Magneto-Thermal Thin Shell Approximation for 3D Finite Element Analysis of No-Insulation Coils

Finite elements; H-φ formulation; magneto-thermal analysis; no-insulation coil; thin shell approximation; <inline-formula xmlns:ali="; > <tex-math notation="LaTeX">$\vec{H}$</tex-math> </inline-formula> −ϕ formulation; Coil; Conductivity; Finite element; Finite element analyse; High-temperature superconductor; Magneto-thermal analysis; No insulations; No-insulation coil; Perpendicular magnetic anisotropy; Thin shell approximation; Thin shells; Xmlns:mml="; Xmlns:xlink="; Xmlns:xsi="; Electronic, Optical and Magnetic Materials; Condensed Matter Physics; Electrical and Electronic Engineering; Physics - Accelerator Physics; Physics - Superconductivity; Computer Science - Computational Engineering; Finance; and Science

Abstract :

[en] For finite element (FE) analysis of no-insulation (NI) high-temperature superconducting (HTS) pancake coils, the high aspect ratio of the turn-to-turn contact layer (T2TCL) leads to meshing difficulties which result in either poor quality mesh elements resulting in a decrease of the solution accuracy or a high number of degrees of freedom. We proposed to mitigate this issue by collapsing the T2TCL volume into a surface and using a so-called thin shell approximation (TSA). Previously, two TSA have been introduced, one to solve the heat equation and the other for an H-φ magnetodynamic formulation. In this work, we propose to combine the magnetodynamic and thermal TSA to create a coupled magneto-thermal TSA for three-dimensional FE analysis. Particular attention is paid to the detailed derivation of the coupling terms. In the context of NI HTS pancake coils, the TSA represents the electric and thermal contact resistance of the T2TCL. For the HTS coated conductor (CC) itself, an anisotropic homogenization is used which represents its multi-layered structure. In axial and azimuthal direction, it resolves the current sharing between the HTS and other layers of the CC. The coupled TSA formulation is verified against a reference model with volumetric T2TCL. The coupled TSA is shown to significantly reduce the solution time as well as the manual effort required for high-quality meshes of the T2TCL. The implementation is open-source and a reference implementation is made publicly available.

Disciplines :

Electrical & electronics engineering

Author, co-author :

Schnaubelt, Erik ; CERN, Meyrin, Switzerland ; Technical University of Darmstadt, Darmstadt, Germany

Atalay, Sina ; CERN, Meyrin, Switzerland ; Boǧaziçi University, Istanbul, Turkey

Wozniak, Mariusz ; CERN, Meyrin, Switzerland

Dular, Julien ; CERN, Meyrin, Switzerland

Geuzaine, Christophe ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Applied and Computational Electromagnetics (ACE)

Vanderheyden, Benoît ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Electronique et microsystèmes

Marsic, Nicolas ; Technical University of Darmstadt, Darmstadt, Germany

Verweij, Arjan ; CERN, Meyrin, Switzerland

Schops, Sebastian ; Technical University of Darmstadt, Darmstadt, Germany

Language :

English

Title :

Magneto-Thermal Thin Shell Approximation for 3D Finite Element Analysis of No-Insulation Coils

Publication date :

May 2024

Journal title :

IEEE Transactions on Applied Superconductivity

ISSN :

1051-8223

Publisher :

Institute of Electrical and Electronics Engineers Inc.

Volume :

Issue :

Pages :

1 - 6

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

http://xplorestaging.ieee.org/ielx7/77/10339679/10349801.pdf?arnumber=10349801

Funders :

German Federal Ministry of Education and Research
TU Darmstadt - Technical University of Darmstadt

Funding text :

The work of Erik Schnaubelt was supported in part by the Wolfgang Gentner Programme of the German Federal Ministry of Education and Research under Grant 13E18CHA and in part by the Graduate School Computational Engineering within the Centre for Computational Engineering at the Technical University of Darmstadt.

Commentary :

Presented at EUCAS 2023, Bologna, Italy. This work has been submitted to the IEEE for possible publication

Available on ORBi :

since 12 June 2025

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