3D simulation of AC loss in a twisted multi-filamentary superconducting wire

Zhao, Junjie; Li, Yingxu; Gao, Yuanwen

doi:10.1016/j.cryogenics.2017.04.004

Cited by 13 publications

(9 citation statements)

References 50 publications

(55 reference statements)

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“…The state variables of the discretized problem are the components of the magnetic field along the edges of the mesh [21]. Its implementation in the commercial software Comsol Multiphysics [22] has become a popular tool for investigating the electrodynamic behavior of superconductors, in particular the AC losses-see for example [15][16][17][18][19][20]. In its original implementation and in most works published in the literature, the equations are implemented in Comsol's general module for partial differential equations 4 .…”

Section: H-formulationmentioning

confidence: 99%

“…The H-formulation has become a popular tool for investigating the electrodynamic behavior of superconductors, in particular the AC losses-see for example [15][16][17][18][19][20]. When used to simulate levitation problems (as in [12][13][14]), the relative movement of the permanent magnet with respect to the superconductor is accounted for by simulating only the superconductor and setting appropriate time-dependent boundary conditions for the magnetic field generated by the permanent magnet.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic modeling of levitation of a superconducting bulk by coupled H-magnetic field and arbitrary Lagrangian–Eulerian formulations

Grilli

Morandi

Silvestri

et al. 2018

Supercond. Sci. Technol.

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Intrinsically stable magnetic levitation between superconductors and permanent magnets can be exploited in a variety of applications of great technical interest in the field of transportation (rail transportation), energy (flywheels) and industry. In this contribution, we present a new model for the calculation of levitation forces between superconducting bulks and permanent magnet, based on the H-formulation of Maxwell's equations coupled with an Arbitrary Lagrangian-Eulerian formulation. The model uses a moving mesh that adapts at each time step based on the time-change of the distance between a superconductor bulk and a permanent magnet. The model is validated against a fixed mesh model (recently in turn validated against experiments) that uses an analytical approach for calculating the magnetic field generated by the moving permanent magnet. Then, it is used to analyze the magnetic field dynamics both in field-cooled and zerofield-cooled conditions and successively used to test different configurations of permanent magnets and to compare them in terms of levitation forces. The easiness of implementation of this model and its flexibility in handling different geometries, material properties, and application scenarios make the model an attractive tool for the analysis and optimization of magnetic levitation-based applications. arXiv:1807.00329v2 [cond-mat.supr-con]

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Section: H-formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic modeling of levitation of a superconducting bulk by coupled H-magnetic field and arbitrary Lagrangian–Eulerian formulations

Grilli

Morandi

Silvestri

et al. 2018

Supercond. Sci. Technol.

View full text Add to dashboard Cite

show abstract

“…It has been implemented in the commercial software COMSOL Multiphysics and with the advantage that it can accurately calculate the AC losses of superconductors in various topologies under different current and magnetic field conditions [9]. Chen et al [10] numerically simulated the vertical dynamic properties of a high-temperature superconducting bulk by H formulation and investigated the effect of thermal effects due to AC losses on its vibrational characteristics; Wu et al [11] established a finite element model based on H formulation to calculate the current density and AC losses of high-temperature superconductors for analyzing the stability and safety of high-temperature superconducting maglev trains; Huang et al [12] numerically simulated the AC losses of high-temperature superconductors levitated under varying fields of different frequencies and amplitudes using H formulation, and conducted experiments to verify the model; Zhao et al [13] established a 3D finite element method based on the H formulation to study the AC losses of twisted low-temperature superconducting wires that can be used in superconducting magnetic levitation systems.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of AC losses in superconducting gravimeter

Xing¹,

Hu²,

Cui³

et al. 2022

Supercond. Sci. Technol.

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The annual drift of μGal level is an important indicator of superconducting gravimeters, which helps geophysicists to clarify the weak geophysical signals. In this paper, a finite element simulation model of the superconducting gravimeter sensor is developed based on the H formulation for evaluating the contribution of the excitation AC losses and the AC losses under operating conditions to the superconducting gravimeter’s drift. The model combines the H formulation and the heat transfer module of COMSOL Multiphysics software to calculate the AC losses of the superconducting gravimeter’s test mass and obtain the distribution images of the test mass’s temperature due to the AC losses-induced heating. The overall temperature rise of the test mass is obtained by assuming that it heats up uniformly and thus combines the temperature dependence factor (10 μGal/mK) of the superconducting gravimeter to derive the instrument drift induced by AC losses. Then, the long-term drift due to excitation losses can reach 0.847 μGal/year, while the operating losses can be 0.45 μGal/year or even less, according to the simulation. In addition, this paper discusses the effects of the parameters (index number, critical electric field and critical current density) in the E-J power law introduced by the H formulation on the AC loss evaluation. It is concluded that the AC losses are sensitive to the critical current density, and increasing the test mass’s critical current density helps enhance the stability of the superconducting gravimeter.

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“…This formulation combines Faraday and Ampere's laws to directly solve for the magnetic field as the dependent variable. Although it has proven to accurately model applications ranging from AC losses [3]- [6] in HTS tapes to the magnetic levitation of permanent magnets over HTS bulks [7]- [10], the use of H in non-conducting domains is problematic. First, the dummy resistivity used to avoid eddy currents in non-conducting domains degrades the matrix conditioning [11] and leads to unwanted currents [12].…”

Section: Introductionmentioning

confidence: 99%

COMSOL implementation of the H-$ϕ$-formulation with thin cuts for modeling superconductors with transport currents

Arsenault,

Alves,

Sirois

2021

Preprint

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Despite the acclaimed success of the magnetic field (H) formulation for modeling the electromagnetic behavior of superconductors with the finite element method, the use of vector-dependent variables in non-conducting domains leads to unnecessarily long computation times. In order to solve this issue, we have recently shown how to use a magnetic scalar potential together with the H-formulation in the COMSOL Multiphysics environment to efficiently and accurately solve for the magnetic field surrounding superconducting domains. However, from the definition of the magnetic scalar potential, the non-conducting domains must be made simply connected in order to obey Ampere's law. In this work, we use thin cuts to apply a discontinuity in φ and make the non-conducting domains simply connected. This approach is shown to be easily implementable in the COMSOL Multiphysics finite element program, already widely used by the applied superconductivity community. We simulate three different models in 2-D and 3-D using superconducting filaments and tapes, and show that the results are in very good agreement with the H-A and H-formulations. Finally, we compare the computation times between the formulations, showing that the H-φ-formulation can be up to seven times faster than the standard H-formulation in certain applications of interest.

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3D simulation of AC loss in a twisted multi-filamentary superconducting wire

Cited by 13 publications

References 50 publications

Dynamic modeling of levitation of a superconducting bulk by coupled H-magnetic field and arbitrary Lagrangian–Eulerian formulations

Dynamic modeling of levitation of a superconducting bulk by coupled H-magnetic field and arbitrary Lagrangian–Eulerian formulations

Numerical simulation of AC losses in superconducting gravimeter

COMSOL implementation of the H-$ϕ$-formulation with thin cuts for modeling superconductors with transport currents

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