Non-uniform Current Density Distribution Research Articles

Influence of the Skin and Proximity Effects on the Thermal Field in Flat and Trefoil Three-Phase Systems with Round Conductors

The passage of current generates heat and increases the temperature of electrical components, which affects the environment, support insulators and contacts. Knowledge of the temperature allows for the determination of important operational parameters. Time-varying currents result in a nonuniform current density distribution due to the skin and proximity effects. As a result, temperature and energy losses are increased compared to the uniform DC current density case. In this paper, these effects are considered for three-phase systems with round conductors in flat and trefoil arrangements. In the first step, the analytical expressions for current distributions are determined and used to construct the heat source density. Then, a suitable Green’s function, which allows for obtaining temperature distribution in analytical form, is used to evaluate temperature at any point throughout the conductors. The temperature differences throughout individual wires are usually negligible, whereas noticeable differences can be observed between the wires. The impact of various parameters is examined, and an approximate closed formula is derived to assess the influence of the skin and proximity effects. When the skin depth is not smaller than the wire radius, the skin effect enlarges the temperature increase by around 2% compared to the DC case. As for the proximity effect, the additional increase can be neglected if the distance is above around 10 wire radii, but for closely spaced wires, it can reach up to around 17%, depending on the arrangement and the distance between the wires. Such an additional increase may result in exceeding the permissible temperatures, which damages particular components of the system; therefore, it is important to take it into account at the design stage.

Numerical investigation of parameter distributions in high-temperature PEMFCs under various cooling surface temperature gradients

Non-uniform current density distribution can lead to localized hotspots, resulting in shortened lifespans of fuel cells. The temperature distributions on the bipolar plate cooling surface significantly influence various parameters within a fuel cell. This study develops a mathematical model for a high-temperature proton exchange membrane fuel cell (HT-PEMFC) to simulate its operation in four different directions of temperature gradient on the cooling surface. The distributions of membrane temperature, proton conductivity, oxygen concentration, activation loss, and current density were obtained to clarify the interaction mechanism between cooling surface temperature and these parameters in fuel cell. The results show that the membrane temperature and proton conductivity increase and the oxygen concentrations decrease with increasing cooling surface temperature. A lower temperature in the catalyst layer regions leads to a decrease in the current density. In particular, when the cooling surface temperature distribution is characterized by a temperature decrease in the upstream area with a high reactant concentration and an increase in the downstream area with a low reactant concentration, the fuel cell has an excellent current density uniformity, which reaches 92.61 % at a voltage of 0.6 V and a cooling surface temperature difference of 10 K.

Corrosion of Passive Aluminum Anodes in a Chloroaluminate Deep Eutectic Solvent for Secondary Batteries: The Bad, the Good, and the Ugly.

The passivity of aluminum is detrimental to its performance as an anode in batteries. Soaking of native oxide-covered aluminum in a chloroaluminate deep eutectic solvent gradually activates the electrode surface, which is reflected in a continuously decreasing open circuit potential. The underlying processes were studied by analyzing the 3 to 7 nm thick layer of native oxide after increasing periods of soaking with secondary neutral mass spectrometry, X-ray photoelectron spectroscopy, and energy-dispersive spectroscopy in a transmission electron microscope. They consistently show permeation of electrolyte species into the layer associated with gradual swelling. After extended periods of soaking at open circuit potentials, local deposits of a range of foreign metals have been found in scanning electron microscopy images of the electrode surface. The pitting corrosion is caused by trace metal ion impurities present in the electrolyte and results in highly nonuniform current density distribution during discharge/charge cycling of battery cells as shown by local deposits of aluminum. The processes during soaking at open circuit potentials have been monitored by electrochemical impedance spectroscopy and could be analyzed by fitting an equivalent circuit model for pitting corrosion.

Study of Beam–Wave Interaction in a Sub-THz Traveling Wave Tube with a Converging Sheet Electron Beam Focused by a Uniform Magnetic Field

A traveling-wave tube (TWT) with a sheet electron beam and staggered double-grating slow-wave structure (SWS) is a promising high-power, wideband terahertz amplifier. In such tubes, electron-optical systems (EOSs) with a converging sheet beam are mostly used, which allow a reduction of the cathode load, increase the lifetime, and enable operation in a continuous-wave (CW) mode. This paper presents the results of a 3D particle-in-cell (PIC) simulation of the 0.22 THz TWT driven with a converged sheet beam, which is compressed to less than 100 μm thickness in the EOS with a magnetically shielded cathode. The beam with high compression has a significant transversal velocity spread and essentially non-uniform current density distribution over the cross-section. These factors significantly affect the beam–wave interaction. We compare the performance of the TWT driven by the compressed sheet beam and by an idealized initially rectilinear beam without any velocity spread.

Development of a Quantitative and Predictive Model for Electrodeposition of Metals and Alloys with Experimental Verifications

Electrodeposition is widely used in the refinery, manufacture, and coating of metals and alloys. Electrodeposition is a complicated process with many factors, such as deposition potential, current density, electrolyte composition and concentration, convection, additives, and temperature, can have significant impacts on the phase composition, morphology, and particle size of the deposited metals/alloys, thus consequentially impacting the physical and chemical properties of the deposited parts. In the past, a recipe for a particular metal/alloy electrodeposition is commonly established through trial-and-error tests, which is very time consuming. Here we report our recent efforts trying to build a quantitative and predictive model based on ex situ and in situ experimental characterizations of electrodeposition processes.To build the model, we chose copper as the model material for electrodeposition. A few electrochemical cells which have different geometries and dimensions and provide non-uniform current density distributions were designed and used. Through variation of the electrode placement and cell geometry, the current density distribution on the working electrode in the electrodeposition process can be tuned. The amount and growth rate of the deposited Cu layer in various electrochemical cells and under different deposition conditions (such as different potential, electrolyte concentration or physical location) were experimentally measured with using carefully calibrated and normalized X-ray diffraction (XRD) data. A multi-physics multi-scale model was developed to quantify the distribution of the current density and the growth rate of deposited Cu at different locations. The experimentally measured data was used to verify and improve the model. The results showed that the model can accurately predict the distribution of the current density with given nominal deposition potential or current, and thus predict the growth rate of the deposited Cu phase.The success of this model offers hopes to rationally design the deposition of metals and alloys to replace conventional trial-and-error method. The impact of different deposition substrates, additives, electrolyte concentrations will also be discussed. Proof-of-concept experiments also demonstrated that this rational design method can be applied to the design of electrodeposition of alloys, offering a much broader range of potential applications.

Electric current and magnetization distributions’ self-organization features in a magnetoresistive film nanoelement under the influence of an external magnetic field

The new generalized Laplace’s equation for an electric potential is presented, which in the general case, is nonlinear for media with resistance anisotropy caused by the anisotropic magnetoresistance (AMR) effect and determined by the orientation of the magnetization vector relative to the current density vector at an arbitrary point of the sample. The solution to this equation is obtained for an anisotropic medium with a non-uniform distribution of current density and magnetization in the case of an oblique-shaped plate of nanoscale thickness. In addition, the analytical solution was obtained for the current density distribution in such a medium using conformal mapping, which confirms the numerical solution in the case of an isotropic conductor. An analysis of the results showed that the presence of the AMR effect leads to a significant change in the current density distribution in the sample compared to the isotropic case, which is expressed in the deviation of the current density vector in perpendicular to the magnetization vector direction in the plate. It has been established that the presence of an external magnetic field in the film plane, which leads to the emergence of an inhomogeneous magnetization distribution, entails self-organization of the electric current distribution. The graphs of the plate resistance as a function of applied magnetic field demonstrate asymmetry for the cases of the direct and reverse directions of the external magnetic field, which cannot be obtained within the framework of simplified models of current flow in media with the AMR effect.

Analysis of light – current characteristics of high-power semiconductor lasers (1060 nm) in a steady-state 2D model

This paper presents a 2D model of a high-power semiconductor laser, which takes into account carrier transport across the layers of its heterostructure and longitudinal spatial hole burning (LSHB), an effect related to the nonuniform gain distribution along the cavity axis. We show that the use of the 2D model which takes into account carrier transport across the layers of the heterostructure allows an appreciable contribution of LSHB to saturation of light – current characteristics to be demonstrated. The LSHB effect, causing a decrease in the output optical power of semiconductor lasers, is shown to be stronger at high drive currents and low output mirror reflectivities. In the case of high drive currents, the LSHB-induced drop in power is related to the faster growth of internal optical and recombination losses because of the nonuniform current density distribution along the cavity axis, such that the highest current density can be almost twice the lowest one. LSHB is shown to increase the power stored in a Fabry – Perot cavity, which is an additional mechanism reducing the output optical power.

Numerical simulation analysis of the performance on the PEMFC with a new flow field designed based on constructal-theory

The design of the flow field structure has an important impact on the performance of PEMFC. An excellent design of the flow field will optimize the gas-liquid distribution inside the fuel cell, and enhance the diffusion of the reactant gases while reducing problems such as water flooding or uneven mass transfer of reactants, thus improving the overall performance of the cell. A new form of flow field based on the design ideas of Constructal-theory and Murray's Law was proposed in this paper. In this study, the PEMFC with the new and conventional flow fields were compared under the same conditions, and it is proved that the cell with the new flow field has a more balanced performance on output power and global pressure drop in contrast with conventional flow fields. In this study, the output power density of the PEMFC with the new flow field increased by an average of 1.35% compared to the PEMFC with Parallel flow field and Single Channel Serpentine flow field, and the pressure drop was reduced by 47.67% and 90.06% respectively compared to the PEMFC with the Single Channel Serpentine flow field and Double Channel Serpentine flow field. Meanwhile, the distribution of current density characteristics in a PEMFC with the new flow field was investigated and optimization of its structure size is analyzed. The reason for its non-uniform distribution of current density was revealed in this study, and an improvement scheme was proposed to improve the uniformity of current density, and the results of structural optimization research will have a certain guiding effect on practical applications.

Unraveling the mechanism of non-uniform zinc deposition in rechargeable zinc-based batteries with vertical orientation

• The non-uniform zinc deposition in the vertical direction is investigated. • Optical observations and stripping/platting model are combined in this work. • The non-uniform deposited zinc is started by nucleation site fracture. • The inhomogeneity is exacerbated by the non-uniform current and hydrogen evolution. Secondary zinc-based batteries demonstrate a bright prospect as a candidate for next-generation electrochemical energy storage devices. However, the inhomogeneous zinc deposition with vertical orientation during electrochemical stripping/platting cycles leads to battery failure quickly and thereby limits commercial applications of zinc-based batteries. In this work, the deposited electrochemical reaction is deeply investigated and the mechanism of inhomogeneous electrochemical deposition is proposed via in-situ optical observation and numerical analysis. During the deposited reaction, zinc atoms prefer to deposit on the nucleation sites on the electrode surface, changing the morphology of nucleation sites and leading to possible fractures. The fractural zinc fragments then accumulate at the bottom and connect to the bulk electrode, which initiate the inhomogeneous distribution in the vertical direction where the protrusion appears at the bottom, and the middle and top parts have rare deposited zinc. The inhomogeneity is exacerbated during stripping/platting reaction cycles due to the non-uniform local current density distribution on the emerging protrusion. Besides, the generated bubbles caused by hydrogen evolution exacerbate the inhomogeneous distribution via changing the ion distribution. Based on the conclusions, a uniform deposition behavior is achieved via modulating the ion distribution by the flowing electrolyte as a demonstration. The unraveled mechanisms can serve as a reference for the design of advanced zinc-based batteries with stable electrodes.

Coupled Finite Element and Extended-QD Circuit Induction Machine Model, Part I: Formulation

The design of squirrel-cage induction motors (IMs) entails the capability to predict the motor efficiency map with high accuracy over an operating range. In particular, modeling harmonic rotor bar currents becomes important for loss analysis. In theory, it is possible to analyze an induction motor using time-stepping finite element analysis (TS-FEA); however, this is not viable due to computational limitations. To bridge this gap, we set forth a computationally efficient method that couples magnetostatic FEA with a qd-circuit model of the cage. The proposed IM model includes the effects of saturation, winding and slot harmonics, as well as nonuniform current density distribution in the rotor bars. The model is presented in two parts. Part I focuses on the formulation of a qd cage circuit model with segmented bars. Part II is a companion paper that proposes an FEA-based parameter estimation and a solution method.

A pluggable current collector for in-operando current measurements in all-vanadium redox flow batteries with flow field

Understanding current distribution in operating Vanadium redox flow batteries (VRFBs) is vital for improving battery design and performance as the non-uniform current density distribution is known as a major cause of the corrosion and side reactions in VRFBs. However, the existing method for current density measurement in the VRFB with flow field is complex and the rib conductive structure of graphite plate is changed which reduces the measurement accuracy and reliability. In this study, we propose a novel pluggable current collector for in-operando current distribution measurements which greatly simplifies the current density distribution measurement process in VRFBs with flow field. The new method relies on eight pluggable graphite units in a flow plate frame to replicate the actual serpentine flow field structure, thereby providing higher measurement reliability compared to the existing methods which are mostly invasive. Using the new method, current density distributions at different electrode compression ratios (CR) and inflow electrolyte rates are investigated. It is found that insufficient supplemental reactant in electrode border region is the main reason for the uneven current density distribution and the current density non-uniformity is intensified in the initial and final stages of cycling process. Increasing CR can improve the current density in the electrode core region. The overall current density uniformity in a VRFB with serpentine flow field can be enhanced by increasing the inflow electrolyte rate. The developed method is believed to facilitate the understanding of the coupled local reactions and transport processes and guide on the future design of VRFBs.

Numerical analysis of temperature and current distributions in large-size intrinsic Josephson junctions with self-heating

In this study, we focused on temperature and current distributions in voltage-state large-size intrinsic Josephson junction (IJJ) mesas with a self-heating effect. Because it is difficult to experimentally obtain temperature and current distributions in IJJ mesas, we numerically computed these distributions by solving non-linear diffusion and temperature dependence circuit equations. The local temperature in the mesa exceeded the critical temperature, and a normal-state appeared in the high bias region. Non-uniform temperature and current density distributions were obtained for each bias point of the current–voltage (I–V) characteristics. Normalized c-axis current distributions decreased with an increase in the bias current in the high bias regions. These results were explained using temperature dependent c-axis resistivity.

Current density distribution in air-breathing microfluidic fuel cells with an array of graphite rod anodes

Scale-up is required in the practical application of microfluidic fuel cells. Using an array of electrodes is demonstrated as a promising way. However, the non-uniform current density distribution in array anodes will significantly limit the power output. In this study, current density distribution in air-breathing microfluidic fuel cells with an array of graphite rod anodes is tested under acidic and alkaline conditions. The array anode is divided into four layers according to their distance to cathode. Current density of each layer is recorded individually. The cell performance under alkaline media is better than that under acidic media and various current density distributions are found under different media. When the air-breathing microfluidic fuel cell is operated under acidic media, at current densities lower than 50 mA cm−3, current densities of two-layer anodes far from the cathode are higher than that of the other layers, while the reverse happens at current densities higher than 50 mA cm−3. This is mainly due to the enhanced fuel transport caused by CO2 bubbles and the lower ohmic resistance. Moreover, the generated CO2 bubbles lead to fluctuation of discharging densities especially at low voltages. However, for the air-breathing microfluidic fuel cell operated under alkaline media, two-layer anodes far from the cathode are main contributor to the total current density at all operation voltages.

Mechanism of Butterfly-Shaped Failure Interface Between Armature and Rails

A large amount of experimental data indicates that a typical butterfly-shaped failure interface will appear in the recovered armature. In order to reveal the mechanisms and their influence on transition, an electromagnetic-thermal-mechanical coupling analysis is carried out on the C type armature and the rectangular section rails. The contact properties subjected to both pretightening force and Lorentz force, transient temperature field, and variation of Lorentz body force density on the interface of armature and rails are discussed by using the 3-D finite method. The results show that the nonuniform distribution of current density, heat flux, and Lorentz force density, which is caused by the pulse current, is the main cause of the butterfly-shaped failure interface.

Multiphysics simulation of added carbon particles within fluidized bed anode zinc-electrode

Batteries will continue to encounter the problem of dendrite formation until a suitable solution is identified to address the problem. Dendrite formation can short circuit batteries cells, reduce their life span, voltages and cause mechanical abrasion to the cells. Batteries electrodes are part of the approaches that can be used to address these problems but depending on the fabrication of these electrodes and dimensions. Before fabricating and incorporating a real anode reactor to a fabricated ZnBr2 cell system, it was necessary to model the behaviour with injected carbon particles in between 254 microns to 354 microns and simulate the geometry in COMSOL to observe their interaction with the electrolyte. This study investigates the performances of a designed anode reactor and to observe within the reactor the effect of having a uniform and non-uniform current density distribution before the fabrication, physically charge and incorporating it to the anode-side of ZnBr2 cell system.

Investigation of the non-uniform distribution of current density in commercial-size proton exchange membrane fuel cells

It is necessary to obtain the current density distribution in order to understand local reactions inside the proton exchange membrane (PEM) fuel cells. Enlarging the active area to commercial-size makes it difficult to maintain uniform assembly pressure, gas supply and heat dissipation inside the fuel cell stack. Existing studies for laboratory-level fuel cells cannot effectively guide the development of large-area fuel cells. In this study, current density distribution inside a 250 cm2 and 3 kW level fuel cell stack is measured and analyzed using the printed circuit board (PCB) technology. A four-layer PCB sensor plate covering 144 current collecting segments and shunt resistors for current measurement is well-designed. The in-house developed measurement system is proved with good function, and the accuracy of current density measurement is within 2%. Results show that the flow field configuration and stack assembly condition greatly affects the uniformity of local current densities. Higher current passes through the area with larger contact pressure, and the current density is low in the poor contact area. The local current density has larger deviations for higher output current, but the normalized current is more uniform. Effects of operating conditions including stoichiometric ratio and flow direction are investigated.

A Phenomenological Model of Resistance Spot Welding on Liquid Metal Embrittlement Severity Using Dynamic Resistance Measurement

Abstract Liquid metal embrittlement (LME) is one of the severe problems of Zn-coated steel in resistance spot welding (RSW). Hence, proper welding schedules for Zn-coated steel are of practical interest. RSW involves a complex interaction between electrical, thermal, and mechanical phenomena. Identification and integration of all these governing physics are almost impossible by performing simple experiments. Hence, phenomenological modeling of RSW has gained a significant attention in the recent past. The complexity of the physical process introduced by the dynamic nature of contact resistance brings challenges for the model. A simplified but effective modeling approach of RSW is proposed where attention is focused on the evaluation of the thermal field using the finite element (FE) method. The interaction of the mechanical and electrical field is performed by the dynamic variation of the contact area, stress concentration, and non-uniform current density distribution in a semi-analytical model. These internal variables of the model are incorporated through the scaling of the governing parameters by the dependence of the transient and converged temperature field within a time step. The transient-dynamic contact resistance is detached from the measurement of total resistance and mapped adaptively by the implicit scheme within a time step of the numerical model. The transient development of the nugget is investigated for dual-phase steel (DP980) with an interrupted test of the dynamic resistance curve. The FE model is validated with experimentally measured results at different process conditions. The characterization of the thermal history from the model relatively identifies the LME phenomena and suggests corresponding modification of the welding schedule.

Three-dimensional simulation of a new cooling strategy for proton exchange membrane fuel cell stack using a non-isothermal multiphase model

In this study, a new cooling strategy for a proton exchange membrane (PEM) fuel cell stack is investigated using a three-dimensional (3D) multiphase non-isothermal model. The new cooling strategy follows that of the Honda’s Clarity design and further extends to a cooling unit every five cells in stacks. The stack consists of 5 fuel cells sharing the inlet and outlet manifolds for reactant gas flows. Each cell has 7-path serpentine flow fields with a counter-flow configuration arranged for hydrogen and air streams. The coolant flow fields are set at the two sides of the stack and are simplified as the convective heat transfer thermal boundary conditions. This study also compares two thermal boundary conditions, namely limited and infinite coolant flow rates, and their impacts on the distributions of oxygen, liquid water, current density and membrane hydration. The difference of local temperature between these two cooling conditions is as much as 6.9 K in the 5-cell stack, while it is only 1.7 K in a single cell. In addition, the increased vapor concentration at high temperature (and hence water saturation pressure) dilutes the oxygen content in the air flow, reducing local oxygen concentration. The higher temperature in the stack also causes low membrane hydration, and consequently poor cell performance and non-uniform current density distribution, as disclosed by the simulation. The work indicates the new cooling strategy can be optimized by increasing the heat transfer coefficient between the stack and coolant to mitigate local overheating and cell performance reduction.

The Interplay of Electrode Heterogeneity, SEI Growth, and Li Plating in Li-Ion Batteries

Newman-type or macrohomogeneous cell models have had a significant contribution toward designing and optimizing Li-ion batteries. In order to lower the computational cost and accommodate limited experimental information, this model assumes that battery electrodes are functionally homogenous. However, this assumption can be far from reality even for commercial-quality electrodes, due to variability in microstructure that arises during the manufacturing process. Previous work in our group showed that electrode heterogeneity can lead to non-uniform distribution of current density, positive and negative electrode states of charge, and charge/discharge capacities [1]. Consequently, heterogeneity can cause faster degradation of materials, prevent maximum utilization of active materials, and even lead to catastrophic failure of the cell. Among the different modes of cell aging, solid electrolyte interphase (SEI) growth and Li plating are considered mainly responsible for capacity fade due to loss of active Li. In this study, we will discuss how electrode heterogeneity can lead to non-uniform SEI growth and Li plating, and how the growth of this resistant layer affects the level of heterogeneity, performance, and lifetime of the cell. To better understand the interplay of the electrode’s heterogeneity and cell aging, we use a combination of a Newman-type model and an equivalent-circuit model for an NMC cathode and graphite anode. The equivalent-circuit model consists of three parallel resistances, each represent high, medium, and low conductivity regions in an electrode film. This research was funded by the BMR program of the US Department of Energy. [1] Forouzan et al., J. Electrochem. Soc. 165, A2127-A2144 (2018).

In Situ Current Distribution Measurements in C-Shaped Armatures

The knowledge of the current density distribution in C-shaped armatures during a railgun experiment can be of crucial importance in the understanding of transition mechanisms and optimization of the electrical contact between rails and armature. That is why we applied during single-shot experiments with C-shaped armatures the measurement technique described, in order to deduce the spatial and temporal current density distribution of C-shaped armatures during the experiment. Based on our experimental results, we observe nonuniform current density distributions in the armature, including areas with high current densities and very low current densities. We compare our findings with the state of the post shot rail surfaces and to strengthen our interpretation we performed 3-D simulations using the COMSOL Multiphysics program.