Research Papers

Stability Issues of Fuel Cell Models in the Activation and Concentration Regimes

[+] Author and Article Information
S. B. Beale

Fellow ASME
Forschungszentrum Jülich GmbH,
Institute of Energy and Climate Research, IEK-3,
Jülich 52425, Germany;
Mechanical and Materials Engineering,
Queen's University,
Kingston, ON K7 L 3N6, Canada
e-mails: s.beale@fz-juelich.de;

U. Reimer

Forschungszentrum Jülich GmbH,
Institute of Energy and Climate Research, IEK-3,
Jülich 52425, Germany
e-mail: u.reimer@fz-juelich.de

D. Froning

Forschungszentrum Jülich GmbH,
Institute of Energy and Climate Research, IEK-3,
Jülich 52425, Germany
e-mail: d.froning@fz-juelich.de

H. Jasak

Mechanical Engineering and Naval Architecture,
University of Zagreb,
Ivana Lucica 5,
Zagreb 10000, Croatia;
Wikki Ltd.,
Unit 459, Southbank House, Black Prince Road,
London SE1 7SJ, UK
e-mails: hrvoje.jasak@fsb.hr;

M. Andersson

Department of Energy Sciences,
Lund University,
Lund 22100, Sweden;
Forschungszentrum Jülich GmbH,
Institute of Energy and Climate Research, IEK-3,
Jülich 52425, Germany
e-mail: martin.andersson@energy.lth.se

J. G. Pharoah

Mechanical and Materials Engineering,
Queen's University,
Kingston, ON K7 L 3N6, Canada
e-mail: pharoah@queensu.ca

W. Lehnert

Forschungszentrum Jülich GmbH,
Institute of Energy and Climate Research, IEK-3,
Jülich 52425, Germany;
Modeling in Electrochemical Process
RWTH Aachen University,
Aachen 52056, Germany;
Jülich 52425, Germany
e-mail: w.lehnert@fz-juelich.de

1Corresponding author.

Manuscript received June 14, 2017; final manuscript received March 26, 2018; published online May 7, 2018. Assoc. Editor: Jacob R. Bowen.

J. Electrochem. En. Conv. Stor. 15(4), 041008 (May 07, 2018) (7 pages) Paper No: JEECS-17-1070; doi: 10.1115/1.4039858 History: Received June 14, 2017; Revised March 26, 2018

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.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Bıyıkoğlu, A. , 2005, “Review of Proton Exchange Membrane Fuel Cell Models,” Int. J. Hydrogen Energy, 30(11), pp. 1181–1212. [CrossRef]
Siegel, C. , 2008, “Review of Computational Heat and Mass Transfer Modeling in Polymer-Electrolyte-Membrane (PEM) Fuel Cells,” Energy, 33(9), pp. 1331–1352. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Keuler, S. , 2013, “Generisches, OpenFOAM-basiertes Brennstoffzellenmodell angewandt auf die Hochtemperatur-Polymerelektrolyt-Brennstoffzelle,” M.Sc. thesis, Fachhochschule Aachen, Jülich, Germany.
Cao, Q. , 2017, “Modelling of High Temperature Polymer Electrolyte Fuel Cells,” Ph.D. thesis, RWTH Aachen University, Aachen, Germany.
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. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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-b007-486c56cafdd5
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.
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. [CrossRef]
Bird, R. B. , Stewart, W. E. , and Lightfoot, E. N. , 1960, Transport Phenomena, Wiley, New York.
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.
Beale, S. B. , 2004, “Calculation Procedure for Mass Transfer in Fuel Cells,” J. Power Sources, 128(2), pp. 185–192. [CrossRef]
Beale, S. B. , 2015, “Mass Transfer Formulation for Polymer Electrolyte Membrane Fuel Cell Cathode,” Int. J. Hydrogen Energy, 40(35), pp. 11641–11650. [CrossRef]
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. [CrossRef]
Spalding, D. B. , 1963, Convective Mass Transfer: An Introduction, Edward Arnold, London, UK.
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. [CrossRef]
Patankar, S. V. , 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere, New York.
Beale, S. B. , 2005, “Mass Transfer in Plane and Square Ducts,” Int. J. Heat Mass Transfer, 48(15), pp. 3256–3260. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Hamann, H. , and Vielstich, W. , 1981, Elektrochemie II–Elektrodenprozesse, Angewandte Elektrochemie, Verlag Chemie, Weinheim, Germany.
Probstein, R. F. , 1989, Physicochemical Hydrodynamics: An Introduction, Butterworths, Boston, MA.
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.
Roache, P. J. , 1998, Fundamentals of Computational Fluid Dynamics, Hermosa, Socorro, NM. [PubMed] [PubMed]


Grahic Jump Location
Fig. 1

Schematic of “quickTest” problem [7]. Properties and boundary values are given in Tables 1 and 2.

Grahic Jump Location
Fig. 2

Polarization curve for SOFC showing a comparison between the original [7] and the present results

Grahic Jump Location
Fig. 3

Typical calculated species distribution in an SOFC cathode

Grahic Jump Location
Fig. 4

Nernst potential versus activity for a PEFC operating with pure hydrogen and oxygen

Grahic Jump Location
Fig. 5

Polarization curve for PEFC example



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In