Inhomogeneous Current Density Research Articles

Modeling the Effect of Cell Orientation on the Performance of an Air-Breathing Polymer Electrolyte Fuel Cell with a Columnar Cathode Plate

Air-breathing polymer electrolyte fuel cells (PEMFCs) are expected to play an important role in the development of sustainable portable and mobile devices, such as unnamed aerial vehicles, motorbikes or laptops. In this work, the performance of air-breathing PEMFCs with a columnar cathode plate design is examined by means of a 3D two-phase, non-isothermal model, and compared against experimental data. The results show that the performance is highly influenced by the cell orientation, namely horizontal (material plane perpendicular to gravity) versus vertical (material plane parallel to gravity). Oxygen transport in horizontal cells is mainly dominated by diffusion, leading to oxygen shortage toward the cell center and an inhomogeneous current density distribution. In contrast, oxygen transport in vertical cells is assisted by natural convection, enhancing oxygen transport throughout the cell and increasing the current density homogeneity. Water saturation is preferentially accumulated close to the cell center, being larger in horizontal cells due to the lower water removal rate of the cathode plate.

Modeling the Effect of Cell Orientation on the Performance of an Air-Breathing Polymer Electrolyte Fuel Cell with a Columnar Cathode Plate

Air-breathing polymer electrolyte fuel cells (PEMFCs) are expected to play an important role in the development of sustainable portable and mobile devices, such as unnamed aerial vehicles, motorbikes or laptops. In this work, the performance of air-breathing PEMFCs with a columnar cathode plate design is examined by means of a 3D two-phase, non-isothermal model, and compared against experimental data. The results show that the performance is highly influenced by the cell orientation, namely horizontal (material plane perpendicular to gravity) versus vertical (material plane parallel to gravity). Oxygen transport in horizontal cells is mainly dominated by diffusion, leading to oxygen shortage toward the cell center and an inhomogeneous current density distribution. In contrast, oxygen transport in vertical cells is assisted by natural convection, enhancing oxygen transport throughout the cell and increasing the current density homogeneity. Water saturation is preferentially accumulated close to the cell center, being larger in horizontal cells due to the lower water removal rate of the cathode plate.

Gradient catalyst layer design towards current density homogenization in PEM water electrolyzer with serpentine flow field

The inhomogeneous current density distribution might cause irreversible damage to the membrane electrode assemblies of proton exchange membrane water electrolyzers. Herein, the impact of gradient catalyst distribution on the current density uniformity inside the electrolyzer with serpentine flow field is investigated using a three-dimensional model. The gradient catalyst distribution in parallel and vertical flow directions is considered. It is found that, at low working voltage (1.8 V), gradient catalyst loading in the vertical flow direction would enhance the current density distribution uniformity by 77.6 %, and at the same time improve the electrolyzer performance by up to 4.0 %, whereas in parallel flow direction the corresponding improvement is by 34.5 % and 4.17 %, respectively. At high working voltage of 2.4 V, due to the pronounced impact of mass transportation process, similar and limited improvement in the current density uniformity (11.47–11.87 %) and electrolyzer performance (1.3–1.45 %) is found under the gradient catalyst loading design in both flow directions. This study provides important guidance for the design of proton exchange membrane water electrolyzer using serpentine flow field.

Magnetic field dependence of critical currents of cross-type Josephson junctions with inhomogeneous critical current density under oblique magnetic fields

Abstract Studies of the magnetic interference of sandwich-type Josephson junctions in which perpendicular or oblique magnetic fields are applied to the junction plane have received less attention than those where the applied magnetic fields are parallel. Recently, it has been theoretically demonstrated that a variety of magnetic interferences of the critical currents appear when oblique magnetic fields are applied to a cross-type junction with homogeneous critical current density. We theoretically investigated the effect of the inhomogeneous critical current density in the junction plane, and found that more complicated magnetic interferences appeared. We considered the distribution of the current density flowing through the junction plane to explore the cause of these complex magnetic interferences.

Electromechanical behavior of a rectangular bulk superconductor with an inhomogeneous critical current density under pulsed-field magnetization

Bulk high-temperature superconductors are widely used in various superconducting devices for their high critical current density and the ability to trap large magnetic field. In some applications, bulk superconductors can be arranged in an array structure to increase the magnetic field strength. However, rectangular bulk superconductors can be arranged more compactly than commonly used cylindrical bulk superconductors. The unique shape of rectangular bulk superconductors results in different distributions of electromagnetic fields, temperature, and stress under a pulsed-field magnetization (PFM) than for cylindrical bulk superconductors. In bulk superconductors, growth sector boundaries and growth sector regions have different critical current density, resulting in an uneven critical current density. Therefore, in this study, the electromagnetic and mechanical behavior of non-uniform rectangular bulk superconductors during the PFM process is investigated. The corresponding distribution and variation in the magnetic field, current, temperature, and stress in the bulk are calculated and analyzed. The influence of rectangle aspect ratio on the electromagnetic and mechanical behavior is discussed. The calculation results show that the magnetic flux jumps occur accompanied by sudden changes in the temperature and pressure. The effect of the aspect ratio of rectangular bulk superconductors on their electromagnetic and mechanical properties is analyzed. The influence of preexisting cracks in a non-uniform rectangular bulk superconductor on the simulation results is discussed. The numerical results indicate that the presence of an edge crack exacerbates the magnetic flux jump as well as the jumps in the temperature and stress. However, a central crack has a relatively small effect on the stability of a bulk superconductor.

Flux jump and mechanical response in inhomogeneous high-temperature superconductor under the pulsed-field magnetization

The high-temperature bulk superconductors with high critical current density are brittle, and can be damaged by large Lorentz forces and thermal stress during magnetization. Several studies have reported the failure of bulk superconductors during flux jumps. In this study, we analyzed the magnetization characteristics and mechanical response of the HTS bulk with inhomogeneous current density along the c-axis. The numerical simulation was consistent with the experimental results presented in the reference. Moreover, a flux jump occurred near the area of the pre-arrangement flux during the second pulsed field magnetization. The maximum temperature is lower than the critical temperature during the flux jump. In the mechanical analysis, the flux jump led to an abrupt change in the maximum stress of the bulk, and the maximum radial stress was significantly higher than the maximum hoop stress during the flux jump. The maximum radial stress increased with decreasing ambient temperature during the flux jump, and the maximum stress area was always near the seeded plane. Subsequently, the magnetization characteristics and mechanical response were studied for different locations of the seeded surface, two concentric superconducting bulks, and non-uniform fields.

Current redistribution during inhomogeneous quench of 2G HTS tapes

Inhomogeneous temperature elevations, also called hot spots, occurring in second generation high-temperature superconductor (2G HTS) tapes may lead to their destruction. A better understanding of inhomogeneous quenches would contribute to develop strategies to better protect superconducting devices based on 2G HTS tapes against hot spots. To do so, we investigated the current redistribution around a dissipative zone in a 2G HTS tape with a combination of experiments and numerical simulations based on the finite element method (FEM). Firstly, the inhomogeneous heat generation in a commercial 2G HTS bare tape (without copper cladding) was observed through the visualization of bubble generation. Secondly, the current redistribution around a dissipative zone in commercial 2G HTS bare tapes from two different manufacturers was investigated using voltage taps on both sides of the tape. The measured voltages showed that the current redistribution around the dissipative area in the top stabilizer layer of the tape is different from that in the bottom stabilizer layer. Using a 3D electro-thermal FEM model, we reproduced these behaviors, assuming a HTS tape architecture with an inhomogeneous local critical current density. Finally, using the same FEM model, we explored the impact of a lack of silver on one lateral side of a 2G HTS tape. Our results indicate that such a lack of silver does not critically affect the quench dynamics.

Spatially Resolved Deconvolution of Loss Processes in PEM Fuel Cells

The complex operating behaviour of PEM Fuel Cells is heavily influenced by different non-linear loss processes, which limit the cell performance. Depending on the operating conditions, the different losses change in magnitude and characteristic time constants [1]. During technical operation of large-sized PEM Fuel Cells, gradients in operating conditions occur along the gas channels, resulting in an inhomogeneous current density distribution. This is caused by the locally varying electrochemical activity due to in-plane gradients in concentrations of reactants and reaction products, gas pressure and temperature. Consequently, each loss process occurs locally distributed to a varying degree. Therefore, a profound knowledge about the spatial distribution of losses is essential for optimizing the operating strategy as well as the cell and stack components.The commonly measured I/V characteristics provide only integral information about the overall performance. Thus, the data obtained represent merely the sum of all loss processes averaged over the entire cell area and do not allow detailed conclusions about the respective spatial distribution along the channel.Inevitably, in order to deconvolute the loss processes in the entire area of large sized cells, an approach is required that provides deeper insight in the processes and their interdependencies. For this purpose, an impedance-based methodology is developed that enables a spatially resolved deconvolution of loss processes. It is based on electrochemical impedance spectroscopy (EIS) and an impedance data analysis by the distribution of relaxation times (DRT) [2,3] that is applied to a segmented cell [4] with almost gradient-free segments. By systematically varying operating conditions the different loss processes are identified, quantified and separated with respect to their characteristic frequencies.In this contribution the design of the test bench and the segmented cell will be presented. Furthermore, first results regarding the electrochemical characterization and the impedance-based deconvolution of loss processes in a segmented cell will be discussed. M. Heinzmann et al., J. Power Sources 402, pp. 24-33 (2018).H. Schichlein et al., J. Appl. Electrochem. 32, pp. 875-882 (2002).E. Ivers-Tiffée et al., J. Ceram. Soc. Japan 125, pp. 193-201 (2017).T. Reshetenko et al., J. Electrochem. Soc. 163, pp. F1100-F1106 (2016)

Thermal Mitigation and Optimization Via Multitier Bond Wire Layout for IGBT Modules Considering Multicellular Electro-Thermal Effect

The stitch wire configuration is widely adopted for large-area IGBT chips. However, an inhomogeneous wire current density introduces uneven self-heating and nonuniform chip heating, which exacerbates the chip thermal stress. In this article, a multicellular electro-thermal model considering the stitch-bonding wires is derived to optimize the wire layout parameters. Furthermore, the current density alleviation of wire bonds is investigated to be the most sensitive and effective method to comprehensively mitigate the thermal nonequilibrium and local overheating. Consequently, an improved multitier layout is proposed to further achieve thermal stress suppression without any additional components and advanced materials. Finally, a triple-tier-bonded IGBT module with optimal design parameters is fabricated to validate the thermal mitigation performance. The prototype experimental results demonstrate that the modeling error is less than 3.0%. The multitier layout decreases the current density by 57.6%, hence, the maximum and average chip temperature are reduced by 21.8% and 12.4%, respectively.

Influence of Device Geometry on Transport Properties of Topological Insulator MicroflakesSupported by the National Natural Science Foundation of China (Grant No. 11961141011), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB28000000), and the National Key Research and Development Program of China (Grant No. 2016YFA0300600).

In the transport studies of topological insulators, microflakes exfoliated from bulk single crystals are often used because of the convenience in sample preparation and the accessibility to high carrier mobilities. Here, based on finite element analysis, we show that for the non-Hall-bar shaped topological insulator samples, the measured four-point resistances can be substantially modified by the sample geometry, bulk and surface resistivities, and magnetic field. Geometry correction factors must be introduced for accurately converting the four-point resistances to the longitudinal resistivity and Hall resistivity. The magnetic field dependence of inhomogeneous current density distribution can lead to pronounced positive magnetoresistance and nonlinear Hall effect that would not exist in the samples of ideal Hall bar geometry.

Skyrmion elongation, duplication, and rotation by spin-transfer torque under spatially varying spin current

The effect of the spatially varying spin current on a skyrmion is numerically investigated. It is shown that an inhomogeneous current density induces an elongation of the skyrmion. This elongation can be controlled using current pulses of different strength and duration. Long current pulses lead to a splitting that forms two replicas of the initial skyrmion while for short pulses the elongated skyrmion relaxes back to its initial circular state through rotation in the MHz-GHz frequency range. The frequency is dependent on the strength of the damping coefficient.

Amorphous-Carbon-Coated 3D Solid Electrolyte for an Electro-Chemomechanically Stable Lithium Metal Anode in Solid-State Batteries.

The use of solid-state electrolyte may be necessary to enable safe, high-energy-density Li metal anodes for next-generation energy storage systems. However, the inhomogeneous local current densities during long-term cycling result in instability and detachment of the Li anode from the electrolyte, which greatly hinders practical application. In this study, we report a new approach to maintain a stable Li metal | electrolyte interface by depositing an amorphous carbon nanocoating on garnet-type solid-state electrolyte. The carbon nanocoating provides both electron and ion conducting capability, which helps to homogenize the lithium metal stripping and plating processes. After coating, we find the Li metal/garnet interface displays stable cycling at 3 mA/cm2 for more than 500 h, demonstrating the interface's outstanding electro-chemomechanical stability. This work suggests amorphous carbon coatings may be a promising strategy for achieving stable Li metal | electrolyte interfaces and reliable Li metal batteries.

Regional resistance-based spatial thermal model for checking non-uniformed temperature distribution and evolution of pouch type lithium-ion batteries

This paper introduces a spatial thermal model for pouch-type lithium-ion batteries. Joule heat is adopted as a single heat generation term of the model, which considers variation in resistance with respect to the regions of the battery. The regional resistance circumvents the complex calculation of the inhomogeneous current density for modeling non-uniform temperature distribution; further, the regional resistance avoids the additional experimental load generally required to measure the entropy change in a function of state of charge (SOC). The regional resistance was calculated from the temperatures measured at nine different locations on the battery, during SOC 5% discharge steps of open circuit voltage test. We found that the acquired regional resistance integrates electrical resistance and effect of entropy changes corresponding to the SOC. The spatial thermal model predicted the temperature evolutions at 1 C and 2 C discharge and was validated experimentally, delivering results within a reasonable error range. The simulation results demonstrated that the model captured non-uniformed temperature distribution.

Role of impurity clusters for the current-driven motion of magnetic skyrmions

We study how impurities influence the current-induced dynamics of magnetic Skyrmions moving in a racetrack geometry. For this, we solve numerically the generalized Landau-Lifshitz-Gilbert equation extended by the current-induced spin transfer torque. In particular, we investigate two classes of impurities, non-conducting and magnetic impurities. The former are magnetically rigid objects and yield to an inhomogeneous current density over the racetrack which we determine separately by solving the fundamental electrostatic equations. In contrast, magnetic impurities leave the applied current density homogeneous throughout the stripe. Depending on parameters, we observe four different scenarios of Skyrmion motions in the presence of disorder, the Skyrmion decay, the pinning, the creation of additional Skyrmions, and ordinary Skyrmion passage. We calculate and discuss phase diagrams in dependence of the impurity concentration and radii of the impurities.

Investigation of Mass Transport Properties of Fibrous Electrodes in Vanadium Redox Flow Batteries By Lattice Boltzmann Simulation

Redox flow batteries (RFBs) are gathering much attention as one of the promising candidates for a large-scale electrical energy storage device that is vital to utilize intermittent renewable energy in the grid [1]. In RFBs, fibrous electrodes have been widely applied presumably due to their large specific surface area and better electric conductance. It has been well recognized that the electrode structure profoundly affects cell performance that is attributed to the reaction and transport properties of the electrode [2,3].In this study, we developed a numerical simulation method to analyze pore-scale inhomogeneous behaviors of fluid and electrochemical reaction in fibrous electrodes using Lattice Boltzmann method (LBM). We focused our attention on porous structure affecting mass transport properties and overpotential in the electrodes for the vanadium redox flow battery.We carried out the numerical analysis in the negative electrode that simulates the RFB fibrous structure, as shown in Fig.1(a). As the calculation procedure first, the mass and the momentum conservation equation for the electrolyte solution were solved, and the chemical species conservation equation for the vanadium ion (V3+) in the electrolyte solution and the charge conservation equation for the electrode and the electrolyte solution were solved. All calculation was carried out by the Lattice Boltzmann code we developed. Numerical analysis of electrochemical reaction and transport field in the negative fibrous electrode under the charge at 50mA/cm2 was performed with different fiber diameter and porosity. As the pressure loss was fixed, the change in total overvoltage was evaluated as the change in energy loss.Figure 1 shows the calculation results of the electrochemical reaction and transport in the fiber electrode with a diameter of 3.75 μm and a porosity of 0.70. A path through which the electrolyte selectively flows is formed in the sparse area of the fibrous electrode and the inhomogeneous vanadium ion concentration and local reaction current density are identical in the electrode. This indicates that the electrolyte flow is locally biased due to the non-uniformity of the electrode. The reactive species concentration decreases due to the electrochemical reaction in the dense fiber region and causes local reaction current density.Based on a series of simulation with different diameter and porosity of the fibrous electrode, we obtained an equation for the electrolyte velocity and pressure drop in the electrode. We also evaluated averaged mass transport coefficients. We confirmed that the mass transfer characteristics are improved when the fiber diameter is large and the porosity is high. This is attributed to the larger the voids, the higher the permeability and the transport by advection was promoted. However, it is noteworthy that the larger diameter and the higher porosity leads to less electrode surface area. In our previous study [3], an optimized electrode architecture with a diameter of 2.4 μm and a porosity of 0.89 was presented by macro-scale simulations.In this fiber-scale simulations, we evaluated overpotential depending on the fiber diameter and the electrode porosity, and demonstrated the LBM simulation applied for optimization of fiber diameter and the electrode porosity in the RFB applications. Acknowledgements This research was supported by a Precursory Research for Embryonic Science and Technology (PRESTO) grant (grant number JPMJPR12C6) from the Japan Science and Technology Agency(JST).

Anisotropic transport induced by DC electrical current bias near the critical current

We investigated the transport characteristics of a square shape superconducting Ta thin film under DC electrical current bias along the diagonal direction. The resistance parallel (R∥) and perpendicular (R⊥) to the DC current, IDC, is measured with various magnetic fields. R∥ and R⊥ show contrasting dependence on IDC. First, the critical current of R∥ is smaller than that of R⊥. Second, R⊥ shows an unexpected reduction at current bias where R∥ shows a rapid increase near the transition from a flux flow state to a normal state. The intriguing anisotropic transport characteristics can be understood by the inhomogeneous current density profile over the square sample. Diagonal DC current induces an anisotropic current density profile where the current density is high near the biasing electrode and low at the center of the sample. Accordingly, the electrical transport in the perpendicular direction could remain less affected even near the critical current of R∥, which leads to the higher critical current in R⊥. Complicated conduction profile may also allow the anomalous reduction in the R⊥ before finally shifting to the normal state.

The thermocapillary effect on gas bubbles growing on electrodes of different sizes

Recently, the strongly inhomogeneous current density occurring near a microelectrode was identified as driving a thermocapillary electrolyte flow near gas bubbles growing during electrolysis (Massing et al., 2019) [1]. The present paper is investigating this effect in more detail under various operating conditions. Furthermore, by simplified modeling, the question is answered of whether this effect is also of importance at large planar electrodes. The direction of the thermocapillary force on the bubble is found to change from retarding to advancing the bubble release when the size of the electrode is increased. Conclusions are drawn on how the thermocapillary effect at planar electrodes depends on the electrode coverage and the bubble departure size, also considering industrially relevant values of the current density.

Numerical simulation of flux jump behavior in REBaCuO ring bulks with an inhomogeneous Jc profile during pulsed-field magnetization

We have investigated the electromagnetic and thermal properties of a REBaCuO ring bulk with an inhomogeneous critical current density, Jc, profile during pulsed field magnetization (PFM) using a numerical simulation and compared those to a bulk with a homogeneous Jc profile. A notch was introduced in the bulk periphery, which was assumed as a crack existing in the actual bulk material. A sudden flux penetration (flux jump) took place through the notch area and as a result, a large temperature rise also took place around this notch. Consequently, the final trapped field profile was simulated to be a ‘C-shaped profile’, which qualitatively reproduced our previous experimental results. The size and position dependences of the notch on the flux penetration behaviour were also simulated, in which a larger and outer notch promotes the flux jump phenomenon easily. On the other hand, in the homogeneous model, under the same conditions, no flux jump phenomenon was observed. These results suggest that the imperfection in the bulk can be a possible starting point of the flux jump. The electromagnetic and thermal hoop stresses were also simulated in the ring bulk during PFM, in which the electromagnetic stress and the thermal stress were both observed to be lower than the fracture strength of the bulk material. This provides good evidence that the experimentally observed ‘C-shaped profile’ results from the flux jump rather than the fracture of the bulk.

A Hybrid Modeling Approach for Current Diffusion in Rectangular Conductors

This paper deals with modeling and simulation of devices where current-carrying conductors are located close to magnetic bodies. These configurations typically occur in electromechanical energy converters such as in slots of electrical machines. Additional losses due to the inhomogeneous current density distribution (“current” or “field” diffusion) at high excitation frequency are a well-known phenomenon. However, classical approaches reach their limits as soon as field diffusion is influenced by ferromagnetic material with non-linear properties. An accurate but time-consuming computation can be achieved by using time-transient quasi-stationary finite-element analysis (FEA). Current diffusion can be described more efficiently by separating the conductor into parallel filaments, following the partial element equivalent circuit (PEEC) approach. As long as linear material characteristics are prevailing, the problem can, thus, be solved efficiently in the frequency domain. In this paper, a hybrid FEA-PEEC modeling approach is presented, where the magnetization of the ferromagnetic material is represented by equivalent currents obtained by 2-D FEA. It is suitable for complex multi-conductor configurations even including non-linear ferromagnetic material. For the proposed method, the resulting linear system is efficiently solvable in the frequency domain by direct solvers. A numerical example from the field of electric traction motors is presented to emphasize the accuracy and benefit of the proposed method for practical electromagnetic computations.

Operando and Ex-Situ Investigation of PEMFC Degradation

One of the key requirements for fuel cell electric vehicles (FCEVs) is longevity with a targeted lifetime of the fuel cell of 5000 - 6000 h. This lifetime needs to be assured in dynamic PEMFC operation including critical events. To mitigate performance degradation a fundamental understanding of the degradation phenomena that occur during different operation conditions are required. Therefore operando electrochemical investigations including monitoring of local operation conditions have been carried out in a broad scope of operation conditions to i) study impact of operation conditions on degradation and ii) identify phenomena that accelerate performance decay (so called accelerated stress tests - AST). Our results show that dynamic load cycling leads to lower performance losses compared to operation at constant current [1]. Moreover, operation in the low current range (i.e. high potential range) exhibited highest irreversible and reversible degradation which is caused by a significantly increased ohmic and mass transport resistance. The observed performance losses are closely linked with inhomogeneous current density distributions. Ex-situ measurements show that MEA regions with particularly high local current densities exhibit more pronounced platinum band formation in the membrane, as shown in the Figure, which is correlated with irreversible cathode degradation. In order to understand the impact of specific operation conditions occurring during load cycling as required for automotive operation specific in-situ ASTs were performed focusing on high potential operation, mechanical stress, temperature cycling and high load operation. Although in-situ ASTs exist for the membrane and the catalyst layer, no in-situ ASTs are available for the GDL so far. Hence our current activity is focused on the development of GDL specific ASTs and quantification of their impact on degradation of individual MEA components. To quantify impact of these ASTs on degradation of individual MEA components aged components were analyzed not only by ex-situ methods, but also by electrochemical characterization in combination of with pristine MEA components. The results clearly show that, for instance, mechanical stress due to freezing water during freeze-thaw cycling has negative effect on mass transport capabilities of the MEA. In this context also mitigation strategies to avoid icing in the cell is proposed which mitigates performance decay [2]. In addition of studying degradation effects caused by operation conditions, we also provide an analysis of effects of different externally introduced contaminants. These include silicon (e.g. from gasket) and nickel (e.g. from defective coatings) which effects on local MEA degradation was studied with DLR’ segmented cell in different operation conditions [3]. Apart from understanding degradation on material level, our activities cover the development of methods for on-line fault diagnostics and state-of-health monitoring in order to identify critical operation conditions characterized by gradients in various parameters and uneven flow distribution between the single cells [4]. The presented work is focused on fault monitoring in PEMFC stacks by evaluation of local performance phenomena and impedance analysis. Combined studies of local current density measurements and impedance data for all single cells in the stack will be presented and links between impedance response, local effects within the cells, and stack fault modes will be highlighted. Acknowledgements: This project has received funding from the Fuel Cells and Hydrogen 2 Joint Undertaking under grant agreement No 779565 (ID-Fast). This Joint Undertaking receives support from the European Union’s Horizon 2020 research and innovation programme.