Numerical investigation of transient responses of a PEM fuel cell using a two-phase non-isothermal mixed-domain model

In this paper, a transient two-phase non-isothermal PEM fuel cell model has been developed based on the previously established two-phase mixed-domain approach. This model is capable of solving two-phase flow and heat transfer processes simultaneously and has been applied herein for two-dimensional time-accurate simulations to fully examine the effects of liquid water transport and heat transfer phenomena on the transient responses of a PEM fuel cell undergoing a step change of cell voltage, with and without condensation/evaporation interfaces. The present numerical results show that under isothermal two-phase conditions, the presence of liquid water in the porous materials increases the current density over-shoot and under-shoot, while under the non-isothermal two-phase conditions, the heat transfer process significantly increases the transient response time. The present studies also indicate that proper consideration of the liquid droplet coverage at the GDL/GC interface results in the increased liquid saturation values inside the porous materials and consequently the drastically increased over-shoot and under-shoot of the current density. In fact, the transient characteristics of the interfacial liquid droplet coverage could exert influences on not only the magnitude but also the time of the transient response process.     

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.     

A two-phase non-isothermal mixed-domain PEM fuel cell model and its application to two-dimensional simulations

In this paper, a two-phase non-isothermal PEM fuel cell model based on the previously developed mixed-domain PEM fuel cell model with a consistent treatment of water transport in MEA has been established using the traditional two-fluid method. This two-phase multi-dimensional PEM fuel cell model could fully incorporate both the anode and cathode sides, properly account for the various water phases, including water vapor, water in the membrane phase, and liquid water, and truly enable numerical investigations of water and thermal management issues with the existence of condensation/evaporation interfaces in a PEM fuel cell. This two-phase model has been applied in this paper in a two-dimensional configuration to determine the appropriate condensation and evaporation rate coefficients and conduct extensive numerical studies concerning the effects of the inlet humidity condition and temperature variation on liquid water distribution with or without a condensation/evaporation interface.     

Modeling two-phase flow in PEM fuel cell channels

This paper is concerned with the simultaneous flow of liquid water and gaseous reactants in mini-channels of a proton exchange membrane (PEM) fuel cell. Envisaging the mini-channels as structured and ordered porous media, we develop a continuum model of two-phase channel flow based on two-phase Darcy's law and the M² formalism, which allow estimate of the parameters key to fuel cell operation such as overall pressure drop and liquid saturation profiles along the axial flow direction. Analytical solutions of liquid water saturation and species concentrations along the channel are derived to explore the dependences of these physical variables vital to cell performance on operating parameters such as flow stoichiometric ratio and relative humility. The two-phase channel model is further implemented for three-dimensional numerical simulations of two-phase, multi-component transport in a single fuel-cell channel. Three issues critical to optimizing channel design and mitigating channel flooding in PEM fuel cells are fully discussed: liquid water buildup towards the fuel cell outlet, saturation spike in the vicinity of flow cross-sectional heterogeneity, and two-phase pressure drop. Both the two-phase model and analytical solutions presented in this paper may be applicable to more general two-phase flow phenomena through mini- and micro-channels.     

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.     

A critical review of two-phase flow in gas flow channels of proton exchange membrane fuel cells

Water management in PEM fuel cells has received extensive attention due to its key role in fuel cell performance. The unavoidable water, from humidified gas streams and electrochemical reaction, leads to gas-liquid two-phase flow in the flow channels of fuel cells. The presence of two-phase flow increases the complexity in water management in PEM fuel cells, which remains a challenging hurdle in the commercialization of this technology. Unique water emergence from the gas diffusion layer, which is different from conventional gas-liquid two-phase flow where water is introduced from the inlet together with the gas, leads to different gas-liquid flow behaviors, including pressure drop, flow pattern, and liquid holdup along flow field channels. These parameters are critical in flow field design and fuel cell operation and therefore two-phase flow has received increasing attention in recent years. This review emphasizes gas-liquid two-phase flow in minichannels or microchannels related to PEM fuel cell applications. In situ and ex situ experimental setups have been utilized to visualize and quantify two-phase flow phenomena in terms of flow regime maps, flow maldistribution, and pressure drop measurements. Work should continue to make the results more relevant for operating PEM fuel cells. Numerical simulations have progressed greatly, but conditions relevant to the length scales and time scales experienced by an operating fuel cell have not been realized. Several mitigation strategies exist to deal with two-phase flow, but often at the expense of overall cell performance due to parasitic power losses. Thus, experimentation and simulation must continue to progress in order to develop a full understanding of two-phase flow phenomena so that meaningful mitigation strategies can be implemented.     

Numerical study of two-phase flow patterns in the gas channel of PEM fuel cells with tapered flow field design

In this study the air–water two-phase flow in a tapered channel of a PEMFC was numerically simulated using the volume of fluid (VOF) method. In particular, a 3D mathematical model of the fuel cell flow channel was used to obtain a reliable evaluation of the fuel cell performance for different taper angles and different temperatures and to calculate the total amount of water produced. This information was then used as boundary conditions to simulate the two-phase flow in the cell channel through a 2D VOF model. Typical operating conditions were assigned and the numerical mesh was constructed to represent the real fuel cell configuration. The results show that tapering the channel downstream enhances the water removal due to increased airflow velocity. In the rectangular channel no film formation is noted with a marked predominance of slug flow. In contrast, as the taper angle is increased the predominant two-phase flow pattern is film flow. Finally many contact angles have been used to simulate the effect of the hydrophobicity of a GDL surface on the motion of the water. As the hydrophobicity of a GDL surface is decreased the presence of film is more evident even for less tapered channels.     

Numerical investigation of flow field configuration and contact resistance for PEM fuel cell performance

A steady-state three-dimensional non-isothermal computational fluid dynamics (CFD) model of a proton exchange membrane fuel cell is presented. Conservation of mass, momentum, species, energy, and charge, as well as electrochemical kinetics are considered. In this model, the effect of interfacial contact resistance is also included. The numerical solution is based on a finite-volume method. In this study the effects of flow channel dimensions on the cell performance are investigated. Simulation results indicate that increasing the channel width will improve the limiting current density. However, it is observed that an optimum shoulder size of the flow channels exists for which the cell performance is the highest. Polarization curves are obtained for different operating conditions which, in general, compare favorably with the corresponding experimental data. Such a CFD model can be used as a tool in the development and optimization of PEM fuel cells.     

Numerical investigation of the impact of gas and cooling flow configurations on current and water distributions in a polymer membrane fuel cell through a pseudo-two-dimensional diphasic model

For optimal performances, proton exchange membrane fuel cells require fine water and thermal management. Accurate modelling of the physical phenomena occurring in the fuel cell is a key issue to improve fuel cell technology. Here, an analytic steady state diphasic 2D model of heat and mass transfer is presented. Through this model, the aim of this work is to study the influence of local events on the global performances of a fuel cell. A part of the complete model is a microscopic representation of the coupling between water transport and charge transfers in the electrodes. The thickness of the liquid layer around the reactive agglomerates is deduced from the saturation. The evolution of the quantity of water within the catalyst layer is monitored and its influence on the global performances of the cell is investigated. In gas diffusion layers (GDLs), liquid and vapour water transport through are computed regarding the temperature. The flow direction of cooling water modifies the current density distribution along the cell. The impact of the direction of air and hydrogen feeding channels are investigated. It can modify greatly the fuel cell mean current density and the net water transport coefficient. The counter-flow mode was preferable. Likewise, thanks to a better membrane hydration, it results in independent performances regarding the hydrogen inlet relative humidity or stoichiometry.     

The effect of flow distributors on the liquid water distribution and performance of a PEM fuel cell

Water management is one of the important factors which determine the performance of a Proton Exchange Membrane (PEM) fuel cell using hydrogen as fuel. For developing efficient water management systems, it is important to know the potential locations of formation and the nature of distribution of liquid water in the fuel cell. In the present study a PEM fuel cell with three different types of flow distributors are modeled and numerically simulated to find out the water formation and distribution characteristics. The model is validated by comparing the simulated polarization curve to experimental data. It is found that the type of flow distributor used plays a major role in determining the distribution of liquid water in the cell. A parallel flow distributor exhibits poor water removal capabilities whereas a serpentine flow distributor exhibits better water removal. A mixed flow distributor is found to give better water distribution characteristics compared to the parallel and serpentine distributors. Further the effect of liquid water formation and distribution on the species transport, temperature distribution and current generation are also investigated.     

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.     

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.     

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.     

Two-phase flow and maldistribution in gas channels of a polymer electrolyte fuel cell

Liquid water transport in a polymer electrolyte fuel cell (PEFC) is a major issue for automotive applications. Mist flow with tiny droplets suspended in gas has been commonly assumed for channel flow while two-phase flow has been modeled in other cell components. However, experimental studies have found that two-phase flow in the channels has a profound effect on PEFC performance, stability and durability. Therefore, a complete two-phase flow model is developed in this work for PEFC including two-phase flow in both anode and cathode channels. The model is validated against experimental data of the wetted area ratio and pressure drop in the cathode side. Due to the intrusion of soft gas diffusion layer (GDL) material in the channels, flow resistance is higher in some channels than in others. The resulting flow maldistribution among PEFC channels is of great concern because non-uniform distributions of fuel and oxidizer result in non-uniform reaction rates and thus adversely affect PEFC performance and durability. The two-phase flow maldistribution among the parallel channels in an operating PEFC is explored in detail.     

Three-dimension simulation of two-phase flows in a thin gas flow channel of PEM fuel cell using a volume of fluid method

This study investigates the two-phase flow in a thin gas flow channel of PEM fuel cells and wall contact angle's impact using the volume of fluid (VOF) method with tracked two-phase interface. The VOF results are compared with experimental data, theoretical solution and analytical data in terms of flow pattern, pressure drop and water fraction. Stable film flow is predicted, as observed experimentally, for the contact angle ranging from 5° to 40° including varying contact angles at different walls of a channel. The contact angle is found to have small impact on the gas pressure drop for the stratified flow regime, but it determines the meniscus of the two-phase interface, which affects the optical detection of the liquid thickness in experiment. The work is important to study of two-phase flow dynamics, multichannel design, experimental design and control of two-phase flows in thin gas flow channels for PEM fuel cells.     

Water management studies in PEM fuel cells,Part I: Fuel cell design and in situ water distributions

A proton exchange membrane fuel cell (PEMFC) must maintain a balance between the hydration level required for efficient proton transfer and excess liquid water that can impede the flow of gases to the electrodes where the reactions take place. Therefore, it is critically important to understand the two-phase flow of liquid water combined with either the hydrogen (anode) or air (cathode) streams. In this paper, we describe the design of an in situ test apparatus that enables investigation of two-phase channel flow within PEMFCs, including the flow of water from the porous gas diffusion layer (GDL) into the channel gas flows; the flow of water within the bipolar plate channels themselves; and the dynamics of flow through multiple channels connected to common manifolds which maintain a uniform pressure differential across all possible flow paths. These two-phase flow effects have been studied at relatively low operating temperatures under steady-state conditions and during transient air purging sequences.     

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.     

In situ investigation of water transport in an operating PEM fuel cell using neutron radiography: Part 1 – Experimental method and serpentine flow field results

Effective management of liquid water produced in the cathodic reaction of a polymer electrolyte membrane (PEM) fuel cell is essential to achieve high cell efficiency. Few experimental methods are available for in situ measurements of water transport within an operating cell. Neutron radiography is a useful tool to visualize water within a cell constructed of many common materials, including metals. The application of neutron radiography to measurements of water content within the flow field channels of an operating 50 cm² PEM fuel cell is described. Details of the experimental apparatus, image processing procedure and quantitative analysis are provided. It is demonstrated that water tends to accumulate in the 180° bends of the serpentine anode and cathode flow fields used in this study. Moreover, the effects of both the current density and cathode stoichiometric ratio on the quantity of accumulated water are discussed.     

Numerical investigation of the performance of symmetric flow distributors as flow channels for PEM fuel cells

This work reports on the performance of a single PEM fuel cell using symmetric flow patterns as gas delivery channels. Three flow patterns, two symmetric and one serpentine, are taken from the literature on cooling of electronics and they are implemented in a computational model as gas flow channels in the anode and cathode side of a PEMFC. A commercial CFD code was used to solve the physics involved in a fuel cell namely: the flow field, the mass conservation, the energy conservation, the species transport, and the electric/ionic fields under the assumptions of steady state and single phase. An important feature of the current modeling efforts is the analysis of the main irreversibilities at different current densities showing the main energy dissipation phenomena in each cell design. Also, the hydraulic performance of the flow patterns was studied by evaluating the pressure drop and pumping power. The first part of this work reveals the advantages of using a serpentine pattern over the base symmetric distributors. The second part is an optimization of the symmetric patterns using the entropy minimization criteria. Such an optimization led to the creation of a flow structure that promotes an improved performance from the point of view of power generation, uniformity of current density, and low pumping power.     

Numerical evaluation of a PEM fuel cell with conventional flow fields adapted to tubular plates

In this research a 3D numerical study on a PEM fuel cell model with tubular plates is presented. The study is focused on the performance evaluation of three flow fields with cylindrical geometry (serpentine, interdigitated and straight channels) in a fuel cell. These designs are proposed not only with the aim to reduce the pressure losses that conventional designs exhibit with rectangular flow fields but also to improve the mass transport processes that take place in the fuel cell cathode. A commercial computational fluid dynamics (CFD) code was used to solve the numerical model. From the numerical solution of the fluid mechanics equations and the electrochemical model of Butler-Volmer different analysis of pressure losses, species concentration, current density, temperature and ionic conductivity were carried out. The results were obtained at the flow channels and the catalyst layers as well as in the gas diffusion layers and the membrane interfaces. Numerical results showed that cylindrical channel configurations reduced the pressure losses in the cell due to the gradual reduction of the angle at the flow path and the twist of the channel, thus facilitating the expulsion of liquid water from the gas diffusion layers and in turn promoting a high oxygen concentration at the triple phase boundary of the catalyst layers. Moreover, numerical results were compared to polarization curves and the literature data reported for similar designs. These results demonstrated that conventional flow field designs applied to conventional tubular plates have some advantages over the rectangular designs, such as uniform pressure and current density distributions among others, therefore they could be considered for fuel cell designs in portable applications.