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i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 8 ( 2 0 1 3 ) 7 7 0 4e7 7 1 4
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Numerical modeling and investigation of gascrossover effects in high temperature protonexchange membrane (PEM) fuel cells
Purushothama Chippar, Hyunchul Ju*
School of Mechanical Engineering, Inha University, 253 Yonghyun-Dong, Nam-Gu, Incheon 402-751,
Republic of Korea
a r t i c l e i n f o
Article history:
Received 14 April 2012
Received in revised form
24 July 2012
Accepted 29 July 2012
Available online 16 August 2012
Keywords:
High temperature proton exchange
membrane fuel cell (HT-PEMFC)
Polybenzimidazole (PBI)
Numerical modeling
Hydrogen crossover
Oxygen crossover
* Corresponding author. Tel.: þ82 32 860 731E-mail address: [email protected] (H. Ju).
0360-3199/$ e see front matter Copyright ªhttp://dx.doi.org/10.1016/j.ijhydene.2012.07.1
a b s t r a c t
A gas crossover model is developed for a high temperature proton exchange membrane
fuel cell (HT-PEMFC) with a phosphoric acid-doped polybenzimidazole membrane. The
model considers dissolution of reactants into electrolyte phase in the catalyst layers and
subsequent crossover of reactant gases through the membrane. Furthermore, the model
accounts for a mixed potential on the cathode side resulting from hydrogen crossover and
hydrogen/oxygen catalytic combustion on the anode side due to oxygen crossover, which
were overlooked in the HT-PEMFC modeling works in the literature. Numerical simulations
are carried out to investigate the effects of gas crossover on HT-PEMFC performance by
varying three critical parameters, i.e. operating current density, operating temperature and
gas crossover diffusivity to approximate the membrane degradation. The numerical results
indicate that the effect of gas crossover on HT-PEMFC performance is insignificant in
a fresh membrane. However, as the membrane is degraded and hence gas crossover
diffusivities are raised, the model predicts non-uniform reactant and current density
distributions as well as lower cell performance. In addition, the thermal analysis demon-
strates that the amount of heat generated due to hydrogen/oxygen catalytic combustion is
not appreciable compared to total waste heat released during HT-PEMFC operations.
Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights
reserved.
1. Introduction face another barrier, namely, the low tolerance of the anode
The application of perfluorosulfonic acid (PFSA) membranes,
such as DuPont’s Nafion� membranes typically used in proton
exchange membrane fuel cells (PEMFCs), is limited to low
temperatures (<90 �C) due to the stringent requirement for
membrane hydration to ensure good proton conductivity.
Therefore, PFSA membrane-based fuel cells suffers from
several issues raised by low temperature operation, such as
complicated water management requirements, high external
humidification, and cooling loads. Furthermore, PFSA
membrane fuel cells, particularly for residential applications,
2; fax: þ82 32 868 1716.
2012, Hydrogen Energy P23
platinum (Pt) catalyst to carbon monoxide (CO) which is
inevitably present in reformate fuel.
Recently, the operation of PEMFCs at elevated temperatures
(100 �Ce200 �C) has receivedmuchattention because of several
benefits, such as faster electrode kinetics, improved mass
transport, simple water management, and higher tolerance to
CO. Therefore, a high-temperature proton exchange fuel cell
(HT-PEMFC) is well suited for most distributed energy or
combined heat and power (CHP) applications in which
a hydrogen rich reformate gas is often used instead of pure
hydrogen. Themain focusofHT-PEMFC research resideson the
ublications, LLC. Published by Elsevier Ltd. All rights reserved.
Table 1 e HT-PEMFC model: governing equations.
Governing equations
Mass V$ðr u!Þ ¼ Sm (1)
Momentum Flow channels ðNavier� Stokes equationsÞ :�1= 3
2�V$ðru!u!Þ ¼ �Vpþ V$s (2)
Porous media ðDarcys equationsÞ :ru!¼ �ðK=nÞVp (3)
Species V$ð u!CiÞ ¼ V$�Deff
i VCi
�þ Si (4)
Charge Proton transport : V$�keffVFe
�þ SF ¼ 0 (5)
Electron transport : V$�seffVFs
�� SF ¼ 0 (6)
Energy V$�rCp u
!T� ¼ V$
�keffVT
�þ ST (7)
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developmentof alternativemembraneswhich canexhibit high
proton conductivity under low humidity conditions at the
elevated temperatures. One of the most promising candidates
is believed to be a phosphoric acid-doped polybenzimidazole
(PBI) membrane. Since Wainright et al. [1] first proposed the
use of phosphoric acid-doped PBImembranes for a HT-PEMFC,
considerable progress has been made in PBI membrane
development. Studies have reported good proton conductivity
[1], excellent thermal stability [2], and nearly zero electro-
osmotic drag [3]. In addition to membrane development,
several experimental efforts have been undertaken to investi-
gate the physiochemical properties of PBI membranes [4e8].
Also, several theoretical HT-PEMFC models have been
developed and introduced in the literature for understanding,
prediction, and optimization of key physical phenomena in
HT-PEMFCs [9e15]. Among these models, Cheddie and Mun-
roe [10] and Sousa et al. [15] account for the effects of gas
solubility into the phosphoric acid/PBI electrolyte. Cheddie
and Munroe [10] presented a two-dimensional (2D),
isothermal HT-PEMFC model wherein hydrogen and oxygen
dissolution into phosphoric acid of catalyst layers (CLs) were
taken into account. However, their model assumed CLs to
comprise only liquid phase electrolyte (phosphoric acid) and
solid-phase electron conducting regions, neglecting gas-phase
reactant transport through CLs. As a result, their numerical
predictions significantly overestimated mass transport loss in
the CLs. Sousa et al. [15] treated CLs as spherical agglomerate
porous structures and applied the CLmodel to a 2D isothermal
HT-PEMFC model. Their numerical predictions indicate that
an optimumphosphoric acid volume fraction in a CL is around
30%e55%. Most recently, Chippar and Ju [16] developed
a three-dimensional non-isothermal HT-PEMFC model and
investigated the impact of a coolant flow rate on multi-
dimensional distributions of species, temperature, and
current density as well as overall cell performance. However,
hydrogen and oxygen crossover through PBI membrane was
not considered in their model.
In this study, gas crossover phenomena in HT-PEMFCs are
newly modeled and implemented into the previous HT-PEMFC
model [16]. Previously, Nam et al. [17] developed the gas cross-
over model for low temperature- (LT-) PEMFCs and numerically
studied the influences of hydrogen and oxygen crossover on
two-phase transportandwateraccumulation insidecellsaswell
as overall cell performance. They also simulated decaying
polarization curves due to membrane degradation using gas
crossover evolution datameasured during long-term LT-PEMFC
operations. We adopted the gas crossover model of Nam et al.
[17] and modified it for HT-PEMFCs. The gas crossover model
rigorously accounts for hydrogen/oxygen dissolution into the
aqueous electrolyte phase and subsequent diffusion through
phosphoric acid-doped PBI membranes in HT-PEMFCs. Note
that, although Cheddie and Munroe [10] and Sousa et al. [15]
modeled the dissolution of the reactant gas into aqueous phos-
phoric acid, the effects of gas crossover through themembrane
on the thermal-electrochemical behavior of cells andoverall cell
performancewere not taken into consideration in theirmodels.
Due to hydrogen crossover from the anode side, a mixed
potential occurs on the cathode side,whereas oxygen crossover
results in hydrogen/oxygen catalytic combustion on the anode
side, which possibly redistributes species and charge profiles
inside HT-PEMFCs and consequently downgrades overall cell
performance. The gas crossover model presented in this paper
entails a detailed account of these gas crossover impacts.
2. Numerical model
The proposed three-dimensional, two-phase, non-isothermal,
electrochemical-transport coupled HT-PEMFC model is based
on our previous HT-PEMFC model [16], and it is further
improved by accounting for the effects of gas dissolution and
subsequent crossover through the PBI membrane. The model
considers all sub-components of an HT-PEMFC: membrane,
catalyst layers (CLs), gas diffusion layer (GDLs), gas channels
(GCs), and bipolar plates (BPs). The governing equations of the
HT-PEMFCmodel, relevant source terms, and electrochemical
properties at the anode and cathode CLs are summarized in
Tables 1e3, respectively. Readers are referred to our previous
publication [16] for a more detailed description of the model.
2.1. Model assumptions
The specific assumptions invoked in the present model are:
(1) Incompressible and laminar flow due to small pressure
gradient and flow velocities.
(2) Ideal gas mixture due to low pressure and high tempera-
ture HT-PEMFC operation.
(3) Isotropic and homogeneous porous layers (GDLs, CLs)
characterized by effective porosity and permeability.
2.2. Transport properties
The diffusivity of species i, in the gasmixture is defined as [18]
Di;M ¼ 1�xiPj¼n
jjsi
xj
Di;j
;where Di;j ¼1:013�10�7T1:75
p�c1=3i þc
1=3j
�2�
1Mi
þ 1Mj
�1=2
cH2¼7:07; cH2O ¼ 12:7; cN2
¼17:9; cO2¼ 16:6:
(22)
Table 2 e HT-PEMFC model: source/sink terms.
Sourceterms
Anode CL Cathode CL
H2
SH2¼ � ja
2F� nxover
H2
dCL� 2
nxoverO2
dCL(8)
O2
SO2¼ jc
4F� nxover
O2
dCL� 12
nxoverH2
dCL(9)
H2O
SH2O ¼ 2nxoverO2
dCL(10a) SH2O ¼ � jc
2Fþ nxover
H2
dCL(10b)
Mass
Sm ¼Xk
Sk ¼ �MH2
ja2F
þ�MO2
nxoverO2
�MH2nxoverH2
�dCL
(11a) Sm ¼Xk
Sk ¼ MO2
jc4F
�MH2Ojc2F
þ�MH2
nxoverH2
�MO2nxoverO2
�dCL
(11b)
Charge
SF ¼ ja (12a) SF ¼ jc (12b)
Heat
ST ¼ jahþ I2
keffþ DHH2
2nxoverO2
dCL(13a) ST ¼ jchþ I2
keffþ jc
dUo
dTT� IxoverH2
dCL
�hþ dUo
dTT
�(13b)
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Note that, in addition to molecular diffusion as defined in
the Eq. (22), species diffusion transport can also be controlled
by the Knudsen diffusion effect due to molecular-to-wall
collision. According to the kinetic theory, the Knudsen diffu-
sivity can be expressed as
Di;K ¼ dp
3
ffiffiffiffiffiffiffiffiffi8RTpMi
s: (23)
Table 3 e HT-PEMFC model: electrochemical properties.
Description Anode CL
Exchange current density � ratio of
the reaction surface to the
CL volume, airef0 (A/m3)
1.0 � 109
Reference H2/O2 molar
concentration, (mol/m3)
40.88
Transfer coefficients, a aa ¼ 0:5
Thermodynamic equilibrium
potential, U0 (V)
0
Surface overpotential,h (V)
fs � fe � U0 ðwith fs ¼ 0ÞTransfer current density, j (A/m3)
ja ¼ airef0;a
CH2
CH2;ref
!1=2�aa þ ac
RuTF
Electrochemical reactions :Xk
siMzi ¼ ne�;where
8<:
Mi ¼ chemicalsi ¼ stoichiomn ¼ number of
Hydrogen oxidation reactionðHORÞat the anode side : H2 � 2Hþ ¼
Oxygen reduction reactionðORRÞat the cathode side : 2H2O�O2 �
Therefore, the effective diffusivity of species in porous
media is obtained by combining both the molecular and
Knudsen diffusion effects with the effects of porosity and
tortuosity of the porous medium using the Bruggemann
correlation [19]:
Di ¼ 3n
�1
Di;Mþ 1Di;K
��1
: (24)
Cathode CL
1.0 � 104
40.88
ac ¼ 0:5
1:1669� 0:24� 10�3ðT� 373:15Þ (14)
(15) fs � fe � U0 ðwith fs ¼ VcellÞ (16)
h
�(17) jc ¼ �airef0;c
CO2
CO2;ref
!3=4
exp
�� ac
RuTFh
�þ IxoverH2
dCL(18)
formula of species ietry coefficientelectrons transferred
(19)
2e� (20)
4Hþ ¼ 4e� (21)
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The dissolution of species in the aqueous electrolyte phase
and their subsequent diffusion are described below. Accord-
ing to Cheddie and Munroe [10], the solubility and diffusivity
of oxygen in a concentrated phosphoric acid can be expressed
in terms of theweight percentage of phosphoric acid,mPA, and
temperature as
HPAO2
¼ 0:1exp
266664
�257:13ðmPAÞ2�431:08ðmPAÞ þ 178:45
�
þ�� 93500ðmPAÞ2þ156646ðmPAÞ � 64288
�T
377775; (25)
DPAO2
¼ 10�9exp
266664
�� 192:55ðmPAÞ2þ323:55ðmPAÞ � 125:61
�
þ�62010ðmPAÞ2�105503ðmPAÞ þ 40929
�T
377775: (26)
Henry’s constant of oxygen in the phosphoric acid-doped
PBI membrane can be obtained as a function of the volume
fraction of phosphoric acid in the membrane, 3PA as [10]
HPBIO2
¼ � 3PA�1:945h
HPAO2
þ 5:79�1� � 3
PA�1:8�i
: (27)
The 3PA in turn depends on the doping level of phosphoric
acid in the membrane, X as [10]
3PA ¼
4:81X� 2
þ 1
�1
: (28)
The X in the above equation can be computed based on the
phosphoric acid concentration, M as [10]
X ¼ 0:012M3 � 0:2111M2 þ 1:2363Mþ 0:7119: (29)
On the other hand, the oxygen diffusion coefficient in the
phosphoric acid-doped PBI membrane can be obtained by
Bruggemann’s relation as [10]
DPBIO2
¼ � 3PA�1:8
DPAO2: (30)
The dissolved concentration of oxygen at the gas/electrolyte
interface in the cathode CL is determined from the partial
pressure of oxygen pO2using Henry’s law as follows:
CPBIO2
¼ HPBIO2
pO2¼ HPBI
O2
�CgO2 ;memRT
�: (31)
Due to lack of studies regarding hydrogen dissolution
into concentrated phosphoric acid, the diffusivity and solu-
bility of hydrogen are assumed to be two times and four
times larger than those of oxygen, respectively, i.e. based on
the transport behavior of hydrogen and oxygen in water
systems [10]:
DPAH2
¼ 2DPAO2; (32)
HPAH2
¼ 4HPAO2: (33)
The proton conductivity of the phosphoric acid-doped PBI
membrane is correlated to the doping level and temperature
as follows [10]:
k ¼ 100T
exp
8:0219�
�2605:6� 70:1X
T
�: (34)
The effective proton conductivity in the CLs is obtained by
combining the effects of the volume fraction of themembrane
phase and tortuosity of the porous medium by using Brugge-
mann’s correlation:
keff ¼ 31:5mck: (35)
2.3. Gas crossover model and relevant source terms
The gas crossover model accounts for the influences of
hydrogen crossover (from the anode to cathode) and oxygen
crossover (from the cathode to anode) on electrochemical
processes and the resultant overall cell performance. The gas
crossover model has been described in detail in a previous
study [17] and hence only a brief summary is repeated here.
The hydrogen crossover through the membrane causes
a mixed potential at the cathode CL due to facile hydrogen
oxidation kinetic and large surface overpotential at the
cathode. Therefore, the final form of the ORR kinetic expres-
sion can be determined as Eq. (18) in Table 3 where the second
term in the right-hand side of Eq. (18) represents the effect of
the hydrogen crossover. Under the assumption that crossed
hydrogen is uniformly and completely oxidized in the cathode
CL, the hydrogen crossover current density, can be defined as
below:
IxoverH2¼ 2Fnxover
H2¼ 2FDPBI
H2
CPBIH2
���aCL
dmem: (36)
On the other hand, the oxygen crossover through the
membrane leads to catalytic hydrogen/oxygen combustion in
the anode CL due to small potential difference between the
solid and electrolyte phases at the anode. The influences of
the hydrogen and oxygen crossover on mass, species
(hydrogen, oxygen, andwater), and energy balance are seen in
their source/sink terms in Table 2.
2.4. Numerical implementation, computational domain,and boundary conditions
The HT-PEMFC model described in Section 2 is numerically
implemented in a commercial computational fluid dynamics
(CFD) program, FLUENT, basing on its user defined functions
(UDF). The convergence criteria for all species and energy
calculation residuals are set to 10�8. Fig. 1 shows the mesh
configuration of the simple single-straight channel geometry.
The physical properties and, cell dimensions and operating
conditions are given in Tables 4 and 5, respectively. The
isothermal boundary condition is applied to the anode and
cathode wall of the computational cell for temperature
calculations. In addition, the no-flux condition is applied to
the outer faces for flow and species transport equations
except for the channel inlets and outlets. The inlet velocities
in the anode and cathode GCs can be expressed as functions of
Fig. 1 e Mesh configuration of three-dimensional, single-
channel HT-PEMFC geometry.
Table 5 e Cell dimensions and operating conditions.
Description Value
Cell length 0.1 m
Anode/cathode channel/rib width 1 � 10�3 m
Anode/cathode channel height 0.7 � 10�3 m
Thickness of the anode/cathode GDLs 250 � 10�6 m
Thickness of the anode/cathode CLs 10 � 10�6 m
Thickness of the membrane 70 � 10�6 m
Anode/cathode inlet pressure 1.0 atm
Anode stoichiometry 2.0 (Pure H2)
Cathode stoichiometry 2.0 (Air)
Anode/cathode inlet temperature 373 K, 453 K
RH of the anode/cathode inlet 0.0%
Phosphoric acid doping level 6.2
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the anode and cathode stoichiometric ratios, the operating
current density, the cross-sectional areas of the anode and
cathode GCs, and the concentrations of hydrogen and oxygen,
which are functions of the anode/cathode inlet pressure and
temperature:
uin;a ¼ xaðI=2FÞAmem
CH2Aa;chan
and uin;c ¼ xcðI=4FÞAmem
CO2Ac;chan
: (37)
3. Results and discussion
To examine the effects of gas crossover on HT-PEMFCs, we
assessed the effects of three critical parameters, namely,
operating current density, operating temperature, and gas
crossover diffusivity itself. Regarding the effect of operating
current density, it is evident that the impact of gas crossover is
Table 4 e Physical properties.
Description Value
Porosity of GDL, CL 0.6, 0.3
Volume fraction
of ionomers in CL
0.4
Permeability of GDL, CL 1 � 10�12, 1.0 � 10�13 m2
Electronic conductivity
in the GDL, CL, BP
1250, 300, 14000 S m�1
Specific heat capacities
of GDL, CL, membrane, BP
568, 3300, 1650, 2930 J kg�1 K�1
Specific heat capacities
of species e H2, O2, N2, H2O
14430, 929, 1042, 1968 J kg�1 K�1
Thermal conductivities
of GDL, CL, membrane, BP
1.2, 1.5, 0.95, 20 W m�1 K�1
Thermal conductivities
of species e H2, O2, N2, H2O
0.2040, 0.0296, 0.0293,
0.02378 W m�1 K�1
more significant at lower current density operation due to the
lower reactant consumption rate and resultant higher
concentration in the CL that leads to a higher dissolution rate
of the reactant gas into the aqueous electrolyte phase. The
hydrogen and oxygen crossover diffusivities given by Cheddie
and Munroe [10] imply that the degree of gas crossover
through a phosphoric acid-doped PBI membrane is consider-
ably altered by operating temperature. Therefore, the oper-
ating temperature is another critical factor to control the gas
crossover behavior inside an HT-PEMFC. Finally, several
degradation mechanisms of the PBI membrane have been
reported in the literature, such as chemical degradation [20],
thermal degradation [21] and phosphoric acid evaporation
[22]. In particular, it should be noted that the phosphoric acid
loss due to evaporation not only decreases the membrane
conductivity but also increases the gas crossover diffusivities
for hydrogen and oxygen [10]. Although all of thesemembrane
degradationmechanisms appear to be highly localized, due to
the lack of experimental data on degradations, we assume the
membrane to be degraded uniformly; thus, the gas crossover
diffusivity is also uniformly raised as a function of the degree
of membrane degradation.
The parametric study was carried out at two operating
temperatures (100 �C and 180 �C) under various operating
current densities and hydrogen/oxygen crossover diffusiv-
ities. Four different cases of gas crossover diffusivity are
defined here. Case 1 assumes that the membrane is perfectly
impermeable to hydrogen and oxygen; hence, their crossover
diffusivities are set to zero. Case 2 represents the case of
a fresh phosphoric acid-doped PBI membrane, and the cross-
over processes for hydrogen and oxygen are approximated
using the crossover diffusivities given by Cheddie andMunroe
[10]. To consider a degradedmembrane, the hydrogen/oxygen
crossover diffusivities were further raised by one and two
orders of magnitude for cases 3 and 4, respectively.
Fig. 2 shows the hydrogen and oxygen concentration
profiles in the anode and cathode CLs for cases 1 to 4 at the
operating current density of 0.2 A cm�2 based on the operating
temperatures of 100 �C and 180 �C. As shown in Fig. 2(a) and
(b), the hydrogen concentration under the land region is lower
than that under the channel region due to the longer transport
path from the anode flow channel. In a comparison of cases 1
to 4 for each operation temperature, the hydrogen distribu-
tions for cases 1, 2, and 3 are almost identical, indicating that
Fig. 2 e Hydrogen concentration contours (in mol mL3) in the anode CL and oxygen concentration contours (in mol mL3) in
the cathode CLs at an operating current density of 0.2 A cmL2: (a) Hydrogen; T[ 100 �C, (b) Hydrogen; T[ 180 �C, (c) Oxygen;
T [ 100 �C and (d) Oxygen; T [ 180 �C.
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 en e r g y 3 8 ( 2 0 1 3 ) 7 7 0 4e7 7 1 4 7709
the effect of crossover though the fresh membrane is negli-
gible (case 2), and even a ten-fold increase in the hydrogen-
permeation coefficient due to membrane degradation is still
acceptable for HT-PEMFC operations (case 3). However, more
severe hydrogen depletion is observed in case 4, which can be
attributed to a combined result of the higher degree of
hydrogen crossover from the anode through the membrane
and the higher rate of catalytic hydrogen/oxygen combustion
at the anode CL driven by stronger oxygen crossover from the
cathode in case 4. In addition, higher hydrogen depletion was
predicted at the higher operating temperature because the
amount of hydrogen crossover increases with temperature.
The same trend is observed in the oxygen concentration
contours in the cathode CL in Fig. 2(c) and (d) where oxygen
depletion near the cathode outlet region is more severe with
a higher degree of membrane degradation (case 4) and/or
a higher operating temperature (180 �C). Note that the severe
oxygen depletion in case 4 is attributed to both its higher
oxygen crossover rate from the cathode to anode aswell as the
higher hydrogen crossover from the anode to cathode that
leads to additional ORR andmixed potential at the cathode CL.
Fig. 3(a) shows the local current density distributions in the
membrane for cases 1 to 4 at the operating current density of
0.2 A cm�2 and the operating temperature of 100 �C. In all
cases, the local current density near the land region is lower
than near the channel region along the in-plane direction (Z ).
Along the cathode flow direction (Y ), the local current density
continuously decreases toward the cathode outlet. These
trends indicate that oxygen depletion is the sole factor in
determining the current density distribution for all the cases.
In a comparison of cases 1 to 4, the current density distribu-
tions for cases 1, 2, and 3 are almost identical, indicating that
the degree of gas crossover up to a ten-fold increase in the gas-
permeation coefficient due to membrane degradation has
a negligible influence on HT-PEMFC performance. However,
spatial non-uniformity in the current density profile is clearly
increased in case 4 due to the higher degree of gas crossover
through the membrane. Fig. 3(b) displays the local current
density contours at 180 �C. As compared with Fig. 3(a), the
local current densities near the cathode outlet are reduced
due to the higher degree of hydrogen and oxygen crossover at
the elevated temperature.
Fig. 4 e Crossover current density distribution (in A mL2) in the membrane at an operating current density of 0.2 A cmL2:
(a) T [ 100 �C and (b) T [ 180 �C.
Fig. 3 e Local current density distribution (in A mL2) in the membrane at an operating current density of 0.2 A cmL2:
(a) T [ 100 �C and (b) T [ 180 �C.
i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 8 ( 2 0 1 3 ) 7 7 0 4e7 7 1 47710
Fig. 5 e Cathode overpotential distribution (in volts) in the CL at an operating current density of 0.2 A cmL2: (a) T [ 100 �Cand (b) T [ 180 �C.
Fig. 6 e Overall polarization curves for cases 1e4 at the
operating temperatures of 100 �C and 180 �C.
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To analyze the degree of hydrogen crossover, the hydrogen
crossover current density was calculated by Eq. (36) and
plotted in Fig. 4 for the same simulation cases (at 0.2 A cm�2
under two operating temperatures of 100 �C and 180 �C). For allcases, the hydrogen crossover current density decreases
toward the anode downstream because the hydrogen
concentration in the anode CL is high near the anode inlet and
continuously depleted along the flow direction by not only
HOR but also hydrogen permeation through the membrane
and the hydrogen/oxygen catalytic combustion due to the
oxygen crossover. In a comparison of cases 2 to 4, the
hydrogen crossover current densities of case 4 are roughly two
orders of magnitude larger than those of case 2, which clearly
indicates that the amount of hydrogen crossover flux is
directly proportional to the considered hydrogen crossover
diffusivity. In addition, much higher hydrogen crossover
current density was predicted with the higher operating
temperature (180 �C) since the hydrogen crossover diffusivity
is a function of increasing temperature.
Fig. 5 shows the cathode overpotential distributions in the
cathode CL for cases 1 to 4 at the operating temperatures of
100 �C and 180 �C. The cathode overpotential increases toward
the land region and cathode downstream due to lower local
oxygen concentrations there as seen in Fig. 2(c) and (d). More
importantly, a comparison of the 100 �C and 180 �C cases
indicates that operating the cell at the higher temperature
significantly reduces the cathode overpotential, although the
available oxygen concentration for ORR in the cathode CL is
lower at 180 �C (see Fig. 2(d)). This is mainly due to the
enhanced electrochemical kinetics of ORR at the elevated
operating temperature.
Fig. 6 shows the effects of hydrogen and oxygen crossover
through the membrane on cell polarization curves at two
different operating temperatures (100 �C and 180 �C). First,
superior cell performance is achieved at the higher operating
temperature due to improved ORR kinetics, better proton
conductivity, and more efficient mass transport with
increasing temperature. Further, the polarization curves
clearly demonstrate that the impact of gas crossover is more
significant at lower current densities, because the hydrogen
and oxygen concentrations remaining in the CLs are higher
under lower current density operations. In addition, the
polarization curves for cases 1 to 3 are similar to each other at
both temperatures (100 �C and 180 �C), which means that
a ten-fold increase in the gas-permeation coefficient (case 3) is
acceptable for HT-PEMFC operations under wide ranges of
operating current density and temperature. However, a more
pronounced effect of gas crossover is seen in case 4, particu-
larly at the higher operating temperature (180 �C). These
results imply that careful attention to suppress gas crossover
is required for low current density and/or high temperature
operations.
Tables 6 and 7 summarize the overall heat balance and the
individual heat sources for cases 1 to 4 under the operating
current density of 0.2 A cm�2 at 100 �C and 180 �C, respectively.The simulation results show that the largest part of the total
waste heat release is due to irreversible ORR reaction at the
cathode, that is, roughly 70% of the total heat generation. In
Table 6 e Summary of energy balance results under operating current density of 0.2 A cmL2 at 100 �C.
Case 1 Case 2 Case 3 Case 4
(1) Anode CL Irreversible reaction heat, [W] ST;irrev;a ¼ RV
j:hdV 0.00344 (0.985%) 0.00345 (0.985%) 0.00345 (0.977%) 0.00348 (0.903%)
Ohmic joule heating, [W] ST;joule;a ¼ RV
I2
keffdV
0.00399 (1.141%) 0.00399 (1.139%) 0.00399 (1.129%) 0.00400 (1.038%)
H2/O2 catalytic combustion heat [W] SxoverT;a ¼ DH SxoverO20.0 0.0000376 (0.011%) 0.000374 (0.106%) 0.00352 (0.911%)
(2) MembraneOhmic joule heating, [W] ST;joule;mem ¼ R
V
I2
keffdV
0.02678 (7.659%) 0.02675 (7.643%) 0.02675 (7.572%) 0.02675 (6.935%)
(3) Cathode CL Irreversible reaction heat, [W] ST;irrev;c ¼RV
j:hdV 0.26724 (76.43%) 0.26740 (76.41%) 0.26883 (76.10%) 0.28304 (73.37%)
Ohmic joule heating, [W] ST;joule;c ¼RV
I2
keffdV
0.01232 (3.524%) 0.01231 (3.516%) 0.01232 (3.487%) 0.01245 (3.227%)
Mixed potential and entropic heat due to
hydrogen crossover, [W] SxoverT;c ¼ �IxoverH2
dCL
�hþ T
dU0
dT
� 0.0 0.000152 (0.043%) 0.00152 (0.428%) 0.01489 (3.859%)
Entropy heat, [W] ST;rev;c ¼RVj$
�TvU0
vT
�dV
0.03588 (10.26%) 0.03589 (10.26%) 0.03605 (10.21%) 0.03763 (9.755%)
Sum (1)þ(2)þ(3), [W] 0.3497 0.3499 0.3533 0.3858
Table 7 e Summary of energy balance results under operating current density of 0.2 A.cmL2 at 180 �C.
Case 1 Case 2 Case 3 Case 4
(1) Anode CL Irreversible reaction heat, [W] ST;irrev;a ¼ RV
j:hdV 0.00235 (0.846%) 0.00236 (0.844%) 0.00238 (0.801%) 0.00253 (0.568%)
Ohmic joule heating, [W] ST;joule;a ¼ RV
I2
keffdV
0.00202 (0.727%) 0.00202 (0.722%) 0.00202 (0.683%) 0.00208 (0.465%)
H2/O2 catalytic combustion heat [W] SxoverT;a ¼ DH SxoverO20.0 0.00023 (0.084%) 0.00226 (0.763%) 0.01562 (3.493%)
(2) MembraneOhmic joule heating, [W] ST;joule;mem ¼ R
V
I2
keffdV
0.01165 (4.193%) 0.01164 (4.160%) 0.01165 (3.929%) 0.01178 (2.639%)
(3) Cathode CL Irreversible reaction heat, [W] ST;irrev;c ¼RV
j:hdV 0.21214 (76.33%) 0.21292 (76.10%) 0.21996 (74.18%) 0.28598 (64.07%)
Ohmic joule heating, [W] ST;joule;c ¼RV
I2
keffdV
0.00623 (2.241%) 0.00623 (2.225%) 0.00629 (2.122%) 0.00725 (1.625%)
Mixed potential and entropic heat due
to hydrogen crossover, [W] SxoverT;c ¼ �IxoverH2
dCL
�hþ T
dU0
dT
� 0.0 0.00072 (0.258%) 0.00717 (2.420%) 0.06686 (14.98%)
Entropy heat, [W] ST;rev;c ¼RVj$
�TvU0
vT
�dV
0.04354 (15.669%) 0.04367 (15.607%) 0.04476 (15.10%) 0.05426 (12.156%)
Sum (1)þ(2)þ(3), [W] 0.2779 0.2798 0.2964 0.4463
i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 8 ( 2 0 1 3 ) 7 7 0 4e7 7 1 47712
addition, it should be noted that the heat generated by
hydrogen/oxygen catalytic combustion on the anode side is
about 3.5% in the most severe gas crossover case in this study
(case 4 at 180 �C and 0.2 A cm�2). Therefore, the contribution of
the hydrogen/oxygen chemical reaction does not seem to be
significant to the total heat release during HT-PEMFC opera-
tions, even when two orders of magnitude greater gas cross-
over diffusivities are considered.
4. Conclusions
In this study, a gas crossover model that considers the
dissolution of hydrogen/oxygen into the electrolyte phase and
subsequent diffusion through a phosphoric acid-doped PBI
membrane was developed and incorporated into a HT-PEMFC
model developed in an earlier study [16]. The main interest of
this study is to numerically assess the impact of gas crossover
on HT-PEMFC performance. The gas crossover model rigor-
ously accounts for the major outcomes of hydrogen and
oxygen crossover, i.e. a mixed potential at the cathode CL and
the hydrogen/oxygen catalytic combustion at the anode CL.
The numerical results show that the gas crossover has
a negligible influence on overall cell performance in a fresh PBI
membrane (case 2) and a moderately degraded membrane
(case 3), which was assumed to have one order of magnitude
higher crossover diffusivities than those of the fresh
membrane. However, the effect of gas crossover begins to
appear in more a severely degraded membrane with two
orders of magnitude larger gas crossover diffusivities (case 4).
A comparison of case 4 with cases 1 to 3 clearly shows that the
increased effect of gas crossover increases the degree of non-
uniformity in the hydrogen, oxygen, and current density
distributions. In addition, the simulation results for case 4
indicate that gas crossover is more detrimental to cell opera-
tion at a higher operating temperature and/or lower current
density due to more facile crossover of hydrogen and oxygen
with elevated temperature and due to higher reactant
concentration in the CL with lower current density. Finally,
the thermal analysis carried out in this study demonstrated
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 en e r g y 3 8 ( 2 0 1 3 ) 7 7 0 4e7 7 1 4 7713
that the heat generated via hydrogen/oxygen catalytic
combustion at the anode CL is not significant, occupying only
3.5% of the total waste heat release in the worst gas crossover
case in this study (case 4 at 180 �C and 0.2 A cm�2). This paper
contributes to enhancing the fundamental understanding of
the gas crossover phenomena occurring during HT-PEMFC
operation. As an extension of this work, our efforts are
underway to numerically study the effects of local heteroge-
neous gas crossover due to membrane pinhole formations.
Acknowledgment
This work was supported by the New & Renewable Energy
R&D program (grant no. 2010T100200501) of the Ministry of
Knowledge Economy of the government of the Republic of
Korea. The authors gratefully acknowledge this support.
Nomenclature
A area, m2
c specific heat, J kg�1 K�1
C molar concentration, mol m�3
Di mass diffusivity of species i, m2 s�1
F Faraday constant, 96487 C mol�1
H Henry’s constant, mol m�3 atm�1
i0 exchange current density, A m�2
I operating current density, A m�2
j transfer current density, A m�3
K hydraulic permeability, m2
M molecular weight, kg mol�1
p partial pressure, Pa
Q heat, watt
R universal gas constant, 8.314 J mol�1 K�1
S source term in the conservation equation
T temperature, K
u! fluid velocity and superficial velocity in a porous
medium, m s�1
U0 thermodynamic equilibrium potential, V
Vcell cell potential, V
X doping level
Greek symbols
a transfer coefficient
3 porosity
3mc volume fraction of the ionomer phase in the CL
f phase potential, V
h overpotential, V
m viscosity, kg m�1 s�1
r density, kg m�3
s viscous shear stress, N m�2
k ionic conductivity, S m�1
x stoichiometry flow ratio
Superscripts
e electrolyte
eff effective value in the porous region
g gas
ref reference value
Subscripts
a anode
c cathode
CL catalyst layer
GC gas channel
GDL gas diffusion layer
H2 hydrogen
i species index
in channel inlet
m mass equation
mem membrane
O2 oxygen
u momentum equation
w water
F potential equation
0 standard condition, viz., 298.15 K and 101.3 kPa
(1 atm)
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