Modeling Studies of a Cylindrical Polymer Electrolyte Membrane Fuel Cell Cathode

Modeling Studies of a Cylindrical Polymer Electrolyte MembraneFuel Cell CathodeSrinivasarao Modekurti,† Brian Bullecks,‡ Debangsu Bhattacharyya,*,§ and Raghunathan Rengaswamy‡

†Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600036, India‡Department of Chemical Engineering, Texas Tech University, Lubbock, Texas 79409, United States§Department of Chemical Engineering, West Virginia University, Morgantown, West Virginia 26506, United States

ABSTRACT: Traditional polymer electrolyte membrane fuel cells (PEMFCs) are planar. High cost and low gravimetric andvolumetric power densities are two major issues with the planar design. To improve the gravimetric and volumetric powerdensities of the PEMFCs and to reduce the cost, a novel cylindrical PEMFC design has been developed. The performance of theair-breathing cylindrical PEMFC is found to be superior to a state-of-the-art planar cell in the high current density region. Tounderstand the effect of various design parameters and operating conditions on the performance of the cylindrical PEMFC, two-dimensional, two-phase, steady-state models of the cylindrical cell for both air-breathing and pressurized conditions have beendeveloped in this work. The developed model of the air-breathing cylindrical PEMFC is validated with in-house experimentaldata. Experiments were conducted with hydrogen on the anode side and air on the cathode side. The cathode catalyst layer ismodeled using spherical agglomerate characterization. With the developed model, the effects of various operating and designparameters on the performance of the cell are studied. These studies show that the performance of the cylindrical cell can befurther improved by optimizing these parameters.

1. INTRODUCTIONPolymer electrolyte membrane fuel cells (PEMFCs) are verypromising for power generation in the low-temperature fuel cellcategory. To make PEMFCs commercially viable, their gravi-metric power density (power density per unit weight of thecell) and the volumetric power density (power density per unitvolume of the cell) should be improved, especially for man-portable and automotive applications. In addition, the manufactur-ing cost of the cell per unit power should be decreased. Thebipolar plates used in the conventional planar PEMFCs cancontribute as high as 42% of the cost and 62% of the weight ofa 1 kW fuel cell stack.1 According to Murphy et al.,2 the bipolarplates contribute to over 80% of the stack weight and almost allof the volume. Replacing the traditional graphite bipolar plateswith a low-cost, lightweight, noncorrosive, less bulky material,or elimination of it, can reduce some of the afore-mentionedproblems.In a recent publication, our group has presented a novel

cylindrical design of a PEMFC that eliminates some of thepreceding problems. The cell uses a wire mesh for reactantdistribution and current collection.3 The cell is found to haveconsiderably higher volumetric and gravimetric power densitiesin addition to lower cost when compared to a state-of-the-artplanar cell. Since the cylindrical cell could be arranged toexploit the gravitational force for water removal, flooding wasnot observed at high current density even by squirting liquid wateron the MEA.A number of patents have described the fabrication of

cylindrical PEM fuel cells.4−7 Green et al.8 have described thedevelopment of a low-weight tubular PEMFC considering stillor slowly moving air. The authors had used an acid-etched,roughened, stainless steel shim for current collection as well asreactant distribution in the cathode side. The authors have

highlighted the importance of the shape and size of the holes,and distribution of acid-etched stainless steel foils for theperformance and water management of a tubular PEMFC.Lee et al.9 have developed an air-breathing PEM fuel cell withcylindrical configuration.Even though there are some experimental studies on the

cylindrical PEMFCs, very few theoretical studies on the tubularPEMFCs can be found in the existing literature. Coursangeet al.10 have compared the cell performance of both tubular andplanar PEMFCs by three-dimensional (3-D) numericalsimulations. Three-dimensional computational fluid dynamics(CFD) models for both planar and tubular PEM fuel cells havebeen presented by Sadiq Al-Baghdadi.11,12

Models of various levels of complexities, ranging from simpleone-dimensional (1-D) single-phase to complex 3-D two-phasemodels are available in the open literature for the planarPEMFCs.13−15 Our group has previously published papers onmodeling of the planar PEMFCs as well as tubular solid oxidefuel cells (SOFCs).16−19 In the present work, we have devel-oped a two-dimensional (2-D) steady-state model of a cylindricalPEMFC cathode under air-breathing and pressurized con-ditions. The model for the air-breathing condition is validatedwith the experimental data from a tubular cell that was fabri-cated. The fabrication and the experimental details of thiscell have been presented in our previous publications andpresentations.3,20,21 Even though there are numerous studies onmodel-based optimization of planar PEMFCs,22−25 opti-mization studies of the tubular PEMFCs are rare in the open

Received: December 4, 2011Revised: February 16, 2012Accepted: March 12, 2012Published: March 12, 2012

Article

pubs.acs.org/IECR

© 2012 American Chemical Society 5003 dx.doi.org/10.1021/ie2028359 | Ind. Eng. Chem. Res. 2012, 51, 5003−5010

pubs.acs.org/IECR

literature. In this paper, a number of sensitivity studies arepresented to motivate possibilities for optimization of thecylindrical PEMFCs.

2. MODEL DEVELOPMENTA schematic of the cylindrical PEMFC is shown in Figure 1.The modeling domain consists of the cathode gas diffusion

layer (GDL) and cathode catalyst layer (CL) for the air-breathingcondition. Under the air-breathing conditions, the GDL is open tothe atmosphere.In developing the half-cell model, the following assumptions

are made: isothermal and steady-state operation; no variation ofthe concentrations/potentials in the θ-direction; ideal gasbehavior of the gas mixture; consideration of Butler−Volmerkinetics for the oxygen reduction reaction; liquid form for watergenerated due to the electrochemical reaction; istotropic gasdiffusivities and water permeability; and negligible anodeoverpotential.2.1. Conservation Equations. Gas Diffusion Layer. The

gaseous transport and the liquid water transport through theGDL are described by Fick’s first law and Darcy’s law,respectively. The conservation equations for the gaseouscomponents can be written as follows:

−∂

∂−

∂

∂− =

⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟r

rJ

r

J

zI

1 ( )0r za, a,

w(1)

where Ja,r and Ja,z are molar fluxes of the component “a” inr- and z-directions, respectively, and are given by

= − ∂ ∂J D C r/ra, aeff

a (2)

= − ∂ ∂J D C z/za, aeff

a (3)

Iw represents the interfacial transfer of water between liquid andvapor states and can be written as26

=ε −

−

+ε ρ

− −

I ks

RTy p p q

ks

Mp p q

(1 )( )

( )(1 )

k

k

w condcell

w w wsat.

evapw

ww w

sat.(4)

In the preceding equation, kcond and kevap are condensation andevaporation constants. s is the saturation level (defined as thefraction of void volume occupied by the liquid water), and εk isthe void fraction. pw and pw

sat. are partial and saturation pressures

of water vapor, respectively. The switching function (q) betweencondensation and evaporation is given by26

=+ | − | −

qp p p p1 ( )/( )

2w w

sat.w w

sat.

(5)

If the partial pressure of water vapor is less than the saturationpressure (pw < pw

sat.), the switching function becomes zero andthe interfacial process is evaporation. On the other hand, ifpw ≥ pw

sat., q becomes unity and the interfacial process iscondensation. The conservation equation for the liquid watercan be written as

−∂

∂−

∂∂

+ =⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟r

rNr

Nz

I1 ( )

0r zw ww

(6)

where Nwr and Nwz are liquid water flux in r- and z-directions,respectively, and are given by

= −ρ

μ− ∂

∂⎛⎝⎜

⎞⎠⎟N

K K

MPs

sr

ddr

cw

w w rl

w w (7)

= −ρ

μ− ∂

∂⎛⎝⎜

⎞⎠⎟N

K K

MPs

sz

ddzw

w w rl

w w

c

(8)

In eqs 7 and 8, Pc is the capillary pressure which is calculated by

= σ θ εP

KJ scos ( )c c

w (9)

where

=

− −− +−

θ <

− + θ >

⎧

⎨⎪⎪

⎩⎪⎪

⎫

⎬⎪⎪

⎭⎪⎪

J s

sss

s s s

( )

1.417(1 ) 2.120(1 ) 1.263(1 )

for 90

1.417 2.120 1.263 for 90

23

contact

2 3contact

(10)

Catalyst Layer. The conservation equations of the speciesalong with the electrochemical reaction can be written as

for O2:

−∂

∂+ −

∂

∂+ =

⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟r

rJ

r

J

zR

1 ( )0

r zO , O ,O

2 22

(11)

for N2:

−∂

∂+ −

∂

∂=

⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟r

rJ

r

J

z1 ( )

0r zN , N ,2 2

(12)

for H2O(v):

−∂

∂+ −

∂

∂− =

⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟r

rJ

r

J

zI

1 ( )0

r zH O, H O,w

2 2

(13)

for H2O(l):

−∂

∂+ −

∂∂

− + =⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟r

rNr

Nz

R I1 ( )

2 0r zw wO w2 (14)

where the term RO2is the consumption of oxygen per unit

volume of the catalyst layer. In this work, the catalyst layer ismodeled using spherical agglomerate characterization as shown

Figure 1. Schematic of a cylindrical PEM fuel cell.

Industrial & Engineering Chemistry Research Article

dx.doi.org/10.1021/ie2028359 | Ind. Eng. Chem. Res. 2012, 51, 5003−50105004

in Figure 2. This characterization assumes that the catalystparticles are spherical agglomerates with a thin film of ionomer

around them. It is also assumed that the water generated due tothe electrochemical reaction forms an ultrathin layer around theionomer film before participating in condensation/evaporation.It is assumed that the diffused oxygen from the manifold to thecatalyst layer dissolves and diffuses through both water andionomer films before reaching the reaction sites. The con-centration of the oxygen at the ionomer/spherical agglomerateinterface is16,17

| =

+δ

ζ

+δ

ζ

⎪

⎪

⎪

⎪

⎧⎨⎩

⎫⎬⎭

⎧⎨⎪⎩⎪

⎛⎝⎜⎜⎛⎝⎜⎜

⎞⎠⎟⎟⎛⎝⎜

⎞⎠⎟

⎞⎠⎟⎟

⎛⎝⎜⎜⎛⎝⎜⎜

⎞⎠⎟⎟⎛⎝⎜⎜

⎞⎠⎟⎟⎛⎝⎜

⎞⎠⎟

⎞⎠⎟⎟⎫⎬⎪⎭⎪

CRT

H C

D ak

D

H

H ak

11

1

r

O

O nscell

O ,mem O ,

mem

O ,mem 1reacn

w

O ,w

,w

O ,mem 1reacn

22 2

2

2

2

2 (15)

The conservation equation for the protons can be written as

−∂

∂−

∂

∂+ =ϕ ϕ⎛

⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟r

rJ

r

J

znFR

1 ( )0

r zO2

(16)

where Jϕr and Jϕz are the ionic fluxes in r- and z-directionswritten as

= −κ ∂ϕ ∂ϕ ϕJ r/r reff

(17)

= −κ ∂ϕ ∂ϕ ϕJ z/z reff

(18)

Considering the species transport and ohmic losses in thecathode, the overpotential within the CL can be calculatedusing the following expression:27

η = − + × −

− + Ω

−V V TRT

nFp I

8.453 10 ( 298.15)

ln( )

r cell oc4

cell

cellO2 (19)

where pO2is the partial pressure of oxygen, Tcell is the operating

temperature of the cell in Kelvin, Ω is the ohmic resistance ofthe cell, and I is the current generated that is calculated by

∫= −ε κ∂ϕ∂=

=

= −

⎛⎝⎜

⎞⎠⎟I

rz w zd d

z

z L r

r0 mem3/2

memCL mem

cell(20)

The boundary conditions for the species at various domains areshown in Table 1.

3. MODEL VALIDATIONTo solve the system of equations, MAPLE and MATLABsoftware have been used. The equations along with theboundary conditions were written and discretized in MAPLE.This generates a system of nonlinear algebraic equations (AEs)that are exported to and solved in MATLAB. A grid sensitivitystudy is carried out for deciding the final grid size so that anacceptable numerical accuracy is achieved, keeping thecomputational burden tractable in the MATLAB environment.At the final grid size, the change in the current density is lesserthan 0.1% from the previous coarser grid size. Figure 3 shows

the model validation for both of the cells with our in-houseexperimental data. The planar cell model has been presentedelsewhere.16 The model parameters and the correlations used inthe model development are presented in Table 2 and Table 3,respectively. The model parameters corresponding to the MEA

Figure 2. Schematic of spherical agglomerate characterization(redrawn from Rao et al.16).

Table 1. Boundary Conditions (C = Concentration, J = Gaseous Flux, N = Liquid Flux)a

variable entrance GC/DL DL/CL CL/mem

CO2CO2

= CO2,o CO2

GC = CO2

DL CO2

DL = CO2

CL, JO2

DL = CO2

CL ∇CO2

CL = 0

CN2CN2 = CN2,o CN2

GC = CN2

DL CN2

DL = CN2

CL, JN2

DL = JN2

CL ∇CN2

CL = 0

CH2O CH2O = CH2O,o CH2OGC = CH2O

DL CH2ODL = CH2O

CL , JH2ODL = JH2O

CL ∇CH2OCL = 0

s s = 0 sGC = sDL PcDL = Pc

CL, NwDL = Nw

CL ∇sCL = 0ϕr ∇ϕr = 0 ϕr = 0

aBoundary conditions along z-direction: Fluxes of all the variables are zero at the channel entrance and exit.

Figure 3. Performance comparison between tubular and planar cells.



are the same in both models. The ohmic resistance used in thismodel is based on the EIS data from our in-house cell.3 Figure 3shows that the errors between the experimental data and modelresults are within acceptable limits. The scaled relative errors incurrent density between the experimental data and modelresults are 0.0915 and 0.1043 for the cylindrical and planarcells, respectively. The concentration profile of O2, the liquidwater saturation profile, and the ionomer potential profile inthe CL of the air-breathing cylindrical cell are shown in Figures4, 5, and 6, respectively. As expected, the figures show thatthere is no change in the concentration of the gaseous speciesin the in-plane direction (z-direction) as the cell is the air-breathing type.

4. MODEL ENHANCEMENT FOR THE PRESSURIZED CELLIn this model, the cathode flow channel is included in themodeling domain. The conservation equations for the gaseouscomponents can be written as

−∂

∂−

−− =

uCz

JI

( ) 2RAD

RAD RAD0ra 1 a,

22

12 w

(21)

where RAD1 and RAD2 are the inner and outer radii of the gaschannel. The term Iw is zero for nonwater components. Forliquid water, the conservation equation can be written as

−ρ ∂

∂−

−+ =

M

s u

zN

I( ) 2RAD

RAD RAD0w

w

gc 1 w

22

12 w

(22)

Table 2. Design and Model Parameters

Design Parametersouter radius of channel, mm(for pressurized conditions)

13 platinumloading,mg cm−2

0.5

outer radius of GDL, mm 5 membranethickness, μm

50

GDL thickness, μm 200 fraction of Pt oncarbon in CL

0.4

GDL porosity 0.7 fraction ofionomer in CL

0.3

CL thickness, μm 15 active area, cm2 10CL porosity 0.42

Model ParametersKwo,GDL, m

2 8.7 × 10−12 ρPt, kg m−3 21450Kwo,CL, m

2 3 × 10−15 ρw, kg m−3 977.3α 1 σ, N m−1 0.0625ragg, μm (tuning parameter) 0.29 θcontact(GDL),

deg110

io, A m−2 (tuning parameter) 0.84 × 10−6 θcontact(CL), deg 100kcond, s

−1 100 Ωplanar3, Ω 0.011

kevap, atm−1 s−1 100 Ωtubular

3, Ω 0.023ρc, kg m−3 1800

Table 3. Correlations Used in Model Development16

Di,eff ε − s D(1 )k i3/2 3/2

m

Dim ∑−= ≠

−⎛

⎝⎜⎜⎜

⎞⎠⎟⎟y

y

D(1 )i

j i j

Nj

ij1;

1

HO2

mem−

⎛⎝⎜

⎞⎠⎟T

1.33 exp666

cell

HO2

w −⎛⎝⎜

⎞⎠⎟T

5.08 exp498

cell

DO2

mem × −− ⎛⎝⎜

⎞⎠⎟T

3.1 10 exp27687

cell

κeff λ − −⎛⎝⎜⎜

⎛⎝⎜

⎞⎠⎟⎞⎠⎟⎟T

100(0.005139 0.00326) exp 12681

3031

wcell

Figure 4. Concentration profile of O2 in the catalyst layer (CL) of theair-breathing cylindrical cell.

Figure 5. Liquid water saturation profile in the catalyst layer (CL) ofthe air-breathing cylindrical cell.

Figure 6. Ionomer potential profile in the catalyst layer (CL) of theair-breathing cylindrical cell.



The polarization curve under pressurized conditions is shownin Figure 7. As the operating pressure is increased, the cell

performance improves in the entire polarization range. In thepolarization range studied, the cell does not reach its limitingcurrent density when the operating pressure is increased fromthe atmospheric pressure to 1.5 atm.

5. PERFORMANCE COMPARISON BETWEEN THECYLINDRICAL AND PLANAR PEMFCS

The planar and tubular cells vary in their concentration andohmic polarizations. A comparison of polarization curveswith and without concentration losses is shown in Figure 8

for both types of cells. The operating conditions and modelparameters used in this study are the same as those used inthe model validation. Figure 8 shows that the concentrationlosses are more in the planar geometry in the entirepolarization range. Mainly due to this, the performance ofthe cylindrical cell is better than the planar cell at highcurrent densities where the concentration polarization is thedominating loss. As shown in Figure 3, this higherperformance is achieved at high current densities eventhough the ohmic resistance of the cylindrical cell is morethan the planar cell.

6. PARAMETRIC STUDIES

Though the air-breathing cell performs reasonably well, it isprimarily limited in oxygen supply at high current density. Amodel of a pressurized cell is developed by enhancing themodel of the air-breathing cell. Then this model is utilized tocarry out a number of parametric studies to study the effectof the cell temperature, platinum loading, and ionomerloading on the cell performance. We believe that results fromsuch studies can reduce the experimental trial-and-errorcycle time that inevitably accompanies the development ofany new technology. First, we present a model enhancementfor a pressurized cell before these parametric studies areundertaken.

6.1. Temperature. An increase in temperature enhancesthe reaction rate and improves the mass-transfer rate. On theother hand, an increase in temperature decreases the molarconcentration of oxygen at a given pressure and also increasesthe ohmic loss of the current collector. At a given operatingpressure, an increase in temperature reduces the proton con-ductivity due to dehydration of membrane at higher tempera-tures. The effect of operating temperature on cell performanceis shown in Figure 9. With the increase in temperature, a negligible

increase in the performance is observed in the 40−50 °C tem-perature range (not shown in the figure). Further rise intemperature (60 °C) results in relatively low performance. Eventhough temperature has a modest effect in the range studied, itcan have strong effect when it exceeds some higher/lowervalues due to drying/freezing.

6.2. Flow Rate. An increase in the cathode air flow ratereduces the concentration losses and hence increases the cellperformance. Since less amount of oxygen is required at lowcurrent densities, the increase in the flow rate has a negligibleeffect on the performance at high voltages. However, as the cellproduces more current, it requires a larger amount of oxygen.The increase in the flow rate not only supplies the requiredamount of oxygen for the cathode reduction reaction but alsoincreases the catalyst utilization. The polarization curves forvarious air flow rates are shown in Figure 10. As the flow rate isincreased from 0.25 to 1 LPM, a significant increase in theperformance improvement is observed. Further rise in the flowrate gave a slight increase in the current in the mass-transferlimiting region.

6.3. Platinum Loading. A greater amount of platinumreduces activation losses. However, this effect is dominant

Figure 7. Performance of the pressurized cylindrical cell for variouspressures.

Figure 8. Polarization curves of the cylindrical (air-breathing) andplanar cells with and without concentration polarization.

Figure 9. Effect of temperature on cell performance.



mainly in the low current density region where the activationloss plays the key role. At high current densities, concentrationand ohmic losses dominate. An increase in the platinum loadingwill in fact lead to an increase in the concentration over-potential due to reduction in the pore volume. The effect ofplatinum loading throughout the polarization range is shown inFigure 11. Figure 11 shows that as the platinum loading is

increased from 0.25 to 0.35 mg/cm2, there is an overall improve-ment in the performance in the entire polarization range. How-ever, as the loading is further increased to 0.45 mg/cm2, there is aninsignificant increase in the performance in the low to mediumcurrent density region. However, the cell performance is worse inthe higher current density region. This suggests that there is anoptimum platinum loading.The saturation profiles in the CL for different platinum

loadings at 0.3 V are shown in Figure 12. The numbers shownon the X- and Y-axes represent the discretizations in ther-direction and z-direction respectively. Number 1 on the X-axisrepresents the GDL/CL interface and number 10 representsthe CL/mem interface. Similarly, on the Y-axis, numbers 1 and20 represent the channel entrance and exit, respectively. Thesaturation is found to be considerably higher for platinumloading of 0.45 mg/cm2 compared to the lower platinum loadings.This is due to a decrease in the porosity with an increase in the Ptloading for a given thickness of the CL. The higher saturationleads to higher concentration losses in the cell with higherplatinum loading in the mass-transfer limited region.

6.4. Ionomer Loading. An increase in the ionomer load-ing results in a decrease in the ionic losses. On the otherhand, the void volume decreases causing higher concen-tration losses. Polarization curves for different ionomerloadings are shown in Figure 13. Figure 13 shows that when

the weight fraction of ionomer is increased from 20 to 30%,performance is improved throughout the operating voltages.When the weight fraction of ionomer is increased to 40%,the cell performance decreased, especially at high currentdensities. This suggests that there is an optimum loading ofionomer for improving the cell performance, especially athigher current densities. This happens because of theinterplay between the ohmic and concentration losses asthe ionomer content is changed.The spatial distribution of ionomer potential in the CL at an

operating voltage of 0.4 V is shown in Figure 14. The gradientin the potential is more for the ionomer loading of 20 wt %. Asthe loading is increased, the overpotential due to protontransport decreases and it has a positive impact on the cellperformance. On the other hand, with the increase in theionomer loading, the void volume reduces and hence themass-transfer losses increase. The partial pressure distribu-tion of oxygen at the voltage of 0.4 V is shown in Figure 15.

Figure 10. Polarization curves at various flow rates of air.

Figure 11. Effect of platinum loading on the cell performance ( f pt =0.2, f ionomer = 0.35, tCL = 20 μm).

Figure 12. Spatial distribution of liquid saturation inside the catalystlayer at 0.3 V.

Figure 13. Polarization curves for various ionomer loadings ( f pt = 0.2,mpt = 0.4 mg/cm2, tCL = 20 μm).



Figures 14 and 15 show that there is a strong trade-off betweenthe ohmic and concentration losses.

7. CONCLUSIONSA two-dimensional two-phase model of a cylindrical PEM fuelcell cathode is developed. The developed model is validatedwith the experimental data from an in-house, air-breathingcylindrical cell. The model is extended to a pressurized cell byconsidering the gas flow channel. As the operating pressure isincreased from atmospheric pressure to 1.5 atm, the cell doesnot reach the limiting current density in the entire polarizationrange. This shows the performance improvements that can beachieved with a pressurized cell compared to the air-breathingcell. Effects of change in the operating conditions (temperatureand flow rate) and catalyst layer design parameters (platinumand ionomer loadings) on the cell performance are studied. Inthese studies, each parameter is varied one at a time, keeping allother parameters constant. The temperature is found to have amodest effect on the performance in the temperature rangestudied. As the air flow rate is increased from a low flow rate,the cell performance improves significantly. Further increase inthe flow rate has negligible effect. The study suggests that thereis an optimum platinum loading because of an interplay

between the change in the activation losses and concentrationlosses as the platinum loading is changed. The study shows thatan optimum loading of ionomer content can improve the cellperformance, especially at higher current densities. This happensbecause of the interplay between the ohmic and concentrationlosses as the ionomer content is changed. The parametric studiesshow that a multivariable optimization study can significantlyimprove the cell performance in the entire polarization range.

■ AUTHOR INFORMATIONCorresponding Author*Tel.:+1-3042939335. Fax: +1-3042934139. E-mail: [email protected] authors declare no competing financial interest.

■ NOMENCLATUREPEMFC = polymer electrolyte membrane fuel cellCFD = computational fluid dynamicsGC = gas channelGDL = gas diffusion layerCL = catalyst layermem = membraneMEA = membrane electrode assemblyCa = concentration of species a (mol m−3)Da

eff = effective diffusivity of species a (m2 s−1)DO2

mem = diffusivity of oxygen in ionomer (m2 s−1)Dw

mem = diffusivity of liquid water in the membrane (m2 s−1)E = activation energy (J mol−1)f pt = weight fraction of platinum on carbonf ionomer = weight fraction of ionomerF = Faraday’s constant (C g−1 equiv−1)HO2

mem = Henry’s constant for air−ionomer interface (atm m3

mol−1)HO2

w = Henry’s constant for air−water interface (atm m3

mol−1)icell = cell current density (A m−2 Pt−1)Iw = interfacial transfer of water between liquid and vapor(mol m−3 s−1)Ja,r = local flux due to diffusion of species a in r-direction(mol m−2 s−1)Ja,z = local flux due to diffusion of species a in z-direction(mol m−2 s−1)Kw = absolute permeability of liquid water inside porousregion (m2)Krl = relative permeabilitympt = platinum loading inside the catalyst layer (kg of Pt m−2

CL−1)Mw = molecular weight of water (g mol−1)n = number of electrons taking part in the oxygen reductionreactionNw = flux of liquid water (mol m−2 s−1)Pc = capillary pressure (atm)R = universal gas constant (J mol−1 K−1)RAD1 = inner radius of the annulus (m)RAD2 = outer radius of the annulus (m)RO2

= rate of oxygen reduction reaction per unit volume ofthe catalyst layer (mol m−3 s−1)s = liquid water saturationtCL = thickness of the catalyst layer (m)Tcell = cell temperature (K)u = air velocity at the cathode inter (m s−1)

Figure 15. Spatial profile of oxygen partial pressure inside the catalystlayer (0.4 V).

Figure 14. Spatial variation of ionomer potential inside the catalystlayer (0.4 V).



mailto:[email protected]

mailto:[email protected]

Vcell = cell voltage (V)

Greek Lettersδmem = thickness of the ionomer film covering theagglomerate (m)δw = thickness of the water layer on top of the agglomerate(m)θcontact = contact angleμw = viscosity of water (kg m−1 s−1)ρw = density of water (kg m3)σ = surface tension (N m−1)

Subscripta = index for the species O2, N2, and H2O (v)

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Modeling Studies of a Cylindrical Polymer Electrolyte Membrane Fuel Cell Cathode

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