2D Numerical Modeling of a HTS Bulk Magnetization based on H formulation Coupled with an Electrical Circuit

Abstract : The magnetization process of high-temperature superconductors (HTS) bulks still has numerical modeling difficulties. The main reason is caused by the strong nonlinearity of such materials. In the modeling of magnetization process of HTS bulk, the current in the magnetizing coil is usually imposed using a peak amplitude and a time constant. The current waveform depends on the parameters of the electrical circuit and the induced currents in the bulk sample play a role in the dynamic of the current in the magnetizing coil. To simulate the whole process of magnetization, it requires modeling the HTS bulk and the coupling through the coil included in the electrical circuit. The magnetization of the HTS bulk assumes to produce high external magnetic field by a coil. As a result, HTS is magnetized and behaves like a strong permanent magnet. The behavior of the YBCO material is characterized by E-J power-law and usually implemented in H formulation, with a constant permeability. In this 2D axisymmetric problem, the electric field and current density have only one component Ej and Jj, but the magnetic field contain Hr and Hz. The modeling of YBCO by using H formulation is usually done without the electrical circuit coupled with the coil. In fact, the current is usually assumed as known and imposed with an additional constraint. However, the magnetic vector potential A has only one component in the 2D problem. To overcome these difficulties and couple the electromagnetic calculations with circuit equations, we propose two solutions, a model based on H formulation with a calculation of the magnetic flux seen by the magnetizing coil or coupling the two formulations H and A in one project. The first approach assumes that the model in the FEM software is based on H formulation and at the same time is calculated the magnetic vector potential A and total magnetic flux Φ seen by the coil. In 2D, this approach leads to the calculation of 3 unknowns instead of 2 when using only H formulation. It is worth mentioning that the calculation of the magnetic flux seen by the coil can also be calculated directly through the magnetic field H with a summation of the flux seen by each turn. The second approach assumes that only the bulk is modeled by H formulation while the coil and air domains are modeled by A formulation with coupling through the electrical equations. The key point is applying suitable boundary conditions between bulk and others domains in order to keep the continuity of H component. This abstract proposed two techniques for modeling HTS bulk by FEM software based on H formulation to deal with the nonlinearity of YBCO material and to couple with the electrical equations. The final work will include details of the proposed techniques with numerical results on a 2D axisymmetric PFM. A comparison between both methods will be done in terms of accuracy.
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https://hal.archives-ouvertes.fr/hal-01908903
Contributor : Kévin Berger <>
Submitted on : Tuesday, October 30, 2018 - 4:06:34 PM
Last modification on : Tuesday, January 22, 2019 - 11:24:40 AM

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Jakub Kapek, Kévin Berger, Jean Lévêque, Smail Mezani. 2D Numerical Modeling of a HTS Bulk Magnetization based on H formulation Coupled with an Electrical Circuit. ASC 2018 - Applied Superconductivity Conference, Oct 2018, Seattle, Washington, United States. page 31/1LPo2B-08 [L17]. ⟨hal-01908903⟩

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