Lattice Boltzmann simulations of anisotropic permeabilities in carbon paper gas diffusion layers

The multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) with multi-reflection solid boundary conditions is used to study anisotropic permeabilities of a carbon paper gas diffusion layer (GDL) in a fuel cell. The carbon paper is reconstructed using the stochastic method, in which various porosities and microstructures are achieved to simulate different samples. The simulated permeability and tortuosity show anisotropic characteristics of the reconstructed carbon papers with in-plane permeability higher than through-plane, and in-plane tortuosity lower than through-plane. The calculated permeabilities are in good agreement with existing measurements. The relationship between the permeability and the porosity is fitted with empirical relations and some fitting constants are determined. Furthermore, the obtained relationship of tortuosity and porosity is used in a fractal model for permeabilities. The results indicate that the fractal model and the Kozeny–Carman equation provide similar predictions on the through-plane permeability of the carbon paper GDL.     

Comparing through-plane diffusibility correlations in PEFC gas diffusion layers using the lattice Boltzmann method

One of the key elements in a polymer electrolyte fuel cell (PEFC) is the gas diffusion layer (GDL). The GDL offers mechanical support to the cell and provides the medium for diffusing the reactant gases from the flow plates to the electrolyte enabling the electrochemical reactions, and therefore the energy conversion. At the same time, it has the task of transporting the electrons from the active sites, near to the electrolyte, towards the flow plates.Describing the fluid flow and mass transport phenomena through the GDLs is not an easy task not only because of their complex geometries, but also because of these phenomena occur at microscale levels. Most of the PEFC models at cell scale make assumptions about certain microscale transport parameters, assumptions that can make a model less close to the reality. The purpose of this study is to analyze five different proposed correlations to estimate the through-plane (TP) diffusibility of digitally created GDLs and using lattice Boltzmann (LB) models. The correlations are ranked depending on their precision, accuracy and symmetry. The results show that the best estimation is given when the porosity and gas-phase tortuosity are taken into account in the correlation.     

Numerical simulation of liquid water and gas flow in a channel and a simplified gas diffusion layer model of polymer electrolyte membrane fuel cells using the lattice Boltzmann method

Numerical simulations using the lattice Boltzmann method (LBM) are developed to elucidate the dynamic behavior of condensed water and gas flow in a polymer electrolyte membrane (PEM) fuel cell. Here, the calculation process of the LBM simulation is improved to extend the simulation to a porous medium like a gas diffusion layer (GDL), and a stable and reliable simulation of two-phase flow with large density differences in the porous medium is established. It is shown that dynamic capillary fingering can be simulated at low migration speeds of liquid water in a modified GDL, and the LBM simulation reported here, which considers the actual physical properties of the system, has significant advantages in evaluating phenomena affected by the interaction between liquid water and air flows. Two-phase flows with the interaction of the phases in the two-dimensional simulations are demonstrated. The simulation of water behavior in a gas flow channel with air flow and a simplified GDL shows that the wettability of the channel has a strong effect on the two-phase flow. The simulation of the porous separator also indicates the possibility of controlling two-phase distribution for better oxygen supply to the catalyst layer by gradient wettability design of the porous separator.     

Numerical simulations of gas resonant oscillations in a closed tube using lattice Boltzmann method

Numerical studies are presented for gas resonant oscillations in a two-dimensional closed tube using the lattice Boltzmann method. A multi-distribution function model of thermal lattice Boltzmann method is adopted in this work. The oscillating flow of the gas is generated by a plane piston at one end, and reflected by the other closed end. Both isothermal and adiabatic walls of the closed tube are considered. Boundary treatments such as moving adiabatic boundary are given in detail. The time dependent velocity, density and temperature at various locations of the tube for various frequencies and wall boundary conditions are presented. Shock waves with resonant frequency or slightly off-resonant frequencies are numerically captured. From the simulation results, the gas flow and heat transfer characteristics obtained are consistent qualitatively with those from previous simulations using conventional numerical methods.     

Lattice Boltzmann simulations of water transport in gas diffusion layer of a polymer electrolyte membrane fuel cell

The effect of wettability on water transport dynamics in gas diffusion layer (GDL) is investigated by simulating water invasion in an initially gas-filled GDL using the multiphase free-energy lattice Boltzmann method (LBM). The results show that wettability plays a significant role on water saturation distribution in two-phase flow in the uniform wetting GDL. For highly hydrophobicity, the water transport falls in the regime of capillary fingering, while for neutral wettability, water transport exhibits the characteristic of stable displacement, although both processes are capillary force dominated flow with same capillary numbers. In addition, the introduction of hydrophilic paths in the GDL leads the water to flow through the hydrophilic pores preferentially. The resulting water saturation distributions show that the saturation in the GDL has little change after water breaks through the GDL, and further confirm that the selective introduction of hydrophilic passages in the GDL would facilitate the removal of liquid water more effectively, thus alleviating the flooding in catalyst layer (CL) and GDL. The LBM approach presented in this study provides an effective tool to investigate water transport phenomenon in the GDL at pore-scale level with wettability distribution taken into consideration.     

Effects of porosity gradient in gas diffusion layers on performance of proton exchange membrane fuel cells

A three-dimensional, two-phase, non-isothermal model has been developed to explore the interaction between heat and water transport in proton exchange membrane fuel cells (PEMFCs). Water condensate produced from the electrochemical reaction may accumulate in the open pores of the gas diffusion layer (GDL) and retard the oxygen transport to the catalyst sites. This study predicts the enhancement of the water transport for linear porosity gradient in the cathode GDL of a PEMFC. An optimal porosity distribution was found based on a parametric study. Results show that a optimal linear porosity gradient with ?₁ = 0.7 and ?₂ = 0.3 for the parallel and z-serpentine channel design leads to a maximum increase in the limiting current density from 10,696 Am⁻² to 13,136 Am⁻² and 14,053 Am⁻² to 16,616 Am⁻² at 0.49 V, respectively. On the other hand, the oxygen usage also increases from 36% to 46% for the parallel channel design and from 55% to 67% for the z-serpentine channel design. The formation of a porosity gradient in the GDL enhances the capillary diffusivity, increases the electrical conductivity, and hence, benefits the oxygen transport throughout the GDL. The present study provides a theoretical support for existing reports that a GDL with a gradient porosity improves cell performance.     

Multi-phase micro-scale flow simulation in the electrodes of a PEM fuel cell by lattice Boltzmann method

The gas diffusion layer of a polymer electrolyte membrane (PEM) fuel cell is a porous medium generally made of carbon cloth or paper. The gas diffusion layer has been modeled conventionally as a homogeneous porous medium with a constant permeability in the literature of PEM fuel cell. However, in fact, the permeability of such fibrous porous medium is strongly affected by the fiber orientation having non-isotropic permeability. In this work, the lattice Boltzmann (LB) method is applied to the multi-phase flow phenomenon in the inhomogeneous gas diffusion layer of a PEM fuel cell. The inhomogeneous porous structure of the carbon cloth and carbon paper has been modeled as void space and porous area using Stokes/Brinkman formulation and void space and impermeable fiber distributions obtained from various microscopic images. The permeability of the porous medium is calculated and compared to the experimental measurements in literature showing a good agreement. Simulation results for various fiber distributions indicate that the permeability of the medium is strongly influenced by the effect of fiber orientation. Present lattice Boltzmann flow models are applied to the multi-phase flow simulations by incorporating multi-component LB model with inter-particle interaction forces. The model successfully simulates the complicated unsteady behaviors of liquid droplet motion in the porous medium providing a useful tool to investigate the mechanism of liquid water accumulation/removal in a gas diffusion layer of a PEM fuel cell.     

Two-phase transport in the cathode gas diffusion layer of PEM fuel cell with a gradient in porosity

Two-phase transport in the cathode gas diffusion layer (GDL) of a proton exchange membrane fuel cell (PEMFC) is studied with a porosity gradient in the GDL. The porosity gradient is formed by adding micro-porous layers (MPL) with different carbon loadings on the catalyst layer side and on the flow field side. The multiphase mixture model is employed and a direct numerical procedure is used to analyze the profiles of liquid water saturation and oxygen concentration across the GDL as well as the resulting activation and concentration losses. The results show that a gradient in porosity will benefit the removal rate of liquid water and also enhance the transport of oxygen through the cathode GDL. The present study provides a theoretical support for the suggestion that a GDL with porosity gradient will improve the cell performance.     

Improved pseudopotential lattice Boltzmann model for liquid water transport inside gas diffusion layers

Liquid water transport inside the gas diffusion layers (GDLs) plays a vital role in water management of proton exchange membrane fuel cells (PEMFCs). In this study, an improved pseudopotential multiphase lattice Boltzmann model is firstly developed to realize the actual density and viscosity ratios in porous media. The proposed model is based on a non-orthogonal multiple-relaxation-time (MRT) LB model and a new improved wettability boundary condition. In terms of the relationship between capillary pressure P_c and saturation s, the proposed model shows a good agreement with the experimental data. Using the validated model, the effects of capillary pressures and contact angles of mixed wettability on the liquid water invasion process for Toray-090 GDLs with two Polytetrafluoroethylene (PTFE) contents (10 wt% and 20 wt%) are studied. It is found that the liquid water shows capillary fingering behaviors and the liquid water saturation profiles along the through-plane direction of the GDLs become more non-uniform with increasing contact angle of PTFE.     

Tomographic analysis of porosity variation in gas diffusion layer under freeze-thaw cycles

Synchrotron X-ray micro-computed tomography (X-ray μCT) is employed to measure the volume variation of gas diffusion layer (GDL) of a polymer electrolyte fuel cell (PEFC). In the present study, 3D structures are reconstructed by merging orthogonal-plane images. Using the 3D reconstruction, the variation of structural parameters such as the porosity in GDL is investigated under freeze-thaw cycles. The freez-thaw cycles are established using cryo system and light source, respectively. As a result, a structural transformation is observed at the interface between GDL and micro porous layer (MPL). In addition, the porosity is critically changed with irreversible transition under freeze-thaw cycles.     

Development of simulated gas diffusion layer of polymer electrolyte fuel cells and evaluation of its structure

In polymer electrolyte fuel cell (PEFC), it is important to understand the behavior of liquid water in gas diffusion layer (GDL) which is one of the constructional elements so as to improve the output performance and the durability. As this behavior of liquid water is attributed to not only the hydrophilicity but also inhomogeneous structure, it is needed to examine in consideration of an actual GDL structure. In this study, as the basic examination of two-phase flow analysis in an actual GDL, a simulated GDL was made by numerical analysis considering the fiber placement. Furthermore, the prediction methods for pore size distribution, permeability and tortuosity of this simulated GDL were developed with the numerical analysis. These parameters of flow and mass transfer were compared with other studies, and the validity of this simulated GDL was confirmed. In addition, effective diffusion coefficient was calculated from tortuosity in simulated GDL, and PEFC output performance was evaluated by a simple model. Moreover, the optimal GDL was examined in consideration of the effect of porosity and fiber diameter at the fiber level.     

Application of lattice Boltzmann method to a micro-scale flow simulation in the porous electrode of a PEM fuel cell

The electrode of a PEM fuel cell is a porous medium generally made of carbon cloth or paper. Such a porous electrode has been widely modeled as a homogeneous porous medium with a constant permeability in the literature of PEM fuel cell. In fact, most of gas diffusion media are not homogeneous having non-isotropic permeability. In case of carbon cloth, the porous structure consists of carbon fiber tows, the bundles of carbon fiber, and void spaces among tows. The combinational effect of the void space and tow permeability results in the effective permeability of the porous electrode. In this work, the lattice Boltzmann method is applied to the simulation of the flow in the electrode of a PEM fuel cell. The electrode is modeled as void space and porous region which has certain permeability and the Stokes and Brinkman equations are solved in the flow field using the lattice Boltzmann model. The effective permeability of the porous medium is calculated and compared to an analytical calculation showing a good agreement. It has been shown that the permeability of porous medium is strongly dependant on the fiber tow orientation in three-dimensional simulations. The lattice Boltzmann method is an efficient and effective numerical scheme to analyze the flow in a complicated geometry such as the porous medium.     

Numerical simulation of direct methanol fuel cells using lattice Boltzmann method

In this study Lattice Boltzmann Method (LBM) as an alternative of conventional computational fluid dynamics method is used to simulate Direct Methanol Fuel Cell (DMFC). A two dimensional lattice Boltzmann model with 9 velocities, D2Q9, is used to solve the problem. The computational domain includes all seven parts of DMFC: anode channel, catalyst and diffusion layers, membrane and cathode channel, catalyst and diffusion layers. The model has been used to predict the flow pattern and concentration fields of different species in both clear and porous channels to investigate cell performance. The results have been compared well with results in literature for flow in porous and clear channels and cell polarization curves of the DMFC at different flow speeds and feed methanol concentrations.     

Effect of weave tightness and structure on the in-plane and through-plane air permeability of woven carbon fibers for gas diffusion layers

In this study, woven gas diffusion layers (GDLs) with varying weave type and tightness are investigated. Plain and twill weave patterns were manufactured in-house. The in-plane and through-plane air permeability of the woven samples were tested, and mercury intrusion porosimetry (MIP) tests were performed to study the pore structure. It was found that the twill weave has a higher permeability than the plain weave, which is consistent with literature. Like non-woven carbon papers, woven GDLs have higher in-plane permeability than through-plane permeability; however it has been shown that it is possible to manufacture a GDL with higher through-plane permeability than in-plane permeability. It was also concluded that the percentage of macropores in the weave is the driving factor in determining the through-plane air permeability. This work lays the groundwork for future studies to attempt to characterize the relationship between the weave structure and the air permeability in woven GDLs.     

An analytical model for the transverse permeability of gas diffusion layer with electrical double layer effects in proton exchange membrane fuel cells

An analytical model is presented for the transverse permeability of gas diffusion layer (GDL) based on an ordered array of parallel charged circular cylinders at the steady state. The formula of calculating the permeability of the transverse direction is given by solving the fluid momentum equation in a unit cell. In the present approach, the proposed model is explicitly related to the porosity and fiber radius of fibrous porous media, the zeta potential, and the physical properties of the electrolyte solution. Besides, the effects of these parameters (the porosity, unit cell aspect ratio, fiber radius, and molar concentration) on the transverse permeability are discussed detailedly. The model predictions are compared with the previous studies in the available literature, and good agreement is found.     

The impact of rib structure on the water transport behavior in gas diffusion layer of polymer electrolyte membrane fuel cells

Using the multiphase lattice Boltzmann method (LBM), the liquid water transport dynamics is simulated in a gas diffusion layer (GDL) of polymer electrolyte membrane fuel cells (PEMFCs). The effect of rib structure on the water invasion process in the micro-porous GDL is explored by comparing the two cases, i.e., with rib and without rib structures. The liquid water distribution and water saturation profile are presented to determine the wetting mechanism in the GDL. The results show that the liquid water transport in the GDL is strongly governed by capillary force and the rib structure plays a significant role on water distribution and water transport behavior in the GDL. Comparison of two cases confirms that the rib structure influences on the location of water breakthrough. The liquid water distribution and water saturation profile indicate that the high resistance force underneath the rib suppresses the growth of water cluster, resulting in the change of flow path. After water breakthrough, the liquid water distribution under the channel has little variation, whereas that under the rib continues to change. The predicted value of effective permeability is in good agreement with Carman-Kozeny correlation and experimental results in the literature. The results suggest that the LBM approach is an effective tool to investigate the water transport behavior in the GDL.     

Effects of basic gas diffusion layer components on PEMFC performance with capillary pressure gradient

The gas diffusion layer (GDL) is composed of a substrate and a micro-porous layer (MPL), and is treated with polytetrafluoroethylene (PTFE) to promote water discharge. Additionally, the MPL mainly consists of carbon black and PTFE. In other words, the optimal design of these elements has a dominant effect on the polymer electrolyte membrane fuel cell (PEMFC) performance. For the GDL, it is crucial to prevent water flooding, and the water flux within the GDL is strongly affected by the capillary pressure gradient. In this study, the PEMFC performance was systematically investigated by varying the substrate PTFE content, MPL PTFE content, and MPL carbon loading per unit area. The effects of each experimental variable on the PEMFC performance and especially on the capillary pressure gradient were quantitatively analyzed when the GDLs were manufactured by the doctor blade manufacturing method. The experimental results indicated that as the PTFE content of the anode and cathode GDL increased, the PEMFC performance deteriorated due to the deformation of the porosity and tortuosity of the GDL. Additionally, the PEMFC performance improved as the MPL PTFE content of the cathode GDL increased at low relative humidity (RH), but the PEMFC performance tendency was reversed at high RH. Further, the MPL carbon loading of 2 mg/${\text{cm}}^2$ demonstrated the best performance, and the advantages and disadvantages of the MPL carbon loading were identified. In addition, the effects of each experimental variable on liquid water, water vapor, and gas permeability were investigated.     

Apparent contact angles of liquid water droplet breaking through a gas diffusion layer of polymer electrolyte membrane fuel cell

The lattice Boltzmann method is used to simulate the three-dimensional dynamic process of liquid water breaking through the gas diffusion layer (GDL) in the polymer electrolyte membrane fuel cell. An accurate method is introduced to analyze asymmetric droplet shape. Ten micro-structures of Toray GDL were built based on a stochastic geometry model. It was found that asymmetric droplets are produced on the GDL surfaces. Their local apparent contact angles vary with different view angles and geometries. They are different to the idealized contact angles by symmetric simplification. It was concluded that the apparent contact angles are influenced by GDL structures and view angles. This information can help to bridge the gap between mesoscale and cell-scale simulations in the field of fuel cell simulation.     

Solving transient heat conduction problems on uniform and non-uniform lattices using the lattice Boltzmann method

The lattice Boltzmann method (LBM) has been used to solve transient heat conduction problems in 1-D, 2-D and 3-D Cartesian geometries with uniform and non-uniform lattices. To study the suitability of the LBM, the problems have also been solved using the finite difference method (FDM). To check the performance of LBM for the non-uniform lattices, the results have been compared with uniform lattices. Cases with volumetric heat generation have also been considered. In 1-D problems, the FDM with implicit scheme was found to take more number of iterations and also the CPU time was more. However, with explicit scheme, with increase in the number of control volumes, the LBM was found faster than the FDM. In 2-D and 3-D problems, with increase in the number of control volumes, the LBM was found faster than the FDM. In 2-D problems, number of iterations in the two methods was comparable, while in 3-D problems, the LBM was found to take less number of iterations. The accurate results were found in all the cases.