Thermal thin shell approximation towards finite element quench simulation

Abstract

Superconducting electromagnets commonly exhibit thin layers with high aspect ratio such as insulation layers or turn-to-turn contacts. A finite element analysis of these devices can lead to unfavorable meshes in these thin layers, either because of a high number of degrees of freedom or mesh elements of poor quality which decrease the accuracy of the simulation results. To mitigate these issues when conducting a thermal finite element analysis solving the heat equation, this work proposes to collapse thin volume layers into surfaces by using a thermal thin shell approximation. The proposed method uses one-dimensional Lagrange elements across the thickness of the thin layer and can handle a variety of interface conditions, multi-layered structures, heat sources, nonlinear material behavior or coupling to physics other than heat transfer. The efficiency of the proposed approximation is highlighted by comparison with a reference model with a conventionally meshed insulation for a model problem exhibiting a brick wall structure where a stationary heat equation is solved. The formulation is then verified against reference models with meshed insulation solving a transient heat equation for an insulated high-temperature superconductor pancake coil exhibiting a local defect which causes a thermal runaway. The benefit of using the model with the thin shell approximation is studied by analyzing pancake coils with different ratios of the insulation layer to the coated conductor thickness. It is shown that the smaller the ratio, the shorter the solution time and the lower the number of unknowns of the thin shell model when compared to the conventionally meshed insulation in order to reach the same numerical accuracy. The method is implemented in an open-source finite element framework and a reference implementation for a simple model problem is shared alongside this paper.

Electromagnetic Simulation of No-Insulation Coils Using H – $\phi$ Thin Shell Approximation

“…The discontinuity of the tangential magnetic field strength can be introduced by two equivalent approaches: using a duplication of mesh DoF as in [17] or by ii) using dedicated FE basis functions with support restricted to one side of Γ c,cl [30]. In this work, we follow the latter approach as it allows to couple the thermal TSA of [16] and this work without needing two different meshes for the thermal and MQS system.…”

“…The TSA model has 2.2 times fewer DoF and 1.9 times shorter total solution time compared to the vol model. As discussed in [16], the more the T2TCL thickness approaches zero (for directly touching turns), the more the solution time is reduced. In such a case, the TSA becomes the only practical method expected to lead to a (correct) solution.…”

“…Furthermore, the effect increases with the number of turns. Last, the construction of a high-quality volumetric mesh of the T2TCL commonly requires user-defined mesh controls which are not needed for the TSA [16]. In summary, the TSA provides an accurate and efficient alternative.…”

“…However, quenches are local effects and no-insulation coils commonly exhibit true three-dimensional (3D) geometries (see, e.g., [14]) making the quench problem in NI coils an intrinsically 3D problem requiring 3D FE models. Full 3D resolution models are difficult due to, e.g., the high aspect ratio of the superconducting layer of coated conductors (CC) [15] and the contact or insulation layers between the turns [16], as well as the current flow across the turn-to-turn contact layer (T2TCL) [12]. In a classical FE method, the T2TCL volume has to be meshed leading to unfavorable meshes since a high number of degrees of freedom (DoF) is needed to ensure an accurate solution, in particular if the problem is highlynonlinear as common in the case of HTS materials due to the power law.…”

“…The TSA-based method is verified against reference models with volumetrically meshed TCT2L and is shown to yield accurate solutions with significantly reduced solution time. The code is made available such that it may serve as a community benchmark [18].…”