[论文解读] Three-dimensional electromagnetic modeling of practical superconductors for power applications

Milan Kapolka|arXiv (Cornell University)|May 31, 2016

Physics of Superconductivity and Magnetism参考文献 64被引用 3

一句话总结

本文提出了一种用于电力应用中实际超导体的新型3D电磁建模框架MEMEP 3D，基于最小电磁熵产生变分法，以矢量势T为主要变量。该方法可精确模拟超导带材和块材中的复杂3D电流分布、交流损耗及各向异性效应，其结果经解析解和实验验证，耦合损耗预测误差小于3%。

ABSTRACT

HTS are feasible for hight power applications because of the smaller consumption demand of the cooling system in comparison to the whole power device. Real industral devices contain superconductors with 2D and 3D geometry (coated conductors tapes represent an example of 2D geometry, since the superconducting layer is very thin). In order to know the feasibility and the optimum design of a certain device, there is a need of software tools. These Numerical tools have hight requirements like fast computation, a physical model for any E(J) relation of the superconductor and any complex geometry such as coils, motors and generators, where E is the electric field and J is the current density. In this work we present a 3D variational model based on a functional that restricts the problem in the superconductor volume. We show the magnetization process of a thin film and a 3D bulk sample. We compare our model of the thin film geometry with the thin film formula, reaching a good agreement. We also compare a striated tape, where the filaments are connected by linear material, with a FEM model. We present several results for a thin film with constant critical current density, Jc, magnetic-field dependent Jc, and an anisotropic E(J) relation. For the latter, E is not parallel to J when the magnetic flux density is not perpendicular to J (force free situation). The last studied situation is the 3D cubic sample. We find the time dependence of the current density and AC loss for each situation. In the cubic bulk sample, we found a non-negligible component of the current density in the direction of the applied field. The presented numerical method is very promising for 3D modeling of superconducting samples and power applications.

研究动机与目标

• 开发一种快速且精确的3D电磁建模框架，用于高功率应用（如电机、发电机和输电线路）中的实际超导体。
• 通过实现有限尺寸超导元件的完整3D仿真，克服2D模型的局限性，包括端部边缘效应和非均匀电流分布的影响。
• 模拟复杂的非线性E(J)关系，包括Jc(B)依赖性和各向异性的‘无应力’效应，这对于实现真实性能预测至关重要。
• 采用OpenMP和BoostMPI实现高效的并行计算，以高计算效率（80%并行效率）处理大规模3D网格。
• 通过与解析解、有限元方法以及交流损耗、磁化和交叉场去磁化实验测量结果的对比，验证模型的准确性。

提出的方法

• 该方法基于3D电磁熵产生最小化的变分公式，以有效磁化强度T为主要未知变量。
• 通过泛函的欧拉方程推导控制方程，采用四面体单元进行有限元离散化求解。
• 模型可处理任意E(J)关系，包括各向同性、通过Kim模型实现的Jc(B)依赖性、各向异性和多值临界态模型。
• 对堆叠带材采用薄膜近似，利用具有对称性的区域以降低计算成本，同时保持精度。
• 通过OpenMP（共享内存）和BoostMPI（分布式内存）实现并行化，支持在计算集群上高效运算。
• 算法采用迭代最小化方法，控制容差（tolJ = 1e-5），并支持外加磁场的可变波形与方向建模。

实验结果

研究问题

• RQ1 3D电磁模型在多丝超导带材中互丝耦合的交流损耗预测方面，精度如何？
• RQ2 在垂直场和倾斜场作用下，具有Jc(B)依赖性的矩形超导棱柱的3D电流分布模式与磁化行为如何？
• RQ3 各向异性的E(J)关系如何影响超导薄膜和块材中无应力电流构型的形成？
• RQ4 3D建模能否再现立方超导块材在交叉场去磁化过程中观察到的非对称磁场捕获现象？
• RQ5 在3D超导体仿真中，对称性与基于扇区的分解在多大程度上可降低计算成本而不牺牲精度？

主要发现

• MEMEP 3D模型对两根焊接带材的耦合交流损耗预测与实验测量结果偏差小于3%，验证了其高精度。
• 模型揭示了在横向磁场下块材超导体中存在非零的z向电流密度分量，表明2D模型未能捕捉的3D电流路径。
• 交叉场去磁化仿真正确预测了Gd-Ba-Cu-O立方块材中非对称的磁场捕获行为，与实验观测一致。
• 模型成功复现了有限长度薄膜在恒定Jc和Jc(B)依赖性条件下的2D解析结果，验证了其核心公式的正确性。
• 采用扇区划分与对称性处理显著降低了计算负载，在集群上实现了80%的并行效率，支持大规模3D仿真。
• 各向异性的E(J)关系使模型能够模拟倾斜磁场下无应力电流构型的形成，揭示了薄膜和棱柱中复杂的3D电流分布模式。