Simulation of current density distribution at PEMFC by using measured electrochemical andphysical properties of membrane
Takuto ARAKI, Takuya TANIUCHI and Kazuo ONDA
Department of Electrical and Electronic Engineering,
Toyohashi University of Technology
1-1 Hibarigaoka, Tempaku, Toyohashi, Aichi 441-8580, Japan
Abstract In order to grasp properly PEMFC power generation performances, it is necessary to know factors forwater management such as transmissivity and electro-osmotic coefficient of water vapor through the membrane,
and factors for power loss such as active and resistive overpotentials. In this study we have measured these factors
to analyze our experimental results of PEMFC power generation tests by our two-dimensional simulation code. It
considers simultaneously the mass, charge and energy conservation equations, and the equivalent electric-circuitfor PEMFC to give numerical distributions of hydrogen/oxygen concentrations, current density, andgas/cell-component temperatures. The numerical distributions of current density under various operating conditions agreed well with the measured distributions by segmented electrodes, which had grooves forhydrogen/oxygen supply and were mold in our test cell being electrically insulated. Hydrogen/oxygen concentration changes measured by gas chromatography along the gas supply grooves gave also the experimental current
distributions, which coincided almost with those by the segmented electrodes. Factors to correct the small difference between the measured and the calculated are also discussed from the stand point of the physical meaning of
the calculated results considering factors which are not taken into account in our code.
Keywords: Polymer Electrolyte Fuel Cell, Current density distribution, Membrane properties measurement, Numerical model of PEMFC
1.INTRODUCTION
Establishing precise numerical model of the proton exchange
membrane fuel cell(PEMFC) provides a useful method toestimate and improve the PEMFC performance. The firstobjective of the present investigation is to build a numericalmodel, which can describe the PEMFC performance such as a
V-i characteristics and current distributions inside the cell. For
building properly the PEMFC model, it is necessary to know thewater management factors such as transmissivity and electro-osmotic coefficient of water vapor through themembrane-electrode assembly (MEA), and power loss factors
such as activation and resistive overpotentials, since thesefactors have significant impacts on performance of PEMFC.
Nevertheless, the effects by these factors on PEMFC have notbeen cleared sufficiently. Then, obtaining the basic information
for PEMFC is a second objective of this study. The comparisonof measured and calculated current distributions is finallyconducted to verify the reliability of our numerical model. This
comparison between power generating experiments and numerical simulations on a same cell configuration has rarely beenreported before. The numerical distributions of current density
under various operating conditions agreed well with the measured distributions by segmented electrodes, which had grooves
for hydrogen/oxygen supply and were mold in our test cell being
electrically insulated. Hydrogen/oxygen concentration changes
measured by gas chromatography along the gas supply grooves
gave also the experimental current distributions, which coincided almost with those by the segmented electrodes. Factors tocorrect the small difference between the measured and thecalculated are also discussed from the standpoint of the physicalmeaning of the calculated results considering factors, which are
not taken into account in our code.
2. MEASUREMENTS OF MEMBRANE PROPERTIES ANDOVERPOTENTIALS
2.1 Over view of experimental apparatus
An overview of the experimental apparatus is illustrated inFig. 1 and is basically same as our previous paper[1]. Fuel
(Hydrogen or modified reformed fuel) and oxidant (Oxygen orAir) from gas cylinders are regulated by mass flow controllers,
and led to fuel cell(FC). The humidifiers placed before FC
control the dew-point temperatures of air and fuel. Electronic
resistive load (PLZ-152WA, Kikusui Elec. Co.) is connected to
FC instead of actual loading, and measuring the current andvoltage of FC. The MEA is set between the two electrodes andcarbon cloths are inserted between the MEA and separators as
diffusion electrodes. One side of which consist of segmented
electrodes with grooves for air or fuel supply and the segmented
Mass flow controller Heating water

Humidifier
Anode

PEFC

Mass flow controller

Humidifier
CathodOxydant
O221％,N278％etc

FuelElectronicloadExhaust gas

AC impedance meter

Figure 1

Experimental apparatus

Exchaust gas

M x ' = DDIF (Ca , DIF − C a ,MEA ) A d DIF(2)

M x ' = Tr (Ca ,MEA − Cc ,MEA ) A d MEA + M OSM
M x ' = DDIF (Cc ,MEA − Cc ,DIF ) A d DIF − M e

M x ' = hc (v )(Cc , DIF − Cc )A − M e

(3)
(4)
(5)

Me and MOSM are water flow rate by generated water and electro-osmosis. Then the electro-osmotic coefficient nd is expressedasMFnd = OSM.
(6)18 I
F is Faraday constant and I is the current through the cell. Fig. 4
shows the nd as a function of relative humidity. The electro-osmotic coefficient nd became large when the humidity
Diffusion electrode MEA
Ca,in
Ma,in
Ca,outMa,outha(ｖ) DDIFCa

Ca,DIF

Diffusion electrode

Tr

hc(ｖ)

Ca,MEA Cc,MEA
Mx
Me
MOSM

Anode channel

Cc,DIF

Cc,in
Mc,in

Cc
Cc,outMc,outCathode channel

Figure 2 Transport model of water vapor in PEFC

Diffusion coeff. DDIF and transmissivity Tr
of water vapor/m2･s-1

2.2 Water Vapor Diffusivity through Diffusion Electrodes, andTransmissivity and Electro-osmotic coefficient through MEA
To obtain the diffusive properties, the cell outlet averaged
humidities at both anode and cathode were measured with
supplying different humidities to both FC inlets. The pattern
diagram of this water (vapor) transport model is depicted in Fig.
2. The mass transfer coefficient at flow velocity v, h(v), increased as gas velocity v increasing, and the diffusive resistanceRh(v)=1/ h(v)·A was relatively much smaller than RDIF and RMEA,
so that the effect of the mass transfer can be ignored in our
experimental conditions.
Measured water vapor diffusivity for diffusion electrode DDIF
at cell temperature Tmem=50˚C and 60˚C are plotted in Fig. 3.
The diffusivity did not change against relative humidity. This
result is consistent with a simple following equation,( DDIF = f ⋅ D Air − H 2O ), where DAir-H2O is water vapor diffusivity inair, and f is effective porosity of diffusion electrodes. In the caseof out carbon cloth, f is calculated to be about 0.25.
Transmissivity through MEA Tr is also shown in Fig. 3. Our
measured Tr was about 7 times higher than the ones by Nguyen
et al.[2] and lower than ones by Yamada et al.[3]. However, thetendency of Tr, which rose as relative humidity increase, wasconsistent with those by Nguyen et al. So we approximate Tr as
to 7 times greater than those of Nguyen et al.
The electro-osmotic coefficient nd is obtained from theequations shown below and the measured DDIF and Tr.
(1)
M x ' = ha (v )(C a − C a , DiF )A

DAir-H2O

DDIF for Carbon Cloth(TDIF=60℃)

10-5(TDIF=50℃)

10

Tr for Nafion112(Yamada et al.,(Tmem=80℃))
Tr for MEA(Tmem=50℃)-6(Tmem=60℃)
Tr for Nafion117(Nguyen et al.,Tmem=60℃)(Tmem=50℃)

10-7
0.4

0.5

0.6

0.7

Relative humidity a

Figure 3 Change of diffusion coefficient DDIF andtransmissivity Tr
by temperature Tmem and relative humidity
1.2

Nafion117(Nguyen et al.)

1.0

Electro-osmotic coeff. ndelectrodes are mold in an electrically insulating plate for measuring current density distributions. Further information of theexperimental conditions will be explained in each section.

Present study(Tmem=60℃)

0.8

Present study(Tmem=50℃)

0.6
0.4
0.2

Nafion112(Yamada et al.,(Tmem=80℃,Carbon Paper))Nafion112(Yamada et al.,(Tmem=80℃,Carbon Cloth))

0.0
0.3

0.4

0.5

0.6

0.7

0.8

0.9

Relative humidity a

Figure 4 Change of electro-osmotic coefficient by temperature and relative humidity
increases. nd at MEA temperature of 50˚C agreed with that by
Nguyen et al. nd by Yamada who performed similar experimentwith us was almost same as ours, especially in a case of using
carbon cloth, however, the tendency of nd against humidity was
inverse.
2.3 Ionic Resistivity and Activation Overpotential of MEA
Resistive and activative overpotentials are important factorsof PEMFC power generation performance. The ionic resistance
was measured by AC impedance meter (SOLARTRON
SI1280B), supplying air with the same humidity to both anodeand cathode to avoid the movement of water through MEA. The
parameters for MEA resistance are the membrane temperature
Tmem and the flow relative humidity a. The resistivity did notdepend on the membrane temperature, but depended only on
relative humidity a. Therefore the following experimental ionicresistivity ρ, a function of only relative humidity a, was employed in the following numerical analysis.
 a − 0.089 
 a − 0.089 
ρ = 57.3 + 383. exp − + 244 exp −
 (7)
0
.
049
0.268 For measuring activation overpotential ηact , the relatively
high flow rates of 600cc/min were provided to hold the low
utilization rate of H2 and O2 in order to prevent variation of ηactalong the flow by the distributed current density. η act wasderived by subtracting the cell voltage Vcell and the resistive
overpotential ir from the Nernst potential VNernst as follows.
(8)η act = VNernst − Vcell − irHere, the spatially averaged partial pressures of active materials
were used to determine VNernst considering water vapor pressures.
The experimental conditions for ηact measurement were asfollows; FC temperature : 60˚C, cathode O2 partial pressure
PO 2 : 0.05, 0.2, 1.0; anode H2 partial pressure PH 2 : 1.0. Since
the activation overpotential increased logarithmically, we
adopted following Tafel approximation to compose a empiricalformula. The eq.(9) are adopted in following numerical analysis.
η = A + B ln i
(9)
here

(
)
B = (− 1.44 × 10 T + 3.584 × 10 )ln P + 0.0234
A = − 5.15 × 10 −4 T + 9.527 × 10 −2 ln PO2 + 0.433
−4

−2

O2

3. MEASUEWMENT OF CURRENT DISTRIBUTIONSCurrent distributions were measured by two different methods
to confirm the reliability of measurements. First method adopted
the segmented electrodes cell to measure the current distribution
by shunt resistances. Another method adopted gas chromatography to measure gas composition changes to be converted tothe current distribution through the decreased flow rate of H2 or
O2. N2 mixture fuel and air were employed in this measurement
to keep the constant flow rate of N2 as reference. H2 gas mixed
with 20% N2 (not CO2) was used as fuel, because CO2 is easy to
be solved in water and not giving the correct reference. The cellconfiguration of current distribution measurement is illustrated
in Fig. 5.
4. NUMERICAL MODEL OF PEMFC
4.1 Numerical procedure
Our model basically consists of the steady state
two-dimensional mass, charge and energy conservation equations with an equivalent electric circuit of PEMFC. Following
assumptions are adapted to derive governing equations[2].
1. Fuel cell is a parallel flow type.
2. Gas flow along a channel is plug flow.
3. Owing to the constant-temperature water circulation throughseparators, the separator temperature is constant. However,temperature changes at PEM and Diffusion layer are considered.
4. The volume of the condensed water is so small that effect bycondensed water at cathode can be neglected.
5. The total gas pressure is constant, neglecting pressure drop
along flow channel.
The mass conservation equations are as follows by using mole

Shunt resistance12mΩ

Segmented electrode＃flow rate Mj of each chemical species j, and current density ithrough MEA. The subscripts a, c and k denote at anode,cathode and either anode or cathode, respectively. d is height(thickness) of channel (layer) and h is channel width.
dM H 2hi
Hydrogen :
=−
(10)
dx
2F
d M O2hi=−(11)
Oxygen :dx
4F
Water liquid :liquid
dM water
M vapor
hd channel,ksaturated  vapor water , k
= 
(12)
P − Pwater
,k
 M

(
+
273
.
15
)
dx
R
T
+
M
k
H2

 water , kvapor
liquiddM vapordM waterdM water,a,aWater vapor (anode):
=−
−
(13)
dx
dx
dx
vapor
liquiddM vapordM waterdM water
hi
,c
,c
=−
+
+
(14)
(cathode):
dx
dx
dx
2F
Here Mvapor is the water vapor mole flow rate from anode tocathode.

dC w
i 
i
RMEA  − Tr
+ nd  − RDIF,cd M vapor
dy
F
2F

h
(15)
=
dx
RMEA + RDIF,a + RDIF,cFive energy conservation different equations for five layers(two gas channels, two diffusion electrodes and one MEA) are
derived.
The equivalent electric circuit for PEMFC is shown in Fig. 6.
Due to the high electric conductivity of the separators, the cellvoltage along channel can be kept constant. Control volume
method and Tri-diagonal matrix algorithm (TDMA) were used
to solve simultaneously equations with an equivalent circuit.
4.2Comparison of the current distributions with the measured
A current density distributions calculated by the numericalmodel are shown in Fig. 7 as an example. The conditions for the
analysis and experiments are summarized in Table 1. Cathodeflow was not humidified to observe the change of current
density clearly. Distributions of current densities were increased
from inlet as the membrane water content increases by generated
water. Then, they decreased from around a middle of a flow
channel, since oxygen partial pressure decreased and activation
overpotential ηact increased along the channel. The position ofcurrent peak was shifted downstream as averaged current
decreasing, because lower averaged current density im means
lower water generation speed and lower oxygen consumption＃8

H2

Acryl frame

Separator
Diffusion layer

Gas sampling port

MEA
Electrode area
：10cm2
Gas sampling port

Catalyst layer

Diffusion
electrode(Carbon Cloth)

Separator

Configuration of cell and segmented electrodes

Vnernst－ηact

Diffusion layer
Separator

O2yx

Figure 5

Membrane resistance

PEM

Figure 6

H2O

Equivalent electric circuit for the PEMFC

Table 1 Experimental conditions
Cell temperature[℃]
Anode flow rate[cc/min]athode flow rate[cc/min]
Anode dew temperature[℃]

60
48
91
60
Not humidified

Cathode dew temperature[℃]
Fuel and oxygen utilization
ratio(im=0.2 [A/cm2])
Fuel and oxygen utilization
ratio(im =0.3[A/cm2])
Fuel and oxygen utilization
ratio(im =0.4[A/cm2])

0.6

Current density [A/cm2]

0.4
0.6
0.6
Measured (im=0.4A/cm2)
Numerical (im=0.4A/cm2)
Measured (im=0.3A/cm2)
Numerical (im=0.3A/cm2)
Measured (im=0.2A/cm2)
Numerical (im=0.2A/cm2)

0.7

0.5
0.4
0.3
0.2
0.1
0.0
0

5

10

15

20

25

Channel length [cm]Figure 7 Comparison between the measured and thenumerical current distributions (Air flow rate : 91cc/min)
which leads to smaller activation overpotential ηact.
The good agreement between the numerical and measured
results indicates that our numerical model using the measured
water management and power loss factors can provide a useful
tool to estimate the PEMFC power generation performance. The
measured showed higher current density at inlet, and lower
current density at outlet than the calculated, especially for higher
oxygen utilization ratio of 80%. This discrepancy might be dueto the flooding by generated water at a downstream cathode,hindering the site for electrochemical reaction. Further studies
are needed on empirical formula for the activation overpotential,
water management factors and diffusion overpotential throughdiffusion electrode.
1.

segmented-electrodes cell. Hydrogen /Oxygen concentration
changes measured by gas chromatography along the gas flows
have also given the experimental current distributions, whichcoincides almost with that by the segmented-electrodes. Degradation factors for cell performance were also discussed from thenumerical results by the simulation code. Also further improvements for out experiment and analysis have been pointed out.

CONCLUSION
The water management factors such as transmissivity andelectro-osmotic coefficient of water vapor through the membrane electrode assembly, and power loss factors such asactivative and resistive overpotentials have been measured.
These factors were adopted to analyze our experimental resultsof PEMFC power generation tests by our two-dimensional
simulation code. The code considers simultaneously the mass,
charge and energy conservation equations with the equivalent
electric-circuit for PEMFC to give numerical distribution ofhydrogen/oxygen concentrations, current density, andgas/cell-component temperatures along gas flow. The calculated
distributions of current density under various operating conditions have agreed well with the measured distributions at

ACKNOWLEDGEMENTS
The present study was conducted in part with the assistance of
Chubu Gas Co., LTD. and New Energy and Industrial Technology Development Organization (NEDO).
NOMENCLATURE
A：membrane active area
[cm2]
a：relative humidity[-]
C：gas concentration[g cm-3]Di：diffusion coefficient of species i[m2 s-1]dl：thickness of layer l[cm]
E゜：standard electromotive force[V]f：effective porosity of diffusion electrode[-]h(v)：mass transfer coefficient at flow velocity v [cm s-1]
im：averaged current density[A cm-2]i：local current density[A/cm2]Mx, Mx’ ：vapor flow rate
[g s-1]Me：vapor flow rate of generated water[g s-1]MOSM ：vapor flow rate of electro-osmosis[g s-1]nd：electro-osmotic coefficient[-]Pi：partial pressure of gas species i[atm]
Rl：gas diffusive resistance of a layer lρ：membrane resistance[Ωcm2]
Tmem ：temperature of MEA[K]
Tr：transmissivity of MEA[cm2 s-1]
Vcell：cell voltage[V]
VNernst ：Nernst potential[V]v：supplied gas velocity[m s-1]wcell：cell width (channel width + rib width)
[cm]
ηact
：activation overpotential[V]ηohm：resistive overpotential[V]ρ：membrane resistivity[Ωcm](Subscripts)
a, c：anode and cathodeliq, vap ：liquid and vapor
mem ：membrane
DIF：diffusion electrode
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No8, (1993) p.2178.
[3] H.Yamada and Y.Morimoto, Proc. 70th anniversary Jpn.
Electrochem., Soc. (2003) p316. (in Japanese)[4] T. Aoki, N. Miyauchi, K. Ito, Y. Inui and K. Onda: Numerical Analysis of Polymer Electrolyte Fuel Cell Using
Empirical Equations for Overpotentials. Trans. IEE Japan,
Vol. 122-B, No. 12, (2002). (in Japanese)[5] S. V. Patankar, Numerical Heat Transfer and Fluid Flow,
Hemisphere Publishing, pp.24-56 (1985).