A generalized numerical model for liquid water in a proton exchange membrane fuel cell with interdigitated design

A new approach to numerical simulation of liquid water distribution in channels and porous media including gas diffusion layers (GDLs), catalyst layers, and the membrane of a proton exchange membrane fuel cell (PEMFC) was introduced in this study. The three-dimensional, PEMFC model with detailed thermo-electrochemistry, multi-species, and two-phase interactions. Explicit gas-liquid interface tracking was performed by using Computational Fluid Dynamics (CFD) software package FLUENT^® v6.2, with its User-Defined Functions (UDF) combined with volume-of-fluid (VOF) algorithm. The liquid water transport on a PEMFC with interdigitated design was investigated. The behavior of liquid water was understood by presenting the motion of liquid water droplet in the channels and the porous media at different time instants. The numerical results show that removal of liquid water strongly depends on the magnitude of the flow field. Due to the blockage of liquid water, the gas flow is unevenly distributed, the high pressure regions takes place at the locations where water liquid appears. In addition, mass transport of the species and the current density distribution is significantly degraded by the presence of liquid water.     

Comparisons and validations of contact angle models

In the numerical simulation of water management for proton exchange membrane fuel cells (PEMFCs), the static contact angle (SCA) model is generally used. However, an empirical correlation for dynamic contact angle (DCA), known as Hoffman function or Kistler's law, was recently employed to numerically simulate the droplet behaviors either in a microchannel or on a surface. In this paper, for the first time, a DCA evolution map is created based on Hoffman function and related experiments to better understand the DCA evolving mechanism; based on this evolution map, the Advancing-Receding DCA (AR-DCA) model is proposed and explained, in addition to the Advancing DCA (A-DCA) model that is based on the original Hoffman's experiments; using user defined function (UDF), the A-DCA and AR-DCA models are implemented with Volume of Fluid (VOF) method in ANSYS Fluent; a series of numerical simulations are conducted with the SCA, A-DCA and AR-DCA models for droplet impact on horizontal and inclined surfaces; the validations of these contact angle models are performed, qualitatively and quantitatively, by comparing the numerical simulation results with the corresponding experimental results from the literature. It is indicated that the AR-DCA model can better simulate the droplet deformation and evolvement, showing its potential for the DCA simulations in a more complex gas-liquid flow domain such as the cathode of PEMFCs.     

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.     

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.     

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.     

Numerical study of water management in the air flow channel of a PEM fuel cell cathode

The water management in the air flow channel of a proton exchange membrane (PEM) fuel cell cathode is numerically investigated using the FLUENT software package. By enabling the volume of fraction (VOF) model, the air–water two-phase flow can be simulated under different operating conditions. The effects of channel surface hydrophilicity, channel geometry, and air inlet velocity on water behavior, water content inside the channel, and two-phase pressure drop are discussed in detail. The results of the quasi-steady-state simulations show that: (1) the hydrophilicity of reactant flow channel surface is critical for water management in order to facilitate water transport along channel surfaces or edges; (2) hydrophilic surfaces also increase pressure drop due to liquid water spreading; (3) a sharp corner channel design could benefit water management because it facilitates water accumulation and provides paths for water transport along channel surface opposite to gas diffusion layer; (4) the two-phase pressure drop inside the air flow channel increases almost linearly with increasing air inlet velocity.     

Two-phase flow and evaporation in model fibrous media: Application to the gas diffusion layer of PEM fuel cells

Two-phase flow dominated by capillary effects in model fibrous media is studied combining pore-network simulations and visualisations on transparent micromodels. It is shown that the process of liquid water invasion in a hydrophobic medium can be simulated using the classical invasion percolation algorithm provided that the contact angle (measured in air, which is the wetting phase) is sufficiently far below 90°. For contact angles approaching 90°, changes in the interface local growth mechanisms lead to changes in the invasion pattern.     

Two-phase flow pressure drop hysteresis in parallel channels of a proton exchange membrane fuel cell

Two-phase flow pressure drop hysteresis was studied in a non-operational PEM fuel cell to understand the effect of stoichiometry, GDL characteristics, operating range, and initial conditions (dry vs. flooded) for flow conditions typical of an operating fuel cell. This hysteresis is noted when the air and water flow rates are increased and then decreased along the same path, exhibiting different pressure drops. When starting from dry conditions, the descending pressure drop tended to be higher than the ascending pressure drop at lower simulated current densities. The hysteresis effect was noted for stoichiometries of 1-4 and was eliminated at a stoichiometry of 5. It was found that the hysteresis was greater when water breakthrough occurred at higher simulated current densities, which is a function of GDL properties. The operating range had to reach a critical simulated current density (800 mA cm⁻² in this case) between the ascending and descending approach to create a pressure drop hysteresis zone. The descending step size does not change the size of the hysteresis effect, but a larger step size leads to lower fluctuations in the pressure drop signal. An initially flooded condition also showed hysteresis, but the ascending approach tended to have a higher pressure drop than the descending approach.     

Two-phase flow pressure drop hysteresis in an operating proton exchange membrane fuel cell

Two-phase flow pressure drop hysteresis was studied in an operating PEM fuel cell. The variables studied include air stoichiometry (1.5, 2, 3, 4), temperature (50, 75, 90 °C), and the inclusion of a microporous layer. The cathode channel pressure drops can differ in PEM fuel cells when the current density is increased along a path and then decreased along the same path (pressure drop hysteresis). Generally, the descending pressure drop is greater than the ascending pressure drop at low current densities (<200 mA cm⁻²), and the effect is worse at low stoichiometries and low temperatures. The results show that the hysteresis occurs with or without the inclusion of a microporous layer. Initial results show a modified Lockhart-Martinelli approach seems to be able to predict the two-phase flow pressure drop during the ascending path. The results compare well with photographs taken from the cathode flow field channel of a visualization cell.     

Three-dimensional numerical simulation of water droplet emerging from a gas diffusion layer surface in micro-channels

The dynamic formation of water droplets emerging from a gas diffusion layer (GDL) surface in micro-channels was simulated using the volume of fluid (VOF) method. The influence of GDL surface microstructure was investigated by changing the pore diameter and the number of pore openings on the GDL surface. Simulation results show that the microstructure of the GDL surface has a significant impact on the two-phase flow patterns in gas flow channels. For a non-uniform GDL surface, three stages were identified, namely emergence and merging on the GDL surface, accumulation on the channel sidewalls and detachment from the top wall. It was also found that if the pore size is small enough, the flow pattern in the channel does not change with further reduction in the pore diameter. However, the two-phase flow patterns change significantly with the wettability of the GDL surface and sidewalls, but remain the same when the liquid flow rate is reduced by two orders of magnitude from the reference case.     

Modeling gas flow in PEMFC channels: Part I – Flow pattern transitions and pressure drop in a simulated ex situ channel with uniform water injection through the GDL

The two-phase flow in the gas channels of a proton exchange membrane fuel cell (PEMFC) is studied with an ex situ setup using a gas diffusion layer (GDL) as the sidewall of the channels. Air is supplied at the channel inlet manifold and water is supplied continuously and uniformly through the GDL along the length of the channel. This is different from the simultaneous air and water introduction at the inlet of the channel as studied by previous two-phase flow researchers. The GDL is compressed between the gas channels and the water chambers to simulate PEMFC conditions. The superficial velocity for air and water ranged from 0.25 to 34.5 m/s and 1.54 × 10⁻⁵ to 1.54 × 10⁻⁴ m/s, respectively. The ex situ setup was run in both vertical and horizontal orientations with two GDLs, – Baseline (Mitsubishi Rayon Co. MRC 105 with 5 wt.% PTFE and coated with an in-house MPL by General Motors) and SGL 25 BC – and three channel treatments – hydrophobic, hydrophilic, and untreated Lexan, with contact angles of 116°, 11° and 86°, respectively. No appreciable effect was noted because of the orientation, GDL type or channel coatings. The flow regime is observed at different locations along the channel and is expressed as a function of the superficial air and water velocities. Flow regime criteria are developed and validated against the range of ex situ data observations. A new variable water flow rate pressure drop model is developed in order to account for the variation of water entering the channel at multiple locations along the flow length. Pressure drop models are developed for specific flow regimes and validated against experimental data. The models are able to predict the experimental pressure drop data with a mean error of less than 14%.     

Effects of hydrophilic/hydrophobic properties of gas flow channels on liquid water transport in a serpentine polymer electrolyte membrane fuel cell

The droplet dynamics in the serpentine flow channel of a hydrogen fuel cell has been numerically investigated to obtain ideas for designing a serpentine channel with the aim of effectively preventing flooding. Three-dimensional two-phase flow simulations employing the volume of fluid (VOF) method have been performed. Liquid droplets emerging from four adjacent pores at the hydrophobic bottom wall are subjected to airflow in the bulk of the serpentine flow channel. The effects of contact angle variation of the channel walls on liquid water removal have been tested in terms of liquid water saturation and coverage of liquid water on the gas diffusion layer (GDL) surface. The numerical results show that the hybrid case, which consists of hydrophilic channel walls at the straight part and hydrophobic walls at the turning part of the serpentine flow channels, enhances water removal compared with two other cases in which the channel wall is homogeneously hydrophilic or hydrophobic. The three-dimensional visualization of liquid water droplets reveals that the hydrophobic wall at the turning part reduces the water saturation in the channel and the hydrophilic wall at the straight part prevents the liquid water from covering the GDL surface.     

Numerical investigation of the impact of two-phase flow maldistribution on PEM fuel cell performance

Flow maldistribution usually happens in PEM fuel cells when using common inlet and exit headers to supply reactant gases to multiple channels. As a result, some channels are flooded with more water and have less air flow while other channels are filled with less water but have excessive air flow. To investigate the impact of two-phase flow maldistribution on PEM fuel cell performance, a Volume of Fluid (VOF) model coupled with a 1D MEA model was employed to simulate two parallel channels. The slug flow pattern is mainly observed in the flow channels under different flow maldistribution conditions, and it significantly increases the gas diffusion layer (GDL) surface water coverage over the whole range of simulated current densities, which directly leads to poor fuel cell performance. Therefore, it is recommended that liquid and gas flow maldistribution in parallel channels should be avoided if possible over the whole range of operation. Increasing the gas stoichiometric flow ratio is not an effective method to mitigate the gas flow maldistribution, but adding a gas inlet resistance to the flow channel is effective in mitigating maldistribution. With a carefully selected value of the flow resistance coefficient, both the fuel cell performance and the gas flow distribution can be significantly improved without causing too much extra pressure drop.     

Performance loss of proton exchange membrane fuel cell due to hydrophobicity loss in gas diffusion layer: Analysis by multiscale approach combining pore network and performance modelling

Loss of hydrophobicity in the gas diffusion layers (GDL) is sometimes suggested as a potential mechanism to explain in part the performance loss of PEMFC. The present study proposes a numerical methodology to analyse this effect by combining pore network modelling (PNM) and performance modelling (PM): the PNM/PM approach. PNM allows simulating the decrease of through-plane gas diffusion coefficient in the GDL as a function of the hydrophobicity loss, which is taken into account through the increase in the fraction of hydrophilic pores in GDL. Then PM based on Darcy equations allows simulating performance loss of PEMFC as a function of gas diffusion decay. This coupling shows that the loss of hydrophobic treatment increases flooding, decreases performance, and increases current density heterogeneities between inlet and outlet of the cell. Interestingly, this degradation is found to be highly non-linear, mainly because of the non-linear influence of the fraction of hydrophilic pores on gas diffusion (this is due to the existence of a percolation threshold associated with the hydrophilic pore sub-network) as well as the non-linear behaviour of electrochemistry with gas diffusion. This study also shows that the loss of hydrophobicity in a GDL is a very suitable candidate to explain performance loss rates that are classically observed during long-term tests. The proposed methodology may also help linking other local properties of components to fuel cell global performance.     

Numerical simulations of two-phase flow in a proton-exchange membrane fuel cell based on the generalized design method

The water management of proton-exchange membrane fuel cell (PEMFC) has a major impact on the performance of the cell system. In order to investigate the influence of air velocity and wettability on the whole process during penetration of liquid water, a generalized two-dimensional model in conjunction with the volume of fluid (VOF) method was used to simulate the whole processes from gas diffusion layer (GDL) to gas channel (GC). The results show that the wettability of the medium plays a significant role than flow rate for the penetration of liquid water in the GDL. It is shown that favorable hydrophobicity and high air velocity in GC is helpful to remove liquid droplets on the GDL surface. By contrast, the stable droplets spacing on GDL surface is more concentrated and the percentage of liquid area is more extensive under the hydrophilic and low-velocity case, which would aggravate the liquid water and hard to remove from the GDL surface.     

Impact of channel geometry on two-phase flow in fuel cell microchannels

An important function of the gas delivery channels in PEM fuel cells is the evacuation of water at the cathode. The resulting two-phase flow impedes reactant transport and causes parasitic losses. There is a need for research on two-phase flow in channels in which the phase fraction varies along the flow direction as in operating fuel cells. This work studies two-phase flow in 60 cm long channels with distributed water injection through a porous GDL wall to examine the physics of flows relevant to fuel cells. Flow regime maps based on local gas and liquid flow rates are constructed for experimental conditions corresponding to current densities between 0.5 and 2 A cm⁻² and stoichiometric coefficients from 1 to 4. Flow structures transition along the length of the channel. Stratified flow occurs at high liquid flow rates, while intermittent slug flow occurs at low liquid flow rates. The prevalence of stratified flow in these serpentine channels is discussed in relation to water removal mechanisms in the cathode channels of PEM fuel cells. Corners facilitate formation of liquid films in the channel, but may reduce the water-evacuation capability. This analysis informs design guidelines for gas delivery microchannels for fuel cells.     

Treatment of two-phase flow in cathode gas channel for an improved one-dimensional proton exchange membrane fuel cell model

It has been reported recently that water flooding in the cathode gas channel has significant effects on the characteristics of a proton exchange membrane fuel cell. A better understanding of this phenomenon with the aid of an accurate model is necessary for improving the water management and performance of fuel cell. However, this phenomenon is often not considered in the previous one-dimensional models where zero or a constant liquid water saturation level is assumed at the interface between gas diffusion layer and gas channel. In view of this, a one-dimensional fuel cell model that includes the effects of two-phase flow in the gas channel is proposed. The liquid water saturation along the cathode gas channel is estimated by adopting Darcy’s law to describe the convective flow of liquid water under various inlet conditions, i.e. air pressure, relative humidity and air stoichiometry. The averaged capillary pressure of gas channel calculated from the liquid water saturation is used as the boundary value at the interface to couple the cathode gas channel model to the membrane electrode assembly model. Through the coupling of the two modeling domains, the water distribution inside the membrane electrode assembly is associated with the inlet conditions. The simulation results, which are verified against experimental data and simulation results from a published computational fluid dynamics model, indicate that the effects of relative humidity and stoichiometry of inlet air are crucial to the overall fuel cell performance. The proposed model gives a more accurate treatment of the water transport in the cathode region, which enables an improved water management through an understanding of the effects of inlet conditions on the fuel cell performance.     

Droplet and slug formation in polymer electrolyte membrane fuel cell flow channels: The role of interfacial forces

A microfluidic device is employed to emulate water droplet emergence from a porous electrode and slug formation in the gas flow channel of a PEM fuel cell. Liquid water emerges from a 50 μm pore forming a droplet; the droplet grows to span the entire cross-section of a microchannel and transitions into a slug which detaches and is swept downstream. Droplet growth, slug formation, detachment, and motion are analyzed using high-speed video images and pressure-time traces. Slug volume is controlled primarily by channel geometry, interfacial forces, and gravity. As water slugs move downstream, they leave residual micro-droplets that act as nucleation sites for the next droplet-to-slug transition. Residual liquid in the form of micro-droplets results in a significant decrease in slug volume between the very first slug formed in an initially dry channel and the ultimate “steady-state” slug. A physics-based model is presented to predict slug volumes and pressure drops for slug detachment and motion.     

Water management studies in PEM fuel cells,Part II: Ex situ investigation of flow maldistribution,pressure drop and two-phase flow pattern in gas channels

Two-phase flow of water and reactant gases in the gas distribution channels of proton exchange membrane fuel cells (PEMFCs) plays a critical role in proper water management. In this work, the two-phase flow in PEMFC cathode parallel channels is studied over a wide range of superficial air velocity (air stoichiometry) and superficial water velocity in a specially designed ex situ experimental setup, which enables the measurement of instantaneous flow rates in individual gas channels and simultaneous visualization of the water flow structure. It is found that the two-phase flow at low superficial air velocities (air stoichiometry below 5) is dominated by slugs or semi-slugs, leading to severe flow maldistribution and large fluctuations in the pressure drop. Slug residence time, measured from the video observation and the instantaneous flow rate data, is found to be a new parameter to describe the slug flow. At higher air velocities, a water film is formed on the channel walls if they are hydrophilic. The pressure drop for the film flow is characterized by smaller but frequent fluctuations, which are found to result from the water buildup at the channel-exit manifold interface. As the superficial air velocity increases further, mist flow is obtained where little water buildup is observed. The water buildup in the gas channels at the two-phase flow is well described by the two-phase friction multiplier, defined as the ratio of the two-phase pressure drop to the single gas phase pressure drop. It is found that the two-phase friction multiplier increases with increasing water flow rate. A flow pattern map is developed using superficial water and air velocities with clearly defined transition regions.     

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.