Jin Zou

Modelling and comparison of trapped fields in (RE)BCO bulk superconductors for activation using pulsed field magnetization

The ability to generate a permanent, stable magnetic field unsupported by an electromotive force is fundamental to a variety of engineering applications. Bulk high temperature superconducting (HTS) materials can trap magnetic fields of magnitude over ten times higher than the maximum field produced by conventional magnets, which is limited practically to rather less than 2 T. In this paper, two large c-axis oriented, single-grain YBCO and GdBCO bulk superconductors are magnetized by the pulsed field magnetization (PFM) technique at temperatures of 40 and 65 K and the characteristics of the resulting trapped field profile are investigated with a view of magnetizing such samples as trapped field magnets (TFMs) in situ inside a trapped flux-type superconducting electric machine. A comparison is made between the temperatures at which the pulsed magnetic field is applied and the results have strong implications for the optimum operating temperature for TFMs in trapped flux-type superconducting electric machines. The effects of inhomogeneities, which occur during the growth process of single-grain bulk superconductors, on the trapped field and maximum temperature rise in the sample are modelled numerically using a 3D finite-element model based on the H-formulation and implemented in Comsol Multiphysics 4.3a. The results agree qualitatively with the observed experimental results, in that inhomogeneities act to distort the trapped field profile and reduce the magnitude of the trapped field due to localized heating within the sample and preferential movement and pinning of flux lines around the growth section regions (GSRs) and growth sector boundaries (GSBs), respectively. The modelling framework will allow further investigation of various inhomogeneities that arise during the processing of (RE)BCO bulk superconductors, including inhomogeneous Jc distributions and the presence of current-limiting grain boundaries and cracks, and it can be used to assist optimization of processing and PFM techniques for practical bulk superconductor applications.

Simulating the In-Field AC and DC Performance of High-Temperature Superconducting Coils

In this paper, the authors investigate numerically the in-field behavior of high-temperature superconducting (HTS) coils and a method to potentially improve their performance using ferromagnetic material as a flux diverter. The ability to accurately predict the electromagnetic behavior of superconductors in complex geometries and electromagnetic environments is crucial to the design of commercially viable superconductor-based electrical devices, such as power transmission cables, superconducting fault current limiters, transformers, and motors and generators. The analysis is carried out using a 2-D axisymmetric model of a circular pancake coil based on the H-formulation and implemented in Comsol Multiphysics 4.3a. We explore the use of flux diverters to improve an HTS coils performance with respect to its dc (maximum allowable/critical current) and ac (ac loss) characteristics, for various background magnetic fields. It is found that while flux diverters can improve the ac properties of coils, they can be detrimental to the dc properties in this particular configuration.

Numerical modelling and comparison of MgB 2 bulks fabricated by HIP and infiltration growth

MgB2 in bulk form shows great promise as trapped field magnets (TFMs) as an alternative to bulk (RE)BCO materials to replace permanent magnets in applications such as rotating machines, magnetic bearings and magnetic separation, and the relative ease of fabrication of MgB2 materials has enabled a number of different processing techniques to be developed. In this paper, a comparison is made between bulk MgB2 samples fabricated by the hot isostatic pressing (HIP), with and without Ti-doping, and infiltration growth (IG) methods and the highest trapped field in an IG-processed bulk MgB2 sample, Bz = 2.12 at 5 K and 1.66 T at 15 K, is reported. Since bulk MgB2 has a more homogeneous Jc distribution than (RE)BCO bulks, studies on such systems are made somewhat easier because simplified assumptions regarding the geometry and Jc distribution can be made, and a numerical simulation technique based on the 2D axisymmetric H-formulation is introduced to model the complete process of field cooling (FC) magnetization. As input data for the model, the measured Jc(B,T) characteristics of a single, small specimen taken from each bulk sample are used, in addition to measured specific heat and thermal conductivity data for the materials. The results of the simulation reproduce the experimental results extremely well: (1) indicating the samples have excellent homogeneity, and (2) validating the numerical model as a fast, accurate and powerful tool to investigate the trapped field profile of bulk MgB2 discs of any size accurately, under any specific operating conditions. Finally, the paper is concluded with a numerical analysis of the influence of the dimensions of the bulk sample on the trapped field.

DC characterization and 3D modelling of a triangular, epoxy-impregnated high temperature superconducting coil

The direct current (dc) characterization of high temperature superconducting (HTS) coils is important for applications, such as electric machines, superconducting magnetic energy storage and transformers. In this paper, the dc characterization of a triangular-shaped, epoxyimpregnated HTS coil wound with YBCO coated conductor intended for use in an axial-flux HTS motor is presented. Voltage was measured at several points along the coil to provide detailed information of its dc characteristics. The coil is modelled based on the H-formulation using a new three-dimensional (3D) technique that utilizes the real superconducting layer thickness, and this model allows simulation of the actual geometrical layout of the HTS coil structure. Detailed information on the critical current density’s dependence on the magnitude and orientation of the magnetic flux density, Jc(B,θ), determined from experimental measurement of a short sample of the coated conductor comprising the coil is included directly in the numerical model by a two-variable direct interpolation to avoid developing complicated equations for data fitting and greatly improve the computational speed. Issues related to meshing the finite elements of the real thickness 3D model are also discussed in detail. Based on a comparison of the measurement and simulation results, it is found that non-uniformity along the length exists in the coil, which implies imperfect superconducting properties in the coated conductor, and hence, coil. By evaluating the current–voltage (I–V) curves using the experimental data, and after taking into account a more practical n value and critical current for the non-uniform region, the modelling results show good agreement with the experimental results, validating this model as an appropriate tool to estimate the dc I–V relationship of a superconducting coil. This work provides a further step towards effective and efficient 3D modelling of superconducting devices for large-scale applications.

Enhanced trapped field performance of bulk high-temperature superconductors using split coil, pulsed field magnetization with an iron yoke

Investigating and predicting the magnetization of bulk superconducting materials and developing practical magnetizing techniques is crucial to using them as trapped field magnets in engineering applications. The pulsed field magnetization (PFM) technique is considered to be a compact, mobile and relative inexpensive way to magnetize bulk samples, requiring shorter magnetization times (on the order of milliseconds) and a smaller and less complicated magnetization fixture; however, the trapped field produced by PFM is generally much smaller than that of slower zero field cooling or field cooling techniques, particularly at lower operating temperatures. In this paper, the PFM of two, standard Ag-containing Gd–Ba–Cu–O samples is carried out using two types of magnetizing coils: (1) a solenoid coil, and (2) a split coil, both of which make use of an iron yoke to enhance the trapped magnetic field. It is shown that a significantly higher trapped field can be achieved using a split coil with an iron yoke, and in order to explain these how this arrangement works in detail, numerical simulations using a 2D axisymmetric finite element method based on the H -formulation are carried to qualitatively reproduce and analyze the magnetization process from both electromagnetic and thermal points of view. It is observed that after the pulse peak significantly less flux exits the bulk when the iron core is present, resulting in a higher peak trapped field, as well as more overall trapped flux, after the magnetization process is complete. The results have important implications for practical applications of bulk superconductors as such a split coil arrangement with an iron yoke could be incorporated into the design of a portable, high magnetic field source/magnet to enhance the available magnetic field or in an axial gap-type bulk superconducting electric machine, where iron can be incorporated into the stator windings to (1) improve the trapped field from the magnetization process, and (2) increase the effective air-gap magnetic field.

Modeling and Comparison of In-Field Critical Current Density Anisotropy in High-Temperature Superconducting (HTS) Coated Conductors

The development of high-temperature superconducting (HTS) wires is now at a stage where long lengths of high quality are commercially available, and of these, (Re)BCO coated conductors show the most promise for practical applications. One of the most crucial aspects of coil and device modeling is providing accurate data for the anisotropy of the critical current density Jc(B, θ) of the superconductor. In this paper, the in-field critical current density characteristics Jc(B, θ) of two commercial HTS coated conductor samples are experimentally measured, and based on these data, an engineering formula is introduced to represent this electromagnetic behavior as the input data for numerical modeling. However, due to the complex nature of this behavior and the large number of variables involved, the computational speed of the model can be extremely slow. Therefore, a two-variable direct interpolation method is introduced, which completely avoids any complex data fitting for Jc(B, θ) and expresses the anisotropic behavior in the model directly and accurately with a significant improvement in computational speed. The two techniques are validated and compared using numerical models based on the H-formulation by calculating the self-field and in-field dc critical currents and the ac loss for a single coated conductor.

Pulsed field magnetization of 0°-0° and 45°-45° bridge-seeded Y-Ba-Cu-O bulk superconductors

Large, single-grain (RE)BCO (where RE = rare earth or Y) bulk superconductors with complicated geometries are required for a variety of potential applications, such as rotating machines, magnetic bearings and magnetic separation. As a consequence, the top multi-seeded melt growth process has been studied over many years in an attempt to deliver large, single grains for practical applications. Among these techniques, the so-called bridge-seeding produces the best alignment of two seeds during melt processing of multi-seed samples. In this paper, the trapped field performance and magnetic flux dynamics of two bridge-seeded, multi-seed samples magnetized by pulsed field magnetization are analyzed: one with a 45°–45° and another with a 0°–0° bridge seed. Based on an analysis of the flux penetration across the seeds and in-between the seeds of the 45°–45° multi-seed sample, an estimated J c distribution over the ab-plane is determined, which provides the basis for further analysis via numerical simulation. A three-dimensional finite-element model, developed to qualitatively reproduce and interpret the experimental results, was employed to investigate the influence of the length of the bridge seed for such multi-seed samples. The simulation results agree well with the observed experimental results, in that the multi-seed samples particular inhomogeneous J c distribution acts to distort the trapped field profile from a traditional conical Beans profile, which is determined by the length and direction of the bridge seed on the bulk surface.

Numerical Analysis of Non-Uniformities and Anisotropy in High-Temperature Superconducting Coils

High-temperature superconducting (HTS) coils play an important role in a number of large-scale engineering applications, such as electric machines employing HTS coated conductors. Non-uniformities and anisotropy in the properties of the coated conductor along its length and width can have a large impact on the performance of the tape, which directly influences the performance of an HTS electric machine. In this paper, the specific influences of non-uniformity and anisotropy on the dc properties of coils, such as the maximum allowable dc current, and the ac properties, such as ac loss, are analyzed using a numerical model based on the H formulation. It is found that non-uniformity along the conductor width has a large effect on the ac properties (i.e., ac loss)of a coil, but a relatively small effect on the dc properties (i.e., critical current). Conversely, non-uniformity along the length has a small effect on the ac coil properties, but has a large effect on the dc properties.

Numerical simulation and analysis of single grain YBCO processed from graded precursor powders

Large single-grain bulk high-temperature superconducting materials can trap high magnetic fields in comparison with conventional permanent magnets, making them ideal candidates to develop more compact and efficient devices, such as actuators, magnetic levitation systems, flywheel energy storage systems and electric machines. However, macro-segregation of Y-211 inclusions in melt processed Y–Ba–Cu–O (YBCO) limits the macroscopic critical current density Jc of such bulk superconductors, and hence, the potential trapped field. Recently, a new fabrication technique with graded precursor powders has been developed, which results in a more uniform distribution of Y-211 particles, in order to further improve the superconducting properties of such materials. In order to develop this graded fabrication technique further, a 3D finite-element numerical simulation based on the H-formulation is performed in this paper. The trapped field characteristics of a graded YBCO sample magnetized by the field cooling method are simulated to validate the model, and the simulation results are consistent with the experimental measurements. In addition, the influence of the graded technique and various graded Jc distributions for pulsed field magnetization, recognized widely as a practical route for magnetizing samples in bulk superconductor applications, is also investigated, with respect to the trapped field and temperature profiles of graded samples. This modelling framework provides a new technique for assessing the performance of various sizes and geometries of graded bulk superconductors, and by adjusting the Y-211, and hence Jc, distribution, samples can be fabricated based on this concept to provide application-specific trapped field profiles, such as the generation of either a high magnetic field gradient or a high level of uniformity for the traditionally conical, trapped field profile.

Mitigation of Demagnetization of Bulk Superconductors by Time-Varying External Magnetic Fields

Large single-grain high-temperature superconducting bulks have significant potential to replace permanent magnets in various engineering applications. However, based on our previous research, the trapped field in a bulk superconductor can be attenuated or even erased when a bulk is subjected to a time-varying external magnetic field. Therefore, it is important to develop a method to protect bulks from demagnetization by improving the thermal conduction of the bulk and/or reducing ac losses. Improvement in the thermal conduction of bulks involves modification of the material fabrication process, which may have a detrimental effect on its superconducting properties. Employing shielding materials around a bulk helps to decrease the ac losses, but also provides a durable way to maintain the original material properties. In this paper, two shielding cases are proposed and evaluated numerically: ring-shaped shielding with a copper coil and surface shielding with a ferromagnetic material. Based on the numerical modeling results, the ring-shaped coil works well for externally applied ac fields of larger magnitude and higher frequency. However, the ferromagnetic material was preferable for surface shielding for relatively lower fields. Finally, an optimal shield design is presented.