Modeling of gas diffusion layers with curved fibers using a genetic algorithm

This paper presents a methodology for modeling microstructures of fibrous porous media with curved fibers. The developed methodology utilizes implicit periodic surface model coupled with the genetic algorithm (GA) optimization to construct the porous microstructures. The fibers profile is represented by the periodic implicit surfaces and their orientation and curvature are determined by GA optimization. To reconstruct the microstructures with higher resemblance to the actual porous media GA is utilized to minimize the fibers stored strain energy and their intersection volumes. Coupling the image processing techniques to the geometry construction procedure the morphological and transport properties of the constructed microstructures are also determined. To verify the feasibility and the accuracy of the proposed methodology the microstructure of Freudenberg H2315 GDL is constructed and characterized. The presented methodology enables a parametric design approach. Thus, the effects of the microstructure's properties e.g., fibers diameter, fibers orientation and porosity of the porous structure on the transport properties of the fibrous media are investigated.     

Structure of porous electrodes in polymer electrolyte membrane fuel cells: An optical reconstruction technique

Computing flows and phase transport in porous media requires a physically representative geometric model. We present a simple method of digitizing the structure of fibrous porous media commonly used in polymer electrolyte membrane (PEM) fuel cells, the so-called gas diffusion layer (GDL). Employing an inverted microscope and image recognition software we process images of the GDL surface collected manually at different focal lengths with micrometer accuracy. Processing the series of images allows retrieval of local depths of the salient in-focus structural elements in each of the different images. These elements are then recombined into a depth-map representing the three-dimensional structure of the GDL surface. Superimposition of the in-focus portions of the structural elements distributed throughout the stack of images yields digitized data describing the geometry and structural attributes of the 3D surface of the GDL fibrous material.     

Combined effects of microstructural characteristics on anisotropic transport properties of gas diffusion layers for PEMFCs

Gas diffusion layer (GDL) plays a key role in proton exchange membrane fuel cells, which provides multi-functions for gas transport, thermal-electrical conduction and mechanical support. Coupling manipulation of different microstructural characteristics could potentially improve transport properties of GDLs. This work proposes an approach to reconstruct heterogenous GDLs and conduct pore-scale modeling to evaluate the anisotropic transport properties. The models are reconstructed using X-ray computed tomography, stochastically reconstruction methods and morphological processing techniques, which consider different fiber diameter, GDL thickness and local porosity distribution type. Combined effects of microstructure characteristics on tortuosity, diffusivity, thermal-electrical conductivity and anisotropic ratios are investigated comprehensively. The results show that the diffusivity with fiber diameter of 7 μm is approximately 7% lower, and the conductivity is 8% higher than that of 9 μm. The anisotropic ratios of diffusivity, thermal conductivity and electrical conductivity range from 1.25 to 1.65, 5 to 20, and 20 to 55, respectively. Local porosity distribution of uniform-fluctuated type, fiber diameter of 7 μm and GDL thickness of 126 μm are suggested to balance diffusivity and thermal-electrical conductivity simultaneously. The methods and results can guide microstructure design of other porous electrodes with higher performance.     

A multi-scale approach to material modeling of fuel cell diffusion media

Effective diffusivity of porous media in fuel cells has been identified as a relevant material property in automotive applications. Pore-scale simulations utilizing imaging data sets of real materials or virtual model representations provide such diffusivity numbers. However, components like the microporous layer (MPL) or the gas diffusion electrode have not been covered adequately so far by efficient and practical modeling approaches due the small pore sizes and resulting Knudsen contribution to diffusion. In this publication we report the development of a numerical method which allows for the determination of binary diffusion coefficients for all Knudsen numbers and demonstrate the application to fuel cell diffusion media in a multi-scale modeling approach. For high Knudsen numbers effective diffusivity is determined by tracking a large number of individual molecules that collide with the pore walls. For low Knudsen numbers, effective diffusivity is determined by solving the Laplace equation on the pore space. Both contributions to the overall diffusivity are merged by applying Bosanquet’s formula. The resulting diffusivity can be used as an effective number for a microporous layer coating of a spatially resolved fibrous diffusion medium. As this multi-scale method is also based on a 3D voxel grid, we could study any distribution of the MPL on and inside the gas diffusion layer (GDL) with this model, e.g. cracks, different penetration depths, etc.     

Recent progress of gas diffusion layer in proton exchange membrane fuel cell: Two-phase flow and material properties

Proton exchange membrane (PEM) fuel cells are a promising candidate as the next-generation power sources for portable, transportation, and stationary applications. Gas diffusion layers (GDL) coated with microporous layers (MPL) are a vital component of PEM fuel cells, providing multiple functions of mechanical support, reactant transport, liquid water removal, waste heat removal, and electron conductance. In this review, we explain several most important aspects in the research and development (R&D) of this fuel cell component, including material characterization, liquid water detection/quantitation, structure reconstruction, fundamental modeling, transport properties, and durability. Specially, the commonly used microstructure reconstruction methods for GDLs are presented and discussed. Visualization techniques for liquid water detection in the GDL and MPL microstructures are described. Major modeling approaches, such as the multiphase mixture (M²) formulation, pore networks model (PNM), lattice Boltzmann method (LBM) and volume of fluid (VOF) approach, are reviewed and explained. Important material properties and parameters that greatly influence two-phase flow and fuel cell performance, and GDL-related material degradation issues are discussed and summarized to further advance on the GDL material design and development.     

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.     

Fractal model for predicting the effective binary oxygen diffusivity of the gas diffusion layer in proton exchange membrane fuel cells

We propose an analytical model to predict the effective binary oxygen diffusivity of the porous gas diffusion layer (GDL) in proton exchange membrane fuel cells (PEMFCs). In this study, we consider the fractal characteristics of the porous GDL as well as its general microstructure, and we adopt the Bosanquet equation to derive effective diffusivity. The fractal characterization of GDL enables us to model effective diffusivity in a continuous manner while taking into account the effect of pore size distribution. Comparison to two other theoretical models that are generally accepted in the simulation of PEMFCs shows similar trends in all three models, indicating that our proposed model is well founded. Furthermore, the predicted effective binary oxygen diffusivities of two samples show that after treatment with polytetrafluoroethylene (PTFE), the effective binary diffusivity of the GDL decreases. Based on the parametric effect analysis, we conclude that effective binary diffusivity is negatively correlated with tortuosity fractal dimension but positively correlated with the fractal dimension of pore area, porosity, or mean pore diameter. The proposed model facilitates fast prediction of effective diffusivity as well as multi-scale modeling of PEMFCs and thus facilitates the design of the GDLs and of PEMFCs.     

Interfacial transport characteristics between heterogeneous porous composite media for effective mass transfer in fuel cells

In this study, a comprehensive computational model based on a full statistical approach was developed to investigate the heterogeneous mass transport properties in the metal foam channels, gas diffusion layers (GDLs), and microporous layers (MPLs) of polymer electrolyte fuel cells (PEFCs) at the 95% confidence level. A series of channels, GDLs, and MPLs were, respectively, generated to reflect the random heterogeneous structures and transport characteristics. The critical hydrophobic pore radius in the mixed wettability GDLs was computed by applying a modified Leverett function. Furthermore, the gas transport phenomenon through a sufficient number of porous transport media was simulated using a D3Q19 (ie, three‐dimensional, 19 velocities) lattice Boltzmann method, and the corresponding mass transport characteristics were mathematically presented as a function of the porosity. The permeabilities in the channels, GDLs, and MPLs were derived from the pressure gradient and the simulated velocity distribution. It was found that the effective mass diffusion coefficient in the GDLs is mainly influenced by molecular diffusion. Nevertheless, Knudsen diffusion is the dominant mass transfer mechanism in the MPLs, because of small pore diameters. In addition, critical hydrophobic pore radius was derived using a modified Leverett function, which enables to estimate the fraction of pores larger than the critical pore radius in GDLs for effective water transport. Moreover, the interfacial areal contact ratio between two adjacent porous media (ie, channel/GDL and GDL/MPL) was calculated. The calculations indicated that the variation in the local porosity of the porous media has a significant influence on the interfacial connections. The proposed model is expected to improve the prediction performance of porous heterogeneous transport media in electrochemical energy systems and the optimization of porous media structures.     

Pore-scale simulations on relative permeabilities of porous media by lattice Boltzmann method

Pore-scale simulations of two phase flows in a packed-sphere bed and in a carbon paper gas diffusion layer (GDL) are carried out using the free energy multiphase lattice Boltzmann method (LBM). The simulations are performed based on the detailed microstructure of the porous media under periodic boundary conditions such that the average phase saturations in the porous medium remain constant. A comparison of the simulated and measured relative permeabilities for the packed sphere bed as a function of non-wetting phase saturation is performed, and effects of the wettability and the anisotropic characteristics of relative permeabilities of the GDL are investigated.     

3D phase-differentiated GDL microstructure generation with binder and PTFE distributions

In this work, a new framework and model for the digital generation and characterization of the microstructure of gas diffusion layer (GDL) materials with localized binder and polytetrafluoroethylene (PTFE) distributions were developed using 3D morphological imaging processing. This new generation technique closely mimics manufacturing processes and produces complete phase-differentiated (void, fiber, binder, and PTFE) digital 3D microstructures in a cost- and time-effective manner for the first time. The results for the digital generation of Toray TGP-H-060 with 5 and 0 wt.% PTFE were in close agreement with confocal laser scanning microscope (CLSM) images as well as 3D X-ray tomography studies. The resulting structure can be readily used for analyzing transport processes utilizing commercial CFD software.     

Radiative properties of materials with surface scattering or volume scattering: A review

Radiative properties of rough surfaces, particulate media and porous materials are important in thermal engineering and many other applications. These properties are often needed for calculating heat transfer between surfaces and volume elements in participating media, as well as for accurate radiometric temperature measurements. In this paper, recent research on scattering of thermal radiation by rough surfaces, fibrous insulation, soot, aerogel, biological materials, and polytetrafluoroethylene (PTFE) is reviewed. Both theoretical modeling and experimental investigation are discussed. Rigorous solutions and approximation methods for surface scattering and volume scattering are described. The approach of using measured surface roughness statistics in Monte Carlo simulations to predict radiative properties of rough surfaces is emphasized. The effects of various parameters on the radiative properties of particulate media and porous materials are summarized.     

Modeling the role of microstructural parameters in radiative heat transfer through disordered fibrous media

Understanding the influence of microstructural parameters on the rate of heat transfer through a disordered fibrous medium is important for the design and development of heat insulation materials. In this work, by generating virtual 3-D geometries that resemble the internal microstructure of fibrous insulation materials, we simulated the influence of diameter, orientation, and emissivity of the fibers, as well as the media’s porosity and thickness on the radiative heat transmittance. Our simulations are based on a Monte Carlo ray tracing algorithm that we have developed for studying radiative heat flow in 3-D disordered media. The media were assumed to be made up of cylindrical opaque fibers with specular surface. The advantage of our modeling approach is that it does not require any empirical input values, and can directly be used to isolate and study the role of individual microstructural parameters of the media. The major limitation of the model is that it is accurate as long as the fibers can be considered large relative to the wavelength of the incoming rays. Our results indicate that heat flux through a fibrous medium decreases by increasing the packing fraction of the fibers when the thickness and fiber diameter are kept constant. Increasing the fibers’ absorptivity (or emissivity) was observed to decrease the radiation transmittance through the media. Our simulations also revealed that for constant porosity and thickness, the heat flux transmitted across the medium can be reduced by using finer fibers. The steady state temperature profiles across the thicknesses of media with different properties were obtained and found to be independent of the fibers’ emissivity.     

Investigation of the 3D model of coupled heat and liquid moisture transfer in hygroscopic porous fibrous media

This paper focuses on the investigation of the 3D mathematical model to simulate the coupled heat and liquid moisture transfer in hygroscopic porous fibrous media. The flow of the liquid moisture, the water vapor sorption/desorption by fibers and the diffusion of the water vapor are taken into account in this 3D model. Prediction-corrector method is used to solve the 3D governing equations. A series of computational results of the coupled heat and moisture transfer are obtained with the specific initial conditions and boundary conditions. The distribution of the water vapor concentration in the void spaces, the volume fraction of the liquid water in the void spaces, the distribution of the water content in fibers and the changes of the temperature in porous fibrous media are computed. It is shown that the effects of the gravity and capillary actions are significant in hygroscopic porous fibrous media. The comparison with the experimental measurements shows the reasonable agreement between the two. The results illustrate that the 3D model of the coupled heat and liquid moisture transfer in hygroscopic porous fibrous media is satisfactory.     

3D classification of polymer electrolyte membrane fuel cell materials from in-situ X-ray tomographic datasets

To conduct simulations of transport properties within fuel cell materials 3D-data are required as input. For a functional simulation of flow and thermal characteristics the morphological features of the gas diffusion layer (GDL) materials must be well-defined. In this regard, the distribution of the distinct substances in the GDL, each of which is represented by a different parameter set, plays a decisive role. By means of synchrotron X-Ray computed tomography a fuel cell equipped with SGL® 28BC GDL material is recorded in 3D. The segmentation of the solid structural components and the identification of water agglomerations in the components are fulfilled by image processing techniques. This step is often realized using a lot of simplifications, like the reduction to only one or two different materials or idealized structural characteristics. In the presented work 8 different phases are defined according to the cell materials, which are the catalyst layer, the carbon fibers, the Teflon (PTFE)-binder, the micro porous layer (MPL), the flow field ribs, the pore spaces as well as the water in pore spaces of the GDL substrate and in the MPL. The image processing steps used for the classification of each voxel into these phases are described in detail in this work. Benefiting from this classification methodology, the macroscopic properties of the GDL materials such as water saturation, diffusivity, thermal and electrical conductivity can be obtained in simulations.     

Liquid transport in gas diffusion layer of proton exchange membrane fuel cells: Effects of micro-porous layer cracks

Micro porous layer (MPL) is a carbon layer (～15 μm) that coated on the gas diffusion layer (GDL) to enhance the electrical conduction and membrane hydration of proton exchange membrane fuel cell (PEMFC). However, the liquid transport behavior from MPL to GDL and its impact on water management remain unclear. Thus, a three-dimensional volume of fluid (VOF) model is developed to investigate the effects of MPL crack properties on liquid water saturation, liquid pathway formation, and the two-phase mass transport mechanism in GDL. Firstly, a stochastic orientation method is used to reconstruct the fibrous structure of the GDL. After that, the liquid water saturation calculated from the numerical results agrees well with the experimental data. With considering the full morphology of the overlap between MPL and GDL, it's found that this overlap determines the preferred liquid emerging port of both MPL and GDL. Three crack design shapes in MPL are proposed on the base of the similarity crack formation processes of soil mud. In addition, the effects of crack shape, distance between cracks, and crack number on liquid water transport from MPL to GDL are investigated. It is found that the liquid water saturation of GDL increases with crack number and the distance between cracks, while presents little correlation to the crack shape. Hopefully, these results can help the development of PEMFC models without reconstructing full MPL morphology.     

Microstructure reconstruction using fiber tracking technique and pore-scale simulations of heterogeneous gas diffusion layer

Two challenging tasks in pore-scale modeling of a gas diffusion layer (GDL) are realistic microstructure reconstruction and stress-strain simulation to differentiate the heterogeneous materials. This study proposes a novel method for reconstructing a GDL using fiber tracking technique and pore-scale modeling to investigate its stress-strain and anisotropic transport properties. X-ray computed tomography, fiber tracking, and morphological processing techniques were employed to reconstruct a realistic GDL. Pore-scale modeling was performed to compute the stress-strain, gas diffusivity, and electrical-thermal conductivity at different compression ratios. The sensitivity of compression speed and Young's modulus were investigated to balance the accuracy and computing cost of stress-strain simulation. The results showed that Young's modulus of 1 GPa and compression speed of 3 m/s meet the requirements for both accuracy and computational cost. The reconstructed GDL showed good agreements with the experimental data when considering fibers' orientation, length, and curvature. It was found that the stress among fibers was approximately five times higher than binders. The anisotropic ratios of diffusivity and conductivity decreased from 1.35 to 1.25, and 15 to 5, respectively, as the compression ratio increased to 25%. This study can provide accurate predictions and guidelines for GDL design with low stress and high performance.     

Scale effect and two-phase flow in a thin hydrophobic porous layer. Application to water transport in gas diffusion layers of proton exchange membrane fuel cells

Pore network simulations are performed to study water transport in gas diffusion layers (GDLs) of polymer electrolyte membrane fuel cells (PEMFCs). The transport and equilibrium properties are shown to be scale dependent in a thin system like a GDL. A distinguishing feature of such a thin system is the lack of length scale separation between the system size and the size of the representative elementary volume (REV) over which are supposed to be defined the macroscopic properties within the framework of the continuum approach to porous media. Owing to the lack of length scale separation, two-phase flow traditional continuum models are expected to offer poor predictions of water distribution in a GDL. This is illustrated through comparisons with results from the pore network model. The influence of inlet boundary conditions on invasion patterns is studied and shown to affect greatly the saturation profiles. The effects of GDL differential compression and partial coverage of outlet surface are also investigated.     

In-plane gas permeability of proton exchange membrane fuel cell gas diffusion layers

A new analytical approach is proposed for evaluating the in-plane permeability of gas diffusion layers (GDLs) of proton exchange membrane fuel cells. In this approach, the microstructure of carbon papers is modeled as a combination of equally-sized, equally-spaced fibers parallel and perpendicular to the flow direction. The permeability of the carbon paper is then estimated by a blend of the permeability of the two groups. Several blending techniques are investigated to find an optimum blend through comparisons with experimental data for GDLs. The proposed model captures the trends of experimental data over the entire range of GDL porosity. In addition, a compact relationship is reported that predicts the in-plane permeability of GDL as a function of porosity and the fiber diameter. A blending technique is also successfully adopted to report a closed-form relationship for in-plane permeability of three-directional fibrous materials.     

Impact of PTFE distribution on the removal of liquid water from a PEMFC electrode by lattice Boltzmann method

It is believed by many that polymer electrolyte membrane fuel cells (PEMFCs) will have a widespread application since they offer important features such as low operating temperature, high power density, and easy scale up. However, operation of PEMFCs is faced with some technical challenges including water management which may lead to flooding of the electrodes. Treatment of the gas diffusion layer (GDL) with a highly hydrophobic material such as PTFE is a common strategy for mitigating this issue. Several investigations have been done to clarify solely the effect of PTFE content. However, effects of PTFE distribution, which can be achieved through different treatment methods, has not been well studied yet. Lattice Boltzmann method (LBM) is one of the best choices for such numerical studies due to its capability of modeling multiphase flow in the complicated microstructure of a porous GDL considering its non-homogeneous and anisotropic transport properties. In the present study, droplet removal from four GDLs with different PTFE distributions through an interdigitated flow field is investigated using LBM. The results demonstrate that regardless of PTFE distribution, the interfacial forces between any untreated carbon fiber and a water droplet will strongly dominate over other forces and hence will prevent its removal. Therefore, it is concluded that an effective water management may be achieved by a suitable treatment method such that no carbon fiber inside the GDL remains uncoated.     

Feasibility of periodic surface models to develop gas diffusion layers: A gas permeability study

A geometric modeling scheme called periodic surface model (PS) is used to construct three dimensional (3D) models of a gas diffusion layer's (GDL) microstructure, which allows for rapid model construction and modification of representative volume elements (RVE) with embedded periodic boundary conditions. The reconstructed PS models are optimized with the help of the genetic algorithm embedded in MATLAB to generate models with refined mesh for computational fluid dynamics (CFD) analysis. The GDL geometry is built in ANSYS/ICEM CFD, automatically, using a customized code that couples MATLAB and ICEM. To verify the validity of the suggested modeling approach the microstructures of the GDLs with different porosity and fiber orientation are generated and the in-plane and through-plane permeability and tortuosity are calculated using ANSYS/FLUENT software. The numerically predicted values of in-plane and through-plane permeability are compared to experimental measurements. Using the genetic algorithm significantly decreases the fibers intersection volume in the RVE, especially as porosity decreases. It has been found that the tortuosity of the GDL is a function of the spatial orientation of the fibers in the RVE, when the fibers are at a small angle, the in-plane tortuosity can be higher than the through-plane tortuosity.