Code stability is a matter of concern for three-dimensional (3D) fuel cell models operating both at high current density and at high cell voltage. An idealized mathematical model of a fuel cell should converge for all potentiostatic or galvanostatic boundary conditions ranging from open circuit to closed circuit. Many fail to do so, due to (i) fuel or oxygen starvation causing divergence as local partial pressures and mass fractions of fuel or oxidant fall to near zero and (ii) nonlinearities in the Nernst and Butler–Volmer equations near open-circuit conditions. This paper describes in detail, specific numerical methods used to improve the stability of a previously existing fuel cell performance calculation procedure, at both low and high current densities. Four specific techniques are identified. A straight channel operating as a (i) solid oxide and (ii) polymer electrolyte membrane fuel cell is used to illustrate the efficacy of the modifications.
Issue Section:
Research Papers
References
1.
Bıyıkoğlu
, A.
, 2005
, “Review of Proton Exchange Membrane Fuel Cell Models
,” Int. J. Hydrogen Energy
, 30
(11
), pp. 1181
–1212
.2.
Siegel
, C.
, 2008
, “Review of Computational Heat and Mass Transfer Modeling in Polymer-Electrolyte-Membrane (PEM) Fuel Cells
,” Energy
, 33
(9
), pp. 1331
–1352
.3.
Weber
, A. Z.
, Borup
, R. L.
, Darling
, R. M.
, Das
, P. K.
, Dursch
, T. J.
, Gu
, W.
, Harvey
, D.
, Kusoglu
, A.
, Litster
, S.
, Mench
, M. M.
, Mukundan
, R.
, Owejan
, J. P.
, Pharoah
, J. G.
, Secanell
, M.
, and Zenyuk
, I. V.
, 2014
, “A Critical Review of Modeling Transport Phenomena in Polymer-Electrolyte Fuel Cells
,” J. Electrochem. Soc.
, 161
(12
), pp. F1254
–F1299
.4.
Andersson
, M.
, Beale
, S.
, Espinoza
, M.
, Wu
, Z.
, and Lehnert
, W.
, 2016
, “A Review of Cell-Scale Multiphase Flow Modeling, Including Water Management, in Polymer Electrolyte Fuel Cells
,” Appl. Energy
, 180
, pp. 757
–778
.5.
Kakaç
, S.
, Pramuanjaroenkij
, A.
, and Zhou
, X. Y.
, 2007
, “A Review of Numerical Modeling of Solid Oxide Fuel Cells
,” Int. J. Hydrogen Energy
, 32
(7
), pp. 761
–786
.6.
Andersson
, M.
, Yuan
, J.
, and Sundén
, B.
, 2010
, “Review on Modeling Development for Multiscale Chemical Reactions Coupled Transport Phenomena in Solid Oxide Fuel Cells
,” Appl. Energy
, 87
(5
), pp. 1461
–1476
.7.
Beale
, S. B.
, Choi
, H.-W.
, Pharoah
, J. G.
, Roth
, H. K.
, Jasak
, H.
, and Jeon
, D. H.
, 2016
, “Open-Source Computational Model of a Solid Oxide Fuel Cell
,” Comput. Phys. Commun.
, 200
, pp. 15
–26
.8.
Le
, A. D.
, Beale
, S. B.
, and Pharoah
, J. G.
, 2015
, “Validation of a Solid Oxide Fuel Cell Model on the International Energy Agency Benchmark Case With Hydrogen Fuel
,” Fuel Cells
, 15
(1
), pp. 27
–41
.9.
Keuler
, S.
, 2013
, “Generisches, OpenFOAM-basiertes Brennstoffzellenmodell angewandt auf die Hochtemperatur-Polymerelektrolyt-Brennstoffzelle
,” M.Sc. thesis, Fachhochschule Aachen, Jülich, Germany.10.
Cao
, Q.
, 2017
, “Modelling of High Temperature Polymer Electrolyte Fuel Cells
,” Ph.D. thesis, RWTH Aachen University, Aachen, Germany.11.
Beale
, S. B.
, Lin
, Y.
, Zhubrin
, S. V.
, and Dong
, W.
, 2003
, “Computer Methods for Performance Prediction in Fuel Cells
,” J. Power Sources
, 118
(1–2
), pp. 79
–85
.12.
Froning
, D.
, Blum
, L.
, Gubner
, A.
, de Haart
, L.
, Spiller
, M.
, and Stolten
, D.
, 2007
, “Experiences With a CFD Based Two Stage SOFC Stack Modeling Concept and Its Application
,” ECS Trans.
, 7
(1
), pp. 1831
–1840
.13.
Kvesić
, M.
, Reimer
, U.
, Froning
, D.
, Lüke
, L.
, Lehnert
, W.
, and Stolten
, D.
, 2012
, “3D Modeling of a 200 cm2 HT-PEFC Short Stack
,” Int. J. Hydrogen Energy
, 37
(3
), pp. 2430
–2439
.14.
Lin
, Y.
, and Beale
, S. B.
, 2005
, “Numerical Predictions of Transport Phenomena in a Proton Exchange Membrane Fuel Cell
,” ASME J. Fuel Cell Sci. Technol.
, 2
(4
), pp. 213
–218
.15.
Schwarz
, D. H.
, and Beale
, S. B.
, 2009
, “Calculations of Transport Phenomena and Reaction Distribution in a Polymer Electrolyte Membrane Fuel Cell
,” Int. J. Heat Mass Transfer
, 52
(17–18
), pp. 4074
–4081
.16.
Beale
, S. B.
, Roth
, H. K.
, Le
, A.
, and Jeon
, D. H.
, 2013
, “Development of an Open Source Software Library for Solid Oxide Fuel Cells
,” National Research Council, Ottawa, ON, Canada, Report No. PET-1607-12
.https://nparc.nrc-cnrc.gc.ca/eng/view/object/?id=ab243f2e-c463-4926-b007-486c56cafdd517.
Beale
, S.
, Le
, A. D.
, Roth
, H.
, Pharoah
, J.
, Choi
, H.-W.
, De Haart
, L.
, and Froning
, D.
, 2011
, “Numerical and Experimental Analysis of a Solid Oxide Fuel Cell Stack
,” ECS Trans.
, 35
(1
), pp. 935
–943
.18.
Nishida
, R.
, Beale
, S.
, Pharoah
, J.
, de Haart
, L.
, and Blum
, L.
, 2018
, “Three-Dimensional Computational Fluid Dynamics Modelling and Experimental Validation of the Jülich Mark-F Solid Oxide Fuel Cell Stack
,” J. Power Sources
, 373
, pp. 203
–210
.19.
Bird
, R. B.
, Stewart
, W. E.
, and Lightfoot
, E. N.
, 1960
, Transport Phenomena
, Wiley
, New York
.20.
Leonide
, A.
, Apel
, Y.
, and Ivers-Tiffee
, E.
, 2009
, “SOFC Modeling and Parameter Identification by Means of Impedance Spectroscopy
,” ECS Trans.
, 19
(20
), pp. 81
–109
.21.
Beale
, S. B.
, 2004
, “Calculation Procedure for Mass Transfer in Fuel Cells
,” J. Power Sources
, 128
(2
), pp. 185
–192
.22.
Beale
, S. B.
, 2015
, “Mass Transfer Formulation for Polymer Electrolyte Membrane Fuel Cell Cathode
,” Int. J. Hydrogen Energy
, 40
(35
), pp. 11641
–11650
.23.
Spalding
, D. B.
, 1960
, “A Standard Formulation of the Steady Convective Mass Transfer Problem
,” Int. J. Heat Mass Transfer
, 1
(2–3
), pp. 192
–207
.24.
Spalding
, D. B.
, 1963
, Convective Mass Transfer: An Introduction
, Edward Arnold
, London, UK
.25.
Knights
, S. D.
, Colbow
, K. M.
, St-Pierre
, J.
, and Wilkinson
, D. P.
, 2004
, “Aging Mechanisms and Lifetime of PEFC and DMFC
,” J. Power Sources
, 127
(1–2
), pp. 127
–134
.26.
Patankar
, S. V.
, 1980
, Numerical Heat Transfer and Fluid Flow
, Hemisphere
, New York
.27.
Beale
, S. B.
, 2005
, “Mass Transfer in Plane and Square Ducts
,” Int. J. Heat Mass Transfer
, 48
(15
), pp. 3256
–3260
.28.
Fraser
, S.
, and Hacker
, V.
, 2008
, “An Empirical Fuel Cell Polarization Curve Fitting Equation for Small Current Densities and No-Load Operation
,” J. Appl. Electrochem.
, 38
(4
), pp. 451
–456
.29.
Reimer
, U.
, Schumacher
, B.
, and Lehnert
, W.
, 2015
, “Accelerated Degradation of High-Temperature Polymer Electrolyte Fuel Cells: Discussion and Empirical Modeling
,” J. Electrochem. Soc.
, 162
(1
), pp. F153
–F164
.30.
Hamann
, H.
, and Vielstich
, W.
, 1981
, Elektrochemie II–Elektrodenprozesse, Angewandte Elektrochemie
, Verlag Chemie
, Weinheim, Germany
.31.
Probstein
, R. F.
, 1989
, Physicochemical Hydrodynamics: An Introduction
, Butterworths
, Boston, MA
.32.
Weller
, H. G.
, Tabor
, G.
, Jasak
, H.
, and Fureby
, C.
, 1998
, “A Tensorial Approach to Computational Continuum Mechanics Using Object Orientated Techniques
,” Comput. Phys.
, 12
(6), pp. 620–631.33.
Roache
, P. J.
, 1998
, Fundamentals of Computational Fluid Dynamics
, Hermosa
, Socorro, NM.Copyright © 2018 by ASME
You do not currently have access to this content.
