A mathematical model for simulating methanol permeation and the mixed potential effect in a direct methanol fuel cell

A mathematical model for simulating methanol permeation and the pertinent mixed potential effect in a direct methanol fuel cell (DMFC) is presented. In this model a DMFC is divided into seven compartments namely the anodic flow channel, the anodic diffusion layer, the anodic catalyst layer, the proton exchange membrane (PEM), the cathodic catalyst layer, the cathodic diffusion layer and the cathodic flow channel. All compartments are considered to have finite thickness, and within every one of them a set of governing equations are given to stipulate methanol transport and oxygen transport. For the flow channels, fluid dynamics, which could substantially lower the local methanol concentration within catalyst layers is taken into account. With the knowledge of local concentrations of the species, the electrochemical reaction rates within both catalyst layers can be quantified by a kinetic Tafel expression. For the anodic catalyst layer the local external current generated by methanol oxidation is computed; for the cathodic catalyst layer, in addition to the local external current generated by oxygen reduction, the local internal current as a result of methanol permeation is also computed. With the information of the local internal current, the mixed potential effect, which is responsible for adversely lowering the cell voltage can be analyzed.     

A two-dimensional two-phase mass transport model for direct methanol fuel cells adopting a modified agglomerate approach

A two-dimensional two-phase mass transport model for liquid-feed direct methanol fuel cells (DMFCs) is presented in this paper. The fluid flow and mass transport across the membrane electrode assembly (MEA) is formulated based on the classical multiphase flow theory in the porous media. The modeling of mass transport in the catalyst layers (CLs) and membrane is given more attentions. The effect of the two-dimensional migration of protons in the electrolyte phase on the liquid flow behavior is considered. Water and methanol crossovers through the membrane are implicitly calculated in the governing equations of momentum and methanol concentration. A modified agglomerate model is developed to characterize the microstructure of the CLs. A self-written computer code is used to solve the inherently coupled differential governing equations. Then this model is applied to investigate the mechanisms of species transport and the distributions of the species concentrations, overpotential and the electrochemical reaction rates in CLs. The effects of radius and overlapping angle of agglomerates on cell performance are also explored in this work.     

Mass transport analysis of a passive vapor-feed direct methanol fuel cell

A two-dimensional, two-phase, non-isothermal model using the multi-fluid approach was developed for a passive vapor-feed direct methanol fuel cell (DMFC). The vapor generation through a membrane vaporizer and the vapor transport through a hydrophobic vapor transport layer were both considered in the model. The evaporation/condensation of methanol and water in the diffusion layers and catalyst layers was formulated considering non-equilibrium condition between phases. With this model, the mass transport in the passive vapor-feed DMFC, as well as the effects of various operating parameters and cell configurations on the mass transport and cell performance, were numerically investigated. The results showed that the passive vapor-feed DMFC supplied with concentrated methanol solutions or neat methanol can yield a similar performance with the liquid-feed DMFC fed with much diluted methanol solutions, while also showing a higher system energy density. It was also shown that the mass transport and cell performance of the passive vapor-feed DMFC depend highly on both the open area ratio of the vaporizer and the methanol concentration in the tank.     

Numerical simulation of mass and charge transfer for a PEM fuel cell

A three-dimensional, steady state, single phase model is developed to study the mass and charge transfer within a proton exchange membrane (PEM) fuel cell. A single set of conservation equations is used for all PEM fuel cell layers and the governing equations are solved numerically using a finite-volume-based computational fluid dynamics technique. The numerical results for the flow field, species transport and phase potential are presented for two designs, namely a PEM fuel cell with conventional and interdigitated flow fields for the reactant supply.     

Two-dimensional two-phase thermal model for passive direct methanol fuel cells

A two-dimensional two-phase thermal model is presented for direct methanol fuel cells (DMFC), in which the fuel and oxidant are fed in a passive manner. The inherently coupled heat and mass transport, along with the electrochemical reactions occurring in the passive DMFC is modeled based on the unsaturated flow theory in porous media. The model is solved numerically using a home-written computer code to investigate the effects of various operating and geometric design parameters, including methanol concentration as well as the open ratio and channel and rib width of the current collectors, on cell performance. The numerical results show that the cell performance increases with increasing methanol concentration from 1.0 to 4.0 M, due primarily to the increased operating temperature resulting from the exothermic reaction between the permeated methanol and oxygen on the cathode and the increased mass transfer rate of methanol. It is also shown that the cell performance upgrades with increasing the open ratio and with decreasing the rib width as the result of the increased mass transfer rate on both the anode and cathode.     

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.     

Numerical analysis for a vapor feed miniature direct methanol fuel cell system

A two-dimensional, multiphase model is presented and analyzed for a vapor feed DMFC system. The DMFC model is based on the multiphase mixture formulation and encompasses all components in the porous regions of a vapor feed DMFC using a single computation domain. The evaporation/condensation phenomenon in the anode flow channel is modeled in a separated way. An iterative numerical scheme is used to solve the governing equations in a coupled manner. Numerical simulations are carried out to explore the transient and polarization characteristics of the DMFC, including methanol crossover through the membrane, temperature evolution, anodic and cathodic overpotentials. The results indicate the anode flow channel for the feeding methanol solution is the key parameter for the DMFC performance. The numerical results are also compared with the experimental data with good agreement.     

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

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

A three-dimensional mathematical model for liquid-fed direct methanol fuel cells

A three-dimensional, single-phase, multi-component mathematical model has been developed for a liquid-fed direct methanol fuel cell (DMFC). The traditional continuity, momentum, and species conservation equations are coupled with electrochemical kinetics in both the anode and cathode catalyst layer. At the anode side, the liquid phase is considered, and at the cathode side only the gas phase is considered. Methanol crossover due to both diffusion and electro-osmotic drag from the anode to the cathode is taken into consideration and the effect is incorporated into the model using a mixed-potential at the cathode. A finite-volume-based CFD technique is used to develop the in-house numerical code and the code is successfully used to simulate the fuel cell performance as well as the multi-component behavior in a DMFC. The modeling results of polarization curves compare well with our experimental data. Subsequently, the model is used to study the effects of methanol crossover, the effects of porosities of the diffusion layer and the catalyst layer, the effects of methanol flow rates, and the effects of the channel shoulder widths.     

A transient, multi-phase and multi-component model of a new passive DMFC

A 2-dimensional, transient multi-phase, multi-component fuel cell model is developed to model a passive fuel delivery system including the fuel cell itself for a direct methanol fuel cell (DMFC). This model captures evaporative effects, as water and fuel management are crucial issues. The evaporation/condensation rates are formulated in a manner to capture non-equilibrium effects between the phases. Also, the full kinetics are modeled at both the anode and cathode catalyst layers, along with the electric potential of the membrane, catalyst and gas diffusion layers. The fuel cell operation is examined by quantifying the fuel consumption due to chemical reaction and evaporation as a function of feed concentration. The passive delivery system utilizes a porous media to passively deliver methanol to the fuel cell while controlling the concentration of methanol at the anode side to limit the amount of methanol cross-over. The results illustrate the feasibility of the passive thermal-management system, and characterize the relevant transport phenomena.     

A CFD model with semi-empirical electrochemical relationships to study the influence of geometric and operating parameters on DMFC performance

A three-dimensional computational fluid dynamics (CFD) model is developed to investigate the influence of geometric and operating parameters on performance of a direct methanol fuel cell (DMFC). Semi-empirical relationships are introduced to describe the electrochemical behaviors required in the CFD governing equations. Coefficients in these semi-empirical relationships are fitted using experimental data. Two geometric configurations with serpentine channels at the anode and cathode are considered in this work. Temperature, methanol concentration, and methanol flow rate are selected as the operating parameters. Due to the computational effort of CFD, an adaptive metamodeling method is developed to reduce the number of data-fitting iterations for obtaining the coefficients in the semi-empirical relationships. The effectiveness of the method is demonstrated by fitting the model using the experimental data collected from the first geometric configuration of the DMFC and comparing the predicted performance of the second configuration with its experimental performance. A commercial CFD system, Fluent 12.0, was used in this research.     

Energy analysis of non-Newtonian nanofluid flow over parabola of revolution on the horizontal surface with catalytic chemical reaction

Nanofluids are special functional fluids, which are designed to reduce the loss of energy and maximize the transport of heat. The thermophoresis and Brownian motion of the particle are important factors in the transport of heat in these fluids. The rise in heat transport shows encouraging effects in control of dissipation of energy and reduces entropy generation. In the current study, two-dimensional non-Newtonian Casson nanofluid flow on an upper horizontal surface of a parabola is investigated. The impact of catalytic surface chemical reactions has been account also due to its industrial importance. For this flow problem, the governing equations are modeled using the law of conservation of mass, momentum, heat, and concentration equation. The fitting transformations are taken to change governing couple partial differential equations and domain into local similar ordinary differential equation and domain of [0,∞). Using the "RK4" approach with Newton's shooting schemes via MATLAB tools, the numerical solution of dimensionless governing equations is sorted. It is observed that the Casson fluid parameter caused a drop in temperature profile, and the chemical reaction parameter is the source of the rise in the temperature field.     

Analysis of heat and mass transport in a miniature passive and semi passive liquid-feed direct methanol fuel cell

A two-dimensional, transient, multi-phase, multi-component, and non-isothermal model has been developed to solve the heat and mass transport in a passive and semi passive liquid-feed direct methanol fuel cell (DMFC). A semi passive DMFC uses channel at the cathode side to facilitate the oxidant transport. The transient characteristics of the temperature, methanol concentration, methanol crossover, useful current density and methanol evaporation are investigated. The results indicate that the temperature in the fuel cell increases during operation as much as 10 °C, due to the heat generation by internal phase change and the electrochemical reactions. However, it is revealed that the temperature distribution is nearly uniform at any time through all porous layers including the fuel cell and fuel delivery system. The effect of using an active feeding system in the cathode and passive methanol feeding in the anode (semi passive system) on the performance of a fuel cell is also studied. The active oxidant feeding to the cathode catalyst layer in the semi passive cell improved the fuel cell performance compared to that in a passive one. However, in general, the performance of passive cell is better than that in a semi passive one because of more temperature increase in the passive system.     

Modelling and analysis of a direct methanol fuel cell with under-rib mass transport and two-phase flow at the anode

For the past decade, extensive mathematical modelling has been conducted on the design and optimization of liquid-feed direct methanol fuel cells (DMFCs). Detailed modelling of DMFC operations reveals that a two-phase flow phenomenon at the anode and under-rib convection due to the pressure difference between the adjacent channels both contribute significantly to mass-transfer in a DMFC and its output performance. In practice, comprehensive simulations based on the finite volume technique for two-phase flow require a high level of numerical complexity in computation. This study presents a complexity-reduced mathematical model that is developed to cover both phenomena for a realistic, but fast, in computation for the prediction and analysis of a DMFC prototype design. The simulation results are validated against experimental data with good agreement. Analysis of the DMFC mass-transfer is made to investigate methanol distribution at anode and its crossover through the proton-exchange membrane. From a comparison of the influence of two-phase flow and under-rib mass-transfer on DMFC performance, the significance of gas-phase methanol transport is established. Simulation results suggest that both the optimization of the flow-field structure and the fuel cell operating parameters (flow rate, methanol concentration and operating temperature) are important factors for competitive DMFC performance output.     

A one-dimensional,two-phase model for direct methanol fuel cells – Part I: Model development and parametric study

A one-dimensional, steady-state, two-phase direct methanol fuel cell (DMFC) model is developed to precisely investigate complex physiochemical phenomena inside DMFCs. In this model, two-phase species transport through the porous components of a DMFC is formulated based on Maxwell–Stefan multi-component diffusion equations, while capillary-induced liquid flow in the porous media is described by Darcy's equation. In addition, the model fully accounts for water and methanol crossover through the membrane, which is driven by the effects of electro-osmotic drag, diffusion, and the hydraulic pressure gradient. The developed model is validated against readily available experimental data in the literature. Then, a parametric study is carried out to investigate the effects of the operating temperature, methanol feed concentration, and properties of the backing layer. The results of the numerical simulation clarify the detailed influence of these key designs and operating parameters on the methanol crossover rate as well as cell performance and efficiency. The results emphasize that the material properties and design of the anode backing layer play a critical role in the use of highly concentrated methanol fuel in DMFCs. The present study forms a theoretical background for optimizing the DMFC's components and operating conditions.     

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.     

Transient modeling and analysis of a passive liquid-feed DMFC

A two-dimensional, transient, multi-phase, multi-component model has been developed for a liquid-feed DMFC delivery system including the fuel cell itself. The model considers the mass transport in the feed delivery system attached to the anode inlet of the fuel cell, and the effect of coupled heat and mass transfer under ambient conditions. The results are compared with the existing experimental data with a high level of agreement. The effects of feed methanol concentration in the reservoir and current density on mass transport and performance of DMFC system are revealed. When initial feed concentration in the reservoir decreases, methanol crossover is minimized, but the duration of cell performance is shortened and fuel cell temperature decreases. The anodic overpotential and its increasing rate become higher, while the decreasing rates of solution leftover and methanol concentration in the reservoir become lower. When current density increases, the duration of the cell performance is shortened. While the anodic overpotential and its increasing rate, cell temperature, decreasing rates of methanol crossover, solution leftover and methanol concentration in the reservoir increase.     

Performance prediction of proton exchange membrane fuel cells using a three-dimensional model

In this study a steady-state three-dimensional computational fluid dynamics (CFD) model of a proton exchange membrane fuel cell is developed and presented for a single cell. A complete set of conservation equations of mass, momentum, species, energy transport, and charge is considered with proper account of electrochemical kinetics based on Butler–Volmer equation. The catalyst layer structure is considered to be agglomerate. This model enables us to investigate the flow field, current distribution, and cell voltage over the fuel cell which includes the anode and cathode collector plates, gas channels, catalyst layers, gas diffusion layers, and the membrane. The numerical solution is based on a finite-volume method in a single solution domain. In this investigation a CFD code was used as the core solver for the transport equations, while mathematical models for the main physical and electrochemical phenomena were devised into the solver using user-developed subroutines. Three-dimensional results of the flow structure, species concentrations and current distribution are presented for bipolar plates with square cross section of straight flow channels. A polarization curve is obtained for the fuel cell under consideration. A comparison between the polarization curves obtained from the current study and the corresponding available experimental data is presented and a reasonable agreement is obtained. Such CFD model can be used as a tool in the development and optimization of PEM fuel cells.     

A study of steady laminar diffusion flame over methanol pool surface

A numerical study of laminar, boundary layer type diffusion flames established over a liquid fuel pool, under the influence of forced air flow parallel to the pool surface, has been carried out. Burning of a confined methanol pool at atmospheric pressure and under normal gravity conditions is investigated. A numerical model, which solves transient, two-dimensional, mass, momentum, species and energy conservation equations, has been employed to predict the flame characteristics. The gas-phase alone is solved in a decoupled manner using appropriate interface boundary conditions, without considering the effects of liquid-phase transport on the combustion process. A single-step global reaction for methanol–air oxidation, considering carbon-dioxide dissociation, is employed to model the chemical kinetics. An optically thin radiation model has also been incorporated to account for thermal radiation losses by absorbing species in a non-luminous flame. At the outset, the model is validated against the experimental results available in literature. Thereafter, it has been used to investigate the influence of free stream air velocity on fuel mass burning rate, flame stand-off distance, temperature and flow fields. The study brings out the variation in the structure of confined laminar boundary layer type diffusion flames over methanol pool for several air velocities under normal gravity environment.