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.
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November 2018
Research-Article
Stability Issues of Fuel Cell Models in the Activation and Concentration Regimes
S. B. Beale,
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;
steven.beale@queensu.ca
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;
steven.beale@queensu.ca
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U. Reimer,
U. Reimer
Forschungszentrum Jülich GmbH,
Institute of Energy and Climate Research, IEK-3,
Jülich 52425, Germany
e-mail: u.reimer@fz-juelich.de
Institute of Energy and Climate Research, IEK-3,
Jülich 52425, Germany
e-mail: u.reimer@fz-juelich.de
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D. Froning,
D. Froning
Forschungszentrum Jülich GmbH,
Institute of Energy and Climate Research, IEK-3,
Jülich 52425, Germany
e-mail: d.froning@fz-juelich.de
Institute of Energy and Climate Research, IEK-3,
Jülich 52425, Germany
e-mail: d.froning@fz-juelich.de
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H. Jasak,
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;
h.jasak@wikki.co.uk
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;
h.jasak@wikki.co.uk
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M. Andersson,
M. Andersson
Department of Energy Sciences,
Lund University,
Lund 22100, Sweden;
Forschungszentrum Jülich GmbH,
Institute of Energy and Climate Research,
Jülich 52425, Germany
e-mail: martin.andersson@energy.lth.se
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
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J. G. Pharoah,
J. G. Pharoah
Mechanical and Materials Engineering,
Queen's University,
Kingston, ON K7 L 3N6, Canada
e-mail: pharoah@queensu.ca
Queen's University,
Kingston, ON K7 L 3N6, Canada
e-mail: pharoah@queensu.ca
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W. Lehnert
W. Lehnert
Forschungszentrum Jülich GmbH,
Institute of Energy and Climate Research, IEK-3,
Jülich 52425, Germany;
Modeling in Electrochemical Process
Engineering,
RWTH Aachen University,
Aachen 52056, Germany;
JARA-HPC,
Jülich 52425, Germany
e-mail: w.lehnert@fz-juelich.de
Institute of Energy and Climate Research, IEK-3,
Jülich 52425, Germany;
Modeling in Electrochemical Process
Engineering,
RWTH Aachen University,
Aachen 52056, Germany;
JARA-HPC,
Jülich 52425, Germany
e-mail: w.lehnert@fz-juelich.de
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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;
steven.beale@queensu.ca
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;
steven.beale@queensu.ca
U. Reimer
Forschungszentrum Jülich GmbH,
Institute of Energy and Climate Research, IEK-3,
Jülich 52425, Germany
e-mail: u.reimer@fz-juelich.de
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
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;
h.jasak@wikki.co.uk
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;
h.jasak@wikki.co.uk
M. Andersson
Department of Energy Sciences,
Lund University,
Lund 22100, Sweden;
Forschungszentrum Jülich GmbH,
Institute of Energy and Climate Research,
Jülich 52425, Germany
e-mail: martin.andersson@energy.lth.se
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
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
Engineering,
RWTH Aachen University,
Aachen 52056, Germany;
JARA-HPC,
Jülich 52425, Germany
e-mail: w.lehnert@fz-juelich.de
Institute of Energy and Climate Research, IEK-3,
Jülich 52425, Germany;
Modeling in Electrochemical Process
Engineering,
RWTH Aachen University,
Aachen 52056, Germany;
JARA-HPC,
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. Nov 2018, 15(4): 041008 (7 pages)
Published Online: May 7, 2018
Article history
Received:
June 14, 2017
Revised:
March 26, 2018
Citation
Beale, S. B., Reimer, U., Froning, D., Jasak, H., Andersson, M., Pharoah, J. G., and Lehnert, W. (May 7, 2018). "Stability Issues of Fuel Cell Models in the Activation and Concentration Regimes." ASME. J. Electrochem. En. Conv. Stor. November 2018; 15(4): 041008. https://doi.org/10.1115/1.4039858
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