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Two-Phase Modeling and Flooding Prediction of Polymer Electrolyte Fuel Cells
Journal of The Electrochemical Society
Abstract
A newly developed theory of liquid water transport in hydrophobic gas diffusion layers is applied to simulate flooding in polymer electrolyte fuel cells ~PEFCs! and its effects on performance. The numerical model accounts for simultaneous two-phase flow and transport of species and electrochemical kinetics, utilizing the well-established multiphase mixture formulation to efficiently model the two-phase transport processes. The two-phase model is developed in a single domain, yielding a single set of governing equations valid in all components of a PEFC. The model is used to explore the two-phase flow physics in the cathode gas diffusion layer. Multidimensional simulations reveal that flooding of the porous cathode reduces the rate of oxygen transport to the cathode catalyst layer and causes a substantial increase in cathode polarization. Furthermore, the humidification level and flow rate of reactant streams are key parameters controlling PEFC performance and two-phase flow and transport characteristics. It is also found that minimization of performance limitations such as membrane dry-out and electrode flooding depends not only on material characteristics but also on the optimization of these operating parameters.
... The governing equations for energy conservation, species conservation of reactants, and continuity and momentum of gas mixtures are written respectively as [8]: ...
... (1) The electrochemical reaction rates in the CLs are modeled using the Butler-Volmer equation [8]: ...
... As part of the validation analysis, the polarization curve of the presented model was compared with the results of Pasaogullari and Wang [8]. As shown in Fig. 2, accurate agreement is achieved between the modeling polarization curve and the experimental results of the reference work [8]. ...
The primary sources of irreversibility in a polymer electrolyte membrane fuel cell are identified using the entropy generation approach. In the current work, a 2D multicomponent lattice Boltzmann method (LBM), which simulates chemical and electrochemical interactions in addition to heat and mass transfer, is used to compute the entropy generation rates in all areas of the proton exchange membrane fuel cell, including the clear and porous channels. The catalyst layer thickness and the temperature gradient have a significant favorable influence on entropy formation. Furthermore, heat transfer in the cell's thinner catalyst layer generates less entropy. Entropy generation on the anode side rises by approximately 66.67%, 183.34%, and 350%, respectively, when the catalyst layer thickness is increased by 25%, 50%, and 75% at a constant average current density of 600 mA.cm-2. Furthermore, on the cathode side, an increase in the catalyst layer thickness of 25%, 50%, or 75% results in an increase in entropy generation of roughly 47.06, 117.65, and 194.12%, respectively, while the average current density is maintained at 600 mA.cm-2. Additionally, for average current densities of 400, 600, and 800 mA.cm-2 , the cathode side generates more entropy than the anode side by approximately 450, 177.78, and 64.28%, respectively.
... This experiment focused exclusively on a Nafion ® 117 membrane, with measurements taken at 30°C for λ v,eq and 80°C for λ l,eq . The equation is expressed as (8) [7,9,13,17,18,21,23,24,26]. ...
... However, these issues did not impede its prevalence in the literature, and an adapted 190 expression for a w has consequently been introduced, as discussed in section 2.6. Finally, a linear expression was arbitrarily employed to connect λ v,eq at a w = 1 to λ l,eq at a w = 3, as indicated in (10) [7,9,13,17,18,21,23,24,26]. In this model, the existence of a w ≥ 3 is deemed either improbable or impossible; hence, the value of 16.8 is retained for higher a w , or higher values should not be considered [26]. ...
... Finally, a linear expression was arbitrarily employed to connect λ v,eq at a w = 1 to λ l,eq at a w = 3, as indicated in (10) [7,9,13,17,18,21,23,24,26]. In this model, the existence of a w ≥ 3 is deemed either improbable or impossible; hence, the value of 16.8 is retained for higher a w , or higher values should not be considered [26]. Nonetheless, providing precise rules is challenging, given the incomplete and subjective nature of this framework. ...
Technologies based on the use of hydrogen are promising for future energy requirements in a more sustainable world. Consequently, modelling fuel cells is crucial, for instance, to optimize their control to achieve excellent performance, to test new materials and configurations on a limited budget, or to consider their degradation for improved lifespan. To develop such models, a comprehensive study is required, encompassing both well-established and the latest governing laws on matter transport and voltage polarisation for Proton Exchange Membrane Fuel Cells (PEMFCs). Recent articles often rely on outdated or inappropriate equations, lacking clear explanations regarding their background. Indeed, inconsistent understanding of theoretical and experimental choices or model requirements hinders comprehension and contributes to the misuse of these equations. Additionally, specific researches are needed to construct more accurate models. This study aims to offer a comprehensive understanding of the current state-of-the-art in PEMFC modeling. It clarifies the corresponding governing equations, their usage conditions, and assumptions, thus serving as a foundation for future developments. The presented laws and equations are applicable in most multi-dimensional, dynamic, and two-phase PEMFC models.
... Later, they helped with the development of multiphysics models for complex transport phenomena in multicomponents of fuel cells. [13][14][15] However, different from fuel cell models, water electrolysis was always numerically studied by spatially lumped models for steady states based on the mass/species conservation. [16][17][18] They had the approximating information of electrochemistry and mass balance, but excluded dimensionally heterogeneous effects. ...
... Using Equations (12)- (14), the temperature-dependent ionic conductivity is evaluated in the ionomer phase. Considering electrochemical reactions and double layer capacitance, the source terms of charge balance equations are given by ...
... θ PTL Contact angle of PTLs π 6 [38] κ l Ionic conductivity of PEM 0.11 S/cm [12] λ 0 l The equivalent conductivity of hydronium ions 145.1 SÁcm 2 /mol [11] λ sat l Liquid water loading in ionomers in saturated equilibrium 23 [11] μ a,an Oxygen viscosity 1.881 Â 10 À5 PaÁs [ 14] μ a,ca Hydrogen viscosity 8.42 Â 10 À6 PaÁs [ 15] μ l Liquid water viscosity 3.56 Â 10 À4 PaÁs [ 15] ξ Water transport coefficient in PEM 3.5 Â 10 À8 mol 2 /(JÁcmÁs) [12] ρ H2O Water density (at 353.15 K) 0.996 g/cm 3 [18] ρ Ir Iridium oxide density 22.56 g/cm 3 [7] ρ Pt Platinum oxide density 21.45 g/cm 3 [7] σ aCL Electric conductivity in the anode catalyst layer 300 S/m [15] σ cCL Electric conductivity in the cathode catalyst layer 300 S/m [15] σ PTL Electric conductivity in the PTLs 1400 S/m [15] ψ The electro-osmotic coefficient 1.5909 [12] Abbreviations: Ass, assumption; Est, estimation. ...
Proton exchange membrane water electrolysis (PEMWE) is currently developed for the design of mature industrial‐scale manufactures with commercialization. It needs reducing hydrogen production cost by lowering material cost and increasing operating current density. In engineering perspectives, the study of electrolytic performance during dynamic operation is crucial for PEMWE system management and process control. However, there is few multiphysics models of PEMWE considering transient behavior. The one‐dimensional (1D) comprehensive dynamic multiphysics model allows to explore temporal transport phenomena in the PEMWE, and predict electrolytic performance. The 1D model is endorsed by the spatially lumped model from the literature. Changing values of structural and physical properties of porous transport layers (PTLs) and catalyst layers (CLs) allows the observation of their effects on the electrolytic performance and transport phenomena in two‐phase flow regime. It suggests that the appropriate PTL properties, and CL fabrication method can lower the cost and remain high electrolytic performance.
... Momentum conservation. The momentum conservation of the two-phase flow can be theoretically expressed as Navier-Stocks equation (Pasaogullari and Wang, 2005), showing ...
... where m ¼ 3 (Pasaogullari and Wang, 2005). The saturation in both phases follows the rules as ...
... D eff is the effective diffusion coefficient of oxygen in domain k. It can be written as (Pasaogullari and Wang, 2005) ...
1D multiphysics modelling of the PEM water electrolysis anode is benefit for detailed investigation of the joint effects of electrochemical performance and multicomponent multiphase flow transport phenomena. Such a model can be effectively applied for the water electrolysis system design and optimization. Recently, the importance of hydraulic effects and dynamic behavior gradually attracts much focus on this specific issue. In this article, a novel 1D dynamic model has been developed for interpreting the multiphysics processes in the PEM water electrolysis anode, which considers the complex fluid dynamics and electrochemistry in the PEM water electrolyzer (PEMWE) components – PEM, the anode catalyst layer and the porous transport layer. As a result, the hydraulic and electrochemical properties of three components were studied for investigation of their effects on the characterization of electrochemical performance and mass transport processes. It concludes that for the improvement of electrolytic performance, the porous transport layer is suggested to be designed for high permeability and low contact angle. The catalyst layer needs to be optimized for its three-phase interface fraction with high coating mass in the membrane assembly.
... K rl and K rg can be calculated as follows: 63 Relative permeability takes values between 0 and 1 and is introduced as a concept to compare the flow of each phase, as the pore space of the porous layer is shared by both gas and liquid phases. 50,66 Conservation equation.-The two-phase flow was simulated using the Eulerian multiphase model. ...
The design of the bipolar plates is essential to ensure a uniform distribution of reactants in the active area. This study designed a flow field that can quickly discharge oxygen. The designed improved performance by up to 12.13% at over 0.15 A cm⁻². With increasing voltage, the reactants supplied to the catalyst-coated membrane (CCM) increased in both flow fields. There was no significant difference in performance between the two flow fields at 2.25 V. This is because the oxygen residence time is long when the current density is low, blocking the water supply. As current density increased, oxygen residence time decreased. The performance of the designed flow field, where many reactants are supplied, was improved. This is because bubble overpotential decreased as more water was supplied to the CCM. However, a continuous increase in current density did not result in a further increase in performance. This is because oxygen coalescence occurs more frequently. Furthermore, it was observed that when the radius of the speed bumps is increased to 0.5 mm, water becomes trapped between them at 3.15 V, where the oxygen generation rate is high. This is because oxygen pushes water between the speed bumps.
... A two-phase model was established in the study performed by Paşaogulları and Wang. 10 The two-phase model includes gas and water phases. As a result of the two-phase investigation, the effects of humidification of the electrodes and water droplets formed in the cathode catalyst layer were observed and lower power and current densities were obtained compared to single-phase investigations. ...
In the present study, the performance parameters for a single-cell PEM fuel cell with 50 cm ² active surface area and 0.0178 cm polymer membrane thickness at 4 different operating temperatures (303, 323, 343, and 363 K) and 4 different operating pressures (3, 6, 9, and 12 atm) was investigated by theoretical analysis. Hydrogen and oxygen partial pressures, membrane resistivity, internal resistance, activation, ohmic and concentration losses, cell voltage, power density, and thermal efficiency were calculated using this analysis. It has been observed that the augmentation of temperature and pressure in the fuel cell leads to a favorable increase in cell voltage, power density, and thermal efficiency. The thermal efficiency values were found to be 23% and 39%, respectively at the following conditions: temperatures of 303 K and 363 K, current density of 1 A/cm ² , and constant pressure. At the same current density, the thermal efficiency is 29% and 32% at 3 atm and 12 atm operating pressures at a constant temperature. When operated under constant current density and temperature conditions, an increase in the operating pressure of the PEMFC from 3 atm to 12 atm results in a corresponding increase in cell voltage, from 0.4422 V to 0.4755 V, respectively. It was observed that the influence of temperature on the thermal efficiency of the PEM fuel cell was led to be higher than the influence of pressure.
... The principal alternative is the multiphase mixture (M 2 ) model, which simplifies the mathematical specification and implementation of the two-fluid model by imposing condensationevaporation equilibrium throughout the PEMFC porous media. [116][117][118] Several authors have remarked on the weaknesses of these standard models, due to their reliance on capillary pressure-saturation relationships with their origins in soil descriptions from Earth sciences 2,113,119 -these are not necessarily relevant model materials with respect to PEMFC porous media. The M 2 model has been explicitly criticised due to the absence of the necessary mass source terms relating to faradaic sources and sinks in the CL; 120 this statement has been disputed by proponents of the M 2 model, 121 and faradaic mass sources do indeed appear in practical implementations. ...
Theoretical models used to describe the catalyst layers (CLs) in polymer electrolyte membrane fuel cells (PEMFCs) are reviewed, with a focus on continuum treatments as incorporated in device-scale models used to predict and optimise PEMFC operating performance. Consideration is given to the mathematical relationships between CL design properties (Pt/C mass ratio, catalyst loading, ionomer loading), and physical properties. Relevant physical models are summarised, considering couplings between the CL and the phenomena of charge transfer, reactant mass transfer, hydrogen oxidation, and oxygen reduction electrode kinetics, heat transfer, and water balance. The relevance of thin film methods (through-thickness homogenisation) is compared to those resolving the macroscopic depth of the CL. Specific continuum homogenisations of microstructural models incorporating CL transport limitations in a continuum treatment, such as the agglomerate model, are discussed.
... Non-pressure dependent Oxygen transport resistance, s/cm O 2 Total oxygen transport resistance, s/cm Normalized roughness factor Normalized roughness factor at dry electrode Normalized roughness factor at fully flooded condition T Temperature, K In addition, Pasaogullari et al. also developed a two-phase PEMFC model to simulate liquid water transport inside the GDL and microporous layer (MPL) using a capillary pressure and saturation function [14,15]. Weber et al. also developed a PEMFC model to study the effects of diffusion media wettability on PEMFC performance [16,17]. ...
While significant progress in PEMFC research has been achieved in recent years, simulation of liquid water formation and transport accurately still remains a significant challenge. Under wet operating conditions, liquid water may condense in the channel, gas diffusion layer, or electrode, which introduces complicated transport phenomena. In this work, we present a physics-based, steady-state, 1-D, non-isothermal, and two-phase PEMFC model that captures the interactive nature of gas and liquid transports to simulate fuel cell performance. Limiting current experiments are employed to study both dry and wet oxygen transport resistances of Toray-H-060 carbon fiber paper with PTFE impregnation and a microporous layer. A two-phase model based on limiting current diagnostics is proposed to simulate water transport in the gas diffusion layer using tendril length to represent liquid water penetration. This newly constructed model is capable of predicting the total transport resistance under dry, transition, and wet regions. In addition, an empirical catalyst utilization model is proposed to correlate the electrode water activity with catalyst utilization. The two-phase electrode model provides key insights into the relationship between catalyst utilization and electrode flooding. The newly developed 1-D two-phase model is highly efficient in predicting PEMFC performance under a wide range of operating conditions and the empirical approach can be applied and adopted to studies with novel materials and designs.
... For example, PEM and AEM fuel-cell catalyst layers can flood with water due to excess water invading gas-filled channels, leading to additional mass-transport limitations and poor cell performance. [27][28][29][30][31][32][33][34] As a result, proper management of water balance is necessary to maintain adequate ion conductivity without flooding. Ion-exchange membranes can also be used in electrodialysis; water transport is similarly important in these systems. ...
The electro-osmotic coefficient of ionomer membranes is a significant water management property that quantifies the number of water molecules dragged with the mobile ion (typically a proton) when that ion moves due to the operation of an electrochemical cell or an electric field. This coefficient becomes critical when attempting to model water distribution and movement in fuel cells and electrolyzers, where water is an important factor influencing device performance. However, there is disagreement on the value of the electro-osmotic coefficient for PFSA membranes and little significant study of the coefficient in anion exchange membranes (AEMs). Here we present an electrochemical, two-electrode method of determining the electro-osmotic coefficient of ionomers using differential relative humidity (RH) measurements. This approach allows for more accurate determination of the electro-osmotic coefficient. We present the electro-osmotic coefficient as a function of temperature and mobile ion for a variety of ionomers, including Nafion, sulfonated polystyrene, Versogen,, and Sustainion. In addition, a model based on the Maxwell-Stefan-Onsager framework is developed for the AEMs, enabling calculation of the membrane water permeability via fitting of the electro-osmotic coefficient. These coefficients will allow for more accurate models of water transport in electrochemical systems, leading to a greater understanding of the inefficiencies in these systems and, hopefully, insight into how to improve them. This work was supported by the HydroGEN Advanced Water Splitting Materials consortium, which is supported by the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, Hydrogen and Fuel Cell Technologies Office, under contract number DE-AC02-05CH11231.
... For example, PEM and AEM fuel-cell catalyst layers can flood with water due to excess water invading gas-filled channels, leading to additional mass-transport limitations and poor cell performance. [27][28][29][30][31][32][33][34] As a result, proper management of water balance is necessary to maintain adequate ion conductivity without flooding. Ion-exchange membranes can also be used in electrodialysis; water transport is similarly important in these systems. ...
Anion-exchange membranes (AEMs) are a possible replacement for perfluorosulfonic-acid membranes in energy-conversion devices, primarily due to the hydroxide mobile ion allowing the devices to operate in alkaline conditions with less expensive electrocatalysts. However, the transport properties of AEMs remain understudied, especially electro-osmosis. In this work, an electrochemical technique, where the open-circuit voltage is measured between two ends of a membrane maintained at different relative humidities, is used to determine the water transport number of various ionomers, including Versogen and Sustainion AEMs and Nafion cation-exchange membrane (CEM), as a function of water content and temperature. In addition, the CEMs and AEMs are examined in differing single-ion forms, specifically proton and sodium (CEM) and hydroxide and carbonate (AEM). Carbonate-form AEMs have the highest transport number (~11), followed by sodium-form CEMs (~8), hydroxide-form AEMs (~6), and proton-form CEMs (~3). Finally, a multicomponent transport model based on the Stefan-Maxwell-Onsager framework of binary interactions is used to develop a link between water transport number and water-transport properties, extracting a range for the unmeasured membrane water permeability of Versogen as a function of water content.
... Complete aqueous flooding, where gas transport is limited to diffusion through the water-filled pores, can severely restrict gas transport to the catalyst layer. Thus, catalyst-layer flooding is of particular interest given the importance of the catalyst in driving device performance (Li et al., 2008;Nara et al., 2013;Pasaogullari and Wang, 2005;Sabharwal and Secanell, 2022). In general, water management in fuel cells is critical to their overall performance (Andersson et al., 2016;O'Hayre et al., 2016;Vielstich et al., 2003;Newman, 2004, 2006). ...
... Therefore, tuning humidification of the membranes is also a basic way of cell performance while accumulation of too much water also impacts performance and lifetime (Zawodzinski et al., 1993). Pasaogullari has reported, anode flooding is most probable for happening at low current, low reactant flow rates and low temperatures due to the lower electro-osmotic forces (Pasaogullari and Wang, 2005). In other words proton flux is large in the anode electrode; therefore a strong electro-osmotic force pulls the H2O from anode to cathode (due to the low water content). ...
Graphene and h-BN have been theoretically simulated for hydrogen storage and oxygen diffusion in a single fuel cell unit. Obviously, the efficiency of the PEM hydrogen fuel cells was significantly related to the amount of H2 concentration, the water activities in catalyst substrates and the polymer of the electrolyte membranes, the temperature and the dependence of such variables in the direction of the fuel and air currents between the anode path and the cathode. The single PEM parameter has been estimated and the results show greater fuel cell efficiency using graphene sheets and h-BN. Maximum efficiency is observed with the stoichiometry of the 5H2, 5O2 and 3 C2F4 molecules during adsorption.
... A value of 2 for the n k exponent in the relative permeabilities in the channels has been found to be sufficient to drain the liquid water in the cell. For the porous media, most authors [45,47,60] recommend a value of three, four or five for this parameter to better fit to the experimental tests even though it is very difficult or impossible to measure it. This may explain the lower averaged values of the liquid water thickness obtained by the model (Fig. 4). ...
Proper management of the liquid water and heat produced in proton exchange membrane (PEM) fuel cells remains crucial to increase both its performance and durability. In this study, a two-phase flow and multicomponent model, called two-fluid model, is developed in the commercial COMSOL Multiphysics® software to investigate the liquid water heterogeneities in large area PEM fuel cells, considering the real flow fields in the bipolar plate. A macroscopic pseudo-3D multi-layers approach has been chosen and generalized Darcy's relation is used both in the membrane-electrode assembly (MEA) and in the channel. The model considers two-phase flow and gas convection and diffusion coupled with electrochemistry and water transport through the membrane. The numerical results are compared to one-fluid model results and liquid water measurements obtained by neutron imaging for several operating conditions. Finally, according to the good agreement between the two-fluid and experimentation results, the numerical water distribution is examined in each component of the cell, exhibiting very heterogeneous water thickness over the cell surface.
... They concluded that the 1D model should be established to predict water management impacts on the fuel cell's performance, and the calculation speed of the 1D model was much faster than that of the 3D model under optimal operating conditions. Pasaogullari et al. [28] developed a multidimensional two-phase model based on the liquid water transport through the hydrophobic GDL. By comparing the single-phase predictions of the polarization curves at different inlet RH, they found that two-phase transport phenomena and water flooding lowered PEMFC performance, which was mainly because of the reduced gas transport and active catalytic area. ...
External humidification has been used as a flexible water management strategy for the proton exchange membrane fuel cell (PEMFC). To study the anode inlet relative humidity (ARH) effect on the performance of PEMFC, the anode inlet water content (AIWC) model is established, including condensation rates and water activity. A comparable analysis between the AIWC model, Fluent model and experiment is conducted at 60 °C operating temperature, four different anode relative humidities (25%, 50%, 75% and 100%), and 100% cathode relative humidity (CRH). The species distributions of water content and hydrogen concentration are presented and analyzed. The results show the relative error of the voltage results derived from the AIWC model has been reduced by 3.2% (the original is 4.6% in the Fluent model) especially at 240 mA·cm⁻² for 50% ARH. An increase in hydrogen humidity can improve the PEMFC output at low ARH (25% and 50%). Meanwhile, at high ARH (100%), the excess water produced does not play a positive role. At 50% ARH, the water content and hydrogen distribution are more uniform all over the anode channels.
... The main barriers to the commercialization of PEMFCs are cost, durability, and water/thermal management [3]. In the PEMFCs, the formations of water both in gas and liquid phases are possible due to the low operating temperature of the PEMFC, which is around 70 Ce90 C, in comparison to other types of fuel cells [4,5]. The liquid form of the water is mainly probable to occur at high humidities or low gas flow rates, hence water management is more critical in these conditions [6]. ...
The formation of water columns inside the gas diffusion layer (GDL) of the proton exchange membrane fuel cell (PEMFC), which is harmful phenomenon, can be controlled by the GDL's microstructure and material. Using computational fluid dynamics (CFD), a three-dimensional model is developed to monitor the impacts of the GDL's porosity and permeability on the maximum GDL liquid removal. In this regard, twenty-four different cases are simulated at the GDL contact angle of 110°. Results indicate that higher permeabilities and porosities improve the GDL liquid removal and the performance of the system. Obtaining the simulation data, an artificial neural network (ANN) model is trained at the current density of 0.41 A/ cm2 and the voltage of 0.6 V to predict the maximum GDL liquid removal in 300000 points and to perform the optimization. The ANN model is trained with four neurons with the respective mean squared error values 6.32422e-6, 1.00637e-5, and 4.12086e-6 for the training, validation, and testing, which approves the accuracy of the model. Using a fitted curve and the ANN model, the optimum values of the porosity and the permeability are computed to be 0.9 and 1.481e-11 (m2), respectively, to reach the maximum GDL liquid removal of 0.373 (kg/m3s).
... The oxygen transport paths are reduced and lead to cathode flooding. 34,35 Wang et al 36 have developed a thermal model under non-isothermal conditions, which led to discovering a new mechanism of heat removal that is similar to the heat pipe effect in the PEMFC. Most of the current experimental and numerical simulation studies on the PEMFC are under steady-state conditions, and the output power provided by PEMFC is always changing in real-time when the FCVs are actually operating to adapt to the complex terrain. ...
Three-dimensional simulations were performed for proton exchange membrane fuel cell (PEMFC) with thin catalyst-coated membrane (CCM) regarding liquid water cooling design. The studied PEMFC follows a counter-flow pattern for the H2 and air stream, which is commonly adopted in today's automotive PEMFCs. For the thermal modeling of the liquid water, conjugate heat transfer model is used. The cooling flow inlet temperature between 60 and 75°C, direction, flow rate between 0.08 and 0.32 L s−1 m−2 as well as the cooling channel number are investigated, specifically. It is found that the cooling inlet temperature directly determines the working temperature of PEMFC under the same cooling flow rate. It means that increasing the cooling inlet temperature can lift the PEMFC operating temperature. The co-direction for the liquid flow and the air stream is found to be better for PEMFC as it can suppress the liquid water formed near cathode outlet. It is then pointed out that the cooling flow rate would determine the along-channel temperature non-uniformity in PEMFC and moderate flow rate is preferred. Reducing the number of the cooling channels while assigning higher flow rate for each channel will slightly lift the PEMFC temperature overall, but this strategy will result in more pumping power loss.
Enhancing the endurance and efficiency of polymer electrolyte membrane fuel cells (PEMFCs) requires efficient thermal management. This comprehensive review examines the primary cooling techniques employed in PEMFC systems, concentrating on techniques for air and liquid cooling. Liquid cooling, which circulates a coolant through channels adjacent to the ability of the fuel cell stack to maintain ideal operating temperatures, is highlighted and significantly reduces temperature variations, thereby improving overall efficiency and lifespan. In contrast, air cooling, while simpler and more cost-effective, is less effective in high-power applications due to its reliance on ambient air for heat dissipation. The review also discusses advancements in thermal management strategies, including innovative designs for heat exchangers and the integration of thermal resistance networks, which enhance heat dissipation efficiency. Furthermore, the paper underscores the importance of developing durable materials to address catalyst and membrane degradation, and it explores the potential for integrating PEMFCs using renewable energy sources to encourage environmentally friendly transportation solutions. By identifying current challenges and proposing future research directions, this review aims to support the continuous creation of effective and reliable PEMFC technologies.
Enhancing the endurance and efficiency of polymer electrolyte membrane fuel cells (PEMFCs) requires efficient thermal management. This comprehensive review examines the primary cooling techniques employed in PEMFC systems, concentrating on techniques for air and liquid cooling. Liquid cooling, which circulates a coolant through channels adjacent to the ability of the fuel cell stack to maintain ideal operating temperatures, is highlighted and significantly reduces temperature variations, thereby improving overall efficiency and lifespan. In contrast, air cooling, while simpler and more cost-effective, is less effective in high-power applications due to its reliance on ambient air for heat dissipation. The review also discusses advancements in thermal management strategies, including innovative designs for heat exchangers and the integration of thermal resistance networks, which enhance heat dissipation efficiency. Furthermore, the paper underscores the importance of developing durable materials to address catalyst and membrane degradation, and it explores the potential for integrating PEMFCs using renewable energy sources to encourage environmentally friendly transportation solutions. By identifying current challenges and proposing future research directions, this review aims to support the continuous creation of effective and reliable PEMFC technologies.
Bi-directional mode switching is a crucial operation in unitized regenerative proton exchange membrane fuel cells (UR-PEMFC). Mass transfer plays a direct role in influencing the performance of both the fuel cell (FC) mode and the electrolytic cell (EC) mode, consequently impacting the round-trip efficiency (RTE). This study enhanced the three-dimensional two-phase model of UR-PEMFC by incorporating the mass transfer dynamics of the flow field. The round-trip efficiency (RTE) was systematically assessed throughout the bidirectional mode switching cycle. The results indicate that UR-PEMFC with triple-serpentine flow fields (TSF) performed well in FC mode, which was attributed to its good oxygen distribution uniformity and liquid water detachment capacity, in EC mode, its poor effective mass transfer coefficient and higher mass transfer resistance led to higher electrolytic energy consumption. However, UR-PEMFCs with TSF and parallel flow field (PFF) had better dynamic response performance during the bidirectional mode switching, and their voltage undershoot (overshoot) and response time were improved, which were attributed to uniform flow field structures. The UR-PEMFC reached optimum RTE operating at 0.1 A/cm2 in FC mode and 1.1 A/cm2 in EC mode, and the RTEs of the UR-PEMFCs with PFF and TSF were more advantageous, their highest RTEs were 36.62% and 36.30%, respectively. This study proposes two switching strategies to enhance the stability of URFC mode switching, offering a viable new approach for optimizing the flow field and improving overall performance.
This study developed a reaction-coupled, multiphase, and multicomponent model to simulate multiphysics transport phenomena in polymer electrolyte membrane fuel cells. The model integrates electrochemical kinetics, hydrodynamics, species transport, and liquid flooding over the entire cell domain, with a specific focus on addressing channel liquid flooding during high current operations. It also captures phase transitions of water in fuel cells, i.e., evaporation and condensation within the cell components. The multiple-relaxation-time lattice Boltzmann method was utilized to solve the cell-scale reaction-coupled multiphase equations. Moreover, this model can predict a two-phase channel film flow with the formation of a capillary meniscus, and this was validated against published experimental polarization curves, a two-phase flow regime, and two-phase pressure drop data. Numerical simulations were conducted under different operating conditions, i.e., humidity, temperature, pressure, and stoichiometric flow ratio, to investigate the physicochemical correlations among local cell performance, liquid distribution, and quantified phase change rates over the computational domain. Furthermore, various combinations of in-plane and through-plane absolute permeabilities were compared to handle the anisotropic liquid transport characteristics in the porous gas diffusion layers. Based on cell performance and channel pressure drop, a figure of merit was established to optimize the operating conditions of the fuel cell. This methodology offers an advanced pathway to balance the dual challenges of water management, thus ensuring hydration of the ionomeric phase and mitigating the accumulation of excess liquid.
Technologies based on the use of hydrogen are promising for future energy requirements in a more sustainable world. Consequently, modelling fuel cells is crucial, for instance, to optimize their control to achieve excellent performance, to test new materials and configurations on a limited budget, or to consider their degradation for improved lifespan. To develop such models, a comprehensive study is required, encompassing both well-established and the latest governing laws on matter transport and voltage polarisation for Proton Exchange Membrane Fuel Cells (PEMFCs). Recent articles often rely on outdated or inappropriate equations, lacking clear explanations regarding their background. Indeed, inconsistent understanding of theoretical and experimental choices or model requirements hinders comprehension and contributes to the misuse of these equations. Additionally, specific researches are needed to construct more accurate models. This study aims to offer a comprehensive understanding of the current state-of-the-art in PEMFC modeling. It clarifies the corresponding governing equations, their usage conditions, and assumptions, thus serving as a foundation for future developments. The presented laws and equations are applicable in most multi-dimensional, dynamic, and two-phase PEMFC models.
During the long-term operation of proton exchange membrane water electrolyzers (PEMWEs), Formation of localized hotspots in the catalyst-coated membrane (CCM) will seriously threaten the safe and efficient operation of the electrolyzer. This paper adopts a combination of dynamic experiments and numerical simulation analysis, aiming to develop the in-situ characterization technology of the thermal characteristics as well as the theoretical analysis of the multiphysics field for the·PEMWE. Based on both experimental and theoretical results, it is concluded that: (1) The high current density leads to an extremely uneven temperature distribution on the surface of the CCM. High temperature difference (as high as 34.04 °C) and high local temperature (up to 98.08 °C) are observed; (2) 30–50% of the electrical energy during the electrolyzer is converted into heat, of which the polarization heat accounts for the major part, followed by proton-conductive Joule heat; (3) The accumulation of gas phase during the transfer process of gas-liquid two phases is the primary cause of the deterioration of heat transfer, which further leads to local overheating. This study provides an experimental and theoretical basis for the safe and efficient operation of proton exchange membrane water electrolysis technology.
Polymer-electrolyte fuel cells are a promising energy-conversion technology. Over the last several decades significant progress has been made in increasing their performance and durability, of which continuum-level modeling of the transport processes has played an integral part. In this review, we examine the state-of-the-art modeling approaches, with a goal of elucidating the knowledge gaps and needs going forward in the field. In particular, the focus is on multiphase flow, especially in terms of understanding interactions at interfaces, and catalyst layers with a focus on the impacts of ionomer thin-films and multiscale phenomena. Overall, we highlight where there is consensus in terms of modeling approaches as well as opportunities for further improvement and clarification, including identification of several critical areas for future research.
Electrochemical energy systems are critical from an environmental perspective and provide a pathway to a sustainable energy future. The widespread adoption of these systems is achieved through various applications such as electrically powered aircraft, vehicles, and grid-scale storage. Within these devices, electrochemical physics originates from reaction-coupled interfacial and transport interactions. Advanced computational modeling strategies consider these interactions at multiple temporal and length scales from atomistic to system level. In this context, mesoscale modeling plays a pivotal role in resolving the intermediate length scales, at the intersection of material characteristics and device operation scale. These modeling strategies are contingent upon resolving the fundamental reactive-transport interactions through solving conservation laws. In this chapter, we focus on such a mesoscale modeling methodology accomplished in the context of intercalation electrodes such as lithium-ion batteries, conversion electrodes such as lithium-sulfur batteries, and flow electrodes such as polymer electrolyte fuel cells. The physics-based mass and charge conservation equations are elucidated first which is followed by key examples pertaining to the performance and durability of such systems.
The hydrogen‐iron (HyFe) flow cell has great potential for long‐duration energy storage by capitalizing on the advantages of both electrolyzers and flow batteries. However, its operation at high current density (high power) and over continuous cycling testing has yet to be demonstrated. In this paper, we discuss our design and demonstration of a water‐management strategy that supports high‐current and long‐cycling performance of a HyFe flow cell. Water molecules associated with the movement of protons from the iron electrode to the hydrogen electrode are sufficient to hydrate the membrane and electrode at a low current density of 100 mA/cm2 during the charge process. At higher charge current density, more aggressive measures must be taken to counter back‐diffusion driven by the acid concentration gradient between the iron and hydrogen electrodes. Our water‐management approach is based on water vapor feeding in the hydrogen electrode and water evaporation in the iron electrode, thus enabling high current density operation of 300 mA/cm2.
The flow field structure has important influences on the mass and heat transfer and the distribution uniformity in the proton exchange membrane electrolysis cell (PEMEC). In this paper, the application and operation modes and the structural parameters of the new interdigitated-jet hole flow field (JHFF) are explored, to guide the processing of the JHFF and provide references for experimental testing. A three-dimensional and two-phase model is established to simulate the effect of JHFF on the performance of PEMEC. The results demonstrate that compared with the application of JHFF only on the anode side, the application of JHFF on both sides of the anode and cathode can increase the temperature distribution uniformity and polarization performance by 41.78% and 16.25%, respectively. By increasing the number of inlet flow channels and using the counter-flow water supply mode, the temperature distribution can be more uniform. The lower the height of jet holes, the better the normal mass transfer and polarization performance, while the worse the temperature distribution uniformity. Reducing the diameter of the inlet jet holes can improve the normal mass transfer performance in the porous electrode. Synthetically, the hole height of 0.2 mm and the hole diameter of 0.4 mm are recommended. The findings provide theoretical guidance for the practical application of JHFF in PEMEC so that the positive role of JHFF in improving electrolysis performance can be fully realized.
Proper water management in Proton Exchange Membrane (PEM) fuel cell is important to achieve high performance. Understanding the percolation of the produced water at the cathode catalyst layer (CL) is critical for any robust water management technique. In this study, an ex-situ experimental setup is used to study percolation in the CL at different injection rates and relative humidity (RH) conditions. The results show that increasing the flow rate force the liquid to flow through the bulk of the pores due to the dominant viscous effect. On the other hand, at low injection rates, the capillary becomes dominant and liquid flow along the roughness of pores surfaces. At flow rates, a big wetted area is captured, compared to high flow rates tests, but the liquid saturation is lower. Another set of testing were done at a fixed flow rate and a varied relative humidity (RH) conditions, where Permeability is calculated based on the steady percolation pressure. The Permeability of the CL for both gas and liquid decreases as RH increases, and that more likely related to ionomer swelling. A correlation between the permeability and water content is derived. A sharp decrease in the permeability is observed at low water content ($\lambda In addition, fractional flow theory (FFT) model is adapted to study immiscible displacement of two-phase flow in a porous medium. The resulting model accurately predicts trapped saturation that occurs during imbibition and drainage of incompressible fluids for any capillary number. It also accurately predicts the fluid-fluid front displacement and critical capillary number at which trapped saturation begins to decrease. The unique aspect of this model is incorporation of a scaling factor, suggested by M ́edici and Allen (2016), that captures the propensity for gas or liquid holdup for any porous media and fluid pair.
In this paper, the impacts of three important parameters of a proton exchange membrane fuel cell (PEMFC) porous layer: the porosity of the catalytic layer (CL), the electrolyte volume fraction of the CL, and the porosity of the gas diffusion layer (GDL) on the performance of the PEMFC were studied. The electrolyte is composed of platinum catalyst and ionomer. Considering the high cost of platinum catalyst, the goal of parameter optimization of the porous layer is to improve the PEMFC output power density while reducing the electrolyte volume fraction. To achieve this goal, a 3‐dimensional two‐phase isothermal PEMFC model was built. Under different operating voltages and porous layer parameters, run the PEMFC physical model to obtain a set of data, use the data to train the neural network to replace the physical model, and then use the multi‐objective optimization algorithm to optimize the porous layer parameters. The results show that when the operating voltage is 0.4951, the porosity of the CL is 0.2647, the electrolyte volume fraction is 0.4471, and the porosity of the GDL is 0.5043, and the overall performance is good. Compared with the original model, the optimized model improves the maximum output power density by 3.56% and reduces the electrolyte volume fraction by 10.58%. The suitable combination of porous layer parameters can increase the output power density of PEMFCs and reduce the volume fraction of electrolyte at the same time, thus saving the catalyst cost.
The hydrogen‐iron (HyFe) flow cell has great potential for long‐duration energy storage by capitalizing on the advantages of both electrolyzers and flow batteries. However, its operation at high current density (high power) and over continuous cycling testing has yet to be demonstrated. In this paper, we discuss our design and demonstration of a water‐management strategy that supports high‐current and long‐cycling performance of a HyFe flow cell. Water molecules associated with the movement of protons from the iron electrode to the hydrogen electrode are sufficient to hydrate the membrane and electrode at a low current density of 100 mA/cm2 during the charge process. At higher charge current density, more aggressive measures must be taken to counter back‐diffusion driven by the acid concentration gradient between the iron and hydrogen electrodes. Our water‐management approach is based on water vapor feeding in the hydrogen electrode and water evaporation in the iron electrode, thus enabling high current density operation of 300 mA/cm2.
The Proton Exchange Membrane Fuel Cell (PEMFC) is a promising candidate for many applications particularly for the transportation in order to decarbonize this sector. Of the barriers, cost and durability represent two of the most significant challenges to achieving clean, reliable and cost-effective fuel cell systems. Proper management of the liquid water and heat produced in PEM fuel cells remains crucial to increase both its performance and durability. Indeed, large liquid water and temperature variations in the cell may accelerate long-term structural problems until irreversible degradation (membrane micro-cracks, pinholes, alteration of the catalyst chemical composition, etc.).In this study, the complex theory of two-phase flow in PEM fuel cells is reviewed with a focus on the local volume-average of the conservation equations in a porous medium. From this theoretical analysis, two multi-physics and multi-component models are developed considering one-fluid and two-fluid dynamics to investigate the liquid water heterogeneities in large area PEM fuel cells. Both models consider the cell as a multi-layered system where each component is accurately in-plane discretized. This pseudo-3D approach is implemented in the commercial COMSOL Multiphysics® software to simulate a large-surface cell operation with a reasonable computing time while keeping the real flow-field design. Numerical results are compared to liquid water measurements obtained by neutron imaging for several operating conditions. The advantages and drawbacks of both models are discussed. In addition, a sensitivity study is performed to analyze some key parameters in the modeling of water transport mechanisms. Finally, the numerical water distribution is examined in each component of the cell with both models.
The high frequency resistance (HFR) is used to characterize the water content in the proton exchange membrane fuel cell (PEMFC), and the change of cell HFR during the storage process after gas purge with different storage and purge conditions is studied in this paper. The repeatability of the experiment is verified firstly. Then, the changes of cell HFR with different storage conditions include cell temperature, environment temperature, initial cell HFR are analyzed. Finally, the effect of purge conditions in the preparation stage on the cell HFR is studied by change the purge flow rate, purge gas type, purge methods. The results show that the cell HFR is affected by both the storage conditions and the purge operation conditions. The time for the PEMFC to reach the maximum HFR increases with the decrease of the environment temperature and the increase of the initial cell temperature. The final stable HFR value decreases with the increases of the environment temperature.
A novel interdigitated flow field design for polymer electrolyte electrolysis cells (proton exchange membrane water electrolysis cells) composed of oxygen exhaust channels apart from liquid water feed channels has been developed for ground and space applications because the design is advantageous in terms of oxygen/water separation without buoyancy, and dispenses with water circulators for bubble removal in a cell and external separators by natural or centrifugal buoyancy. Finite element modeling of water transport in the polymer electrolyte (proton exchange) membrane in a cell with the interdigitated flow fields is conducted. Current-voltage (I–V) measurement of the cell is also performed for comparison with numerical modeling. Deviation of the experimental I–V characteristics from those of the numerical model indicates a possible water transport path in the in-plane direction of hydrophobic microporous layers (MPLs) coated on gas diffusion layers installed between the anode catalyst layers (CLs) and oxygen flow channels in the cell. Analysis of the deviation associated with the limitation of water transport also suggests fractional bubble coverage of produced oxygen gas at the CLs. The hydrophobic MPL acts to separate oxygen gas and pressurized liquid water due to the capillary pressure, while it determines the limitation of water transport to the CLs with the oxygen bubble coverage.
In honor of the 100th anniversary of The Electrochemical Society, a retrospective look at the development of fuel cell technology over the past 100 years is presented. The development of fuel cells can be traced back over 160 years to Sir William Grove's invention in 1839. The history of these very early years have been described elsewhere. Additionally, comprehensive technical reviews of fuel cell technology are also available (see, for example, Ref. 4 and 5), as well as recent review articles on the latest developments. Therefore, this paper will emphasize the progress on fuel cells that has been presented in the Journal of The Electrochemical Society (JES) and other ECS publications throughout the Society's first 100 years. This historical review includes all the major types of fuel cells, which are named according to the electrolyte employed in the cells: the alkaline fuel cell (AFC), the polymer-electrolyte fuel cell (PEFC), the phosphoric-acid fuel cell (PAFC), the molten-carbonate fuel cell (MCFC), and the solid-oxide fuel cell (SOFC). We will review the significant advances that have occurred and how these developments have been influenced by external factors. Research groups that have made substantial contributions to these developments and the fuel cell literature in ECS publications will be given special emphasis.
Exact integral solutions for the horizontal, unsteady flow of two viscous, incompressible fluids are derived. Both one-dimensional and radial displacements are calculated with full consideration of capillary drive and for arbitrary capillary-hydraulic properties. One-dimensional, unidirectional displacement of a nonwetting phase is shown to occur increasingly like a shock front as the pore-size distribution becomes wider. This is in contrast to the situation when an inviscid nonwetting phase is displaced. The penetration of a nonwetting phase into porous media otherwise saturated by a wetting phase occurs in narrow, elongate distributions. Such distributions result in rapid and extensive penetration by the nonwetting phase. The process is remarkably sensitive to the capillary-hydraulic properties that determine the value of knw/k w at large wetting phase saturations, a region in which laboratory measurements provide the least resolution. The penetration of a nonwetting phase can be expected to be dramatically affected by the presence of fissures, worm holes, or other macropores. Calculations for radial displacement of a nonwetting phase resident at a small initial saturation show the displacement to be inefficient. The fractional flow of the nonwetting phase falls rapidly and, for a specific example, becomes 1% by the time one pore volume of water has been injected.
A computational fluid dynamics multiphase model of a proton-exchange membrane (PEM) fuel cell is presented. The model accounts for three-dimensional transport processes including phase change and heat transfer, and includes the gas-diffusion layers (GDL) and gas flow channels for both anode and cathode, as well as a cooling channel. Transport of liquid water inside the gas-diffusion layers is modeled using viscous forces and capillary pressure terms. The physics of phase change is accounted for by prescribing local evaporation as a function of the undersaturation and liquid water concentration. Simulations have been performed for fully humidified gases entering the cell. The results show that different competing mechanisms lead to phase change at both anode and cathode sides of the fuel cell. The predicted amount of liquid water depends strongly on the prescribed material properties, particularly the hydraulic permeability of the GDL. Analysis of the simulations at a current density of 1.2 A/cm(2) show that both condensation and evaporation take place within the cathode GDL, whereas condensation prevails throughout the anode, except near the inlet. The three-dimensional distribution of the reactants and products is evident, particularly under the land areas. For the conditions investigated in this paper, the liquid water saturation does not exceed 10% at either anode or cathode side, and increases nonlinearly with current density. (C) 2003 The Electrochemical Society.
In this paper, experimental and simulated data for the diffusion of water across Nafion membranes as a function of the water activity gradient are presented. The gradient in the activity of water across the membrane was varied by changing the flow rate and pressure of nitrogen gas on one side of the membrane. The other side of the membrane was equilibrated with liquid water. It was found that the model predictions are very sensitive to the value of the diffusion coefficient of water in Nafion. Using the Fickian diffusion coefficient extracted from self-diffusion measurements reported in the literature, the model simulations matched experimental data with less than 5% error over a wide range of operating conditions. (C) 2000 The Electrochemical Society.
A two-dimensional, two-phase, multicomponent, transient model was developed for the cathode of the proton exchange membrane
fuel cell. Gas transport was addressed by multicomponent diffusion equations while Darcy’s law was adapted to account for
the capillary flow of liquid water in the porous gas diffusion layer. The model was validated with experimental results and
qualitative information on the effects of various operating conditions and design parameters and the transient phenomena upon
imposing a cathodic overpotential were obtained. The performance of the cathode was found to be dominated by the dynamics
of liquid water, especially in the high current density range. Conditions that promote faster liquid water removal such as
temperature, dryness of the inlet gas stream, reduced diffusion layer thickness, and higher porosity improved the performance
of the cathode. There seems to be an optimum in the diffusion layer thickness at the low current density range. The model
results showed that for a fixed electrode width, a greater number of channels and shorter shoulder widths are preferred. The
transient profiles clearly showed that liquid water transport is the slowest mass-transfer phenomenon in the cathode and is
primarily responsible for mass-transfer restrictions especially over the shoulder. © 2001 The Electrochemical Society. All
rights reserved.
In this part of the paper, we present a model to treat formation and transport of liquid water in proton exchange membrane
(PEM) fuel cells (FCs) in three-dimensional (3-D) geometry. The performance of modern-day PEM FCs at high current density
are largely dictated by the effective management of liquid water. In the first part of this paper, a rigorous model was presented
to model PEM FCs using a computational fluid dynamic technique. It was found that under the assumption of no liquid water
formation, the model consistently overpredicted measured polarization behavior. In the model presented here, the phase change
process is modeled as an equilibrium process, while the transport of liquid water is governed by pressure, surface tension,
gravity and electro-osmotic drag. Results show that the inclusion of liquid water transport greatly enhances the predictive
capability of the model and is necessary to match experimental data at high current density. © 2003 The Electrochemical Society.
All rights reserved.
A 2-D mathematical model for the entire sandwich of a proton-exchange membrane fuel cell including the gas channels was developed. The self-consistent model for porous media was used for the equations describing transport phenomena in the membrane, catalyst layers, and gas diffusers, while standard equations of Navier-Stokes, energy transport, continuity, and species concentrations are solved in the gas channels. A special handling of the transport equations enabled us to use the same numerical method in the unified domain consisting of the gas channels, gas diffusers, catalyst layers and membrane. It also eliminated the need to prescribe arbitrary or approximate boundary conditions at the interfaces between different parts of the fuel cell sandwich. By solving transport equations, as well as the equations for electrochemical reactions and current density with the membrane phase potential, polarization curves under various operating conditions were obtained. Modeling results compare very well with experimental results from the literature. Oxygen and water vapor mole fraction distributions in the coupled cathode gas channel-gas diffuser were studied for various operating current densities. Liquid water velocity distributions in the membrane and influences of various parameters on the cell performance were also obtained.
A micro‐macroscopic coupled model, aimed at incorporating solid‐state physics of electrode materials and interface morphology and chemistry, has been developed for advanced batteries and fuel cells. Electrochemical cells considered consist of three phases: a solid matrix (electrode material or separator), an electrolyte (liquid or solid), and a gas phase. Macroscopic conservation equations are derived separately for each phase using the volume averaging technique and are shown to contain interfacial terms which allow for the incorporation of microscopic physical phenomena such as solid‐state diffusion and ohmic drop, as well as interfacial phenomena such as phase transformation, precipitation, and passivation. Constitutive relations for these interfacial terms are developed and linked to the macroscopic conservation equations for species and charge transfer. A number of nonequilibrium effects encountered in high‐energy‐density and high‐power‐density power sources are assessed. Finally, conditions for interfacial chemical and electrical equilibrium are explored and their practical implications are discussed. Simplifications of the present model to previous macrohomogeneous models are examined. In a companion paper, illustrative calculations for nickel‐cadmium and nickel‐metal hydride batteries are carried out. The micro‐macroscopic model can be used to explore material and interfacial properties for desired cell performance.
A transient, multidimensional model has been developed to simulate proton exchange membrane fuel cells. The model accounts simultaneously for electrochemical kinetics, current distribution, hydrodynamics. and multicomponent transport. A single set of conservation equations valid for flow channels, gas-diffusion electrodes, catalyst layers, and the membrane region are developed and numerically solved using a finite-volume-based computational fluid dynamics technique. The numerical model is validated against published experimental data with good agreement. Subsequently, the model is applied to explore hydrogen dilution effects in the anode feed. The predicted polarization curves under hydrogen dilution conditions are in qualitative agreement with recent experiments reported in the literature. The detailed two-dimensional electrochemical and flow/transport simulations further reveal that in the presence of hydrogen dilution in the fuel stream, hydrogen is depleted at the reaction surface, resulting in substantial anode mass transport polarization and hence a lower current density that is limited by hydrogen transport from the fuel stream to the reaction site. Finally, a transient simulation of the cell current density response to a step change in cell voltage is reported.
We present here an isothermal, one-dimensional, steady-state model for a complete polymer electrolyte fuel cell (PEFC) with a 117 Nafion membrane. In this model we employ water diffusion coefficients electro-osmotic drag coefficients, water sorption isotherms, and membrane conductivities, all measured in our laboratory as functions of membrane water content. The model predicts a net-water-per-proton flux ratio of 0.2 H2O/H+ under typical operating conditions, which is much less than the measured electro-osmotic drag coefficient for a fully hydrated membrane. It also predicts an increase in membrane resistance with increased current density and demonstrates the great advantage of a thinner membrane in alleviating this resistance problem. Both of these predictions were verified experimentally under certain conditions.
This paper presents a fit between model and experiment for well‐humidified polymer electrolyte fuel cells operated to maximum current density with a range of cathode gas compositions. The model considers, in detail, losses caused by: (i) interfacial kinetics at the Pt/ionomer interface, (ii) gas‐transport and ionic‐conductivity limitations in the catalyst layer, and (iii) gas‐transport limitations in the cathode backing. Our experimental data were collected with cells that utilized thin‐film catalyst layers bonded directly to the membrane, and a separate catalyst‐free hydrophobic backing layer. This structure allows a clearer resolution of the processes taking place in each of these distinguishable parts of the cathode. In our final comparison of model predictions with the experimental data, we stress the simultaneous fit of a family of complete polarization curves obtained for gas compositions ranging from 5 atm to a mixture of 5% in , employing in each case the same model parameters for interfacial kinetics, catalyst‐layer transport, and backing‐layer transport. This approach allowed us to evaluate losses in the cathode backing and in the cathode catalyst layer, and thus identify the improvements required to enhance the performance of air cathodes in polymer electrolyte fuel cells. Finally, we show that effects of graded depletion in oxygen along the gas flow channel can be accurately modeled using a uniform effective oxygen concentration in the flow channel, equal to the average of inlet and exit concentrations. This approach has enabled simplified and accurate consideration of oxygen utilization effects.
This paper presents a mathematical model of the solid-polymer-electrolyte fuel cell and apply it to (i) investigate factors that limit cell performance and (ii) elucidate the mechanism of species transport in the complex network of gas, liquid, and solid phases of the cell. Calculations of cell polarization behavior compare favorably with existing experimental data. For most practical electrode thicknesses, model results indicate that the volume fraction of the cathode available for gas transport must exceed 20% in order to avoid unacceptably low cell-limiting current densities. It is shown that membrane dehydration can also pose limitations on operating current density; circumvention of this problem by appropriate membrane and electrode design and efficient water-management schemes is discussed. The authors' model results indicate that for a broad range of practical current densities there are no external water requirements because the water produced at the cathode is enough to satisfy the water requirement of the membrane.
This chapter outlines several theoretical models currently prevailing for multiphase flow and heat transfer in porous media. In particular, a multiphase mixture model is elaborated and compared with the traditional multiphase flow model and unsaturated flow theory. This model is rigorously derived from the traditional multiphase flow model (MFM) without making further approximations. The new model views the multiple phases as constituents of a mixture, and thus consists only of the conservation equations for the whole multiphase mixture. All primary variables in this model are mixture properties; therefore, complex tasks to track phase interfaces separating various subregions and handle phase appearance or disappearance are avoided. The chapter discusses fundamental systems rather than specific applications. To establish a fundamental theoretical framework, basic concepts associated with multiphase transport in porous media are discussed. The chapter reviews both theoretical and experimental work for single component two-phase systems with major applications to thermal engineering, while general multiphase, multicomponent systems in connection with a wide variety of engineering applications, such as drying of porous materials, groundwater contamination, and remediation. The chapter concludes that the studies of heat transfer in multicomponent porous media systems are only at the initial stage, and very extensive research is needed in this technologically important and fundamentally intricate subfield of heat transfer.
A mathematical model of transport in a solid-polymer-electrolyte fuel cell is presented. A two-dimensional membrane-electrode assembly is considered. Water management, thermal management, and utilization of fuel are examined in detail. Because the equilibrium sorption of water between the gas phase and the polymer-electrolyte depends strongly on temperature, water and thermal management are interrelated. The rate of heat removal is shown to be a critical parameter in the operation of these fuel cells.
Water uptake and transport properties of Nafion[reg sign] 117 membranes at 30 C are reported here. Specifically, the authors have determined the amount of water taken up by membranes immersed in liquid water and by membranes exposed to water vapor of variable water activity. Transport parameters measured are the diffusion coefficient and relaxation time of water in the membrane and the protonic conductivity of the membrane as functions of membrane water content. The ratio of water molecules carried across the membrane per proton transported, the electro-osmotic drag coefficient, also was determined for a limited number of membrane water contents. The drag coefficient is contrasted with the experimentally determined net water transport across an operating PEM fuel cell.
This paper reports on the proper balance between water production and removal which is particularly important for successfully operating solid, polymer-electrolyte fuel cells. Imbalance between production and evaporation rates can result in either flooding of the electrodes or membrane dehydration, both of which severely limit performance. We present a mathematical model of the solid-polymer-electrolyte fuel cell that identifies operating conditions that result in a water balance. The model is one dimensional and is derived from basic principles of gas-phase transport. The mechanisms of membrane water transport are not included explicitly in the model, and the membrane is taken as uniformly wetted, which renders the model most applicable to thin membranes. We suggest how humidification of reactant gases can be adjusted as current density is varied during an experiment (at constant temperature, pressure, and reactant feed rates) in order to accommodate the fuel cell's changing demands for water. Humidification requirements of inlet reactant gases for a wide range of practical operating temperatures, pressures, and gas feed rates have been identified. The analysis also identifies conditions in which reactant transport limitations govern the behavior of the fuel cell.
A mathematical model for an ion-exchange membrane attached to a gas-fed porous electrode is derived and discussed. The model is applied to simulate the oxygen electrode of a polymer-electrolyte fuel cell. Our discussion focuses on cell polarization characteristics, water transport, and catalyst utilization—all of which must be considered for fuel-cell design. Calculated polarization behavior is shown to compare favorably with published experimental data. Our results indicate that if the membrane maintains full saturation, its contribution to the total cell resistance is most significant at higher operating current densities (greater than 200 mA/cm2). Polarization resistance due to the oxygen reduction reaction appears to be important for all practical current densities. Water transport, driven by pressure and electric-potential forces, is shown to be a complicated function of the cell operating conditions. The utilization and distribution of noble-metal catalyst is discussed.
High-current-density performance of polymer electrolyte fuel cells ~PEFCs! is known to be limited by transport of reactants and products. In addition, at high current densities, excessive amount of water is generated and condenses, filling the pores of electrodes with liquid water, and hence limiting the reactant transport to active catalyst. This phenomenon known as ''flooding'' is an important limiting factor of PEFC performance. In this work, the governing physics of water transport in both hydrophilic and hydrophobic diffusion media is described along with one-dimensional analytical solutions of related transport processes. It is found that liquid water transport across the gas diffusion layer ~GDL! is controlled by capillary forces resulting from the gradient in phase saturation. A one-dimensional analytical solution of liquid water transport across the GDL is derived, and liquid saturation in excess of 10% is predicted for a local current density of 1.4 A/cm 2
This paper compares direct methanol fuel cells (DMFCs) employing two types of Nafion{reg{underscore}sign} (E.I.DuPont de Nemours and Company) membranes of different equivalent weight (EW). Methanol and water uptakes in 1,100 and 1,200 EW Nafion membranes were determined by weighing PâOâ-dried and methanol solution-equilibrated membranes. Both methanol and water uptakes in the 1,200 EW membrane were about 70--74% of those in the 1,100 EW membrane. The methanol crossover rate corresponding to that in a DMFC at open circuit was measured using a voltammetric method in the DMFC configuration and under the same cell operating conditions. After accounting for the thickness difference between the membrane samples, the methanol crossover rate through a 1,200 EW membrane was 52% of that through an 1,100 EW membrane. To resolve the cathode and anode performances in an operating DMFC, a dynamic hydrogen electrode was used as a reference electrode. Results show that in an operating DMFC the cathode can be easily flooded, as shown in a DMFC using 1,100 EW membrane. An increase in methanol crossover rate decreases the DMFC cathode potential at open circuit. At a high cell current density, the DMFC cathode potential can approach that of a Hâ/air cell.
Water uptake and transport parameters measured at 30°C for several available perfluorosulfonic acid membranes are compared.
The water sorption characteristics, diffusion coefficient of water, electroosmotic drag, and protonic conductivity were determined
for Nafion® 117, Membrane C, and Dow XUS 13204.10 developmental fuel cell membrane. The diffusion coefficient and conductivity
of each of these membranes were determined as functions of membrane water content. Experimental determination of transport
parameters, enables us to compare membranes without the skewing effects of extensive features such as membrane thickness which
contributes in a nonlinear fashion to performance in polymer electrolyte fuel cells.
When interdigitated gas distributors are used in a PEM fuel cell, fluids entering the fuel cell are forced to flow through the electrodes porous layers. This characteristic increases transport rates of the reactants and products to and from the catalyst layers and reduces the amount of liquid water entrapped in the porous electrodes thereby minimizing electrode flooding. To investigate the effects of the gas and liquid water hydrodynamics on the performance of an air cathode of a PEM fuel cell employing an interdigitated gas distributor, a 2-D, two-phase, multicomponent transport model was developed. Darcy's law was used to describe the transport of the gas phase. The transport of liquid water through the porous electrode is driven by the shear force of gas flow and capillary force. An equation accounting for both forces was derived for the liquid phase transport in the porous gas electrode. Higher differential pressures between inlet and outlet channels yield higher electrode performance, because the oxygen transport rates are higher and liquid water removal is more effective. The electrode thickness needs to be optimized to get optimal performance because thinner electrode may reduce gas-flow rate and thicker electrode may increase the diffusion layer thickness. For a fixed-size electrode, more channels and shorter shoulder widths are preferred.
The very high power density available from proton-exchange membrane (PEM) fuel cells combined with the potential for very low cost suggests the PEM fuel cell as the most probable power plant for the next generation, non-polluting automobile engine. The demonstrated capability of the PEM fuel cell to produce power from avilable hydrocarbon fuels opens the possibility of reliable, efficient, power generation located near the user. This review summarizes the operating principles of the fuel cell stack and power systems, describes the current status of the technology, focusing on recent developments, and discusses the technical challenges and commercial prospectis for this fuel cell technology.
The water transport numbers for protons in a variety of available poly (perfluorosulfonic acid) membranes are presented as a function of water content. The data indicate that, for membranes equilibrated with water vapor over a wide range of activities, a water drag coefficient of unity is observed. Several implications of these results, both fundamental and for fuel cell applications, are discussed.
Polymer electrolyte membrane (PEM) fuel cells have received increasing attention from both the public and fuel cell community due to their great potential for transport applications. The phenomenon of water flooding in the PEM fuel cells is not well understood, and few modelling studies have included the effect of water flooding. On the other hand, water management is one of the critical issues to be resolved in the design and operation of PEM fuel cells. In the present study, a mathematical model has been formulated for the performance and operation of a single polymer electrolyte membrane fuel cell. This model incorporates all the essential fundamental physical and electrochemical processes occurring in the membrane electrolyte, cathode catalyst layer, electrode backing and flow channel. A special feature of the model is that it includes the effect of variable degree of water flooding in the cathode catalyst layer and/or cathode electrode backing region on the cell performance. The model predictions have been compared with the existing experimental results available in the literature and excellent agreement has been demonstrated between the model results and the measured data for the cell polarisation curves. Hence, this model can be used for the optimisation of PEM fuel cell design and operation, and can serve as a building block for the modelling and understanding of PEM fuel cell stacks and systems.
The formation–distribution of condensed water in diffusion medium of proton exchange membrane fuel cells, and its tendency to reduce the local effective mass diffusivity and to influence cell performance, are studied. First the local effective mass diffusivity of a fibrous diffusion medium is determined as a function of the local porosity and local water saturation, using the network model for species diffusion. Then using this along with the hydrodynamics of capillary, two-phase flow in hydrophobic porous media, the water formation rate (hydrogen–oxygen reaction), and condensation kinetics, the one-dimensional distribution of water saturation is determined and roles of fiber diameter, porosity, and capillary pressure on cell performance are explored. The results point to a two-layer medium (similar to the added conventional microlayer) which is then analyzed for optimum performance.
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.
Two-phase flow and transport of reactants and products in the air cathode of proton exchange membrane (PEM) fuel cells is studied analytically and numerically. Single- and two-phase regimes of water distribution and transport are classified by a threshold current density corresponding to first appearance of liquid water at the membrane/cathode interface. When the cell operates above the threshold current density, liquid water appears and a two-phase zone forms within the porous cathode. A two-phase, multicomponent mixture model in conjunction with a finite-volume-based computational fluid dynamics (CFD) technique is applied to simulate the cathode operation in this regime. The model is able to handle the situation where a single-phase region co-exists with a two-phase zone in the air cathode. For the first time, the polarization curve as well as water and oxygen concentration distributions encompassing both single- and two-phase regimes of the air cathode are presented. Capillary action is found to be the dominant mechanism for water transport inside the two-phase zone of the hydrophilic structure. The liquid water saturation within the cathode is predicted to reach 6.3% at 1.4 A cm−2 for dry inlet air.
Two-phase transport of reactants and products constitutes an important limit in performance of polymer electrolyte fuel cells (PEFC). Particularly, at high current densities and/or low gas flow rates, product water condenses in open pores of the cathode gas diffusion layer (GDL) and limits the effective oxygen transport to the active catalyst sites. Furthermore, liquid water covers some of the active catalytic surface, rendering them inactive for electrochemical reaction. Traditionally, these two-phase transport processes in the GDL are modeled using so-called unsaturated flow theory (UFT), in which a uniform gas-phase pressure is assumed across the entire porous layer, thereby ignoring the gas-phase flow counter to capillarity-induced liquid motion. In this work, using multi-phase mixture (M2) formalism, the constant gas pressure assumption is relaxed and the effects of counter gas-flow are studied and found to be a new oxygen transport mechanism. Further, we analyze the multi-layer diffusion media, composed of two or more layers of porous materials having different pore sizes and/or wetting characteristics. Particularly, the effects of porosity, thickness and wettability of a micro-porous layer (MPL) on the two-phase transport in PEFC are elucidated.
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