A Review of Recent Development Transport and Performance Modeling of PEM Fuel Cells

8/19/2019 A Review of Recent Development Transport and Performance Modeling of PEM Fuel Cells

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Review

A review of recent development: Transport and performance modeling

of PEM fuel cells

Horng-Wen Wu

Department of System and Naval Mechatronic Engineering, National Cheng Kung University, 1 Ta-Hsueh Road, Tainan 701, Taiwan, Republic of China

h i g h l i g h t s

This study reviews 2010–2015 two- and three-dimensional models on PEM fuel cells. Characteristics of transport in membrane, catalyst layers, gas diffusion layers, and channel are studied. This review offers valid findings for improving transport and performance of PEM fuel cells. This review presents a few highlighted areas on PEM fuel cells to be fundamentally realized.

a r t i c l e i n f o

Article history:

Received 2 October 2015Received in revised form 9 December 2015Accepted 17 December 2015Available online 31 December 2015

Keywords:

ReviewRecent developmentProton exchange membrane fuel cellPerformanceTransportModeling

a b s t r a c t

This study reviews technical papers on transport and performance modeling of proton exchange mem-brane (PEM) fuel cells during the past few years. The PEM fuel cell is a promising alternative powersource for various applications in stationary power plants, portable power device, and vehicles. PEM fuelcells provide low operating temperatures and high-energy efficiency with zero emissions. A PEM fuel cellis a multiple distinct parts device and a series of mass, momentum and energy transport through gaschannels, electric current transport through membrane electrode assembly and electrochemical reactions

at the triple-phase boundaries. These transport processes play crucial roles to determine electrochemicalreactions and cell performance, so studies on the transport and performance modeling have been donedeeply. This review shows how these modeling studies offer valid findings for transport and performancemodeling of PEM fuel cells and recommendations that can be applied in enhancing transport processesfor improving the cell performance.

2015 Elsevier Ltd. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 832. Fundamental model description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

2.1. Governing equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 842.1.1. Mass conservation equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

2.1.2. Momentum conservation equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 842.1.3. Energy conservation equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 842.1.4. Species transport equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 842.1.5. Charge equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

2.2. Numerical technique. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 852.3. Reliable solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

3. Characteristics of transport in membrane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 853.1. Water content and operation condition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 853.2. Property and geometric parameter of membrane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873.3. Geometric surfaces of membrane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

4. Characteristics of transport in catalyst layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 884.1. Catalyst layer structure parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 884.2. Geometric surfaces of catalyst layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

http://dx.doi.org/10.1016/j.apenergy.2015.12.075

0306-2619/ 2015 Elsevier Ltd. All rights reserved.

Applied Energy 165 (2016) 81–106

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5. Characteristics of transport in gas diffusion layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.1. Properties of gas diffusion layer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895.2. Pore structure of gas diffusion layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 905.3. Various configurations of gas diffusion layer surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

6. Characteristics of transport in flow field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 926.1. Two-phase flow and droplet dynamics in the channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 926.2. Channel configuration and geometric parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 946.3. External additions in the channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1006.4. Cross-sectional shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1026.5. Non-conventional channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1026.6. Flow field orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1036.7. Flow plate material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

7. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

Nomenclature

a electrocatalytic surface area per unit volume (m1)C mole concentration (mol m3)C p constant pressure specific heatD diffusivity (m2 s1)Db installed distance of two trapezoid baffles (mm)

E voltage (V)F Faraday’s constant (96,478 C mol1)H ; h height of gas flow channel (mm)H b height of trapezoid baffle (mm)hfg vaporization latent heati current density (A m2) j exchange current density (A m3)K permeability (m2)K rg the relative permeability of gas phaseK rl the relative permeability of liquid phasek gap sizekc constant of water condensationke constant of water evaporationkeff effective thermal conductivity (W K

1 m1)L length of gas flow channel (mm)

M molecular weight (kg mol1)MEA membrane electrode assemblyN number of rectangular blocksNFP Nafion weight ratioOPCF Open Pore Cellular FoamP pressure (Pa)PEM proton exchange membraneRe Reynolds numberRu universal gas constant (8.314 J mol

1 K1)Rch tapered ratioRagg agglomerate radius cmRH relative humidityS entropy (J K1)S T source term of energy equationS e source term of potential equation for the hydrogen

transportS i source term of species transport equationS l source term of water in liquid phaseS s source term of potential equation for the electron trans-

portSt stoichiometry ratios water saturation rate of pores in porous mediaT temperature (K)t time (s)t b; w width of gas flow channel (mm)

t r distance between two gas flow channels (mm)~u velocity vectors (m s1)V voltage (V) x mole fractionY mass fraction

a electric conductivity (X1 m1); wave amplitudeb wave numbere porosityeD dry porosity of electrodesf stoichiometric flow ratiog overpotentialh angle of trapezoid bafflejm ionic conductivity of the membranejs electric conductivity of the gas diffusion layerleff the effective viscosity of fluid (m s

2)q density of gas (kg m3)rs;eff effective electronic conductivity (X

1 m1)re;eff effective ionic conductivity (X

1 m1)/ phase potentialr gradient operator

Superscript eff effective g gas phases current conductors dissolvesat saturations coefficient of Bruggeman

Subscript a anodeagg agglomeratec cathodecell cell

e electrolyte phaseeff effectiveH2 hydrogenH2O wateri, j speciesl liquid water0 reference stateO2 oxygens solid phase

82 H.-W. Wu/ Applied Energy 165 (2016) 81–106

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1. Introduction

Over the past several decades, a combustion engine is widelyapplied to a power source for land vehicles, commercial marinevessels, stationary power plants, and so on [1]. However, the crisesof energy and environment are caused by consuming fossil fuelslong time and large amount. In addition, the Cancun Agreements

recognized the goals to limit average global temperature warmingwithin 1.5–2 C, and to reduce emissions emitted by membercountries under the Kyoto Protocol in a range of 25–40% below1990 levels by 2020 [2]. Therefore, researchers around the worldhave been developing technology on alternative power sources topossibly replace combustion engines and on alternative fuels forsolving the crises. A fuel cell is the most promising one of thesealternative power sources because it is an energy converter whichconverts the chemical energy of a fuel directly and efficiently toelectricity through a chemical reaction that brings high efficiency,simplicity, low emissions, and silence [3]. The PEM fuel cell has pri-mary advantages compared with other fuel types such as no risk of electrolyte leakage, short warm-up time, and high specific power.PEM fuel cell therefore becomes a most desirable option for powergeneration in the 21th century [4–8].

As shown in Fig. 1, a typical PEM fuel cell consists of bipolarplates with channels machined on either side for reactant distribu-tion over the electrode surface, a membrane electrode assembly(MEA), and porous gas diffusion layers sandwiching the MEA. Thenonlinear transport processes and electrochemical reaction occurfor the PEM fuel cell during operation as follows. Humidifiedhydrogen enters anode flow channel grooved in an anode bipolarplate, is transported through the channel, and diffuses into anodegas diffusion layer then into anode catalyst layer. At the same time,oxygen enters cathode flow channel grooved in a cathode bipolar

plate and is transported through the channel, and diffuses intocathode gas diffusion layer then into cathode catalyst layer, mem-brane, anode catalyst layer, and anode gas diffusion layer. Whenhydrogen is oxidized at the anode catalyst layer, protons and elec-trons are generated. The protons go through the membrane and theelectrons go through an external circuit. Oxygen then reacts withprotons and electrons at the cathode catalyst layer to form water.

Water is transported out of the cathode catalyst layer, throughcathode gas diffusion layer, and finally out of the cathode flowchannel.

In summary, the phenomena involved in PEM fuel cell operationare quite complex including inherently three-dimensional heattransfer, species and charge transport, multi-phase flows, and elec-trochemical reactions. Because the phenomena take place in thecompact and complex design of PEM fuel cell, it is quite difficultand expensive to conduct measurements within the fuel cell. Acomprehensive and well-verified mathematical and numericalmodel can thus be established to offer detailed information onfluid flows, heat transfer, and chemical reactions within the fuelcell [9–13]; in particular, it is not necessary to offer precise valuesfor every computed quantity over the computational domain, butwould rather offer correct trends over a wide range of operatingconditions. The numerical studies on well-verified transport mod-eling of PEM fuel cell accurately predict the trends of cell perfor-mance varying operating parameters. Available operatingparameters and their conditions can be determined to improveperformance of PEM fuel cell via the appropriate transport model-ing. The well-described transport phenomena through the model-ing can help realize the cause of improved performance of PEM fuelcell and the practicability of actual application in the real fuel cell.

Modeling of PEM fuel cell may fall into three categories includ-ing analytic, semi-empirical, and mechanistic models [9]. Among

Fig. 1. Typical PEM fuel cell structure.

H.-W. Wu / Applied Energy 165 (2016) 81–106 83

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these models, mechanistic models accurately predict performanceover a wide range of operation conditions. They are very useful formaking quick predictions for designs that already exist. They canbe used to predict the performance of innovative designs, or theresponse of the fuel cell to parameter changes. The mechanisticmodeling has one-dimensional, two-dimensional, and three-dimensional models according to different space dimensions but

the use of a one-dimensional modeling limits the description of fluid flow in the gas channels, as the fluid flow direction withinthe channels is normal to the gas’ diffusion direction. Therefore,this study reviews the latest studies on PEM fuel cell using two-dimensional, and three-dimensional models. In general, thesemodels numerically solve the governing partial differential equa-tions that represent the fluid flow, heat transfer, species and chargetransport, and the chemical and electrochemical reactions thattake place in fuel cells. The numerical solution can offer spatial dis-tributions of physical quantities in the fuel cell, such as the distri-butions of the fluid velocity, temperature, pressure, speciesconcentration, electric current, water content, and power density.

2. Fundamental model description

The PEM fuel cell is a sophisticated multiple-physics couplingsystem. The fuel cell computational fluid dynamic model iscomposed of the flow momentum, energy, mass species transport,electrochemical reactions, and current transfer within distinct sub-regions with various material properties and source terms. Severalassumptions on the model are made as follows:

(a) The flow is laminar and incompressible on the basis of smallgas pressure gradient and low Reynolds number.

(b) Both the fuel and oxidant gases are considered as ideal gases.(c) Porous properties of electrodes and membrane are homoge-

neous and isotropic.(d) Gravity effect is ignored.(e) Ohmic potential resistance between solid layers such as flow

channel, diffusion layer, catalyst layer and exchange mem-branes is overlooked.

(f) Butler–Volmer equation is used to compute the fuel and oxi-dant electrochemical reactions in the catalyst layers.

Fundamental model description includes governing equations,numerical technique, and reliable solutions [4,5,7]. The governingequations under the above-mentioned assumptions are describedbelow.

2.1. Governing equations

If steady-state is considered, then @ @ t

¼ 0 in the following equa-tions. If single-phase is considered, then s ¼ 0, and S l ¼ 0 in the fol-

lowing equations.

2.1.1. Mass conservation equation

@ ðeqÞ@ t

þr ðq~uÞ ¼ 0 ð1Þ

where e ¼ ð1 sÞeD, eD is dry porosity of electrodes, s is watersaturation, q is the density of gas mixture, and ~u is the vector of velocity; q ¼

PiY iqi.

2.1.2. Momentum conservation equation

e@ ðq~uÞ@ t þr ðeq~u~uÞ ¼ erP þr ðeleff r~uÞ

leff

e2~uK ð2Þ

where ~u is velocity vector, P the pressure, e porosity, q the densityof fluid, leff the effective viscosity of fluid, and K permeability.

2.1.3. Energy conservation equation

@ ðqC pT Þ@ t

þ ðeqC pÞð~u rT Þ ¼ r ðkeff rT Þ þ S T ð3Þ

where T is the temperature, C p is constant pressure specific heat,and keff is the effective thermal conductivity. The source term

S T ¼ i2mjm

in the membrane, S T ¼ i2ejs

þ S lhfg in the gas diffusion layer,

S T ¼ T ðDS Þ

4F þ gh i

j þ i2m

jmþ i

2e

jsþ S lhfg in the catalyst layer, and S T = 0

in the flow channel.

2.1.4. Species transport equation

@ ðeY iÞ@ t

þr ðeq~uY iÞ ¼ r J i þ S i S l ð4Þ

where Y i the mass fraction.

J i ¼ qDeff i rY i þ qY iM Deff i rM qY i

Xi

Deff j rY j qY i DM M

X j

Deff j Y j

ð5Þ

where Deff i is the effective diffusivity for specie i, and Deff

j is theeffective diffusivity for specie j.

In Eq. (4), the S i is the mass generation source term which is ja M H2=2F for hydrogen, jc M O2=4F for oxygen, and jc M H2O=2F for water vapor; S l is considered for two-phase, and expressed bythe following correlations:

S l ¼ M H2Okc

eY H2OqRuT

ðP H2O P satÞ; if P H2O > P sat

keesðP sat P H2OÞ; if P H2O < P sat

( ð6Þ

Following the Bruggeman correlation to account for the effectsof porosity and tortuosity in porous electrodes and membrane, thisstudy modifies the effective mass diffusion coefficient as

Deff i ¼ Die1:5 ð7Þ

where the diffusion coefficient of species is a function of tempera-ture and pressure, i.e.,

DiðT ;P Þ ¼ D0;iT

T 0

1:5P 0P

ð8Þ

For PEM fuel cell operation, the second specie on anode side andcathode side is water vapor, which is assumed to exist at the satu-ration pressure. The molar fraction of water vapor is expressed asfollows:

xH2O;v ¼P satH2OðT Þ

P g ð9Þ

where saturation pressure P satH2O is a function of temperature and is

given by

log10P satH2O

ðT Þ ¼ 2:1794þ 0:02953 T 9:1837 T 2 þ 1:4454 T 3

ð10Þ

where T is the temperature in K. The sum of all mass fractions isnotably equal to unity.X

Y i ¼ 1 ð11Þ

If two-phase is considered, then liquid water transport equationis expressed by the following equation [7]:



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@ ðeqlsÞ@ t

r qlKK rl

ll

@ P c @ s rs

r

qlK rlllK rg

rP

¼ S l ð12Þ

where q l is the density of liquid water, ll is the viscosity of liquidwater, M H2O is the molecular weight of water, K rl is the relative per-meability of liquid phase, K rg is the relative permeability of gasphase, and P c is capillary pressure.

2.1.5. Charge equation

The potential equations for both solid and electrolyte phases areobtained by applying Ohmic’s law:

r ðrs;eff r/sÞ ¼ S s ð13Þ

r ðre;eff r/eÞ ¼ S e ð14Þ

The source terms in the electron and proton transport equa-tions, i.e., Eqs. (13) and (14), result from the electrochemical reac-tion occurring in the catalyst layers of anode and cathode sides.

Anode Catalyst layer

S e ¼ ja; S s ¼ ja ð15Þ

Cathode Catalyst layer

S e ¼ jc ; S s ¼ jc ð16Þ

The ja and jc are the exchange current density at anode side andcathode side, calculated by the Butler–Volmer expression [7]:

ja ¼ ðairef o Þa

C H2

C ref H2

!12

expðaaaF =RTÞga expðaac F =RTÞga

ð17Þ

jc ¼ ðairef o Þc

C O2

C ref O2

! expðac aF =RTÞgc expða

c c F =RTÞgc

ð18Þ

where a is the electrocatalytic surface area per unit volume, m1. gathe overpotential at anode, and gc the overpotential at cathode:

ga ¼ /m /s;a

gc ¼ /s;c /m V O

where V O is the open circuit voltage.

2.2. Numerical technique

Before numerical methods are applied to solve the governingequations, the discretization of these equations has to be carriedout by several techniques such as finite difference, finite element,finite volume, and so on. This therefore leads to a set of simultane-ous linear algebraic equations that are solved numerically in acomputational mesh. The solutions to this set of equations are

obtained according to the boundary conditions that are specifiedaccording to the operating conditions of the fuel cell.

2.3. Reliable solutions

Insufficient mesh discretization may cause solution errors, sothe denser and finer meshes along the interface boundaries (suchas the interface between membrane and catalyst, the interfacebetween catalyst layer and diffusion layer, the interface betweendiffusion layer and channel) and near channel walls are used totreat with steep gradient in the flow variables distribution toobtain more accurate solution. The sensitivity test of mesh andtime step (for transient case) has to be made before the numericalmethod is applied to solve the problems. The sensitivity test of

mesh has to use at least three sizes of grid or node and that of timestep has to employ at least three sizes of time step to make sure

that the solutions are independent and convergent. In addition,the numerical modeling has to be validated by experimental dataor previous study’s data for wide operating conditions before theyare employed in the modeling. Validation would be an importantcomponent of modeling work; in particular, Wang and Chen[14,15] validated detailed liquid water distribution in PEM fuelcells with neutron radiography data.

The reviewed models separately investigated characteristics of transport in membrane, catalyst layers, gas diffusion layers, andflow field and their effects on the cell performance [5,6,9] as fol-lows. The following models took into consideration isothermaland non-isothermal conditions. The isothermal considerationmeans that temperature change in the PEM fuel cell is not takeninto account in the model. The non-isothermal considerationmeans that temperature change in the PEM fuel cell is taken intoaccount in the model. The non-isothermal models can predict thereal situations in the PEM fuel cell. However, the isothermal andnon-isothermal models predict almost the same performance onlywhen a single fuel cell operates with a small dimension and higherconductivities of the porous layers and the bipolar plates. In addi-tion, the isothermal consideration can simplify and accelerate thesolving processes.

3. Characteristics of transport in membrane

The membrane transports water from the cathode to the anodeby ionic drag and mass diffusion. In polymer membrane material,proton transport is achieved by water contained in the membraneand the electric field between the anode and the cathode. The pro-tonic conductivity of membrane is therefore heavily dependent onits water content and has a significant impact on the cellperformance.

3.1. Water content and operation condition

The water content in the membrane during the cell operation isdetermined by the balance of water or its transport. Hydration of the membrane is essential to minimize resistivity and Ohmic lossesin the fuel cell. External humidification is often used when reactingwater is insufficient to achieve full hydration of the membrane,especially in the cathode inlet regions. Nevertheless, in the fuelcell, this leads to excess water accumulation, which causes floodingin the catalyst layer, and generates a decrease in the active reactionarea and a drop in voltage. In addition, the water eventuallyappears in gas channels and leads to an increase in parasitic pump-ing power and even channel clogging. Proper humidification of thereactants can improve membrane hydration, and an appropriateflow stoichiometry can increase liquid water removal. Kim [16]therefore developed a two-dimensional, steady, and isothermal

five-layer MEA model to examine how relative humidity (RH)and stoichiometry of reactants influence membrane water contentand cell performance. He observed that at a constant cathode RHequal to 100%, a lower anode RH provides sufficient water to main-tain membrane hydration by water back-diffusion and henceenhances the cell performance. Higher anodic stoichiometryreduces cathodic water saturation by increasing water back-diffusion, making membrane hydration and thus enhancing thecell performance. Higher cathodic stoichiometry also reduceswater saturation at the cathode, which promotes the back-diffusion of water to make membrane hydration and thenenhances the cell performance. He et al. [17] presented a three-dimensional, two-phase transport mixed-domain model to explorewater management issues with the existence of condensation/

evaporation for a full PEM fuel cell by finite element-upwind finitevolume method with Newton’s linearization schemes. Their model


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involves both anode and cathode sides in three water phaseswithin membrane with corresponding interfacial boundary condi-tions considering the equality of water flux on the interfacesbetween the membrane and the catalyst layers. They showed thatthey obtain a fast convergent nonlinear iteration and the mass bal-ance errors less than 5%. Once the liquid water is formed, it goesinto the gas diffusion layer by the gaseous phase. The liquid waterleaves the gas diffusion layer only as the rising gradient of capillarypressure finally overcomes the viscous drag.

Dadda et al. [18] adopted a multi-species, two-dimensional, and

transient non-isothermal numerical model to investigate how heatand mass transfer influence potential variation in the membrane of a PEM fuel cell. Their results showed that the voltage loss is moreimportant in the regions with less water content. In addition, as thepressure gradient increases, the voltage loss across the membranerises. An applied heat flux on the membrane outlet does not affectthe voltage loss. An imposed water flux at the cathode side of themembrane can decrease the voltage loss rather than an appliedheat flux on the membrane outlet because the membrane becomesmore hydrated. The imposed negative water flux should be con-trolled because a permanent damage could appear in the mem-brane as too much water is removed. Decreasing the pressuregradient decreases the voltage loss since it forced less water trans-port from the cathode to the anode.

Afshari and Houreh [19] employed a three-dimensional, non-isothermal model to study the performance of the porous metal

foam in membrane humidifier for a PEM fuel cell. Their model isto solve the conservation equations of mass, momentum, speciesand energy for all regions of the humidifier. They discovered thatwater recovery ratio and dew point at dry side outlet are higherwith the metal foam installed at wet side and both sides than withthe conventional humidifier, indicating a better humidifier perfor-mance. On the contrary, employing metal foam at dry side has nopositive effect on humidifier performance. Ahmadi et al. [20] con-ducted a three-dimensional, single phase model in a PEM fuel cellwith straight flow channels to investigate transport phenomena

and the effect of inlet gases humidity on the cell performance. Theirresults indicated that the inlet gases humidity and membranewater management are the most important parameters that affectcell performance and transport phenomenain thefuel cell. At lowervoltage (for example 0.6 V), electrochemical reaction rate risesowing to much oxygen consumption. An increase in oxygen con-sumption leads to the increase in water formation and the amountof forming water along the cell. The current density loss is more atrelativehumidityof 25% because of severe drying of membrane anda great decrease in ionic conductivity for this humidity.

Houreh and Afshari [21] developed a three-dimensional, non-isothermal numerical model to compare the performance betweencounter-flow humidifier and parallel-flow humidifier, and foundthat the performance of counter-flow humidifier is better than that

of the parallel-flow humidifier; this is because temperatureincreases and mass flow rate decreases at dry side inlet.

Fig. 2. Cell temperature distribution in the MEA with Nafion 112, 115 and 117 when total heat release is fixed at 10,000 W m2 (a) cell temperature contours and (b) celltemperature distribution in the through-plane direction [28].



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Nevertheless, the humidifier performance at the low flow ratesimproves slightly by increasing the temperature of inlet dry gas.The increase in relative humidity at dry side inlet does notprovide any benefit. Tiss et al. [22] presented a two-dimensional,non-isothermal model considering the membrane water content,thermal and mass diffusion in the cathode of a PEM fuel cell. Theydiscovered that membrane water content can be affected by the

parameters in the cathode such as humidification temperature,inlet velocity, and membrane characteristics. When the humidifi-cation temperature rises, the water content in the membraneincreases and the pore size becomes larger to improve protontransport. As the inlet velocity of the gas channel increases, con-vection and diffusion of water from backing layer to membranebecome more significant than the water dragged by protons andthe water content thus increases. The increase in Reynolds numbercauses higher gas velocity and hence more removal of the liquidwater. Xing et al. [23] developed a two-dimensional, isothermal,two-phase flow agglomerate model to explore how dry Nafionionomer volume fraction and cathode relative humidity affectmembrane and ionomer swelling and the cell performance for aPEM fuel cell. Their results showed that the optimum ionomerwater content increases with an increase in the ionomer content.The optimum cathode relative humidity is between 60% and 80%for dry Nafion ionomer volume fraction of 40%. At higher currentdensities, the optimum cathode relative humidity initiallydecreases then increases with increasing the ionomer content.

3.2. Property and geometric parameter of membrane

The water adsorption and desorption coefficients are the mostimportant properties of membrane. The function of membrane isto conduct protons from anode to cathode when repelling the elec-trons, therefore forcing the electrons to travel through the outercircuit to generate electric work. In fact, proton conductivity isbasically because of proton migration inside the hydrated mem-brane and increases with the water activity. The water uptakeand loss is thus also of fundamental importance for the properfunctioning and the long-time stability of PEM fuel cells becauseit is related to irreversible dimension changes of the material anda morphological instability, which can be connected to themechanical properties of the membrane, in particular, its elasticmodulus.

Verma and Pitchumani [24] used a two-dimensional, singlephase, transient, and isothermal model to predict transient watercontent distribution in the membrane of a single-channel PEM fuelcell. They discovered that step increase in current density leads toanode dryout because of electro-osmotic drag, causing voltage

reversal and may lead to cell degradation. The transient variationin voltage is strongly correlated to the water diffusion in porousmedia and membrane properties such as water diffusion coeffi-cient, electro-osmotic drag coefficient, ionic conductivity, thick-ness, and equivalent weight. As water uptake capacity increases,the undershoot in voltage response decreases owing to theincrease in back diffusion rate. The voltage reversal can be avoided

by a graded membrane design. Chaudhary et al. [25] developed atwo-phase, non isothermal, transient and two-dimensional modelto water uptake by the membrane in a PEM fuel cell. They consid-ered two approaches of water-uptake by the membrane includingthe Schroeder’s paradox and individual contributions of watervapor and liquid water. They observed that water uptake by mem-brane, current density, water content of the membrane, tempera-ture of the cell, and so on, significantly vary for the twoapproaches. Transient rate of sorption or desorption of water bymembrane could respond to water content of membrane whenthe cell voltage was applied by a step change.

Wu et al. [26] examined the non-equilibrium membrane waterabsorption/desorption processes along with non-equilibriumcondensation/evaporation processes employing a transient three-dimensional non-isothermal model that fully coupled multi-species and multi-phase transport, electrochemical kinetics, andheat transfer processes for a single channel of a PEM fuel cell. Theirresults showed that the cell current density increases with adecrease in water sorption/desorption rate coefficient since themembrane tends to be better hydrated. In addition, compared withthe liquid production modeling the response time of PEM fuel cellsin vapor production modeling is substantially overestimated owingto the slow condensation process.

Iranzo et al. [27] developed a three-dimensional non-isothermalmodel for a PEM fuel cell with serpentine flow field bipolar platesto investigate how the membrane thermal conductivity affects thecell performance. They found that the membrane thermal conduc-tivity has positive influences on the cell performance, especially athigher current densities, increasing the cell electric power up to

50%. This is because of the better thermal and water managementwhich causes an increased membrane water content and hencehigher protonic conductivity. With higher thermal conductivity,the membrane can better remove the heat produced by the cath-ode electrochemical reaction and by the Ohmic heat within thecell.

Karpenko-Jereb et al. [28] developed a one-dimensional isother-mal model for water and charge transport through the membranewith temperature dependent properties in a PEM fuel cell. Thedependency of diffusion and electro-osmotic coefficients on themembrane water concentration is approximated by linear func-tions. This developed membrane model was coupled with thethree-dimensional CFD code AVL FIRE to simulate polarizationcurves of the cell at various relative humidity values of the inlet

air at the cathode. Their results displayed that a lower inlet relativehumidity decreases water concentration in the membrane andthen decreases proton conductivity and current density. Junget al. [29] presented a non-isothermal and two-dimensionalagglomerate model to investigate how Nafion thickness influencestemperature distribution inside the MEA of a PEM fuel cell. Theirresults showed that Nafion 117 MEA has the highest cell tempera-ture in the cathode catalyst layer as indicated in Fig. 2a amongNafion 112, 115 and 117 MEAs (thickness of Nafion 117 larger thanthickness of Nafion 115 which is larger than thickness of Nafion112), because of the most of the heat releases by the oxygen reduc-tion reaction in the cathode catalyst layer. This means that theraised thickness of Nafion can act as an additional heat transferbarrier, which reduces heat transfer from cathode catalyst layer

to anode side. The cell temperature in the cathode increases withan increase in Nafion thickness as displayed in Fig. 2b owing toFig. 3. Schematic of PEM fuel cell cathode with agglomerate in catalyst layer [32].


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the heat accumulation. Nevertheless, the cell temperature distribu-tions in the cathode are similar to those in the anode.

3.3. Geometric surfaces of membrane

Deflecting the MEA from shoulder to shoulder is one of approaches to improving the performance of PEM fuel cells to fixboundary conditions for the same reacting area as the shoulderwidth reduces by diffusing more reactants through the gas diffu-sion layer to the reacting area. Pourmahmoud et al. [30] presenteda three-dimensional non-isothermal model for parallel flow chan-nels, gas-diffusion electrodes, catalyst layers, and the membraneregion in a PEM fuel cell with deflected MEA. Their results showedthat fuel cell performance is larger for non-zero deflection param-eter than for zero deflection parameter because of greater facewidth and more reactants diffusing through the gas diffusion layerover the reacting area. As the deflection parameter increases up tothe maximum value equal to channel height, the fuel cell perfor-mance will reach the maximum.

4. Characteristics of transport in catalyst layers

At theanode catalystlayer, water vapor is absorbed into theelec-trolyte and the water molecules tend to transport with the protonsthrough the membrane toward the cathode catalyst by the electro-osmotic drag. On the other hand, the electrons are transported fromtheanode catalystlayerthroughexternal circuit to reach thecathodecatalyst. At thecathodecatalyst,water is formed at theplatinum cat-alyst surface and the promoted local water concentration tends tocounteract the water transport from the anode side.

4.1. Catalyst layer structure parameters

To simulate the catalyst layer accurately is a challenge since itsstructure characteristics and properties cover the extent frommicroscopic to macroscopic scales. The complicated porous cata-lyst layer structure composed of Pt, carbon support, ionomer elec-trolyte, gas pores, and liquid water clearly stands for a multiscale,multiphase problem having all sorts of reactions, and mass andheat transport phenomena. Das et al. [31] developed a two-dimensional, two-phase, volume-averaged isothermal model tostudy how structure of catalyst layer and its surface wettabilityaffect liquid water transport in the cathode catalyst layer of aPEM fuel cell. The catalyst layer is assumed to be a macro-homogenous layer, and thus the physical structure of cathode cat-

alyst layer would be quantified by its porosity. The porosity of cat-alyst layer depends on the platinum (Pt) and Nafion loadings; then,

their results are discussed as the functions of Pt and Nafion load-ings. They found that the catalyst layer wetting properties affectthe flooding in the cathode catalyst layer, and the liquid water sat-uration in a hydrophilic cathode catalyst layer decreases with an

increase in the surface wettability or a decrease in the contactangle. Nonetheless, the catalyst layer wettability little influencesthe liquid water transport inside the gas diffusion layer. On thecontrary, the cathode catalyst layer structure (platinum and Nafionloadings) affects both the liquid water and oxygen transports sig-nificantly throughout the thicknesses of cathode catalyst layerand gas diffusion layer. In addition, the linear decrease of activereaction area with liquid water saturation is not enough to catchthe true behavior of oxygen transport because the linear decreaseapproach overestimates the active reaction surface area in thecathode catalyst layer. The highest liquid water saturation in thecathode catalyst layer is found under the rib while the lowest valuefound under the flow channel. The wetting and geometric charac-teristics of cathode catalyst layer influence the liquid water trans-

port significantly, and the liquid water saturation in a hydrophiliccatalyst layer decreases with an increase in cathode catalyst layersurface wettability or a decrease in cathode catalyst layer contactangle. Dobson et al. [32] presented a two-dimensional, isothermal,constant pressure numerical model to calculate agglomerate sizeand porosity within the catalyst layer. Their results showed thata unique set of agglomerate size and porosity can accurately char-acterize the cell performance over a wide range of operating condi-tions. The uncertainty can also be decreased in model predictionswith the proposed least-square methodology.

Cetinbas et al. [33] built a three-dimensional isothermal modelfor a PEM fuel cell cathode using a modified agglomerate approachon the basis of discrete catalyst particles. Their results indicatedthat similar to the classical approach, the modified three-

dimensional model is capable of reproducing previous articles’trends of reactant, reaction rate, and overpotential distributions,but the macro-homogenous model cannot predict mass transportlosses accurately. In addition, their model can properly predictthe effect of Pt loading in the diffusion-loss region while the clas-sical approach offers nearly identical results with variation of Ptloading. Roshandel and Ahmadi [34] presented a two-dimensional, isothermal, computational model on the basis of agglomerate structure of catalyst layer to explore how catalystloading gradient in the catalyst layer affects the performance of aPEM fuel cell. Their model is set up on the basis of agglomerate cat-alyst and describes reactant species and charge (ion and electron)transport at the cathode of a PEM fuel cell. The catalyst layer isconsidered to be a region composed of small homogenous agglom-

erates and the agglomerate is enclosed by the electrolyte film asindicated in Fig. 3. The feasibility of catalyst loading is thought

Fig. 4. Sphere-packing schemes (a) tetragonal, and (b) rhombohedral packing in catalyst layer composition [33].



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about in two direction, ‘‘across the layer” from membrane/catalystlayer interface to catalyst layer/gas diffusion layer interface and ‘‘incatalyst plane” under both channel and land areas. They found thatthe catalyst loading distribution in the both directions affects thecatalyst use significantly. By bipolar plate configuration, gas diffu-sion layer/catalyst layer characteristics and external load regimeinfluence the location of maximum local current density. Employ-

ing catalyst in locations with higher reaction rates improves thecell performance.Cetinbas et al. [35] developed a two-dimensional steady-state

isothermal model of species and charge transport for the cathodecatalyst layer of a PEM fuel cell employing packing arrangementsin catalyst layer on the basis of two regularly packed spheres:rhombohedral and tetragonal as shown in Fig. 4. Furthermore,the equations used in the agglomerate model are reformulated tocorrectly explain the decrease in the agglomerate surface areaowing to overlapping particles. They investigated how Pt|C weightratio and Pt loading affect the optimum ionomer loading, as well ascatalyst layer thickness affects performance. They observed thatfor Pt|C greater than 15%, as the amount of carbon decreases, thelimiting current reaches earlier because of a lower effective surfacearea by increasing the overall porosity. With the rhombohedralpacking scheme for NFP = 30% and Pt = 0.2 mg/cm2, the currentdensity improves with catalyst layer thickness from 6 to 10 lmbecause the porosity increases from 3.5% to 42% and it enhancesreactant transport. For catalyst layer thickness larger than 10 lm,the current density decreases owing to higher charge transferlosses.

Xing et al. [36] developed a two-dimensional, steady-state, non-isothermal, two-phase, and agglomerate model for a PEM fuel cellto study how operating temperature and width ratio of channelaffect cell performance. They discovered that heat accumulatesinside the cathode catalyst layer on the area under the channel.The higher the operating temperature is, the better the cell perfor-mance becomes; this is because the kinetics increase, the liquidwater saturation on the cathode reduces and the water carrying

capacity of the anode gas increases. Using higher temperature of the anode improves the cell performance on account of an increasein the oxygen reduction reaction. In addition, enlarging the chan-nel/rib width ratio enhances the cell performance because of anincrease in the reaction area of the oxygen with the cathode cata-lyst layer and an increase in the amount of water at both the anodeand cathode. Obut and Alper [37] presented a three-dimensional,non-isothermal and two-phase numerical model in a straight flowfield channel to investigate the influence of cathode catalyst layerparameters such as catalyst layer thickness, ionomer film thick-ness, agglomerate size and porosity on the performance of a PEMfuel cell. Their results revealed how these catalyst layer parametersinfluence diffusion coefficients, electrical, and proton conductivi-ties, and effectiveness factor determines the area specific power

density and mass specific power density of the PEM fuel cellseparately.

Cetinbas et al. [38] employed an improved agglomerateapproach in a two-dimensional cathode model [35] for speciesand charge transport to optimize the catalyst layer compositionsimultaneously in both the in-plane and through-thickness direc-tions to maximize the current density at activation, Ohmic anddiffusion-loss regimes. They observed that the zones of high con-centration shift from under the land to under the channel with adecrease in the operating voltage. Highest performance improve-ments in all operating regimes are obtained by optimizing NFPshowing that ion transport is relative important. Bidirectionally-graded distributions have higher performances than theunidirectionally-graded catalyst layer since they improve transport

properties as desired exactly at the high reaction-rate zones. Two-variable optimization on NFP/Pt and NFP/C distributions can obtain

higher performances than single-variable optimization, owing tosuperposition of benefits from two constituents.

Hao et al. [39] developed a three-dimensional model of a fullPEM fuel cell with the catalyst layer sub-mode at the low-Pt load-ing catalyst layer considering the interfacial transport resistancesat ionomer, water film and Pt particle surfaces. They found thatthe electrode transport resistance dramatically increases not only

for Pt loading lower than 0.1 mg/cm

2

but also for catalyst materialfraction lower than 0.2. The agglomerate has negligible influenceon the cell performance if the agglomerate radius is smaller than150 nm.

4.2. Geometric surfaces of catalyst layer

Since the 10 lm thickness of catalyst layer is much smallercompared with the 0.1 mm thickness of gas diffusion layer, thesimplest description of the catalyst layer is offered by the interfacemodel in which a catalyst layer of infinitesimal thickness isassumed between the membrane and the gas diffusion layer. Thestructure of the catalyst layer is then ignored. The influence of cat-alytic activity is introduced as the boundary condition at the mem-

brane/gas diffusion layer interface. Since there are few reports oneffect of various geometric catalyst layer surfaces and catalystlayer boundaries, Perng and Wu [40] assumed catalyst layer tobe an ultra-thin layer and employed a two-dimensional isothermalmodel at the cathodic half-cell of a PEM fuel cell to investigate howthe prominence-like form catalyst layer surface and number of prominence influence the cell performance. They found that theprominent catalyst layer can promote local cell performance sinceit produces a better convection performance and a greater flowvelocity than the flat catalyst layer surface. In addition, the overallcell performance increases with an increase in the amount of theprominence because of speeding the fuel flow and magnifyingthe reaching area of the fuel gas.

5. Characteristics of transport in gas diffusion layer

Gas diffusion layers serve to provide structural support of thecatalyst layer and to transport the reactant and product towardand from the catalyst layer. In addition, they provide an interfacewhere ionization takes place and transport electrons through thecatalyst layer. A gas diffusion layer also plays an important rolein heat transport from the reacting site and the water managementof the cell. Without a gas diffusion layer, the membrane would bedried out by the channel gases.

5.1. Properties of gas diffusion layer

The performance of a PEM fuel cell is strongly influenced by

interdependent properties such as water management, porosityand graded structure of gas diffusion layer. The gas diffusion layershould possess the combined and balanced properties of hydrophobicity (water expelling) and hydrophilicity (water retain-ing). These properties have to be balanced carefully to ensure thatthe fuel cell system works without flooding and high humidity.

Ismail et al. [41] used a three-dimensional single phase isother-mal numerical model for a PEM fuel cell with one turn of a serpen-tine channel to study how the anisotropic gas permeability andelectrical conductivity of gas diffusion layer influence the cell per-formance. They found that the cell performance is little influencedby the anisotropy in the permeability of the gas diffusion layer.However, the cell performance is influenced significantly by theelectrical conductivity of the gas diffusion layer. This is because

the activation overpotential increases owing to the reduced solidpotential. Park et al. [42] performed a three-dimensional,



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two-phase unsteady, isothermal numerical model to examine theliquid water behavior in the gas diffusion layer under pressuregradient. Their results displayed that the contact angle of liquidwater and pressure gradient are the key factors that decide thestart of liquid water transport within the gas diffusion layer whichis initially wet with static liquid water. The larger contact angleremoves water faster from the gas diffusion layer at the fixed

pressure gradient. The pressure gradient caused by the reactantflow within flow channel and gas diffusion layer can effectivelyremove liquid water from the gas diffusion layer.

Khajeh-Hosseini-Dalasm et al. [43] used a three-dimensionaltransient two-phase non-isothermal model to investigate howoperating temperature and channel inlet humidity affect thephase-change rate in the cathode gas diffusion layer of a PEM fuelcell during startup. They incorporated a nonequilibrium evaporation–condensation interfacial mass-transfer rate in the model toconsider supersaturation and subsaturation. They observed thatwhen the case is dominant in condensation, it reaches steady statemore quickly. The maximum temperature decreases as timeincreases because of vapor-phase diffusion and phase change. Asoperating temperature decreases, the vaporation rate decreasesowing to the decreased saturation vapor pressure. As the inlethumidity of channel increases, the condensation rate increasesbecause of the lower difference between the saturated vapor pres-sure and the water vapor partial pressure. Hossain et al. [44] estab-lished a three-dimensional two-phase isothermal numerical modelinside the catalyst layers, gas diffusion layers and the flow chan-nels with one-dimensional water transport in the membrane of aPEM fuel cell to examine transport of species in a gas diffusionlayer considering the influences of liquid water saturation. A com-parison investigation between liquid water saturation modelemploying power law with exponential factors and a percolationbased model has been thoroughly made. Their results showed thatthe power law model with exponential factor of two offers a goodexpression of species diffusivity and generates much closer agree-ment with experimental cell voltage; by contrast, the percolation

based model overpredicts cell voltage. The impacts of isotropicand anisotropic permeability of gas diffusion layer have also beenexplored and their results indicated that a higher isotropic perme-ability or a combination of higher in-plane and lower through-plane permeability causes higher performance of a PEM fuel cell.The cell performance substantially reduces with lower in-planeand higher through-plane permeability of gas diffusion layer.

Abdollahzadeh et al. [45] developed a two-dimensional two-phase isothermal flow and transport numerical model in cathodegas diffusion layer of a PEM fuel cell without considering the flowand transport in channels. A wide parameter study was done toinvestigate how different operational and gas diffusion layerfactors affect cell performance. On the effect of gas diffusion layerfactors, they observed that the cell performance improves with an

increase in porosity of gas diffusion layer because of increasing dif-fusion coefficient for diffusion of reactants. Although the decreasein thickness of gas diffusion layer till 0.35 mm enhances the cellperformance, the more decrease less than 0.35 mm reduces the cellperformance. The cell performance increases with an increase inpermeability of gas diffusion layer owing to increasing flow rateof gas phase in gas diffusion layer. As the hydrophobicity of gas dif-fusion layer rises, the cell performance increases because of thebetter water removal from gas diffusion layer resulting from anincrease in capillary forces. de Souza et al. [46] investigated howthe hydrophobic characteristics of the gas diffusion layer affectthe water removal rate in rectangular and tapered channelsthrough a volume-of-fluid method to simulate two-phase, two-dimensional isothermal flow. They found that the water removal

rate is enhanced by greater liquid contact angles in the gas diffu-sion layer for a rectangular channel but not for a tapered channel.

Karimi et al. [47] presented a two-dimensional isothermalapproach for a single PEM fuel cell based on conservation lawsand electrochemical equations to provide useful insight into watertransport mechanisms and their effect on the cell performance.Theirresults have revealed that inlet stoichiometry and humidifica-tion, and cell operating pressure are important factors influencingcell performance and two-phase transport characteristics. The

water content in the anode side, which inclines to dry, has greatimpacton thecell performance. Theliquid saturation in the cathodegas distribution layer could be as high as 20%. The existence of liq-uid water in the gas diffusion layer decreases oxygen transport andsurface coverage of active catalyst so as to degrade the cell perfor-mance.The quality in thecathode gas channel is greater than 99.7%,which indicates that liquid water in the cathode gas channel is pre-sent in too small amounts to interrupt the gas phase transport. Caoet al. [48] developed a three-dimensional, two-phase, and non-isothermal numerical model of PEMfuel cell to investigate howani-sotropic features of gas diffusion layer, boundary temperature of flow plate, and gas inlet humidity affect the cell performance. Theirresults showed that the modeling of gas diffusion layer predictsmore accurate current density and temperature distributions withanisotropic properties than with isotropic properties. In addition,cooling inlet region and heating outlet region have a better cell per-formance while fully humidified gas, particularly in the outletregion, has a worse cell performance. Inamuddin et al. [49]employed a three-dimensional non-isothermal numerical modelof a PEM fuel cell to study how porosity and thickness of gas diffu-sion layer influencecell performance. They found that high porosityobtains high current density owing to more reactants reaching thereaction site. Larger thickness of the gas diffusion layer increasesthe consumption rate of reactant species at the interface betweenthe gas diffusion layer and catalyst layer. The effect of attachmentof bipolar plate to the gas diffusion layer reduces the amount of reactants to reach the catalyst layer particularly under the landarea. Nevertheless, this effect decreases with increasing overallporosity and the thickness of the gas diffusion layer.

5.2. Pore structure of gas diffusion layer

Simulating the transport inside gas diffusion layers is an essen-tial part of a fuel cell model due to the vital role of gas diffusionlayers. The macroscopic model is mostly employed and requiresempirical correlations such as the effective coefficients to accountfor the porous media property. These correlations can be devel-oped from the pore-level information obtained from direct model-ing/simulation. In addition, the pore-level study can providefundamental details regarding interaction between transport andpore structure, which is beyond the capability of a usual macro-scopic model.

Wang et al. [50] combined a stochastic model for reconstructing

the gas diffusion layer with direct simulation to study the pore-level transport in gas diffusion layers of PEM fuel cells. The carbonpaper gas diffusion layer is considered by a stack of layers witheach layer modeled by planar line tessellations which are dilatedto three dimension. The direct simulation was then applied forreconstructing gas diffusion layer structure to simulate themomentum and species transport in the pore, electronic conduc-tion in the solid matrix, and heat transfer for both phases. Distribu-tions of the velocity, species concentration, temperature, andelectronic potential in the gas diffusion layer were shown at thepore level. Their results indicated that the tortuosity of gas diffu-sion passage is 1.2 remarkably different from the tortuosity of solidmatrix across the gas diffusion layer which is 3.8. This differenceresults from the lateral alignment feature of the thin carbon fiber,

letting the solid-phase transport happen largely in lateral direc-tion. The values of tortuosity and permeability obtained from their



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modeling are fairly agreeable with the ones in the article. Further-more, diffusion commands the species transport in the pore evenat high net water flux per proton flux. Kopanidis et al. [51]employed a direct three-dimensional microscale model of a partof cathode channel in a PEM fuel cell and carbon cloth gas diffusionlayer to study local heat and fluid flow at the gas diffusion layer’spore scale and their influences on condensation of water vapor that

leads to flooding. The momentum, energy, and water vapor trans-port equations were solved at steady state and in three-dimensional space with different inlet velocities and cloth fibermaterial properties, applying a conjugate heat transfer method tocompute temperature distributions inside the solid fibers. Thethree patterns are as follows: (1) fixed fiber temperature assump-tion (T = 353 K), (2) conjugate heat transfer solution through fibermaterial supposing ELAT carbon cloth properties and (3) conjugateheat transfer solution through fiber material supposing pure car-bon (graphite) properties. They found that the conjugate heattransfer solutions lead to lower outflow temperatures with oneaccord compared with the assumption of constant fiber tempera-ture. In particular, the commercial cloth properties (ELAT) causelower outflow temperature and are more responsible to convec-tion; in other words, higher inlet velocities cause greater tempera-ture variations.

Yin et al. [52] presented a three-dimensional, unsteady, two-phase isothermal volume of fluid model based on the microstruc-ture of gas diffusion layer to study how pressure gradient and con-tact angle affect liquid water transport along the in-plane directioncaused by cross flow. Their results indicated that the more thepressure gradient is, the earlier the transition from ‘‘fingeringtransport” mode to ‘‘steady transport” mode gets. The transitionalso gets earlier as the contact angle decreases. This is because of acceleration of the liquid water intrusion. As the pressure gradientrises, the mass flux of liquid water through gas diffusion layer inquasi steady state increases; in contrast, as the contact angledecreases, the mass flux increases.

Ramos-Alvarado et al. [53] proposed two models for the air–

cathode of a PEM fuel cell using a two-phase non-equilibriumapproach based on experimental correlations determined by themincluding porosity, capillary pressure, and permeability of the gasdiffusion material to predict performance curves and liquid watersaturation distribution. The first model is a one-dimensionalmodel, in which the influence of employing experimental watertransport properties of the gas diffusion layer is assessed via watersaturation distribution in the gas diffusion layer. The second modelis a two-dimensional model used to predict experimental polariza-tion curves. They discovered that using experimental correlationsof the gas diffusion layer predicts more liquid water saturationthan using empirical correlations for the capillary pressure curvesand permeability. The cell has better performance for an untreatedgas diffusion layer than for a wet-proofed gas diffusion layer with

20% of PTFE; this is because the wet-proofing gas diffusion layerpromotes water removal and decreases the gases diffusivity andthe electric conductivity of the material. The operating currentdensity impacts water saturation greater than the inlet air relativehumidity does. The liquid water saturation below the land of thecurrent collectors is higher than that under the channels owingto the impermeability of the current collector to the water, andowing to the long pathway between the region below the landand the interface with the gas channels.

5.3. Various configurations of gas diffusion layer surfaces

The gas diffusion layer surface configuration affects the contactresistance, the gas diffusion layer porosity, and the fraction of the

pores occupied by liquid water and ultimately the performance

of PEM fuel cell. To explore the effects of gas diffusion layercompression on fuel cell performance, Bao et al. [54] developed athree-dimensional, unsteady, two-phase isothermal numericalmodel for the cathode side of a PEM fuel cell composed of gaschannel, gas diffusion layer and catalyst layer to examine howthe gas diffusion layer deformation impacts water droplet move-ment in the gas channel. The transport of the liquid–gas interface

was treated by a volume-of-fluid method. They observed thatwhen fuel cells are assembled, the cross sections of gas channelchange as a result of different water droplet movements. A largepressure between the gas channel and the gas diffusion layer forceswater droplets to move out of the gas channel earlier and faster.Furthermore, an enough fast gas velocity makes the droplet sus-pend in the gas channel and move out of the gas channel to obtaina high cell performance. Ahmadi et al. [55] presented a singledomain isothermal model of PEM fuel cell to investigate howprominent gas diffusion layer affects cell performance. The promi-nent gas diffusion layer is specified by rectangular configuration.Their results revealed that prominent gas diffusion layer increasesthe velocity because of a decrease in the cross sectional area of gasflow in a gas channel. Increasing velocity magnitude improves thesupply of the reactant gases to the catalyst layer to enhance the cellperformance.

Bao et al. [56] presented a three-dimensional volume of fluidnumerical mode to examine how the deformation of the gas diffu-sion layer affects the water transport characteristics in the cathodeof a PEM fuel cell. The parameters include different inlet flow rates,amount of liquid water in the gas diffusion layer, positions of waterdroplet in the flow channel, and contact angles between the gasdiffusion layer and flow channel surfaces. They found that liquidwater droplet leaving the gas diffusion layer is driven by the sur-face tension as the gas flow rate is low; however, it leaving thegas diffusion layer is driven by the gas flow at high gas flow rates.Meantime, the deformation of the gas diffusion layer and other fac-tors greatly affect the water droplet dynamics. Chippar et al. [57]described a three-dimensional, two-phase, isothermal PEM fuel

cell model considering compression model of the gas diffusionlayer in a straight channel. Their work was to study the impactsof non-uniform compression of the gas diffusion layer and gas dif-fusion layer intrusion into a channel owing to the channel and ribstructure of the flow-field plate. Their results indicated that thenon-uniform compression and intrusion of gas diffusion layerincrease the level of non-uniformity in the current density in themembrane and accordingly decrease overall cell performance. Par-ticularly, in-plane gradients in the liquid saturation, oxygen con-centration, membrane water content, and current densitydistributions considerably increase because of differences in theporous properties between the rib and channel areas. The amountof water accumulation in the gas diffusion layer against the ribsturns greater with reduced porosity and permeability of gas diffu-

sion layer owing to compression, which causes a decrease in theoxygen concentration and local current density near the ribs.Because of gas diffusion layer compression, the lower local currentdensity near the ribs increases the local current density near thechannels under galvanostatic operation, which promotes thenon-uniformity in the current density distribution. As a result,the combined impacts of non-uniform compression and intrusionof gas diffusion layer introduce substantial Ohmic and concentra-tion polarizations, which are most obvious at high currentdensities.

Wang et al. [58] developed a two-dimensional, isothermalnumerical model solving continuity equationand Darcy’s law to cal-culatethesaturationfieldinthedouble-layergasdiffusionmediaforaPEMfuelcell.Theyfoundthattheoverallsaturationleveldecreases

as the polytetrafluoroethylene loading increases. The interface


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between thetwo gas diffusion media layers canregulatethe satura-

tion level by decreasing the driving saturation degree for watertransport. The double-layer gas diffusion media has a higher maxi-mum current density owing to better water management.

6. Characteristics of transport in flow field

Humidified hydrogen enters anode flow channel transportedthrough the channel, and diffuses into anode gas diffusion layerthen into anode catalyst layer. Meanwhile, oxygen enters cathodeflow channel transported through the channel, and diffuses intocathode gas diffusion layer then into cathode catalyst layer, mem-brane, anode catalyst layer, and anode gas diffusion layer. Water istransported out of the cathode catalyst layer, through cathode gas

diffusion layer, and finally out of the cathode flow channel. Theflow field of flow channels within a PEM fuel cell then influences

reactant transport, water management, and reactant utilization

efficiency, and thus the final performance of a PEM fuel cell system.

6.1. Two-phase flow and droplet dynamics in the channel

The water management in the gas channels is one of the mostimportant issues in the PEM fuel cell investigations, because if itis so poor to locally accumulate liquid water, the reactant transportwill be impeded and high pressure drops and the poor cell perfor-mance will be caused. The accumulation of liquid water is causedby liquid water formation and distribution in the channel. Liquidwater formation and distribution in the channel is related totwo-phase flow and droplet dynamics, so it is an important areaof research [10]. Golpaygan et al. [59] developed a three-dimensional multiphase isothermal flow numerical model to

investigate flow dynamics of water droplets in a single channelof the PEM fuel cell employing the volume-of-fluid approach to

Fig. 5. Structures of PEM fuel cells with: (a) parallel, (b) interdigitated, and (c) serpentine flow designs on the cathode side [67].



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track the deformation of free surfaces. They observed that for agiven gas velocity, the existence of liquid water in the channelcauses an increase in the pressure drop because of the increasedflow resistance. Pressure fluctuation is harmful to the cell perfor-mance because it interferes with air supply to active sites, resultingfrom causing fluctuations in the current density. Higher flow rate

leads to a substantial increase in the droplet height, so the flowseparation downstream of the droplet appears obviously; and thisshows a larger pressure fluctuation across the droplet. Reynoldsnumber affects the height of the droplet strongly in the channelowing to an increase in shear and inertia of the flow. At high Cap-illary number, the droplet deforms more since surface tensionforce is small and shear force is large. The wetted contact area of the droplet and the wall therefore decreases dramatically. Qinet al. [60] employed the volume-of-fluid method to numericallystudy the process of water removal and transport for an isothermaland three-dimensional flow channel with a hydrophilic plate in themiddle of a PEM fuel cell. They found that the liquid water dropletcan be removed effectively from the MEA surface owing to theexistence of the hydrophilic plate, and once it is detached fromthe MEA surface, the water droplet is transported downstreamwithout blocking the reactant gas transported into the MEA. The

wettability, length, and height of the plate all affect the watertransport and dynamics and the associated pressure drop in theflow channel. The wettability is represented by the water dropletcontact angle at the wall surface. However, a short plate inclinesto generate the spike in the pressure drop, and a long plate inclinesto have a great pressure drop in the flow channel. For both effectivewater removal and low pressure drop in the channel, the contactangle is found to be 60, length of the plate 1 mm and height of the plate 0.7 mm.

Fontana et al. [61] employed a two-dimensional dynamic andisothermal model to numerically investigate the liquid watertransport inside a tapered flow channel of a PEM fuel cell. Theyfound that the liquid water distribution and transport within thechannel depend on the air velocity. Near the channel exit, a liquidfilm on the gas diffusion layer surface is formed because of highergas velocity; on the contrary, in the central part and near the chan-nel inlet slugs are formed since the slope of the bottom wall of thechannel impedes the accumulation of liquid water. The slugsbehave as the primary mechanism of water removal, eliminatingattached droplets when they move to the channel outlet and help-ing to reduce the water saturation inside the channel, but theycause an increase in the pressure drop.

Mondal et al.[62] studied how surface wettability propertiesand inlet air velocities affect water droplet movement in PEM fuelcell flow channels with hydrophilic surfaces employing three-

Fig. 6. Effect of channel height on cell performance of a cell with: (a) parallel, (b)interdigitated, and (c) serpentine flow fields [67].

Fig. 7. Effect of channel width on cell performance of a cell with: (a) parallel, (b)interdigitated, and (c) serpentine flow fields [67].


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dimensional CFD method coupled with the isothermal VOF methodto track liquid–gas interface. Their results showed that the waterdroplet moves faster with increasing air flow velocities and withincreasing the contact angle hydrophilic surface owing to less liq-

uid–wall contact area. Ferreira et al. [63] employed three-dimensional, transient, isothermal, two-phase model with volumeof fluid method to analyze how hydrogen inlet velocity, operatingtemperature and channel walls wettability affect water movementin an anode gas channel of a PEM fuel cell. They observed thatwater moves as films on the upper surface of the channel forhydrophilic channel walls while it moves as a droplet for hydrophi-lic channel hydrophobic. In addition, water removes faster ashydrogen inlet velocity, operating temperature and channel wallswettability increase. Nevertheless, increasing hydrogen wouldcause a considerable pressure drop. The average pressure dropincreases slightly with increasing temperature and channel wallswettability while the temporal pressure drop varies with changingtemperature and channel walls wettability.

Jo and Kim [64] developed a three-dimensional, isothermalnumerical model with volume of fluid method to explore howthe location of the water inlet pore, the contact angle of the gas dif-fusion layer surface, the contact angle of the other channel walls,the air inlet velocity, and the water injection velocity impact waterdroplet dynamics within a right angle gas channel of a PEM fuelcell. Their results indicated that as the contact angle of the gas dif-fusion layer surface decreases, droplets emerging from the outerand inner pores move along the side walls or the outer loweredges. The water coverage ratio of the gas diffusion layer surfaceincreases but the water volume fraction decreases with an increasein the hydrophobicity of the side and top walls. The higher the sur-face water coverage ratio of gas diffusion layer is, the harder thereactants diffuse into reaction sites; however, the lower water vol-

ume fraction can avoid water flooding in the gas channel. There is agood trade-off between the surface water coverage ratio of gas

diffusion layer and the water volume fraction to get a better effecton the fuel cell performance. The water volume fraction decreaseswith an increase in the air inlet velocity but increases with anincrease in the water inlet velocity. Lorenzini-Gutierrez et al. [65]

applied a three-dimensional, isothermal numerical model withvolume of fluid method to investigate how superficial air velocity,channel surface wettability, and channel crosssection affect liquidwater removal characteristics. Their results indicated that therange of contact angle from 60 to 65 is beneficial for the channelwalls to get top wall film flow, slight fluctuations in pressure dropand a better liquid removal rate. The trapezoidal cross-section withopen angle of 50–60 enhances the formation of top wall films andobtains more stable two-phase pressure drop and liquid removalrate than rectangular one.

6.2. Channel configuration and geometric parameter

The flow field of a bipolar plate distributes reactant gases to

reaction sites and removes water out of the fuel cell, significantlyaffecting the performance of PEM fuel cells. Numerous flow fieldconfigurations have been presented and studied in the past. These

Fig. 8. (a) Definition of the channel assembled angle, (b) 1-channel serpentine flow-field pattern, (c) 2-channel serpentine flow-field pattern, and (d) 3-channel serpentineflow-field pattern [76].

Fig. 9. Novel parallel flow channel design with low-pressure and high-pressureflow channels [80].



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conventional designs can be classified into four categories: pin-type, parallel, serpentine, and interdigitated. Among them, parallel

and serpentine designs are the most widely known and employedones. Parallel designs have the advantage of low pressure drop.However, the flow resistance is difficult to maintain at the samelevel in each flow path causing a non-uniform distribution of thereactants. Serpentine designs usually give high fuel cell perfor-mance but they typically have relatively long reactant flow path,leading to substantial pressure drop. Additionally, reactant concen-tration significantly decreases from the inlet to the outlet of theflow channel. This decrease leads to considerable Nernst lossesand non-uniform electric current density distribution, reducingboth the overall performance and lifetime of PEM fuel cells. There-fore, it is essential to investigate and optimize the flow distribution

within these configurations in order to eliminate the stagnantareas and hence improve performance.

Hassanzadeh et al. [66] established a two-dimensional non-isothermal numerical model to solve governing equations of mass,momentum, energy, and species conservation for the developinglaminar flow in cathode and anode flow channels of a PEM fuel cell.Each of the flow channels was regarded as two parallel planes with

one porous plane (simulating electrode surface) and the otherimpermeable plane (simulating bipolar plate surface). Two flowsituations included uniform air suction or air injection in a fuel cellchannel and humidified air and humidified hydrogen with fixedmass flux boundary condition for oxygen in the cathode channeland hydrogen in the anode channel. The local and the averagedfriction coefficient, Nusselt number and Sherwood number weredetermined for various flow conditions such as different stoi-chiometries, operating current densities and operating pressuresof the cell. They found that the velocity decreases owing to the suc-tion at the porous plane and the velocity peak shifts toward theporous plane, so velocity gradient and accordingly the shear stressincrease on the porous plane and decrease on the non-porousplane along the flow direction. Correlations for the averaged fric-tion coefficient, Nusselt and Sherwood numbers are set up; theyare useful in flow field modeling and design of a PEM fuel cell. Chiuet al. [67] presented a two-phase, three-dimensional, isothermaltransport model based on the two-fluid approach for a PEM fuelcell with parallel flow field, interdigitated flow field, and serpen-tine flow field as indicated in Fig. 5 to study the transport phenom-ena and cell performance. As shown in Figs. 6 and 7, reducingchannel height or width of parallel and serpentine flow channelscan improve the cell performance with low operation voltagebecause of higher gas velocity with more water removal.

Henriques et al. [68] developed a three-dimensional, isothermalnumerical model of the PEM fuel cell having a design of parallelchannels crossed by a transversal flow channel to examine the

Fig. 10. Total and net power densities at different pressure differences between lowpressure and high-pressure flow channels with a stoichiometry ratio of 5 [80].

Fig. 11. Distribution of velocity vectors and pressure in a cross section at the mid-length of the cathode flow channel, gas diffusion layer and catalyst layer at different

pressure differences between high-pressure and low-pressure flow channels with a stoichiometry ratio of 5 (a) no back pressure; (b) low back pressure on channels 1 and 3;(c) medium back pressure on channels 1 and 3 and (d) high back pressure on channels 1 and 3 [80].


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influences of liquid water contents and current density. Their

results indicated that excluding the transversal channel, employinga design of straight channels with larger width can enhance theirperformance up to 26.4%. This is since increasing the cross-section area of channel forces more air to flow through the fuel cell,and the water distribution is then more uniform through the cata-lyst layer. Tehlar et al. [69] established an isothermal model toexamine different channel-rib geometries and gas diffusion layercharacteristics. Their results showed that cross convection in a ser-pentine channel can significantly increase the current density andconsequently the power density of PEM fuel cells. The cell perfor-mance is strongly dependent on gas diffusion layer compression,flow velocity, and rib width. As the rib width decreases to increasethe compression of gas diffusion layer, the cross convectionincreases to promote oxygen supply under the rib. Nevertheless,

negative effects induced by membrane drying, or Ohmic resistancelimit the development potential of decreasing the rib width.Increasing micro-porous layer or gas diffusion layer thickness aug-ments the under rib conversion but meanwhile reduces the overallaverage current density owing to longer through-plane pathwaysfor the reactants. When the thickness of gas diffusion layer underthe rib increases, current densities may rise up to about 20% highercurrent densities. Exact knowledge of characteristics of the gas dif-fusion layer and its compression is suitable to understand channel-to-channel cross convection and optimize performance of a PEMfuel cell.

Wang et al. [70] employed a three-dimensional, two-phase isothermal numerical model to study how the size of serpentine channel affects the performance of a PEM fuel cell with

serpentine flow fields. Their results indicated that smaller channelsize enhances the cell performance and has more uniform current

density distribution since it improves liquid water removal and

promotes oxygen transport to the porous layers. Nevertheless,smaller channel size increases the total pressure drops across thecell and more pump work. A flow channel cross-sectional area of 0.535 0.535 mm2 then obtains the optimal cell performance.Manso et al. [71] applied a three-dimensional non-isothermalnumerical model including the mass conservation equations,Navier–Stokes equations, species transport equations, and theenergy equation to examine how the height/width ratio affectsthe performance of a PEM fuel cell with serpentine flow channel.They observed that the higher height/width ratio has a higher per-formance owing to uniform current distributions with the highermaximum and minimum intensity values and temperature distri-butions with smaller gradients. The 10/06 and 12/05 of aspect ratiohave the best polarization curves.

Yang et al. [72] used a in-house genetic algorithm with a com-mercial code, COMSOL to explore the optimization method of channel geometries for a PEM fuel cell. The geometry variableswere channel-to-rib widths and channel height. The cell outputpower is considered as the objective function for the optimization.Their results displayed that channel-to-rib width of 1.84:1 has thebest performance and 0.54:1 worst performance. A channel heightof 0.515 mm has the best fuel cell performance. A 2:1 channel-to-rib width ratio has better performance than a 0.5:1 channel-to-ribwidth ratio. This result consists with the optimization result. Yanget al. [73] furth

A Review of Recent Development Transport and Performance Modeling of PEM Fuel Cells

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