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

Abstract

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 $\vec{H}-φ$ 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.

Figures (8)

• Figure 1: Computational domain $\Omega$ of the pancake coil with exterior boundary $\partial \Omega = \Gamma$. It consists of an insulating domain $\Omega_\text{i}$ and a conducting domain $\Omega_\text{c}$ which is divided into the bare CC $\Omega_\text{c,b}$, the T2TCL $\Omega_\text{c,cl}$ and current leads. The cross-section view in (b) is taken at the red dotted line shown in (a).
• Figure 2: One turn of the HTS pancake coil (top view): for the TSA approach, the T2TCL is represented by a virtual domain $\hat{\Omega}_\text{c,cl}$ in which an internal FE discretization is used to solve the magneto-thermal problem.
• Figure 3: HTS pancake coil (top view): for the TSA approach, the T2TCL volume $\Omega_\text{c,cl}$ (left) is collapsed into the T2TCL surface $\Gamma_\text{c,cl}$ (right).
• Figure 4: Local defect and zoom on the mesh of the volumetric T2TCL.
• Figure 5: The source current $I_\text{src}$ and the central axial magn. flux density $B_{z, \text{c}}$.