Development of a three-dimensional finite-element model for high-temperature superconductors based on the H-formulation

Grilli, Francesco; Brambilla, Roberto; Sirois, Frédéric; Stenvall, Antti; Memiaghe, S.

doi:10.1016/j.cryogenics.2012.03.007

Cited by 103 publications

(99 citation statements)

References 17 publications

(20 reference statements)

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“…14,15 In this work, we intend to build a 3D model to analyze the performance degradation and AC loss of Nb 3 Sn superconducting strands; however, rare experiments are available for comparison to our simulation. Prior to implementing 3D modelling, it is necessary to validate the proposed approach by comparing its results with the corresponding 2D scenario.…”

Section: A Validation Of the 3d Modelmentioning

confidence: 99%

“…2 In recent years, attempts have been made to study the electromagnetic behaviors of some superconductors by numerical simulation. [3][4][5][6][7][8][9][10][11][12][13][14][15][16] As for finite element modelling (FEM), the extreme complexity of hierarchical geometry and structure of Nb 3 Sn strand and CICC requires a special concern for the modelling of the strand entity. Therefore this will inevitably consume large amounts of CPU time and memory capacity in meshing and calculating process.…”

Section: Introductionmentioning

confidence: 99%

“…So, 2D simulations mainly focus on high-temperature superconductors (HTS) with homogenous material and standard bulk shape. 3,4,6,[8][9][10][11][13][14][15] As the advance of computer technology, it becomes feasible to use FEM to cope with Nb 3 Sn strand at the cost of long-time computation and large memory. Even so, modelling the strand down to filament level is still troublesome.…”

Section: Introductionmentioning

confidence: 99%

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Electromagnetic behaviors of superconducting Nb3Sn wire under a time-dependent current injection

Gao

2014

AIP Advances

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We build a 3D model to analyze the electromagnetic behaviors of Nb3Sn filamentary strand exposed to a time-varying current injection, under the consideration of n value and strain effect. Electromagnetic behaviors, performance degradation and AC loss are investigated. Results show that the filament bundles prevent a further field penetration from the outer shell into the interior matrix. Different current/field profiles occur in the strand and outside. Compared to the critical current, the average transport current keeps a high value with little change over a broader strain range, and has a larger magnitude by several orders of magnitude. Increasing the strain results in a suppression of the current transport capacity, and part of the current is expelled into the metal matrix causing larger AC loss. The larger twist pitch implies a longer current circuit and more magnetic flux enclosed, thus increasing the loss. More details are presented in the paper.

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Section: A Validation Of the 3d Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Electromagnetic behaviors of superconducting Nb3Sn wire under a time-dependent current injection

Gao

2014

AIP Advances

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“…The so-called H -formulation has set the standard for the simulations of superconductor hysteresis losses employing the power-law-based eddy current model (ECM) [4][5][6][7][8]. This formulation, in which the ECM of the magnetoquasistatic Maxwell's theory is formulated in terms of the magnetic field intensity H , has such advantages as easy implementation in commercial FEM software packages [9] and allows setting intuitively the driving quantities of the problem.…”

Section: Introductionmentioning

confidence: 99%

A Finite Element Simulation Tool for Predicting Hysteresis Losses in Superconductors Using an H-Oriented Formulation with Cohomology Basis Functions

Lahtinen

Stenvall

Sirois

et al. 2015

J Supercond Nov Magn

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Currently, modelling hysteresis losses in superconductors is most often based on the H -formulation of the eddy current model (ECM) solved using the finite element method (FEM). In the H -formulation, the problem is expressed using the magnetic field intensity H and discretized using edge elements in the whole domain. Even though this approach is well established, it uses unnecessary degrees of freedom (DOFs) and introduces modelling error such as currents flowing in air regions due to finite air resistivity. In this paper, we present a modelling tool utilizing another H -oriented formulation of the ECM, making use of cohomology of the air regions. We constrain the net currents through the conductors by fixing the DOFs related to the so-called cohomology basis functions. As air regions will be truly non-conducting, DOFs and running times of these nonlinear simulations are reduced significantly as compared to the classical H -formulation. This fact is demonstrated through numerical simulations.

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“…The use of a position-dependent J c for AC loss calculations can often give a better agreement with experimental data [43,44]. A position-dependent J c can also be used to simulate the presence of defects [45,46]. Similarly to the J c (B) dependence, once the form for the spatial variation of J c is chosen, its implementation in the model does not present particular obstacles.…”

Section: Accuracy Of Current Numerical Modelsmentioning

confidence: 99%

Potential and limits of numerical modelling for supporting the development of HTS devices

Sirois¹,

Grilli²

2015

Supercond. Sci. Technol.

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In this paper, we present a general review of the status of numerical modelling applied to the design of high temperature superconductor (HTS) devices. The importance of this tool is emphasized at the beginning of the paper, followed by formal definitions of the notions of models, numerical methods and numerical models. The state-of-the-art models are listed, and the main limitations of existing numerical models are reported. Those limitations are shown to concern two aspects: one the one hand, the numerical performance (i.e. speed) of the methods themselves is not good enough yet; on the other hand, the availability of model file templates, material data and benchmark problems is clearly insufficient. Paths for improving those elements are provided in the paper. Besides the technical aspects of the research to be further pursued, for instance in adaptive numerical methods, most recommendations command for an increased collective effort for sharing files, data, codes and their documentation.

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Development of a three-dimensional finite-element model for high-temperature superconductors based on the H-formulation

Cited by 103 publications

References 17 publications

Electromagnetic behaviors of superconducting Nb3Sn wire under a time-dependent current injection

Electromagnetic behaviors of superconducting Nb3Sn wire under a time-dependent current injection

A Finite Element Simulation Tool for Predicting Hysteresis Losses in Superconductors Using an H-Oriented Formulation with Cohomology Basis Functions

Potential and limits of numerical modelling for supporting the development of HTS devices

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