To describe the performance curves of a polymer electrolyte membrane fuel cell we present a Bernardi-Verbrugge-like model. The model contains an improved description of the cathode diffusion and reactive regions. This improvement was motivated by the need to correct the behavior of the Bernardi-Verbrugge model at high cell current densities, where concentration overpotentials and flooding phenomena start to appear. To achieve this goal, we derived a new expression for the overpotential of the cathode reactive region. The advantage of having such an expression is twofold: false(ifalse) elimination of strong nonlinearities in the solution scheme (with the result of having a fast and stable numerical code), and false(normaliifalse) clear inclusion of concentration and flooding phenomena. Extensive applications of the model are presented. The comparison between the results of our simulations and experimental data show astonishingly good agreements. © 2002 The Electrochemical Society. All rights reserved.
A one-dimensional, biphasic, multicomponent steady-state model based on phenomenological transport equations for the catalyst layer, diffusion layer, and polymeric electrolyte membrane has been developed for a liquid-feed solid polymer electrolyte direct methanol fuel cell ͑SPE-DMFC͒. The model employs three important requisites: ͑i͒ implementation of analytical treatment of nonlinear terms to obtain a faster numerical solution as also to render the iterative scheme easier to converge, ͑ii͒ an appropriate description of two-phase transport phenomena in the diffusive region of the cell to account for flooding and water condensation/ evaporation effects, and ͑iii͒ treatment of polarization effects due to methanol crossover. An improved numerical solution has been achieved by coupling analytical integration of kinetics and transport equations in the reaction layer, which explicitly include the effect of concentration and pressure gradient on cell polarization within the bulk catalyst layer. In particular, the integrated kinetic treatment explicitly accounts for the nonhomogeneous porous structure of the catalyst layer and the diffusion of reactants within and between the pores in the cathode. At the anode, the analytical integration of electrode kinetics has been obtained within the assumption of macrohomogeneous electrode porous structure, because methanol transport in a liquid-feed SPE-DMFC is essentially a single-phase process because of the high miscibility of methanol with water and its higher concentration in relation to gaseous reactants. A simple empirical model accounts for the effect of capillary forces on liquid-phase saturation in the diffusion layer. Consequently, diffusive and convective flow equations, comprising Nernst-Plank relation for solutes, Darcy law for liquid water, and Stefan-Maxwell equation for gaseous species, have been modified to include the capillary flow contribution to transport. To understand fully the role of model parameters in simulating the performance of the DMCF, we have carried out its parametric study. An experimental validation of model has also been carried out.
This paper analyzes the effects of the catalyst layer porous structure on the performances of polymer electrolyte membrane fuel cells. Comparing the characteristic lengths of the porous structure with the characteristic lengths of the diffusion phenomena shows that the oxygen and hydrogen concentrations in the electrolyte phase change significantly at the pore scale level; therefore, the related diffusion phenomena need a nonhomogeneous description. These rapidly varying concentrations are coupled to the cell potentials through the reaction rate expression, i.e., the Butler-Volmer equation. Thus, to employ a macrohomogeneous description of the fuel cell without loss of accuracy, it is necessary to find an effective expression for the reaction rate which does not depend explicitly on the rapidly varying concentrations. This is done here through an analytical averaging procedure and results in an effective Butler-Volmer expression that includes implicitly the effects of nonhomogeneity of the porous structure. This expression is compared with the ordinary Butler-Volmer expression and with the agglomerate models in the literature. The former turns out to be valid only in the limit of low current densities, and the latter only in the high porosity limit. Finally, the effective Butler-Volmer expression is inserted in the framework of macrohomogeneous models. From the analysis of the model results, one can conclude that the effects of the porous structure on the cell performances are crucial for the correct description of the cell concentration polarization and the estimation of the effective Tafel slope at high current densities.The main goal of fuel cell modeling is the description of the device performances starting from the underlying physical phenomena, material parameters, and operating conditions. The models should be as simple as possible to reduce the numerical complexity but accurate enough to describe correctly the fuel cell operation. Some assumptions are often used to simplify the mechanistic models such as: 1 one-dimensional ͑1D͒ geometry, constant gas porosity, fully hydrated membrane, isothermal conditions, steady-state operation, and homogeneity of the media. Qualitative considerations can be used to estimate the applicability range of such assumptions. For example, the 1D geometry approximation can be applied when the gas concentrations do not vary too much along the flow channels, as in the case of high stoichiometric flow ratio, and when channels and ribs are sufficiently thin to render homogeneous the delivery of electrons and reactants. Where the approximations are no longer applicable, the underlying assumptions must be relaxed, and the models become more complex. In the literature, several models have been presented with the aim of going beyond the following approximations: 1D geometry, 2-4 constant gas porosity in the diffusive region, 4-6 fully hydrated electrolyte membrane, 7,8 isothermal conditions, 8,2 and steady-state operation. 9,4 Although these extensions are straightforward, relaxation ...
This paper presents a modified version of the well-known model of Bernardi and Verbrugge which was developed to simulate the behavior of polymer electrolyte fuel cells. The modified version is based on a different treatment of the electrokinetic model equations, the Butler-Volmer equations. Such equations are analytically integrated in the reactive regions of the electrodes, eliminating the main nonlinear terms in the full mathematical model. It is shown that the modified Bernardi-Verbrugge model is as accurate as the original model, that it allows an extension of the cell current density over which it is possible to find solutions, that the full numerical procedure is very stable, and that the simulations are up to three orders of magnitude faster than those performed with the original model.The mathematical modeling and the numerical simulation of polymer electrolyte membrane fuel cells ͑PEMFCs͒ is receiving, in these last years, more and more attention. Pioneering works can be considered those of Bernardi and Verbrugge 1,2 and those of Springer et al. 3,4 which made a jump from an empirical approach to a more phenomenological and mechanistic type of approach. In these works, the membrane electrode assembly ͑MEA͒ was divided into several regions, and for each region, equations for the charge and mass transport were written down. The description of the MEA was kept at the one-dimensional ͑1-D͒ level, mainly because the essential features of the performance curve of a MEA ͑cell potential vs. cell current density͒ are already well described at this level, while the computational complexity is still affordable.Since then, most of the successive work followed two main streams. In one case, effort has been paid to go from the 1-D modeling to 2-D and even 3-D modeling. These higher dimensionality models offer the possibility of describing the hydrodynamics and multicomponent transport inside the flow channel for reactant distribution ͑see Fig. 1 of the next section͒, and of taking into account different geometries, or flow field configurations, of the flow channels. Clear prototype works of 2-D modeling and simulation have been made by Gurau et al., 5 by Kulikovsky et al., 6 and by Um et al., 7 A 3-D modeling has been developed by Divisek et al., 8 but unfortunately, no implementation of the model has been performed.In the other work stream, attention has been devoted to the inclusion into the models of a more extended phenomenology, such as heat transport, proton transport in membrane with variable water content, membrane permeability, electrode flooding, transient phenomena, etc. ͑for reviews on the state of the art see Gottesfeld and Zawodzinski, 9 and Gurau 10 ͒. However, the approaches developed in these works are, very often, only devoted to partial aspects, losing the ability to construct global models.In this work, we reviewed critically the 1-D model of Bernardi and Verbrugge 1,2 ͑BV model͒, and we developed a modified version of such a model, the modified BV model ͑MBV͒, with the aim to establish a numerical...
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