Two-dimensional Model Research Articles

Modeling and Experimental Validation on a Bipolar Membrane Electrodialysis Stack for Lithium Sulfate Separation

Recycling lithium-ion battery materials is a crucial step to achieving a circular economy. Among a few methods for recycling spent battery materials, a novel hydrometallurgical recycling process with leaching by acids and precipitation by bases was proposed [1]. Lithium sulfate (Li2SO4) leachate solution is generated at the end of the closed-loop recycling process. Such Li2SO4 solution can be separated by electrodialysis (ED) to form H2SO4 and LiOH solutions, which are reused for leaching and precipitation of the recycling process. The present study attempts to model this ED process and validate the model with experimental data.An ED stack based on bipolar membranes (EDBM); see Fig. 1a, was built with repetitive unit cells, each consisting of a bipolar membrane, anion exchange membrane (AEM), and cation exchange membrane (CEM). Li2SO4 enters the dilute channel and splits into SO4 2- and Li+, which travel through the AEM and CEM, respectively. Water electrolysis occurs within the bipolar membrane to produce H+ and OH-, which react with SO4 2- and Li+ to form H2SO4 and LiOH, respectively; see Fig. 1b. A two-dimensional (2D) multiphysics model is developed to elucidate the coupled transport processes within the unit cell. Conservation equations for mass, momentum, and species are solved. The transport of ions is described by the Nernst-Planck equation. Electroneutrality equations are satisfied in these membranes and channels. Electro-osmotic water transport across the membranes is considered.The effective cross-sectional area of the stack was 121.8 cm2 (70mm×174mm). The flow channel between consecutive membranes was 0.8 mm, with a mesh inserted to facilitate mixing. Experiments were carried out with the EDBM stack over different conditions such as current density, number of cell pairs, and flow rates. All experiments were operated at constant current mode [2]. The feed, acid, and base solutions were recirculated through their tanks at initial concentrations of 1.1, 0.1, and 0.1 mol/L. The ion concentrations of the solutions were measured periodically with inductively coupled plasma (ICP) mass spectrometry. The weight and the pH value of the solution tanks were also recorded.The concentration of H2SO4 is found to increase with time linearly, whereas that of LiOH levels off due to a significant electro-osmosis that drags water through the CEM into the concentrate channel. This drag reduces the performance of EDBM due to the dilution of water into the concentrate compartment. However, electro-osmotic water transport also leads to a velocity increase in the concentrate channel, which is consistent with the simulation results in our previous ED model [3]. It is found that the voltage loss across the bipolar membrane ca. 1V accounts for a significant part of the unit cell of about 1.27V.The migration of ions in electrodialysis mainly relies on diffusion and electric drive. The streamlines and the concentration distribution of Li+ under different voltages indicate that increasing voltage accelerates ion migration, see Fig. 1(c). Furthermore, the effect of the potential and concentration variations on EDBM performance is also investigated. The effects of applied current density and inlet velocity are studied on species concentrations and fluxes. Increasing the stack current density accelerates the separation process, see Fig. 1(d). It is found that increasing the solution flow rate can increase LiOH solution concentration, ion recovery rate, and current efficiency. However, the impact of the flow rate is low.This work demonstrates that EDBM can be a simple and energy-saving alternative to the current chemical precipitation method to produce LiOH from Li2SO4. The present study provides new insights into optimal operation and design for Li2SO4 EDBM. The findings are helpful in determining how the stack can be scaled up for practical application.[1] A review of recycling spent lithium-ion battery cathode materials using hydrometallurgical treatments, JCY Jung, PC Sui, J Zhang, J. Energy Storage 35, 102217, 2021.[2] Electrodialysis of a Lithium Sulphate Solution: An Experimental Investigation. B Kang, D Kang, JCY Jung, A Asadi, PC Sui, J. Electrochem. Soc. 169 (6), 063515, 2022.[3] A Comprehensive Computational Fluid Dynamics Modeling of Lithium Sulphate Electrodialysis, A Asadi, HB Harandi, JCY Jung, PC Sui, J. Electrochem. Soc. 170(9), 093502, 2023. Figure 1

(Battery Student Slam 8 Award Winner) A Comparison of Different Convergence Criteria to Improve the Performance of a P2D Modelling Algorithm of a Lithium-Ion Battery

Lithium-ion batteries (LiBs) are used as the storage for electric vehicles, grid energy and consumer electronics mainly due to the LiBs’ high energy density, long cycle life, and reliable manufacturing. Effective performance and diagnostic management of LiBs is important and is implemented via Battery Management Systems (BMS) [1]. A BMS should also maximise the safety and lifetime of battery packs and therefore, needs to estimate the internal battery states including the state of charge (SoC), state of health (SoH), state of power (SoP), state of function (SoF), and state of safety (SoS) [2]. Accurate estimation of the battery SoX can be realized with the help of a battery model; an algorithm representing the electrochemical, mechanical, electrical, and thermal behaviour of the LiB cells.Cell-level battery models typically fall into three categories: (i) Empirical Models, (ii) Equivalent Circuit Models (ECM) and (iii) Physics-based Electrochemical Models (EM). Electrochemical Models represent the internal cell processes within a cell based on its governing fundamental physical and electrochemical equations [3].The Partial two-dimensional (P2D) model is considered a high-fidelity Electrochemical Model (EM), which in its most basic form, captures three major physio-chemical processes in a cell: mass transfer via reduction/oxidisation (redox) reactions, diffusion of neutral lithium in the electrodes and diffusion of lithium-ions in the electrolyte. The P2D model captures the different physio-chemical phenomena using a set of coupled Partial Differential Algebraic Equations (PDAEs) [4].Despite accuracy, P2D models are complex mathematical models with typically no analytical solution [5]. Therefore, to implement the full-order version of the P2D model, numerical-iterative solver algorithms are required. Multiple works have looked at different methods of optimizing and solving the P2D model. These methods include using different discretisation schemes, such as the finite difference method and the finite volume method, using different iterative solvers and different convergence criteria [5]. However, the different works on iterative solvers we have reviewed to date [5], haven’t investigated the effects of the different criteria on improving the performance of P2D iterative solvers.Hence, in this work, we aim to build on our previous work [6], where we proposed an algorithm to implement the P2D model using the finite volume spatial discretisation method (FVM) and Euler time integration method. We then analyse how the role of (i) the choice of convergence criteria, (ii) the choice of initial guess and (iii) the choice of root-finding method used to converge to the convergence criteria, can be varied to improve the performance of the iterative solver.Therefore, the contributions of this work can be summarised as: An algorithm that implements the isothermal P2D model of a LiB using the Finite Volume Method and Euler integration methods.An analysis of the changes in algorithm performance when the following performance factors are varied; (i) The convergence criteria, (ii) the choice of initial guess and (iii) the choice of root-finding method.An optimal configuration of performance criteria that solves the isothermal-P2D model for a 1C discharge simulation, with an average speed of 3 seconds and a root mean square error of less than 1% when compared to the commercial solver COMSOL. [1] C. P. Grey and D. S. Hall, “Prospects for lithium-ion batteries and beyond—a 2030 vision,” Nature Communications 2020 11:1, vol. 11, no. 1, pp. 1–4, Dec. 2020, doi: 10.1038/s41467-020-19991-4.[2] L. Lu, X. Han, J. Li, J. Hua, and M. Ouyang, “A review on the key issues for lithium-ion battery management in electric vehicles,” Journal of Power Sources, vol. 226. pp. 272–288, Mar. 15, 2013. doi: 10.1016/j.jpowsour.2012.10.060.[3] S. Abada, G. Marlair, A. Lecocq, M. Petit, V. Sauvant-Moynot, and F. Huet, “Safety focused modeling of lithium-ion batteries: A review,” J Power Sources, vol. 306, pp. 178–192, Feb. 2016, doi: 10.1016/J.JPOWSOUR.2015.11.100.[4] M. Doyle, T. F. Fuller, and J. Newman, “Modeling of Galvanostatic Charge and Discharge of the Lithium/Polymer/Insertion Cell,” J Electrochem Soc, vol. 140, no. 6, pp. 1526–1533, Jun. 1993, doi: 10.1149/1.2221597/XML.[5] A. M. Ramos, “On the well-posedness of a mathematical model for Lithium-ion batteries,” Appl Math Model, vol. 40, no. 1, pp. 115–125, May 2015, doi: 10.48550/arxiv.1506.00605.[6] T. Wickramanayake, M. Javadipour, and K. Mehran, “A Novel Root-Finding Algorithm to Solve the Pseudo-2D Model of a Lithium-ion Battery,” 2023 IEEE International Conference on Electrical Systems for Aircraft, Railway, Ship Propulsion and Road Vehicles and International Transportation Electrification Conference, ESARS-ITEC 2023, 2023, doi: 10.1109/ESARS-ITEC57127.2023.10114840.

Numerical Investigation on Two-Phase Flow-Electrochemical Reaction Coupling in PEM Water Electrolyzers Porous Transport Layer Under High Operating Pressures

Proton exchange membrane water electrolyzers (PEMWEs) operated at high pressures have advantages such as lower energy consumption, reduced noise, and absence of component slippage. They have a more robust potential for commercial applications than other electrolyzers. The transport characteristics of two-phase flow within the porous transport layer (PTL) and channels are not well understood, especially under high-pressure conditions. The gas bubbles generated in the catalyst layer (CL) pass through the PTL and reach the flow channel. However, oxygen evolution reaction in the anode CL may be limited if these bubbles block the pathway of liquid water, causing reactant starvation. The interaction between electrochemical reactions and gas bubbles thus directly impacts a PEMWE's efficiency. This study aims to investigate the coupling between the two-phase flow and electrochemical reactions under high-pressure conditions.A two-dimensional (2D) CFD model was developed to simulate the bubbly flow through a reconstructed PTL. The volume of fluid (VOF) method was employed to capture bubble growth, movement, and detachment, as illustrated in Figure 1. The coupling of bubble transport and electrochemical reactions was achieved through the application of a weighted averaging method. A cross-section of a stochastically reconstructed titanium felt model was generated as the computational domain; see Fig. 1(a). The computation domain consists of a liquid water channel, a PTL, and a simplified CL interface at the bottom. The CL's reaction rate is modeled as a function of local bubble coverage on the CL interface. Transient simulations of the two-phase flow of the PEMWE anode side were carried out for pressures ranging from 1 bar to 200 bar. The simulation results elucidate the flow characteristics of liquid water in the PTL under high-pressure conditions and quantitatively reveal the coupling between two-phase flow and electrochemical reactions. The behavior of the two-phase flow in PEMWE is found to be sensitive to operating pressure. As the operating pressure increases, the size of bubbles generated on the CL interface decreases, resulting in a higher permeability of liquid water than that under low pressures. When the flow rate of liquid water in the channel is sufficiently high, bubbles do not fully develop and are rapidly removed from the domain. This phenomenon significantly shifts the two-phase flow regime within the channels,. Furthermore, the activation overpotential is substantially reduced under high-pressure conditions. The present study demonstrates a numerical simulation tool for high-pressure PEMWE. A future study of a full 3D PTL model is currently underway. Figure 1

Dynamic Characteristics of Composite Sandwich Panel with Triangular Chiral (Tri-Chi) Honeycomb under Random Vibration.

A full triangular chiral (Tri-Chi) honeycomb, combining a honeycomb structure with triangular chiral configuration, notably impacts the Poisson's ratio (PR) and stiffness. To assess the random vibration properties of a composite sandwich panel with a Tri-Chi honeycomb core (CSP-TCH), a two-dimensional equivalent Reissner-Mindlin model (2D-ERM) was created using the variational asymptotic method. The precision of the 2D-ERM in free and random vibration analysis was confirmed through numerical simulations employing 3D finite element analysis, encompassing PSD curves and RMS responses. Furthermore, the effects of selecting the model class were quantified through dynamic numerical examples. Modal analysis revealed that the relative error of the first eight natural frequencies predicted by the 2D-ERM consistently remained below 7%, with the modal cloud demonstrating high reliability. The PSD curves and their RMS values closely aligned with 3D finite element results under various boundary conditions, with a maximum error below 5%. Key factors influencing the vibration characteristics included the ligament-rib angle of the core layer and layup modes of the composite facesheets, while the rib-to-ligament thickness ratio and the aspect ratio exert minimal influence. The impact of the ligament-rib angle on the vibration properties primarily stems from the significant shift in the core layer's Poisson's ratio, transitioning from negative to positive. These findings offer a rapid and precise approach for optimizing the vibration design of CSP-TCH.

Numerical Study of Liquid Water Formation and Transport in Porous Media

Fundamental understanding of liquid water formation and transport in fuel cells is of great importance for achieving high durability, reliability, and maximizing cell performance. For low temperature fuel cells, water may exist as vapor or liquid phase and is involved in various electrochemical reactions and transport mechanisms. The condensation process occurs when local water vapor pressure exceeds the saturation pressure. In this work, we first investigate the permeation of liquid water in the gas diffusion layer (GDL). To this aim, a two-dimensional isothermal model considering reconstructed GDL microstructure in conjunction with VOF model is implemented. The effects of mixed wettability of materials, operating temperature, and Polytetrafluoroethylene (PTFE) loadings on liquid water transport in the porous media are investigated numerically. The liquid water breakthrough and the capillary fingering regime are captured and compared. The results show that liquid water saturation in the GDL increases with decreasing PTFE loadings. Moreover, the results demonstrated that the local microstructure in the GDL has a strong effect and can dominate the overall water distribution. To further study water condensation, the isothermal model is expanded to non-isothermal for including physics of phase change heat transfer and species transport. In addition, anisotropic thermal conductivity is incorporated to study its effect on temperature distribution and liquid water distribution. The results show that initially the liquid water is formed as micro droplets and then these micro droplets are combined to form large droplets. Moreover, the impacts of water generation rate, temperature gradient, operating pressure, and contact angle on condensation have been investigated. The findings of this work are expected to provide insights into designing more reliable GDL in fuel cells. Figure 1

Modelling the impact of sediment composition on long-term estuarine morphodynamics

Sediment composition, characterized by different contents of cohesive and non-cohesive sediments, is known to play a role on long-term estuarine and deltaic morphodynamics, but the exact impact is poorly understood. We establish a two-dimensional morphodynamic model to investigate the influence of different sediment compositions on the development of a schematic fluvio-deltaic system driven by river and tides. Though excluding the density effects, results suggest that the model captures the development of distributary channels and elongated sand bars with resemblance to that in the Yangtze Estuary. Sensitivity simulations show fundamentally different channel-shoal patterns take shape under different sediment compositions. Ebb dominance and associated seaward sediment flushing lead to faster morphodynamic development and more prograded delta under larger river discharge and sediment supply. We detect a positive correlation between the content of cohesive sediment and the speed of development, particularly cohesive sediment content is <50%. However, when the proportion of mud is larger (i.e., 50–75%), a deceleration of the morphological development occurs after 200 years. A sand-dominated environment exhibits the largest channel numbers and fast channel formation near the mouth within the first 300 morphodynamic years. Spatial distribution of bottom sediments changes with morphology, exhibiting increasing mud deposits near the mouth, whilst the sand remains inside the estuary. This study indicates the importance and need for a more realistic representation of bed compositions in long-term estuarine morphodynamic simulations.

Numerical Investigation of Flow Distribution in PEMFC and Pemwe Stacks Considering Two-Phase Flow in the Stack Headers

PEM fuel cell (PEMFC) and PEM water electrolyzer (PEMWE) stacks are assembled by connecting a series of unit cells. The stack headers are conduits formed by the ports of these unit cells; see Fig. 1(a). The flow field in the headers affects the flow uniformity of the stack, which significantly impacts the stack’s performance and lifespan. This study aims to investigate the fluid flows in the stack headers of PEMFC and PEMWE. A specific objective of this study is to understand how two-phase flow (liquid water and gases) in the headers would impact the flow distribution inside the stacks.The present study investigates the flow inside a stack by two-dimensional (2D) and three-dimensional (3D) models, as shown in Figure 1(b) and (c) respectively. The 3D model was constructed with an inlet header and an outlet header with flow resistors in between to represent the unit cells.1,2 CFD simulations using ANSYS Fluent were performed over a 100-cell PEMFC stack based on the k-ε RNG turbulence model. The two-dimensional 100-cell PEMFC stack model was built with COMSOL Multiphysics and considers the diffusion and transport, proton and electron conduction, electrochemical reactions on the catalytic layer, and heat transfer in the unit cells. The flow distribution obtained from the 3D model was used as the boundary conditions for the 2D model to calculate the effects of flow distribution on the overall performance of the stack. It should be pointed out that in the 3D models of PEMFC and PEMWE headers, simulations using the volume of fluid (VOF) model to track the liquid water droplets in a PEMFC and bubbles in a PEMWE were carried out to gain insights into the impact of two-phase flow on stack header flow sharing.The simulation results show the existence of unstable and highly transient turbulence within the PEMFC outlet header, as seen in Figs. 1(d) and 1(e). Jet flows from individual cells cause vortices inside the header, reducing the effective flow area. Liquid water accumulates on the inner wall of the header and is swept out by the cross-flow. In the dead-end region, liquid water undergoes helical motion under the influence of vortices, resulting in a longer residence time in the header and making it less prone to be expelled. This study parametrically investigated the effects of header size and air stoichiometry. As the cross-sectional area of the inlet header decreases from A=1,225 mm2 to A=857.5 mm2, the coefficient of mass flow variation within the stack increases, indicating a decrease in the uniformity of flow distribution inside the stack, as shown in Fig. 1(f). The air stoichiometry also affects the flow distribution inside the stack; as the air stoichiometry λ decreases from 2.2 to 1.4, the uniformity of gas distribution in the stack deteriorates significantly.The methodology used in the present study provides a reference for the parameter design and operating conditions of PEMFC and PEMWE stacks. It helps to gain insights into the optimization of stack header design and energy management.

Coupling Microkinetics with Continuum Transport Models to Understand CO2R on Planar and Optimized Patterned Electrodes

Electrochemical CO2 reduction has emerged as an attractive technique to sustainably produce valuable fuels and chemicals, while reducing CO2 emissions. In addition to the specific electrode material, the microenvironment local to the electrode interface – e.g., the electrolyte pH, CO2 concentration, buffer concentration – plays a significant role in determining the selectivity and activity of the electrolyzer. In this work, we demonstrate a multi-scale approach, where microkinetic simulations of Au are coupled to a two-dimensional continuum transport model in a flow reactor configuration. Specifically, concentrations and potentials solved for in the continuum model are fed into microkinetic models along the planar electrode surface, which return concentration fluxes that are used to update the continuum model. We find that local quantities at the electrode interface, such as the CO2 concentration and pH, vary not only with the applied potential and flow rate, but also with position on the electrode. We investigate two ways to increase CO2 availability at the interface: (1) increasing the applied flow rate, thus reducing the boundary layer thickness, and (2) introducing an inert defect in the middle of the electrode, allowing CO2 to partially replenish within the depletion boundary layer. Inspired by the effect of a single inert defect, we explore electrodes patterned with inert defects and multiple catalyst materials, i.e. a generalized tandem system. We show how the specific pattern of the electrode can be optimized in order to target a specific desired product. The different parts of the electrode have different goals that work together: converting CO2 to CO, converting CO to C2+ products, and allowing concentrations to replenish through the boundary layer. Overall, our aim is to demonstrate the need for multi-dimensional, multi-scale approaches to simulating CO2 reduction to elucidate the reaction environment near the electrode.This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL release number: LLNL-ABS-857537.

A Novel Multi-Stage Stochastic Estimation Algorithm for Estimating the Parameters of the Extended Single Particle Model of a Lithium-Ion Battery

Lithium-ion batteries (LiBs) are commonly used as energy storage for many applications due to LiBs’ high energy density, long cycle life, and reliable manufacturing processes. Hence, effective performance management of LiBs is important and is implemented via Battery Management Systems (BMS)[1]. A BMS also maximises the safety and lifetime of battery packs; and therefore, needs to estimate the internal battery states including State of Charge (SoC) and State of Safety (SoS). Accurate estimation of battery SoX can be realized with the use of an accurate battery model [2].From the different types of battery models, electrochemical models (EMs) are considered the most accurate type of cell-level model [2]. EMs are sets of coupled-partial differential equation systems, where each equation is derived from the physics occurring in the cell. Of the different EMs, the partial two-dimensional model (P2D) is considered the most accurate cell-level model. However, the P2D model is complex and has no analytical solution, thus requiring computationally expensive iterative solvers for implementation. This makes practical implementation of the P2D model on BMS platforms challenging. Hence, most approaches seen in the literature prefer the use of reduced order versions (ROM) of the P2D model, that require far less computational power for implementation [1].One such ROM is the extended Single Particle Model (eSPM) which differs from the P2D model in considering each electrode to be modelled by a single spherical particle and charge conservation in the electrolyte to follow a simplified linear relationship. These assumptions help the model be accurate up to a 2C operational current, and enable an analytical solution to be derived using direct solving of the eSPM equations [2]. Due to fast-forward computation and reasonable accuracy, we’ve chosen the eSPM model for parameter estimation (PE). For accurate measurements of the model parameters, expensive and invasive experimental techniques are typically required. Non-destructive PE methods have a growing interest in the literature as they are not only non-invasive but also enable real-time dynamic PE to be done on a BMS [3].PE of EMs can be categorized under two approaches: deterministic methods and stochastic methods. Deterministic methods require a form of gradient descent to be used, wherein partial derivatives of the parameters of the model need to be calculated. This approach tends to be computationally expensive and tends to converge to local minima instead of searching the parameter space thoroughly. Hence, stochastic approaches incorporate randomness, thus searching the entire parameter space for the global optima [3]. Multiple different stochastic approaches have been employed for PE of EMs [4]. In this work, we compare and contrast some of the commonly used approaches and propose a novel multi-stage approach based on a combination of different stochastic PE algorithms.The proposed algorithm (see Figure (1)) requires three sets of data as inputs: the cell chemistry, constant current discharge data and the parameter boundaries of the eSPM model. Using these definitions, the first stage of the algorithm estimates a parameter set that has a reasonable level of accuracy i.e. less than 4% root mean square error (RMSE). The second stage of the algorithm does region-by-region optimisation, where parameters sensitive to different regions of the discharge curve are varied until the overall error is reduced to less than 1% RMSE. The proposed approach significantly reduces the estimation processing time compared to the ‘brute-force’ approach and is flexible in selecting different algorithms for each stage.Thus, contributions of this paper are briefly explained as follows: A performance comparison of the proposed algorithm with different stochastic estimation algorithms including the genetic algorithm, the particle swarm optimisation algorithm and the simulated annealing algorithm.A fast and adaptable multi-stage PE algorithm for the LiB eSPM model, with average estimation speeds of less than fifteen minutes for a typical BMS processor, with accuracy of less than 1% RMSE error.Validation of the algorithm with dynamic drive-cycle test data. [1] L. Lu et al, “A review on the key issues for lithium-ion battery management in electric vehicles,” Journal of Power Sources, vol. 226. pp. 272–288, Mar. 15, 2013. doi: 10.1016/j.jpowsour.2012.10.060.[2] S. Abada et al, “Safety focused modeling of lithium-ion batteries: A review,” J Power Sources, vol. 306, pp. 178–192, Feb. 2016, doi: 10.1016/J.JPOWSOUR.2015.11.100.[3] E. Miguel et al, “Review of computational parameter estimation methods for electrochemical models,” Journal of Energy Storage, vol. 44. Elsevier Ltd, Dec. 15, 2021. doi: 10.1016/j.est.2021.103388.[4] A. Jokar et al, “An Inverse Method for Estimating the Electrochemical Parameters of Lithium-Ion Batteries,” J Electrochem Soc, vol. 163, no. 14, p. A2876, Oct. 2016, doi: 10.1149/2.0191614JES. Figure 1

Exploring an Electrochemical Batch Reactor for Nutrient Recovery from Wastewater: Continuum Modeling Analysis of Hydrodynamics and Tertiary Current Distribution

Advancing electrochemical reactors for nutrient recovery from wastewater requires an integration of continuum modeling alongside experimental investigations to appropriately capture transport effects on electrode performance. This continuum modeling approach facilitates the comprehensive evaluation and optimization of electrochemical reactor performance, especially with respect to intricate phenomena that may be challenging to observe solely through experimentation. The optimization process not only enhances the efficacy of existing batch reactors but also lays the foundation for designing and scaling up continuous electrochemical reactors for nutrient recovery [1].A key transport phenomenon in electrochemistry is hydrodynamics because flow dynamics around electrodes dictate mass transport magnitude and uniformity, thereby impacting current distribution, efficiency, and electrolytic energy consumption during electrolysis. Achieving homogeneous velocity fields while avoiding undesirable flow features is essential to prevent non-uniform potential and current density distributions along the electrodes, mitigating side reactions and ensuring the overall efficacy of the electrochemical processes [2].In this study, a two-dimensional model of an electrochemical batch reactor was developed using COMSOL Multiphysics software to investigate reactor hydrodynamics, electrochemical reactions, and mass transfer of species. Employing the finite element method, the model incorporated the k-epsilon turbulence model for hydrodynamics simulation, widely used in literature for simulating fluid flow and mixing behavior [3]. Electrochemical reactions at the cathode (oxygen reduction) were modeled using the Butler-Volmer equation, while the Tafel equation was applied at the anode (hydrogen evolution). Boundary conditions were a grounded counter electrode (anode) and a potential of -1.1 vs Ag/AgCl(sat.) applied to the working electrode (cathode). Fick's second law diffusion-convective equation was employed to model the mass transfer of species, including hydroxide and oxygen.Preliminary findings indicate that while impellers contribute to turbulence and affect local conditions around electrodes, the impact on the backside of the modeled electrodes is relatively weak (Figure 1). This observation may adversely influence mass transfer rates and electrochemical reactions, underscoring the significance of integrating these results with electrochemical reactions for a comprehensive understanding of reactor behavior. Additional results will be presented at the meeting.

(Invited) Integrated Approach of Modeling, X-Ray and Electrochemical Characterization to Understand Low Iridium Loading Catalyst Layers Integration and Durability

Proton exchange membrane water electrolyzers (PEMWEs) will share more than 40 % of green hydrogen production market by 2050. Currently, iridium catalyst in the anode catalyst layers amounts to 1 mg/cm2. To enable low-loading (0.4 mg/cm2) or ultra-low loading (<0.1 mg/cm2) designs we need to better understand both integration of catalysts into catalyst layer and their durability. At low loadings catalyst layer in-plane electric conductivity can be compromised, requiring either supported catalyst layers or the need for microporous layer (MPL) design. For durability study it is necessary to understand the pathway of surface of IrOx transformation during accelerated stress tests (ASTs) and identify optimal beginning of life (BOL) structure for long-duration deployment. In this work we evaluate the structure and performance of amorphous and crystalline IrOx catalysts at the BOL and EOL to build structure-to-property relations. Rheology studies are conducted to identify the optimal ink recipe for each of the catalysts for blade coating deposition method. We use operando x-ray diffraction technique to evaluate catalyst structure evolution during AST cycling. X-ray computed tomography (CT) was used to evaluate catalyst layer – MPL interfaces under various operando conditions. The morphological information was integrated into the two-dimensional model to better understand interfaces for the low-loading PEMWEs.

Investigation of Delamination Characteristics in 3D-Printed Hybrid Curved Composite Beams.

This study focuses on understanding the impact of different material compositions and printing parameters on the structural integrity of hybrid curved composite beams. Using the continuous filament fabrication technique, which is an advanced fused deposition modelling process, composite curved beams made of short carbon and various continuous fibre-reinforced nylon laminae were fabricated and subjected to four-point bending tests to assess their delamination characteristics. The results show that the presence of five flat zones in the curved region of a curved beam achieves 10% and 6% increases in maximum load and delamination strength, respectively, against a smooth curved region. The delamination response of a curved composite beam design consisting of unidirectional carbon/nylon laminae is superior to that of a curved beam made of glass fibre/nylon laminae, while the existence of highly strengthened glass fibre bundles is alternatively quite competitive. Doubling the number of continuous fibre-reinforced laminae results in an increase of up to 36% in strength by achieving a total increase in the beam thickness of 50%, although increases in mass and material cost are serious concerns. The hybrid curved beam design has a decrease in the maximum load and the strength by 11% and 13%, respectively, when compared with a non-hybrid design, which consists of some type of stronger and stiffer nylon laminae instead of short carbon fibre-reinforced conventional nylon laminae. Two-dimensional surface-based cohesive finite element models, which have a good agreement with experimental results, were also established for searching for the availability of useful virtual testing. The results from this study will greatly contribute to the design and numerical modelling of additively manufactured hybrid composite curved beams, brackets, and fittings.

Exploring Aeration Strategies for Enhanced Simultaneous Nitrification and Denitrification in Membrane Aerated Bioreactors: A Computational Approach.

In this study we employ computational methods to investigate the influence of aeration strategies on simultaneous nitrification-denitrification processes. Specifically, we explore the impact of periodic and intermittent aeration on denitrification rates, which typically lag behind nitrification rates under identical environmental conditions. A two-dimensional deterministic multi-scale model is employed to elucidate the fundamental processes governing the behavior of membrane aerated biofilm reactors (MABRs). We aim to identify key factors that promote denitrification under varying aeration strategies. Our findings indicate that the concentration of oxygen during the off phase and the duration of the off interval play crucial roles in controlling denitrification. Complete discontinuation of oxygen is not advisable, as it inhibits the formation of anaerobic heterotrophic bacteria, thereby impeding denitrification. Extending the length of the off interval, however, enhances denitrification. Furthermore, we demonstrate that the initial inoculation of the substratum (membrane in this study) influences substrate degradation under periodic aeration, with implications for both nitrification and denitrification. Comparison between continuous and periodic/intermittent aeration scenarios reveals that the latter can extend the operational cycle of MABRs. This extension is attributed to relatively low biofilm growth rates associated with non-continuous aeration strategies. Consequently, our study provides a comprehensive understanding of the intricate interplay between aeration strategies and simultaneous nitrification-denitrification in MABRs. The insights presented herein can contribute significantly to the optimization of MABR performance in wastewater treatment applications.

Deep neural networks as variational solutions for correlated open quantum systems

In this work we apply deep neural networks to find the non-equilibrium steady state solution to correlated open quantum many-body systems. Motivated by the ongoing search to find more powerful representations of (mixed) quantum states, we design a simple prototypical convolutional neural network and show that parametrizing the density matrix directly with more powerful models can yield better variational ansatz functions and improve upon results reached by neural density operator based on the restricted Boltzmann machine. Hereby we give up the explicit restriction to positive semi-definite density matrices. However, this is fulfilled again to good approximation by optimizing the parameters. The great advantage of this approach is that it opens up the possibility of exploring more complex network architectures that can be tailored to specific physical properties. We show how translation invariance can be enforced effortlessly and reach better results with fewer parameters. We present results for the dissipative one-dimensional transverse-field Ising model and a two-dimensional dissipative Heisenberg model compared to exact values.

Two-dimensional migration characteristics of contaminant through composite liner with arbitrarily distributed defects

Previous studies indicate that liner defects can significantly accelerate contaminant migration in landfill, shortening the migration time by orders of magnitude. Although the effect of defects upon contaminant migration and barrier capacity of liner system has been investigated based on several theoretical models, they are always limited to one-dimensional scopes. Here a two-dimensional (2-D) model was established for contaminant transport through composite liner to the soil layer, with geomembrane (GM) defects arbitrarily distributed along the horizontal direction, and then Laplace transform, Fourier transform, and boundary transform method were utilized to derive its semi-analytical solution, which was verified by experimental data and numerical results. The obtained solution can take nonuniformly distributed defects into account and demonstrates the 2-D contaminant concentration and flux profiles in the spatiotemporal domain. Computational results of the solution are employed to illustrate the roles of material coefficients and modeling sizes upon the variations of contaminant concentration and flux. Results support that contaminant migration is expedited by the GM defect in landfill, and geosynthetics clay liner can reduce the pollution level caused by GM failure. Moreover, the contaminant flux will not be significantly influenced by the defect positions, which, however, leads to non-negligible impact on concentration profiles.

Using the kano quality model to evaluate the functions of automotive smart head-up displays

The development of novel technologies has resulted in changes in the functions offered by head-up displays (HUDs), which differ considerably from conventional digital dashboard displays. This study aimed to create a scientific framework for automotive services for automobile manufacturers to review their service models and solutions as they transition to developing autonomous vehicles. This study used the two-dimensional Kano quality model to identify and classify quality characteristics of HUDs. A Kano questionnaire survey was conducted to collect data on customer satisfaction with different quality characteristics. These characteristics were then ranked in the order of their importance to consumers, thereby identifying quality characteristics that must be prioritized for providing high-quality services with HUDs. Data were collected on their emphases on and satisfaction with 32 quality characteristics belonging to seven factors across two dimensions, namely tangible specific functions and intangible value-added services. The seven factors were speed and distance support, driver alerts, information and communication, display settings, active matching, automatic systems, and software–hardware integration. A statistical analysis was performed to determine the presence of significant differences in the customers’ perception of the quality characteristics. On the basis of the analysis results, 11 quality characteristics were classified as attractive quality, four as one-dimensional quality, six as must-be quality, seven as indifferent quality, and four as reverse quality. By referencing the classification of quality characteristics in their products, automotive companies can adopt the product improvement priority scheme proposed in this study to effectively enhance customer satisfaction with their services.

Assessing the Efficiency of Fully Two-Dimensional Hydraulic HEC-RAS Models in Rivers of Cyprus

Floods are among the most widespread and recurrent natural disasters globally. In the European region, climate change leads to an increase in the incidence and intensity of flooding. For effective management of the phenomenon, the European Union instituted Directive 2007/60/EC for the assessment and management of flood risks in order to reduce the negative consequences of flooding on human health, economic activities, the environment, and cultural heritage. Cyprus, as a member of the European Union, had to comply with the provisions of the directive. Within the second implementation of the directive, combined 1D/2D hydraulic models were conducted. These data served as a benchmark for the present research, in which the differences in the inundated area, depths, and simulation time are investigated using a full 2D hydraulic simulation. The present research examines two Areas of Potentially Significant Flood Risk, one in an urban and one in a rural area. Overall, the proposed 2D methodology was found to represent inundated areas to a good extent with almost zero deviation in comparison to the 1D/2D method. This study demonstrated the adequacy of the 2D hydraulic simulation method, which offers greater flexibility in modeling a variety of hydraulic scenarios, enabling planning and flood risk management that is vital for protecting communities, infrastructure and the environment from the devastating impacts of floods.

Comparative Studies on the Radiative Heat Transfer in Arc Plasma and Its Impact in a Model of a Free-Burning Arc

The radiative heat transfer in arc plasma models is considered from the point of view of its description in terms of a net emission coefficient, the method of spherical harmonics in its lowest order, and the discrete ordinate method. Net emission coefficients are computed, applying approximate analytical and numerical approaches and a multi-band representation of the spectral absorption coefficient with three kinds of its averaging and two datasets. Self-consistent access to the radiative heat transfer is applied to a two-dimensional axisymmetric model of a free-burning arc in argon at atmospheric pressure. The results obtained from the models employing the net emission coefficient, the method of spherical harmonics, and the discrete ordinate method are compared.

Study of the comfortable efficiency of the automobile using the seat’s Negative-Stiffness-Structure via two mathematical models

The isolating performance of NSS (Negative-Stiffness-Structure) on ameliorating the automotive’s comfortable in all vertical, pitching, and rolling directions has been not studied yet. Thus, two vibration models of the automobile including the two-dimensional (2-D) model and three-dimensional (3-D) model are built to evaluate automobile’s comfortable efficiency under various conditions. The reduction of the seat and automobile accelerations has been used as an evaluation index. Results present that seat’s vertical acceleration using NSS is evidently improved compared without NSS in two models of the automobile. Especially, the seat’s root-mean-square acceleration with NSS is strongly deteriorated by 65.1% with 2-D model and reduced by 69.7% with 3-D model in comparison without NSS. However, the seat’s NSS does not affect the pitching vibration of the automobile’s body. Besides, from the comparison results between 2-D and 3-D models, seat’s NSS could strongly ameliorate the comfortable efficiency in both vertical and rolling vibrations while the seat’s NSS does not affect improving the automobile’s pitching angle of the automobile. Therefore, to fully assess NSS’s isolating performance as well as improve the comfortable efficiency of the automobile in all vibration directions, 3-D model of the automobile should be used.

Study on energy-saving applications of vacuum ejectors across various operational demands

Vacuum suction technology is a pivotal innovation within the Industry 4.0 revolution. Ejectors serve as the core of vacuum systems with distinct advantages such as simple structure, low cost, and ease of operation. However, traditional fixed ejectors suffer from low efficiency, energy waste, and poor adaptability. This study aims to optimize the design of vacuum ejectors to meet various requirements, achieving energy efficiency and high performance in automated production. On this basis, an energy-saving vacuum system based on dual ejectors is proposed, which can switch between single and dual ejectors depending on different working stages. When the vacuum reaches 90 kPa, the required motive pressure and the entrainment ratio are selected as the screening indicators for the vacuum ejector. A two-dimensional axisymmetric model is established and verified through experimentation. The key parameters are identified through a single-factor analysis. A multi-factor analysis is employed to determine the recommended values for each parameter and their respective applications. The energy-saving effects of the optimized ejectors are evaluated in conjunction with the automated processes. The findings indicate that the vacuum system based on dual ejectors can achieve rapid response and low air consumption. This paper contributes to advancing the research on energy-saving applications of ejectors.