Transport Current Distribution Research Articles

Numerical study on the transport current distribution in the multi-layer CORC coil

The conductor on round core (CORC) cable has attracted increasing attention due to its strong and high-efficient current carrying capacity. It is considered as one of ideal candidate cables for manufacturing nuclear fusion magncets. Under the circumstance, the transport current distribution of the coils wound by CORC cables has significant impacts on the operating performance of nuclear fusion magnets. Considering the difficulty in experimental tests, numerical model is an effective way to illustrate transport current distribution of the multi-layer CORC coil and provide further insights into its working performance. Therefore, in this work, A 3D finite element model based on the H formulation is proposed to simulate a single-turn and multi-layer CORC coil. The validity of the model has been verified by experimental results. Based on the proposed model, the transport current distribution of the multi-layer straight CORC cable and the multi-layer CORC coil is compared and discussed. In addition, the current density distribution on the superconducting tapes of the multi-layer CORC coil is also investigated. This work can provide an important reference for the design and practical application of multi-layer CORC coils.

Numerical study on the electromagnetic characteristics of multi-layer CORC cables

Due to the high isotropy and low AC losses, the multi-layer conductor on round core (CORC) cable is a good candidate for high field magnets, such as central solenoid magnets in fusion. Considering the difficulty in experimental measurement, numerical model is an effective way to illustrate the electromagnetic characteristics of the multi-layer CORC cable and provide further insights into its working performance. In this work, a 3D finite element model based on H formulation is proposed to simulate a CORC cable with as many as 18 layers considering electromagnetic coupling. The validity of the model has been verified by experimental results. Based on the proposed model, the DC transport current distribution characteristics and charge-discharge loss characteristics of multi-layer CORC cables wound in the same and opposite winding directions are investigated respectively. This work can provide an important reference for the design of multi-layer CORC cables for high-current or high-field application.

Measuring the through-plane and in-plane oxygen apparent diffusion coefficients in the gas diffusion layer

Accurately predicting oxygen mass transport resistance and current distribution in fuel cells requires significant knowledge of oxygen diffusion coefficients in both in-plane and through-plane directions. However, there are few methods for measuring in-plane oxygen diffusion coefficients, which are important parameters for simulating oxygen flux distribution in gas diffusion layers (GDLs). In this study, we establish measurement methods and calculations for both in-plane and through-plane oxygen diffusion coefficients. Using in-house designed cells, we measure the in-plane and through-plane oxygen apparent diffusion coefficients of a commercial carbon paper (AvCarb EP40) at various torques and gas flow rates. We also simulate oxygen flux distributions in the GDL under each torque and gas flow rate. Our results show that the channel part is the major contributor to total oxygen flux at high torque conditions and that an increase in torque leads to a decrease in the contribution from the land part. Simulation results also suggest that a higher gas flow rate and lower torque contribute to a more uniform distribution of oxygen flux in the GDL.

Dependence of dynamic resistances in high-temperature semiconducting quasi-isotropic strands on magnitude and orientation of AC magnetic field

The dynamic resistance of a superconductor appears if it carries a direct current (DC) current and is simultaneously exposed to alternative current (AC) magnetic fields if its amplitude is higher than its full penetrated field. Due to its strong anisotropy, the dynamic resistance of high-temperature superconducting (HTS) tape is not only affected by the magnitude of AC magnetic fields but also their orientations. In particular, the dynamic resistance has considerable effect on the current distribution in HTS cables (except for Roebel cables) and even cable-in-conduit conductors made from those HTS cables, except for dissipative loss. This paper presents the behavior of dynamic resistance in an HTS quasi-isotropic strand (Q-IS), which consists of four sub-stacked 2G HTS tapes proposed by our group at North China Electric Power University, while it carries a DC current and simultaneously experiences an AC magnetic field with different magnitudes and orientations. An angular dependence of dynamic resistance in a single 2G HTS tape in an AC magnetic field with various orientations is first performed in simulations and experiments, respectively. The experimental results are in good agreement with the simulated ones, which shows that the dynamic resistance of a Q-IS also exhibits quasi-isotropic characteristics and has an important effect on the distribution of DC transport current. The related results are promising for the design and application of other DC HTS cables, feeders and magnets.

Trapped magnetic field distribution above a superconducting linear Halbach array

In applications requiring a large magnetic force, permanent magnets with non-parallel magnetization directions can be assembled in a Halbach array to generate a large gradient of magnetic flux density. The saturation magnetization of permanent magnets, however, brings a fundamental limit on the performance of this configuration. In the present work, we investigate experimentally the assembly of cuboid bulk, large grain melt-textured YBa2Cu3O superconductors ( mm3) with orthogonal c-axes so as to form a basic unit of Halbach array. The experiments are carried out at 77 K. The experimental distribution of the magnetic flux density above the array of trapped-field superconductors is compared to a similar array made of permanent magnets. A simple analytical model is developed and is shown to accurately reproduce the main experimental observations. The results suggest that a redistribution occurs in the current flowing in the central sample when the distance between the superconductors is reduced, whereas the neighbouring superconductors are unaffected. It is shown that this current redistribution yields a reduced contribution of the central sample to the magnetic flux density above the centre of the array and a new negative contribution associated with stray fields to the magnetic flux density at this location. This interpretation is confirmed by modelling of the distribution of transport currents in the superconductor using a 3D finite element model.

Transport current distribution in soldered joint of BSCCO and REBCO tapes

Transport current density distribution at the solder joints of BSCCO tapes and GdBCO tapes are examined by means of scanning 3-dimensional (3D) Hall sensor. After measuring the three components, B x, B y and B z , of self field distribution near the tape induced by the transport current, the current density distribution was calculated by solving the inverse problem through matrix method implemented in the code in MATLAB environment. By using this technique, we successfully obtained the profiles for perpendicular component J z of transport current that is passing through the joint area.

A Comparative study of transport current loss in HTS coils for superconducting wireless power transfer

This paper focuses on the transport current loss modelling for HTS coated conductor coils under high-frequency AC current, which is essential when applying superconducting technology in wireless power transfer system (WPT). The pancake coil, spiral coil and solenoid coil designs were proposed, whose study were carried out based on the Finite Element Method in 2D using H-formulation. The transport current loss in each layer for each coil when applying high-frequency AC current were simulated in the FEM platform. The variation of the transport current loss distribution from different layers of the HTS coated conductor according to changing current input was simulated and compared for different operating frequencies. Finally, the frequency and current dependence of the transport current loss in different layers was shown and compared. The simulation demonstrates that the transport current loss in copper layer could be much higher than the transport current loss in the HTS layer at high current and frequency level due to the skin effect. The results also present that the pancake coil design and spiral coil design could be applied to relatively lower frequency WPT application while solenoid coil design can achieve lowest total loss in higher frequency application. These results are essential when designing HTS coils for WPT system.

Electrostatics to Electrodynamics Via an Additional Frame of Reference

There are many different methods for modeling the electric field coupled with electrolytic transport. Many mechanistic methods are based on Maxwell's equations and Gauss' law of electrostatics with added simplifications and/or assumptions. One common simplification is that the accumulation of charge density may be neglected and electroneutrality may be assumed. Another method might allow for the accumulation of charge density which may then be used as in independent variable in Poisson's equation to calculate the electric field, where Poisson's equation is developed from Gauss' law of electrostatics. One such common example is the Nernst-Planck-Poisson equation set. This research presents a method to go from electrostatics to electrodynamics using an additional frame of reference and also invoking Newton's third law, allowing the incorporation of Ohm's law into Maxwell's equations. This approach allows for the derivation of electrodynamics that may be used to model the electric field coupled with electrolytic transport. In addition, this research presents a model and results where an electrolyte transport equation is coupled with an electrodynamic equation for the electric field. This model is used to simulate a variety of phenomena including liquid-junctions and electric current distributions. Results are compared with experimental and numerical results of others. The overall model is also tested for multi-dimensional multi-component transport and electric current distributions. This model is also applied to the more complex situation of a multi-scale lithium-ion battery with different sized electrodes undergoing charging.

Simulations of Current Distribution Along a Rotating Cylinder Electrode Under Turbulent Flow Conditions and Continuous Mode of Operation

This communication deals with the simulations of turbulent flow, mass transport and tertiary current distribution on the cathode of a rotating cylinder electrode reactor (RCE) in continuous mode of operation. The electrolyte inlet was located at the bottom and the electrolyte exit at the top. Silver electrodeposition (1300 ppm Ag(I) in 23000 ppm CN− at pH 13) was employed as a model system. A 316-type stainless steel cylinder with a 3.8 cm diameter and a length of 11 cm was used as a cathode, while six Ti-IrO2 plates were used as anodes. Electrolyzes were performed at holding potential of −1.2 V SCE, which guaranteed mass transport control. The volumetric inflow rate tested was 0.1 L min− 1 giving a mean flow rate of 0.037 cm s− 1 (performed at the inter-electrode gap). The rotational speeds at the RCE surface were 100, 200, 300, 400, and 600 rpm (peripheral velocity of 10.5, 20.9, 31.4, 41.9, and 62.8 cm s− 1; Re of 7600, 15100, 22700, 30200, and 45400, respectively). It is worth mentioning that the peripheral velocities predominate in two magnitude orders over the inflow electrolyte rate. Therefore, the mass transport is determined by the electrode rotation speed.1 Simulations were obtained solving the RANS equations with the standard k−ε turbulence model. For mass transport simulations, the averaged diffusion-convection equation was solved. For the simulations of tertiary current distribution, wall functions were adapted. The current distribution along the RCE interface in the z-coordinate developed one edge effect near to the electrolyte inlet, afterwards, homogeneous current distribution was attained. The edge effect is formed by the abruptly silver concentration depletion at the electrolyte inlet. Excellent agreement between mass transport correlation and current distribution simulations with experimental data were obtained. References M. Rosales, and J.L. Nava, J. Electrochem. Soc., 164 (11), E3345 (2017).

Thickness-Dependent Current Density and Flux Distribution in Thin Current-Carrying Superconducting Films Exposed to a Magnetic Field

With the rapid development of high-temperature superconductors, it is of great significance to get the precise current density and flux distribution within thin high-temperature superconducting films subjected to a transport current and an applied magnetic field. The transport current distribution and flux density in thin high-temperature superconducting films are calculated by a numerical method based on the Kim model and exponential model in this paper. The influences of transport current, applied magnetic field, width, and thickness of a superconducting film on the current distribution are discussed. The results reveal that the thickness has a significant effect on the critical current density of superconducting films.

Stability Considerations Using a Microscopic Stability Model Applied to a 2G Thin Film Coated Superconductor

A numerical, finite element simulation of local temperature fields, critical current and transport current distributions is applied to a 2G thin film coated high-temperature superconductor. The focus is on simulation of quenches originating from transport current locally exceeding critical current density. As in previous reports, a statistical treatment of superconductor parameters (critical temperature, current and magnetic field) is applied for this analysis; it shall take into account uncertainties possibly arising from shortcomings in conductor manufacture or during measurements of their properties. The results of the calculations are used as quasi-boundary (driving) conditions for a subsequent transient microscopic numerical stability analysis. Traditionally, stability analysis usually applies analytic stability functions that incorporate conventional, phonon-related timescales, t and disturbances. The question is whether decay of electron pairs and subsequent relaxation of the excited state to a new dynamic equilibrium carrier concentration, the “electron aspect” of the stability problem, under the same disturbances, proceeds on another timescale, t ′. Is this timescale identical to the traditional (phonon) timescale, t? If not, how large are the differences? The recently reported microscopic stability model, now applied to a thin film conductor, is consulted to find an answer to these questions. A time limit, t Quench, can be extracted from the simulations, as the time of immediate onset of a quench. This is a new approach in stability considerations since, conventionally, a temperature limit, T < T Crit, is set as stability criterion. If electrical operation or cooling conditions cannot immediately respond to this challenge, the thin film superconductor, if this time limit is exceeded, will hardly be able to return to zero loss current transport.

Selective detection of AC transport current distributions in GdBCO coated conductors using low temperature scanning Hall probe microscopy

Selective detection of AC transport current distributions in GdBCO coated conductors using low temperature scanning Hall probe microscopy

Simulations of Turbulent Flow, Mass Transport, and Tertiary Current Distribution on the Cathode of a Rotating Cylinder Electrode Reactor in Continuous Operation Mode during Silver Deposition

This work presents numerical simulations of turbulent flow, mass transport and tertiary current distribution on the cathode of a rotating cylinder electrode reactor (RCE) in a continuous operation mode. A configuration of a RCE with electrolyte inlet at the bottom and the electrolyte exit at the top was employed. Silver electrodeposition (12.15 mol m−3 (1300 ppm) Ag(I), 883.5 mol m−3 (23000 ppm) CN−, pH 13 and 150 mS cm−1 conductivity) was used as a test system. Bulk electrolysis in the RCE was performed at a constant potential of − 1.2 V vs. SCE, which ensured complete mass transport control. A constant volumetric inflow rate of 0.1 L min−1 at the RCE inlet was employed. CFD simulations were obtained solving the RANS equations with the standard k − ε turbulence model. For mass transport simulations, the averaged diffusion-convection equation was solved. For the simulations of tertiary current distribution, wall functions were employed. The tertiary current distribution on the RCE interface along the z-coordinate presented one border effect close to the electrolyte inlet, afterwards, even current distribution was obtained. The border effect is created by the abruptly silver concentration depletion at the electrolyte inlet. Good agreement between mass transport correlation and current distribution simulations with experimental data were attained.

Transport Performance and Current Distribution of HTS Current Lead Prepared by YBCO Tapes

High-temperature superconducting (HTS) current lead has been prepared by the trifluoro acetates-metal organic deposition (TFA-MOD) processed YBCO tapes. The YBCO tape has higher critical current density J c and better magnetic property than the Bi2223 tape. Furthermore, the thermal conductivity of the YBCO tape with a thin Ag layer is much lower than that of the Ag-sheathed Bi2223 tape. The critical current of the YBCO tapes ranges from 150 to 180 A in liquid nitrogen and self-field. A current lead is composed of eight bundles stacked by two YBCO tapes (16 tapes), Cu end caps, and a pair of stainless-steel boards. Rogowski coils and Hall sensors used for estimation of current distribution are attached on each YBCO bundle. The transport current of 1.6 kA was carried with no voltage on every YBCO tape at 77 K. Although voltage of several tens of microvolts on some YBCO tapes appeared, transport current of 1.8 kA was successfully carried with no quenching. The voltages between the Cu cap and YBCO tapes almost linearly increased with increasing transport current, and they range from 0.75 to 0.93 mV and 1.02 to 1.21 mV at 1.8 kA, respectively. The low voltages correspond to 0.42-0.52 μΩ and 0.57-0.67 μΩ. The low contact resistance results in low joule heating at Cu joints. The current calculated by Rogowski coils in eight bundles varies from 137 to 355 A at 1.8 kA and sweep rate of 800 A/s. Therefore, the imbalance among eight bundles is evaluated to be 218 A. The current of eight bundles calculated by Rogowski coils sums up to 1808 A, which is the slight difference of 8 A in comparison with transport current of 1800 A. Rogowski coils and Hall sensors are effective at evaluating of current distribution for current lead.

Observation of self-magnetic field relaxations in Bi2223 and Y123 HTS tapes after over-current pulse and DC current operation

The development of power transmission lines based on long-length HTS tapes requires the production of high quality tapes. Due to fault conditions, technical mistakes and human errors during the operation of a DC power transmission line, an over-current pulse, several times larger than the rated current, could occur. To study the effect of such over-current pulses on the transport current density distribution in the HTS tapes, we simulated two start-up scenarios for one BSCCO and two YBCO tapes. The first start-up scenario is an initial over-current pulse during which the transport current was turned on rapidly, rising to 900A during the first milliseconds, then reduced to a 100A DC current. The second start-up scenario is normal operation, and involved increasing the transport current slowly from 0A to 100A at a rate of 1A/s. For both scenarios, we then measured the vertical component of the self-magnetic field by means of a Hall probe above the tape, and afterward, by solving a linear equation of the inverse problem we obtain the current density profiles. We observe a change of the self-magnetic field above the edge of the BSCCO and YBCO tapes during 30min after the 5ms of over-current pulse and during the normal operation. The current density profiles are peaked in the centre for over-current pulse, and more peaked around the edge of the HTS tape for normal operation, which means that the limited time over-current pulse changes the current density profiles of the HTS tapes. We observe also a loop of current for YBCO tapes and we show the role of the HTS tape stabilizer.

TFA-MOD 法 YBCO 線材を用いた超伝導電流リードの通電特性と電流分布の評価

TFA-MOD 法 YBCO 線材を用いた超伝導電流リードの通電特性と電流分布の評価

Analysis of Current Distribution in Bi-2223/Ag Insert Pancake Coil

A Bi-2223/Ag insert was fabricated to assemble a high field superconducting magnet. The insert consists of 17 double pancakes, with turn to turn and layer to layer insulations. To get the current distribution in each turn of the pancake coil, a numerical method of magnetization in a thin film derived from E.Zeldov was employed. To improve the calculation accuracy, we add the I C data tested from the experiments into the code directly. In the calculation, we take several different cases into account, such as High Field-Low Current (HFLC) case, Low Field-High Current (LFHC) case, which will have an effect on the current distributions. The overall process is divided into three sections: Firstly, we calculate the nonuniform but symmetrical transport current distributions through the transport current model. Secondly, the non-uniform and asymmetrical transport current distributions is recalculated through the magnetic field and transport current model. Thirdly, the screening current distributions are calculated after the coil is discharged.

Modeling the effect of non-ideal flow pattern on tertiary current distribution in a filter-press-type electrochemical reactor for copper recovery

This work presents the numerical modeling of the effect of hydrodynamics on mass transport and tertiary current and potential distribution in a filter press type electrochemical reactor used to study the copper recovery process. The operating conditions of the reactor were in turbulent regime and under charge and mass transfer mixed control.For hydrodynamics, the Reynolds averaged Navier–Stokes equations and the standard k–ɛ turbulence model were used. The mass transfer model was a combination of the convection–diffusion equation and a wall function adapted for mass transfer. The Butler–Volmer kinetics for copper reduction, simplified Tafel equations for water oxidation and ohmic potential drop through the electrolyte were also incorporated into the model. The strategic part of the proposed numerical modeling is the concentration wall function that allows linking the transport equations with Cu2+ concentration at the interface in order to obtain, along with interfacial potential, the electrode kinetics. Using this approach it was possible to model a very complex interrelation between physical phenomena and the electrochemical reaction taking place in a reactor under a turbulent flow regime using moderate computer resources. The numerical results obtained are in agreement with experimental data of mass transfer coefficient and current–potential behavior.

Analysis of Tertiary Current Distribution Modeling in a Turbulent Flow inside Parallel-Plate Electrochemical Reactor Used for Copper Recovery

The effect of hydrodynamics and electrical field on the performance of electrochemical cells is a central issue in electrochemical reactor engineering. This work presents an approach for such issue by modeling the effect of hydrodynamics on the mass transport and tertiary current and potential distribution in a parallel-plate electrochemical reactor used to study the copper recovery process. The operating conditions of the reactor were in turbulent regime and under charge and mass transfer mixed control. For hydrodynamics, the Reynolds averaged Navier–Stokes (RANS) equations, the standard k–ε turbulence model and wall functions were used. The mass transfer model was a combination of the convection–diffusion equation and a wall function adapted for mass transfer. The Butler-Volmer kinetics for copper reduction and simplified Tafel equations for water oxidation were also included in the model. The electrical continuity equation was used for evaluating the ohmic potential drop. An important part of the proposed numerical modeling is the concentration wall function that allows linking the transport equations with Cu2+ concentration at the interface in order to obtain, along with interfacial potential, the electrode kinetics. Using this approach it was possible to model a very complex interrelation between physical phenomena and the electrochemical reaction taking place in a reactor under a turbulent flow regime using moderate computer resources. The numerical results obtained are in agreement with experimental data of mass transfer coefficient and current-potential behavior. Fig 1 illustrate the effect of the velocity field on the overpotential distribution over the cathode.

Modelling of Effect of Non-Uniform Current Density on the Performance of Soluble Lead Redox Flow Batteries

Soluble lead acid redox flow battery (SLRFB) offers a number of advantages. These advantages can be harnessed after problems associated with buildup of active material on electrodes (residue) are resolved. A mathematical model is developed to understand residue formation in SLRFB. The model incorporates fluid flow, ion transport, electrode reactions, and non-uniform current distribution on electrode surfaces. A number of limiting cases are studied to conclude that ion transport and electrode reaction on anode simultaneously control battery performance. The model fits the reported cell voltage vs. time profiles very well. During the discharge cycle, the model predicts complete dissolution of deposited material from trailing edge side of the electrodes. With time, the active surface area of electrodes decreases rapidly. The corresponding increase in current density leads to precipitous decrease in cell potential before all the deposited material is dissolved. The successive charge-discharge cycles add to the residue. The model correctly captures the marginal effect of flow rate on cell voltage profiles, and identifies flow rate and flow direction as new variables for controlling residue buildup. Simulations carried out with alternating flow direction and a SLRFB with cylindrical electrodes show improved performance with respect to energy efficiency and residue buildup.