start

  1. Download the precompiled ONELAB software bundle for Windows, Linux or macOS.
  2. Launch the Gmsh app .
  3. Open cylinder/cylinder.pro.
  4. Press Run.

References and tutorials

  • Video tutorials on technical details of formulations during the GetDP workshop at CERN, April 2021 (part 1, part 2, slides). See also the podcasts of the entire event here.
  • Life-HTS presentation at the HTS 2020 motor school, September 2020.
  • Life-HTS presentation at the HTS 2020 workshop, June 2021.
  • Finite Element Formulations for Systems with High-Temperature Superconductors, J. Dular, C. Geuzaine and B. Vanderheyden, IEEE Transactions on Applied Superconductivity, vol. 30, no. 3, pp. 1–13, 2019. DOI: 10.1109/TASC.2019.2935429.
    Comparison of h-conform and b-conform formulations for HTS, with discussion of the large time step approach for good fast estimates, and presentation of a coupled h-a-formulation for systems with both HTS and FM (preprint).
  • On the Stability of Mixed Finite-Element Formulations for High-Temperature Superconductors, J. Dular, M. Harutyunyan, L. Bortot, S. Schöps, B. Vanderheyden, and C. Geuzaine, IEEE Transactions on Applied Superconductivity, vol. 31, no. 6, pp. 1-12, 2021. DOI: 10.1109/TASC.2021.3098724.
    Derivation of h-a-formulation and t-a-formulation, with analysis of their numerical stability when considered as perturbed saddle point problems (preprint). Slides from HTS Modeling 2020.
  • What Formulation Should One Choose for Modeling a 3D HTS Motor Pole with Ferromagnetic Materials? J. Dular, K. Berger, C. Geuzaine and B. Vanderheyden, accepted for publication in IEEE Transactions on Magnetics, 2022. DOI: 10.1109/TMAG.2022.3167839.
    Comparison of eight different formulations for a 3D problem (magnet) with both HTS and FM (preprint).

Information

Models are developed by Julien Dular, Christophe Geuzaine and Benoît Vanderheyden in Montefiore at the University of Liège, Belgium. Research is funded by the F.R.S.-FNRS.

If you have any question, suggestion or if you find any bug, you are welcome to contact us directly using this e-mail address julien.dular at uliege.be.