Numerical analysis of high-frequency induction heating includingtemperature dependence of material characteristics

We have carried out a numerical analysis of the magnetic field on high-frequency induction heating. This analysis includes the dependence of various magnetic properties on temperature. The required characteristics are obtained experimentally. We compare the experimental results with the theoretical values obtained by approximations. Until now, the current density inside the exciting coil on this kind of problem has been assumed to be uniform, which is different from actual phenomena. We propose a new method which takes the inhomogeneous distribution of exciting current into account. In this analysis, the eddy current of the exciting coil is also taken into account     

Development of design for large scale conductors and coils using MgB2 for superconducting magnetic energy storage device

MgB₂ wires are commercially available, and their superconducting characteristics have been continuously developed in the last decade. The relatively high critical temperature of these wires has attracted the attention of researchers, especially in the field of superconducting magnetic energy storage (SMES) coil applications in terms of its relatively high critical temperature, as it enables the use of liquid hydrogen for cooling the coils. The sensitivity of multi-filament MgB₂ wires to bending strain makes the design of large-scale conductors and coils for an SMES system technologically difficult, and the careful investigation of the applied strains during manufacturing is required. Two-conventional methods have been introduced for the fabrication of the coils: wind-and-react (W&R) and react-and-wind (R&W). These methods have been demonstrated to be suitable for the production of large-scale MgB₂ magnets to maximize the coil performance. The W&R and R&W methods have been successfully applied to the designs of conductors and coils, and small W&R test coil fabrication, as well as stability demonstrations are performed in this study. Our study is the first to demonstrate the feeding of hundreds of amperes of transport current using multifilamentary MgB₂ wires at around liquid hydrogen temperature in the practical background magnetic field of 2 T. The minimum quench energy and normal zone propagation velocity are also experimentally investigated for the protection of the actual coils for SMES application.     

4C code analysis of thermal–hydraulic transients in the KSTAR PF1 superconducting coil

The KSTAR tokamak, in operation since 2008 at the National Fusion Research Institute in Korea, is equipped with a full superconducting magnet system including the central solenoid (CS), which is made of four symmetric pairs of coils PF1L/U–PF4L/U. Each of the CS coils is pancake wound using Nb₃Sn cable-in-conduit conductors with a square Incoloy jacket. The coils are cooled with supercritical He in forced circulation at nominal 4.5 K and 5.5 bar inlet conditions. During different test campaigns the measured temperature increase due to AC losses turned out to be higher than expected, which motivates the present study.The 4C code, already validated against and applied to different types of thermal–hydraulic transients in different superconducting coils, is applied here to the thermal–hydraulic analysis of a full set of trapezoidal current pulses in the PF1 coils, with different ramp rates. We find the value of the coupling time constant nτ that best fits, at each current ramp rate, the temperature increase up to the end of the heating at the coil outlet. The agreement between computed results and the whole set of measured data, including temperatures, pressures and mass flow rates, is then shown to be very good both at the inlet and at the outlet of the coil. The nτ values needed to explain the experimental results decrease at increasing current ramp rates, consistently with the results found in the literature.     

Study on cross section of high temperature superconducting coil

It is in particular of importance for HTS coils to secure a larger central magnetic field and/or a large stored energy with shorter length of HTS tapes. The critical current of an HTS tape depends on both the flux density and the flux angle against tapes. From this point, the performance improvement of HTS coils is taken into account with an analytical model. The minimum volume coil derived from the Fabry Factor constant curve is taken concerning the original coil shape, which is often employed in low temperature superconducting coils. The coil critical current was analyzed in consideration of the anisotropic properties of the tape.The electric field of HTS tapes in the coil was calculated at the coil critical current and the high electric field portion were cut out. The optimal coil cross section is obtained by iterating this calculation process. As a result, the critical current and the stored energy density of the coil were improved. The stored energy density increased about 17% and the central magnetic field was almost kept constant regardless of 19% reduction of HTS tapes, as compared with the original coil with the rectangular cross section.     

Surface flashover characteristics in liquid nitrogen for application of superconducting pancake coils

For the development of superconducting power apparatus, it is necessary to establish the dielectric technology in coolants like LN₂. Among the dielectric technology, surface flashover characteristics are studied with several simplified spacers at the structural aspects. Double pancake coil can apply to transformer and fault current limiter, etc. To design dielectric system of high temperature superconducting transformer consisting of double pancake coils, this study discusses an effective insulator composition. Circular shape insulator divided into two parts should be inserted between coils and the insulator should cover electric stresses concentrated at the circumference of the coils which are in the same section of double pancake coils facing each other.     

Critical current test results of 13 T-46 kA Nb3Al cable-in-conduit conductor

In the framework of ITER-EDA, a 13 T-46 kA Nb₃Al conductor with stainless steel jacket has been developed in order to demonstrate applicability of an Nb₃Al conductor with react-and-wind technique to ITER-TF coils. Using a 3.5 m sample consisting of a pair of conductors with 0% and 0.4% bending strain, the critical current performances of the Nb₃Al conductors were studied to verify that the conductor achieves the expected performance and the bending strain of 0.4% does not originate degradation. The critical currents were measured at background magnetic fields of 7, 9, 10 and 11 T at temperatures from 6 to 9 K. The expected critical currents were evaluated taking into account the variation of the strain in the cross-section due to the bending strain as well as self-field and non-uniform current distribution as results of an imbalance in the joint resistance and inductances. The calculation results indicate that the current distribution is almost uniform and the experimental results showed good agreement with the expected critical currents. Accordingly, we can conclude that the fabrication process of this conductor is appropriate and the react-and-wind technique using the Nb₃Al conductor is applicable to ITER-TF coils. In addition, the critical current of the Nb₃Al conductor is expected to be 108 kA at 13 T and 4.5 K, resulting in a sufficient margin against the nominal current of 46 kA. Furthermore, it was found that the decrease in the critical current by thermal strain can be made small by applying the bending strain to the conductor so as to reduce the compressive strain at higher fields, i.e. inner side of the coil, in the conductor cross-section.     

The propagation of the resistive region in high current density superconducting coils

A method is given describing the propagation phenomenon of the resistive region within the winding of superconducting coils wound from semi-stabilized filamentary conductors. The method permits the approximate calculation of the velocities of propagation of the normal conducting front in superconducting coils of high current density. The calculation is carried out assuming that the parameters of the conductor materials, the short sample data, and the heat transfer coefficient from the conductor into the ambient medium are given. The propagation velocities of the normal front have been measured in insulated wires freely immersed in liquid helium, in test samples using conventional interleaving material, and in a compact multilayer coil wound from the same wire. The calculated results are compared with experimental data.     

Reduction of fault current peak in an inductive high-Tc superconducting fault current limiter

This paper dealt with current-limiting performances of an inductive high-T_c superconducting fault current limiter with an auxiliary coil. The fault current limiter mainly consists of the primary copper coil, secondary high-T_c superconducting rings, and auxiliary high-T_c superconducting coils, which are magnetically coupled through three-legged core. The superconducting fault current limiter as a series element in the power system is inserted to limit the fault current. The device presents fast variable-impedance features in the event of a fault condition. The fault current peak can become relatively large for certain ranges of the flux and the fault instant due to the core saturation. The auxiliary coil proposed in this paper was proven to increase the impedance of the SFCL up to more than 31% while preventing the core saturation.     

Specific heat jump of two-band superconductor KFe2As2 using Ginzburg-Landau theory

In this study specific heat jump using two-gap Ginzburg-Landau (GL) theory has been calculated. In contrast to the previous approaches, we have taken into account intergradient order parameters interaction in the GL free energy functional. The thermodynamic magnetic field revealed nonlinear temperature dependence due to interband interaction between order parameters and their gradients. The calculations showed that the specific heat jump in two-order parameter superconductors was smaller than that of single-order parameter superconductors. It has been shown that such a model is in good agreement with experimental data for KFe₂As₂ superconductors.     

An investigation of horizontal axis coils for eddy current inspection

The possible use of horizontal axis eddy current coils for the inspection of fast breeder reactor primary vessels is being investigated. An approach which considers both theoretical modelling work and experimental work has been adopted. Owing to the lack of analytical theory for the horozontal coil case, the initial work has concentrated on determining the impedance change of a horizontal axis air-cored coil when it is brought close to a conducting half-space. An analytical solution (due to Burke) has been considered, along with a newly developed approximate model, for a range of different coils above various conducting media. The approximate model assumes a uniform H field at the material surface and has been extended to consider layered half-spaces such as stainless steel over liquid sodium. The trends exhibited by the impedance change values obtained from both theories compared well with the experimental data.     

Two-dimensional normal zone propagation in BSCCO-2223 pancake coils

We present the results of an experimental and analytical study of two-dimensional normal zone propagation in pancake test coils, wound with silver-sheathed BSCCO-2223 tapes. Two test coils were studied in detail, one having three and the other eight layers. Each test coil was housed in an adiabatic environment whose temperature (20-70 K) was controlled and maintained by a two-stage G-M cryocooler and placed in a background field (0-6 T) generated by a Bitter magnet. With a test coil carrying a transport current (0-200 A), a local heat disturbance was applied by a heater attached to the outermost layer of the coil. The resulting electrical and thermal responses of the coil were recorded with voltage taps and thermometers attached to the coil. A normal zone propagation code was developed to accurately simulate the voltage and temperature responses of each coil for both quenching and recovering events. The code solves the nonlinear transient heat diffusion equation in two-dimensional cylindrical coordinates with a finite difference method. As an application of this code, a two-coil system, with each coil comprised of one double pancake wound with silver-sheathed BSCCO tape, was studied for its quench behaviour as one of the coils was driven normal locally. The simulation results indicate that the value of a shunt resistor connected across the terminals of each coil has a profound effect on the level of hot-spot temperature reached in the quench initiation spot.     

A universal expression for the propagation rate of the normal phase over a high-temperature superconducting film with a transport current

The transport-current-initiated propagation of the normal phase over a high-temperature superconducting film located on a thermally stabilized substrate has been studied theoretically. A universal expression for the propagation rate of the normal phase is obtained that takes into account the influence of the substrate on the evolution of thermal instability in the film and can be applied for an arbitrary dependence of the critical current on temperature. The resulting expression is shown to describe the experimental data satisfactorily. Pis’ma Zh. Tekh. Fiz. 24, 22–26 (January 26, 1998)     

Multiscale fatigue crack growth modelling for welded stiffened panels

The influence of welding residual stresses in stiffened panels on effective stress intensity factor (SIF) values and fatigue crack growth rate is studied in this paper. Interpretation of relevant effects on different length scales such as dislocation appearance and microstructural crack nucleation and propagation is taken into account using molecular dynamics simulations as well as a Tanaka–Mura approach for the analysis of the problem. Mode I SIFs, K_I, were calculated by the finite element method using shell elements and the crack tip displacement extrapolation technique. The total SIF value, K_tot, is derived by a part due to the applied load, K_appl, and by a part due to welding residual stresses, K_res. Fatigue crack propagation simulations based on power law models showed that high tensile residual stresses in the vicinity of a stiffener significantly increase the crack growth rate, which is in good agreement with experimental results.     

Variation of Quench Propagation Velocities in YBCO Cables

We show by modelling that the quench propagation velocity is not constant in HTS coils but it changes during the quench. Due to the large temperature margin between the operation and the current sharing temperatures, the normal zone does not propagate with the temperature front. This means that the temperature will rise in a considerably larger volume when compared to the quenched volume. Thus, the evolution of the temperature distribution below current sharing temperature T _{c s} after the quench onset affects the normal zone propagation velocity in HTS more than in LTS coils. This can be seen as an acceleration of the quench propagation velocities while the quench evolves when margin to T _{c s} is high. In this paper, we scrutinize quench propagation in a stack of YBCO cables with an in-house finite element method software which solves the heat diffusion equation. We compute the longitudinal and transverse normal zone propagation velocities at various distances from the hot spot to demonstrate the distance-variation of these velocities. According to the results in our particular simulation case, the longitudinal normal zone propagation velocity is 30 % higher far away from the quench origin compared to its immediate vicinity when T _op=4.2 K and T _{c s} =15 K.     

Fundamental studies for the application of quench protection systems based on an active power method for cryocooled LTS coils

When the quenching occurs in a superconducting coil, excessive joule heating in normal area may damage the coil. It is necessary to detect quenching in the coil as soon as possible and discharge the magnetic energy stored in the coil. Therefore, we propose a superconducting coil protection system based on an active power method. The system is highly resistant to the noise and does not require cancel voltage taps, so it is useful for both AC and DC coils. We have presented the effectiveness of the system using some test coils cooled in LN₂ or LHe. However, we have not discussed the effectiveness of the proposed system for helium-free cryocooled magnets, in which a larger temperature rise occurs after quenching than in liquid-cooled magnets. In this paper, we verify the effectiveness and practicality of the proposed system through coil protection tests for a cryocooled Nb₃Al LTS coil.     

Supersonic plasmatron nozzle profiling with the real properties of high temperature working gas

The effects of real gases (excitation of vibrational degrees of freedom, dissociation and ionization) taken into account for supersonic nozzle profiling. The paper presents the method of the supersonic nozzle profiling for non-monotonic dependence of adiabatic index on temperature. The results of nozzle profile calculation for two sets of input parameters, based on independently determined specific heat for molecular nitrogen N₂ and products of its thermal decomposition in the temperature range of 260–10⁵ K and atmospheric pressure are presented. The experimental set-up based on proposed method of supersonic nozzle has been developed and manufactured. The gas velocity at different distances from the nozzle outlet has been measured. Results show the existence of the supersonic and transsonic flow regimes after the nozzle.     

Genesis of High Hardness in Hot-Rolled Coils of Cold Reducers’ Grade Steels

A significant quantity of cold-reducible hot-rolled (HR) coils is produced every year. These are basically low-carbon steels; however, the quality of HR coils with respect to cold reducibility had not been entirely satisfactory. The hardness of HR coil was generally higher (≥65 HR_B) than desirable for attaining satisfactory cold reducibility. A systematic study was, therefore, undertaken with the objective to control the hardness to ≤55 HR_B by modifying the existing chemistry, finish rolling temperature (FRT), and the coiling temperature (CT). To find the optimum conditions for lower hardness, trial rolling of slabs of cold reducers’ grade of selected chemistry was conducted under varied conditions. An assessment of hardness across the width and of the microstructure was carried out. The evolution of microstructure in the HR band at different locations from the edge of the strip and the genesis for the resulting hardness profile across the width of the HR coil were examined in detail. The influence of grain size on hardness was also analyzed. The paper outlines the role of finish rolling temperature, coiling temperature, chemistry, and grain size in restricting the hardness to values below 55 HR_B.     

Field and temperature dependencies of critical current on industrial Nb3Sn strands

The increasing need for high field magnetic devices has focused attention on filamentary Nb₃Sn conductors, whose critical data are superior to NbTi conductors. To choose the suitable operating parameters and to determine the stability margin of magnet systems, it is very important to know the effect of temperature and magnetic field on the superconducting properties, especially on the critical current. Up to now, for design calculation, the so-called “Summers model” was assessed theoretically on experimental data obtained by Spencer et al., (The temperature and magnetic field dependence of superconducting critical current densities of multiinflammatory Nb₃Sn and NbTi composite wires. IEEE Trans Mag, Mag-15 (1979) 76) and Suenaga et al., Superconducting critical-current densities of commercial multifilamentary Nb₃Sn(Ti) wires made by the bronze process. Cryogenics (1985) 25, 123). Apart these very useful preliminary experimental data, very little has been done on the very different industrial strands which are now produced in the industry. Industrial Nb₃Sn strands are generally tested and checked only at 4.2 K and their operating design temperature is often very different, sometimes around 6 K. It is now urgent to validate the model and to confirm that the data taken up to now in the design calculations are conservative.     

Coil geometry models for power loss analysis and hybrid inductive link for wireless power transfer applications

This paper presents a hybrid inductive link for Wireless Power Transfer (WPT) applications. Achieving better power transfer efficiency over a relatively wider distance across coils is the prime objective in most of the WPT systems, but often suffers from power loss in the near field area of inductively coupled coils. One of the reasons for this power loss is the pattern of the magnetic field produced by the source coil used in the WPT system. Mostly the nature of magnetic field produced by the source coil is distributed radially over the coil, in which the produced magnetic field is not fully utilized. Achieving better efficiency and load current by reducing power loss is the main driving force of this work. One of the viable methods to reduce the power loss is by increasing the field intensity thereby redirecting the flux lines flow to be directional. With this aim, three coils such as solenoid, spiral and conical are designed and simulated to determine the magnetic field strength using Finite Element Method. The conical coil produces the highest self-inductance of 8.63 µH and a field strength of 1.542 Wb with the coil thickness of 3.20 mm. Then, WPT system is demonstrated with the inclusion of Maximum Power Point Tracking algorithm for improving efficiency. The schematic of flux generation of both in the transmitter and receiver sections are demonstrated and analyzed graphically. The efficiency of both simulation and experimental measurements are matched well with similar progression. The effect of parameters (angle, distance, and load resistance) on the efficiency is explored. The outcomes conclude that the inductive coupling has achieved 73% (average case) power transfer wirelessly over a distance of 5 cm with an input voltage of 5 V and 5 MHz frequency.     

Instabilities above critical current region in Bi-2223/Ag superconducting coils cooled by liquid nitrogen

A sudden drop of the coil voltage and a hysteresis of I-V curve were observed in measurement of one-layer Bi-2223/Ag coils cooled by liquid nitrogen at currents well above critical current region. Their temporal behavior indicates, that the improvement of the cooling and corresponding decrease of temperature after the jump takes place. To study this phenomenon we measured I-V curves of two Bi-2223/Ag coils made from tapes with various degree of critical current homogeneity and analogical curves of two non-superconducting coils made from thin Cu tapes having various widths. In Cu coils we really observed a sudden drop of the temperature, measured in parallel with Cu resistance drop, after reaching heat flux of about 0.4 W cm⁻² during current ramping up. In spite of non-superconducting character of the tape, the hysteresis, i.e. difference between increasing branch and decreasing branch of I-V curves, was observed too! Approximately the same value of heat flux, at current corresponding to the jump, was found also in superconducting coil on segment with least value of local critical current. We conclude that observed voltage drop of the Bi-2223/Ag does not bear upon superconducting nature of the coil and, as that for Cu coil, can be explained by dynamics of heat transfer to liquid nitrogen and its history.