A review of recent development: Transport and performance modeling of PEM fuel cells

Applied Energy 165 (2016) 81–106

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

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 2015 Received in revised form 9 December 2015 Accepted 17 December 2015

Keywords: Review Recent development Proton exchange membrane fuel cell Performance Transport Modeling

a b s t r a c t This study reviews technical papers on transport and performance modeling of proton exchange membrane (PEM) fuel cells during the past few years. The PEM fuel cell is a promising alternative power source for various applications in stationary power plants, portable power device, and vehicles. PEM fuel cells provide low operating temperatures and high-energy efficiency with zero emissions. A PEM fuel cell is a multiple distinct parts device and a series of mass, momentum and energy transport through gas channels, electric current transport through membrane electrode assembly and electrochemical reactions at the triple-phase boundaries. These transport processes play crucial roles to determine electrochemical reactions and cell performance, so studies on the transport and performance modeling have been done deeply. This review shows how these modeling studies offer valid findings for transport and performance modeling of PEM fuel cells and recommendations that can be applied in enhancing transport processes for improving the cell performance. Ó 2015 Elsevier Ltd. All rights reserved.

Contents 1. 2.

3.

4.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fundamental model description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Governing equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1. Mass conservation equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2. Momentum conservation equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3. Energy conservation equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.4. Species transport equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.5. Charge equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Numerical technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Reliable solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Characteristics of transport in membrane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Water content and operation condition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Property and geometric parameter of membrane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Geometric surfaces of membrane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Characteristics of transport in catalyst layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Catalyst layer structure parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Geometric surfaces of catalyst layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

http://dx.doi.org/10.1016/j.apenergy.2015.12.075 0306-2619/Ó 2015 Elsevier Ltd. All rights reserved.

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

Nomenclature a C Cp D Db E F H; h Hb hfg i j K K rg K rl k kc ke keff L M MEA N NFP OPCF P PEM Re Ru Rch Ragg RH S ST Se Si Sl Ss St s T t tb; w

5.

6.

7.

electrocatalytic surface area per unit volume (m1) mole concentration (mol m3) constant pressure specific heat diffusivity (m2 s1) installed distance of two trapezoid baffles (mm) voltage (V) Faraday’s constant (96,478 C mol1) height of gas flow channel (mm) height of trapezoid baffle (mm) vaporization latent heat current density (A m2) exchange current density (A m3) permeability (m2) the relative permeability of gas phase the relative permeability of liquid phase gap size constant of water condensation constant of water evaporation effective thermal conductivity (W K1 m1) length of gas flow channel (mm) molecular weight (kg mol1) membrane electrode assembly number of rectangular blocks Nafion weight ratio Open Pore Cellular Foam pressure (Pa) proton exchange membrane Reynolds number universal gas constant (8.314 J mol1 K1) tapered ratio agglomerate radius cm relative humidity entropy (J K1) source term of energy equation source term of potential equation for the hydrogen transport source term of species transport equation source term of water in liquid phase source term of potential equation for the electron transport stoichiometry ratio water saturation rate of pores in porous media temperature (K) time (s) width of gas flow channel (mm)

tr ~ u V x Y

a

b

e eD

f

g

h

jm js leff q rs;eff re;eff

/

r

distance between two gas flow channels (mm) velocity vectors (m s1) voltage (V) mole fraction mass fraction electric conductivity (X1 m1); wave amplitude wave number porosity dry porosity of electrodes stoichiometric flow ratio overpotential angle of trapezoid baffle ionic conductivity of the membrane electric conductivity of the gas diffusion layer the effective viscosity of fluid (m s2) density of gas (kg m3) effective electronic conductivity (X1 m1 ) effective ionic conductivity (X1 m1 ) phase potential gradient operator

Superscript eff effective g gas phase s current conductor s dissolve sat saturation s coefficient of Bruggeman Subscript a agg c cell e eff H2 H2O i, j l 0 O2 s

anode agglomerate cathode cell electrolyte phase effective hydrogen water species liquid water reference state oxygen solid phase

Characteristics of transport in gas diffusion layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.1. Properties of gas diffusion layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.2. Pore structure of gas diffusion layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.3. Various configurations of gas diffusion layer surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Characteristics of transport in flow field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 6.1. Two-phase flow and droplet dynamics in the channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 6.2. Channel configuration and geometric parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 6.3. External additions in the channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.4. Cross-sectional shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.5. Non-conventional channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.6. Flow field orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 6.7. Flow plate material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

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

1. Introduction Over the past several decades, a combustion engine is widely applied to a power source for land vehicles, commercial marine vessels, stationary power plants, and so on [1]. However, the crises of energy and environment are caused by consuming fossil fuels long time and large amount. In addition, the Cancun Agreements recognized the goals to limit average global temperature warming within 1.5–2 °C, and to reduce emissions emitted by member countries under the Kyoto Protocol in a range of 25–40% below 1990 levels by 2020 [2]. Therefore, researchers around the world have been developing technology on alternative power sources to possibly replace combustion engines and on alternative fuels for solving the crises. A fuel cell is the most promising one of these alternative power sources because it is an energy converter which converts the chemical energy of a fuel directly and efficiently to electricity through a chemical reaction that brings high efficiency, simplicity, low emissions, and silence [3]. The PEM fuel cell has primary 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 power generation in the 21th century [4–8]. As shown in Fig. 1, a typical PEM fuel cell consists of bipolar plates with channels machined on either side for reactant distribution over the electrode surface, a membrane electrode assembly (MEA), and porous gas diffusion layers sandwiching the MEA. The nonlinear transport processes and electrochemical reaction occur for the PEM fuel cell during operation as follows. Humidified hydrogen enters anode flow channel grooved in an anode bipolar plate, is transported through the channel, and diffuses into anode gas diffusion layer then into anode catalyst layer. At the same time, oxygen enters cathode flow channel grooved in a cathode bipolar

83

plate and is transported through the channel, and diffuses into cathode gas diffusion layer then into cathode catalyst layer, membrane, anode catalyst layer, and anode gas diffusion layer. When hydrogen is oxidized at the anode catalyst layer, protons and electrons are generated. The protons go through the membrane and the electrons go through an external circuit. Oxygen then reacts with protons and electrons at the cathode catalyst layer to form water. Water is transported out of the cathode catalyst layer, through cathode gas diffusion layer, and finally out of the cathode flow channel. In summary, the phenomena involved in PEM fuel cell operation are quite complex including inherently three-dimensional heat transfer, species and charge transport, multi-phase flows, and electrochemical reactions. Because the phenomena take place in the compact and complex design of PEM fuel cell, it is quite difficult and expensive to conduct measurements within the fuel cell. A comprehensive and well-verified mathematical and numerical model can thus be established to offer detailed information on fluid flows, heat transfer, and chemical reactions within the fuel cell [9–13]; in particular, it is not necessary to offer precise values for every computed quantity over the computational domain, but would rather offer correct trends over a wide range of operating conditions. The numerical studies on well-verified transport modeling of PEM fuel cell accurately predict the trends of cell performance varying operating parameters. Available operating parameters and their conditions can be determined to improve performance of PEM fuel cell via the appropriate transport modeling. The well-described transport phenomena through the modeling can help realize the cause of improved performance of PEM fuel cell and the practicability of actual application in the real fuel cell. Modeling of PEM fuel cell may fall into three categories including analytic, semi-empirical, and mechanistic models [9]. Among

Fig. 1. Typical PEM fuel cell structure.

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

these models, mechanistic models accurately predict performance over a wide range of operation conditions. They are very useful for making quick predictions for designs that already exist. They can be used to predict the performance of innovative designs, or the response of the fuel cell to parameter changes. The mechanistic modeling has one-dimensional, two-dimensional, and threedimensional 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 within the channels is normal to the gas’ diffusion direction. Therefore, this study reviews the latest studies on PEM fuel cell using twodimensional, and three-dimensional models. In general, these models numerically solve the governing partial differential equations that represent the fluid flow, heat transfer, species and charge transport, and the chemical and electrochemical reactions that take place in fuel cells. The numerical solution can offer spatial distributions of physical quantities in the fuel cell, such as the distributions of the fluid velocity, temperature, pressure, species concentration, electric current, water content, and power density.

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

2. Fundamental model description

where Y i the mass fraction.

The PEM fuel cell is a sophisticated multiple-physics coupling system. The fuel cell computational fluid dynamic model is composed of the flow momentum, energy, mass species transport, electrochemical reactions, and current transfer within distinct subregions with various material properties and source terms. Several assumptions on the model are made as follows: (a) The flow is laminar and incompressible on the basis of small gas 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 homogeneous and isotropic. (d) Gravity effect is ignored. (e) Ohmic potential resistance between solid layers such as flow channel, diffusion layer, catalyst layer and exchange membranes is overlooked. (f) Butler–Volmer equation is used to compute the fuel and oxidant electrochemical reactions in the catalyst layers. Fundamental model description includes governing equations, numerical technique, and reliable solutions [4,5,7]. The governing equations under the above-mentioned assumptions are described below. 2.1. Governing equations If steady-state is considered, then @t@ ¼ 0 in the following equations. If single-phase is considered, then s ¼ 0, and Sl ¼ 0 in the following equations.

2.1.3. Energy conservation equation

@ðqC p TÞ þ ðeqC p Þð~ u  rTÞ ¼ r  ðkeff rTÞ þ ST @t

where T is the temperature, C p is constant pressure specific heat, and keff is the effective thermal conductivity. The source term 2

2

ST ¼ jimm in the membrane, ST ¼ jies þ Sl hfg in the gas diffusion layer, h i 2 2 ST ¼ Tð4FDSÞ þ g  j þ jimm þ jies þ Sl hfg in the catalyst layer, and ST = 0 in the flow channel. 2.1.4. Species transport equation

@ðeY i Þ uY i Þ ¼ r  J i þ Si  Sl þ r  ðeq~ @t

J i ¼ qDeff i rY i þ

where e ¼ ð1  sÞeD , eD is dry porosity of electrodes, s is water saturation, q is the density of gas mixture, and ~ u is the vector of P velocity; q ¼ i Y i qi .

e

@ðq~ l e2~ uÞ u u~ uÞ ¼ erP þ r  ðeleff r~ uÞ  eff þ r  ðeq~ @t K

ð2Þ

X eff DM X eff Dj rY j  qY i D Yj M j j i

Deff j

where is the effective diffusivity for specie i, and is the effective diffusivity for specie j. In Eq. (4), the Si is the mass generation source term which is ja M H2 =2F for hydrogen, jc M O2 =4F for oxygen, and jc M H2 O =2F for water vapor; Sl is considered for two-phase, and expressed by the following correlations:

(

Sl ¼

M H2 O kc

eY H2 O qRu T ðP H2 O

 Psat Þ; if PH2 O > Psat

ke esðPsat  PH2 O Þ;

if PH2 O < Psat

ð6Þ

Following the Bruggeman correlation to account for the effects of porosity and tortuosity in porous electrodes and membrane, this study modifies the effective mass diffusion coefficient as 1:5 Deff i ¼ Di e

ð7Þ

where the diffusion coefficient of species is a function of temperature and pressure, i.e.,

 Di ðT; PÞ ¼ D0;i

T T0

1:5   P0 P

ð8Þ

For PEM fuel cell operation, the second specie on anode side and cathode side is water vapor, which is assumed to exist at the saturation pressure. The molar fraction of water vapor is expressed as follows:

P sat H2 O ðTÞ Pg

ð9Þ

where saturation pressure P sat H2 O is a function of temperature and is given by 2 3 log10 Psat H2 O ðTÞ ¼ 2:1794 þ 0:02953  T  9:1837  T þ 1:4454  T

ð10Þ where T is the temperature in K. The sum of all mass fractions is notably equal to unity.

X

2.1.2. Momentum conservation equation

M

Deff i rM  q Y i

ð4Þ

ð5Þ

2.1.1. Mass conservation equation

ð1Þ

qY i

Deff i

xH2 O;v ¼

@ðeqÞ uÞ ¼ 0 þ r  ðq~ @t

ð3Þ

Yi ¼ 1

ð11Þ

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

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



   @ðeql sÞ ql KK rl @Pc ql K rl rs  r  r P ¼ Sl r @t ll @s ll K rg

ð12Þ

where ql is the density of liquid water, ll is the viscosity of liquid water, MH2 O is the molecular weight of water, K rl is the relative permeability of liquid phase, K rg is the relative permeability of gas phase, and Pc is capillary pressure. 2.1.5. Charge equation The potential equations for both solid and electrolyte phases are obtained by applying Ohmic’s law:

r  ðrs;eff r/s Þ ¼ Ss

ð13Þ

r  ðre;eff r/e Þ ¼ Se

ð14Þ

The source terms in the electron and proton transport equations, i.e., Eqs. (13) and (14), result from the electrochemical reaction occurring in the catalyst layers of anode and cathode sides. Anode Catalyst layer

Se ¼ ja ;

Ss ¼ ja

ð15Þ

Cathode Catalyst layer

Se ¼ jc ;

Ss ¼ jc

ref

ja ¼ ðaio Þa

ref

jc ¼ ðaio Þc

!12



C ref H2 ! C O2  C ref O2

that the solutions are independent and convergent. In addition, the numerical modeling has to be validated by experimental data or previous study’s data for wide operating conditions before they are employed in the modeling. Validation would be an important component of modeling work; in particular, Wang and Chen [14,15] validated detailed liquid water distribution in PEM fuel cells with neutron radiography data. The reviewed models separately investigated characteristics of transport in membrane, catalyst layers, gas diffusion layers, and flow field and their effects on the cell performance [5,6,9] as follows. The following models took into consideration isothermal and non-isothermal conditions. The isothermal consideration means that temperature change in the PEM fuel cell is not taken into account in the model. The non-isothermal consideration means that temperature change in the PEM fuel cell is taken into account in the model. The non-isothermal models can predict the real situations in the PEM fuel cell. However, the isothermal and non-isothermal models predict almost the same performance only when a single fuel cell operates with a small dimension and higher conductivities of the porous layers and the bipolar plates. In addition, the isothermal consideration can simplify and accelerate the solving processes.

ð16Þ

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

C H2

85

expðaaa F=RTÞga  expðaac F=RTÞga

expðaca F=RTÞgc  expðacc F=RTÞgc





ð17Þ

ð18Þ

where a is the electrocatalytic surface area per unit volume, m1. ga the 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 governing equations, the discretization of these equations has to be carried out by several techniques such as finite difference, finite element, finite volume, and so on. This therefore leads to a set of simultaneous linear algebraic equations that are solved numerically in a computational mesh. The solutions to this set of equations are obtained according to the boundary conditions that are specified according to the operating conditions of the fuel cell. 2.3. Reliable solutions Insufficient mesh discretization may cause solution errors, so the denser and finer meshes along the interface boundaries (such as the interface between membrane and catalyst, the interface between catalyst layer and diffusion layer, the interface between diffusion layer and channel) and near channel walls are used to treat with steep gradient in the flow variables distribution to obtain more accurate solution. The sensitivity test of mesh and time step (for transient case) has to be made before the numerical method 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 time step has to employ at least three sizes of time step to make sure

3. Characteristics of transport in membrane The membrane transports water from the cathode to the anode by ionic drag and mass diffusion. In polymer membrane material, proton transport is achieved by water contained in the membrane and the electric field between the anode and the cathode. The protonic conductivity of membrane is therefore heavily dependent on its water content and has a significant impact on the cell performance. 3.1. Water content and operation condition The water content in the membrane during the cell operation is determined by the balance of water or its transport. Hydration of the membrane is essential to minimize resistivity and Ohmic losses in the fuel cell. External humidification is often used when reacting water is insufficient to achieve full hydration of the membrane, especially in the cathode inlet regions. Nevertheless, in the fuel cell, this leads to excess water accumulation, which causes flooding in the catalyst layer, and generates a decrease in the active reaction area and a drop in voltage. In addition, the water eventually appears in gas channels and leads to an increase in parasitic pumping power and even channel clogging. Proper humidification of the reactants can improve membrane hydration, and an appropriate flow 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 content and cell performance. He observed that at a constant cathode RH equal to 100%, a lower anode RH provides sufficient water to maintain membrane hydration by water back-diffusion and hence enhances the cell performance. Higher anodic stoichiometry reduces cathodic water saturation by increasing water backdiffusion, making membrane hydration and thus enhancing the cell performance. Higher cathodic stoichiometry also reduces water saturation at the cathode, which promotes the backdiffusion of water to make membrane hydration and then enhances the cell performance. He et al. [17] presented a threedimensional, two-phase transport mixed-domain model to explore water management issues with the existence of condensation/ evaporation for a full PEM fuel cell by finite element-upwind finite volume method with Newton’s linearization schemes. Their model

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

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) cell temperature distribution in the through-plane direction [28].

involves both anode and cathode sides in three water phases within membrane with corresponding interfacial boundary conditions considering the equality of water flux on the interfaces between the membrane and the catalyst layers. They showed that they obtain a fast convergent nonlinear iteration and the mass balance errors less than 5%. Once the liquid water is formed, it goes into the gas diffusion layer by the gaseous phase. The liquid water leaves the gas diffusion layer only as the rising gradient of capillary pressure finally overcomes the viscous drag. Dadda et al. [18] adopted a multi-species, two-dimensional, and transient non-isothermal numerical model to investigate how heat and mass transfer influence potential variation in the membrane of a PEM fuel cell. Their results showed that the voltage loss is more important in the regions with less water content. In addition, as the pressure gradient increases, the voltage loss across the membrane rises. An applied heat flux on the membrane outlet does not affect the voltage loss. An imposed water flux at the cathode side of the membrane can decrease the voltage loss rather than an applied heat flux on the membrane outlet because the membrane becomes more hydrated. The imposed negative water flux should be controlled because a permanent damage could appear in the membrane as too much water is removed. Decreasing the pressure gradient decreases the voltage loss since it forced less water transport from the cathode to the anode. Afshari and Houreh [19] employed a three-dimensional, nonisothermal model to study the performance of the porous metal

foam in membrane humidifier for a PEM fuel cell. Their model is to solve the conservation equations of mass, momentum, species and energy for all regions of the humidifier. They discovered that water recovery ratio and dew point at dry side outlet are higher with the metal foam installed at wet side and both sides than with the conventional humidifier, indicating a better humidifier performance. On the contrary, employing metal foam at dry side has no positive effect on humidifier performance. Ahmadi et al. [20] conducted a three-dimensional, single phase model in a PEM fuel cell with straight flow channels to investigate transport phenomena and the effect of inlet gases humidity on the cell performance. Their results indicated that the inlet gases humidity and membrane water management are the most important parameters that affect cell performance and transport phenomena in the fuel cell. At lower voltage (for example 0.6 V), electrochemical reaction rate rises owing to much oxygen consumption. An increase in oxygen consumption leads to the increase in water formation and the amount of forming water along the cell. The current density loss is more at relative humidity of 25% because of severe drying of membrane and a great decrease in ionic conductivity for this humidity. Houreh and Afshari [21] developed a three-dimensional, nonisothermal numerical model to compare the performance between counter-flow humidifier and parallel-flow humidifier, and found that the performance of counter-flow humidifier is better than that of the parallel-flow humidifier; this is because temperature increases and mass flow rate decreases at dry side inlet.

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Nevertheless, the humidifier performance at the low flow rates improves slightly by increasing the temperature of inlet dry gas. The increase in relative humidity at dry side inlet does not provide 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. They discovered that membrane water content can be affected by the parameters in the cathode such as humidification temperature, inlet velocity, and membrane characteristics. When the humidification temperature rises, the water content in the membrane increases and the pore size becomes larger to improve proton transport. As the inlet velocity of the gas channel increases, convection and diffusion of water from backing layer to membrane become more significant than the water dragged by protons and the water content thus increases. The increase in Reynolds number causes higher gas velocity and hence more removal of the liquid water. Xing et al. [23] developed a two-dimensional, isothermal, two-phase flow agglomerate model to explore how dry Nafion ionomer volume fraction and cathode relative humidity affect membrane and ionomer swelling and the cell performance for a PEM fuel cell. Their results showed that the optimum ionomer water 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 current densities, the optimum cathode relative humidity initially decreases then increases with increasing the ionomer content. 3.2. Property and geometric parameter of membrane The water adsorption and desorption coefficients are the most important properties of membrane. The function of membrane is to conduct protons from anode to cathode when repelling the electrons, therefore forcing the electrons to travel through the outer circuit to generate electric work. In fact, proton conductivity is basically because of proton migration inside the hydrated membrane and increases with the water activity. The water uptake and loss is thus also of fundamental importance for the proper functioning and the long-time stability of PEM fuel cells because it is related to irreversible dimension changes of the material and a morphological instability, which can be connected to the mechanical properties of the membrane, in particular, its elastic modulus. Verma and Pitchumani [24] used a two-dimensional, single phase, transient, and isothermal model to predict transient water content distribution in the membrane of a single-channel PEM fuel cell. They discovered that step increase in current density leads to anode dryout because of electro-osmotic drag, causing voltage

Fig. 3. Schematic of PEM fuel cell cathode with agglomerate in catalyst layer [32].

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reversal and may lead to cell degradation. The transient variation in voltage is strongly correlated to the water diffusion in porous media and membrane properties such as water diffusion coefficient, electro-osmotic drag coefficient, ionic conductivity, thickness, and equivalent weight. As water uptake capacity increases, the undershoot in voltage response decreases owing to the increase in back diffusion rate. The voltage reversal can be avoided by a graded membrane design. Chaudhary et al. [25] developed a two-phase, non isothermal, transient and two-dimensional model to water uptake by the membrane in a PEM fuel cell. They considered two approaches of water-uptake by the membrane including the Schroeder’s paradox and individual contributions of water vapor and liquid water. They observed that water uptake by membrane, current density, water content of the membrane, temperature of the cell, and so on, significantly vary for the two approaches. Transient rate of sorption or desorption of water by membrane could respond to water content of membrane when the cell voltage was applied by a step change. Wu et al. [26] examined the non-equilibrium membrane water absorption/desorption processes along with non-equilibrium condensation/evaporation processes employing a transient threedimensional non-isothermal model that fully coupled multispecies and multi-phase transport, electrochemical kinetics, and heat transfer processes for a single channel of a PEM fuel cell. Their results showed that the cell current density increases with a decrease in water sorption/desorption rate coefficient since the membrane tends to be better hydrated. In addition, compared with the liquid production modeling the response time of PEM fuel cells in vapor production modeling is substantially overestimated owing to the slow condensation process. Iranzo et al. [27] developed a three-dimensional non-isothermal model for a PEM fuel cell with serpentine flow field bipolar plates to investigate how the membrane thermal conductivity affects the cell performance. They found that the membrane thermal conductivity has positive influences on the cell performance, especially at higher current densities, increasing the cell electric power up to 50%. This is because of the better thermal and water management which causes an increased membrane water content and hence higher protonic conductivity. With higher thermal conductivity, the membrane can better remove the heat produced by the cathode electrochemical reaction and by the Ohmic heat within the cell. Karpenko-Jereb et al. [28] developed a one-dimensional isothermal model for water and charge transport through the membrane with temperature dependent properties in a PEM fuel cell. The dependency of diffusion and electro-osmotic coefficients on the membrane water concentration is approximated by linear functions. This developed membrane model was coupled with the three-dimensional CFD code AVL FIRE to simulate polarization curves of the cell at various relative humidity values of the inlet air at the cathode. Their results displayed that a lower inlet relative humidity decreases water concentration in the membrane and then decreases proton conductivity and current density. Jung et al. [29] presented a non-isothermal and two-dimensional agglomerate model to investigate how Nafion thickness influences temperature distribution inside the MEA of a PEM fuel cell. Their results showed that Nafion 117 MEA has the highest cell temperature in the cathode catalyst layer as indicated in Fig. 2a among Nafion 112, 115 and 117 MEAs (thickness of Nafion 117 larger than thickness of Nafion 115 which is larger than thickness of Nafion 112), because of the most of the heat releases by the oxygen reduction reaction in the cathode catalyst layer. This means that the raised thickness of Nafion can act as an additional heat transfer barrier, which reduces heat transfer from cathode catalyst layer to anode side. The cell temperature in the cathode increases with an increase in Nafion thickness as displayed in Fig. 2b owing to

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

the heat accumulation. Nevertheless, the cell temperature distributions 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 fix boundary conditions for the same reacting area as the shoulder width reduces by diffusing more reactants through the gas diffusion layer to the reacting area. Pourmahmoud et al. [30] presented a three-dimensional non-isothermal model for parallel flow channels, gas-diffusion electrodes, catalyst layers, and the membrane region in a PEM fuel cell with deflected MEA. Their results showed that fuel cell performance is larger for non-zero deflection parameter than for zero deflection parameter because of greater face width and more reactants diffusing through the gas diffusion layer over the reacting area. As the deflection parameter increases up to the maximum value equal to channel height, the fuel cell performance will reach the maximum. 4. Characteristics of transport in catalyst layers At the anode catalyst layer, water vapor is absorbed into the electrolyte and the water molecules tend to transport with the protons through the membrane toward the cathode catalyst by the electroosmotic drag. On the other hand, the electrons are transported from the anode catalyst layer through external circuit to reach the cathode catalyst. At the cathode catalyst, water is formed at the platinum catalyst surface and the promoted local water concentration tends to counteract the water transport from the anode side. 4.1. Catalyst layer structure parameters To simulate the catalyst layer accurately is a challenge since its structure characteristics and properties cover the extent from microscopic to macroscopic scales. The complicated porous catalyst layer structure composed of Pt, carbon support, ionomer electrolyte, gas pores, and liquid water clearly stands for a multiscale, multiphase problem having all sorts of reactions, and mass and heat transport phenomena. Das et al. [31] developed a twodimensional, two-phase, volume-averaged isothermal model to study how structure of catalyst layer and its surface wettability affect liquid water transport in the cathode catalyst layer of a PEM fuel cell. The catalyst layer is assumed to be a macrohomogenous layer, and thus the physical structure of cathode catalyst layer would be quantified by its porosity. The porosity of catalyst layer depends on the platinum (Pt) and Nafion loadings; then,

their results are discussed as the functions of Pt and Nafion loadings. They found that the catalyst layer wetting properties affect the flooding in the cathode catalyst layer, and the liquid water saturation in a hydrophilic cathode catalyst layer decreases with an increase in the surface wettability or a decrease in the contact angle. Nonetheless, the catalyst layer wettability little influences the liquid water transport inside the gas diffusion layer. On the contrary, the cathode catalyst layer structure (platinum and Nafion loadings) affects both the liquid water and oxygen transports significantly throughout the thicknesses of cathode catalyst layer and gas diffusion layer. In addition, the linear decrease of active reaction area with liquid water saturation is not enough to catch the true behavior of oxygen transport because the linear decrease approach overestimates the active reaction surface area in the cathode catalyst layer. The highest liquid water saturation in the cathode catalyst layer is found under the rib while the lowest value found under the flow channel. The wetting and geometric characteristics of cathode catalyst layer influence the liquid water transport significantly, and the liquid water saturation in a hydrophilic catalyst layer decreases with an increase in cathode catalyst layer surface wettability or a decrease in cathode catalyst layer contact angle. Dobson et al. [32] presented a two-dimensional, isothermal, constant pressure numerical model to calculate agglomerate size and porosity within the catalyst layer. Their results showed that a unique set of agglomerate size and porosity can accurately characterize the cell performance over a wide range of operating conditions. The uncertainty can also be decreased in model predictions with the proposed least-square methodology. Cetinbas et al. [33] built a three-dimensional isothermal model for a PEM fuel cell cathode using a modified agglomerate approach on the basis of discrete catalyst particles. Their results indicated that similar to the classical approach, the modified threedimensional model is capable of reproducing previous articles’ trends of reactant, reaction rate, and overpotential distributions, but the macro-homogenous model cannot predict mass transport losses accurately. In addition, their model can properly predict the effect of Pt loading in the diffusion-loss region while the classical approach offers nearly identical results with variation of Pt loading. Roshandel and Ahmadi [34] presented a twodimensional, isothermal, computational model on the basis of agglomerate structure of catalyst layer to explore how catalyst loading gradient in the catalyst layer affects the performance of a PEM fuel cell. Their model is set up on the basis of agglomerate catalyst and describes reactant species and charge (ion and electron) transport at the cathode of a PEM fuel cell. The catalyst layer is considered to be a region composed of small homogenous agglomerates and the agglomerate is enclosed by the electrolyte film as indicated in Fig. 3. The feasibility of catalyst loading is thought

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about in two direction, ‘‘across the layer” from membrane/catalyst layer interface to catalyst layer/gas diffusion layer interface and ‘‘in catalyst plane” under both channel and land areas. They found that the catalyst loading distribution in the both directions affects the catalyst use significantly. By bipolar plate configuration, gas diffusion layer/catalyst layer characteristics and external load regime influence the location of maximum local current density. Employing catalyst in locations with higher reaction rates improves the cell performance. Cetinbas et al. [35] developed a two-dimensional steady-state isothermal model of species and charge transport for the cathode catalyst layer of a PEM fuel cell employing packing arrangements in 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 to correctly explain the decrease in the agglomerate surface area owing to overlapping particles. They investigated how Pt|C weight ratio and Pt loading affect the optimum ionomer loading, as well as catalyst layer thickness affects performance. They observed that for Pt|C greater than 15%, as the amount of carbon decreases, the limiting current reaches earlier because of a lower effective surface area by increasing the overall porosity. With the rhombohedral packing scheme for NFP = 30% and Pt = 0.2 mg/cm2, the current density improves with catalyst layer thickness from 6 to 10 lm because the porosity increases from 3.5% to 42% and it enhances reactant transport. For catalyst layer thickness larger than 10 lm, the current density decreases owing to higher charge transfer losses. Xing et al. [36] developed a two-dimensional, steady-state, nonisothermal, two-phase, and agglomerate model for a PEM fuel cell to study how operating temperature and width ratio of channel affect cell performance. They discovered that heat accumulates inside the cathode catalyst layer on the area under the channel. The higher the operating temperature is, the better the cell performance becomes; this is because the kinetics increase, the liquid water 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 increase in the oxygen reduction reaction. In addition, enlarging the channel/rib width ratio enhances the cell performance because of an increase in the reaction area of the oxygen with the cathode catalyst layer and an increase in the amount of water at both the anode and cathode. Obut and Alper [37] presented a three-dimensional, non-isothermal and two-phase numerical model in a straight flow field channel to investigate the influence of cathode catalyst layer parameters such as catalyst layer thickness, ionomer film thickness, agglomerate size and porosity on the performance of a PEM fuel cell. Their results revealed how these catalyst layer parameters influence diffusion coefficients, electrical, and proton conductivities, and effectiveness factor determines the area specific power density and mass specific power density of the PEM fuel cell separately. Cetinbas et al. [38] employed an improved agglomerate approach in a two-dimensional cathode model [35] for species and charge transport to optimize the catalyst layer composition simultaneously in both the in-plane and through-thickness directions to maximize the current density at activation, Ohmic and diffusion-loss regimes. They observed that the zones of high concentration shift from under the land to under the channel with a decrease in the operating voltage. Highest performance improvements in all operating regimes are obtained by optimizing NFP showing that ion transport is relative important. Bidirectionallygraded distributions have higher performances than the unidirectionally-graded catalyst layer since they improve transport properties as desired exactly at the high reaction-rate zones. Twovariable optimization on NFP/Pt and NFP/C distributions can obtain

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higher performances than single-variable optimization, owing to superposition of benefits from two constituents. Hao et al. [39] developed a three-dimensional model of a full PEM fuel cell with the catalyst layer sub-mode at the low-Pt loading catalyst layer considering the interfacial transport resistances at ionomer, water film and Pt particle surfaces. They found that the electrode transport resistance dramatically increases not only for Pt loading lower than 0.1 mg/cm2 but also for catalyst material fraction lower than 0.2. The agglomerate has negligible influence on the cell performance if the agglomerate radius is smaller than 150 nm. 4.2. Geometric surfaces of catalyst layer Since the 10 lm thickness of catalyst layer is much smaller compared with the 0.1 mm thickness of gas diffusion layer, the simplest description of the catalyst layer is offered by the interface model in which a catalyst layer of infinitesimal thickness is assumed between the membrane and the gas diffusion layer. The structure of the catalyst layer is then ignored. The influence of catalytic activity is introduced as the boundary condition at the membrane/gas diffusion layer interface. Since there are few reports on effect of various geometric catalyst layer surfaces and catalyst layer boundaries, Perng and Wu [40] assumed catalyst layer to be an ultra-thin layer and employed a two-dimensional isothermal model at the cathodic half-cell of a PEM fuel cell to investigate how the prominence-like form catalyst layer surface and number of prominence influence the cell performance. They found that the prominent catalyst layer can promote local cell performance since it produces a better convection performance and a greater flow velocity than the flat catalyst layer surface. In addition, the overall cell performance increases with an increase in the amount of the prominence because of speeding the fuel flow and magnifying the reaching area of the fuel gas. 5. Characteristics of transport in gas diffusion layer Gas diffusion layers serve to provide structural support of the catalyst layer and to transport the reactant and product toward and from the catalyst layer. In addition, they provide an interface where ionization takes place and transport electrons through the catalyst layer. A gas diffusion layer also plays an important role in heat transport from the reacting site and the water management of the cell. Without a gas diffusion layer, the membrane would be dried 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, porosity and graded structure of gas diffusion layer. The gas diffusion layer should possess the combined and balanced properties of hydrophobicity (water expelling) and hydrophilicity (water retaining). These properties have to be balanced carefully to ensure that the fuel cell system works without flooding and high humidity. Ismail et al. [41] used a three-dimensional single phase isothermal numerical model for a PEM fuel cell with one turn of a serpentine channel to study how the anisotropic gas permeability and electrical conductivity of gas diffusion layer influence the cell performance. They found that the cell performance is little influenced by the anisotropy in the permeability of the gas diffusion layer. However, the cell performance is influenced significantly by the electrical conductivity of the gas diffusion layer. This is because the activation overpotential increases owing to the reduced solid potential. Park et al. [42] performed a three-dimensional,

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two-phase unsteady, isothermal numerical model to examine the liquid water behavior in the gas diffusion layer under pressure gradient. Their results displayed that the contact angle of liquid water and pressure gradient are the key factors that decide the start of liquid water transport within the gas diffusion layer which is initially wet with static liquid water. The larger contact angle removes water faster from the gas diffusion layer at the fixed pressure gradient. The pressure gradient caused by the reactant flow within flow channel and gas diffusion layer can effectively remove liquid water from the gas diffusion layer. Khajeh-Hosseini-Dalasm et al. [43] used a three-dimensional transient two-phase non-isothermal model to investigate how operating temperature and channel inlet humidity affect the phase-change rate in the cathode gas diffusion layer of a PEM fuel cell during startup. They incorporated a nonequilibrium evapora tion–condensation interfacial mass-transfer rate in the model to consider supersaturation and subsaturation. They observed that when the case is dominant in condensation, it reaches steady state more quickly. The maximum temperature decreases as time increases because of vapor-phase diffusion and phase change. As operating temperature decreases, the vaporation rate decreases owing to the decreased saturation vapor pressure. As the inlet humidity of channel increases, the condensation rate increases because of the lower difference between the saturated vapor pressure and the water vapor partial pressure. Hossain et al. [44] established a three-dimensional two-phase isothermal numerical model inside the catalyst layers, gas diffusion layers and the flow channels with one-dimensional water transport in the membrane of a PEM fuel cell to examine transport of species in a gas diffusion layer considering the influences of liquid water saturation. A comparison investigation between liquid water saturation model employing power law with exponential factors and a percolation based model has been thoroughly made. Their results showed that the power law model with exponential factor of two offers a good expression of species diffusivity and generates much closer agreement with experimental cell voltage; by contrast, the percolation based model overpredicts cell voltage. The impacts of isotropic and anisotropic permeability of gas diffusion layer have also been explored and their results indicated that a higher isotropic permeability or a combination of higher in-plane and lower throughplane permeability causes higher performance of a PEM fuel cell. The cell performance substantially reduces with lower in-plane and higher through-plane permeability of gas diffusion layer. Abdollahzadeh et al. [45] developed a two-dimensional twophase isothermal flow and transport numerical model in cathode gas diffusion layer of a PEM fuel cell without considering the flow and transport in channels. A wide parameter study was done to investigate how different operational and gas diffusion layer factors affect cell performance. On the effect of gas diffusion layer factors, they observed that the cell performance improves with an increase in porosity of gas diffusion layer because of increasing diffusion coefficient for diffusion of reactants. Although the decrease in thickness of gas diffusion layer till 0.35 mm enhances the cell performance, the more decrease less than 0.35 mm reduces the cell performance. The cell performance increases with an increase in permeability of gas diffusion layer owing to increasing flow rate of gas phase in gas diffusion layer. As the hydrophobicity of gas diffusion layer rises, the cell performance increases because of the better water removal from gas diffusion layer resulting from an increase in capillary forces. de Souza et al. [46] investigated how the hydrophobic characteristics of the gas diffusion layer affect the water removal rate in rectangular and tapered channels through a volume-of-fluid method to simulate two-phase, twodimensional isothermal flow. They found that the water removal rate is enhanced by greater liquid contact angles in the gas diffusion layer for a rectangular channel but not for a tapered channel.

Karimi et al. [47] presented a two-dimensional isothermal approach for a single PEM fuel cell based on conservation laws and electrochemical equations to provide useful insight into water transport mechanisms and their effect on the cell performance. Their results have revealed that inlet stoichiometry and humidification, and cell operating pressure are important factors influencing cell performance and two-phase transport characteristics. The water content in the anode side, which inclines to dry, has great impact on the cell performance. The liquid saturation in the cathode gas distribution layer could be as high as 20%. The existence of liquid water in the gas diffusion layer decreases oxygen transport and surface coverage of active catalyst so as to degrade the cell performance. The quality in the cathode gas channel is greater than 99.7%, which indicates that liquid water in the cathode gas channel is present in too small amounts to interrupt the gas phase transport. Cao et al. [48] developed a three-dimensional, two-phase, and nonisothermal numerical model of PEM fuel cell to investigate how anisotropic features of gas diffusion layer, boundary temperature of flow plate, and gas inlet humidity affect the cell performance. Their results showed that the modeling of gas diffusion layer predicts more accurate current density and temperature distributions with anisotropic properties than with isotropic properties. In addition, cooling inlet region and heating outlet region have a better cell performance while fully humidified gas, particularly in the outlet region, has a worse cell performance. Inamuddin et al. [49] employed a three-dimensional non-isothermal numerical model of a PEM fuel cell to study how porosity and thickness of gas diffusion layer influence cell performance. They found that high porosity obtains high current density owing to more reactants reaching the reaction site. Larger thickness of the gas diffusion layer increases the consumption rate of reactant species at the interface between the gas diffusion layer and catalyst layer. The effect of attachment of bipolar plate to the gas diffusion layer reduces the amount of reactants to reach the catalyst layer particularly under the land area. Nevertheless, this effect decreases with increasing overall porosity 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 essential part of a fuel cell model due to the vital role of gas diffusion layers. The macroscopic model is mostly employed and requires empirical correlations such as the effective coefficients to account for the porous media property. These correlations can be developed from the pore-level information obtained from direct modeling/simulation. In addition, the pore-level study can provide fundamental details regarding interaction between transport and pore structure, which is beyond the capability of a usual macroscopic model. Wang et al. [50] combined a stochastic model for reconstructing the gas diffusion layer with direct simulation to study the porelevel transport in gas diffusion layers of PEM fuel cells. The carbon paper gas diffusion layer is considered by a stack of layers with each layer modeled by planar line tessellations which are dilated to three dimension. The direct simulation was then applied for reconstructing gas diffusion layer structure to simulate the momentum and species transport in the pore, electronic conduction in the solid matrix, and heat transfer for both phases. Distributions of the velocity, species concentration, temperature, and electronic potential in the gas diffusion layer were shown at the pore level. Their results indicated that the tortuosity of gas diffusion passage is 1.2 remarkably different from the tortuosity of solid matrix across the gas diffusion layer which is 3.8. This difference results from the lateral alignment feature of the thin carbon fiber, letting the solid-phase transport happen largely in lateral direction. The values of tortuosity and permeability obtained from their

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modeling are fairly agreeable with the ones in the article. Furthermore, diffusion commands the species transport in the pore even at high net water flux per proton flux. Kopanidis et al. [51] employed a direct three-dimensional microscale model of a part of cathode channel in a PEM fuel cell and carbon cloth gas diffusion layer to study local heat and fluid flow at the gas diffusion layer’s pore scale and their influences on condensation of water vapor that leads to flooding. The momentum, energy, and water vapor transport equations were solved at steady state and in threedimensional space with different inlet velocities and cloth fiber material properties, applying a conjugate heat transfer method to compute temperature distributions inside the solid fibers. The three patterns are as follows: (1) fixed fiber temperature assumption (T = 353 K), (2) conjugate heat transfer solution through fiber material supposing ELAT carbon cloth properties and (3) conjugate heat transfer solution through fiber material supposing pure carbon (graphite) properties. They found that the conjugate heat transfer solutions lead to lower outflow temperatures with one accord compared with the assumption of constant fiber temperature. In particular, the commercial cloth properties (ELAT) cause lower outflow temperature and are more responsible to convection; in other words, higher inlet velocities cause greater temperature variations. Yin et al. [52] presented a three-dimensional, unsteady, twophase isothermal volume of fluid model based on the microstructure of gas diffusion layer to study how pressure gradient and contact angle affect liquid water transport along the in-plane direction caused by cross flow. Their results indicated that the more the pressure gradient is, the earlier the transition from ‘‘fingering transport” mode to ‘‘steady transport” mode gets. The transition also gets earlier as the contact angle decreases. This is because of acceleration of the liquid water intrusion. As the pressure gradient rises, the mass flux of liquid water through gas diffusion layer in quasi steady state increases; in contrast, as the contact angle decreases, 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-equilibrium approach based on experimental correlations determined by them including porosity, capillary pressure, and permeability of the gas diffusion material to predict performance curves and liquid water saturation distribution. The first model is a one-dimensional model, in which the influence of employing experimental water transport properties of the gas diffusion layer is assessed via water saturation distribution in the gas diffusion layer. The second model is a two-dimensional model used to predict experimental polarization curves. They discovered that using experimental correlations of the gas diffusion layer predicts more liquid water saturation than using empirical correlations for the capillary pressure curves and permeability. The cell has better performance for an untreated gas diffusion layer than for a wet-proofed gas diffusion layer with 20% of PTFE; this is because the wet-proofing gas diffusion layer promotes water removal and decreases the gases diffusivity and the electric conductivity of the material. The operating current density impacts water saturation greater than the inlet air relative humidity does. The liquid water saturation below the land of the current collectors is higher than that under the channels owing to the impermeability of the current collector to the water, and owing to the long pathway between the region below the land and the interface with the gas channels. 5.3. Various configurations of gas diffusion layer surfaces The gas diffusion layer surface configuration affects the contact resistance, the gas diffusion layer porosity, and the fraction of the pores occupied by liquid water and ultimately the performance

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of PEM fuel cell. To explore the effects of gas diffusion layer compression on fuel cell performance, Bao et al. [54] developed a three-dimensional, unsteady, two-phase isothermal numerical model for the cathode side of a PEM fuel cell composed of gas channel, gas diffusion layer and catalyst layer to examine how the gas diffusion layer deformation impacts water droplet movement in the gas channel. The transport of the liquid–gas interface was treated by a volume-of-fluid method. They observed that when fuel cells are assembled, the cross sections of gas channel change as a result of different water droplet movements. A large pressure between the gas channel and the gas diffusion layer forces water droplets to move out of the gas channel earlier and faster. Furthermore, an enough fast gas velocity makes the droplet suspend in the gas channel and move out of the gas channel to obtain a high cell performance. Ahmadi et al. [55] presented a single domain isothermal model of PEM fuel cell to investigate how prominent gas diffusion layer affects cell performance. The prominent gas diffusion layer is specified by rectangular configuration. Their results revealed that prominent gas diffusion layer increases the velocity because of a decrease in the cross sectional area of gas flow in a gas channel. Increasing velocity magnitude improves the supply of the reactant gases to the catalyst layer to enhance the cell performance. Bao et al. [56] presented a three-dimensional volume of fluid numerical mode to examine how the deformation of the gas diffusion layer affects the water transport characteristics in the cathode of a PEM fuel cell. The parameters include different inlet flow rates, amount of liquid water in the gas diffusion layer, positions of water droplet in the flow channel, and contact angles between the gas diffusion layer and flow channel surfaces. They found that liquid water droplet leaving the gas diffusion layer is driven by the surface tension as the gas flow rate is low; however, it leaving the gas diffusion layer is driven by the gas flow at high gas flow rates. Meantime, the deformation of the gas diffusion layer and other factors 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 diffusion layer in a straight channel. Their work was to study the impacts of non-uniform compression of the gas diffusion layer and gas diffusion layer intrusion into a channel owing to the channel and rib structure of the flow-field plate. Their results indicated that the non-uniform compression and intrusion of gas diffusion layer increase the level of non-uniformity in the current density in the membrane and accordingly decrease overall cell performance. Particularly, in-plane gradients in the liquid saturation, oxygen concentration, membrane water content, and current density distributions considerably increase because of differences in the porous properties between the rib and channel areas. The amount of water accumulation in the gas diffusion layer against the ribs turns greater with reduced porosity and permeability of gas diffusion layer owing to compression, which causes a decrease in the oxygen concentration and local current density near the ribs. Because of gas diffusion layer compression, the lower local current density near the ribs increases the local current density near the channels under galvanostatic operation, which promotes the non-uniformity in the current density distribution. As a result, the combined impacts of non-uniform compression and intrusion of gas diffusion layer introduce substantial Ohmic and concentration polarizations, which are most obvious at high current densities. Wang et al. [58] developed a two-dimensional, isothermal numerical model solving continuity equation and Darcy’s law to calculate the saturation field in the double-layer gas diffusion media for a PEM fuel cell. They found that the overall saturation level decreases as the polytetrafluoroethylene loading increases. The interface

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

between the two gas diffusion media layers can regulate the saturation level by decreasing the driving saturation degree for water transport. The double-layer gas diffusion media has a higher maximum current density owing to better water management.

6. Characteristics of transport in flow field Humidified hydrogen enters anode flow channel transported through the channel, and diffuses into anode gas diffusion layer then into anode catalyst layer. Meanwhile, oxygen enters cathode flow channel transported through the channel, and diffuses into cathode gas diffusion layer then into cathode catalyst layer, membrane, anode catalyst layer, and anode gas diffusion layer. Water is transported out of the cathode catalyst layer, through cathode gas diffusion layer, and finally out of the cathode flow channel. The flow 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 most important issues in the PEM fuel cell investigations, because if it is so poor to locally accumulate liquid water, the reactant transport will be impeded and high pressure drops and the poor cell performance will be caused. The accumulation of liquid water is caused by liquid water formation and distribution in the channel. Liquid water formation and distribution in the channel is related to two-phase flow and droplet dynamics, so it is an important area of research [10]. Golpaygan et al. [59] developed a threedimensional multiphase isothermal flow numerical model to investigate flow dynamics of water droplets in a single channel of the PEM fuel cell employing the volume-of-fluid approach to

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Fig. 7. Effect of channel width on cell performance of a cell with: (a) parallel, (b) interdigitated, and (c) serpentine flow fields [67]. Fig. 6. Effect of channel height on cell performance of a cell with: (a) parallel, (b) interdigitated, and (c) serpentine flow fields [67].

track the deformation of free surfaces. They observed that for a given gas velocity, the existence of liquid water in the channel causes an increase in the pressure drop because of the increased flow resistance. Pressure fluctuation is harmful to the cell performance because it interferes with air supply to active sites, resulting from causing fluctuations in the current density. Higher flow rate leads to a substantial increase in the droplet height, so the flow separation downstream of the droplet appears obviously; and this shows a larger pressure fluctuation across the droplet. Reynolds number affects the height of the droplet strongly in the channel owing to an increase in shear and inertia of the flow. At high Capillary number, the droplet deforms more since surface tension force is small and shear force is large. The wetted contact area of the droplet and the wall therefore decreases dramatically. Qin et al. [60] employed the volume-of-fluid method to numerically study the process of water removal and transport for an isothermal and three-dimensional flow channel with a hydrophilic plate in the middle of a PEM fuel cell. They found that the liquid water droplet can be removed effectively from the MEA surface owing to the existence of the hydrophilic plate, and once it is detached from the MEA surface, the water droplet is transported downstream without blocking the reactant gas transported into the MEA. The

wettability, length, and height of the plate all affect the water transport and dynamics and the associated pressure drop in the flow channel. The wettability is represented by the water droplet contact angle at the wall surface. However, a short plate inclines to generate the spike in the pressure drop, and a long plate inclines to have a great pressure drop in the flow channel. For both effective water removal and low pressure drop in the channel, the contact angle 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 and isothermal model to numerically investigate the liquid water transport inside a tapered flow channel of a PEM fuel cell. They found that the liquid water distribution and transport within the channel depend on the air velocity. Near the channel exit, a liquid film on the gas diffusion layer surface is formed because of higher gas velocity; on the contrary, in the central part and near the channel inlet slugs are formed since the slope of the bottom wall of the channel impedes the accumulation of liquid water. The slugs behave as the primary mechanism of water removal, eliminating attached droplets when they move to the channel outlet and helping to reduce the water saturation inside the channel, but they cause an increase in the pressure drop. Mondal et al.[62] studied how surface wettability properties and inlet air velocities affect water droplet movement in PEM fuel cell flow channels with hydrophilic surfaces employing three-

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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 serpentine flow-field pattern [76].

dimensional CFD method coupled with the isothermal VOF method to track liquid–gas interface. Their results showed that the water droplet moves faster with increasing air flow velocities and with increasing the contact angle hydrophilic surface owing to less liquid–wall contact area. Ferreira et al. [63] employed threedimensional, transient, isothermal, two-phase model with volume of fluid method to analyze how hydrogen inlet velocity, operating temperature and channel walls wettability affect water movement in an anode gas channel of a PEM fuel cell. They observed that water moves as films on the upper surface of the channel for hydrophilic channel walls while it moves as a droplet for hydrophilic channel hydrophobic. In addition, water removes faster as hydrogen inlet velocity, operating temperature and channel walls wettability increase. Nevertheless, increasing hydrogen would cause a considerable pressure drop. The average pressure drop increases slightly with increasing temperature and channel walls wettability while the temporal pressure drop varies with changing temperature and channel walls wettability. Jo and Kim [64] developed a three-dimensional, isothermal numerical model with volume of fluid method to explore how the location of the water inlet pore, the contact angle of the gas diffusion layer surface, the contact angle of the other channel walls, the air inlet velocity, and the water injection velocity impact water droplet dynamics within a right angle gas channel of a PEM fuel cell. Their results indicated that as the contact angle of the gas diffusion layer surface decreases, droplets emerging from the outer and inner pores move along the side walls or the outer lower edges. The water coverage ratio of the gas diffusion layer surface increases but the water volume fraction decreases with an increase in the hydrophobicity of the side and top walls. The higher the surface water coverage ratio of gas diffusion layer is, the harder the reactants diffuse into reaction sites; however, the lower water volume fraction can avoid water flooding in the gas channel. There is a good trade-off between the surface water coverage ratio of gas

diffusion layer and the water volume fraction to get a better effect on the fuel cell performance. The water volume fraction decreases with an increase in the air inlet velocity but increases with an increase in the water inlet velocity. Lorenzini-Gutierrez et al. [65] applied a three-dimensional, isothermal numerical model with volume of fluid method to investigate how superficial air velocity, channel surface wettability, and channel crosssection affect liquid water removal characteristics. Their results indicated that the range of contact angle from 60° to 65° is beneficial for the channel walls to get top wall film flow, slight fluctuations in pressure drop and a better liquid removal rate. The trapezoidal cross-section with open angle of 50–60° enhances the formation of top wall films and obtains more stable two-phase pressure drop and liquid removal rate 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, significantly affecting the performance of PEM fuel cells. Numerous flow field configurations have been presented and studied in the past. These

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

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

conventional designs can be classified into four categories: pintype, parallel, serpentine, and interdigitated. Among them, parallel and serpentine designs are the most widely known and employed ones. Parallel designs have the advantage of low pressure drop. However, the flow resistance is difficult to maintain at the same level in each flow path causing a non-uniform distribution of the reactants. Serpentine designs usually give high fuel cell performance but they typically have relatively long reactant flow path, leading to substantial pressure drop. Additionally, reactant concentration significantly decreases from the inlet to the outlet of the flow channel. This decrease leads to considerable Nernst losses and non-uniform electric current density distribution, reducing both the overall performance and lifetime of PEM fuel cells. Therefore, it is essential to investigate and optimize the flow distribution

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within these configurations in order to eliminate the stagnant areas and hence improve performance. Hassanzadeh et al. [66] established a two-dimensional nonisothermal numerical model to solve governing equations of mass, momentum, energy, and species conservation for the developing laminar 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 other impermeable plane (simulating bipolar plate surface). Two flow situations included uniform air suction or air injection in a fuel cell channel and humidified air and humidified hydrogen with fixed mass flux boundary condition for oxygen in the cathode channel and hydrogen in the anode channel. The local and the averaged friction coefficient, Nusselt number and Sherwood number were determined for various flow conditions such as different stoichiometries, operating current densities and operating pressures of the cell. They found that the velocity decreases owing to the suction at the porous plane and the velocity peak shifts toward the porous plane, so velocity gradient and accordingly the shear stress increase on the porous plane and decrease on the non-porous plane along the flow direction. Correlations for the averaged friction coefficient, Nusselt and Sherwood numbers are set up; they are useful in flow field modeling and design of a PEM fuel cell. Chiu et al. [67] presented a two-phase, three-dimensional, isothermal transport model based on the two-fluid approach for a PEM fuel cell with parallel flow field, interdigitated flow field, and serpentine flow field as indicated in Fig. 5 to study the transport phenomena and cell performance. As shown in Figs. 6 and 7, reducing channel height or width of parallel and serpentine flow channels can improve the cell performance with low operation voltage because of higher gas velocity with more water removal. Henriques et al. [68] developed a three-dimensional, isothermal numerical model of the PEM fuel cell having a design of parallel channels crossed by a transversal flow channel to examine the

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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Fig. 12. Transient performance of a PEM fuel cell operating with a dead-end anode for galvanostatic boundary condition at current density 5000 A m2 for RHa 0%, RHc 0%; RHa 0%, RHc 100%; RHa 100%, RHc 0%; and RHa 100%, RHc 100% for (a) cell performance; (b) average hydrogen concentration at the anode; (c) average liquid saturation at the anode; (d) average nitrogen concentration at the anode. Note that the performance at t = 0 s corresponds to open-end anode operation [83].

influences of liquid water contents and current density. Their results indicated that excluding the transversal channel, employing a design of straight channels with larger width can enhance their performance up to 26.4%. This is since increasing the crosssection area of channel forces more air to flow through the fuel cell, and the water distribution is then more uniform through the catalyst layer. Tehlar et al. [69] established an isothermal model to examine different channel-rib geometries and gas diffusion layer characteristics. Their results showed that cross convection in a serpentine channel can significantly increase the current density and consequently the power density of PEM fuel cells. The cell performance is strongly dependent on gas diffusion layer compression, flow velocity, and rib width. As the rib width decreases to increase the compression of gas diffusion layer, the cross convection increases to promote oxygen supply under the rib. Nevertheless, negative effects induced by membrane drying, or Ohmic resistance limit the development potential of decreasing the rib width. Increasing micro-porous layer or gas diffusion layer thickness augments the under rib conversion but meanwhile reduces the overall average current density owing to longer through-plane pathways for the reactants. When the thickness of gas diffusion layer under the rib increases, current densities may rise up to about 20% higher current densities. Exact knowledge of characteristics of the gas diffusion layer and its compression is suitable to understand channelto-channel cross convection and optimize performance of a PEM fuel cell. Wang et al. [70] employed a three-dimensional, twophase 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 channel size 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 the cell 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-isothermal numerical model including the mass conservation equations, Navier–Stokes equations, species transport equations, and the energy equation to examine how the height/width ratio affects the performance of a PEM fuel cell with serpentine flow channel. They observed that the higher height/width ratio has a higher performance owing to uniform current distributions with the higher maximum and minimum intensity values and temperature distributions with smaller gradients. The 10/06 and 12/05 of aspect ratio have the best polarization curves. Yang et al. [72] used a in-house genetic algorithm with a commercial code, COMSOL to explore the optimization method of channel geometries for a PEM fuel cell. The geometry variables were channel-to-rib widths and channel height. The cell output power is considered as the objective function for the optimization. Their results displayed that channel-to-rib width of 1.84:1 has the best performance and 0.54:1 worst performance. A channel height of 0.515 mm has the best fuel cell performance. A 2:1 channel-torib width ratio has better performance than a 0.5:1 channel-to-rib width ratio. This result consists with the optimization result. Yang et al. [73] further developed an automated connection between genetic algorithm optimization and fuel cell performance to optimize the bipolar plate channel geometry of a PEM fuel cell. First, they used a two-dimensional CFD model to obtain the optimal result in order to speed up the optimization calculation, slightly sacrificing the model accuracy. They then applied a

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interface between the cathode diffusion layer and catalyst layer owing to the forced convection. For both flow channels, greater channel to rib width ratio leads to larger overshoot, smaller undershoot, and longer response time. Li et al. [76] employed a three-dimensional, two-phase multicomponent model with statistical tools to investigate the current density, membrane water content, and local temperature for six flow-channel patterns of a PEM fuel cell. Furthermore, two channel assembled angles (defined as shown in Fig. 8a) and three serpentine flow-channel configurations (shown in Fig. 8b–d) were used as basic elements to assemble six flow-channel patterns. Under the same operating conditions, although the polarizations of the cells are similar, their results showed that the range of the uniformity of various physical properties changes for various flowchannel patterns. Because of the right distributions of reactants, the membrane water content, temperature, and current density are distributed more uniformly in channel-perpendicular flow-fields than in channel-overlapping ones. Furthermore, the membrane water content, temperature, and current density are distributed more uniformly in fewer cathodic serpentine channels than in more channels. On the contrary, the more cathodic serpentine channels have less pressure drop in the channels. Sala et al. [77] first performed analytical calculations for a PEM fuel cell to obtain the flow rate, pressure drop and velocity in the flow field for single, double, and quadruple serpentine flow channels with an active area of 25 cm2. Their results of analytical calculations were then compared with the results of a three-dimensional and single-phase simulation for all the configurations; finally, the best pattern was defined for the feeding channels so as to augment mass transport and obtain the best velocity profile. Effects of the temperature and of the humidity were also studied performing experiments at 60 °C and 70 °C and between 60% and 100% of humidity of the reactant gasses. They found that a multiple serpentine leads to lower values of pressure drop and velocities to reduce losses and promote reactant movements into the gas diffusion layer. They developed a configuration with smoothed angles to get a good trade-off between the configuration of rounded and

Fig. 13. Impact of tapered flow channel on the polarization curves of the cell performance: (a) no baffle plate, (b) k = 0.2, and (c) k = 0.005 [87].

three-dimensional CFD model and experiment with the same geometries to verify the optimization result. Their results showed that channel-to-rib width of 2.8:0.5 obtains the best performances for normal channel arrangement and 4.2:0.3 for reverse channel arrangement. Baschuk and Li [74] applied an isothermal, steady state, twodimensional numerical model for a PEM fuel cell. They found that the length of the flow channel affects the current density of a PEM fuel cell significantly, with a longer channel length producing a lower performance compared with a shorter channel length because of a greater change in water content inside the longer channel length. Wang et al. [75] applied a three-dimensional, two-phase isothermal numerical model to explore transient characteristics of a PEM fuel cell with parallel and interdigitated flow channels upon variations in voltage load. They observed that when the voltage decreasing rate is lower, the overshoot peak becomes lower and the response time is shorter. The overshoot peaks and the undershoot valleys of the interdigitated flow channel are all greater than those of the parallel flow channel because the interdigitated flow channel has higher oxygen concentrations on the

Fig. 14. Configuration of the rectangular block numbers in the anode and cathode channel [88].

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Fig. 15. Polarization curves compared for rectangular block numbers and no rectangular cylinder [88].

Fig. 16. Comparison of the pressure drop for N = 1–7 with that for no rectangular block for the channel at the (a) anode (b) and cathode [88].

squared bends. The velocity profile develops well for most of the pattern except for some inner side of the bends. The squaresmoothed bends configuration is a good compromise between the velocity and the ratio of the contact surface area. The highest power density occurs at 70 °C and at the humidity of 60% for the cathode and 80% for the anode. Guo et al. [78] developed a network-based optimization model for the optimal channel dimensions of flow fields to obtain a uniform flow distribution and enhance the performance of PEM fuel cells. They explored various flow field configurations, including parallel, parallel-in-series, and serpentine employing the presented optimization model. Their optimization results illustrated that the optimized designs substantially improve the flow velocity distribution among all the configurations. The optimized designs considering reactant consumption show more uniform flow velocity distribution when the entire fuel cell is involved. In addition, they studied the cell performance for the conventional and optimized flow field with a three-dimensional, two-phase, and nonisothermal numerical model of a PEM fuel cell, and their computational results displayed that the optimized designs considering reactant consumption generate the highest maximum power density for each configuration. Jiao et al. [79] carried out a threedimensional non-isothermal numerical simulation for a PEM fuel cell to investigate how induced cross flow affects the flow pattern and cell performance with a previously presented and experimentally studied novel parallel flow channel design [80] as shown in Fig. 9. Fig. 9 displays that the flow channel design can evoke cross flow between the high-pressure and low-pressure flow channels. Fig. 10 shows that the total power output and net power output are generally augmented by raising the back pressure but the power output improves less significantly at higher back pressures. The highest net power output is at the pressure difference of 500 Pa, and the power improvement cannot conquer the power consumption by further raising the pressure difference. This is because the flow direction is primarily from the flow channel to gas diffusion layer and catalyst layer as the cross flow is not evoked; nevertheless, with evoked cross flow, the primary flow direction in the low-pressure channel turns from the catalyst layer to the flow channel with substantially increased velocity because of the cross flow as illustrated in Fig. 11. The result confirms the net power output enhancement of the novel parallel flow channel design presented in [80]. In a PEM fuel cell with a dead-end anode, water vapors may accumulate at the anode side and condense into liquid. When oxygen is supplied from air at the cathode side, the nitrogen from air crosses over the membrane to the anode side and may accumulate. Sasmito and Mujumdar [81] employed a two-phase nonisothermal numerical model for the dead-end anode outlet to solve conservation equations of mass, momentum, species, energy, charge with a phenomenological membrane model and agglomerate model for catalyst layer. Their results displayed that the cell performance reduces because the amount of available hydrogen decreases owing to accumulation of water and nitrogen in the anode region with time. Increasing purge frequency raises the cell performance. Purge duration longer than 1 s is sufficient to recover the cell performance. Gomez et al. [82] therefore developed a single cell two-dimensional, transient, two-phase non-isothermal flow model of a PEM fuel cell with a dead-end anode to realize local distribution of liquid water, hydrogen, oxygen, water vapor and nitrogen. They solved the governing conservation equations of mass, momentum, species, charge and energy coupled with electrochemistry, a phenomenological membrane model and agglomerate catalyst layer model. Their results revealed that the inlet conditions of anode and cathode become a limiting parameter for the stack performance. As displayed in Fig. 12a, the cell performance is higher and can keep longer duration for both the

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Fig. 17. (a) Schematic diagrams of a PEM fuel cell with trapezoid baffles, (b) illustration of a trapezoid baffle, (c) illustration of boundary conditions in a PEM fuel cell [91].

humidified anode and cathode than for other cases. On the other hand, the cell performance drops to zero less than 100 s for dry cathode and less than 50 s for the dry and humidified anode. The reason for the cell voltage drop in the dry cathode cases is that the hydrogen depletes (Fig. 12b) and nitrogen crosses over (Fig. 12d) together with membrane drying. As the membrane contains no water content, the chemical bond of the ionomer becomes weak, the membrane pore is empty, and it is thus easier for nitrogen to permeate through the membrane. In addition, no liquid water accumulation is observed in the dry cathode cases (Fig. 12c); this implies that anode flooding does not occur at this condition. Jian et al. [83] developed a three-dimensional steady nonisothermal numerical model based on the electrochemical, current distribution, fluid motion continuity equation, momentum and energy equation, boundary layer theory to simulate a PEM fuel cell with interdigitated flow field using the computational fluid

dynamics. They analyzed how the humidification in the anode or cathode affects the current density and temperature differences. Their results showed that the humidification strongly influences the current density and temperature difference and then affects the cell performance. At the fixed operation conditions and low humidification conditions, anode humidification can augment the cell performance and improve the range of PEM humidification. Guilin et al. [84] employed a three-dimensional, non-isothermal and two-phase numerical model on the basis of computation fluid dynamics to describe flow and heat transfer of a PEM fuel cell with serpentine fluid channel. They explored how temperature on membrane surface, condensation rate, pressure loss, and net water flux coefficient vary with operation voltage and RH. Their results illustrated that the temperature ‘‘channel effect” can appear obviously and the temperature becomes lower when the operation voltage is higher; the condensation rate will increase along the flow direction

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Fig. 19. Comparison of performance curves between serpentine and spiral channels [93].

Fig. 18. Effects of various (a) angles and (b) heights of trapezoid baffles on the cell polarization curves [91].

to accumulate water; the cathode has higher pressure loss than the anode in the same case; the net water flux coefficient changes slightly at suitable voltage and RH, and varies from 0.4 to 0.54.

6.3. External additions in the channel The use of external additions in the flow channel-bed or along the axis of the channel such as partial block, baffle, and rib has demonstrated to be an effective way to force the gas to diffuse more in the gas diffusion layer and then increase the amount of gas that reaches the catalyst layer and reacts. The more reacting gas in the catalyst layer then enhances the fuel cell performance. Tiss et al. [85] presented a two-dimensional single-domain isothermal model to study the mass transport in a PEM fuel cell with partial blocks installed in the flow channel. Their results showed that partial blocks in the gas channel enhance the PEM fuel cell performance because of promoting reactant gas distribution in the gas diffusion layer, and partial blocks obtain a better cell performance with a degree tilt of 4.9° than with a degree tilt of 6.6 and 8.2. Dehsara and Kermani [86] studied how bipolar channel indentation affects the cell performance employing threedimensional, compressible, isothermal and single-phase calculation of a PEM fuel cell. Three straight channels with different bed shapes were considered, namely, flat, semicircular and wavy channel-beds. Their results revealed that flow channel indentations in the anode and cathode sides promote the net transport of reacting species through the porous layers into the catalyst layer. The improvement of the cell performance because of channel indentation is in the extent of 18–22%. The channel with wavy-bed shape has slightly better performance than that with semicircular one since the wavy indents have sharper crest than the

semicircular ones, and the wavy-channel bed penetrates the reacting species into deeper and ends inside the reaction sites. Perng and Wu [87] employed the projection finite element and an element-by-element preconditioned conjugate gradient approach to solve a two-dimensional non-isothermal model of a PEM fuel cell at the cathode. They investigated how the tapered flow channel installed with a baffle plate enhances the cell performance. As indicated in Fig. 13a that at lower operating voltage conditions, the overall cell performance rises as the tapered ratio Rch declines, and the maximum increasing overall cell performance is 8.24% at Rch = 0.25 and Vcell = 0.2 without a baffle plate. This result is because the lower outlet height of flow channel raises the tapered impact to augment the local current density across the catalyst layer, and has a better local cell performance. Fig. 13b shows that the tapered ratio affects the overall cell performance slightly compared with no baffle plate at the higher operating voltages, and the tapered ratio of 0.25 gets the best overall cell performance at the lower operating voltages. In addition, for different tapered ratios, the maximum increasing overall cell performance is 12.86% at cell voltage Vcell = 0.2 and gap size k = 0.2. This result is since the tapered ratio of 0.25 makes a larger amount of fuel gas flow into the gas diffusion layer and a more effective decrease in the deflecting phenomenon than the other tapered ratios. About the polarization characteristics of the cell performance for different Rch values at the narrow gap size (k = 0.005) as shown in Fig. 13c, the tapered ratio 0.25 achieves the best overall current density under the lower operating voltages, and the maximum increasing overall current density is 15.48% at Vcell = 0.2 and k = 0.005. The maximum increasing overall current density is greater at the narrow gap size than the one at the broad gap size owing to the enhanced the blockage impact with the tapered flow to strengthen composite effect more than the broad gap size. The tapered flow channel by a baffle plate promotes the fuel transport rate and the reaction in the catalyst layer hence progresses. From these results in the their study, the tapered flow channel by a baffle plate employed for all cases promotes the overall cell current density of a PEM fuel cell, and the flow channel designs are attainable in a real PEM fuel cell system. Wu and Ku [88] developed a three-dimensional non-isothermal numerical model in the anode and cathode channel to explore how

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Fig. 20. Velocity and vorticity distributions occurring for various sections (Ai–Ao, Bi–Bo, Ci–Co) in spiral channels at anode side [93].

number (N) of the rectangular block transversely installed along the axis in the channel (Fig. 14) affects the cell performance of a PEM fuel cell. For N = 1, the rectangular block is positioned at 1/2 length from inlet, i.e., at the central location of the channel length. For N = 3, the three rectangular blocks are positioned separately at 1/4, 1/2 and 3/4th length from the inlet. For N = 5, the five rectangular blocks are positioned separately at the locations of 1/6, 1/3, 1/2, 2/3 and 5/6th length from the inlet. For N = 7, the seven rectangular blocks are positioned separately at the locations of 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, and 7/8th length from the inlet. Fig. 15 reveals that the change of overall cell performance for any type of rectangular block is insignificantly small at the higher operating voltages, but the rectangular blocks affect the polarization characteristics substantially at the lower voltages. Furthermore, the cell performance is raised with increasing the number of rectangular blocks. The fuel gases are driven to pass through the gas diffusion layer and catalyst layer to promote the chemical reaction happening in the catalyst layer and thus the performance with rectangular blocks in the anode and cathode channels. N = 7 shows the maximum cell performance among all numbers, owing to the strongest blockage impact containing a large region. In Fig. 16, increasing N produces more gas reactant transport through gas diffusion layer and more chemical reaction happens, which accordingly raises

the cell performance. Nevertheless, the increase in the number of rectangular blocks infers more powerful blockage impact and greater pressure drop. Pressure loss rises substantially as N is greater than 5. The intervention of the rectangular blocks creates greater pressure loss and needs greater pumping power to deliver fuel. Yang et al. [89] presented the multi-factor constrained optimization approach integrated with the design of experiments, full factorial experimental design, genetic algorithm and threedimensional non-isothermal flow model in a wavy channel connected with a gas diffusion layer. The Forchheimer–Brinkman extended Darcy model and two-equation energy model are applied to the fluid flow and heat transfer in the porous media. The factors include Reynolds number (Re), wave amplitude (a), wave number (b) and gas diffusion layer porosity (e) in the level of 200 6 Re 6 1000, 0.1 6 a 6 0.3, and 2 6 b 6 10, 0.4 6 e 6 0.5. Their results displayed that values of Nusselt numbers inside the wavy channel are larger compared with the straight channel. Additionally, the optimization of this problem is also obtained employing a full factorial experimental design and the genetic algorithm approach. The objective function assigned by thermal performance factor has a correlation function with three design parameters of wave amplitude a, wave number b, and gas diffusion layer porosity

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e. Compared with the straight channel, the wavy channel is better heat exchange between flow and the wall. The local and average Nusselt numbers hold a maximum value at the inlet and decrease with flow direction owing to the heat transfer from the flow toward the wall. The distribution of frictional force in the wavy channel is profoundly influenced by wave amplitude a and wave number b. With the optimization process and the full factorial experimental design and regression, they develop a correlation equation among thermal performance factor. The prediction of thermal performance factor has the maximum error of 6.2% from their regression model compared with the simulation results. Bilgili et al. [90] conducted a three-dimensional computational model at different operating conditions of stoichiometry, relative humidity, and temperature to explore the performance of a PEM fuel cell including rectangular obstacles with constant height and length of the obstacle in the flow channels of anode and cathode. Their results indicated that the obstacles within the gas flow channels promote the concentration distribution across the channels and the transport of the reactant gases past the gas diffusion layer. Consequently, an improvement of around 4–6.5% on the polarization curves is obtained by varying the operating conditions under high current densities. Perng and Wu [91] employed the SIMPLE-C method with preconditioned conjugate gradient methods and developed a threedimensional numerical simulation to investigate the effect of trapezoid baffles on non-isothermal reactant transports and the cell net power in a PEM fuel cell. The PEM fuel cell consists of anode fluid channel, anode gas diffusion layer, anode catalyst layer, membrane, cathode catalyst layer, cathode gas diffusion layer, and cathode fluid channel as shown in Fig. 17. The geometry of trapezoid baffles is prescribed by four different angles (h = 45°, 60°, 75°, and 90°) and three heights (Hb = 0.75, 1.125, and 1.5 mm) in their study. The other geometries of their paper are adopted by the following: L = 50 mm, Wb = 4.0 mm, H = tb = tr = 1.5 mm, and Db = 7.0 mm. The cell net power is used to calculate the real augmentation of cell performance owing to the extra pumping power created by the pressure drop through the cell. Their results indicated that the novel gas channel with trapezoid baffles, whose angle is 60° and height is 1.125 mm, promotes the cell net power about 90% more than traditional gas channel without baffles. In Fig. 18, inserting the trapezoid baffles in the flow channel obviously raises the current density and power density of the cell for different operating voltages. Furthermore, a greater angle of trapezoid baffle generates higher current density and power density. This result is created by the trapezoid baffles because of these trapezoid baffles obstructing the fuel gas, forcing more fuel into the gas diffusion layer and accordingly enhancing chemical reaction in the catalyst layer. In Fig. 17b, the current density and power density are magnificently promoted when the height of trapezoid baffle increases; nonetheless, the difference of polarization curves between no-baffles and 0.75 mm-baffles cases is slight. This result means that the blockage effect of trapezoid baffle on the polarization curves is small as its height is 0.75 mm. The numerical results of Fig. 18 clearly display that the greater angle and height of trapezoid baffles substantially intensify the blockage effect and then enhance the cell performance. 6.4. Cross-sectional shape There are different velocity distributions in the sections of channel’s cross-section shapes such as semicircular, trapezoidal, triangular, and rectangular to affect liquid water removal and oxygen utilization. Wang et al. [92] investigated numerically how cathode channel shapes affect the local transport characteristics and cell performance employing a three-dimensional, two-phase, and

non-isothermal numerical model for a PEM fuel cell. The cathode channel shapes include triangle, trapezoid, and semicircle, and rectangular channels. They observed that at the higher operating voltages, the performance of cells with different channel shapes is similar. Nevertheless, at the lower operating voltages, the cell performance arranged from large to small is followed by triangle, semicircle, trapezoid, and rectangular channel. The triangle, trapezoid, and semicircle channel designs raise significantly flow velocity of reactant, promoting liquid water removal and oxygen consumption. These designs then raise the limiting current density and enhance the cell performance compared with rectangular channel design. 6.5. Non-conventional channel For the conventional channel geometry, such as the parallel, the serpentine, and the interdigitated channels, there exist many sharp turns which cause large pressure drops in the flow field. To avoid the sharp turns, spiral or annular or Bio inspired channels can be an alternative to replace the conventional channels. Jang et al. [93] developed a seven-layer non-isothermal numerical model consisting of cathode channel, cathode gas diffusion layer, cathode catalyst layer, membrane, anode catalyst layer, anode gas diffusion layer, and anode channel to simulate the performance of a PEM fuel cell with spiral and serpentine channels. Fig. 19 indicates that the average current density of the spiral channel is 11.9% higher than that of the serpentine channel. This result can be explained by Fig. 20 that a pair of secondary vortices with opposing directions forms at section Bi–Bo, and a more complex secondary flow pattern exists at section Ci–Co. These secondary vortices enhance heat and mass transfer in the curved channels and then improve the cell performance. Roshandel et al. [94] presented a three-dimensional, multi-component isothermal numerical model to investigate various flow channel designs in the bipolar plate of a PEM fuel cell. They employed Bio inspired flow field (BI) to allow gases to enter the middle of cell and to distribute past symmetric diagonal parallel channels and to exit through the middle. The distance between channels reduces when the flow approaches the outlet to offer more uniform velocity, pressure, and species distribution through the cell. Their results indicated that the patterns with inspiration from the nature display a more appropriate and homogeneous velocity and species distribution across the channels. The obtained voltage and the power density are promoted in the new proposal pattern. The power density of BI inspired flow channel is higher than that of parallel channel up to 56% and higher than that of serpentine flow channel up to 26% without considering the liquid water formation and temperature changes. Employing the new innovative design not only produces more efficient fuel cells but also achieves cheaper and lighter ones. Khazaee et al. [95] employed a complete three-dimensional and single phase computational dynamics model for the annular PEM fuel cell to examine how changing gas diffusion layer and membrane properties affect the performances, current density, and gas concentration. The presented model was a full cell model, which included all the parts of the PEM fuel cell, flow channels, gas diffusion electrodes, catalyst layers, and membrane. Combined transport and electrochemical kinetics equations are solved in a single domain, and therefore no boundary condition is necessary at the interface between cell components. Their results showed that the performance of the cell enhances with increasing the thickness and with decreasing the porosity of gas diffusion layer; which is different from planner PEM fuel cell. Decreasing the thickness of the membrane also increases the performance of the cell. Increasing the thermal conductivity of the membrane increases the overall cell performance because of raising the lateral

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conduction of heat generated at the cathode catalyst layer toward the anode gas diffusion layer. 6.6. Flow field orientation During the operation of PEM fuel cell, the flow field orientation plays an important role on the cell performance because it affects heat and mass transport in the fuel cell [4]. Bao and Bessler [96] built up a two-dimensional single-phase model for the steadystate and transient analysis of PEM fuel cells. Viscous flow is conducted into a multi-component model in the membrane according to diluted and concentrated solution theories. A Butler–Volmer formulation for the current–overpotential relationship is set up on the basis of electrochemical oxygen reduction. Their model is then used to analyze how operating condition affects the cell output and water management; in particular, net water transport coefficient along the channel. They found that in a PEM fuel cell, the long-channel configuration is favorable to internal humidification and water removal at anode for correct gas flow rate and humidity of reactants at counterflow mode. For full humidification, the net water transport can alter its direction as a function of location in the channel, as a result of a balance among electro-osmotic drag, back diffusion, and water flow. At a suitable humidity of reactants and fuel flow rate, preventing anode dehydration and cathode flooding can be obtained without substantial effect on the cell performance. As dry reactants are used, the counterflow mode shows an effective internal humidification and thus a better performance compared with coflow mode, particularly at a typical reactant stoichiometry for practical fuel operation. If the dynamics of water transport is considered, the variation between the maximum and minimum water intake in the membrane turns smaller. Obayopo et al. [97] applied a three-dimensional, non-isothermal, singlechannel numerical model of a PEM fuel cell to investigate the effects of several key parameters, including channel geometries (width and depth), flow orientation and gas diffusion layer porosity on performance, and species distribution. The key factors range from 0.6 to 1.6 mm of channel width, 0.5 to 3.0 mm of channel depth, and 0.1 to 0.7 of the gas diffusion layer porosity. Their results showed that the optimum value of channel depth is 2.0 mm and that of channel width is 1.2 mm at a cell potential of 0.3 V and a temperature of 70 °C. Counterflow channel generates better performance than coflow channel for the cell particularly at higher current voltages; this is because counterflow channel has more uniform distribution of hydrogen species in the channel. The cell performance is much smaller at porosity values of 0.1–0.4 than at porosity values of 0.5–0.7. Hashemi et al. [98] established a non-isothermal, threedimensional numerical model to investigate the performance of PEM fuel cells for straight and serpentine flow fields. Their model implemented the major transport phenomena in a fuel cell including mass, energy transport, electrode kinetics, and potential fields to determine oxygen and hydrogen concentrations distributions, current density and temperature distributions. Two cases comprising of co-flow and counter-flow are deliberated for all flows in the cell with constant activation overpotential in anode and cathode. They observed that serpentine flow field has better current density and temperature distributions. At high current densities, the modeling results are different from experimental results owing to assuming one-phase model that ignores the water flooding inside cathode and drying inside anode. Current density is greater for the longer electrical current path. Yang et al. [99] employed a two-dimensional non-isothermal model to study local fuel starvation and carbon corrosion phenomena at channel-clogging conditions in a PEM fuel cell. Their results demonstrated that in-plane convection is the main type for hydrogen transport at the outer edge of the flooded area. The hydrogen depletion length depends

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on the cell voltage and on the total length scale of the flooded area. Nonetheless, when the reactant moves deep inside, the dominating transport type switches to diffusion because of nitrogen accumulation within the anode. In addition, when nitrogen dilutes hydrogen outside the flooded region, the length scale of hydrogen to consume completely decreases significantly and extends the area subject to hydrogen depletion and carbon corrosion. 6.7. Flow plate material A traditional material is graphite, but matching grooved flow fields on both sides of a graphite plate costs too high for mass production and commercialization of PEM fuel cells. Alternative materials for bipolar plates are therefore developed such as metal material [100] and porous metal material [101,102] to reduce manufacturing cost for PEM fuel cell. Fink and Fouquet [101] presented one-dimensional model coupled with three-dimensional, non-isothermal model (AVL FIRE code) between the gas diffusion layers and flow channels for a PEM fuel cell with metallic bipolar plate. Their results indicated that the heat transfer in the cathode reaction layer is so strong that the low contact resistance generates a low electric potential drop and a high current density. Carton and Olabi [102] developed a three-dimensional, isothermal numerical model for Open Pore Cellular Foam (OPCF) material of a flow distributer. They found that OPCF material can increase the PEM fuel cell performance compared with conventional flow plates since this material helps to reduce mass transport losses. In addition, OPCF material can create a tortuous gas flow through the structure and offer a low pressure drop from inlet to outlet. 7. Conclusion This study has reviewed latest studies on transport and performance modeling of PEM fuel cells using two-dimensional and three-dimensional models. First, a fundamental model of computational fluid dynamics was described for a PEM fuel cell. The effects of characteristics of transport in membrane, catalyst layer, diffusion layer, and flow fields were then discussed with their effects on the cell performance. The main results about transport characteristics in membrane are shown as follows: (1) Higher anodic stoichiometry or cathodic stoichiometry reduces cathodic water saturation to enhance cell performance; (2) Installing the metal foam at wet side and both sides indicates a better humidifier performance; (3) The water content in the membrane increases with increasing the humidification temperature and the inlet velocity of the gas channel; (4) The voltage reversal due to step increase in current density can be avoided by increasing water uptake capacity; (5) The cell current density increases with a decrease in water sorption/desorption rate coefficient; (6) An imposed water flux at the cathode side of the membrane can decrease the voltage loss rather than an applied heat flux on the membrane outlet; (7) The performance of counterflow humidifier is better than that of the parallel-flow humidifier; (8) The cell temperature increases with an increase in the thickness of Nafion; and (9) The cell performance is larger for non-zero deflection parameter than for zero deflection parameter. The main results about transport characteristics in catalyst layers are shown as follows: (1) Increasing the surface wettability or lowering the contact angle can reduce the liquid water saturation in a hydrophilic cathode catalyst layer for a rectangular channel but not for a tapered channel; (2) A modified agglomerate approach on the basis of discrete catalyst particles can properly predict the effect of Pt loading in the diffusion-loss region; (3) The catalyst loading distribution in the both directions of ‘‘across the layer” and ‘‘in catalyst plane” affects the catalyst use significantly; (4)

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The performance improves with catalyst layer thickness from 6 to 10 lm but deteriorates for catalyst layer thickness larger than 10 lm; (5) Employing higher temperature on the anode or enlarging the width of the channel/rib ratio improves the cell performance; (6) Two-variable optimization on NFP/Pt and NFP/C distributions can obtain higher performances than single-variable optimization; and (7) The prominent catalyst layer can enhance local cell performance surface, and the overall cell performance increases with an increase in the amount of the prominence. The main results about transport characteristics in gas diffusion layers are shown as follows: (1) The larger contact angle generates faster water removal from the gas diffusion layer at the same pressure gradient; (2) The high isotropic permeability or a combination of high in-plane and low through-plane permeability causes higher performance of a PEM fuel cell; (3) The decrease in thickness of gas diffusion layer till 0.35 mm enhances cell performance, but the more decrease less than 0.35 mm reduces cell performance; (4) As the hydrophobicity of gas diffusion layer increases, cell performance increases; (5) There exists an optimized thickness and porosity combination to get better fuel cell performance; (6) The cell performance of an untreated gas diffusion layer is better than that of a wet-proofed gas diffusion layer with 20% of PTFE; and (7) A prominent gas diffusion layer improves the supply of the reactant gases to the catalyst layer to enhance cell performance. The main results about transport characteristics in flow field are shown as follows: (1) Reducing channel height or width of parallel and serpentine flow channels can improve the cell performance at low operation voltage; (2) The optimal cell performance occurs for a cell with a flow channel cross-sectional area of 0.535–0.535 mm2. A 2:1 channel-to-rib width ratio geometry performs better than the 0.5:1 channel-to-rib width ratio; (3) A quadruple serpentine configuration is a good compromise between the values of the velocities and the ratio of the contact surface area for single, double, and quadruple serpentine flow field channels; (4) A hydrophilic plate in the middle of a flow channel can remove the liquid water droplet on the membrane-electrode assembly surface effectively; (5) The water volume fraction decreases with an increase in the air inlet velocity but increases with an increase in the water inlet velocity; (6) Near the tapered channel exit, a liquid film on the gas diffusion layer surface is formed because of higher gas velocity; on the contrary, in the central part and near the channel inlet slugs are formed; (7) In the channel, external additions such as partial blocks, flow channel indentations, and tapered flow channel with a baffle plate improve the cell performance; (8) Among different cathode channel shapes, the cell performance is the best for the triangle channel, followed by the semicircle channel, the trapezoid channel, and the rectangular channel. The average current density of the spiral channel is 11.9% higher than that of the serpentine channel; (9) Increasing purge frequency raises the cell performance for a PEM fuel cell with a dead-end anode; (10) The average current density of the spiral channel is 11.9% higher than that of the serpentine channel. The power density of BI inspired flow channel is higher than that of parallel channel up to 56% and higher than that of serpentine flow channel up to 26% without considering the liquid water formation and temperature variations; (11) Counterflow generates better performance than coflow for the fuel cell especially at higher current voltages. Serpentine flow field shows better distribution of current density and temperature than straight flow field; (12) The hydrogen depletion length depends on the cell voltage and on the total length scale of the flooded area; and (13) OPCF material can increase the PEM fuel cell performance compared with conventional flow plates. Detailed and accurate transport modeling can effectively offer the improvements in fuel cell design so that designers may achieve optimal flow, heat and water management in the PEM fuel cell.

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