Three-dimensional mathematical model of a high temperature polymer electrolyte membrane fuel cell

Polymer electrolyte fuel cells are regarded as one of the most promising alternatives to the depleting and high pollutant fossil fuel energy sources. High temperature Polymer electrolyte fuel cells are especially suitable for stationary power applications. However, the length scale of a PEM fuel cells main components range from the micro over the meso to the macro level, and the time scales of various transport processes range from milliseconds up to a few hours. This combination of various spatial and temporal scales makes it extremely challenging to conduct in-situ measurements or other observations through experimental means. Thus, numerical simulation becomes a very important tool to help understand the underlying electrochemical dynamics and transient transport phenomena within PEM fuel cells. In this thesis research a comprehensive, three- dimensional mathematical model is developed which accounts for the convective and diffusive gas flow in the gas channel, multi-component diffusion in the porous backing layer, electrochemical reactions in the catalyst layers, as well as flow of charge and heat through the solid media. The governing equations which mathematically describe these transport processes, are discretized and solved using the finite-volume based software, Ansys FLUENT, with its in-built CFD-solvers. To handle the significant non-linearity stemming from these transport phenomena, a set of numerical under-relaxation schemes are developed using the programming language C++. Good convergence is achieved with these schemes, though the model is based on a serpentine single-channel flow approach. The model results are validated against experimental results and good agreement is achieved. The result shows that the activation overpotential is the greatest cause of voltage loss in a high temperature PEM fuel cell. The degree of oxygen depletion in the catalyst layer, under the ribs, is identified and quantified for a given set of input parameters. This factor is followed by membrane resistance to protonic migration. The model can thus be suitable applied as a tool to predict cell performance. The results also show that performance is influenced by not just one, but a combination of inter-related factors, thus temperature increases, and flow rate changes will only be effective if simultaneously, the concentration of inlet oxygen, and the mobility of proton-ions in the membrane is increased. Not only does the model results verify these phenomena, but provide a quantitative output for any given set of input parameters. It can therefore be suitably applied as an optimisation tool in high temperature PEM fuel cell design

Numerical investigation of ion transport mechanisms in electrochemical energy storage devices: Similarity correlation and exergy destruction analysis

The shift towards renewable sources of energy requires the development of electrochemical energy storage solutions due to their scalability and ability to handle intermittency. In this thesis, the ion transport mechanisms are studied by modeling redox flow batteries (RFBs) and intercalation-based Li-ion batteries. Redox flow batteries are an emerging technology which allows independent scaling of energy and power density making them suitable candidates for grid-scale energy storage. In RFBs the redox active species is dissolved in electrolytes and stored in tanks. The electrolyte is pumped through the reactor where electrochemical reactions occur. Contemporary RFB research is focused around developing newer materials. However, the fundamental mechanisms causing polarization losses and energy inefficiencies that are inherent to the RFB design, and independent of chemistry, have received lesser attention in research. In this thesis, we present a transient multi-species RFB model using homogenized Poisson-Nernst-Planck formulation with hydrodynamic dispersion in porous media for the species transport. The RFBs modeled here can use either cost-effective non-selective separators or crossover reducing ion-exchange membranes. We also introduce Marcus-Hush-Chidsey kinetic theory based on microscopic electron transfer and solvent reorganization in modeling the redox reactions for RFBs instead of the most commonly used Butler Volmer empirical model. We detail the finite volume formulation with implicit time stepping along with a logarithmic transform of the concentration fields to solve the system of equations. A detailed stability analysis is conducted using the fixed-point iteration scheme for the two kinetic models to establish convergence. For RFBs using non-selective separators, we use Damköhler numbers to classify three RFB operating regimes: redox shuttle limited, ohmic polarized, and sufficient supporting electrolyte. The sufficient supporting electrolyte regime ensures the least capacity fade due to crossover. In the case of RFBs using ion-exchange membranes, we perform comprehensive exergy destruction analysis, using the first and second laws of thermodynamics, to quantify the energy losses arising due to electron-conduction, pore-scale mass transfer, reaction kinetics, species transport, and electrolyte mixing in the tanks. Mapping of these exergy losses enables the identification of major sources of irreversibilities for designing more energy efficient RFBs. The non-dimensional nature of results presented in this study should find applicability towards designing efficient low-cost RFBs by modifying the flow conditions, reactor geometry, electrode morphology, and engineering the redox active species and the salt ions. Li-ion batteries, in contrast with RFBs, operate on the principle of intercalation of lithium ions. The strong anisotropic behavior of graphite platelets restricts the transport of lithium ions through the electrode thickness limiting the thickness. However, thick Li-ion battery electrodes could enable batteries that cost less and have higher gravimetric and volumetric energy density. With the help of a porous electrode model with anisotropic transport processes, we propose and develop a design criterion for bi-tortuous graphite electrodes with electrolyte-rich macro-pores. Macro-pores with optimal aspect ratio spaced at short intervals enable maximum enhancement in Li-ion intercalation

State Of the Art Report in the fields of numerical analysis and scientific computing. Final version as of 16/02/2020 deliverable D4.1 of the HORIZON 2020 project EURAD.: European Joint Programme on Radioactive Waste Management

Document information Project Acronym EURAD Project Title European Joint Programme on Radioactive Waste Management Project Type European Joint Programme (EJP) EC grant agreement No. 847593 Project starting / end date 1 st June 2019-30 May 2024 Work Package No. 4 Work Package Title Development and Improvement Of NUmerical methods and Tools for modelling coupled processes Work Package Acronym DONUT Deliverable No. 4.

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal