Fuel cells : state of the art

Publication CIMNEThis report pretends to explain the state of the art of fuel cells and the applications focused on aviation, such as unmanned aerial vehicles (UAV). A fuel cell is an electromechanical device that ha the ability to convent chemical energy of a reactant directly into electricity with high efficiency. When the fuel reacts with the oxidant, the electromechanical reaction takes place and some energy is released, usually low-voltage DC electrical energy and heat. The former is used to do useful work directly and the latter is wasted or can be used in cogeneration applications. In the following sections, two concepts will be described: the unit cell and the fuel cell. The unit is the basic operating device that converts chemical energy into electricity. Multiple unit cells connected together in series make up the fuel cell, giving the desired voltage in a specific application.Preprin

Modelització d’una pila de combustible tipus PEM mitjançant el Mètode dels Elements Finits

En aquest Projecte Final de Carrera es pretén modelar matemàticament una pila de combustible per tal de predir el seu comportament mitjançant el Mètode dels Elements Finits. Primerament es fa un estudi de l’estat de l’art de les piles de combustible on, entre altres aspectes, es presenten les equacions generals que serveixen de base pel model matemàtic en qüestió. Abans de presentar el model es fa un breu resum teòric del Mètode dels Elements Finits i del programari emprat en la modelització, que és GiD i el seu mòdul Tdyn. Definides la teoria i les eines necessàries per a la modelització, es desenvolupa el model matemàtic de les piles de combustible, considerant una sèrie de simplificacions degudament justificades. Les variables que defineixen el problema són la pressió dels gasos reactius, la fracció molar, la velocitat, els potencials elèctric i iònic, i les densitats de corrent elèctric i iònic. Els resultats obtinguts es comparen amb estudis anteriors similars al que s’ha dut a terme i es comprova que hi ha una similitud raonable. A més, es fa un estudi fluidodinàmic de la distribució del mòdul de la velocitat de l’hidrogen a l’ànode segons la velocitat d’entrada i la mida de la pila. Si s’augmenta la velocitat d’entrada, el perfil de velocitats és més homogeni al llarg de la pila, que és el què es vol aconseguir. Tot i així, augmentar la velocitat del gas reactiu empitjora el rendiment de la pila. De manera alternativa, si es redueix la mida de la pila a la meitat el perfil de velocitats també s’homogeneïtza de forma notable sense reduir el rendiment

Analysis of droplet dynamics on the GDL surface of a PEM fuel cell cathode

A fuel cell is an electrochemical device that has the ability to turn the chemical energy in a fuel directly into electricity with high e ciency. Inside the fuel cell, oxidation and reduction electrochemical reactions take place producing low-voltage current (DC) and heat. The former is used to do useful work while the latter is wasted or can be used in cogeneration applications. Fuel cells are usually compared with other energy convertors, like reciprocating engines or batteries. Batteries and fuel cells have the same operating principle, based on the electrochemical reactions at the anode and the cathode. The main di erence being that batteries store the reactant inside the cell instead of in a separate storage tank. There are di erent types of fuel cells depending on the materials used in the electrolytes, the substances that react in the anode and the cathode or the working temperature. The current work focuses on Polymer Electrolyte Membrane (PEM) fuel cells, which can work between -40 and 100 C and use hydrogen as fuel, oxygen as cathode reactant and Na on® as the electrolyte (Figure 1.1). The working principle of the PEM fuel cell is based on two electrochemical reactions. The process starts at the anode, where the hydrogen ows in the anode Gas Flow Channel (GFC) and di uses through the pores in the Gas Di usion Layer (GDL). Attached to the GDL is the Catalyst Layer (CL). The CL is made using a platinum-based ink which is painted on either the PEM or the GDL. The ink contains carbon, Pt and electrolyte. The resulting coating is a thin (about 10 m) porous layer. The Pt catalyses the rst reaction: the hydrogen oxidation reaction.H2 ! 2H+ + 2e- (1.1) After this reaction, the next layer is the membrane which is made of Na on®. The membrane allows the protons to travel across its section but it is impermeable for the electrons and gases. The electrons have to go back through the GDL and the current collector (that act as the walls of the anode gas ow channel) in order to meet the protons at the other side of the membrane, thus generating the desired electric current. In the cathode, the oxygen ows in the cathode gas channels, di uses through the GDL and in the catalyst layer reacts with the protons from the membrane, performing the second reaction: 2H+ + 2e- + 1 2 O2 ! 2H2OThe union of the anode GDL and CL, membrane and cathode CL and GDL is also known as Membrane Electrode Assembly (MEA). When fuelled with hydrogen, the fuel cell has zero emissions, since the only product of the electrochemical reaction is water and heat. The water generated in the reaction is one of the key factors in uencing the fuel cell performance. The membrane needs water in order to conduct the protons; if there is not enough water, the membrane dries out and the fuel cell cannot work any longer. Alternatively, if there is too much water, the pores in the CL and GDL ood preventing the reactant gases from di using through it. The exceeding water has therefore to be evacuated through the cathode gas channels. This is the starting point of the present work. There are three types of two-phase ow in the gas channels depending on di erent factors. Their names change depending on the author, however, these ows are usually known as droplet, lm and slug ow [2], as shown on Figure 1.2. The present work focuses on droplet ow and the conditions that lead to lm and slug ow. Since it is very di cult to develop an analytical equation for the shape of a water lm, the best way to proceed is the analysis of a single static and deformed droplet and then identify the conditions that lead to lm and slug ow formation. In addition, the area coverage of the formed droplets is another variable that needs to be considered, and this variable takes values from 0 to 1 only when the ow is identi ed as droplet ow

On the application of the PFEM to droplet dynamics modeling in fuel cells

The Particle Finite Element Method (PFEM) is used to develop a model to study two-phase flow in fuel cell gas channels. First, the PFEM is used to develop the model of free and sessile droplets. The droplet model is then coupled to an Eulerian, fixed-grid, model for the airflow. The resulting coupled PFEM-Eulerian algorithm is used to study droplet oscillations in an air flowand droplet growth in a lowtemperature fuel cell gas channel. Numerical results show good agreement with predicted frequencies of oscillation, contact angle, and deformation of injected droplets in gas channels. The PFEM-based approach provides a novel strategy to study droplet dynamics in fuel cells.Postprint (published version

An implicit surface tension model for the analysis of droplet dynamics

A Lagrangian incompressible fluid flow model is extended by including an implicit surface tension term in order to analyze droplet dynamics. The Lagrangian framework is adopted to model the fluid and track its boundary, and the implicit surface tension term is used to introduce the appropriate forces at the domain boundary. The introduction of the tangent matrix corresponding to the surface tension force term ensures enhanced stability of the derived model. Static, dynamic and sessile droplet examples are simulated to validate the model and evaluate its performance. Numerical results are capable of reproducing the pressure distribution in droplets, and the advancing and receding contact angles evolution for droplets in varying substrates and inclined planes. The model is stable even at time steps up to 20 times larger than previously reported in literature and achieves first and second order convergence in time and space, respectively. The present implicit surface tension implementation is applicable to any model where the interface is represented by a moving boundary mesh.Peer ReviewedPostprint (published version

Numerical study of droplet dynamics in a polymer electrolyte fuel cell gas channel using an embedded Eulerian-Lagrangian approach

An embedded Eulerian-Lagrangian formulation for the simulation of droplet dynamics within a polymer electrolyte fuel cell (PEFC) channel is presented. Air is modeled using an Eulerian formulation, whereas water is described with a Lagrangian framework. Using this framework, the gas-liquid interface can be accurately identified. The surface tension force is computed using the curvature defined by the boundary of the Lagrangian mesh. The method naturally accounts for material property changes across the interface and accurately represents the pressure discontinuity. A sessile drop in a horizontal surface, a sessile drop in an inclined plane and droplets in a PEFC channel are solved for as numerical examples and compared to experimental data. Numerical results are in excellent agreement with experimental data. Numerical results are also compared to results obtained with the semi-analytical model previously developed by the authors in order to discuss the limitations of the semi-analytical approach.Peer ReviewedPostprint (published version

Modeling of droplet dynamics in a proton exchange fuel cell electrode channel

Fuel cells are promising alternatives to conventional energy conversion devices. Cells fueled with hydrogen are environmentally friendly and their effciency is up to 3 times higher than that of high-temperature combustion devices. However, they are still expensive and their durability is limited. One of the key factors in fuel cell performance is the so-called water management. Water produced within the fuel cell is evacuated through the gas channels, but at high current densities water can block the channel, limiting the current density generated in the fuel cell and thus reducing its effciency. Novel numerical analysis methods with feasible computational cost and high accuracy could help characterizing droplet transport in gas microchannels. In this work we focus on modeling and simulation of droplet emergence, deformation and detachment in fuel cell gas channels as this defines the most common mode of liquid transport in the problem at hand. However, methods presented could be applied to other problems involving a gas-liquid system, where liquid is found as small droplets or films. A semi-analytical model of a water droplet emerging from a pore of the gas diffusion layer surface in a Polymer Electrolyte fuel cell channel is developed. The geometry of the static and deformed shape is characterized and the main geometric variables (i.e. radius, height, perimeter) are assumed to depend on the contact angles only. The forces acting on the droplet are the drag force of the air and the surface tension force, which acts as adhesion force. The analytical study solves the problem of a growing droplet in a gas ow channel to see the effects of: i) air velocity and liquid mass ow in droplet deformation and oscillation; and, ii) droplet height in frequency of oscillation. The predicted values for both drag and surface tension force are higher than the results found in literature. Higher air velocity values lead to more deformation of the droplet and oscillation with lower frequency but higher amplitude. Similar effects have been identified when the liquid mass ow is increased, leading to faster detachment of the droplet. A continuum Lagrangian formulation for the simulation of droplet dynamics is proposed next. This model is developed in two and three dimensions. Using the Lagrangian framework, liquid surface can be accurately identified. The surface tension force is computed using the curvature defined by the boundary of the Lagrangian mesh. Special emphasis is given to the treatment of the surface tension term in the linearized version of governing equations. The corresponding tangent matrix allows for alleviating the severe time step size restrictions associated to the capillary wave scale. A dynamic contact angle condition is developed in order to include effects of rough surfaces in contact line evolution. Numerical examples of sessile drop in a horizontal surface and sessile drop in an inclined plane are compared to experimental results. Results show excellent agreement with experimental data. Numerical results are also compared the semi-analytical model previously developed by the authors in order to discuss the limitations of the semi-analytical approach. An embedded formulation for the simulation of immiscible coupled gas-liquid problems is then presented. Previous model considered only the liquid domain, and air ow effects were not included at the continuum level. The embedded method is particularly designed for handling gas-liquid systems where liquid represents a small fraction of the total domain. Gas and liquid are modeled using the Eulerian and the Lagrangian formulation, respectively. The Lagrangian domain (liquid) moves on top of the fixed Eulerian mesh. The location of the material interface is accurately defined by the position of the boundary mesh of the Lagrangian domain. The individual fluid problems are solved in a partitioned fashion and are coupled using a Dirichlet-Neumann algorithm. Neumann part of the coupling includes the entire stress tensor (normal and tangential components). Representation of the pressure discontinuity across the interface does not require any additional techniques being an intrinsic feature of the method. The proposed formulation is validated with several numerical examples and a convergence analysis is included as well. Finally, the embedded formulation is used to model the problem of interest, which is the dynamics of a droplet in a PEFC electrode channel. Numerical examples include a time detachment analysis, where the droplet pins and detachment occurs when a threshold value of contact angle hysteresis is reached. Results show good agreement with experimental data available, and results using the semi-analytical method again show the limitations of this model. An extension to the previous example includes water injection into the gas channel in order to compare results with previous studies in literature.Las pilas de combustible son una alternativa prometedora a los dispositivos de conversión de energía convencionales. Las pilas alimentadas con hidrogeno son respetuosas con el medio ambiente y su eficiencia es hasta 3 veces mayor que la de los dispositivos de combustión de alta temperatura. Sin embargo, su precio todavía es elevado y su durabilidad es limitada. Uno de los factores clave en el rendimiento de las pilas de combustible es la denominada gestión del agua. El agua producida dentro de la pila es evacuada a través de los canales de gas, pero en condiciones de alta densidad de corriente, el agua puede bloquear el canal, limitando la densidad de corriente generada en la pila de combustible y reduciendo así su eficiencia. Nuevos métodos de análisis numérico con un coste computacional factible y una mayor precisión podrán ayudar a caracterizar el transporte de gotas en microcanales de gas. En este trabajo nos centramos en la formación de la gota, su deformación y posterior desprendimiento en los canales de gas de las pilas de combustible, ya que esto define el modo de transporte de la fase líquida más común en el problema analizado. Sin embargo, los métodos presentados podrán ser aplicados a otros problemas relacionados con un sistema gas-líquido, donde el líquido se encuentra como pequeñas gotas o películas. En la presente tesis, se ha desarrollado un modelo semi-analítico de una gota de agua que emerge de un poro de la superficie de la capa de difusión en un canal de una pila de combustible tipo PEFC (Polymer Electrolyte fuel cell). La geómetra de la gota estática y deformada se ha caracterizado y se ha supuesto que las principales variables geométricas (radio, altura, perímetro) sólo dependen de los ángulos de contacto. Las fuerzas que actúan sobre la gota son la fuerza de arrastre del aire y la fuerza de tensión superficial, que actúa como fuerza de adherencia. El estudio analítico resuelve el problema de una gota que crece en un canal de gas para ver los efectos de: i) la velocidad del aire y del caudal de líquido en la deformación de las gotas y su oscilación; y, ii) la altura de la gota en la frecuencia de oscilación. Los valores predichos tanto para la fuerza de arrastre como para la tensión superficial son más altos que los resultados encontrados en la literatura. A mayor velocidad del aire, mayor es la deformación de la gota y sus oscilaciones tienen menor frecuencia pero mayor amplitud. Se han identificado efectos similares cuando se incrementa el caudal de líquido, dando lugar a un desprendimiento más rápido de la gota. Los valores de oscilación de frecuencia predichos son significativamente menores que los valores de la literatura, pero estos resultados han sido obtenidos en condiciones distintas de inyección de agua. Como alternativa al modelo semi-analítico, se propone una formulación continua Lagrangiana para la simulación de la dinámica de gotas. El modelo se ha desarrollado en dos y tres dimensiones. Utilizando el enfoque Lagrangiano, la superficie del líquido se puede identificar con precisión. La fuerza de tensión superficial se calcula utilizando la curvatura definida por el borde de la malla Lagrangiana. Se hace especial hincapié en el tratamiento del término de tensión superficial en la versión linealizada de las ecuaciones de gobierno. La matriz tangente correspondiente permite suavizar las restricciones de paso de tiempo asociadas a la escala de la onda capilar. Se ha incluido una condición de ángulo de contacto dinámico con el fin de incluir los efectos de las superficies rugosas en la evolución de la línea de contacto. Los resultados obtenidos en los ejemplos numéricos de una gota estática en una superficie horizontal y en un plano inclinado se han comparado con resultados experimentales. Los resultados muestran una excelente concordancia con los datos experimentales. También se han comparado los resultados numéricos con el modelo semi-analítico desarrollado previamente por los autores con el _n de discutir las limitaciones del enfoque semi-analítico. Con el _n de incluir los efectos del aire sobre la gota, se presenta una formulación incrustada (embedded de su terminología en inglés) para la simulación de problemas de varios fluidos inmiscibles. El modelo anterior sólo considera el dominio de líquido, y los efectos del flujo de aire no se incluyen. El método está diseñado especialmente para la simulación de sistemas gas-líquido donde el líquido representa una pequeña fracción del dominio. El gas y el líquido se modelan mediante las formulaciones Euleriana y Lagrangiana, respectivamente. El dominio Lagrangiano (líquido) se mueve por encima de la malla Euleriana fija. La ubicación de la interfaz material se define exactamente por la posición del borde de la malla del dominio Lagrangiano. Los problemas de cada fluido se resuelven de una manera particionada y se acoplan mediante un algoritmo de Dirichlet-Neumann. La representación de la discontinuidad de la presión a través de la interfaz no requiere técnicas adicionales, ya que es una característica intrínseca del método. La formulación propuesta se valida con varios ejemplos numéricos y también se ha incluido un análisis de convergencia. Finalmente, la formulación embedded se utiliza para modelar el problema objetivo, que es la dinámica de una gota en un canal de una pila PEFC. Los ejemplos numéricos incluyen un análisis del tiempo de desprendimiento, donde la línea de contacto de la gota se fija y el desprendimiento se produce cuando se alcanza un valor de umbral de la histéresis del ángulo de contacto. Los resultados concuerdan satisfactoriamente con los datos experimentales disponibles, y los resultados utilizando el modelo semi-analítico muestran de nuevo las limitaciones de este modelo. Finalmente el ejemplo anterior se extiende incluyendo la inyección de agua en el canal de gas con el fin de comparar los resultados con estudios previos encontrados en la literatura

Fuel cells : state of the art

Publication CIMNEThis report pretends to explain the state of the art of fuel cells and the applications focused on aviation, such as unmanned aerial vehicles (UAV). A fuel cell is an electromechanical device that ha the ability to convent chemical energy of a reactant directly into electricity with high efficiency. When the fuel reacts with the oxidant, the electromechanical reaction takes place and some energy is released, usually low-voltage DC electrical energy and heat. The former is used to do useful work directly and the latter is wasted or can be used in cogeneration applications. In the following sections, two concepts will be described: the unit cell and the fuel cell. The unit is the basic operating device that converts chemical energy into electricity. Multiple unit cells connected together in series make up the fuel cell, giving the desired voltage in a specific application

An embedded approach for immiscible multi-fluid problems

An embedded formulation for the simulation of immiscible multi-fluid problems is proposed. The method is particularly designed for handling gas-liquid systems. Gas and liquid are modeled using the Eulerian and the Lagrangian formulation, respectively. The Lagrangian domain (liquid) moves on top of the fixed Eulerian mesh. The location of the material interface is exactly defined by the position of the boundary mesh of the Lagrangian domain. The individual fluid problems are solved in a partitioned fashion and are coupled using a Dirichlet-Neumann algorithm. Representation of the pressure discontinuity across the interface does not require any additional techniques being an intrinsic feature of the method. The proposed formulation is validated, and its potential applications are shown. Copyright (C) 2015 John Wiley & Sons, Ltd.Peer Reviewe

Effect of lining thermal inertia on small-scale compartment fire

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