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Journal of Power Sources 192 (2009) 544551
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Journal of Power Sources
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Assembly pressure and membrane swelling in PEM fuel cells
Y. Zhou, G. Lin, A.J. Shih, S.J. Hu
Department of Mechanical Engineering, The University of Michigan, Ann Arbor, MI 48109-2125, USA
a r t i c l e i n f o
Article history:Received 15 December 2008Received in revised form 21 January 2009Accepted 28 January 2009Available online 7 February 2009
Keywords:Assembly pressureDeformationCurrent distribution
a b s t r a c t
Assembly pressure and membrane swelling induced by elevated temperature and humidity cause inho-mogeneous compression and performance variation in proton exchange membrane (PEM) fuel cells. Thisresearch conducts a comprehensive analysis on the effects of assembly pressure and operating tem-perature and humidity on PEM fuel cell stack deformation, contact resistance, overall performance andcurrent distribution by advancing a model previously developed by the authors. First, a finite elementmodel (FEM) model is developed to simulate the stack deformation when assembly pressure, tempera-ture and humidity fields are applied. Then a multi-physics simulation, including gas flow and diffusion,proton transport, and electron transport in a three-dimensional cell, is conduced. The modeling resultsreveal that elevated temperature and humidity enlarge gas diffusion layer (GDL) and membrane inhomo-geneous deformation, increase contact pressure and reduce contact resistance due to the swelling andMembrane swellingmaterial property change of the GDL and membrane. When an assembly pressure is applied, the fuel celloverall performance is improved by increasing temperature and humidity. However, significant spatial
variation of current distri
Fuel cells are promising alternative power devices due to theirigh theoretical efficiency and environmental friendliness. In par-icular, proton exchange membrane (PEM) fuel cells are attractiveor automotive and portable applications because of their low oper-ting temperature, fast start-up, and low emissions. A PEM fuel celltack consists of several single cells connected in series by bipolarlates (BPP) which provide reactants to the membrane electrodessembly (MEA). Assembly pressure can increase the overall elec-rical conductivity of the gas diffusion layer (GDL), improve contactesistance, and hence, reduce the electrical resistance losses insidecell. Assembly pressure also determines the contact status and
tack deformation especially that of the GDL, which is the mosteformable component in a PEM fuel cell stack. Under the land of aipolar plate, the GDL is compressed by the assembly force. Underhe channel area, the GDL protrudes into the channel cavities. Thehickness and porosity of the GDL are affected under compression;onsequently, the mass, heat, and charge transfer properties arehanged.
It is well recognized that the GDL can influence PEM fuel cellerformance significantly . However, most of PEM fuel cellerformance models do not consider this GDL inhomogeneousompression and only limited research has been conducted to
Corresponding author. Tel.: +1 734 615 4315; fax: +1 734 647 7303.E-mail address: email@example.com (S.J. Hu).
378-7753/$ see front matter 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.jpowsour.2009.01.085
n is observed at elevated temperature and humidity. 2009 Elsevier B.V. All rights reserved.
address this issue. Zhou et al.  developed a multi-physics modelto investigate the effects of assembly pressure on PEM fuel cell per-formance by considering contact resistance and flow resistance. Sunet al.  assumed a GDL compression ratio and analyzed the influ-ence of performance and current density distribution. Hottinen etal.  conducted a study on the effect of inhomogeneous compres-sion of GDL on the mass and charge transfer in PEM fuel cells usingexperimentally obtained GDL parameters as a function of compres-sion thickness. However, the room temperature and dry conditionswere assumed in both modeling and experimental investigation onGDL deformation.
Room temperature and dry conditions do not reflect the realPEM fuel cell operating conditions since most fuel cells operate atelevated temperatures and 100% relative humidity (RH). Elevatedtemperature and high RH influence PEM fuel cell polarization lossesin many ways including catalyst activity , membrane mechan-ical and electrical properties , and gas transport , etc. Inaddition, GDL and MEA deformation are also affected. Since therelative position between the top and bottom end plate of PEM fuelcell stack is fixed after assembly, the polymer membrane is spa-tially confined under the BPP (with the gas flow channels) and theporous carbon electrodes, as shown in Fig. 1. As the RH increases,membrane absorbs water, swells and pushes the electrodes. As a
consequence, GDL will be further compressed under the land andthe protrusion into channel increases due to the tendency of mem-brane swelling. This membrane swelling also changes the localcontact forces due to the redistribution of the stress field in fuelcell stacks.
Y. Zhou et al. / Journal of Power Sources 192 (2009) 544551 545
Fig. 1. Schematic of assembly and swelling in a PEM fuel cell.
Table 1Simulation cases.
Base case Case 1 Case 2 Case 3
Pressure (MPa) 0 3 3 3T (C) 25 25 85 85RH (%) 40 40 40 90
Table 2Geometric and physical parameters for the structural deformation and mass transferanalysis.
BPP thickness (h1) 2 mmGDL thickness (h2) 100 mCatalyst layer thickness (h3) 20 mMembrane thickness (h4) 50 mChannel height (h5) 0.5 mmChannel width (w1) 1 mmLand width (w2) 1 mmChannel length 5 mmGDL initial porosity 0.6 Catalyst layer porosity 0.06 GDL electric conductivity UncompressedIn-plane 3.4 104 S m1 Through-plane 1.4 102 S m1 GCC
Table 4Youngs modulus (MPa) at various temperature and humidity for Nafion 112 .
H = 30% H = 50% H = 70% H = 90%
DL permeability 1.76 1011 m2atalyst layer electronic conductivity 100 S m1 atalyst layer ionic conductivity 1.7 S m1 
This paper investigates the influence of operating conditionstemperature and RH) on stack deformation and contact resistancey improving the model previously developed by the authors ith respect to the effects of assembly pressure on fuel cell per-
ormance by incorporating temperature and RH effects with GDLeformation and contact resistance. Furthermore, this paper also
nvestigates the current density distribution. During the operationf a PEM fuel cell, significant variation of the local current densityxists across the plane of the cell. This causes sharp local tem-erature and stress gradient as well as degrading the efficiency of
ater management . Current density distribution is also an
mportant measure to evaluate fuel cell performance and durabil-ty. Current density distributions under various assembly pressurend operating conditions are investigated.
able 3omponent material mechanical properties [6,12,13].
omponent (material) Elastic modulus (MPa) Poissons ratio Coe
PP (graphite) 10,000 0.25 5DL (carbon paper) Nonlinear elastic 0.25 0.embrane (Nafion 112) Table 4 0.253 123
T = 25 C 197 192 132 121T = 45 C 161 137 103 70T = 65 C 148 117 92 63T = 85 C 121 89 59 46
A sequential approach is implemented in this study. A finiteelement model (FEM) is first developed to model the stack defor-mation under different levels of assembly pressure, temperatureand RH. Component deformation, the change of material proper-ties and local contact pressure are obtained from the FEM model.Then gas flow and diffusion, chemical reactions, ion and electrontransport are modeled based the updated geometry and materialproperties. Contact resistance is also analyzed using the model. Theimpact of assembly pressure and operating conditions is evaluatedby fuel cell performance and current density distributions.
2. Model description
A FEM based structural model is developed to simulate stackdeformation under various assembly pressures, temperatures andRHs. Upon obtaining the deformed geometry and material proper-ties of GDL and membrane, a computational fluid dynamic (CFD)based fuel cell performance model is developed to analyze themulti-component gas transport, chemical reactions, charge transferand contact resistance based on the deformed GDL shape and mod-ified GDL gas transport parameters. Specifically, the local contactforce between BPP and GDL can be obtained. The contact resis-tance is then simulated based on Zhou et al.  and included in themulti-physics performance model to predict fuel cell performance.
Four different cases are modeled to analyze assembly pressure,temperature and relative humidity impacts as shown in Table 1.
2.1. Stack deformation model under elevated temperature andhumidity
The model used in the current investigation is an extensionof the model developed by Zhou et al. . In the current work,temperature- and humidity-dependent properties of the mem-brane are incorporated in investigating stack deformation undervarious assembly pressures and operating conditions. The geomet-ric parameters and physical properties of the components are listedin Tables 24, where the elastic constants, coefficients of swellingand thermal expansion of the component materials, are c