Predictions of phase temperatures in a porous cathode of polymer electrolyte fuel cells using a two-equation model

In this study, both solid-phase and fluid-phase temperatures inside a porous cathode of a polymer electrolyte fuel cell in contact with an interdigitated gas distributor are predicted numerically. The porous cathode consists of a catalyst layer and a diffusion layer. The heat transfer in the catalyst layer is coupled with species transports via a macroscopic electrochemical model. On the other hand, in the diffusion layer, the energy equations based on the local thermal non-equilibrium (LTNE) are derived to resolve the temperature difference between the solid phase and the fluid phase. As for the species transports, the Bruggemann model is employed to describe the effective diffusivities of the oxygen and water vapor in the porous cathode. Results show that the wall temperature decreases with increasing the intrinsic heat transfer coefficient. As the intrinsic heat transfer coefficients increase, the porous electrode becomes local thermal equilibrium with a strong thermal interaction (heat transfer) between the solid and fluid phases. Under the conditions of high intrinsic heat transfer coefficients, the temperature difference between the solid matrices and the reactant fluids are negligible.     

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.     

Start-up and steady-state operation of a passive vapor-feed direct methanol fuel cell fed with pure methanol

A transient, two-dimensional, two-phase, multi-component, non-isothermal model is developed to investigate the start-up and steady-state characteristics of a fully passive, vapor-feed direct methanol fuel cell fed with pure methanol. The model considers the species, heat, charge and electrolyte-dissolved water transport in a single computational domain. During the steady-state operation, methanol loss due to evaporation from the cell to the ambient decreases with an increasing current density. Both the scale analysis and the predictions from the full numerical model reveal that the transient response time depends primarily on the cell load. At high current densities, mass consumption in the anode catalyst layer becomes dominant in the cell transient response time, whereas for the lower current densities, both the diffusive liquid transport in the anode and the mass consumption in the anode catalyst layers are predominant.     

Parameter sensitivity examination for a complete three-dimensional,two-phase,non-isothermal model of polymer electrolyte membrane fuel cell

Parameter sensitivity analysis is carried out for a complete three-dimensional, two-phase, non-isothermal model of polymer electrolyte membrane (PEM) fuel cell with a parallel flow field design. The model couples the two-phase flow of the multi-component reactants and liquid water, species transport, electrochemical reactions, proton and electron transport, and the electro-osmosis transport, back diffusion of water in the membrane, and energy transport. Twenty nine parameters, which are classified into the structural or transport parameters of porous layers (tortuosity, porosity, permeability, proton conductivity, electron conductivity, and thermal conductivity) as well as the electrochemical parameters (anodic and cathodic exchange current densities, anodic and cathodic transfer coefficients for anode and cathode reactions), are used to implement individual parameter investigation. The results show the parameters can be divided in to strongly sensitive, conditional sensitive and weak sensitive parameters according to its effect on the cell polarization curve. The optimization of parameters of cathode gas diffusion layer (GDL) and catalyst layer (CL) is more important to improve cell performance than that of anode GDL and CL because liquid water transport and removal affect significantly membrane hydration and reactant transport. Electrochemical parameters determine the activation potential and the slope of ohmic polarization hence these parameters can be used to fit experimental polarization curve more effectively than the other parameters.     

Effect of humidity of reactants on the cell performance of PEM fuel cells with parallel and interdigitated flow field designs

This study investigates the effects of the relative humidity (RH) of the reactants on the cell performance and local transport phenomena in proton exchange membrane fuel cells with parallel and interdigitated flow fields. A three-dimensional model was developed taking into account the effect of the liquid water formation on the reactant transport. The results indicate that the reactant RH and the flow field design all significantly affect cell performance. For the same operating conditions and reactant RH, the interdigitated design has better cell performance than the parallel design. With a constant anode RH = 100%, for lower operating voltages, a lower cathode RH reduces cathode flooding and improves cell performance, while for higher operating voltages, a higher cathode RH maintains the membrane hydration to give better cell performance. With a constant cathode RH = 100%, for lower operating voltages, a lower anode RH not only provides more hydrogen to the catalyst layer to participate in the electrochemical reaction, but also increases the difference in the water concentrations between the anode and cathode, which enhances back-diffusion of water from the cathode to the anode, thus reducing cathode flooding to give better performance. However, for higher operating voltages, the cell performance is not dependent on the anode RH.     

Modeling of water transport through the membrane electrode assembly for direct methanol fuel cells

In this work, a one-dimensional, isothermal two-phase mass transport model is developed to investigate the water transport through the membrane electrode assembly (MEA) for liquid-feed direct methanol fuel cells (DMFCs). The liquid (methanol–water solution) and gas (carbon dioxide gas, methanol vapor and water vapor) two-phase mass transport in the porous anode and cathode is formulated based on classical multiphase flow theory in porous media. In the anode and cathode catalyst layers, the simultaneous three-phase (liquid and vapor in pores as well as dissolved phase in the electrolyte) water transport is considered and the phase exchange of water is modeled with finite-rate interfacial exchanges between different phases. This model enables quantification of the water flux corresponding to each of the three water transport mechanisms through the membrane for DMFCs, such as diffusion, electro-osmotic drag, and convection. Hence, with this model, the effects of MEA design parameters on water crossover and cell performance under various operating conditions can be numerically investigated.     

Three-dimensional two-phase flow model of proton exchange membrane fuel cell with parallel gas distributors

A non-isothermal, steady-state, three-dimensional (3D), two-phase, multicomponent transport model is developed for proton exchange membrane (PEM) fuel cell with parallel gas distributors. A key feature of this work is that a detailed membrane model is developed for the liquid water transport with a two-mode water transfer condition, accounting for the non-equilibrium humidification of membrane with the replacement of an equilibrium assumption. Another key feature is that water transport processes inside electrodes are coupled and the balance of water flux is insured between anode and cathode during the modeling. The model is validated by the comparison of predicted cell polarization curve with experimental data. The simulation is performed for water vapor concentration field of reactant gases, water content distribution in the membrane, liquid water velocity field and liquid water saturation distribution inside the cathode. The net water flux and net water transport coefficient values are obtained at different current densities in this work, which are seldom discussed in other modeling works. The temperature distribution inside the cell is also simulated by this model.     

Water management in alkaline anion exchange membrane fuel cell anode

Water management is an important issue for alkaline anion exchange membrane fuel cell (AAEMFC) due to its significant role in the energy conversion processes. In this study, a numerical model is developed to investigate the water transport in AAEMFC anode. The gas and liquid transport characteristics in the gas diffusion layer (GDL) and catalyst layer (CL) with different designs and under various operating conditions are discussed. The results show that the current density affects the liquid water distribution in anode most significantly, and the temperature is the second considerable factor. The stoichiometry ratio of the supplied reactant has insignificant effect on the liquid water transport in anode. The change of liquid water amount in anode with cathode relative humidity follows a similar trend with anode inlet relative humidity. Some numerical results are also explained with published experimental and modeling data with reasonable agreement.     

Study on the effect of humidity and stoichiometry on the water saturation of PEM fuel cells

This paper investigates the effects of relative humidity (RH) and stoichiometry of reactants on the water saturation and local transport process in proton exchange membrane fuel cells. A two‐dimensional model was developed, taking into account the effect of the formation of liquid water on the reactant transport. The results indicate that the reactant RH and stoichiometry significantly affect cell performance. At a constant anode RH = 100%, a lower cathode RH maintains membrane hydration to give better cell performance. At a constant cathode RH = 100%, a lower anode RH not only provides more hydrogen to the catalyst layer to participate in the electrochemical reaction but also increases the difference in the water concentrations between the anode and cathode. This enhances the back‐diffusion of water from the cathode to the anode, reducing possible flooding for better cell performance. Higher anodic stoichiometry results in the reduction of cathodic water saturation by increasing water back‐diffusion, thereby enhancing fuel cell performance. Higher cathodic stoichiometry also reduces water saturation by drying more liquid water to increase cathode local current density. Copyright © 2011 John Wiley & Sons, Ltd.     

A hybrid model of cathode of PEM fuel cell using the interdigitated gas distributor

A two-dimensional (2D), single- and two-phase, hybrid multi-component transport model is developed for the cathode of PEM fuel cell using interdigitated gas distributor. The continuity equation and Darcy's law are used to describe the flow of the reactant gas and production water. The production water is treated as vapor when the current density is small, and as two-phase while the current density is greater than the critical current density. The advection–diffusion equations are utilized to study species transport of multi-component mixture gas. The Butler–Volmer equation is prescribed for the domain in the catalyst layer. The predicted results of the hybrid model agree well with the available experimental data. The model is used to investigate the effects of operating conditions and the cathode structure parameters on the performance of the PEM fuel cell. It is observed that liquid water appears originally in the cathodic catalyst layer over outlet channel under intermediate current and tends to be distributed uniformly by the capillary force with the increase of the current. It is found that reduction of the width of outlet channel can enhance the performance of PEM fuel cell via the increase of the current density over this region, which has, seemingly, not been discussed in previous literatures.     

Analyses of mass and heat transport interactions in a direct methanol fuel cell

In this paper, a two-dimensional, two-phase, non-isothermal model is presented to predict the electrochemical, mass transfer and heat transfer behaviors in a direct methanol fuel cell (DMFC). Governing equations including the momentum, continuity, heat transfer, proton and electron transport, species transport for water, methanol, and all the gas species (carbon dioxide, methanol vapor, water vapor, oxygen, and nitrogen) and the auxiliary equations are coupled to studying the various phenomena in DMFC. The modeling results agree well with the four different experimental data in an extensive range of operation conditions. A parametric study is also performed to examine the effects of the cell voltage on the different variables, such as cell temperature, liquid methanol concentration distribution, oxygen concentration distribution, and anode gas pressure distribution. The results show that the cell temperature is highly sensitive to the change in the cell voltage as well as methanol concentration distribution. Moreover, it is found that the cell voltage significantly influences the oxygen concentration distribution and the anode gas pressure distribution.     

A complete two-phase model of a porous cathode of a PEM fuel cell

This paper has developed a complete two-phase model of a proton exchange membrane (PEM) fuel cell by considering fluid flow, heat transfer and current simultaneously. In fluid flow, two momentum equations governing separately the gaseous-mixture velocity (u_g) and the liquid-water velocity (u_w) illustrate the behaviors of the two-phase flow in a porous electrode. Correlations for the capillary pressure and the saturation level connect the above two-fluid transports. In heat transfer, a local thermal non-equilibrium (LTNE) model accounting for intrinsic heat transfer between the reactant fluids and the solid matrices depicts the interactions between the reactant-fluid temperature (T_f) and the solid-matrix temperature (T_s). The irreversibility heating due to electrochemical reactions, Joule heating arising from Ohmic resistance, and latent heat of water condensation/evaporation are considered in the present non-isothermal model. In current, Ohm's law is applied to yield the conservations in ionic current (i_m) and electronic current (i_s) in the catalyst layer. The Butler–Volmer correlation describes the relation of the potential difference (overpotential) and the transfer current between the electrolyte (such as Nafion™) and the catalyst (such as Pt/C).     

Analyses of heat and water transport interactions in a proton exchange membrane fuel cell

A two-phase non-isothermal model is developed to explore the interaction between heat and water transport phenomena in a PEM fuel cell. The numerical model is a two-dimensional simulation of the two-phase flow using multiphase mixture formulation in a single-domain approach. For this purpose, a comparison between non-isothermal and isothermal fuel cell models for inlet oxidant streams at different humidity levels is made. Numerical results reveal that the temperature distribution would affect the water transport through liquid saturation amount generated and its location, where at the voltage of 0.55 V, the maximum temperature difference is 3.7 °C. At low relative humidity of cathode, the average liquid saturation is higher and the liquid free space is smaller for the isothermal compared with the non-isothermal model. When the inlet cathode is fully humidified, the phase change will appear at the full face of cathode GDL layer, whereas the maximum liquid saturation is higher for the isothermal model. Also, heat release due to condensation of water vapor and vapor-phase diffusion which provide a mechanism for heat removal from the cell, affect the temperature distribution. Instead in the two-phase zone, water transport via vapor-phase diffusion due to the temperature gradient. The results are in good agreement with the previous theoretical works done, and validated by the available experimental data.     

An approach for determining the liquid water distribution in a liquid-feed direct methanol fuel cell

In determining the liquid water distribution in the anode (or the cathode) diffusion medium of a liquid-feed direct methanol fuel cell (DMFC) with a conventional two-phase mass transport model, a current-independent liquid saturation boundary condition at the interface between the anode flow channel and diffusion layer (DL) (or at the interface between the cathode flow channel and cathode DL) needs to be assumed. The numerical results resulting from such a boundary condition cannot realistically reveal the liquid distribution in the porous region, as the liquid saturation at the interface between the flow channel and DL varies with current density. In this work, we propose a simple theoretical approach that is combined with the in situ measured water-crossover flux in the DMFC to determine the liquid saturation in the anode catalyst layer (CL) and in the cathode CL. The determined liquid saturation in the anode CL (or in the cathode CL) can then be used as a known boundary condition to determine the water distribution in the anode DL (or in the cathode DL) with a two-phase mass transport model. The numerical results show that the water distribution becomes much more realistic than those predicted with the assumed boundary condition at the interface between the flow channel and DL.     

Development of direct methanol alkaline fuel cells using anion exchange membranes

Research into the development of direct methanol alkaline fuel cell (DMAFC) using an anion exchange polymer electrolyte membrane is described. The commercial membrane used had a higher electric resistance, but a lower methanol diffusion coefficient than Nafion^® membranes. Fuel cell tests were performed using carbon supported Pt catalyst, and the effect of temperature, methanol concentration, methanol flow rate, air pressure and Pt loading were investigated. It was found that the cell performance improved drastically with a membrane assembly electrode (MEA) which did not include the gas diffusion layer on the anode, because of lower reactant mass transfer resistance. To give suitable cathode performance, humidification of the air and a subtle balance between the air pressure and water transport is required.     

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.     

Water transport characteristics in a passive liquid-feed DMFC

A two-dimensional, two-phase, non-isothermal model was developed to investigate the water transport characteristics in a passive liquid-feed direct methanol fuel cell (DMFC). The liquid–gas two-phase mass transport in the porous anode and cathode was formulated based on multi-fluid model in porous media, and water and methanol crossover through the membrane were considered with the effect of diffusion, electro-osmotic drag, and convection. The model enabled numerical investigation of the effects of various operating parameters, such as current density, methanol concentration, and air humidity, as well as the effect of the cathode hydrophobic air filter layer, on the water transport and cell performance. The results showed that for the free-breathing cathode, gas species concentration and temperature showed evident differences between the cell and the ambient air. The use of a hydrophobic air filter layer at the cathode helped to achieve water recovery from the cathode to the anode, although the oxygen transport resistance was increased to some extent. It was further revealed that the water transport can be influenced by the ambient relative humidity.     

Unsteady-state modelling for a passive liquid-feed DMFC

An unsteady-state model was developed for a liquid-feed Direct Methanol Fuel Cell (DMFC) delivery considering two-phase system. The model considered the mass and heat transport in the feed delivery system attached to the anode and cathode of the fuel cell. The results were then compared with the experimental data from in-house fabricated DMFC and steady-state model. It was observed that the unsteady-state model gave more similar results with experimental data then the steady-state model. The effects of feed methanol concentration in the reservoir and current density on mass transport to the catalyst layer were revealed.     

Mathematical modeling of novel porous transport layer architectures for proton exchange membrane electrolysis cells

Thin foil based porous transport layers (PTLs) that contain highly structured pore arrays have shown promise as anode PTLs in proton exchange membrane electrolysis cells. These novel PTLs, fabricated with advanced manufacturing techniques, produce thin, tunable, multifunctional layers with reduced flow and interfacial resistances and high thermal and electric conductivities. To further optimize their design, it is important to understand their fundamental impact on the transport of protons, electrons, and liquid/vapor mixtures in the electrode. In this work, we develop a two-dimensional multiphysics model to simulate the coupled electrochemistry and multiphase transport in an electrolysis cell operated with the novel PTL architecture. The results show that larger pores improve access of water to the anode catalyst layer, which is beneficial for both the oxygen evolution reaction and membrane hydration. Larger pore sizes also improve oxygen gas transport from the catalyst layer, because generated oxygen gas is forced to travel in-plane through the anode catalyst layer until it reaches a pore opening that is connected to a channel. The discussed results confirm that the proposed thin foil based PTLs are fundamentally different from conventional PTLs, such as felts or layered meshes. The model developed in this work also provides generalizable insight into fundamental PEMEC phenomena, such as the competition between liquid and gas phase transport, membrane hydration and water management, and nonuniform electrochemical reactions, which are processes relevant to all PEMEC designs.