Rigorous 3-D Mathematical Modeling of PEM Fuel Cells

Mazumder, Sandip; Cole, J. Vernon

doi:10.1149/1.1615608

Cited by 190 publications

(76 citation statements)

References 28 publications

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“…1. A finite volume method using a computational grid [13,14] is used to solve mass, charge, energy, momentum balances including transport through porous media, and chemical and electrochemical reactions within the porous electrodes in a gas diffusion electrode model. In this model, steady state conditions are imposed.…”

Section: Description Of the Tubular Sofcmentioning

confidence: 99%

Current and voltage distributions in a tubular solid oxide fuel cell (SOFC)

et al. 2007

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International audienceOne of the major obstacles to improving electrochemical performance of SOFCs is the limitation with respect to current collecting. The aim of this study is to examine these limitations on the basis of a model of a single cell of tubular SOFC. The simulation results allow us to understand and analyze the effects of ionic and electronic ohmic drops on cell performance. This paper describes a model using the CFD-Ace software package to simulate the behaviour of a tubular SOFC. Modelling is based on solving conservation equations of mass, momentum, energy, species and electric current by using a finite volume approach on 3D grids of arbitrary topology. The electrochemistry in the porous gas diffusion electrode is described using Butler-Volmer equations at the triple phase boundary. The electrode overpotential is computed at each spatial location within the catalyst layer by separately solving the electronic and ionic electric potential equations. The 3D presentation of the current densities and the electronic and ionic potentials allows analysis of the respective ohmic drops. The simulation results show that the principal limitations are at the cathodic side. The limitations due to ionic ohmic drops, classically considered to be the main restrictions, are confirmed. The particular interest of our study is that it also shows that, because of the cylindrical geometry, there is a significant electronic ohmic drop

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Section: Description Of the Tubular Sofcmentioning

confidence: 99%

Current and voltage distributions in a tubular solid oxide fuel cell (SOFC)

et al. 2007

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“…The first phenomenological model of a PEMFC with a Nafion 1 membrane was by Bernardi and Verbrugge [10]; since then, significant developments have been made. For example, three dimensional models have been reported by Mazumder [11,12], and by Hu and Berning [13,14]. Noponen et al [15][16][17] used finite element software to model concentration and current distributions [15] and to map liquid saturation and temperature distributions [16,17] for comparison with experimental data.…”

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confidence: 99%

Modelling and experimental validation of a high temperature polymer electrolyte fuel cell

2007

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A steady-state, isothermal, one dimensional model of a proton exchange membrane fuel cell (PEMFC), with a polybenzimidazole (PBI) membrane, was developed. The electrode kinetics were represented by the Butler-Volmer equation, mass transport was described by the multi-component Stefan-Maxwell equations and Darcy's law and the ionic and electronic resistances described by Ohm's law. The model incorporated the effects of temperature and pressure on the open circuit potential, the exchange current density and diffusion coefficients, together with the effect of water transport across the membrane on the conductivity of the PBI membrane. The polarisation curves predicted by the model were validated against experimental data for a PEMFC operating in the temperature range of 125-200°C. There was good agreement between experimental and model data of the effect of temperature and oxygen/air pressure on cell performance. The model was used to simulate the effect of catalyst loading and the Pt/carbon ratio on cell performance and, in the latter case, a 40 wt.% Pt/C ratio gave the highest peak power density.Notations A act Active area of catalyst particles (m 2 ) A D Anode diffusion region (No units) A M Anode microporous region (No units) A R Anode reaction region (No units) A F Anode flow region (No units) a Height of catalyst (m) b Width of catalyst (m) c i Molar density/concentration of component i (mol m -3 ) C D Cathode diffusion region (No units) C R Cathode reaction/catalyst region (No units) c Depth of catalyst (No units) D ij Stefan-Maxwell diffusivities (m 2 s -1 ) D eff ij Effective Stefan-Maxwell diffusivities (m 2 s -1 ) D ij Symmetric diffusivities (m 2 s -1 ) E Potential (V) E 0 0 Standard state reference potential (V) F Faraday constant (A s mol -1 ) G Gibbs free energy (J mol -1 ) H Enthalpy (J mol -1 ) I Cell current density (A m -2 ) j e Electronic current (A m -2 ) j i Ionic/proton current (A m -2 ) j o Exchange current density (A m -2 ) j o b Exchange current density at electrode b (A m -2 ) j o a Exchange current density in anode (A m -2 ) j b V Current density source term in cathode (A m -3 ) j a V Current density source term in anode (A m -3 ) j c V Current density source term in cathode (A m -3 ) J i Diffusion flux (kg m -2 s -1 ) k Permeability of the porous media (m 2 ) L Catalyst loading (g m -2 ) M Membrane region (No units) M cat Mass of the catalyst (g) M i Mass of species i (kg mol -1 ) n Number of electrons (No units) N i Total flux of species i (kg m -2 s -1 ) p Total pressure (m -1 kg s -2 )

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“…In other words, the energy balance becomes a specification of the temperature. While most models still treat the membrane in this fashion, some have started to include nonisothermal effects and behavior [46,47,65,71,73,79,89,102,105,111,[123][124][125]. Those models that are nonisothermal along the gas channel but assume that the fuel-cell sandwich remains isothermal are not discussed in this section since the membrane is essentially taken to be isothermal [9,66,67,76].…”

Section: Energy Balancementioning

confidence: 99%

“…While some models neglect the summation altogether [46,65,71,73,105,124], others rightfully do not. While the enthalpy gradient of the water in the membrane can be taken as insignificant, that of the protons cannot and this results in the phenomenon of Joule heating [59,127,128].…”

Section: Energy Balancementioning

confidence: 99%