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The durability of polymer electrolyte membrane fuel cells (PEMFC) is governed by a nonlinear coupling between system demand, component behavior, and physicochemical degradation mechanisms, occurring on timescales from the sub-second to the thousand-hour. We present a simulation methodology for assessing performance and durability of a PEMFC under automotive driving cycles. The simulation framework consists of (a) a fuel cell car model converting velocity to cell power demand, (b) a 2D multiphysics cell model, (c) a flexible degradation library template that can accommodate physically-based component-wise degradation mechanisms, and (d) a time-upscaling methodology for extrapolating degradation during a representative load cycle to multiple cycles. The computational framework describes three different time scales, (1) sub-second timescale of electrochemistry, (2) minute-timescale of driving cycles, and (3) thousand-hour-timescale of cell ageing. We demonstrate an exemplary PEMFC durability analysis due to membrane degradation under a highly transient loading of the New European Driving Cycle (NEDC).
The instability of ultra-thin films of an electrolyte bordering a dielectric gas in an external tangential electric field is scrutinized. The solid wall is assumed to be either a conducting or charged dielectric surface. The problem has a steady one-dimensional solution. The theoretical results for a plug-like velocity profile are successfully compared with available experimental data. The linear stability of the steady-state flow is investigated analytically and numerically. Asymptotic long-wave expansion has a triple-zero singularity for a dielectric wall and a quadruple-zero singularity for a conducting wall, and four (for a conducting wall) or three (for a charged dielectric wall) different eigenfunctions. For infinitely small wave numbers, these eigenfunctions have a clear physical meaning: perturbations of the film thickness, of the surface charge, of the bulk conductivity, and of the bulk charge. The numerical analysis provides an important result: the appearance of a strong short-wave instability. At increasing Debye numbers, the short-wave instability region becomes isolated and eventually disappears. For infinitely large Weber numbers, the long-wave instability disappears, while the short-wave instability persists. The linear stability analysis is complemented by a nonlinear direct numerical simulation. The perturbations evolve into coherent structures; for a relatively small external electric field, these are large-amplitude surface solitary pulses, while for a sufficiently strong electric field, these are short-wave inner coherent structures, which do not disturb the surface.
The measurement of the active material volume fraction in composite electrodes of lithium-ion battery cells is difficult due to the small (sub-micrometer) and irregular structure and multi-component composition of the electrodes, particularly in the case of blend electrodes. State-of-the-art experimental methods such as focused ion beam/scanning electron microscopy (FIB/SEM) and subsequent image analysis require expensive equipment and significant expertise. We present here a simple method for identifying active material volume fractions in single-material and blend electrodes, based on the comparison of experimental equilibrium cell voltage curve (open-circuit voltage as function of charge throughput) with active material half-cell potential curves (half-cell potential as function of lithium stoichiometry). The method requires only (i) low-current cycling data of full cells, (ii) cell opening for measurement of electrode thickness and active electrode area, and (iii) literature half-cell potentials of the active materials. Mathematical optimization is used to identify volume fractions and lithium stoichiometry ranges in which the active materials are cycled. The method is particularly useful for model parameterization of either physicochemical (e.g., pseudo-two-dimensional) models or equivalent circuit models, as it yields a self-consistent set of stoichiometric and structural parameters. The method is demonstrated using a commercial LCO–NCA/graphite pouch cell with blend cathode, but can also be applied to other blends (e.g., graphite–silicon anode).
One of the bottlenecks hindering the usage of polymer electrolyte membrane fuel cell technology in automotive applications is the highly load-sensitive degradation of the cell components. The cell failure cases reported in the literature show localized cell component degradation, mainly caused by flow-field dependent non-uniform distribution of reactants. The existing methodologies for diagnostics of localized cell failure are either invasive or require sophisticated and expensive apparatus. In this study, with the help of a multiscale simulation framework, a single polymer electrolyte membrane fuel cell (PEMFC) model is exposed to a standardized drive cycle provided by a system model of a fuel cell car. A 2D multiphysics model of the PEMFC is used to investigate catalyst degradation due to spatio-temporal variations in the fuel cell state variables under the highly transient load cycles. A three-step (extraction, oxidation, and dissolution) model of platinum loss in the cathode catalyst layer is used to investigate the cell performance degradation due to the consequent reduction in the electro-chemical active surface area (ECSA). By using a time-upscaling methodology, we present a comparative prediction of cell end-of-life (EOL) under different driving behavior of New European Driving Cycle (NEDC) and Worldwide Harmonized Light Vehicles Test Cycle (WLTC).
Instabilities of the interface between two thin liquid films under DC electroosmotic flow are investigated using linear stability analysis followed by an asymptotic analysis in the long-wave limit. The two-liquid system is bounded by two rigid plates which act as substrates. The Boltzmann charge distribution is considered for the two electrolyte solutions and gives rise to a potential distribution in these liquids. The effect of van der Waals interactions in these thin films is incorporated in the momentum equations through the disjoining pressure. Marginal stability and growth rate curves are plotted in order to identify the thresholds for the control parameters when instabilities set in. If the upper liquid is a dielectric, the applied electric field can have stabilizing or destabilizing effects depending on the viscosity ratio due to the competition between viscous and electric forces. For viscosity ratio equal to unity, the stability of the system gets disconnected from the electric parameters like interface zeta potential and electric double-layer thickness. As expected, disjoining pressure has a destabilizing effect, and capillary forces have stabilizing effect. The overall stability trend depends on the complex contest between all the above-mentioned parameters. The present study can be used to tune these parameters according to the stability requirement.
In this study the dynamics and stability of thin and electrically conductive aqueous films under the influence of a time-periodic electric field are explored. With the help of analytical linear stability analysis for long wavelength disturbances, the stability threshold of the system as a function of various electrochemical parameters and transport coefficients is presented. The contributions of parameters like surface tension, disjoining pressure, electric double layer (Debye length and interfacial zeta potential), and unsteady Maxwell and viscous stresses are highlighted with the help of appropriate dimensionless groups. The physical mechanisms affecting the stability of thin films are detailed with the above-mentioned forces and parametric dependence of stability trends is discussed.
Modeling and simulation play a key role in analyzing the complex electrochemical behavior of lithium-ion batteries. We present the development of a thermodynamic and kinetic modeling framework for intercalation electrochemistry within the open-source software Cantera. Instead of using equilibrium potentials and single-step Butler-Volmer kinetics, Cantera is based on molar thermodynamic data and mass-action kinetics, providing a physically-based and flexible means for complex reaction pathways. Herein, we introduce a new thermodynamic class for intercalation materials into the open-source software. We discuss the derivation of molar thermodynamic data from experimental half-cell potentials, and provide practical guidelines. We then demonstrate the new class using a single-particle model of a lithium cobalt oxide/graphite lithium-ion cell, implemented in MATLAB. With the present extensions, Cantera provides a platform for the lithium-ion battery modeling community both for consistent thermodynamic and kinetic models and for exchanging the required thermodynamic and kinetic parameters. We provide the full MATLAB code and parameter files as supplementary material to this article.
Proton Exchange Membrane Fuel Cells (PEMFC) are energy efficient and environmentally friendly alternatives to conventional energy conversion systems in many yet emerging applications. In order to enable prediction of their performance and durability, it is crucial to gain a deeper understanding of the relevant operation phenomena, e.g., electrochemistry, transport phenomena, thermodynamics as well as the mechanisms leading to the degradation of cell components. Achieving the goal of providing predictive tools to model PEMFC performance, durability and degradation is a challenging task requiring the development of detailed and realistic models reaching from the atomic/molecular scale over the meso scale of structures and materials up to components, stack and system level. In addition an appropriate way of coupling the different scales is required.
This review provides a comprehensive overview of the state of the art in modeling of PEMFC, covering all relevant scales from atomistic up to system level as well as the coupling between these scales. Furthermore, it focuses on the modeling of PEMFC degradation mechanisms and on the coupling between performance and degradation models.
Simulation-based degradation assessment of lithium-ion batteries in a hybrid electric vehicle
(2017)
The insufficient lifetime of lithium-ion batteries is one of the major cost driver for mobile applications. The battery pack in vehicles is one of the most expensive single components that practically must be excluded from premature replacement (i.e., before the life span of the other components end). Battery degradation is a complex physicochemical process that strongly depends on operating condition and environment. We present a simulation-based analysis of lithium-ion battery degradation during operation with a standard PHEV test cycle. We use detailed multiphysics (extended Newman-type) cell models that allow the assessment of local electrochemical potential, species and temperature distributions as driving forces for degradation, including solid electrolyte interphase (SEI) formation [1]. Fig. 1 shows an exemplary test cycle and the predicted resulting spatially-averaged SEI formation rate. We apply a time-upscaling approach to extrapolate the degradation analysis over long time scales, keeping physical accuracy while allowing end-of-life assessment [2]. Results are presented for lithium-ion battery cells with graphite/LFP chemistry. The behavior of these cells in terms of degradation propensity, performance, state of charge and other internal states is predicted during long-term cycling. State of health (SOH) is quantified as capacity fade and internal resistance increase as function of operation time.
One of the practical bottlenecks associated with commercialization of lithium-air cells is the choice of an appropriate electrolyte that provides the required combination of cell performance, cyclability and safety. With the help of a two-dimensional multiphysics model, we attempt to narrow down the electrolyte choice by providing insights into the effect of the transport properties of electrolyte, electrode saturation (flooded versus gas diffusion), and electrode thickness on a single discharge performance of a lithium-air button cell cathode for five different electrolytes including water, ionic liquid, carbonate, ether, and sulfoxide. The 2D distribution of local current density and concentrations of electrochemically active species (O2 and Li+) in the cathode is also discussed w.r.t electrode saturation. Furthermore, the efficacy of species transport in the cathode is quantified by introducing two parameters, firstly, a transport efficiency that gives local insight into the distribution of mass transfer losses, and secondly, an active electrode volume that gives global insight into the cathode volume utilization at different current densities. A detailed discussion is presented toward understanding the design-induced performance limitations in a Li-air button cell prototype.
Practical bottlenecks associated with commercialization of Lithium-air cells include capacity limitation and low cycling efficiency. The origin of such losses can be traced to complex electrochemical side reactions and reactant mass transport losses[1]. The efforts to minimize such losses include exploration of various electrolytes with additives[2], and cell component geometry and material design. Given the wide range of options for such materials, it is almost impractical to experimentally setup and characterize all those cells. Consequently, modeling and simulation studies are efficient alternatives to analyze spatially and temporally resolved cell behavior for various combinations of materials[3]. In this study, with the help of a two-dimensional multi physics model, we have focused on the effect of electrode and electrolyte interaction (electrochemistry), choice of electrolyte (species transport), and electrode geometry (electrode design) on the performance of a lithium-air button cell. Figure1a shows the schematics of the 2D axisymmetric computational domain. A comparative analysis of five different electrolytes was performed while focusing on the 2D distribution of local current density and the concentration of electro-chemically active species in the cell, that is, O2and Li+. Using two different cathode configurations, namely, flooded electrode and gas diffusion electrode (GDE)[4] at different cathode thickness, the effect of cell geometry and electrolyte saturation on cell performance was explored. Further, a detailed discussion on electrode volume utilization (cf. Figure1b) is presented via changes in the active volume of cathode that produces 90% of the total current with the cell current density for different combinations of electrolyte saturations and cathode thickness.