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

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

Three-dimensional model for stacks of tubular high temperature proton exchange membrane fuel cells incorporating a thin layer approach for the membrane electrode assembly

A three-dimensional, non-isothermal, steady state model for stacks of tubular high temperature proton exchange membrane fuel cells (HT PEM FCs) is developed. It is based on a thin layer approach for the membrane-electrode assembly while retaining Butler-Volmer kinetics, concentration and Ohmic losses on both electrodes. It solves for flow, temperature and concentration fields as well as locally resolved current densities for multiple cells. Single cell results for the polarization curve compare well with experimental data for single tubular HT PEM FCs. The model allows for efficient simulations of stacks of multiple tubular HT PEM FCs with a shared air channel in which the interactions between local FC performance and flow, temperature and concentration fields pose a major design challenge. The effects of flow field design, flow rate and cell distance in a stack of 7 tubular cells are investigated and basic approaches for the design of such stacks are derived.     

Maintaining equal operating conditions for all cells in a fuel cell stack using an external flow distributor

This paper presents a novel fuel cell stack architecture that allows each fuel cell to work at the same condition, maintaining the same performance from each individual cell and creating a maximum power output from the cell stack. A fuel cell stack having four PEM fuel cells was fabricated to experimentally compare its performance when fuel and air supplying/distribution schemes are different. The performance of the fuel cell stack and individual cells in the stack is measured to achieve a detailed evaluation of the effect of the different fuel and air supplying schemes. Experimental data shows that non-uniform flow distribution to individual cells has a considerable influence on individual cell performance, which affects the power output of the fuel cell stack. The fuel cell stack with the novel approach of fuel and air feeding shows a better power output performance compared to a different fuel and air feeding approach to the fuel cell stack.     

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

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

A dynamic model for high temperature polymer electrolyte membrane fuel cells

A dynamic one-dimensional isothermal phenomenological model was developed in order to describe the steady-state and transient behavior of high temperature polymer electrolyte membrane fuel cells (PEMFC). The model accounts for transient species mass transport at the bipolar plates and gas diffusion layers and the electric double layers charge/discharge. To record the impedance spectra, a small sinusoidal voltage perturbation was imposed to the simulator over a wide range of frequencies, and the resultant current density amplitude and phase were recorded.The steady-state behavior of the fuel cell, as well as the impedance spectra were obtained and compared to experimental data of two different fuel cells equipped with different MEAs based on phosphoric acid polybenzimidazole membrane. This approach is new and allows a deeper analysis of the controlling phenomena. The model fitted quite well the I-V curves for both systems, but fairly well the Nyquist plots. The differences observed in the Nyquist plots were attributed to proton resistance in the catalyst layer and the gas diffusion limitations to cross the phosphoric acid layer that coats the catalyst, phenomena not included in the proposed phenomenological model.     

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.     

Some issues on performance analysis of fuel cells in thermodynamic point of view

In order to develop a new fuel cell and/or to enhance fuel cell performance, it is very important to understand clearly what the real performance of a fuel cell is. However, some important issues for the assessment of a fuel cell performance still require additional considerations. For example, the performance of a fuel cell is generally described based on an isothermal condition in spite of the non-uniform cell temperature distributions under real operating conditions. For this purpose, a formulation for the performance of a fuel cell operating at an isentropic condition (e.g., non-uniform cell temperature) is introduced in this study and compared with a reversible isothermal case (e.g., uniform cell temperature). Also, it is necessary to reveal the real difference in the performance of a fuel cell and a heat engine. Understanding of the purpose of the hybridization of a fuel cell with a heat engine is another important issue. In the present study, issues related to the performance of a fuel cell are considered from a thermodynamic point of view.     

Three-dimensional computational fluid dynamics model of a tubular-shaped PEM fuel cell

A full three-dimensional, non-isothermal computational fluid dynamics model of a tubular-shaped proton exchange membrane (PEM) fuel cell has been developed. This comprehensive model accounts for the major transport phenomena in a PEM fuel cell: convective and diffusive heat and mass transfer, electrode kinetics, and potential fields. In addition to the tubular-shaped geometry, the model feature an algorithm that allows for more realistic representation of the local activation overpotentials which leads to improved prediction of the local current density distribution. Three-dimensional results of the species profiles, temperature distribution, potential distribution, and local current density distribution are presented. The model is shown to be able to understand the many interacting, complex electrochemical, and transport phenomena that cannot be studied experimentally.     

Estimation of fuel cell operating time for predictive maintenance strategies

Durability is one of the limiting factors for spreading and commercialization of fuel cell technology. That is why research to extend fuel cell durability is being conducted world wide. A pattern-recognition approach aiming to estimate fuel cell operating time based on electrochemical impedance spectroscopy measurements is presented here. It is based on extracting the features from the impedance spectra. For that purpose, two approaches have been investigated. In the first one, particular points of the spectrum are empirically extracted as features. In the second approach, a parametric modeling is performed to extract features from both the real and the imaginary parts of the impedance spectrum. In particular, a latent regression model is used to automatically split the spectrum into several segments that are approximated by polynomials. The number of segments is adjusted taking into account the a priori knowledge about the physical behavior of the fuel cell components. Then, a linear regression model using different subsets of extracted features is employed for an estimate of the fuel cell operating time. The effectiveness of the proposed approach is evaluated on an experimental dataset. Allowing the estimation of the fuel cell operating time, and consequently its remaining duration life, these results could lead to interesting perspectives for predictive fuel cells maintenance policy.     

Optimization of the efficiency and degradation rate of an automotive fuel cell system

In this contribution an approach for the analysis of the operation parameters of a fuel cell system is presented, which can be used for a lifetime and efficiency optimization. For this purpose, a physically-based polarization curve model of an automotive fuel cell stack is derived, which enables a realistic simulation study. Furthermore, the influence of degradation based on semi-empirical correlations for the loss of catalytic activity is included. This stack model is combined with a simplified fuel cell system model and used for a subsequent simulation study with focus on the system efficiency on the one hand and the lifetime on the other hand. The results show that an adaption of the operation parameters of the system can partly counteract the deterioration of the efficiency due to degradation. Furthermore, the lifetime of the stack could be enhanced at the cost of lower efficiency.     

Transient response of high temperature PEM fuel cell

A transient three-dimensional, single-phase and non-isothermal numerical model of polymer electrolyte membrane (PEM) fuel cell with high operating temperature has been developed and implemented in computational fluid dynamic (CFD) code. The model accounts for transient convective and diffusive transport, and allows prediction of species concentration. Electrochemical charge double-layer effect is considered. Heat generation according to electrochemical reaction and ohmic loss are involved. Water transportation across membrane is ignored due to low water electro-osmosis drag force of polymer polybenzimidazole (PBI) membrane. The prediction shows transient in current density which overshoots (undershoots) the stabilized state value when cell voltage is abruptly decreased (increased). The result shows that the peak of overshoot (undershoot) is related with cathode air stoichiometric mass flow rate instead of anode hydrogen stoichiometric mass flow rate. Current is moved smoothly and there are no overshoot or undershoot with the influence of charge double-layer effect. The maximum temperature is located in cathode catalyst layer and both fuel cell average temperature and temperature deviation are increased with increasing of current load.     

Analysis of the water and thermal management in proton exchange membrane fuel cell systems

Water and thermal management is essential to the performance of proton exchange membrane (PEM) fuel cell system. The key components in water and thermal management system, namely the fuel cell stack, radiator, condenser and membrane humidifier are all modeled analytically in this paper. Combined with a steady-state, one-dimensional, isothermal fuel cell model, a simple channel-groove pressure drop model is included in the stack analysis. Two compact heat exchangers, radiator and condenser are sized and rated to maintain the heat and material balance. The influence of non-condensable gas is also considered in the calculation of the condenser. Based on the proposed methodology, the effects of two important operating parameters, namely the air stoichiometric ratio and the cathode outlet pressure, and three kinds of anode humidification, namely recycling humidification, membrane humidification and recycling combining membrane humidification are analyzed. The methodology in this article is helpful to the design of water and thermal management system in fuel cell systems.     

Dynamic modeling of a PEM fuel cell with temperature effects

With the aim of dynamic simulation and control, a new non-linear state-space dynamic non-isothermal polymer electrolyte membrane fuel cell (PEMFC) model is developed in this paper. This mathematical model is developed based on mass and energy equation. The present model takes in account subsequent factors as the effects of charge double layer capacitance, the geometrical capacity and the effect of temperature gradient. In this paper, the authors propose a combination of several dynamic equations to study the effect of suddenly variation of some operating parameters like load resistance, gas pressure and gas temperature input. The results are compared to those of an isothermal model. This model will be extremely functional for the best possible design and real-time control of PEMFC systems. The present model is executed in MATHCAD software and the fuel cell is symbolized by an equivalent circuit which incorporates gas diffusion layer, membrane and electrodes. The analysis results show that the main elements that influence the performance of the cell are load resistance and functioning temperature.     

A semi-empirical method for electrically modeling of fuel cell: Executed on a direct methanol fuel cell

In this paper, a novel semi-empirical modeling method to mathematically derive a nonlinear equivalent circuit from a special group of impedance fuel cell models is proposed. As an example, a 5-cm² direct methanol fuel cell (DMFC) was modeled by this method. The derived equivalent circuit is composed of lumped nonlinear resistors, capacitors and an inductor. The nonlinear circuit has an impedance equivalent to the target fuel cell in various operating conditions and provides a good approximation of the static and transient behaviors of the fuel cell. The equivalent circuit fuel cell model was validated by comparing its numerical simulation results with its polarization curve and the dynamic behavior of the target DMFC. These comparisons were performed while the DMFC was operating under square current pulses with different upper and low current levels.     

Static and dynamic modeling of a diesel fed fuel cell power supply

Fuel cell supplied auxiliary power units could ease the development of fuel cell systems in transportation application if they are fed by conventional hydrocarbons like diesel. Then a fuel processor has to be used to convert the hydrocarbon in a hydrogen rich gas mixture with a low rate of contaminant. The temperatures of the fuel processor modules and the mass flows have to be controlled. The energetic macroscopic representation (EMR) is a causal, graphic modeling tool for complex multi-domain systems that can be used for the design of the control structure through the inversion of model. In this work EMR is used to model a diesel supplied low temperature fuel cell unit including the fuel processor, the fuel cell stack (HTPEM) as well as the supply system of the mass flows. The presented fuel processor and HTPEM models are validated against experimental results. The structure of the temperature and mass flow controls in the fuel processor and supply system are derived. Both the model and the control are implemented in Matlab/Simulink™ and validated.     

A simple electric circuit model for proton exchange membrane fuel cells

A simple and novel dynamic circuit model for a proton exchange membrane (PEM) fuel cell suitable for the analysis and design of power systems is presented. The model takes into account phenomena like activation polarization, ohmic polarization, and mass transport effect present in a PEM fuel cell. The proposed circuit model includes three resistors to approach adequately these phenomena; however, since for the PEM dynamic performance connection or disconnection of an additional load is of crucial importance, the proposed model uses two saturable inductors accompanied by an ideal transformer to simulate the double layer charging effect during load step changes. To evaluate the effectiveness of the proposed model its dynamic performance under load step changes is simulated. Experimental results coming from a commercial PEM fuel cell module that uses hydrogen from a pressurized cylinder at the anode and atmospheric oxygen at the cathode, clearly verify the simulation results.     

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

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

Multi-input and multi-output neural model of the mechanical nonlinear behaviour of a PEM fuel cell system

A fuel cell system model is necessary to prepare and analyse vibration tests. However, in the literature, the mechanical aspect of the fuel cell systems is neglected. In this paper, a neural network modelling approach for the mechanical nonlinear behaviour of a proton exchange membrane (PEM) fuel cell system is proposed. An experimental set is designed for this purpose: a fuel cell system in operation is subjected to random and swept-sine excitations on a vibrating platform in three axes directions. Its mechanical response is measured with three-dimensional accelerometers. The raw experimental data are exploited to create a multi-input and multi-output (MIMO) model using a multi-layer perceptron neural network combined with a time regression input vector. The model is trained and tested. Results from the analysis show good prediction accuracy. This approach is promising because it can be extended to further complex applications. In the future, the mechanical fuel cell system controller will be implemented on a real-time system that provides an environment to analyse the performance and optimize mechanical parameters design of the PEM fuel system and its auxiliaries.     

Surrogate model for proton exchange membrane fuel cell (PEMFC)

The main goal of this work is to realize a PEMFC model that can be used efficiently for the global modelling of the fuel cell system. The modelling method proposed in the paper is an approach from an empirical point of view that allows a PEMFC model of “black-box” class to be developed. Moving least squares (MLS) have therefore been employed to approximate the cell voltage characteristics V, using an experimental dataset measured in determinate conditions. The MLS approach appears to present a good balance of response surface accuracy, smoothness, robustness, and ease of use. This kind of numerical model offers good perspectives for the systems identification, the simulation of the systems, the design and the optimization of process control, etc. The results prove that the method is suitable for predicting and describing the fuel cell behaviour in all the points of the approximation domain. The proposed model can be included in a numerical application to optimize the operation of an existing fuel cell system.