A novel ribbed cathode polar plate design in piezoelectric proton exchange membrane fuel cells

Contents lists available atScienceDirect

Journal of Power Sources

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / j p o w s o u r

A novel ribbed cathode polar plate design in piezoelectric proton exchange

membrane fuel cells

H.K. Ma

∗

, S.H. Huang, Y.Z. Kuo

Department of Mechanical Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan, ROC

a r t i c l e i n f o

Article history: Received 6 June 2008

Received in revised form 7 July 2008 Accepted 9 July 2008 Available online xxx Keywords: Piezoelectric PZT-PEMFC Rib width Frequency Current density

a b s t r a c t

Previous studies have indicated that a novel design for proton exchange membrane fuel cells with a piezoelectric (PZT) device, which is regarded as an actuator for pumping air onto the cathode channel, can offer better performance with higher current generation. These results indicate that piezoelectric proton exchange membrane fuel cells (PZT-PEMFCs) may compress more air into the catalyst layer and thus may enhance electrochemical reactions, resulting in higher current output. At the same time, produced water vapor is pumped out from the cathode channel during the compression process. Previous studies on PZT-PEMFCs without ribs showed the strong effect of ohmic and concentration losses. In this study, a shallow rib is chosen to reduce the aforementioned losses and pressure drop in the cathode channel. The rib design is an important parameter that can be used as the support for the membrane electrode assembly (MEA). A transient three-dimensional model is built to simulate and compare the performance of PZT-PEMFCs both with and without ribs. Water vapor, oxygen, and current density profiles in the PZT-PEMFC are studied in detail. The major operating parameters include the rib width and the PZT vibration frequency. Our results show that the ribbed cathode channel can reduce ohmic losses and double current generation. Moreover, at higher PZT vibration frequency (f = 64 Hz), an air-breathing PZT-PEMFC compresses more oxygen into the catalyst layer and thus enhances the electrochemical reaction, resulting in a higher current output (0.208 A cm−2_).

© 2008 Elsevier B.V. All rights reserved.

1. Introduction

Air-breathing proton exchange membrane fuel cells (AB-PEMFCs) have attracted attention as substitutes for currently used batteries. During AB-PEMFC operation, liquid water is transported by electro-osmotic drag, back diffusion, and convection in the membrane. The electro-osmotic drag coefficient has been found to be a function of the water content of the membrane and tempera-ture[1–4]. Generally, the electro-osmotic drag coefficient increases with increasing water content in the membrane. At high water con-tent, the electro-osmotic drag coefficient increases with increasing temperature. Yi and Nguyen[5]showed that PEMFC performance was improved by anode humidification and positive differential pressure between the cathode and anode. Ge and Yi[6]predicted that the dry reactant gases could be successfully humidified inter-nally and could maintain high performance when the PEMFC was operated in counter flow mode. Thus, water transport and man-agement is dependent upon the structure and properties of the cell components, reactant stream humidification, flow field layout, and

∗ Corresponding author. Tel.: +886 2 23629976; fax: +886 2 23631755. E-mail address:[email protected](H.K. Ma).

structural and wetting properties of the gas diffusion media and micro-porous layer[7].

In general, AB-PEMFCs do not need an additional oxygen supply device; their performance is proportional to the oxygen transfer coefficient[8]. Santa Rosa et al.[9]developed an open-air cathode PEMFC stack with an air fan. This design combined oxidant sup-ply and stack cooling. Using numerical analysis, Zhang et al.[10] presented various stack and cell parameters for stack designs with an array of air-breathing fuel cell cartridges. Matamoros and Brug-gmann[11]showed that dehydrating phenomena slightly affected the performance of AB-PEMFCs. Moreover, catalyst loading, rela-tive humidity, temperature, hydrogen stoichiometry, gas-diffusion layer thickness, and cathode structure are important parameters in the performance of AB-PEMFCs[12,13].

Proper flow field design of the AB-PEMFC may help address the water-flooding problem and enhance cell performance. For inter-digitated flow fields, the reactant gas can be delivered to the catalyst layer and can increase the electrochemical reaction rate[14]. How-ever, while pin-type flow fields have a lower reactant pressure, they have uneven gas distribution and poor water removal and cell performance[15]. The single-serpentine flow field exhibits better performance than double- and triple-serpentine flow fields[16]. In addition, a new convection-enhanced serpentine flow field has 0378-7753/$ – see front matter © 2008 Elsevier B.V. All rights reserved.

jT transfer current (A)

j0 reference current density at a known open circuit

voltage (A m−3)

keff effective thermal conductivity (W m−1K−1)

M mass (kg)

N amount of species

P pressure (N m−2)

R gas constant (J mol−1K−1)

t time (s)

T temperature (K)

Va anode inlet velocity (m s−1)

Vc cathode inlet velocity (m s−1)

VPZT motion equation of the piezoelectric device (m s−1)

Yi mass fraction of ith species

∀ volume (m3₎ Greek letters ε porosity  over potential (V)  permeability (m2₎  viscosity (kg m−1s−1)  density (kg m−3)  shear stress (N m−2)  equivalence ratio ωi production rates (kg m−3s−1) Subscript act. actual stoi. stoichiometry

been proposed by Xu and Zhao[17]to increase the mass transport rate and remove liquid water trapped in the porous media. Further-more, the parallel flow field with an incorporated baffle exhibited better performance because the baffle effect forces the reactant gas to pass through the diffusion layer[18]. Moreover, Ma et al. [19,20]have proposed a novel cathode channel design that utilizes the piezoelectric (PZT) effect in AB-PEMFC systems, known as the PZT-PEMFC. The PZT-PEMFC can feed air into the cathode chan-nel through a gas pump with a piezoelectric actuation structure. A higher PZT vibration frequency leads to a higher oxygen concen-tration at the cathode channel, and most of the produced water vapor can be pumped out of the cathode channel by PZT vibrations. This design can reduce the water-flooding problem and increase cell efficiency.

Studies have shown that a ribbed design affects cell perfor-mance and species distribution, and that a narrower channel with a wider rib spacing yields better performance[21,22]. Although PZT-PEMFCs may increase cell efficiency and reduce water flood-ing, a rib-free design may induce a large resistance. Thus, ribs are necessary on the cathode side of the PZT-PEMFC. Jeong et al. [23] showed that a single cell with a cathode open area of 77% exhibited the best performance. This result was related to oxy-gen transport from the atmosphere to the catalyst layer. Hottinen

2. Mechanisms of PZT-PEMFC

The PZT-PEMFC (Fig. 1) contains a piezoelectrically actuated micro-diaphragm that is installed in the cathode channel. This device is regarded as an original gas pump design and can draw air into the cathode channel without an external air pump. While the actuator moves outward, the volume of the cathode channel increases, and the air is drawn into the chamber (Fig. 2). How-ever, when the actuator moves inward, the volume of the cathode channel decreases, and the air is compressed into the catalyst layer. Previous studies have proposed an ideal air-breathing PZT-PEMFC cycle that describes four piezoelectric actuation processes. In addi-tion, the motion of the PZT device was assumed to be a step function [19,20]. In this study, a sine function was applied for the motion of PZT device as it may improve both the electrochemical reaction in the catalyst layer and the power output.

In addition, the PZT-PEMFC can also be used in stacks.Fig. 3 shows that two cathode channels and two-cell stacks can be driven by one PZT device.

2.1. Equivalence ratio

The equivalence ratio, defined as the actual fuel-to-air ratio divided by theoretical fuel-to-air ratio, is an important parameter

Fig. 2. Actuating mechanisms in a PZT-PEMFC system.

for discussing air–fuel mixing phenomena in internal combustion engines[26]. Similarly, the equivalence ratio is also an important parameter for air-breathing PZT-PEMFCs. The theoretical demand of air for generating 1 A of current is 17.96 mg min−1, and the (hydrogen/air)stoi. is 0.03. In this study, the equivalence ratio

is defined as the ratio of (hydrogen/air)act. to (hydrogen/air)stoi.

Fuel-rich conditions ( > 1) are found in air-deficient and incom-plete hydrogen reactions at low PZT vibration frequencies. On the contrary, fuel lean conditions ( < 1) are found at high PZT vibration frequencies, where sufficient air is drawn into the cathode channel, resulting in an increase in hydrogen consump-tion.

2.2. Actuation analysis of PZT-PEMFC

The driving forces at the anode and cathode inlets are different. The inlet hydrogen velocity at the anode is assumed to be constant. However, the inlet air velocity at the cathode is driven by PZT vibra-tions. Thus, the velocity V is divided into the anode velocity Vaand

cathode velocity Vc. The equation of motion for the PZT is a sine

function given by −−→ VPZT= d dt



−0.0005 ×



sin



2ft − 2



. (1)

Also, the inflow and outflow periods in the channel as induced by the sine function are shown inFig. 4. The inlet air-flow rate at

Fig. 3. The outlook of a PZT-PEMFC stack.

Fig. 4. The sine function of periodical flow at cathode.

the cathode is expressed by the Reynolds Transport Theorem as DM Dt = D(

∀

) Dt = ∂ ∂t



C∀ d

∀

+



CS,PZT −−→VPZT· −→n dA +



CS,in c−→Vc· −→n dA = 0. (2) The gas density is expressed by the equation of state for an ideal gas, so the mass conservation equation is derived as

1 R ∂ ∂t



C∀ P T d

∀

+ cs,PZT−−→VPZTAPZT− c−→VcAin= 0. (3)

The inlet velocity at the cathode, −→Vc, is derived as

− → Vc= 1 cAin



1 R ∂ ∂t



C∀ P T d

∀

+ CS−−→VPZTAPZT



. (4)

3. Theoretical model for PZT-PEMFC

A numerical model of the novel fuel cell, based on the SIM-PLEC procedure, has also been developed. The assumptions are as follows:

(1) The reactants and products are treated as ideal gases. (2) The Stefan–Maxwell equations are applied to multispecies

dif-fusion.

(3) Contact electrical and heat resistances among the channel layer, diffusion layer, catalyst layer, and membrane are ignored. (4) The Nernst–Planck equation is used for proton transport

through the membrane.

(5) Ohm’s law is applied across the entire region of the polariza-tion curve.

(6) The porosity and permeability of the porous media are uni-form, and the porous media are isotropic and homogeneous. (7) The effect of gravity is ignored.

(8) The amplitude of the PZT device is assumed constant for all frequencies, and the motion of PZT device is assumed to be a sine function.

(9) The water in the fuel cell is assumed to be vapor. (10) The relative humidity of fuel and air is 100%.

The membrane electrode assembly (MEA) parameters refer to a DuPont membrane, and the dimensions of the PEMFC are shown inFig. 5. The compositions of the inlet humidified fuel and air are shown inTable 1. In addition, the inlet fuel velocity is 1 m s−1. The inlet air velocities vary with different PZT frequencies, as shown in Table 2.

Fig. 5. Dimensions of PZT-PEMFC.

Table 1

Gas composition of fuel and air at inlet conditions

Fuel Hydrogen_{Water vapor} 43.9%_56.1%

Air

Nitrogen 69.8%

Oxygen 22.1%

Water vapor 8.1%

Unit: molar concentration.

3.1. Channel layer

The governing equations in the channel include the continuity, momentum, and species equations. The continuity equation is

∂

∂t +

∇

· ( V) = 0. (5)

The momentum equation is ∂

∂t( V) + (

∇

·  V V) = −

∇

p +

∇

· . (6)

The energy equation is ∂

∂t(h) +

∇

· ( Vh) =

∇

· q +  :

∇

V + dp

dt. (7)

The species equation is ∂

∂t(Yi)+

∇

· ( VYi)=

∇

· Ji, (8)

where Yiis the mass fraction in the gas phase of the ith species. Ji

is the diffusive flux, which can be expressed as Ji= Di,eff

∇

Yi+Y_MiDi,eff

∇

M − M

j Di,eff

∇

Yj −

∇

M

j Di,eff

∇

Yj, (9)

where Di,effYi is the Fickian diffusion coefficient, which is

induced by the concentration gradient. Other terms are the cor-rections of multiple species within the porous medium. The fluid diffusion coefficient should be modified to Di,eff, which is derived

by Bruggeman[27]. Table 2 Operating parameters Anode inlet Va 1 m s−1 Pressure 1 atm Temperature 323 K Cathode inlet Vc Eq.(4), m s−1 Pressure 1 atm Temperature 323 K ∂ ∂t(ε V) + (

∇

· ε V V) = −ε

∇

p +

∇

· (ε) + ε2_{ V} k (11)

whereε2_{V/k is Darcy’s drag force describing the fluid flowing}

through the porous media.

The energy equation is written as ∂

∂t(εh) +

∇

· (ε Vah) =

∇

· q + ε :

∇

Va+ ε dp

dt − jT +i · i

 . (12) The species equation is

∂

∂t(εYi)+

∇

· (ε VaYi)=

∇

· Ji. (13)

3.3. Catalyst layer

The important governing equations in the catalyst layer are the species and current conservation equations. Because the electro-chemical reaction and current generation take place in this layer, the species and current conservation equations should be written in the forms given below.

The species equation is ∂

∂t(εYi)+

∇

· (ε VYi)=

∇

· Ji+ ωi, (14) whereωiis the production rate in the gas phase of the ith species.

The transfer current jTcan be expressed by the Butler–Volmer

equa-tion as jT=

_N j0 k=1[ k,ref] ˛k



exp



_˛ aF RT



− exp



˛cF RT 



N k=1 [ k] ˛k , (15) where is an over potential, defined as the difference between the solid potential and the porous (or liquid) potential.

Fig. 7. Water vapor distribution in different time (rib width = 2 mm, f = 8 Hz).

Fig. 8. Current density profiles with different rib width (f = 16 Hz).

The current conservation equation is given by

∇

· i = 0. (16)

Because the current flows through the porous medium, it can be divided into two parts. The first part is

i = if+ is, (17)

where ifis the current flowing through the fluid, and isis the

cur-rent flowing through the solid. Because they are porous media, the

electrons transfer from fluid to solid and solid to fluid. Thus, the transfer current can be written as

jT=

∇

· is= −

∇

· if (18)

Using Ohm’s law, this can be changed to

∇

· (f∇ϕf)= −

∇

· (s∇ϕs)= jT. (19)

4. Results and discussion

A novel ribbed PZT-PEMFCs design has been developed, and a three-dimensional, transitional model has been successfully built to analyze its performance and primary phenomena.

4.1. Influence of rib design on current density

The rib design is an important parameter in the fuel cell for reducing internal resistance and for preventing MEA fracture due to the pressure difference between the anode and cathode. However, previous studies[19,20]did not have any ribs in the cathode chan-nel. As shown inFig. 6, only the unribbed design has a small current density, 0.12 A cm−2, due to higher resistance. A ribbed cathode channel can reduce cathode open air area, which decreases the resistance and doubles the current density[22,23]. However, the ribbed design has a water-accumulation problem. Therefore, the current decreases with time. As shown inFig. 7, water vapor may be blocked and may be accumulated near the rib with time.

Fig. 10. Water vapor profiles under different rib width.

4.2. Influence of rib width on current density

Although water may accumulate near the rib and may reduce internal resistance in wider ribs,Fig. 8shows that both a wider rib and a thinner rib have a slight effect on cell performance. However, a current overshoot may occur at the initial stage in the wide rib case. The current will then decay and be lower than in the thin rib case.

4.3. Influence of PZT frequency on current density

As the PZT vibrates at low frequencies, it is shown inFig. 9that current generation is lower compared with high PZT vibration fre-quencies. However, a current overshoot occurs in the wide rib case, especially at the high PZT vibration frequency. In addition, the cur-rent decreases with time at the low PZT vibration frequency (f = 8, 16 Hz) due to the lower air-flow rate in the cathode channel.Fig. 10 illustrates that the current may decay with time because the accu-mulated water vapor cannot be pumped out immediately in the cathode channel with low PZT vibration frequencies. The simu-lations show that the water distribution in the cathode channel is only slightly different under both rib-width cases.Fig. 11also shows that the rib width slightly affects oxygen distribution in the cathode channel. Therefore, it may be the reason for the slight difference in current density between the two different widths (Fig. 9).

The simulation result of this study is a quasi-steady state, and it consists of 64 cycles in 1 s, i.e., f = 64 Hz. In order to reduce compu-tational time, the time scale is chosen as 1 s.

4.4. Influence of equivalence ratio on current density

When the PZT vibrates at high frequencies, more air can be drawn into the cathode channel, leading to a reduction in the equiv-alence ratio. Therefore, higher current density can be found at

f = 64 Hz, where the equivalence ratios are 1.72 and 1.54 with rib

sizes of 1 and 2 mm, respectively (Table 3). In contrast, with higher equivalence ratios, less air will be drawn into the cathode chan-nel at low PZT frequencies. When the rib width increases from 1 to 2 mm, the difference in the equivalence ratio is 2.76% at a high PZT frequency of f = 64 Hz. However, the difference in equivalence ratio is only 0.35% at a low PZT frequency of f = 8 Hz.

The simulations indicate that the equivalence ratio is not affected by the rib width (Fig. 12). In addition, the current den-sity is high at high frequencies. Both of the different rib widths generate almost the same current density, 0.205 and 0.208 A cm−2, using 1 and 2 mm rib widths, respectively, at f = 64 Hz. Therefore, the effect of the PZT vibration frequency is stronger than the effect of rib width in the air-flow rate.

Table 3

Air-flow rate at different PZT frequencies and equivalence ratio at the same time (t = 1 s)

PZT frequency (Hz) Air-flow rate (mg s−1_{) Equivalence ratio}

Rib width = 1 mm 8 17.19 13.06 16 36.90 6.08 32 73.89 3.04 64 130.50 1.72 Rib width = 2 mm 8 17.43 12.88 16 36.45 6.16 32 73.50 3.05 64 145.80 1.54

Fig. 12. Current density profiles under different equivalent ratio.

5. Conclusions

A novel ribbed PZT-PEMFCs design has been developed, and a three-dimensional, transitional model has been successfully built to consider its primary phenomena and fuel cell performance. A ribbed cathode channel can reduce the internal resistance and can double the current density. However, the ribbed design may cause the accumulation of water vapor near the rib. At higher PZT vibra-tion frequency (f = 64 Hz), an air-breathing PZT-PEMFC compresses more oxygen into the catalyst layer and thus enhances the electro-chemical reaction, resulting in a higher current output. At the same time, the accumulated water vapor may be pumped out from the cathode channel during the compression process. In addition, the effect of PZT vibration frequency is stronger than the effect of the rib width on the air-flow rate and current density. The optimal cur-rent density for the ribbed PZT-PEMFCs in the cathode below 0.7 V is 0.208 A cm−2at f = 64 Hz.

Acknowledgement

This research was funded by the National Science Council of the Republic of China (NSC 96-2221-E-002-074-MY2).

References

[1] T.F. Fuller, J. Newman, J. Electrochem. Soc. 139 (1992) 1332–1337.

[2] T.A. Zawodzinski, J. Davey, J. Valerio, S. Gottesfeld, Electrochim. Acta 40 (1995) 297–302.

[3] S.H. Ge, B.L. Yi, P.W. Ming, J. Electrochem. Soc. 153 (2006) A1443–A1450. [4] M. Ise, K.D. Kreuer, J. Maier, Solid State Ionics 125 (1999) 213–223. [5] J.S. Yi, T.V. Nguyen, J. Electrochem. Soc. 145 (1998) 1149–1159. [6] S.H. Ge, B.L. Yi, J. Power Sources 124 (2003) 1–11.

[7] H. Li, Y. Tang, Z. Wang, Z. Shi, S. Wu, D. Song, J. Zhang, K. Fatih, J. Zhang, H. Wang, Z. Liu, R. Abouatallah, A. Mazza, J. Power Source 178 (2008) 103–117. [8] Y. Wang, M. Ouyang, J. Power Sources 164 (2007) 721–729.

[9] D.T. Santa Rosa, D.G. Pinto, V.S. Silva, R.A. Silva, C.M. Rangel, Int. J. Hydrogen Energy 32 (2007) 4350–4357.

[10] Y. Zhang, A. Mawardi, R. Pitchumani, J. Power Sources 173 (2007) 264–276. [11] L. Matamoros, D. Bruggemann, J. Power Sources 173 (2007) 367–374. [12] S.U. Jeong, E.A. Cho, H.J. Kim, T.K. Lim, I.H. Oh, S.H. Kim, J. Power Sources 159

(2006) 1089–1094.

[13] S.U. Jeong, E.A. Cho, H.J. Kim, T.K. Lim, I.H. Oh, S.H. Kim, J. Power Sources 158 (2006) 348–353.

[14] H.K. Ma, S.H. Huang, Proceedings of the 4th International Conference on Fuel Cell Science, Engineering and Technology, 2006.

[15] X. Li, I. Sabir, Int. J. Hydrogen Energy 30 (2004) 259–371.

[16] X.D. Wang, Y.Y. Duan, W.M. Yan, X.F. Peng, J. Power Sources 175 (2007) 397–407. [17] C. Xu, T.S. Zhao, Electrochem. Commun. 9 (2007) 497–503.