Modelling of polymer electrolyte membrane fuel cell stacks based on a hydraulic network approach

Polymer electrolyte membrane (PEM) fuel cells convert the chemical energy of hydrogen and oxygen directly into electrical energy. Waste heat and water are the reaction by‐products, making PEM fuel cells a promising zero‐emission power source for transportation and stationary co‐generation applications. In this study, a mathematical model of a PEM fuel cell stack is formulated. The distributions of the pressure and mass flow rate for the fuel and oxidant streams in the stack are determined with a hydraulic network analysis. Using these distributions as operating conditions, the performance of each cell in the stack is determined with a mathematical, single cell model that has been developed previously. The stack model has been applied to PEM fuel cell stacks with two common stack configurations: the U and Z stack design. The former is designed such that the reactant streams enter and exit the stack on the same end, while the latter has reactant streams entering and exiting on opposite ends. The stack analysed consists of 50 individual active cells with fully humidified H₂ or reformate as fuel and humidified O₂ or air as the oxidant. It is found that the average voltage of the cells in the stack is lower than the voltage of the cell operating individually, and this difference in the cell performance is significantly larger for reformate/air reactants when compared to the H₂/O₂ reactants. It is observed that the performance degradation for cells operating within a stack results from the unequal distribution of reactant mass flow among the cells in the stack. It is shown that strategies for performance improvement rely on obtaining a uniform reactant distribution within the stack, and include increasing stack manifold size, decreasing the number of gas flow channels per bipolar plate, and judicially varying the resistance to mass flow in the gas flow channels from cell to cell. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

Externally cooled high temperature polymer electrolyte membrane fuel cell stack

One key issue in high temperature polymer electrolyte membrane fuel cell (HT-PEMFC) stack development is heat removal at the operating temperature of 140–180 °C. Conventionally, this process is done using coolants such as thermooil, steam or pressurized water. In this contribution, external liquid cooling designs are described, which are avoiding two constraints. First, in the cell active area, no liquid coolant is present avoiding any sealing problems with respect to the electrode. Secondly, the external positioning allows high temperature gradients between the heat removal zone and the active area resulting in a good adjustability of appropriate reformate conversion temperatures (e.g. 160 °C) and a more compact cell design. Different design concepts were investigated using modeling techniques and a selection of them has also been investigated experimentally. The experiments proved the feasibility of the external cooling design and showed that the temperature gradients within the active area are below 15 K under typical operating conditions.     

Network based optimization model for pin-type flow field of polymer electrolyte membrane fuel cell

The flow field of a bipolar plate distributes reactants for polymer electrolyte membrane (PEM) fuel cells and removes the produced water from the fuel cells. It greatly influences the performance of fuel cells, especially the concentration losses. Pin-type design, as one of the widely utilized flow field configurations, has the advantage of low pressure drop but the disadvantage of uneven flow distribution and stagnant areas. In this paper, a network-based optimization model was developed to optimize the pin-type flow field configuration. Two optimization cases, uniform flow distribution with and without considering reactant consumption along flow channels, were investigated and the corresponding optimized designs were developed. Three-dimensional numerical simulations of PEM fuel cell were conducted to validate the proposed optimization model and also to compare the performance of the fuel cells using the optimized designs and the regular pin-type design. The numerical results verified the designs generated with the present optimization model. Both the optimized designs exhibited substantially higher fuel cell performance compared to the regular pin-type configuration. Moreover, the optimized design with considering reactant consumption performed even better than the one without considering the consumption, emphasizing the significance of reactant consumption in the flow field optimization model.     

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.     

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.     

Current distribution in polymer electrolyte membrane fuel cell with active water management

Air delivery is typically the greatest parasitic power loss in polymer electrolyte membrane fuel cell (PEMFC) systems. We here present a detailed study of an active water management system for PEMFCs, which uses a hydrophilic, porous cathode flow field, and an electroosmotic (EO) pump for water removal. This active pumping of liquid water allows for stable operation with relatively low air flow rates and low air pressure and parallel cathode channel architectures. We characterize in-plane transport issues and power distributions using a three by three segmented PEMFC design. Our transient and steady state data provide insight into the dynamics and spatial distribution of flooding and flood-recovery processes. Segment-specific polarization curves reveal that the combination of a wick and an EO pump can effect a steady state, uniform current distribution for a parallel channel cathode flow field, even at low air stoichiometries (α_air = 1.5). The segmented cell measurements also reveal the mechanisms and dynamics associated with EO pump based recovery from catastrophic flooding. For most operating regimes, the EO pump requires less than 1% of the fuel cell power to recover from near-catastrophic flooding, prevent flooding, and extend the current density operation range.     

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.     

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.     

Analysis and control of a fuel delivery system considering a two-phase anode model of the polymer electrolyte membrane fuel cell stack

The fuel delivery system using both an ejector and a blower for a PEM fuel cell stack is introduced as a fuel efficiency configuration because of the possibility of hydrogen recirculation dependent upon load states.A high pressure difference between the cathode and anode could potentially damage the thin polymer electrolyte membrane. Therefore, the hydrogen pressure imposed to the stack should follow any change of the cathode pressure. In addition, stoichiometric ratio of the hydrogen should be maintained at a constant to prevent a fuel starvation at abrupt load changes.Furthermore, liquid water in the anode gas flow channels should be purged out in time to prevent flooding in the channels and other layers. The purging control also reduces the impurities concentration in cells to improve the cell performance.We developed a set of control oriented dynamic models that include a anode model considering the two-phase phenomenon and system components The model is used to design and optimize a state feedback controller along with an observer that controls the fuel pressure and stoichiometric ratio, whereby purging processes are also considered. Finally, included is static and dynamic analysis with respect to tracking and rejection performance of the proposed control.     

Design strategy for a polymer electrolyte membrane fuel cell flow-field capable of switching between parallel and interdigitated configurations

Novel water management strategies are important to the development of next generation polymer electrolyte membrane fuel cell systems (PEMFCs). Parallel and interdigitated flow fields are two common types of PEMFC designs that have benefits and draw backs depending upon operating conditions. Parallel flow fields rely predominately on diffusion to deliver reactants and remove byproduct water. Interdigitated flow fields induce convective transport, known as cross flow, through the porous gas diffusion layer (GDL) and therefore are superior at water removal beneath land areas which can lead to higher cell performance. Unfortunately, forcing flow through the GDL results in higher pumping losses as the inlet pressure for interdigitated flow fields can be up to an order of magnitude greater than that for a parallel flow field. In this study a flow field capable of switching between parallel and interdigitated configurations was designed and tested. Results show, taking into account pumping losses, that using constant stoichiometry the parallel flow field results in a higher system power under low current density operation compared to the interdigitated configuration. The interdigitated flow-field configuration was observed to have lower overvoltage at elevated current densities resulting in a higher maximum power and a higher limiting current density. An optimal system power curve was produced by switching from parallel to interdigitated configuration based on which produces a higher system power at a given current density. This design method can be easily implemented with current PEMFC technology and requires minimal hardware. Some of the consequences this design has on system components are discussed.     

An experimental investigation of electro-osmotic drag coefficients in a polymer electrolyte membrane fuel cell

Through the use of a water balance experiment, the electro-osmotic drag coefficients of Nafion 115 were obtained under several conditions (as a function of water content and thermodynamics conditions). For the cases when the anode was fully hydrated (corresponding to water content λ ≈ 14 in the adjacent membrane) and the cathode suffered from drying when dry air was supplied (λ ≈ 2), the electro-osmotic drag coefficients varied from 0.82 (±0.06) to 0.50 (±0.03) H₂O/H⁺ when the current density varied from 0.4 to 1.0 A cm⁻² (95% confidence level). When the current density increased, the electro-osmotic drag coefficient decreased. When the water content at the anode increased from λ ≈ 5 to λ ≈ 14, the cathode was supplied with dry air (λ ≈ 2), and the fuel cell discharged constant current density at 0.6 A cm⁻², the electro-osmotic drag coefficient increased from 0.44 (±0.06) to 0.68 (±0.06) H₂O/H⁺ (95% confidence level). Higher relative humidity gas leads to a higher electro-osmotic drag coefficient at constant current density.     

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.     

Synchrotron X-ray tomography for investigations of water distribution in polymer electrolyte membrane fuel cells

Synchrotron X-ray tomography is used to visualize the water distribution in gas diffusion layers (GDL) and flow field channels of a polymer electrolyte membrane fuel cell (PEMFC) subsequent to operation. An experimental setup with a high spatial resolution of down to 10 μm is applied to investigate fundamental aspects of liquid water formations in the GDL substrate as well as the formation of water agglomerates in the flow field channels. Detailed analyses of water distribution regarding the GDL depth profile and the dependence of current density on the water amount in the GDL substrate are addressed. Visualizations of water droplets and wetting layer formations in the flow field channels are shown. The three-dimensional insight by means of this quasi in situ tomography allows for a better understanding of PEMFC water management at steady state operation conditions. The effect of membrane swelling as function of current density is pointed out. Results can serve as an essential input to create and verify flow field simulation outputs and single-phase models.     

Along‐channel flooding prediction of polymer electrolyte membrane fuel cells

Non‐uniform current distribution in polymer electrolyte membrane (PEM) fuel cells results in local over‐heating, accelerated ageing, and lower power output than expected. This issue is quite critical when a fuel cell experiences water flooding. In this study, the performance of a PEM fuel cell is investigated under cathode flooding conditions. A two‐dimensional approach is proposed for a single PEM fuel cell based on conservation laws and electrochemical equations to provide useful insight into water transport mechanisms and their effect on the cell performance. The model results show that inlet stoichiometry and humidification, and cell operating pressure are important factors affecting cell performance and two‐phase transport characteristics. Numerical simulations have revealed that the liquid saturation in the cathode gas distribution layer (GDL) could be as high as 20%. The presence of liquid water in the GDL decreases oxygen transport and surface coverage of active catalyst, which in turn degrades the cell performance. The thermodynamic quality in the cathode flow channel is found to be greater than 99.7%, indicating that liquid water in the cathode gas channel exists in very small amounts and does not interfere with the gas phase transport. A detailed analysis of the operating conditions shows that cell performance should be optimized based on the maximum average current density achieved and the magnitude of its dispersion from its mean value. Copyright © 2010 John Wiley & Sons, Ltd.     

Ex situ and modeling study of two-phase flow in a single channel of polymer electrolyte membrane fuel cells

In this study, we investigate the air-water two-phase flow in a single flow channel of polymer electrolyte membrane (PEM) fuel cells. In the ex situ study, both straight and serpentine channels with various gas diffusion layer (GDL) surfaces are studied. Focus is placed on the two-phase flow patterns, which are optically characterized using a microscope with a high-resolution camera, and the two-phase pressure amplifiers. We find that the GDL surface properties slightly affect the flow pattern and two-phase pressure amplifier in the flow field configuration. Flow pattern transition occurs at the superficial gas velocity of around 1 m s⁻¹, and the pressure amplifier can reach as high as 10. A two-fluid model is also presented together with one dimensional (1-D) analytical solution, and acceptable agreement is achieved between the model prediction and experimental data at high gas flow rates.     

A model-based parametric analysis of a direct ethanol polymer electrolyte membrane fuel cell performance

In the present work, a model-based parametric analysis of the performance of a direct ethanol polymer electrolyte membrane fuel cell (DE-PEMFC) is conducted with the purpose to investigate the effect of several parameters on the cell's operation. The analysis is based on a previously validated one-dimensional mathematical model that describes the operation of a DE-PEMFC in steady state. More precisely, the effect of several operational and structural parameters on (i) the ethanol crossover rate from the anode to the cathode side of the cell, (ii) the parasitic current generation (mixed potential formation) and (iii) the total cell performance is investigated. According to the model predictions it was found that the increase of the ethanol feed concentration leads to higher ethanol crossover rates, higher parasitic currents and higher mixed potential values resulting in the decrease of the cell's power density. However there is an optimum ethanol feed concentration (approximately 1.0 mol L⁻¹) for which the cell power density reaches its highest value. The platinum (Pt) loading of the anode and the cathode catalytic layers affects strongly the cell performance. Higher values of Pt loading of the catalytic layers increase the specific reaction surface area resulting in higher cell power densities. An increase of the anode catalyst loading compared to an equal one of the cathode catalyst loading has greater impact on the cell's power density. Another interesting finding is that increasing the diffusion layers’ porosity up to a certain extent, improves the cell power density despite the fact that the parasitic current increases. This is explained by the fact that the reactants’ concentrations over the catalysts are increased, leading to lower activation overpotential values, which are the main source of the total cell overpotentials. Moreover, the use of a thicker membrane leads to lower ethanol crossover rate, lower parasitic current and lower mixed potential values in comparison to the use of a thinner one. Finally, according to the model predictions when the cell operates at low current densities the use of a thick membrane is necessary to reduce the negative effect of the ethanol crossover. However, in the case where the cell operates at higher current densities (lower ethanol crossover rates) a thinner membrane reduces the ohmic overpotential leading to higher power density values.     

Analysis and control of a hybrid fuel delivery system for a polymer electrolyte membrane fuel cell

A polymer electrolyte membrane fuel cell (PEM FC) system as a power source used in mobile applications should be able to produce electric power continuously and dynamically to meet the demand of the driver by consuming the fuel, hydrogen. The hydrogen stored in the tank is supplied to the anode of the stack by a fuel delivery system (FDS) that is comprised of supply and recirculation lines controlled by different actuators. Design of such a system and its operation should take into account several aspects, particularly efficient fuel usage and safe operation of the stack.     

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.