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The influence of permeability changes for a 7-serpentine channel pem fuel cell performance

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The inﬂuence of permeability changes for a 7-serpentinechannel pem fuel cell performance
Elena Carcadea
a,
*, D.B. Ingham
b
, I. Stefanescu
a
, R. Ionete
a
, H. Ene
c
a
National R & D Institute for Cryogenics & Isotopic Technologies, 240050 Rm.Valcea, Romania
b
University of Leeds, Centre for Computational Fluid Dynamics, LS2 9JT Leeds, UK
c
Institute of Mathematics of the Romanian Academy, 010702 Bucharest, Romania
a r t i c l e i n f o
Article history:
Received 22 February 2010Received in revised form27 July 2010Accepted 16 September 2010Available online 9 October 2010
Keywords:
PerformanceFuel cellPermeabilityNumerical simulation
a b s t r a c t
The performance of a fuel cell is determined by several parameters, which describe thefundamental, electrochemical and physical properties of the fuel cell layers, operationalconditions, geometry/structure of the ﬂow ﬁeld. One of these parameters is the perme-ability of the porous layers.The paper presents results obtained for different cases in which we vary the permeabilityof the gas diffusion/catalyst layers of a 7-serpentine channel fuel cell. Simulations havebeen carried out for permeability’s values 10
9
to 10
12
(m
2
), in order to investigate theinﬂuence of this parameter on the water formation and transport. Taking into accountsome results related to: water mass fraction distributions at the interface between theanode/cathode and the membrane, water content, liquid water activity and currentdensity, we obtained a range for the optimum permeability (10
12
to 10
10
). The main goalwas to obtain an optimum value of the permeability that will lead to a uniform distributionof reactant species and current density over the fuel cell active area.Copyright
ª
2010, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rightsreserved.
1. Introduction
The operation of a PEM fuel cell depends on numeroustransport phenomena (charge-transport and multi-compo-nent, multi-phase ﬂow in porous media, heat and masstransfer) and on the different physical properties or operating parameters (permeability, porosity, relative humidity). Toincorporate all relevant phenomena that take place in thevarious fuel cell components, the model must be three-dimensional, non-isothermal, multi-component and multi-phase. In addition, the model should take into account chargetransfer, change of phase, electrochemical reactions. Thisresults in a highly complicated model. The transportprocesses then becomes signiﬁcantly more complicated dueto the coupled ﬂow of liquid water and gaseous reactants intheporousmedia.Theliquidwatertransport(capillaryaction,evaporation and condensation), or the interaction betweenthe single- and two-phase zones effects on the gas transport/distribution are topics that remain to be explored. In two-phase porous systems, it is necessary to account for the effectof the many different variables (e.g. structure of porousmatrix, ﬂuid properties and pore blockage) can have on theﬂow of each phase.Recent studies indicate that the PEM fuel cell performancemay be strongly inﬂuenced by the permeability of the gasdiffusion layer (GDL). The permeability is a material propertythat characterizes the resistance to the ﬂow of gas exhibitedby the porous media. It is considered that the permeability of the GDL components is an important parameter that must beanalyzed for understanding the relationship between the GDLchemicalandstructural propertiesanditsfunctionin thePEMfuel cell.
*
Corresponding author
. Fax:
þ
40250732746.E-mail addresses: lili@icsi.ro, lilicarcadea@yahoo.com (E. Carcadea), D.B.Ingham@leeds.ac.uk (D.B. Ingham), Ene@imar.ro (H. Ene).
Available at www.sciencedirect.comjournal homepage: www.elsevier.com/locate/he
international journal of hydrogen energy 36 (2011) 10376
e
10383
0360-3199/$
e
see front matter Copyright
ª
2010, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.doi:10.1016/j.ijhydene.2010.09.050
The relative permeability depends on the parameters, suchas: the structure of the porous media, the saturation of themedia (
s
), the surface tension of the ﬂuid (
s
), the contact angleof the ﬂuid with the solid phase (
q
c
), and the history of ﬂowthroughthemedia.Typically,whenaparameterdependsonsomany variables it is simpliﬁed to a more manageable expres-sion which captures the most dominant interactions [1]. It hasbecome common practice in the porous media literature toassume therelativepermeability isafunctionof the saturationonly, and that is why the model used must describe the two-phaseﬂowinordertocapturetheformation,phasechangeandtransport of water, both in the liquid and gas phases.In a recent review on gas diffusion layer characterization,Mathias [2] considered that the permeability is a relevantparameter in the fuel cell performance. The same parameterwas analyzed analytically by Feser [3] and numerically byPharaoh [4], particularly with respect to PEM fuel cells thatemploy serpentine ﬂow ﬁelds.Valuesoftheporousmediapermeabilityvarygreatlyinthemodeling literature, spanning a few orders of magnitude,from10
19
m
2
[5]to10
6
m
2
[6].Experimentaldeterminationof through-plane permeability is reported by Mathias [2] to be of the order of 5
e
10
10
12
m
2
. Prasanna [7] report1
e
8
10
11
m
2
and show a signiﬁcant decrease if the Teﬂonloading of gas diffusion layer is increased.It is important to understand the link between the gasdiffusionlayerpermeabilityandthetransportorreactantsandwater (vapor and liquid) through this layer. There are manypapers that considered the two phase ﬂow modeling neededforthepredictionoftheliquidwaterandforminimizationofitsdetrimental effecton fuelcell performance. Namand Kaviany[8]havemodeledthetwo-phasetransportinthemulti-layeredcathode GDL using the unsaturated ﬂow theory (UFT), whichassumes a constant gas-phase pressure throughout, andwhich therefore neglects the gas ﬂow which is counter to theliquid ﬂow. The UFT theory was also used in this paper toaccount for a 7-serpentine channel PEM fuel cell performancewhen we vary the permeability of the porous media.
2. Mathematical model
e
governingequations
Using as a basis our one-phase model [9], a two-phase modelthat accounts for both the gas and liquid phases has beendeveloped. This model takes into consideration the phasechange inside the gas diffusion layer and this allows us toapproximate the liquid water transport in the fuel cell.The assumptions made in the two-phase model take intoaccounttheassumptionsmadeinthesinglephasemodelplusthe assumptions needed for implementing the phase changeof water:
the fuel cell operates under steady-state conditions
the ﬂow in the channels is considered to be laminar
themembraneisconsideredimpermeableforthegas-phase
the produced water is assumed to be in the liquid phase
no other species exist in the liquid phase, i.e. it consists of liquid water only
phase change occurs only within the porous electrodes.
2.1. Model equations
Fuel cell operation is governed by the conservation of mass,momentum, species and charge. Note that the Navier-Stokesequations, the species and charge transport equations, andthe electrochemical equations applied are presented in ourprevious work [9] and therefore are not repeated here. Thepresent paper accounts for the liquid water transport andformation in order to determine the inﬂuence of the satura-tion for the relative permeability. Therefore, the equationspresented in this section simply describe the aspects relatedto the two-phase ﬂow in a PEM fuel cell.Based on the above assumptions, the liquid water forma-tion and transport is governed by the following conservation
Fig. 1
e
Schematic of the bipolar plate and of fuel channelof the simulated PEM fuel cell.Table 1
e
Material properties and transport parameters.
Property Value
Hydrophobic GDL contact angle,
c
100
Hydrophilic CL contact angle,
c
70
Porosity of GCL 0.5Porosity of CL 0.5Mass Flow (Kg/s)Anode 1.5e
e
05Cathode 1.3e
e
04Mass fraction of H
2
Anode 0.9Cathode 0Mass fraction of H
2
OAnode 0.1Cathode 0.22Mass fraction of O
2
Anode 0Cathode 0.25
international journal of hydrogen energy 36 (2011) 10376
e
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10377
equation for the volume fraction of liquid water,
s
, or watersaturation [10]:
V
$
ð
r
l
u
!
l
s
Þ¼
S
l
(1)where the subscript
l
stands for liquid water,
r
l
is the liquiddensity,
s
is the saturation,
u
!
l
is the liquid water velocity andthe source term
S
l
is the condensation rate that is modeledaccording to the following formula:
S
l
¼
c
r
max
ð
1
s
Þ
p
wv
p
sat
RT M
w
;
H
2
O
;
½
s
r
l
(2)This source term in not applied in the PEM fuel cellmembrane,itisusedjustintheporouselectrodes.Theconstantcondensation rate
c
r
isgiven by theexpression:
c
r
¼
100
s
1
.Equation (2) models various physical processes related totwo-phase ﬂow that can take place inside a fuel cell(condensation, vaporization, capillary diffusion, and surfacetension).Many fuel cell models that account for two-phase transportin the gas diffusion layer are based on the unsaturated ﬂowtheory (UFT). UFT entailsanessential assumption, namely: thegas-phase pressure is constant across the porous medium;therefore the liquid-phase pressure simply becomes the nega-tive of capillary pressure between the gas and liquid phases:
p
c
¼
p
g
p
l
(3)It is assumed that the liquid velocity
u
!
l
is equivalent to thegas velocity inside the gas channel. Inside the highly resistantporous zones, the liquid-phase ﬂux is expressed by Darcy’slaw using the relative permeability of the individual phases:
u
!
l
¼
Kk
rl
m
l
V
p
l
(4)where
k
rl
represents the relative permeability of the liquidphase.In this paper, the GDL is assumed to be isotropic and therelative permeability of each individual phase is proportionalto the cube of the phase saturation:
k
rl
¼
s
3
;
k
rg
¼ð
1
s
Þ
3
(5)The unsaturated ﬂow approximation involves a constantgas-phase pressure across the porous media, and thus theliquid pressure can be expressed by:
p
l
¼
p
c
þ
p
g
;
V
p
l
¼
V
p
c
;
(6)Thus, using the above equations for replacing the convec-tive term in Eq. (1), we obtain:
V
$
r
l
Ks
3
m
l
d
p
c
d
s
V
s
¼
S
l
(7)
Fig. 2
e
Water mass fraction distribution at the interface between the anode CL and the membrane.
international journal of hydrogen energy 36 (2011) 10376
e
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10378
The capillary pressure between the gas and liquid phases iscomputed as a function of the saturation,
s
, by the formula:
p
c
¼
s
cos
ð
q
Þ
3
K
1
=
2
J
ð
s
Þ
(8)where the Leverett function,
J
(
s
), is given by:
J
ð
s
Þ¼
1
:
417
ð
1
s
Þ
2
:
120
ð
1
s
Þ
2
þ
1
:
263
ð
1
s
Þ
3
if
q
<
90
1
:
417
s
2
:
120
s
2
þ
1
:
263
s
3
if
q
>
90
(9)In the formula (8),
q
is the contact angle of the gas diffusionlayer and is dependent upon the hydrophilic
ð
0
<
q
<
90
Þ
orhydrophobic
ð
90
<
q
<
180
Þ
nature of the material used in theGDL fabrication. The surface tension
s
, for the liquid water airsystem is a constant,
s
¼
0
:
0625 N/m.Properties important in a two-phase ﬂow study and takeninto consideration in this paper, such as the molar ﬂux of water,
a
, and the osmotic drag coefﬁcient,
n
d
, are evaluated asfunctions of the water content,
l
, and water activity,
a
. Allthese parameters are given by the expressions [11]:
a
¼
p
wv
p
sat
þ
2
s
(10)
l
¼
0
:
043
þ
17
:
18
$
a
39
:
85
a
2
þ
36
:
0
a
3
0
<
a
114
þ
1
:
4
$
ð
a
1
Þ
for 1
a
3 (11)where the saturation pressure can be computed as follows:log
10
p
sat
¼
2
:
1794
þ
0
:
02953
$
ð
T
273
:
15
Þ
9
:
1837
10
5
ð
T
273
:
15
Þ
2
þ
1
:
4454
10
7
ð
T
273
:
15
Þ
3
(12)
n
d
¼
0
:
0028
$
l
þ
0
:
05
l
3
:
5
10
19
(13)
a
¼
n
d
$
j
k
F
D
w
V
C
w
(14)where
k
is the anode or cathode,
D
w
and
C
w
are the waterdiffusion coefﬁcient and water concentration across themembrane, respectively.The expressions for the water concentration and waterdiffusion coefﬁcient from Eq. (14) are given by [12]:
C
wk
¼
r
mo
dry
M
mo
dry
l
k
(15)
D
w
¼
D
l
exp
2416
1303
1
T
D
l
¼
10
10
l
<
2
D
l
¼
10
10
ð
1
þ
2
ð
l
2
ÞÞ
2
l
3
D
l
¼
10
10
ð
3
1
:
67
ð
l
3
ÞÞ
3
l
4
:
5
D
l
¼
1
:
25
10
10
l
4
:
5(16)where
r
m,
dry is the dry membrane density, and
M
m,
dry is themembrane equivalent weight.
Fig. 3
e
Water mass fraction distribution at the interface between the cathode CL and the membrane.
international journal of hydrogen energy 36 (2011) 10376
e
10383
10379
3. Numerical algorithm
The CFD software Fluent was used for all the numericalcalculations performed, using appropriately speciﬁedboundary conditions of the fuel cell under investigation inorder to analyze the ﬂuid ﬂow dynamics and fuel cell perfor-mance. Thus, the solution to the governing partial differentialequations is uniquely determined.The numerical simulation model is based on the SIMPLEC(semi-implicit method for pressure linked equations consis-tent)algorithmusingasegregatedsolverinFluent6.3[13].Thesource terms generated by the electrochemical reaction areinserted in to the mass, momentum and species conservationequations using a User Deﬁne Function (UDF) included in theFuel Cell Module. The coupled set of equations was solvediteratively until the relative error in each ﬁeld reacheda speciﬁc convergent standard (usually 10
8
).The geometry analyzed in this work has GDL, CL and MEAwidth
length equal to 10 cm
10 cm and on the bordersthere is a sponge rubber of size 1.52 cm (width)
1.52 cm(length). The length of the ﬂow path geometry is 49.17 cm foreach channel. The cross-sectional ﬂow area is 1.5 cm(height)
1.5 cm (width). The rib between two adjacentchannels is 1.3 cm (in the
y
-direction). The number of computational cells used in the model was about 2.2 millioncells. The geometry analyzed in this paper will be also testedexperimentally and a schematic of the bipolar plate and of fuel channel of the simulated PEM fuel cell is shown in Fig. 1.Table 1 summarizes few material properties and transportparameters used in the CFD calculations, which are assumedbased on the data that will be used in experiments. Thefeeding gases has a relative humidity of 2.65% for hydrogenat the anode side (fuel composition in mass fraction terms is0.9/0.1 for H
2
/H
2
O) and 65% for air in the cathode side(oxidant composition in mass fraction terms is 0.25/0.22/0.53for O
2
/H
2
O/N
2
) and entered the cell at 80
Celsius. From Table1, we can see that values for the mass ﬂow rate and massfraction were prescribed at the inlet of both the anode andcathode ﬂow channels in order to solve the problemdescribed.Regarding the boundary conditions for the outlets, sincethe reactant gas ﬂow channels are separate and generallyhave different pressures then pressure boundary conditionsare used. The interfaces between the layers are interior faces,and therefore no boundary conditions are prescribed. Dirich-let boundary conditions with constant values are set for thesolid phase potential on the lateral sides of the fuel cell (0V tothe anode and 0.5V to the cathode side) and zero ﬂux condi-tions are applied at the inlet and outlet.
Fig. 4
e
Liquid water activity in the membrane.
international journal of hydrogen energy 36 (2011) 10376
e
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