A three-dimensional pore-scale model of the cathode electrode in polymer-electrolyte membrane fuel cell by lattice Boltzmann method
Introduction
A sustainable, high quality life is the basic driver for providing a clean, safe, reliable and secure energy supply in the world. Fuel cells and hydrogen systems are important technologies which may contribute positively to the future world energy demand. Among different types of fuel cells, proton exchange membrane (PEM) fuel cells currently hold the most promising prospect. They can be employed in a wide range of applications, ranging from very small portable devices such as mobile phones and laptops, through transport applications like cars, delivery vehicles, buses and ships, to combined heat and power generators in stationary applications in the domestic and industrial sectors [1].
Nevertheless, some barriers such as high cost and operational difficulties hinder PEM fuel cells' wide commercialization, which make fundamental research for their development inevitable. Modeling of reactant gas transport accompanied by electrochemical reactions in the electrodes is of great importance, especially in the cathode where the oxygen reduction reaction is sluggish and inefficient [2]. Numerous numerical models of the cathode electrode with different features can be found in the literature [3]. In most of these models, the gas diffusion layer (GDL) of cathode electrode is considered as a homogeneous and isotropic porous medium, while in reality that is not the case [4]. In this regard, pore-scale modeling techniques which can realistically capture the microstructure of the cathode GDL are extremely attractive.
Some researchers have used more conventional methods, such as the finite volume, to model electrodes of a PEMFC. Harvey et al. [5], for example, used such a method to investigate different approaches to modeling the catalyst layer of PEM fuel cells. They compared three catalyst treatments of thin-film model, discrete-catalyst volume model and agglomerate model, and concluded that only the agglomerate model could capture mass transport limitations that occur at high current densities. Sahraoui et al. [6] presented a two-dimensional, finite-volume model of a PEM fuel cell taking into consideration the finite thicknesses of the catalyst layer and membrane. Sun et al. [7] also introduced a two-dimensional model for PEM fuel cell cathode that treated the catalyst layer as agglomerates of polymer electrolyte coated catalyst particles. They showed that the cathode over-potential inside the catalyst layer was non-uniform influenced by the channel-land geometry.
In the past decade, lattice Boltzmann method has emerged as a powerful pore-scale modeling technique applicable in complicated, heterogeneous, anisotropic porous media such as GDLs of PEM fuel cells. Lattice Boltzmann method is superior to other conventional numerical modeling techniques through many aspects such as capability of dealing with complex boundaries of a complicated microstructure, easy parallelizable algorithm development, and facility in modeling multi-phase fluid flow in a porous medium [8].
However, a significant challenge for lattice Boltzmann modeling of the cathode electrode is a proper way to consider electrochemical reaction in the catalyst layer [9]. To the best of the authors' knowledge the electrochemical reaction is taken into account in only a few two-dimensional lattice Boltzmann investigations, such as those presented by Chen et al. [10], [11], [12]; moreover, no such three-dimensional modeling, taking into account the electrochemical reaction, was found in the literature. In the present study, a single-phase, three-dimensional model of the cathode electrode of a PEM fuel cell is presented in which the catalyst layer is considered as a thin interface where the electrochemical reaction occurs. The proposed model is implemented to investigate the effects of GDL microstructure on the distributions of species and current density. An advantage of the proposed model over previous lattice Boltzmann models [10], [11], [12] is the use of an active approach for species transport. In the preceding investigations [10], [11], [12], a passive approach was applied in which the velocity field is only solved for nitrogen that is taken as the solvent. This may lead to lack of accuracy especially when the density of other species is comparable to that of nitrogen which may happen at high over-potentials; in such cases no species can be considered as a solvent [13]. On the other hand, in an active approach the internally coupled velocity fields of all species are solved individually which can lead to more accurate results.
Section snippets
Framework of lattice Boltzmann method
Lattice Boltzmann method is a powerful numerical modeling technique that has attracted much interest in the past decade. In this method, a fluid is assumed to be composed of virtual fluid particles which move and collide with each other in a lattice structure. These particles are treated by a distribution function rather than by positions and velocity vectors [14]. This kinetic nature of lattice Boltzmann method provides some superior features relative to other numerical methods, such as the
Three-dimensional reconstruction of GDL microstructure
In the early efforts of lattice Boltzmann simulation of fluid flow in pore spaces of a GDL, very simplified microstructures were used [23], [24]. However, with today's enhancement of electron microscopy methods, more realistic delineations of GDL microstructure can be provided by different three-dimensional reconstruction methods. Generally, the implemented methods for three-dimensional reconstruction of a GDL can be classified into two categories: imaging combination and stochastic generation.
Computational domain and boundary conditions
The computational domain consists of a portion of GDL, catalyst layer and land as shown in Fig. 5. As mentioned previously, the catalyst layer is simply treated as a thin interface on the bottom surface of the computational domain on which electrochemical reaction occurs. Two opposite lateral sides of computational domain are considered as the inlet (plane x = 0) and outlet (plane x = 100 μm), while the other two lateral sides (planes y = 0 and y = 100 μm) are assumed as symmetry planes.
The
Preliminary results and discussion
The purpose of this article is to present the details of the proposed three-dimensional model for the cathode electrode of a PEM fuel cell. Therefore, only some preliminary results are presented here to demonstrate the capabilities of the model. Further simulations will be performed to investigate more thoroughly the effects of realistic microstructure of GDLs on a PEM fuel cell performance. Such simulations will require more sophisticated computational facilities that are not currently
Conclusions
In the present study, a three-dimensional pore-scale model based on lattice Boltzmann method is proposed for the cathode electrode of a PEM fuel cell, taking into account the electrochemical reaction on the catalyst layer and microstructure of the GDL. The model enables us to simulate single-phase, multi-species reactive flow in a heterogeneous, anisotropic GDL through an active approach. Reactive flow in three reconstructed GDLs with different anisotropy parameters is simulated to investigate
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