- Email: [email protected]
Investigation of contact pressure distribution over the active area of PEM fuel cell stack
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 3 0 6 2 e3 0 7 1
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Investigation of contact pressure distribution over the active area of PEM fuel cell stack E. Alizadeh*, M.M. Barzegari, M. Momenifar, M. Ghadimi, S.H.M. Saadat Malek Ashtar University of Technology, Fuel Cell Technology Research Laboratory, Iran
article info
abstract
Article history:
Contact pressure distribution over the active area of proton exchange membrane fuel cell
Received 5 October 2015
(PEMFC) has significant effects on the performance of PEMFCs. Even clamping pressure
Received in revised form
over the membrane electrode assembly (MEA) affects contact resistance, characteristics of
5 December 2015
porous media and sealing task. This paper develops a PEM fuel cell model to study the
Accepted 8 December 2015
contact pressure distribution over the membrane electrode assembly using finite element
Available online 6 January 2016
model. At first, the three-dimensional model of a single cell was reduced to a twodimensional model to decrease the calculation time. After validation of the obtained re-
Keywords:
sults via the pressure sensitive films, the effect of some parameters such as thickness and
PEM fuel cell
material of the end plates, sealant hardness, number of the stack's cells and position of the
Finite element method
cell on the contact pressure distribution over the MEA were investigated. The results reveal
End plates
that optimizing mentioned parameters leads to design PEM fuel cells with proper contact
Contact pressure distribution
pressure distribution over the MEA.
MEA
Copyright © 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Recently, proton exchange membrane fuel cell has attracted much attention due to its high efficiency, low temperature, quick startup and being clean energy converter which converts the energy stored in hydrogen and oxygen into electricity. The premise for a wide diffusion of this technology mainly depends on two crucial factors: cost reduction and energy efficiency improvement. Clamping system is one of the most important parameters of PEMFCs. The purposes of the clamping systems can be mentioned as providing sealing pressure and proper pressure distribution at various interfaces and decreasing contact resistance between interfaces. Uneven contact pressure
distribution over the MEA results in non-uniform current density and heat generation distribution which may cause hot spot formation in the MEA [1,2]. High clamping pressure leads to an increase in the contact area between bipolar plate (BPP) and gas diffusion layer (GDL) which decreases the contact resistance. However, a large pressure may cause GDL to become over-compressed which results in decrease of GDL's porosity [3e5]. There are few literatures about designing clamping systems. Most of them studied the effect of clamping system on different parameters such as interfacial contact resistance [6e9] and ohmic resistance [10,11]. Researchers demonstrated that around 59% of the total power loss in a polymer electrolyte membrane fuel cell can be due to contact resistance between BPPs and GDLs [5]. Contact pressure distribution varies
* Corresponding author. E-mail address: [email protected] (E. Alizadeh). http://dx.doi.org/10.1016/j.ijhydene.2015.12.057 0360-3199/Copyright © 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 3 0 6 2 e3 0 7 1
throughout each individual cell and the stack itself. Moreover, contact pressure distribution may affect thermal conductivity and seal performance [7]. Lai et al. [6] implemented the model on a 2D bipolar plate/gas diffusion layer assembly based on the experimental interfacial contact resistivity. They showed that the contact resistant decreases as rapid as the clamping pressure. In addition, Zhou et al. [7] developed a 2D simulation and optimized the structure of the bipolar plate ribs to have better contact resistance. Wu et al. [8] proved that the contact resistance can be reduced by controlling the surface roughness of the bipolar plate and the fiber configuration of the gas diffusion layer. Zhou et al. [10] investigated the effect of nonuniformity of the contact pressure distribution on the electrical contact resistance. They proved that when there is no separation between two neighboring components, the electrical contact resistance cannot be reduced by improving the contact pressure distribution. Zhang et al. [11] proposed two semi-empirical methods for estimating the contact resistance between BPPs and GDLs based on an experimental contact resistanceepressure constitutive relation. Wen et al. [12] investigated the effects of different combinations of bolts configuration and clamping torque on the performance of a single PEMFC and a 10-cell stack using pressure sensitive films. They showed that the uniformity of the contact pressure distribution, the ohmic resistance and the mass transport limit current has linear correlations with the mean contact pressure. They also proved that increasing the mean contact pressure improves the uniformity of the contact pressure distribution and reduces the contact ohmic resistance. Montanini et al. [9] measured the clamping pressure distribution using piezo-resistive sensor arrays and digital image correlation techniques. They showed that increasing end plates stiffness leads to obtain more efficient load transmission mechanism. Wang et al. [13] used pressure sensitive films to compare their new clamping system with conventional clamping system and they concluded that their new clamping system has better contact pressure distribution than conventional one. The purpose of this paper was to improve a twodimensional model that can accurately prognosticate compression pressure distributions over the active area of the PEMFC stack. The active area of tested MEA was 400 cm2 (20 cm 20 cm). Simulation results were validated through experiments with pressure sensitive films to optimize the compression pressure distribution. For decreasing computation time, two-dimensional simulation was applied after verifying with three-dimensional simulation. The effects of end plates material and thickness, number of cells, position of the cell in the stack and sealant hardness on the contact pressure distribution of MEA were studied.
Description of the model Geometry The PEM fuel cell model geometry is illustrated in Fig. 1(a). The present model consists of end plates, current collectors, cooling plates, bipolar plates, MEA, sealants and fastening elements (bolts and nuts). The contact behavior between
3063
these components is nonlinear. It is assumed that gas diffusion layers are integrated into the membrane. Fig. 1(b) demonstrated the two-dimensional single cell model which includes all components of PEMFCs. Dimensions of the fuel cell components which are used for modeling are as follows. The active area of MEA is 400 cm2 (20 cm 20 cm). Bipolar plates and cooling plates with dimensions of 295 mm 295 mm 3 mm are used. Current collectors are copper alloy with thicknesses of 4 mm and the same length and width as bipolar plates. In addition, the model comprises two end plates with dimensions of 350 mm 350 mm and variable thickness. GDL and membrane dimensions are 202 mm 202 mm and 295 mm 295 mm, respectively. The thickness of carbon paper GDL is 0.235 mm and the thickness of membrane is 0.09 mm. All of the sealants have width and thickness of 3 mm and 1.15 mm, respectively. Designed sealant groove width is 6 mm for both bipolar and cooling plates. Moreover, designed sealant groove depths are assumed to be 0.76 mm and 0.95 mm for bipolar plates and cooling plates, respectively.
Mechanical properties The mechanical properties of the fuel cell components are listed in Table 1.
Numerical simulation Commercial finite elements numerical code ABAQUS has been used for simulation of the fuel cell behavior. Four-node bilinear plane-strain quadrilateral reduced integration elements (CPE4R) are used to mesh the components of the twodimensional model. In order to reduce the size of the problem and simulation time, symmetry conditions were applied onto all internal section boundaries. The schematic diagram of a quarter-cell is shown in Fig. 2. In addition, the bolt load is applied as concentrated force on the end plate. Fig. 3 shows three-dimensional model of the single cell. As shown in Fig. 3(a), only one eighth of three-dimensional sample was modeled due to its symmetric condition. Eight node linear brick reduced integration elements (C3D8R) are used to mesh the components of the model. Moreover, the bolts loads are applied on the washer exerted to the end plate which is shown in Fig. 3(b). The membranes are very thin in comparison with GDLs. Therefore, their influence on the mechanical characteristics is negligible. In this work, the membrane layers are integrated into the GDLs similar to those given in Refs. [15,16]. In finite element model, magnitudes of bolts loads are adjusted to become equal to the real one. The applied pressure over the MEA varies from 0.5 MPa to 1.5 MPa for the PEM fuel cells reported in different studies [15,16]. In this article, the considered mean pressure is set as 1 MPa. The contact properties are assumed to be penalty with the friction of 0.3 for contact surfaces which one is sealant and other are 0.1. In this paper, 60 Shore A EPDM1 which is a kind of elastomer is used as fuel cell sealant. Generally, elastomer is assumed to be incompressible. Elastomer is often modeled as 1
Ethylene Propylene Diene Monomer.
3064
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 3 0 6 2 e3 0 7 1
Fig. 1 e (a) Exploded PEM fuel cell view, (b) Two-dimensional PEM fuel cell model.
Table 1 e Mechanical properties of the PEM fuel cell components. Component End plates Bipolar plates Cooling plates Current collectors GDL [14]
Material
Young's modulus (MPa)
Poisson's ratio
Density (Kg/m3)
Aluminum Stainless Steel 316L Graphite Graphite Copper Carbon paper
70000 209000 5100
0.33 0.3 0.25
2700 7800 2100
100000 10
0.33 0.25
8900 400
Fig. 2 e Symmetric two-dimensional model of the PEM fuel cell.
Fig. 3 e (a) Three-dimensional model of the PEM single cell, (b) Symmetric conditions and load configurations of PEM fuel cell model.
hyperelastic. These materials have strongly nonlinear stressestrain relation and do not follow the Hook's law. It is most common to measure elastomeric experimental data using engineering stress and strain. The appropriate experiments are not yet clearly determined by international standards organizations. The mechanical tests which are performed on rubbers classify into two groups: compression and tension. The compression state is always uniaxial, while
tension can be applied in a uniaxial, planar or equi-biaxial state [17e19]. Gracia et al. [20] investigated the results of two industrial components made of filled rubber subjected to several loads. In addition, they applied finite element analysis with the overlay model. Ghorayshi [21] determined the parameters of Prony series in hyper-viscoelastic material models using finite element method (FEM). Jang et al. [22] carried out uniaxial and
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 3 0 6 2 e3 0 7 1
3065
Fig. 4 e The uniaxial compression specimen (a) Experiment, (b) Simulation. biaxial tension tests to obtain material constants and stressestrain curves. The results demonstrated that FEM can be used to predict the behavior of components. Yang et al. [23] proposed a visco-hyperelastic constitutive equation to describe the large deformation response of incompressible rubber under high strain rates. They conducted the quasistatic compression tests on rubber specimens and fitted them with the experimental data obtained using a simple least squares approach. As the sealant becomes compressed by the assembly pressure, exerted compressive stress on the sealant is dominated in accordance with tension stress. Therefore, it seems that just using the compression test data gives the proper accuracy for simulation of the sealant. In this article, uniaxial compression test has been done using accurate universal testing machine with a load capacity of 20 KN. EPDM compound was used for producing compression test specimen. According to ISO-7743, test specimen is a cylinder with height and diameter of 12.5 mm and 29.5 mm, respectively. Fig. 4(a) and (b) show the uniaxial compression specimen for two cases of experiment and simulation, respectively. The compression rate has significant effect on stressestrain curve. Fig. 5 illustrates the typical rate-dependent
Fig. 5 e Response zone for typical viscoelastic solid [24].
responses obtained from a viscoelastic solid. The strain rate should be chosen similar to the real condition. Since the state of the fuel cell is similar to the equilibrium response, the slow loading rate was applied. However, obtaining equilibrium response is difficult in according to difficult determination of proper compression of rubber. Therefore, the multi-step relaxation test was employed. At the first place, specimens are preloaded five cycles to overcome the Mullins' effect [23,25]. Fig. 6 shows the multi-step relaxation test for eighteen stages and five minute delay for each stage. Connecting the minimum point for each stage leads to sample's equilibrium response. The stressestrain data obtained from experimental results are used in ABAQUS to define hyperelastic properties of sealants and to find optimum strain energy density. Hyperelastic material models such as Mooney-Rivlin, Arruda-Boyce, Yeoh, Neo-Hookean and Ogden [25] are used to fit the test data and extract hyperelastic constants. The Neo-Hookean model [26] is stable in whole strain domain. As shown in Fig. 7, NeoHookean model has good agreement with the uniaxial compression test data. After finding proper strain energy density function, the associated simulation has been done to validate the results.
Fig. 6 e Multi-step relaxation test with five minutes delay for each stage.
3066
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 3 0 6 2 e3 0 7 1
Fig. 7 e Uniaxial, biaxial and planar fittings with NeoHookean model using experimental data.
Simulation has been performed with the validated strain energy density function to obtain the proper friction coefficient which can satisfy the test result without lubrication. The comparison between the test data and the simulation with and without friction is shown in Fig. 8. The calculated friction coefficient is assumed to be 0.3 (contact model) in the test. The defined contact model for the surfaces is C3DHRH with hybrid formulation.
Results and discussions In this section, the contact pressure distribution over the active area of the MEA is studied. The results are obtained based on 60 Shore A EPDM. Three-dimensional simulation is very time consuming and complicated. Three-dimensional PEM single cell simulation takes about two hundred times more than twodimensional one with the same components. Therefore, threedimensional simulations are verified with two-dimensional simulations and the results are compared with the
Fig. 8 e Comparison between test data and simulation with and without friction.
Fig. 9 e Contact pressure distribution over the MEA of twodimensional and three-dimensional PEM single cell model with different thicknesses of end plates.
experimental results obtained from pressure sensitive films. Effects of the parameters on the contact pressure distribution are investigated with the validated two-dimensional model. With respect to symmetry of the fuel cell, the pressure distribution along the X axis and Y axis of the MEA surface are the same. Therefore, the contact pressure along perpendicular bisector of one side of MEA is selected in three-dimensional model to present the contact pressure distribution. Fig. 9 presents the contact pressure distribution along the mentioned axis. In this figure, the contact pressure distribution is investigated for the stainless steel end plates with the thickness of 30 mm and 50 mm. As shown, there is a good agreement between the results of two-dimensional and three-dimensional simulations. A slight incoherence of the results in Fig. 9 reduces by increasing the thickness of end plates.
Fig. 10 e Position of pressure sensitive film in PEM fuel cell.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 3 0 6 2 e3 0 7 1
3067
Fig. 11 e Contact pressure distribution over the MEA of PEM Single cell, (a) Stainless steel end plate with 30 mm thickness (b) Stainless steel end plate with 50 mm thickness.
Fig. 12 e Contact pressure distribution over the MEA of PEM Single cell with flat bipolar plate and bipolar plate with flow field.
Fig. 10 represents the situation of the pressure sensitive films in the experimental setup. Pressure films consist of lots of microcapsules which are broken after applying clamping pressure. Thus, a color-forming material was released on the film and absorbed by it. There is a relation between the color intensity in the pressure sensitive films and the amount of applied pressure. Fig. 11 shows the contact pressure distribution over the active area of the single cell with two different end plates thicknesses using pressure sensitive film. The pressure sensitive film was placed instead of membrane between GDLs to have the same behavior with the real cell. Range of pressure measurement is between 0.5 MPa and 2.5 MPa. Therefore, the pressure magnitude of white zone in the pressure sensitive film is less than 0.5 MPa which is shown in Fig. 11(a). Thus, the experimental results have agreement with the simulation results of the end plates with 30 mm thicknesses (Fig. 9). Therefore, two-dimensional model is used to simplify the simulation of PEM fuel cell. In previous simulations, it is assumed that bipolar plates do not have flow field and are flat. Fig. 12 demonstrates the effect of flow fields on the contact pressure over the MEA in single cell. The
Fig. 13 e Stress distribution over the MEA of PEM single cell.
3068
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 3 0 6 2 e3 0 7 1
Fig. 14 e Contact pressure distribution over the MEA of PEM Single cell for different end plates materials and thicknesses.
Fig. 16 e Contact pressure distribution over the MEA of PEM Single cell for three different hardness of the sealant.
Thickness of end plate oscillatory curve in this figure relates to the flow field of bipolar plate. As shown, there is no contact pressure under the channel. Therefore, magnitudes of contact pressure drop to zero under the channel and rise up under the rib. According to Fig. 12, the results of the case using flat bipolar plate has the same trend as bipolar plate with flow field. However, contact pressure over the MEA in flat bipolar plate decreases with increase of the contact area. Fig. 13 presents stress distribution contour along the MEA. This figure reveals that the edge of the MEA tolerates the maximum stress. This phenomenon happens due to the clamping systems and configuration of bolts. In this figure, the thicknesses of end plates are assumed to be 30 mm. After verifying the results of contact pressure distribution, the effect of thickness and material of end plates, sealant hardness, cells number and position of cell have been analyzed.
As mentioned, sufficient clamping pressure distribution should be applied to the fuel cell stack in order to have a proper efficiency. Therefore, end plate should be designed in such a way that it could satisfy fuel cell desired conditions. Metallic plates such as steel and aluminum are the most common applicable materials which used for end plates. However, composite material is used due to its low density and electrical insulation [27]. Fig. 14 shows the contact pressure distribution over the MEA for two different materials (aluminum and steel) with the thickness of 30 mm and 50 mm. The compression ratio parameter is defined as minimum contact pressure divided by maximum contact pressure. The compression ratio for stainless steel and aluminum end plates are shown in Fig. 15. As expected, the contact pressure ratio tends to 1 by increasing the end plates thicknesses.
Fig. 15 e Contact pressure ratio for Steel and Aluminum with different thicknesses of end plates.
Fig. 17 e Contact pressure distribution over the MEA of single cell, three cells and fifteen cells stacks.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 3 0 6 2 e3 0 7 1
3069
Fig. 18 e Contact pressure distribution over the MEA of fifteen cells stack.
Sealant hardness In this section, effect of hardness of the sealant on the exerted clamping force and contact pressure distribution is investigated. According to the large number of sealants used in the fuel cell stack, investigating the influence of the sealant hardness is important to have the desirable pressure distribution. Fig. 16 shows the single cell contact pressure distribution over the MEA for three different hardness of the sealant. As shown, the contact pressure distribution trend is not varied significantly by changing sealants hardness, but the applied pressure for having the same contact pressure becomes lower when softer sealant is used. In addition, increasing sealant hardness causes the stress concentration as illustrated in Fig. 16. Steel end plate with thickness of 30 mm is considered.
As shown in Fig. 16, the sudden jumps of contact pressure near the boundary of the MEA happen due to the geometry of the model (sealant place) and the sealant properties. The reason of contact pressure jump at the side of MEA is the placement of sealant which is located on the MEA surface (Fig. 2). Therefore, the sealant hardness has effect on the contact pressure of this point directly. The reaction force generated on the sealant due to the clamping pressure exerts on the MEA. The jump for the sealant with 30 Shore A and 90 Shore A leads to decrease and increase the contact pressure, respectively. The sealant with 90 Shore A is harder than 60 Shore A and 30 Shore A. Therefore, the reaction force exerted on MEA (for the 90 Shore A sealant) causes the contact pressure to increase near the sealant groove. For the 30 Shore A sealant, the contact pressure decreases because the reaction force of the sealant is not high enough to compress the MEA in comparison with surrounding points (Fig. 16).
Number of cells
Fig. 19 e Contact pressure distribution over the MEA of first cell and middle cell of fifteen cells stack.
Deflection of the end plates is divided between the cells of the fuel cell stack. Simulation results for different number of cells are shown in Fig. 17. In this figure, contact pressure distribution over the MEA of single cell is compared with pressure distributions over the MEA of stack with three and fifteen cells. The active area is 20 cm 20 cm and the end plates thicknesses are assumed to be 30 mm. As expected, contact pressure distribution over the active area of fuel cell with fewer cells is more uneven than the others. Bolts torque are equal for all simulations. In addition, experimental tests were performed to investigate the effect of number of the cells on the contact pressure distribution over the MEA. The test was carried out for stack with fifteen cells using pressure sensitive film which is shown in Fig. 18. Comparing Fig. 18 with Fig. 11(a) demonstrates that
3070
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 3 0 6 2 e3 0 7 1
increasing the number of the cells leads to obtain more even contact pressure distribution. In this experimental test, steel end plate with thickness of 30 mm is used. Contact pressure distribution over the active area of middle cell of stack is illustrated in and Fig. 18.
[7]
[8]
Position of cell in the stack Fig. 19 shows simulation results of contact pressure distribution over the MEA of first cell and middle cell of stack with fifteen cells. As shown, position of the cell has influence on the contact pressure distribution. The contact pressure distribution over the MEA of the first cell is usually the most uneven one. Moreover, the middle cell has the best compression pressure distribution in the stack as noted in Ref. [28]. The thickness of the end plate is assumed to be 30 mm for two-dimensional model.
[10]
Conclusion
[12]
In this paper, a finite element simulation method is used to investigate the effect of thickness and material of end plates, sealant hardness, number and position of cells on the contact pressure distribution over the surface of the MEA. Twodimensional model is used instead of three-dimensional model and the results are compared with experimental results which were obtained by pressure sensitive films. It is concluded that increasing the flexural rigidity of the end plates leads to decrease in deflection of them. Increasing the flexural rigidity of end plates can be obtained by selecting suitable thickness and proper material. In addition, the other way to decrease deflection of the end plates is to reduce the applied torque on the bolts which can be accomplished using softer sealant. Furthermore, increasing the number of cell causes to have better contact pressure distribution over the MEA.
references
[9]
[11]
[13]
[14]
[15]
[16]
[17]
[18]
[19] [1] Asghari S, Shahsamandi MH, Ashraf Khorasani MR. Design and manufacturing of end plates of a 5 kW PEM fuel cell. Int J Hydrogen Energy 2010;35:9291e7. [2] Montanini R, Squadrito G, Giacoppo G. Experimental evaluation of the lamping pressure distribution in a PEM fuel cell using matrix-based piezoresistive thin-film sensors. In: XIX IMEKO World Congress fundamental and applied metrology September 6 11; 2009. Lisbon, Portugal. [3] Yu Fu, Ming Hou, Xiqiang Yan, Junbo Hou, Xiaokuan Luo, Zhigang Shao, et al. Research progress of aluminum alloy end plates for PEMFCs. J Power Sources 2007;166:435e40. [4] Patermarakis G, Papandreadis N. Effect of the structure of porous anodic Al2O3 films on the mechanism of their hydration and pore closure during hydrothermal treatment. Electrochim Acta 1993;38:1413e20. [5] Thompson GE. Porous anodic alumina: fabrication, characterization and applications. Thin Solid Films 1997;297:192e201. [6] Lai Xinmin, Liu Dong’an, Peng Linfa, Ni Jun. A mechanicaleelectrical finite element method model for predicting contact resistance between bipolar plate and gas
[20]
[21]
[22]
[23]
[24]
diffusion layer in PEM fuel cells. J Power Sources 2008;182:153e9. Zhou P, Wu CW, Ma GJ. Contact resistance prediction and structure optimization of bipolar plates. J Power Sources 2006;159:1115e22. Wu Zhiliang, Zhou Yuanyuan, Lin Guosong, Wang Shuxin, Hu S Jack. An improved model for predicting electrical contact resistance between bipolar plate and gas diffusion layer in proton exchange membrane fuel cells. J Power Sources 2008;182:265e9. Montanini R, Squadrito G, Giacoppo G. Measurement of the clamping pressure distribution in polymer electrolyte fuel cells using piezoresistive sensor arrays and digital image correlation techniques. J Power Sources 2011;196:8484e93. Zhou P, Lin P, Wu CW, Li Z. Effect of nonuniformity of the contact pressure distribution on the electrical contact resistance in proton exchange membrane fuel cells. Int J Hydrogen Energy 2011;36:6039e44. Zhang Lianhong, Liu Ying, Song Haimin, Wang Shuxin, Zhou Yuanyuan, Hu S Jack. Estimation of contact resistance in proton exchange membrane fuel cells. J Power Sources 2006;162:1165e71. Wen Chih-Yung, Lin Yu-Sheng, Lu Chien-Heng. Experimental study of clamping effects on the performances of a single proton exchange membrane fuel cell and a 10-cell stack. J Power Sources 2009;192:475e85. Wang Xinting, Song Ying, Zhang Bi. Experimental study on clamping pressure distribution in PEM fuel cells. J Power Sources 2008;179:305e9. Kusoglu A, Karlsson AM, Santare MH, Cleghorn S, Johnson WB. Mechanical response of fuel cell membranes subjected to a hygro-thermal cycle. J Power Sources 2006;161:987e96. Tang Y, Santare MH, Karlsson AM, Cleghorn S, Johnson WB. Stresses in proton exchange membranes due to hygrothermal loading. J Fuel Cell Sci Technol 2006;3:119e24. Kusoglu A, Karlsson AM, Santare MH, Cleghorn S, William BJ. Mechanical behavior of fuel cell membranes under humidity cycles and effect of swelling anisotropy on the fatigue stresses. J Power Sources 2007;170:345e58. Miller K. Testing elastomer for hyperelastic material models in finite element analysis. Axel Products Testing and Analysis Report. 2000. Pearson I, Pickering M. The determination of a highly elastic adhesive's material properties and their representation in finite element analysis. Finite Elem Anal Des 2001;37:221e32. Sasso M, Palmieri G, Chiappini G, Amodio D. Characterization of hyperelastic rubber-like materials by biaxial and uniaxial stretching tests based on optical methods. Polym Test 2008;27:995e1004. Gracia LA, Liarte E, Pelegay JL, Calvo B. Finite element simulation of the hysteretic behaviour of an industrial rubber. Application to design of rubber components. Finite Elem Anal Des 2010;46:357e68. Ghoreishy Mir Hamid Reza. Determination of the parameters of the Prony series in hyper-viscoelastic material models using the finite element method. Mater Des 2012;35:791e7. Jang WJ, Lee J, Woo CS, Kim BK, Lee SB. An experimental study and finite element analysis of weatherstrip. Int J Precis Eng Manuf 2011;12(No. 1):97e104. Yang LM, Shim VPW, Lim CT. A visco-hyperelastic approach to modelling the constitutive behaviour of rubber. Int J Impact Eng 2000;24:545e60. Amin AFMS, Alam MS, Okui Y. An improved hyperelasticity relation in modeling viscoelasticity response of natural and high damping rubbers in compression: experiments, parameter identification and numerical verification. Mech Mater 2002;34:75e95.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 3 0 6 2 e3 0 7 1
[25] Mullins L. Effect of stretching on the properties of rubber. Rubber Res 1947;16:275e89. [26] Boulanger P, Hayes M. Finite amplitude waves in MooneyRivlin and Hadamard materials, in topics in finite elasticity. International Center for Mechanical Sciences; 2001. [27] Yu Ha Na, Kim Seong Su, Do Suh Jung, Lee Dai Gil. Composite end plates with pre-curvature for PEMFC
3071
(polymer electrolyte membrane fuel cell). Compos Struct 2010;92:1498e503. € f Thomas, Ihonen Jari K. Modeling [28] Mikkola Mikko, Tingelo compression pressure distribution in fuel cell stacks. J Power Sources 2009;193:269e75.
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Investigation of contact pressure distribution over the active area of PEM fuel cell stack E. Alizadeh*, M.M. Barzegari, M. Momenifar, M. Ghadimi, S.H.M. Saadat Malek Ashtar University of Technology, Fuel Cell Technology Research Laboratory, Iran
article info
abstract
Article history:
Contact pressure distribution over the active area of proton exchange membrane fuel cell
Received 5 October 2015
(PEMFC) has significant effects on the performance of PEMFCs. Even clamping pressure
Received in revised form
over the membrane electrode assembly (MEA) affects contact resistance, characteristics of
5 December 2015
porous media and sealing task. This paper develops a PEM fuel cell model to study the
Accepted 8 December 2015
contact pressure distribution over the membrane electrode assembly using finite element
Available online 6 January 2016
model. At first, the three-dimensional model of a single cell was reduced to a twodimensional model to decrease the calculation time. After validation of the obtained re-
Keywords:
sults via the pressure sensitive films, the effect of some parameters such as thickness and
PEM fuel cell
material of the end plates, sealant hardness, number of the stack's cells and position of the
Finite element method
cell on the contact pressure distribution over the MEA were investigated. The results reveal
End plates
that optimizing mentioned parameters leads to design PEM fuel cells with proper contact
Contact pressure distribution
pressure distribution over the MEA.
MEA
Copyright © 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Recently, proton exchange membrane fuel cell has attracted much attention due to its high efficiency, low temperature, quick startup and being clean energy converter which converts the energy stored in hydrogen and oxygen into electricity. The premise for a wide diffusion of this technology mainly depends on two crucial factors: cost reduction and energy efficiency improvement. Clamping system is one of the most important parameters of PEMFCs. The purposes of the clamping systems can be mentioned as providing sealing pressure and proper pressure distribution at various interfaces and decreasing contact resistance between interfaces. Uneven contact pressure
distribution over the MEA results in non-uniform current density and heat generation distribution which may cause hot spot formation in the MEA [1,2]. High clamping pressure leads to an increase in the contact area between bipolar plate (BPP) and gas diffusion layer (GDL) which decreases the contact resistance. However, a large pressure may cause GDL to become over-compressed which results in decrease of GDL's porosity [3e5]. There are few literatures about designing clamping systems. Most of them studied the effect of clamping system on different parameters such as interfacial contact resistance [6e9] and ohmic resistance [10,11]. Researchers demonstrated that around 59% of the total power loss in a polymer electrolyte membrane fuel cell can be due to contact resistance between BPPs and GDLs [5]. Contact pressure distribution varies
* Corresponding author. E-mail address: [email protected] (E. Alizadeh). http://dx.doi.org/10.1016/j.ijhydene.2015.12.057 0360-3199/Copyright © 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 3 0 6 2 e3 0 7 1
throughout each individual cell and the stack itself. Moreover, contact pressure distribution may affect thermal conductivity and seal performance [7]. Lai et al. [6] implemented the model on a 2D bipolar plate/gas diffusion layer assembly based on the experimental interfacial contact resistivity. They showed that the contact resistant decreases as rapid as the clamping pressure. In addition, Zhou et al. [7] developed a 2D simulation and optimized the structure of the bipolar plate ribs to have better contact resistance. Wu et al. [8] proved that the contact resistance can be reduced by controlling the surface roughness of the bipolar plate and the fiber configuration of the gas diffusion layer. Zhou et al. [10] investigated the effect of nonuniformity of the contact pressure distribution on the electrical contact resistance. They proved that when there is no separation between two neighboring components, the electrical contact resistance cannot be reduced by improving the contact pressure distribution. Zhang et al. [11] proposed two semi-empirical methods for estimating the contact resistance between BPPs and GDLs based on an experimental contact resistanceepressure constitutive relation. Wen et al. [12] investigated the effects of different combinations of bolts configuration and clamping torque on the performance of a single PEMFC and a 10-cell stack using pressure sensitive films. They showed that the uniformity of the contact pressure distribution, the ohmic resistance and the mass transport limit current has linear correlations with the mean contact pressure. They also proved that increasing the mean contact pressure improves the uniformity of the contact pressure distribution and reduces the contact ohmic resistance. Montanini et al. [9] measured the clamping pressure distribution using piezo-resistive sensor arrays and digital image correlation techniques. They showed that increasing end plates stiffness leads to obtain more efficient load transmission mechanism. Wang et al. [13] used pressure sensitive films to compare their new clamping system with conventional clamping system and they concluded that their new clamping system has better contact pressure distribution than conventional one. The purpose of this paper was to improve a twodimensional model that can accurately prognosticate compression pressure distributions over the active area of the PEMFC stack. The active area of tested MEA was 400 cm2 (20 cm 20 cm). Simulation results were validated through experiments with pressure sensitive films to optimize the compression pressure distribution. For decreasing computation time, two-dimensional simulation was applied after verifying with three-dimensional simulation. The effects of end plates material and thickness, number of cells, position of the cell in the stack and sealant hardness on the contact pressure distribution of MEA were studied.
Description of the model Geometry The PEM fuel cell model geometry is illustrated in Fig. 1(a). The present model consists of end plates, current collectors, cooling plates, bipolar plates, MEA, sealants and fastening elements (bolts and nuts). The contact behavior between
3063
these components is nonlinear. It is assumed that gas diffusion layers are integrated into the membrane. Fig. 1(b) demonstrated the two-dimensional single cell model which includes all components of PEMFCs. Dimensions of the fuel cell components which are used for modeling are as follows. The active area of MEA is 400 cm2 (20 cm 20 cm). Bipolar plates and cooling plates with dimensions of 295 mm 295 mm 3 mm are used. Current collectors are copper alloy with thicknesses of 4 mm and the same length and width as bipolar plates. In addition, the model comprises two end plates with dimensions of 350 mm 350 mm and variable thickness. GDL and membrane dimensions are 202 mm 202 mm and 295 mm 295 mm, respectively. The thickness of carbon paper GDL is 0.235 mm and the thickness of membrane is 0.09 mm. All of the sealants have width and thickness of 3 mm and 1.15 mm, respectively. Designed sealant groove width is 6 mm for both bipolar and cooling plates. Moreover, designed sealant groove depths are assumed to be 0.76 mm and 0.95 mm for bipolar plates and cooling plates, respectively.
Mechanical properties The mechanical properties of the fuel cell components are listed in Table 1.
Numerical simulation Commercial finite elements numerical code ABAQUS has been used for simulation of the fuel cell behavior. Four-node bilinear plane-strain quadrilateral reduced integration elements (CPE4R) are used to mesh the components of the twodimensional model. In order to reduce the size of the problem and simulation time, symmetry conditions were applied onto all internal section boundaries. The schematic diagram of a quarter-cell is shown in Fig. 2. In addition, the bolt load is applied as concentrated force on the end plate. Fig. 3 shows three-dimensional model of the single cell. As shown in Fig. 3(a), only one eighth of three-dimensional sample was modeled due to its symmetric condition. Eight node linear brick reduced integration elements (C3D8R) are used to mesh the components of the model. Moreover, the bolts loads are applied on the washer exerted to the end plate which is shown in Fig. 3(b). The membranes are very thin in comparison with GDLs. Therefore, their influence on the mechanical characteristics is negligible. In this work, the membrane layers are integrated into the GDLs similar to those given in Refs. [15,16]. In finite element model, magnitudes of bolts loads are adjusted to become equal to the real one. The applied pressure over the MEA varies from 0.5 MPa to 1.5 MPa for the PEM fuel cells reported in different studies [15,16]. In this article, the considered mean pressure is set as 1 MPa. The contact properties are assumed to be penalty with the friction of 0.3 for contact surfaces which one is sealant and other are 0.1. In this paper, 60 Shore A EPDM1 which is a kind of elastomer is used as fuel cell sealant. Generally, elastomer is assumed to be incompressible. Elastomer is often modeled as 1
Ethylene Propylene Diene Monomer.
3064
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 3 0 6 2 e3 0 7 1
Fig. 1 e (a) Exploded PEM fuel cell view, (b) Two-dimensional PEM fuel cell model.
Table 1 e Mechanical properties of the PEM fuel cell components. Component End plates Bipolar plates Cooling plates Current collectors GDL [14]
Material
Young's modulus (MPa)
Poisson's ratio
Density (Kg/m3)
Aluminum Stainless Steel 316L Graphite Graphite Copper Carbon paper
70000 209000 5100
0.33 0.3 0.25
2700 7800 2100
100000 10
0.33 0.25
8900 400
Fig. 2 e Symmetric two-dimensional model of the PEM fuel cell.
Fig. 3 e (a) Three-dimensional model of the PEM single cell, (b) Symmetric conditions and load configurations of PEM fuel cell model.
hyperelastic. These materials have strongly nonlinear stressestrain relation and do not follow the Hook's law. It is most common to measure elastomeric experimental data using engineering stress and strain. The appropriate experiments are not yet clearly determined by international standards organizations. The mechanical tests which are performed on rubbers classify into two groups: compression and tension. The compression state is always uniaxial, while
tension can be applied in a uniaxial, planar or equi-biaxial state [17e19]. Gracia et al. [20] investigated the results of two industrial components made of filled rubber subjected to several loads. In addition, they applied finite element analysis with the overlay model. Ghorayshi [21] determined the parameters of Prony series in hyper-viscoelastic material models using finite element method (FEM). Jang et al. [22] carried out uniaxial and
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 3 0 6 2 e3 0 7 1
3065
Fig. 4 e The uniaxial compression specimen (a) Experiment, (b) Simulation. biaxial tension tests to obtain material constants and stressestrain curves. The results demonstrated that FEM can be used to predict the behavior of components. Yang et al. [23] proposed a visco-hyperelastic constitutive equation to describe the large deformation response of incompressible rubber under high strain rates. They conducted the quasistatic compression tests on rubber specimens and fitted them with the experimental data obtained using a simple least squares approach. As the sealant becomes compressed by the assembly pressure, exerted compressive stress on the sealant is dominated in accordance with tension stress. Therefore, it seems that just using the compression test data gives the proper accuracy for simulation of the sealant. In this article, uniaxial compression test has been done using accurate universal testing machine with a load capacity of 20 KN. EPDM compound was used for producing compression test specimen. According to ISO-7743, test specimen is a cylinder with height and diameter of 12.5 mm and 29.5 mm, respectively. Fig. 4(a) and (b) show the uniaxial compression specimen for two cases of experiment and simulation, respectively. The compression rate has significant effect on stressestrain curve. Fig. 5 illustrates the typical rate-dependent
Fig. 5 e Response zone for typical viscoelastic solid [24].
responses obtained from a viscoelastic solid. The strain rate should be chosen similar to the real condition. Since the state of the fuel cell is similar to the equilibrium response, the slow loading rate was applied. However, obtaining equilibrium response is difficult in according to difficult determination of proper compression of rubber. Therefore, the multi-step relaxation test was employed. At the first place, specimens are preloaded five cycles to overcome the Mullins' effect [23,25]. Fig. 6 shows the multi-step relaxation test for eighteen stages and five minute delay for each stage. Connecting the minimum point for each stage leads to sample's equilibrium response. The stressestrain data obtained from experimental results are used in ABAQUS to define hyperelastic properties of sealants and to find optimum strain energy density. Hyperelastic material models such as Mooney-Rivlin, Arruda-Boyce, Yeoh, Neo-Hookean and Ogden [25] are used to fit the test data and extract hyperelastic constants. The Neo-Hookean model [26] is stable in whole strain domain. As shown in Fig. 7, NeoHookean model has good agreement with the uniaxial compression test data. After finding proper strain energy density function, the associated simulation has been done to validate the results.
Fig. 6 e Multi-step relaxation test with five minutes delay for each stage.
3066
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 3 0 6 2 e3 0 7 1
Fig. 7 e Uniaxial, biaxial and planar fittings with NeoHookean model using experimental data.
Simulation has been performed with the validated strain energy density function to obtain the proper friction coefficient which can satisfy the test result without lubrication. The comparison between the test data and the simulation with and without friction is shown in Fig. 8. The calculated friction coefficient is assumed to be 0.3 (contact model) in the test. The defined contact model for the surfaces is C3DHRH with hybrid formulation.
Results and discussions In this section, the contact pressure distribution over the active area of the MEA is studied. The results are obtained based on 60 Shore A EPDM. Three-dimensional simulation is very time consuming and complicated. Three-dimensional PEM single cell simulation takes about two hundred times more than twodimensional one with the same components. Therefore, threedimensional simulations are verified with two-dimensional simulations and the results are compared with the
Fig. 8 e Comparison between test data and simulation with and without friction.
Fig. 9 e Contact pressure distribution over the MEA of twodimensional and three-dimensional PEM single cell model with different thicknesses of end plates.
experimental results obtained from pressure sensitive films. Effects of the parameters on the contact pressure distribution are investigated with the validated two-dimensional model. With respect to symmetry of the fuel cell, the pressure distribution along the X axis and Y axis of the MEA surface are the same. Therefore, the contact pressure along perpendicular bisector of one side of MEA is selected in three-dimensional model to present the contact pressure distribution. Fig. 9 presents the contact pressure distribution along the mentioned axis. In this figure, the contact pressure distribution is investigated for the stainless steel end plates with the thickness of 30 mm and 50 mm. As shown, there is a good agreement between the results of two-dimensional and three-dimensional simulations. A slight incoherence of the results in Fig. 9 reduces by increasing the thickness of end plates.
Fig. 10 e Position of pressure sensitive film in PEM fuel cell.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 3 0 6 2 e3 0 7 1
3067
Fig. 11 e Contact pressure distribution over the MEA of PEM Single cell, (a) Stainless steel end plate with 30 mm thickness (b) Stainless steel end plate with 50 mm thickness.
Fig. 12 e Contact pressure distribution over the MEA of PEM Single cell with flat bipolar plate and bipolar plate with flow field.
Fig. 10 represents the situation of the pressure sensitive films in the experimental setup. Pressure films consist of lots of microcapsules which are broken after applying clamping pressure. Thus, a color-forming material was released on the film and absorbed by it. There is a relation between the color intensity in the pressure sensitive films and the amount of applied pressure. Fig. 11 shows the contact pressure distribution over the active area of the single cell with two different end plates thicknesses using pressure sensitive film. The pressure sensitive film was placed instead of membrane between GDLs to have the same behavior with the real cell. Range of pressure measurement is between 0.5 MPa and 2.5 MPa. Therefore, the pressure magnitude of white zone in the pressure sensitive film is less than 0.5 MPa which is shown in Fig. 11(a). Thus, the experimental results have agreement with the simulation results of the end plates with 30 mm thicknesses (Fig. 9). Therefore, two-dimensional model is used to simplify the simulation of PEM fuel cell. In previous simulations, it is assumed that bipolar plates do not have flow field and are flat. Fig. 12 demonstrates the effect of flow fields on the contact pressure over the MEA in single cell. The
Fig. 13 e Stress distribution over the MEA of PEM single cell.
3068
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 3 0 6 2 e3 0 7 1
Fig. 14 e Contact pressure distribution over the MEA of PEM Single cell for different end plates materials and thicknesses.
Fig. 16 e Contact pressure distribution over the MEA of PEM Single cell for three different hardness of the sealant.
Thickness of end plate oscillatory curve in this figure relates to the flow field of bipolar plate. As shown, there is no contact pressure under the channel. Therefore, magnitudes of contact pressure drop to zero under the channel and rise up under the rib. According to Fig. 12, the results of the case using flat bipolar plate has the same trend as bipolar plate with flow field. However, contact pressure over the MEA in flat bipolar plate decreases with increase of the contact area. Fig. 13 presents stress distribution contour along the MEA. This figure reveals that the edge of the MEA tolerates the maximum stress. This phenomenon happens due to the clamping systems and configuration of bolts. In this figure, the thicknesses of end plates are assumed to be 30 mm. After verifying the results of contact pressure distribution, the effect of thickness and material of end plates, sealant hardness, cells number and position of cell have been analyzed.
As mentioned, sufficient clamping pressure distribution should be applied to the fuel cell stack in order to have a proper efficiency. Therefore, end plate should be designed in such a way that it could satisfy fuel cell desired conditions. Metallic plates such as steel and aluminum are the most common applicable materials which used for end plates. However, composite material is used due to its low density and electrical insulation [27]. Fig. 14 shows the contact pressure distribution over the MEA for two different materials (aluminum and steel) with the thickness of 30 mm and 50 mm. The compression ratio parameter is defined as minimum contact pressure divided by maximum contact pressure. The compression ratio for stainless steel and aluminum end plates are shown in Fig. 15. As expected, the contact pressure ratio tends to 1 by increasing the end plates thicknesses.
Fig. 15 e Contact pressure ratio for Steel and Aluminum with different thicknesses of end plates.
Fig. 17 e Contact pressure distribution over the MEA of single cell, three cells and fifteen cells stacks.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 3 0 6 2 e3 0 7 1
3069
Fig. 18 e Contact pressure distribution over the MEA of fifteen cells stack.
Sealant hardness In this section, effect of hardness of the sealant on the exerted clamping force and contact pressure distribution is investigated. According to the large number of sealants used in the fuel cell stack, investigating the influence of the sealant hardness is important to have the desirable pressure distribution. Fig. 16 shows the single cell contact pressure distribution over the MEA for three different hardness of the sealant. As shown, the contact pressure distribution trend is not varied significantly by changing sealants hardness, but the applied pressure for having the same contact pressure becomes lower when softer sealant is used. In addition, increasing sealant hardness causes the stress concentration as illustrated in Fig. 16. Steel end plate with thickness of 30 mm is considered.
As shown in Fig. 16, the sudden jumps of contact pressure near the boundary of the MEA happen due to the geometry of the model (sealant place) and the sealant properties. The reason of contact pressure jump at the side of MEA is the placement of sealant which is located on the MEA surface (Fig. 2). Therefore, the sealant hardness has effect on the contact pressure of this point directly. The reaction force generated on the sealant due to the clamping pressure exerts on the MEA. The jump for the sealant with 30 Shore A and 90 Shore A leads to decrease and increase the contact pressure, respectively. The sealant with 90 Shore A is harder than 60 Shore A and 30 Shore A. Therefore, the reaction force exerted on MEA (for the 90 Shore A sealant) causes the contact pressure to increase near the sealant groove. For the 30 Shore A sealant, the contact pressure decreases because the reaction force of the sealant is not high enough to compress the MEA in comparison with surrounding points (Fig. 16).
Number of cells
Fig. 19 e Contact pressure distribution over the MEA of first cell and middle cell of fifteen cells stack.
Deflection of the end plates is divided between the cells of the fuel cell stack. Simulation results for different number of cells are shown in Fig. 17. In this figure, contact pressure distribution over the MEA of single cell is compared with pressure distributions over the MEA of stack with three and fifteen cells. The active area is 20 cm 20 cm and the end plates thicknesses are assumed to be 30 mm. As expected, contact pressure distribution over the active area of fuel cell with fewer cells is more uneven than the others. Bolts torque are equal for all simulations. In addition, experimental tests were performed to investigate the effect of number of the cells on the contact pressure distribution over the MEA. The test was carried out for stack with fifteen cells using pressure sensitive film which is shown in Fig. 18. Comparing Fig. 18 with Fig. 11(a) demonstrates that
3070
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 3 0 6 2 e3 0 7 1
increasing the number of the cells leads to obtain more even contact pressure distribution. In this experimental test, steel end plate with thickness of 30 mm is used. Contact pressure distribution over the active area of middle cell of stack is illustrated in and Fig. 18.
[7]
[8]
Position of cell in the stack Fig. 19 shows simulation results of contact pressure distribution over the MEA of first cell and middle cell of stack with fifteen cells. As shown, position of the cell has influence on the contact pressure distribution. The contact pressure distribution over the MEA of the first cell is usually the most uneven one. Moreover, the middle cell has the best compression pressure distribution in the stack as noted in Ref. [28]. The thickness of the end plate is assumed to be 30 mm for two-dimensional model.
[10]
Conclusion
[12]
In this paper, a finite element simulation method is used to investigate the effect of thickness and material of end plates, sealant hardness, number and position of cells on the contact pressure distribution over the surface of the MEA. Twodimensional model is used instead of three-dimensional model and the results are compared with experimental results which were obtained by pressure sensitive films. It is concluded that increasing the flexural rigidity of the end plates leads to decrease in deflection of them. Increasing the flexural rigidity of end plates can be obtained by selecting suitable thickness and proper material. In addition, the other way to decrease deflection of the end plates is to reduce the applied torque on the bolts which can be accomplished using softer sealant. Furthermore, increasing the number of cell causes to have better contact pressure distribution over the MEA.
references
[9]
[11]
[13]
[14]
[15]
[16]
[17]
[18]
[19] [1] Asghari S, Shahsamandi MH, Ashraf Khorasani MR. Design and manufacturing of end plates of a 5 kW PEM fuel cell. Int J Hydrogen Energy 2010;35:9291e7. [2] Montanini R, Squadrito G, Giacoppo G. Experimental evaluation of the lamping pressure distribution in a PEM fuel cell using matrix-based piezoresistive thin-film sensors. In: XIX IMEKO World Congress fundamental and applied metrology September 6 11; 2009. Lisbon, Portugal. [3] Yu Fu, Ming Hou, Xiqiang Yan, Junbo Hou, Xiaokuan Luo, Zhigang Shao, et al. Research progress of aluminum alloy end plates for PEMFCs. J Power Sources 2007;166:435e40. [4] Patermarakis G, Papandreadis N. Effect of the structure of porous anodic Al2O3 films on the mechanism of their hydration and pore closure during hydrothermal treatment. Electrochim Acta 1993;38:1413e20. [5] Thompson GE. Porous anodic alumina: fabrication, characterization and applications. Thin Solid Films 1997;297:192e201. [6] Lai Xinmin, Liu Dong’an, Peng Linfa, Ni Jun. A mechanicaleelectrical finite element method model for predicting contact resistance between bipolar plate and gas
[20]
[21]
[22]
[23]
[24]
diffusion layer in PEM fuel cells. J Power Sources 2008;182:153e9. Zhou P, Wu CW, Ma GJ. Contact resistance prediction and structure optimization of bipolar plates. J Power Sources 2006;159:1115e22. Wu Zhiliang, Zhou Yuanyuan, Lin Guosong, Wang Shuxin, Hu S Jack. An improved model for predicting electrical contact resistance between bipolar plate and gas diffusion layer in proton exchange membrane fuel cells. J Power Sources 2008;182:265e9. Montanini R, Squadrito G, Giacoppo G. Measurement of the clamping pressure distribution in polymer electrolyte fuel cells using piezoresistive sensor arrays and digital image correlation techniques. J Power Sources 2011;196:8484e93. Zhou P, Lin P, Wu CW, Li Z. Effect of nonuniformity of the contact pressure distribution on the electrical contact resistance in proton exchange membrane fuel cells. Int J Hydrogen Energy 2011;36:6039e44. Zhang Lianhong, Liu Ying, Song Haimin, Wang Shuxin, Zhou Yuanyuan, Hu S Jack. Estimation of contact resistance in proton exchange membrane fuel cells. J Power Sources 2006;162:1165e71. Wen Chih-Yung, Lin Yu-Sheng, Lu Chien-Heng. Experimental study of clamping effects on the performances of a single proton exchange membrane fuel cell and a 10-cell stack. J Power Sources 2009;192:475e85. Wang Xinting, Song Ying, Zhang Bi. Experimental study on clamping pressure distribution in PEM fuel cells. J Power Sources 2008;179:305e9. Kusoglu A, Karlsson AM, Santare MH, Cleghorn S, Johnson WB. Mechanical response of fuel cell membranes subjected to a hygro-thermal cycle. J Power Sources 2006;161:987e96. Tang Y, Santare MH, Karlsson AM, Cleghorn S, Johnson WB. Stresses in proton exchange membranes due to hygrothermal loading. J Fuel Cell Sci Technol 2006;3:119e24. Kusoglu A, Karlsson AM, Santare MH, Cleghorn S, William BJ. Mechanical behavior of fuel cell membranes under humidity cycles and effect of swelling anisotropy on the fatigue stresses. J Power Sources 2007;170:345e58. Miller K. Testing elastomer for hyperelastic material models in finite element analysis. Axel Products Testing and Analysis Report. 2000. Pearson I, Pickering M. The determination of a highly elastic adhesive's material properties and their representation in finite element analysis. Finite Elem Anal Des 2001;37:221e32. Sasso M, Palmieri G, Chiappini G, Amodio D. Characterization of hyperelastic rubber-like materials by biaxial and uniaxial stretching tests based on optical methods. Polym Test 2008;27:995e1004. Gracia LA, Liarte E, Pelegay JL, Calvo B. Finite element simulation of the hysteretic behaviour of an industrial rubber. Application to design of rubber components. Finite Elem Anal Des 2010;46:357e68. Ghoreishy Mir Hamid Reza. Determination of the parameters of the Prony series in hyper-viscoelastic material models using the finite element method. Mater Des 2012;35:791e7. Jang WJ, Lee J, Woo CS, Kim BK, Lee SB. An experimental study and finite element analysis of weatherstrip. Int J Precis Eng Manuf 2011;12(No. 1):97e104. Yang LM, Shim VPW, Lim CT. A visco-hyperelastic approach to modelling the constitutive behaviour of rubber. Int J Impact Eng 2000;24:545e60. Amin AFMS, Alam MS, Okui Y. An improved hyperelasticity relation in modeling viscoelasticity response of natural and high damping rubbers in compression: experiments, parameter identification and numerical verification. Mech Mater 2002;34:75e95.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 1 ( 2 0 1 6 ) 3 0 6 2 e3 0 7 1
[25] Mullins L. Effect of stretching on the properties of rubber. Rubber Res 1947;16:275e89. [26] Boulanger P, Hayes M. Finite amplitude waves in MooneyRivlin and Hadamard materials, in topics in finite elasticity. International Center for Mechanical Sciences; 2001. [27] Yu Ha Na, Kim Seong Su, Do Suh Jung, Lee Dai Gil. Composite end plates with pre-curvature for PEMFC
3071
(polymer electrolyte membrane fuel cell). Compos Struct 2010;92:1498e503. € f Thomas, Ihonen Jari K. Modeling [28] Mikkola Mikko, Tingelo compression pressure distribution in fuel cell stacks. J Power Sources 2009;193:269e75.