Simulation of Current Density Distribution at PEMFC by using Measured ElectroChemical and Physical Properties of Membrane
K. Onda, H. Koori, T. Taniuchi, T. Araki
Toyohashi University of Technology, Toyohashi, Japan
Introduction
Establishing precise numerical model of the proton exchange membrane fuel cell(PEMFC) provides a useful method to estimate and improve the PEMFC performance. The first objective of thepresent investigation is to build a numerical model, which can describe the PEMFC performancesuch as a V-i characteristics and current distributions inside the cell. For building properly thePEMFC model, it is necessary to know the water management factors such as transmissivity andelectro-osmotic coefficient of water vapor through the membrane-electrode assembly (MEA), andpower loss factors such as activation and resistive overpotentials, since these factors have significant impacts on performance of PEMFC. Nevertheless, the effects by these factors on PEMFC havenot been cleared sufficiently. Then, obtaining the basic information for PEMFC is a second objective of this study. The comparison of measured and calculated current distributions is finallyconducted to verify the reliability of our numerical model.
Measurement of water management factors and power loss factors
To obtain the diffusive properties of MEA, the cell outlet humidities at both anode and cathodewere measured with supplying air or nitrogen with different humidities to fuel cell inlets. The
measurement procedure is essentially the same as those described previously(1). The measured
water vapor diffusivity through MEA Ddiff did not change much against relative humidity and wasdescribed by the relation Ddiff=f·DH2O-Air, where DH2O-Air is water vapor diffusivity in air, and f is theporosity of diffusion electrodes. In our case of carbon cloth, f was calculated to be about 0.25. The
measured transmissivity through MEA Tr was about 7 times higher than that by Nguyen et al.(2) andlower than by Yamada et al.(3). However, the increasing tendency of Tr against relative humidity
increase was consistent with that by Nguyen et al. Therefore we approximate Tr to be 7 times
greater than that by Nguyen et al. Electro-osmotic coefficient nd is determined similarly to thediffusion coefficient, except the electric current flowing condition to transport water electro-osmotically. The measured nd increased when the relative humidity increases. nd at of 50˚Cagreed with that by Nguyen et al., but showed a different tendency against relative humidity whencompared to nd by Yamada et al., who performed similar experiment with us using carbon cloth.
Resistive and activation overpotentials are also important factors to decide PEMFC power generation performance. The ionic resistance of MEA was measured by AC impedance meter (SOLARTRON SI1280B), supplying air with the same humidity to both anode and cathode to avoid thewater movement through MEA. Parameters for MEA resistance are membrane temperature Tmem
and relative humidity a. The resistivity did not depend on Tmem, but depended only on a. When theactivation overpotential ηact was measured, the relatively high flow rate of 600cc/min was supplied
to keep the low utilization rates of H2 and O2, in order to prevent the change of ηact by distributed
current density along flow. ηact was obtained by subtracting the cell voltage Vcell and the resistive

K. Onda et al.
overpotential η ohm from the Nernst potential VNernst , i.e., ηact = VNernst − Vcell − ηohm . Spatially average
partial pressures of active materials were used to determine VNernst considering water vapor pressures. The experimental conditions to measure ηact were FC temperature of 60˚C, cathode O2 partialpressure ratio PO of 0.05, 0.2, 1.0, anode gas of pure H2 and atmospheric pressure of cathode andanode gas. The measured ηact increased almost linearly against PO except for a region where current
density is very small.
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Numerical model of PEMFC
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 through separators, the separator temperature is constant.
4. The volume of the condensed water is so small that effect by condensed water at cathode can beneglected.
5. The total gas pressure is constant, neglecting pressure drop along flow channel.
The mass conservation equations are as follows by using mole flow rate Mj of each chemicalspecies j, and current density i through MEA. The subscripts a, c and k denote at anode, cathodeand either anode or cathode, respectively. d is height (thickness) of channel (layer) and h is channel
width.
dM H
d MO
hihi
Hydrogen :(1)
Oxygen :
(2)
=−=−
dx
2F
dx
4FliquiddM water
M vaporhd channel
saturated,k vapor water ,k(3)Water liquid :P − Pwater= ,k M
(273.
15)+dx
RTM+kH water ,kvaporliquiddM vapordM waterdM water,a,aWater vapor (anode):
(4)
=−−dx
dx
dx
vapor
liquiddM vapordM waterdM waterhi,c,c(5)(cathode) :=−++dxdx
dx
2F
Here Mvapor is the water vapor mole flow rate from anode to cathode.
222d M vapor=dx

ii dCw+ nd  − Rdiff,cRMEA  − TrFF2dyhRMEA + Rdiff,a + Rdiff,c(6)where RMEA is dMEA /(Tr·A) and Rdiff,k is ddiff,k /(Ddiff,k ·A)
Five energy conservation different equations for five layers (two gas channels, two diffusion
electrodes and one MEA) are derived, but only two equations for MEA and diffusion electrode areshown below due to limitations of space.

K. Onda et al.

tmem

MEA :

T −T
T −Td dT 
 k mem mem  = k diff ,a− mem mem dif ,a + k dif ,c−mem mem dif ,cdy dy ∆xdiff ,a−mem∆xdiff ,c−mem

−  ∑ N j ,a H j −T jdif , a− ∑ N j ,c H j −T  − N H ∆H LHV + i (VNernst − ηohm − η act )j∑ (M c ) dx = (HdTk

DE :jp, jvapor
water ,kj

dif , c2liquid− H water),kliquiddM water,kdx(7)+ U (Ts − Tk )(8)

Here Nj and Hj represent the mole flux along y direction and enthalpy of the j species, respectively.
U is heat transfer coefficient. ηohm is resistive overpotential by eq. (9) as a function of the MEA
resistivity ρ.

a1ρda t memi∫a aa − acηohm = a(9)H2cSeparator
Diffusion layer

The equivalent electric circuit for PEMFC is shown inFig. 1. Due to the high electric conductivity of theseparators, the cell voltage along channel can be kept
constant. Control volume method and Tri-diagonal
matrix algorithm (TDMA) were used to solve simultaneously equations (1) - (8) with an equivalent circuit.

Catalyst layer
Membrane resistance

PEM

Vnernst－ηact

Catalyst layerDiffusion layer
Separator

O2yx
H2O
Measurement of current distribution
Fig 1 Equivalent electric circuit
Current distributions were measured by two different
for the PEFC
methods to confirm its reliability. One method adopted
the segmented electrodes cell to measure the current distribution by shunt resistances. Anothermethod adopted the gas chromatography to measure gas composition changes to be converted tothe distributed current through the decreased flow rate of H2 or O2. N2 mixed fuel and air wereemployed in this measurement to reserve the constant flow rate of N2 as reference. H2 mixed with
20% of N2 (not CO2) was used as fuel, because CO2 is apt to be absorbed in water and not giving
the proper reference. Figure 2 shows the measured current density distributions for two average
0.7

0.6

0.6
2

C u r r en t densit y [ A / c m ]2

C ur r en t densi t y [ A / c m ]

0.5

0.4

0.3

0.2

G as c h r o m at o g r ap h (A n o d e)
G as c h r o m at o g r ap h (C at h o d e )Segm e n t e d el ec t r o d e c el l

0.10.50.40.30.2

G as c h r o m at o gr ap h ( A n o d e )G as c h r o m at o gr ap h ( C at h o d e)
Segm en t ed e l ec t r o d e c e l l

0.10.00.012345E l ec t r o d e n u m b er

67812345E lec t r od e nu mb er

Figure 2 Comparison of measured current distributions
i mean im=0.3A/cm2 (left), im=0.4A/cm2 (right)678

K. Onda et al.

current densities im of 0.3A/cm2 and 0.4A/cm2. The current density by gas chromatography fluctuated to some extent, but compatible with the one by segmented electrodes cell. Thus we could
confirm the measurement reliability of current density distribution.
Results of numerical simulation and comparison with measured current distribution
The current density distributions calculated by the numerical model are shown in Fig. 3. The
conditions for the analysis are summarized in Table 1. The good agreement between the numericaland 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 due to 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 through diffusion electrode.
Reference[1] T.Kyakuno, K.Hattori, K.Ito and K.
Onda, Proc. 2003 IEEJ Conf., P7-151(2003). (in Japanese)[2] T.V.Nguyen and R.E.White, J. Electrochem. Soc., Vol.140, No8, p.2178(1993).
[3] H.Yamada and Y.Morimoto, Proc. 70thanniversary Jpn. Electrochem., p316 Soc.
(2003). (in Japanese)

Table 1 Experimental conditions
used in the numerical model
left
Cell temperature[℃]
Anode flow rate[cc/min]Cathode flow rate[cc/min]
Anode dew temperature[℃]
Cathode dew temperatuer[℃]
Fuel and oxygen utilization
20.4, 0.4 0.4, 0.26 0.4, 0.2

20.6, 0.6 0.6, 0.4 0.6, 0.3

20.6, 0.6 0.8, 0.53 0.8, 0.4

ratio(i m =0.2 [A/cm ])Fuel and oxygen utilization
ratio(i m =0.3[A/cm ])Fuel and oxygen utilization
ratio(i m =0.4[A/cm ])M e asu r e d ( i m= 0 . 4 A / c m )

2m2

2

0.4

0.3
0.2

0.1

0.0

N u m e r i c a l (i m =0 . 3 A / c m )0.5

N u m e r i c a l (i m =0 . 2 A / c m )

0.4

0.3

0.2

0.1

5101520

C han nel l en gt h [ c m](Air flow rate : 91cc/min)

2505101520

C h ann el L en gt h [ c m](Air flow rate : 136cc/min)25

2

M e asu r e d (i m =0 . 2 A / c m )

2

20.0
0

2

N u me r i ca l (i m =0 . 3 A / c m )0.6

2

M e asu r e d ( i m= 0 . 2 A / c m )2C u r r ent den sit y [ A / cm ]2

2C ur r ent d ensit y [ A / cm ]N u me r i ca l (i m =0 . 3 A / c m )N u me r i ca l (i m =0 . 2 A / c m )2M e asu r e d (i m =0 . 3 A / c m )20.6

C ur r ent d en sit y [ A / c m ]2M e a su r e d (i m =0 . 2 A / c m )0.7

2M e asu r e d ( i m= 0 . 3 A / c m )M e a su r e d (i m =0 . 3 A / c m )0.5

2N u me r i ca l (i m =0 . 4 A / c m )2N u m e r i c a l (i =0 . 4 A / c m )0.7

N u me r i ca l (i m =0 . 4 A / c m )0.6

2M e asu r e d (i m =0 . 4 A / c m )22

M e a su r e d (i m =0 . 4 A / c m )0.7

centerright
60
48
91
136
18260
Not humidified

2N u me r i ca l (i =0 . 2 A / c m )
m

0.5
0.4

0.3
0.2

0.1

0.0
05

101520C hann el l en gt h / c m(Air flow rate : 182cc/min)Figure 3 Comparison between the measured and the numerical current distributions

25