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Research Papers

Bifurcation Analysis of a Two-Phase PEMFC Model

[+] Author and Article Information
Markus Grötsch

 Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstraße 1, 39106 Magdeburg, Germanygroetsch@mpi-magdeburg.mpg.de

Richard Hanke-Rauschenbach, Michael Mangold

 Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstraße 1, 39106 Magdeburg, Germany

J. Fuel Cell Sci. Technol 5(2), 021001 (Apr 10, 2008) (9 pages) doi:10.1115/1.2885392 History: Received June 28, 2007; Revised January 11, 2008; Published April 10, 2008

A major issue of polymer-electrolyte-membrane (PEM) fuel cell operation is the water management of the cells. This article tries to contribute to an improved understanding of flooding/drying out effects by performing a analysis for a rigorous two-phase PEM fuel cell model. The model is examined by means of a bifurcation analysis. This investigation is performed numerically with parameter continuation methods. The nonlinear behavior is qualified and possible instabilities are detected. A steady state multiplicity is found. The multiplicity is physically explained and the influence of selected fuel cell parameters is investigated. The multiplicity is finally verified in a dynamic simulation. The future work aims at a model reduction of the analyzed fuel cell model to gain a low order model suitable for model-based control strategies.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Sandwich model of the considered PEMFC, consisting of GDLs, catalyst layers, and the membrane. Also shown is the modeling direction z, the modeling domains κ∊{1,2,3,4,5}, and its boundaries {dΩ1,…,dΩ6}.

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Figure 2

One-parameter continuation of the cell current Icell: (a) shows the overall (steady state) voltage-current profile; in (b), a detail of (a) is depicted. In (c) and (d), the liquid water saturation and the mass fraction of oxygen at the left border of the catalyst layer (cathode side) are shown, respectively.

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Figure 3

Influence of the relative humidity in the anode and cathode bulks upon the found steady state multiplicity: (a) shows the resulting parameter portrait when the load resistance R and the relative humidity in the cathode bulk and anode bulk (for three cases: RHAbulk=0.8,0.86,1) are changed. In (b), three (a) corresponding one-parameter continuations (I, II, and III) of R are depicted and (c) shows the corresponding voltage-current profiles for the three parameter continuations I, II, and III of (a) and (b).

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Figure 4

Influence of fHI upon the found steady state multiplicity: (a) shows the resulting parameter portrait when the load resistance R and fHI are varied. In (b), two one-parameter continuations (I and II) corresponding to (a) are shown.

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Figure 5

Influence of the porosity π on the multiplicity: (a) shows the resulting parameter portrait when the load resistance R and the porosity π are changed. In (b), two one-parameter continuations (I and II) corresponding to (a) are depicted.

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Figure 6

Influence of the permeability K on the multiplicity: (a) shows the resulting parameter portrait when the load resistance R and the permeability K are changed. In (b), two one-parameter continuations (I and II) corresponding to (a) are shown.

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Figure 7

Step response of the fuel cell model: (a) shows the steady state voltage-current profile and the three considered load cases: R=RI,RII,RIII. In (b)–(d) the time plots of the load resistance R, the cell voltage Vcell, and the liquid water saturation at the left border in the catalyst layer at the cathode side are displayed. Numbers 1–4 mark the steady states reached during the dynamic simulation. Note the large time scale in (b)–(d).

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