Magneto-Thermal Thin Shell Approximation for Open-Source Transient Analysis of Superconducting Magnets
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High-temperature superconductors (HTS) for particle accelerator magnets have the potential to exceed the magnetic field limits of low-temperature superconductors. To understand the transient behavior of HTS coils, numerical tools such as the finite element (FE) method are crucial. The simulation of transients in superconducting magnets and in particular quench behavior are intrinsically multi-physical problems involving coupled electromagnetism, thermodynamics and eventually solid mechanics. In particular, no-insulation (NI) pancake coils, i.e., coils wound without turn-to-turn (T2T) electrical insulation, are interesting due to their increased electrical and thermal stability. However, the simulation of the T2T contact region of NI coils with thin volumes as part of a three-dimensional FE analysis often results in unfavorable meshes, either because of a high number of unknowns or mesh elements with a high aspect ratio. We propose circumventing these issues by simulating the T2T thermal and electrical contact region as a surface using a thin shell approximation to solve a transient, coupled magneto-thermal problem. The approximation is based on a one-dimensional spatial discretization of the magnetic field, and temperature across the thickness of the thin shell using Lagrange basis functions. The approach does not require a volumetric mesh representation of the T2T contact region, thus alleviating the above-mentioned meshing and solving related problems. In general, the proposed method allows for multi-layered thin regions and is customized in this work to treat NI coils. A comparison of accuracy, efficiency, and robustness with reference solutions with volumetrically meshed T2T region is presented. The work has been carried out using solely open-source software, namely GetDP as the FE framework and Gmsh for meshing.
