Computation of 2-D current distribution in superconductors of arbitrary shapes using a new semi-analytical method

Sirois, Frédéric; Roy, F.

doi:10.1109/tasc.2007.902117

Cited by 20 publications

(17 citation statements)

References 17 publications

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“…One of these algorithms, called DASPK was already used in our previous works [7,8], and is used here to solve the obtained system of differential algebraic equations(DAE). Finally, after ( ) is known in all the elements, AC losses are computed using the following formula…”

Section: Methodsmentioning

confidence: 99%

A new numerical approach to find current distribution and AC losses in coaxial assembly of twisted HTS tapes in single layer arrangement

Siahrang

Sirois

Grilli

et al. 2010

J. Phys.: Conf. Ser.

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A new numerical approach to find current distribution and AC losses in coaxial assembly of twisted HTS tapes in single layer arrangement Abstract. This paper presents a novel technique for evaluating AC losses and current distribution in single layer assemblies of coaxially wound thin conductors, such as YBCO coated conductors. The proposed approach takes into account the twisted geometry of the individual superconducting tapes by considering the integral relation between the magnetic vector potential and the current density in the tapes (Biot-Savart formula). The integrals are solved numerically and semi-analytically, and the results are used to generate a discretized system of equations based on the magnetic flux diffusion equation (eddy current problem). The latter is solved using an efficient time transient solver (DASPK). It is assumed that, due to the helical symmetry of the problem, it is sufficient to solve for the current distribution in half of a single tape crosssection, even if many tapes are present, which allows a drastic reduction of the 3-D problem to a simple 1-D domain. The method was used to evaluate the AC losses of a HTS cable made of coated conductors, and it was observed that for a given radius of the former and number of tapes, twisted tapes with smaller pitch have lower AC losses.

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Section: Methodsmentioning

confidence: 99%

A new numerical approach to find current distribution and AC losses in coaxial assembly of twisted HTS tapes in single layer arrangement

Siahrang

Sirois

Grilli

et al. 2010

J. Phys.: Conf. Ser.

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“…One needs to begin the derivation from (3). In our modelling tool, integration over triangular element carrying constant current density is done utilizing the formulas presented in [32].…”

Section: Extending the Algorithm For Triangular Elementsmentioning

confidence: 99%

Utilizing Triangular Mesh With MMEV to Study Hysteresis Losses of Round Superconductors Obeying Critical State Model

Ruuskanen

Stenvall

Lahtinen

2015

IEEE Trans. Appl. Supercond.

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Nature's minimum energy principle formulated in minimum magnetic energy variation (MMEV) and coupled with the Bean's critical state model (CSM) has resulted in feasible tools to model hysteresis losses in superconductors. These tools have been applied for single wires as well as for multi-turn coils in two-dimensional modelling domains. However, so far the discretization of the modelling domain has always relied on regular rectangular meshes. Therefore, the mesh representation of round filaments suffers from large discretization error if the mesh is not refined considerably more than triangular meshing would need. In this paper, we study the utilisation of triangular mesh in such a hysteresis loss modelling tool. We present the required extension to the already available knowledge that is needed to implement such a modelling tool. With our home-brewed tool, we study the convergence of the simulated transport current losses in the cross-section of a round wire represented with triangular and rectangular meshes of different types and of different densities. According to the results, triangular meshing is considerably more efficient than rectangular meshing for simulating transport current losses in the investigated situation.Index Terms-Critical state model, hysteresis losses, minimum magnetic energy variation, numerical modelling.

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“…In Fig. 3, we present a comparative result between numerical solutions of the normalized current density (J/J c ) obtained with our hybrid method (HM) and with the semi-analytical method (SAM, [3]) at time t = T 0 /4. As can be seen, we find exactly the same solutions, to within numerical errors and mesh differences.…”

Section: Numerical Application: Long Cylinder In a Transverse Magmentioning

confidence: 99%

“…However, in the case of large n values, this approach is prone to numerical oscillations and convergence problems. Others schemes using integral formulas in a semi-analytical form were proposed as an alternative to finite elements, but the same limitations occur for large n values [2], [3]. In this paper, we present a model combining Maxwell's equations directly to a J(E) power law J(E) = J c (E/E c ) 1 n .…”

Section: Introductionmentioning

confidence: 99%

New Hybrid FE-FV Method for Computing Current Distribution in 2-D Superconductors: Application to an HTS Cylinder in Transverse Magnetic Field

Kameni

Netter²,

Sirois³

et al. 2009

IEEE Trans. Appl. Supercond.

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International audienceThis paper presents a new numerical method based on finite elements - finite volumes (FE-FV) for solving 2-D diffusion problems in high temperature superconductors (HTS). The approach does not involve directly the resistivity term (ρ), generally used to model the E(J) characteristic as a power law, i.e E(J) = ρ(J)J, with ρ(J) ∝ Jn−1. Instead, we use a J(E) constitutive law J ∝ E 1 , with E = E e z (a single component), which leads to a scalar non-linear differential equation. After presenting in details the developments, the method is tested in the case of a superconducting cylinder submitted to a transverse magnetic field. The current density obtained is compared to another numerical technique (the semi-analytical method) in order to validate the results. Although not fully optimized yet, it appears that the proposed method is very stable, especially for large n-values (greater than 100)

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Computation of 2-D current distribution in superconductors of arbitrary shapes using a new semi-analytical method

Cited by 20 publications

References 17 publications

A new numerical approach to find current distribution and AC losses in coaxial assembly of twisted HTS tapes in single layer arrangement

A new numerical approach to find current distribution and AC losses in coaxial assembly of twisted HTS tapes in single layer arrangement

Utilizing Triangular Mesh With MMEV to Study Hysteresis Losses of Round Superconductors Obeying Critical State Model

New Hybrid FE-FV Method for Computing Current Distribution in 2-D Superconductors: Application to an HTS Cylinder in Transverse Magnetic Field

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