Evaluation of the Applicability of Phenomenological HTS Models for Numerical Analysis of Quenches in Coated Conductors: Simulations vs. Experiments

The electrical resistivity of coated conductors is strongly related to the inter-dependent set of parameters (J, H, T), respectively current density, magnetic field and temperature. On the one hand, it is difficult to isolate the contribution of each of these parameters on the resistivity measured experimentally. On the other hand, numerical methods, which may allow this separation, require a good knowledge of the fundamental laws governing the superconducting transition which are, up to now, derived from curve fitting with experimental data. In this paper, we investigate the influence of phenomenological formulas on the outputs of a recently developed finite element model. The outputs are compared against experimental voltage curves, which have been obtained under pulsed transport currents between 80 and 160 A and external magnetic fluxes of 0 to 350 mT. The comparisons indicate that the numerical models may reproduce well the measurements, using the right set of phenomenological laws parameters. Nevertheless, the solution may still be inaccurate at low field values and high current amplitudes, where the curvature of the simulated E-J curves is more pronounced, indicating that further refinement is required in order to obtain models valid over a wider range of parameters.

3D Modeling of Coupling Between Superconducting Filaments via Resistive Matrix in AC Magnetic Field

Bertrand Dutoit, Francesco Grilli, Yong Yang

The ac loss of superconducting composite depends strongly on coupling between superconducting filaments via the resistive matrix. The established technique for loss reduction using twisted filaments relies on the decoupling of the filaments below a critical coupling field Bc, which increases with the reduction of the twist pitch and the matrix conductivity. Although the concept of Bc may be clearly demonstrated using two infinite slabs of finite length, further details on its correlation with the filament/conductor geometry are not yet available. The main obstacle is due to the fact that any accurate analysis of such a problem must be carried out in 3d. In this paper, we describe the initial results from 3d modeling using Cedrat‘s Flux3D, for which a superconductor module for handling power-law E-J characteristics was developed. Using a simple model of two rectangular superconductors connected through a normal metal, we demonstrate the feasibility for quantitative modeling of their coupling behavior over a wide range of field sweep rates for different conductor geometries. Typical examples were given for cases not addressed by the existing approximate theory, as well as for the evolution of field profile for varying field sweep rate. ample of a very low resistivity in the matrix, it is also suggested that onset of coupling is strongly dependent on the shape of the conductor and individual filaments. Qualitatively speaking, conductors with a large aspect ratio have a greater tendency to couple due to a larger demagnetising effect, as confirmed by experimental studies. While the mechanism that promotes the coupling of the filaments through the resistive matrix in ac magnetic fields is well understood conceptually, quantitative calculation of the critical coupling field is only limited to the simplified scenario of infinite slabs. The main difficulty is that we are dealing with a 3d problem with conductors of finite length and induced currents flowing both along and perpendicular to the long axis. Fortunately 3d calculations of superconductors in magnetic fields are becoming a reality thank to the rapid enhancement in computing power to desktop computers and progress in the implementation of numerical techniques for modeling superconductors.

2003

Finite Element Method Modelling of Superconductors: from 2D to 3D

Bertrand Dutoit, Francesco Grilli

A 3D numerical modelling technique for solving problems involving superconducting materials is presented. The model is implemented in finite element method software and is based on a recently developed 3D formulation for general electro-magnetic problems with solid conductors. It has been adapted for modelling of superconductors with non-linear resistivity in 3D, characterized by a power-law E-J relation. It has firstly been compared with an existing and verified 2D model: compared are the current density distribution inside the conductors and the self-field ac losses for different applied transport currents. Secondly, the model has been tested for computing the current distribution with typical 3D geometries, such as corner-shaped and twisted superconductors. Finally, it has been used with two superconducting filaments in the presence of external magnetic field for verifying the existence of coupling currents. This effect deals with the finite length of the conductors and cannot be taken into account by 2D models.

2004

Modeling and Characterization of Coated Conductors Applied to the Design of Superconducting Fault Current Limiters

François Roy

The Superconducting Fault Current Limiter (SFCL) appears to be a device of great interest to efficiently build the electrical grid of tomorrow. With the recent progress made by the superconducting wires manufacturers, there are needs coming from the industry to evaluate the potential of such devices. In the present thesis work, the behavior under external field and transport current of the last generation of wire is investigated. This study is conduct both experimentally and numerically in order to link the physics occurring at the wires level to the design of SFCLs as a whole. From the nature of the material, the resistance appears non-uniformly in high temperature superconductors. For the purpose of building SFCLs it is important to obtain a fast and uniform resistive transition (quench) when a fault occurs through those conductors. This in order to reduce the local heat generation that may damage the device. This fast quenching property is related to the Normal Zone Propagation Velocity (NZPV). In this work the NZPV is measured using a localized magnetic field to initiate quenches in commercial coated conductors. Those velocities have been measured to be larger than 14 cm/s for pulsed currents above the critical value. The NZPV experiments have demonstrated that the superconductor non-uniformity (generated by the localized field) helps to reduce the initial delay before the quench initiation for transport currents in the range of the critical value. However, for larger transport currents the effect of the non-uniformity on the delay is less important since, with increasing transport current amplitudes, the normal state transition has shown to occur more as a consequence of the heat generated in the stabilizer than as the unique consequence of the advancement of the normal zone in the superconductor. From the experimental measurements, it has been shown that a reduction of the liquid-nitrogen temperature (subcoooled) increases the NZPV. This effect has been observed taking into account of the increase of the critical current associated with the temperature reduction. Nevertheless, it is not clear if it is the heat transfer or the estimation of the critical current that is responsible for this effect. In order to validate the numerical models, time-resolved voltage traces obtained from the experiments have been compared to the outputs of the models. Those are based on the thermal- and electrical-diffusion equations. From the simulations, it has been demonstrated that the NZPV can be increased by three methods: by using a thick diffusive substrate, by inserting a resistive interface between the superconductor and the stabilizer as well as by increasing the heat generation in the stabilizer. In light of those results, it seems that the insertion of a resistive layer is the most promising approach to improve the NZPV in coated conductors. As a matter of fact, a resistive interface increases the normal-zone size and keeps an acceptable temperature level along the conductor during quenches. The present work allowed to simulate the flux-flow regime in coated conductors. Comparing those simulations to experimental data have shown that the power-law may be inappropriate to simulate this regime under weak external magnetic fields. In addition, it appears that the role of transient heat transfer with the surroundings needs to be studied in more details to determine the specifications of a prospected SFCL made of coated conductors.