Three-dimensional computational analysis of transport phenomena in a PEM fuel cell

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Abstract

A comprehensive non-isothermal, three-dimensional computational model of a polymer electrolyte membrane (PEM) fuel cell has been developed. The model incorporates a complete cell with both the membrane-electrode-assembly (MEA) and the gas distribution flow channels. With the exception of phase change, the model accounts for all major transport phenomena.

The model is implemented into a computational fluid dynamics code, and simulations are presented with an emphasis on the physical insight and fundamental understanding afforded by the detailed three-dimensional distributions of reactant concentrations, current densities, temperature and water fluxes. The results show that significant temperature gradients exist within the cell, with temperature differences of several degrees K within the MEA. The three-dimensional nature of the transport is particularly pronounced under the collector plates land area and has a major impact on the current distribution and predicted limiting current density.

Introduction

Fuel cells convert the chemical energy of hydrogen and oxygen directly into electricity. Their high efficiency and low emissions have made them a prime candidate for powering the next generation of electric vehicles, and their modular design and the prospects of micro-scaling them have gained the attention of cellular phone and laptop manufacturers. Their scalability and relative flexibility in terms of fuel makes them prime candidates for a variety of stationary applications including distributed residential power generation. The basic structure and operation principle of the polymer electrolyte membrane (PEM) fuel cell considered here are illustrated in Fig. 1.

The polymer electrolyte consists of a perfluorinated polymer backbone with sulfonic acid side chains. When fully humidified, this material becomes an excellent protonic conductor. The membrane, the catalyst (platinum supported on carbon particle) and the two electrodes (teflonated porous carbon paper or cloth) are assembled into a sandwich structure to form a membrane-electrode-assembly (MEA). The MEA is placed between two graphite bipolar plates with machined groves that provide flow channels for distributing the fuel (hydrogen) and oxidant (oxygen from air).

The hydrogen rich fuel fed to the anode side diffuses through the porous gas-diffusion electrode (GDE). At the catalyst layer, the hydrogen splits into hydrogen protons and electrons according to: 2H2⇒4H++4eDriven by an electric field, the H+ ions migrate through the polymer electrolyte membrane. The oxygen in the cathode gas stream diffuses through the towards the catalyst interface where it combines with the hydrogen protons and the electrons to form water according to: O2+4H++4e⇒2H2OThe overall reaction is exothermic and can be written as: 2H2+O2⇒2H2O+electricity+heatSeveral coupled fluid flow, heat and mass transport processes occur in a fuel cell in conjunction with the electrochemical reaction. These processes have a significant impact on two important operational issues: (i) thermal and water management; (ii) mass transport limitations. Water management ensures that the PEM remains fully hydrated to maintain good ionic conductivity and performance. Water content of the membrane is determined by the balance between water production and three water transport processes: electro-osmotic drag of water, associated with proton migration through the membrane from the anode to the cathode side; back diffusion from the cathode; and diffusion of water to/from the oxidant/fuel gas streams. Without control, an imbalance between production and removal rates of water can occur. This results in either dehydration of the membrane, or flooding of the electrodes; both phenomena have a very detrimental effect on performance and fuel cells have to be carefully designed to avoid the occurrence of either phenomenon. Thermal management is required to remove the heat produced by the electrochemical reaction (up to ∼50% of the energy produced during high power density operation) in order to prevent drying out of the membrane and excessive thermal stresses that may result in rupture of the membrane. The small temperature differentials between the fuel cell stack and the operating environment make thermal management a challenging problem in PEMFCs.

Because of the highly reactive environment of a fuel cell it is not possible to perform detailed in situ measurements during operation. Such information has been sought through modelling and simulation in order to improve understanding of water and species transport, optimize thermal management and shorten the design and optimization cycles. Modelling of fuel cells is challenging, because the processes involve multi-component, multi-phase, and multi-dimensional flow, heat and mass transfer with electrochemical reactions, all occurring in irregular geometries including porous media. Numerous authors have developed fuel cell models accounting for various physical processes. The most prominent earlier works stem from Bernardi and Verbrugge [3], [4] and Springer et. al. [14], who developed one-dimensional, isothermal models of the MEA. Fuller and Newman [8] published a quasi two-dimensional model based on concentration theory. The work by Nguyen and White [12], and Yi and Nguyen [21] was two-dimensional in nature, but the GDEs were omitted, assuming “ultrathin” electrodes. The importance of accounting for temperature gradients in fuel cells modelling was demonstrated in the work of Woehr et. al. [20] and Djilali and Lu [7]. The important issue of water flooding was addressed by Baschuk and Li in a recent one-dimensional model [2].

Earlier models were primarily analytic and required a number of simplifications due to the limitations of the numerical techniques. More recently, a general trend can be observed to apply the methods of computational fluid dynamics to fuel cell modelling. Gurau et al. [9] published a fully two-dimensional model of a whole fuel cell, i.e. two gas-flow channels separated by the MEA. Um et al. [18] and Wang et al. [19] have developed a similar model and included two phase flow. However, the underlying assumption was isothermal behaviour, which is a serious modelling limitation as we will see later. The local temperature distribution has a significant impact on the amount of water that undergoes phase change, and therefore the isothermal assumption can lead to results that are not physically representative when phase change is accounted for. Finally as a result of the architecture of a cell, the transport phenomena in a fuel cell are inherently three-dimensional, but no models have yet been published to address this.

In this paper we address simultaneously the need to account for thermal gradients and multi-dimensional transport using a computational fluid dynamics based approach that couples convective transport in the gas-flow channels with transport and electrochemistry in the MEA.

Section snippets

Model description

The PEM fuel cell model presented here is a comprehensive three-dimensional, non-isothermal, steady-state model providing a detailed description of the following transport phenomena:

  • multi-component flow;

  • convective heat and mass transport in the flow channels;

  • diffusion of reactants through porous electrodes;

  • electrochemical reactions;

  • migration of H+ protons through the membrane;

  • transport of water through the membrane;

  • transport of electrons through solid matrix;

  • conjugate heat transfer.

The

Fuel cell performance

The fuel cell performance is shown in terms of the polarization in Fig. 4. The results agree well with the experiments [17] in the low and intermediate current density region. The discrepancy at high current densities is attributed to the fact that experimental data at the higher current densities was insufficient, and in fact the experimental curve in this region is a curve fit weighted by the lower current density data. It should also be pointed out that the exact geometry of the fuel cell

Conclusions

A comprehensive three-dimensional computational model of a PEM fuel cell has been developed. With the exception of phase change, the model accounts for all major transport phenomena in the flow channels, electrodes and electrolyte membrane. Results that are physically consistent and in good agreement with available experimental data are obtained. The three-dimensional nature of the distribution of flow velocities, species concentration, mass transfer rates, electric current and temperature was

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