How to Choose the Superconducting Material Law for the Modelling of 2G-HTS Coils

How to Choose the Superconducting Material Law for the Modelling of 2G-HTS Coils
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如何选择超导材料定律来建模 2G-HTS 线圈

DOI:
10.3390/ma12172679
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发表时间:
2019
期刊:
影响因子:
3.4
通讯作者:
H. S. Ruiz
H. S. Ruiz
中科院分区:
材料科学3区
文献类型:
--
作者:
B. C. Robert;M. Fareed;H. S. Ruiz

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为了揭示材料定律的选择对超导线圈电磁特性数值模拟和分析的影响,本文比较了作为第二代高温超导(2G-HTS)带材电导特性建模工具的E-J幂定律的四种最常见的方法。所考虑的材料定律是:(I)著名的E-J临界态类模型,具有恒定的临界电流密度,与磁场无关;(Ii)经典的Kim模型,它引入了与环境磁场的各向同性依赖关系;(Iii)具有正交场依赖关系的半经验类Kim模型,Jc(B),广泛用于高温超导薄膜的模拟;以及(Iv)实验测量的超强2G-HTS带材的E-J材料定律,它解释了场中临界电流密度Jc(B;θ),其导出函数类似于Kim模型,但考虑了一些微观结构参数,如超导层的电子质量各向异性比(γ)。特别注意了那些在宏观方法中可以通过成熟的实验装置来测量的物理量,例如测量超导线圈每圈的临界电流密度,由此产生的磁场分布,以及在自场条件下施加的不同幅度的交流传输电流的滞后损耗曲线。我们证明,尽管所有这些超导材料定律从纯定性的角度来看都是同样有效的,但临界态类模型不能预测超导线圈每一圈的临界电流密度的局部变化,或其沿超导带宽度的非均匀分布。然而,根据感兴趣的物理量和数值预测与实验测量之间的误差容限,本文为不同的外加电流区域建立了判定准则,其中可以保证一个或另一个模型的适用性,而不管超导带的实际磁角各向异性特性是否已知。
In an attempt to unveil the impact of the material law selection on the numerical modelling and analysis of the electromagnetic properties of superconducting coils, in this paper we compare the four most common approaches to the E-J power laws that serve as a modelling tool for the conductivity properties of the second generation of high-temperature superconducting (2G-HTS) tapes. The material laws considered are: (i) the celebrated E-J critical-state like-model, with constant critical current density and no dependence with the magnetic field; (ii) the classical Kim’s model which introduces an isotropic dependence with the environment magnetic field; (iii) a semi-empirical Kim-like model with an orthonormal field dependence, Jc(B), widely used for the modelling of HTS thin films; and (iv) the experimentally measured E–J material law for SuperPower Inc. 2G-HTS tapes, which account for the magneto-angular anisotropy of the in-field critical current density Jc(B;θ), with a derived function similar to Kim’s model but taking into account some microstructural parameters, such as the electron mass anisotropy ratio (γ) of the superconducting layer. Particular attention has been given to those physical quantities which within a macroscopic approach can be measured by well-established experimental setups, such as the measurement of the critical current density for each of the turns of the superconducting coil, the resulting distribution of magnetic field, and the curve of hysteretic losses for different amplitudes of an applied alternating transport current at self-field conditions. We demonstrate that although all these superconducting material laws are equally valid from a purely qualitative perspective, the critical state-like model is incapable of predicting the local variation of the critical current density across each of the turns of the superconducting coil, or its non-homogeneous distribution along the width of the superconducting tape. However, depending on the physical quantity of interest and the error tolerance allowed between the numerical predictions and the experimental measurements, in this paper decision criteria are established for different regimes of the applied current, where the suitability of one or another model could be ensured, regardless of whether the actual magneto angular anisotropy properties of the superconducting tape are known.
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