Numerical studies of liquid water behaviors in PEM fuel cell cathode considering transport across different porous layers

In this paper, a two-phase two-dimensional PEM fuel cell model, which is capable of handling liquid water transport across different porous materials, is employed for parametric studies of liquid water transport and distribution in the cathode of a PEM fuel cell. Attention is paid particularly to the coupled effects of two-phase flow and heat transfer phenomena. The effects of key operation parameters, including the outside cell boundary temperature, the cathode gas humidification condition, and the cell operation current, on the liquid water behaviors and cell performance have been examined in detail. Numerical results elucidate that increasing the fuel cell temperature would not only enhance liquid water evaporation and thus decrease the liquid saturation inside the PEM fuel cell cathode, but also change the location where liquid water is condensed or evaporated. At a cell boundary temperature of 80 °C, liquid water inside the catalyst layer and gas diffusion media under the current-collecting land would flow laterally towards the gas channel and become evaporated along an interface separating the land and channel. As the cell boundary temperature increases, the maximum current density inside the membrane would shift laterally towards the current-collecting land, a phenomenon dictated by membrane hydration. Increasing the gas humidification condition in the cathode gas channel and/or increasing the operating current of the fuel cell could offset the temperature effect on liquid water transport and distribution.     

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.     

Analysis of an active tubular liquid-feed direct methanol fuel cell

A two-dimensional, two-phase, non-isothermal model was developed for an active, tubular, liquid-feed direct methanol fuel cell (DMFC). The liquid-gas, two-phase mass transport in the porous anode and cathode was formulated based on the multi-fluid approach in the porous media. The two-phase mass transport in the anode and cathode channels was modeled using the drift-flux and the homogeneous mist-flow models, respectively. Water and methanol crossovers through the membrane were considered due to the effects of diffusion, electro-osmotic drag, and convection. The model enabled a numerical investigation of the effects of various operating parameters, such as current density, methanol flow rate, and oxygen flow rate, on the mass and heat transport characteristics in the tubular DMFC. It was shown that by choosing a proper tube radius and distance between the adjacent cells, a tubular DMFC stack can achieve a much higher energy density compared to its planar counterpart. The results also showed that a large anode flow rate is needed in order to avoid severe blockage of liquid methanol to the anode electrode due to the gas accumulation in the channel. Besides, lowering the flow rate of either the methanol solution or air can lead to a temperature increase along the flow channel. The methanol and water crossovers are nearly independent of the methanol flow rate and the air flow rate.     

A three-dimensional two-phase flow model for a liquid-fed direct methanol fuel cell

A three-dimensional, two-phase, multi-component model has been developed for a liquid-fed DMFC. The modeling domain consists of the membrane, two catalyst layers, two diffusion layers, and two channels. Both liquid and gas phases are considered in the entire anode, including the channel, the diffusion layer and the catalyst layer; while at the cathode, two phases are considered in the gas diffusion layer and the catalyst layer but only single gas phase is considered in the channels. For electrochemical kinetics, the Tafel equation incorporating the effects of two phases is used at both the cathode and anode sides. At the anode side the presence of gas phase reduces the active catalyst areas, while at the cathode side the presence of liquid water reduces the active catalyst areas. The mixed potential effects due to methanol crossover are also included in the model. The results from the two-phase flow mode fit the experimental results better than those from the single-phase model. The modeling results show that the single-phase models over-predict methanol crossover. The modeling results also show that the porosity of the anode diffusion layer plays an important role in the DMFC performance. With low diffusion layer porosity, the produced carbon dioxide cannot be removed effectively from the catalyst layer, thus reducing the active catalyst area as well as blocking methanol from reaching the reaction zone. A similar effect exits in the cathode for the liquid water.     

The gas diffusion layer in polymer electrolyte membrane fuel cells: A process model of the two-phase flow

A two-phase flow process model for the gas diffusion layer (GDL) of a polymer electrolyte membrane fuel cell, considering also the cathode catalyst layer (CL), is presented. For this purpose, a systematic analysis of the factors affecting flooding and drying, including the liquid accumulation in the gas channel (CH), was performed using a one-dimensional reference model for the GDL and a compact channel model. The treatment proposed for the CH-GDL interface was compared with other boundary conditions in the literature. It was concluded that the liquid accumulation in the channel is determinant for estimating the steady state and transient GDL flooding, but that predicting the saturation level in the CL can help for determining operation policies for precluding flooding in the GDL-CL composite, in the absence of an adequate channel model. Bifurcation behavior, associated with the water phase change, was identified by means of the compact model.     

Transport phenomena within the porous cathode for a proton exchange membrane fuel cell

A two-phase, one-dimensional steady model is developed to analyze the coupled phenomena of cathode flooding and mass-transport limiting for the porous cathode electrode of a proton exchange membrane fuel cell. In the model, the catalyst layer is treated not as an interface between the membrane and gas diffusion layer, but as a separate computational domain with finite thickness and pseudo-homogenous structure. Furthermore, the liquid water transport across the porous electrode is driven by the capillary force based on Darcy's law. And the gas transport is driven by the concentration gradient based on Fick's law. Additionally, through Tafel kinetics, the transport processes of gas and liquid water are coupled. From the numerical results, it is found that although the catalyst layer is thin, it is very crucial to better understand and more correctly predict the concurrent phenomena inside the electrode, particularly, the flooding phenomena. More importantly, the saturation jump at the interface of the gas diffusion layer and catalyst layers is captured, when the continuity of the capillary pressure is imposed on the interface. Elsewise, the results show further that the flooding phenomenon in the CL is much more serious than that in the GDL, which has a significant influence on the mass transport of the reactants. Moreover, the saturation level inside the cathode is determined, to a great extent, by the surface overpotential, the absolute permeability of the porous electrode, and the boundary value of saturation at the gas diffusion layer-gas channel interface. In order to prevent effectively flooding, it should remove firstly the liquid water accumulating inside the CL and keep the boundary value of liquid saturation as low as possible.     

Transient analysis for the cathode gas diffusion layer of PEM fuel cells

A one-dimensional, non-isothermal, two-phase transient model has been developed to study the transient behaviour of water transport in the cathode gas diffusion layer of PEM fuel cells. The effects of four parameters, namely the liquid water saturation at the interface of the gas diffusion layer and flow channels, the proportion of liquid water to all of the water at the interface of the cathode catalyst layer and the gas diffusion layer, the current density, and the contact or wetting angle, on the transient distribution of liquid water saturation in the cathode gas diffusion layer are investigated. Especially, the time needed for liquid water saturation to reach steady state and the liquid water saturation at the interface of the cathode catalyst layer and gas diffusion layer are plotted as functions of the above four parameters. The ranges of water vapour condensation and liquid water evaporation are identified across the thickness of the gas diffusion layer. In addition, the effects of the above four parameters on the steady state distributions of gas phase pressure, water vapour concentration, oxygen concentration and temperature are also presented. It is found that increasing any one of the first three parameters will increase the water saturation at the interface of the catalyst layer and gas diffusion layer, but decrease the time needed for the liquid water saturation to reach steady state. When the liquid water saturation at the interface of the gas diffusion layer and flow channels is high enough (≥0.1), the liquid water saturation at steady state is almost uniformly distributed across the thickness of the gas diffusion layer. It is also found that, under the given initial and boundary conditions in this paper, evaporation takes place within the gas diffusion layer close to the channel side and is the major process for water phase change at low current density (<2000 A m⁻²); condensation occurs close to the catalyst layer side within the gas diffusion layer and dominates the phase change at high current density (>5000 A m⁻²). For hydrophilic gas diffusion layers, both the time needed for liquid water saturation to reach steady state and the water saturation at the interface of the catalyst layer and gas diffusion layer will increase when the contact angle increases; but for hydrophobic gas diffusion layers, both of them decrease when the contact angle increases.     

Phase change in the cathode side of a proton exchange membrane fuel cell

A three-dimensional steady state two-phase non-isothermal model which highly couples the water and thermal management has been developed to numerically investigate the spatial distribution of the interfacial mass transfer phase-change rate in the cathode side of a proton exchange membrane fuel cell (PEMFC). A non-equilibrium evaporation-condensation phase change rate was incorporated in the model which allowed supersaturation and undersaturation take place. The most significant effects of phase-change rate on liquid saturation and temperature distributions are highlighted. A parametric study was also carried out to investigate the effects of operating conditions; namely as the channel inlet humidity, cell operating temperature, and inlet mass flow rate on the phase-change rate. It was also found that liquid phase assumption for produced water in the cathode catalyst layer (CL) changed the local distribution of phase-change rate. The maximum evaporation rate zone (above the channel near the CL) coincided with the maximum temperature zone and resulted in lowering the liquid saturation level. Furthermore, reduction of the channel inlet humidity and an increase of the operation temperature and inlet mass flow rate increased the evaporation rate and allowed for dehydration process of the gas diffusion layer (GDL) to take place faster.     

A two-phase flow and transport model for the cathode of PEM fuel cells

A unified two-phase flow mixture model has been developed to describe the flow and transport in the cathode for PEM fuel cells. The boundary condition at the gas diffuser/catalyst layer interface couples the flow, transport, electrical potential and current density in the anode, cathode catalyst layer and membrane. Fuel cell performance predicted by this model is compared with experimental results and reasonable agreements are achieved. Typical two-phase flow distributions in the cathode gas diffuser and gas channel are presented. The main parameters influencing water transport across the membrane are also discussed. By studying the influences of water and thermal management on two-phase flow, it is found that two-phase flow characteristics in the cathode depend on the current density, operating temperature, and cathode and anode humidification temperatures.     

Characteristics of water transport through the membrane in direct methanol fuel cells operating with neat methanol

The water required for the methanol oxidation reaction in a direct methanol fuel cell (DMFC) operating with neat methanol can be supplied by diffusion from the cathode to the anode through the membrane. In this work, we present a method that allows the water transport rate through the membrane to be in-situ determined. With this method, the effects of the design parameters of the membrane electrode assembly (MEA) and operating conditions on the water transport through the membrane are investigated. The experimental data show that the water flux by diffusion from the cathode to the anode is higher than the opposite flow flux of water due to electro-osmotic drag (EOD) at a given current density, resulting in a net water transport from the cathode to the anode. The results also show that thinning the anode gas diffusion layer (GDL) and the membrane as well as thickening the cathode GDL can enhance the water transport flux from the cathode to the anode. However, a too thin anode GDL or a too thick cathode GDL will lower the cell performance due to the increases in the water concentration loss at the anode catalyst layer (CL) and the oxygen concentration loss at the cathode CL, respectively.     

Parametric study of the cathode and the role of liquid saturation on the performance of a polymer electrolyte membrane fuel cell—A numerical approach

A two-dimensional two-phase steady state model of the cathode of a polymer electrolyte membrane fuel cell (PEMFC) is developed using unsaturated flow theory (UFT). A gas flow field, a gas diffusion layer (GDL), a microporous layers (MPL), a finite catalyst layer (CL), and a polymer membrane constitute the model domain. The flow of liquid water in the cathode flow channel is assumed to take place in the form of a mist. The CL is modeled using flooded spherical agglomerate characterization. Liquid water is considered in all the porous layers. For liquid water transport in the membrane, electro-osmotic drag and back diffusion are considered to be the dominating mechanisms. The void fraction in the CL is expressed in terms of practically achievable design parameters such as platinum loading, Nafion loading, CL thickness, and fraction of platinum on carbon. A number of sensitivity studies are conducted with the developed model. The optimum operating temperature of the cell is found to be 80-85 °C. The optimum porosity of the GDL for this cell is in the range of 0.7-0.8. A study by varying the design parameters of the CL shows that the cell performs better with 0.3-0.35 mg cm⁻² of platinum and 25-30 wt% of ionomer loading at high current densities. The sensitivity study shows that a multi-variable optimization study can significantly improve the cell performance. Numerical simulations are performed to study the dependence of capillary pressure on liquid saturation using various correlations. The impact of the interface saturation on the cell performance is studied. Under certain operating conditions and for certain combination of materials in the GDL and CL, it is found that the presence of a MPL can deteriorate the performance especially at high current density.     

Three-dimensional transient two-phase study of the cathode side of a PEM fuel cell

A three-dimensional transient two-phase isothermal model has been developed for the cathode side of a proton exchange membrane fuel cell (PEMFC). This has been done in order to fully investigate the effects and the time variation of liquid water formation as well as the gas phase transport under the start up condition. It is considered that the generated water in the cathode catalyst layer (CL) is liquid water and that the gas diffusion layer (GDL) is hydrophobic. A non-equilibrium water condensation-evaporation is also assumed. The time variations of liquid water distribution in along-channel and through-plane directions are investigated. This is to determine the liquid water accumulation at the start up time (above the channel under the CL), then the movement of the liquid water in the domain and the final accumulation at the steady state condition (above the rib and near the CL). It has also been found that it takes less time for a high average current density to attain the steady state condition which is due to the capillary pressure gradient inside the porous media. Validation of the numerical results has been implemented via a polarization curve comparison with the experimental data. Both sets show good agreement.     

A pore network study on the role of micro-porous layer in control of liquid water distribution in gas diffusion layer

In proton exchange membrane fuel cell (PEMFC), a hydrophobic micro-porous layer (MPL) is usually placed between catalyst layer (CL) and gas diffusion layer (GDL) to reduce flooding. Recent experimental studies have demonstrated that liquid water saturation in GDL is drastically decreased in the presence of MPL. However, theoretical studies based on traditional continuum two-phase flow models suggest that MPL has no effect on liquid water distribution in GDL. In the present study, a pore network model with invasion percolation algorithm is developed and used to investigate the impacts of the presence of MPL on liquid water distribution in GDL from the viewpoint at the pore level. A uniform pressure and uniform flux boundary conditions are considered for liquid water entering the porous layer in PEMFC. The simulation results reveal that liquid water saturation in GDL is reduced in the presence of MPL, but the reduction depends on the condition of liquid water entering the porous layer in PEMFC.     

质子交换膜燃料电池建模及水热传输特性分析

针对质子交换膜燃料电池(PEMFC)水管理开展了研究,建立了一维非等温两相流解析模型,研究了不同电流密度、微孔层接触角和不同加湿方案对电池内部水分布和温度分布的影响,提出了更好的进气加湿方案。结果表明:电流密度增大会导致阳极拖干、阴极水淹加剧,导致电池各部分温度上升。因各层材料亲水性不同,在交界面处能观察到液态水阶跃现象。增大微孔层接触角促进阴极液态水反扩散到阳极,一定程度上缓解阳极变干,但过大的接触角可能导致阴极水淹加剧。通过采取"阳极充分加湿、阴极低加湿"的进气加湿方案可以有效提高电池性能,并且能在一定程度改善电池内部受热,提高电池使用寿命。     

A single-phase model for liquid-feed DMFCs with non-Tafel kinetics

An isothermal single-phase 3D/1D model for liquid-feed direct methanol fuel cells (DMFC) is presented. Three-dimensional (3D) mass, momentum and species transport in the anode channels and gas diffusion layer is modeled using a commercial, finite-volume based, computational fluid dynamics (CFD) software complemented with user supplied subroutines. The 3D model is locally coupled to a one-dimensional (1D) model accounting for the electrochemical reactions in both the anode and the cathode, which provides a physically sound boundary condition for the velocity and methanol concentration fields at the anode gas diffusion layer/catalyst interface. The 1D model – comprising the membrane–electrode assembly, cathode gas diffusion layer, and cathode channel – assumes non-Tafel kinetics to describe the complex kinetics of the multi-step methanol oxidation reaction at the anode, and accounts for the mixed potential associated with methanol crossover, induced both by diffusion and electro-osmotic drag. Polarization curves computed for various methanol feed concentrations, temperatures, and methanol feed velocities show good agreement with recent experimental results. The spatial distribution of methanol in the anode channels, together with the distributions of current density, methanol crossover and fuel utilization at the anode catalyst layer, are also presented for different opperating conditions.     

Water distribution measurement for a PEMFC through neutron radiography

Neutron radiography has been used for in situ and non-destructive visualization and measurement technique for liquid water in a working proton exchange membrane fuel cell (PEMFC). In an attempt to differentiate water distribution in the anode side from that in the cathode side, a specially designed cell was machined and used for the experiment. The major difference between our design and traditional flow field design is the fact the anode channels and cathode channels were shifted by a channel width, so that the anode and cathode channels do not overlap in the majority of the active areas.

The neutron radiography experiments were performed at selected relative humidities, and stoichiometry values of cathode inlet. At each operating condition, the water distribution in anode/cathode gas diffusion layers (GDLs) was obtained. Image processing with four different spatial masks was applied to those images to differentiate liquid water in four different types of areas. Results indicate that the reactant gas relative humidity and stoichiometry significantly influence current density distribution and water distribution.     

Modeling of a passive DMFC operating with neat methanol

A mathematical model is developed to simulate the fundamental transport phenomena in a passive direct methanol fuel cell (DMFC) operating with neat methanol. The neat methanol operation is realized by using a ‘pervaporation’ membrane that allows the methanol concentration from the neat methanol in the fuel reservoir to be declined to an appropriate level in the anode catalyst layer (CL). The water required by the methanol oxidation reaction on the anode is passively obtained by diffusion from the cathode through the membrane. The numerical results indicate that the methanol delivery rate from the fuel reservoir to the anode CL is predominately controlled by the pervaporation process. It is also found that under the neat methanol operating condition, water distribution across the membrane electrode assembly is greatly influenced by the membrane thickness, the cathode design, the operating temperature, and the ambient relative humidity.     

Quantification and characterization of water coverage in PEMFC gas channels using simultaneous anode and cathode visualization and image processing

A new technique is presented to characterize and quantify the two-phase flow in the anode and cathode flow field channels using simultaneous anode and cathode visualization combined with image processing. In situ visualization experiments were performed at 35 °C with stoichiometric ratios (an/ca) of 1.5/2.5, 1.5/5, 3/8 to elucidate two-phase flow dynamics at lower temperature/low power conditions, when excess liquid water in the cell can be especially prevalent. Video processing algorithms were developed to automatically detect and quantify dynamic and static liquid water present in the flow field channels, as well as discern the distribution of water among different two-phase flow structures. The water coverage ratio was introduced as a parameter to capture the time-averaged flow field water content information through recorded high speed video sequences. The automated processing allows for efficient and robust spatial and temporal averaging of steady state channel water over very large visualization data sets acquired through high speed imaging. The developed algorithm calculates the water coverage ratio using the liquid water in the channels which is contacting the GDL surface, and selectively removes the superficial condensation on the visualization window from the coverage area. The water coverage ratio and distribution metrics techniques were demonstrated by comparing the performance of Freudenberg and Toray gas diffusion layers (GDLs) from a water management perspective, including direct anode to cathode comparisons of simultaneous water coverage data for each GDL sample. The anode water coverage ratio was found to exceed the cathode for both GDL samples at most operating conditions tested in this work. The Freudenberg GDL consistently demonstrated a higher water coverage ratio in the flow field gas channels than the Toray GDL, while the Toray GDL indicated a propensity for greater water retention within the membrane electrode assembly (MEA) based on performance, high frequency resistance (HFR), and water coverage metrics.     

Modeling the phenomena of dehydration and flooding of a polymer electrolyte membrane fuel cell

A one-dimensional, two-phase, transient PEM fuel cell model including gas diffusion layer, cathode catalyst layer and membrane is developed. The electrode is assumed to consist of a network of dispersed Pt/C forming spherically shaped agglomerated zones that are filled with electrolyte. Water is modeled in all three phases: vapor, liquid and dissolved in the ionomer to capture the effect of dehydration of the ionomer as well as flooding of the porous media. The anode is modeled as a sophisticated spatially reduced interface. Motivated by environmental scanning electron microscope (ESEM) images of contact angles for microscopic water droplets on fibers of the gas diffusion layer, we introduce the feature of immobile saturation. A step change of the saturation between the catalyst layer and the gas diffusion layer is modeled based on the assumption of a continuous capillary pressure at the interface. The model is validated against voltammetry experiments under various humidification conditions which all show hysteresis effects in the mass transport limited region. The transient saturation profiles clearly show that insufficient liquid water removal causes pore flooding, which is responsible for the oxygen mass transport limitation at high current density values. The simulated and measured current responses from chronoamperometry experiments are compared and analyzed.     

Three-dimensional multiphase modeling of alkaline anion exchange membrane fuel cell

Alkaline anion exchange membrane (AAEM) fuel cell is becoming more attractive because of its outstanding merits, such as fast electrochemical kinetics and low dependence on non-precious catalyst. In this study, a three-dimensional multiphase non-isothermal AAEM fuel cell model is developed. The modeling results show that the performance is improved with more anode humidification, but the improvement becomes less significant at higher humidification levels. The humidification level of anode can change the water removal mechanisms: at partial humidification, water is removed as vapor; and for full humidification, water is removed as liquid. Cathode humidification is even more critical than anode. Liquid water supply in cathode has a positive effect on performance, especially at high current densities. With more liquid water supply in cathode, liquid water starts moving from channel to CL, rather than being removed from CL. Liquid water supply in cathode is needed to balance the water amounts in anode and cathode. Decreasing the membrane thickness generally improves the cell performance, and the improvement is even enhanced with thinner membranes, due to the faster water diffusion between anode and cathode, which reduces the mass transport losses.