Effect of operating conditions and geometric structure on the gas crossover in PEM fuel cell

Sustainable Energy Technologies and Assessments 37 (2020) 100584

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Original article

Effect of operating conditions and geometric structure on the gas crossover in PEM fuel cell

T

⁎

The-Truc Nguyena,b, , Kazuyoshi Fushinobua a b

Department of Mechanical Engineering and Science, Tokyo Institute of Technology, Japan School of Transport Engineering, Hanoi University of Science and Technology, Viet Nam

A R T I C LE I N FO

A B S T R A C T

Keywords: PEM fuel cell Hydrogen crossover Oxygen crossover Membrane degradation FreeFem++

Gas crossover is an unavoidable phenomenon in proton exchange membrane fuel cells. Gas crossover leads to heat and water generations without conducting any useful works, hence increasing fuel consumption. Particularly, Gas crossover can result in the degradation and formation of pinholes inside the membrane. Therefore, the gas crossover is a critical factor significantly affecting the durability of a fuel cell and quality of the membrane. Herein, we numerically investigate the effects of gas crossover across the membrane in a proton exchange membrane fuel cell. A two-dimensional, two-phase, steady state model of the gas crossover using the partial differential equation solver FreeFem++, was built to investigate the crossover characteristics of hydrogen and oxygen across the membrane versus changes in operating conditions and various geometric structure of components in the proton exchange membrane fuel cell. Results indicated that higher equivalent weight of Nafion® is required to significantly decrease gas crossover phenomenon while the cell performance was reduced negligibly. In addition, as the increase in the stoichiometric flow ratio and channel length, the gas crossover decreased and the cell performance improved.

Introduction Proton exchange membrane (PEM) fuel cell is one of the most promising sustainable energy source for automobile and stationary applications. However, wide commercialization of PEM fuel cell significantly depends on advances in enhancing its reliability and durability as well as reducing its cost. The improvement of the fuel cell durability, hence reduces the replacement frequency of the fuel cell stack, can considerably drop the operation cost of the fuel cell. The degradation of a PEM fuel cell can be attributed to degradations of their components, such as membrane, catalyst layers, gas diffusion layers, and bipolar plates. Therefore, although many researchers have investigated in the durability of fuel cell, determining the degradation rate as well as improving the durability of fuel cell is still complicated. In addition, many other factors, such as gas crossover, manufacturing/ design issues, material characteristics, and operation conditions, can also substantially degrade PEM fuel cell, in which gas crossover is a key factor determining the durability of PEM fuel cell. Hydrogen and oxygen, which diffuse across the membrane to the opposite electrodes, react to each other to form hydrogen peroxide (H2O2). This reaction takes place at the anode, cathode or inside the membrane under platinum nanoparticle catalyst (so-called Pt band) [1]. H2O2 then diffuses ⁎

through the membrane and probably decomposes into peroxide (OH•) and hydroperoxide (HOO•) radicals in the presence of heat or Fe2+/ Fe3+ Fenton’s cations [1]. Finally, the OH% radical attack on the most vulnerable sites in polymer structure, such as carboxylic acid groups of the main chain and C-S bonds of the side chain, which is called “unzipping reaction” [1,2]. This degradation mechanism will result in the membrane thinner and form pinholes in the surface of the membrane. In addition to investigations by experiment, defining numerical models for predicting the permeability of the reactant gases diffusing across the membrane interests and attracts many researchers. Nam et al. [3] and Chippar and Ju [4] introduced models for calculating gas crossover current density, Iicr , which is parameters for evaluating gas crossover through the membrane. In their models, the Iicr was based on gas diffusion coefficient, Dicr , species concentration at catalyst layer and membrane thickness, while gas diffusion coefficients were assumed constant. Schalenbach et al. [5] developed a model to investigate the effects of membrane thickness and operating pressure on gas crossover through the membrane by using a crossover flux density, ϕicr . However, in this model, the permeability of gas in the membrane, εicr , is set as a constant parameter. The amount of gas crossover was also calculated using a crossover equivalent current density, icr [6]. This variable showed the rates of oxygen or hydrogen, transporting from the cathode

Corresponding author at: Department of Mechanical Engineering and Science, Tokyo Institute of Technology, Japan. E-mail addresses: [email protected], [email protected] (T.-T. Nguyen).

https://doi.org/10.1016/j.seta.2019.100584 Received 7 May 2019; Received in revised form 19 September 2019; Accepted 12 November 2019 2213-1388/ © 2019 Elsevier Ltd. All rights reserved.

Sustainable Energy Technologies and Assessments 37 (2020) 100584

T.-T. Nguyen and K. Fushinobu

σsld σm

Nomenclature C D E H j K KP kT M s ug VO2 X λ ψw ρ

Concentration [mol/m3] Diffusion coefficient [m2/s] Activation energy [J/mol] Henry’s constant, [Pa·m3/mol] Volume reaction rate [A/m3] Gas permeation in Nafion® [mol/(m·s·Pa)] Relative permeability [m2] Thermal conductivity [W/(m·K)] Molar mass [kg/mol] Liquid water saturation Gas velocity [m/s] Oxygen molar volume [m3/mol] Mole fraction Water content Association parameter for water Density of gas mixture [kg/m3]

Electronic conductivity [S/m] Ionic conductivity [S/m]

Suffix a c eff eq g i l m N sld w wv

Anode Cathode Effective Equilibrium Gas phase Components H2, O2 and H2O Liquid phase Ionic phase Nafion Solid phase Water Water vapor

Governing transport equations

to the anode (or on opposite direction) through the membrane. Ito et al. [7] reported that permeated gases were dissolved in liquid water, and determined as a function of the solubility (S) and diffusivity (D) of gases in the liquid water. However, the gases permeate not only through the water phase (ion clusters region) in the membrane but also through the amorphous phase of the hydrophobic backbone region of Nafion® [8]. In our previous report [9], we built a single-phase model of PEM fuel cell to investigate the diffusion coefficient of gas crossover through the membrane under the various temperatures and relative humidity. However, this model is suitable at very low current densities, i.e nearly open circuit voltage (OCV) condition, because the simulation process only performed in the membrane electrode assembly (MEA) region with some parameters relating to liquid water, convection transport, catalyst layers’ (CL) thickness were not accounted [9]. In this study, a new numerical simulation model has been developed using the partial differential equation solver FreeFem++ [10]. A steady-state, two-dimensional, two-phase and non-isothermal model of a single PEM fuel cell was considered to determine the gas crossover through the membrane under high current density condition with different operating conditions of temperatures, relative humidity, outlet pressures, stoichiometric flow rate. In addition, the effects of physical properties of the materials and morphological structures, such as membrane and GDL thicknesses, GDL porosity, equivalent weight of the membrane were also investigated.

A two-dimensional, two-phase, non-isothermal model was established in this report, which accounted for the transport of gas species, dissolved and liquid water, heat and charge as described in Table 1. The source terms of the governing equations are also summarized in Table 2. The diffusivity of liquid saturation Ds in GDL and CL can was defined as follows [11]:

Ds = −

K 0Krl dpc μl ds

(19)

where pc is the capillary pressure and is calculated by the empirical correlation:

ε 0.5 pc = pg − pl = σ cosθ ⎛ 0 ⎞ J (s ) ⎝K ⎠

(20)

J(s) was the Leverett function representing that the dimensionless capillary pressure as a function of liquid saturation. For the hydrophilic (θc < 90°) and hydrophobic (θc > 90°) in porous media, the Leverett functions are given by the relations [11]. B.C.08

B.C.02

B.C.09

B.C.04

AGDL

CCL

ACH

Model features and basic assumption

ACL

Numerical simulation PEM

H2, H2O

Two-dimensional computational domain of a typical PEM fuel cell is shown in Fig. 1, which includes flow channels (CHs), gas diffusion layers (GDLs), catalyst layers (CLs) for anode and cathode side, and a proton exchange membrane (PEM). The following assumptions were employed:

CCH

CGDL

O2, H2O O2 Cross.

• The processes were in steady state, • The gas mixtures were assumed to be ideal gas, • Mixtures of hydrogen and water vapor, oxygen and water vapor were feed as fuel and oxidant, respectively, • Contact resistance between different layer was ignored, • Gas crossover through the membrane was assumed to be only con-

Flow direction

Flow direction

H2 Cross.

Ionic charge, H2O (l) Electronic charge

y

Electronic charge

x

centration gradient between the anode and cathode.

B.C.05 B.C.01

B.C.06

B.C.07

B.C.10

B.C.11 B.C.03

Fig. 1. Computational domain of PEM fuel cell. 2

B.C.12

Sustainable Energy Technologies and Assessments 37 (2020) 100584

T.-T. Nguyen and K. Fushinobu

Table 1 Governing equations [11,12]. Governing equation

General form governing equation

Domain

Mass

∇. (ρg ug ) = Sm

Momentum

∇. (ρg ug ug ) = ∇. (μg ∇ug ) − ∇pg + Su

Channels, and CLs Channels, and CLs Channels, and CLs GDLs and

Species

∇. (ug Ci ) = ∇.

Electronic charge Ionic charge

(Dieff

∇Ci ) + Si

0 = ∇. (σsld ∇ϕs ) + Sϕsld

0 = ∇. (σm ∇ϕm) + Sϕm

Energy

∇. (ρcT ug T ) = ∇. (kTeff ∇T ) + ST

Dissolved water

−∇

Liquid water

∇.

(

mM ρM tCL

LM =

nd σ ∇ϕm F m

η ⎛ρl g Krl ug ⎞ ⎝ ηl Krg ⎠

) = ∇. ⎛⎝

ρN EW

DwN ∇λ ⎞ + Sλ ⎠

= ∇. (ρl Ds ∇s ) + Sl

To account for the impact of the CL morphology on oxygen transport in the cathode CL, the reaction rate is modeled by a two-phase agglomerate approach. The volume reaction rate in the cathode CL is described as [13]

Eqs.

GDLs

(1)

GDLs

(2)

GDLs

(25)

jc =

(3)

+

2

CLs

(4)

CLs and Membrane All domains

(5)

CLs and Membrane

(7)

All domains

(8)

pO2

4F δN aratio DON

HOw δw 2 aratio DOw HON 2

+

2

1 ξk agg

HON2

(26)

where δw, aratio, ξ , ϕ , and DOw2 are water film thickness around catalyst pellet, outer surface area, effectiveness factor, Thiele’s modulus of the agglomerate, and oxygen diffusivity in liquid water, respectively, and defined as follows

(6)

(27)

δ w = sεCL/ aratio aratio = 2(1 − εCL)/(rpell +

δN )

(28)

ξ = [3ϕcoth (3ϕ) − 1]/(3ϕ2) Table 2 Source terms for the governing equations [11,12].

ϕ=

rpell

kagg

3

DiN (1 − εCL )

(29)

(30)

Source term

Unit

Domain

Eqs.

Sm = SO2 + S H2 + Swv

[mol/ (m3∙s)] [kg/(m2∙s)]

Channels, GDLs and CLs GDLs and CLs

(9)

[mol/ (m3∙s)] [mol/ (m3∙s)] [mol/ (m3∙s)]

Anode CL

(11)

Cathode CL

(12)

CLs Channels, GDLs

(13)

kagg =

[A/m ]

Anode CL Cathode CL

(14)

where ηc and αc are overpotential and transfer coefficient at the cathode side, respectively, and defined as

[A/m3]

Anode CL Cathode CL

(15)

ηc = Voc − ϕS + ϕM

(33)

[W/m3]

(16)

α c = 0.495 + 2.3 × 10−3 (T − 300)

(34)

[mol/ (m3∙s)]

Channels, GDLs and CLs Anode CL Cathode CL

[mol/ (m3∙s)]

Cathode CL Channels, GDLs

Su = −

μg ug ja 2F

SO2 = −

jc 4F

Swphase − Sλ − Swphase

⎧− ⎨ ⎩ − ja (ACL) =⎧ ⎨ ⎩ + jc (CCL)

Swv =

3

+ ja (ACL) Sϕm = ⎧ ⎨ ⎩ − jc (CCL)

(

ST = |j| |η| −

T ΔS nF

)+

2 im σm

+

is2 σs

+ Sl hlg

N

⎧ ζ ρ (λeq − λ ) ⎪ a EW Sλ = jc ⎨ ρ N eq ⎪ ζ c EW (λ − λ ) + 2F ⎩ N

Sl =

⎧ Svl − ζ ρ (λeq − λ ) c EW ⎨ Svl ⎩

J (s ) =

(10)

ε (1 − s ) X

wv ⎧ kc Δp RT = l ⎨ ke Δpεsρ , w ⎩

ref aagg, c jo, c ⎡ −α F (1 − α c ) F ⎞ ⎤ exp ⎛ c ηc ⎞ − exp ⎛ ηc 4F COref2 ⎢ RT RT ⎠ ⎝ ⎠⎥ ⎝ ⎦ ⎣

(18)

⎛ p H2 ⎞ ja = aagg, a × joref , a ⎜ ref N ⎟ ⎝ CO2 HH2 ⎠

1.42(1 − s ) − 2.12(1 − s )2 ⎤ ⎧ ⎪ cosθc ⎡ , θ < 90° ⎢ ⎥ c +1.26(1 − s )3 ⎣ ⎦ ⎨ ⎪ cosθc [1.42s − 2.12s 2 + 1.26s 3], θc > 90° ⎩

Mw

0.5

−(1 − αa ) F ⎞ α F ηa − exp ⎛ a ηa⎞ ⎤ × ⎡exp ⎛ ⎢ RT RT ⎠ ⎥ ⎝ ⎠ ⎝ ⎣ ⎦

with ηa is overpotential at the anode side (21)

ηa = ϕS − ϕM

(36)

The specific area of agglomerate aagg is accounted as [13]

aagg =

mPt As (1 − εCL ) tCL LPt / C

(37)

where the reaction surface area per unit platinum mass is calculated as follows

(22)

As = (227.79f 3 − 158.57f 2 − 201.53f + 159.5) × 103

In the catalyst layers, the total volume includes three phases: solid catalyst (LPt/C) (Platinum and Carbon), ionomer (LM), and void space (εCL) [13]. The porosity of CL is expressed as

εCL = 1 − LPt / C − LM

(32)

(35)

, Δp = (pXwv − pwsat ) ≥ 0 Δp = (pXwv − pwsat ) < 0

(31)

Because of the faster dissolving rate of hydrogen into electrolyte and water, the effectiveness factor of the hydrogen oxidation reaction (HOR) at anode CL is set to 1.0. Therefore, in order to simplify the kinetics expression at anode CL, the B-V equation is used to express the HOR kinetics as follows [13]

(17)

In considering the phase change, Swphase stands for rate of mass exchanged between the vapor and liquid during phase change, can be calculated via condensation and evaporation process as [11]

Swphase

ψw Mw μ w (VO2 )0.6

By combining Bulter-Volmer (B-V) kinetics with the effectiveness factor of the agglomerate, the reaction rate coefficient of the oxygen reduction reaction (ORR) within agglomerate is calculated by [13]

Kp

S H2 = −

Sϕsld

DOw2 = 7.4 × 10−8T

(38)

with f is the platinum ration

f=

(23)

mPt mPt + mC

(39)

where

LPt / C = LPt + LC =

mPt mC + ρPt tCL ρC tCL

Gas crossover through the membrane (24)

Hydrogen and oxygen were driven across the Nafion® membrane by 3

Sustainable Energy Technologies and Assessments 37 (2020) 100584

T.-T. Nguyen and K. Fushinobu

their concentration gradient between the two opposite sites. The gas crossover is evaluated by the gas diffusion coefficient, which was calculated as [14]:

DiN = K iN HiN

Table 3 Physical parameters and operation conditions [11,13,16,17].

(40)

where K iN is the hydrogen or oxygen permeability coefficients in the membrane that are expressed as [15]:

1 1 ⎤ ⎡ EH K HN2 = (0.29 + 2.2f wv ) × 10−14exp ⎢ 2 ⎜⎛ − ⎟⎞ ⎥ R ⎝ Tref T⎠ ⎦ ⎣

1 1 ⎤ ⎡ EO KON2 = (0.11 + 1.9f wv ) × 10−14exp ⎢ 2 ⎜⎛ − ⎟⎞ ⎥ R ⎝ Tref T⎠ ⎦ ⎣

(41)

λVw Vdry + λVw

Unit

Value

Gas channel length, Ly Channel width Channel depth GDL thickness Membrane thickness Outlet pressure Platinum density, ρPt Carbon density, ρC

[m] [m] [m] [m] [m] [atm] [kg/m3] [kg/m3] [kg/m3]

0.02/0.148 6 × 10−4 1 × 10−3 190 × 10−6 150 × 10−6 1/2/3 2.145 × 104 1800 988

Membrane dry density, ρN Pt specific heat, cp, Pt

[kg/m3] [J/(kg∙K)]

2000 1.3 × 102 1090.0

Liquid water density, ρwl

(42)

The variable, fw, is the volume fraction of water in the membrane and it is calculated as [15]:

fw =

Parameter or constant

(43)

where Vw and Vdry are the molar volumes of water and dry membrane, respectively.

Membrane specific heat, cp, M

[J/(kg∙K)]

Liquid water specific heat, cpl , w

[J/(kg∙K)]

4180.0

Porosity of GDL, ε Water transfer coefficient in CL, ζa = ζc Liquid saturation diffusivity in channel, Ds Condensation rate, kcon Evaporation rate, keva Electronic conductivity of GDL, σs,GDL Electronic conductivity of CL, σs,CL

[−] [1/s] [m2/s] [1/s] [1/(Pa∙s)] [S/m] [S/m] [A/m2]

0.6 1.3 1.0 × 10−3 1.0 5 × 10−5 1000.0 500.0 1 × 10−4

[A/m2] [mol/m3]

10( 56.4

[mol/m3]

3.39

[−] [N/m] [°C] [J/(mol∙K)] [J/(mol∙K)]

0.5 0.0625 120 0.104 −326.36

Reference exchange current density in anode, i 0,refa

Boundary conditions

Reference exchange current density in cathode, i 0,refc Reference

The boundary conditions used in this calculation are detailed in Fig. 1. At the inlets of the anode and cathode, the corresponding equations of the boundary conditions for the chemical species and energy transport, and liquid water are:

X 0w,a =

X 0w,c =

psat RHa pa

psat RHc pc

, X H0 2 = 1 − X 0w,a , T = Ta0, sa = 0

, XO02 = 1 − X 0w,c, T = Tc0, sc = 0

Reference

Anode transfer coefficient, αa Surface tension, σ Contact angle, θ Entropy of hydrogen oxidation, ΔSa Entropy of oxygen reduction, ΔSc

(44)

u0g,a =

2FCH0 2 Ach

, u0g,c =

)

Numerical solution methodology

ξc I 0Areact 4FCO02 Ach

3.507 − 4001 T

values Areact and Ach are the electrochemical reaction area and the crosssectional area of the channel, respectively.

(45)

The gas velocities at the inlets of both the anode and cathode were defined by their respective stoichiometric flow ratios

ξa I 0Areact

ref hydrogen molar concentration, CH 2 ref oxygen molar concentration, CO2

The numerical solution implemented in this work was based on the finite element method (FEM). First, a mesh is generated over the all computational domain in Fig. 1 based on the Delaunay-Voronoi algorithm with inner elements generated with a density is proportional to

(46)

where I0 is the specified reference current density, ξa and ξc are the stoichiometric flow ratio of the anode and cathode, respectively. The

Fig. 2. Flow diagram of the solution procedure: green lines - parameters input; purple lines - model interaction; red lines - model output. 4

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T.-T. Nguyen and K. Fushinobu

membrane, as shown in Fig. 6. This causes the membrane to become more flexible, that in turn increases the diffusion coefficient of gas crossover. As shown in Fig. 7(a), at 80 °C, 80% RH, 1 atm, and Iave = 1.0 A/ cm2, the diffusion coefficient of hydrogen crossover decreased with increasing the stoichiometric ratio (ξ). Because of the accelerated removal rate of liquid water to the outlet channel, when the stoichiometric ratio increased, the accumulation of liquid water in the cathode side decreases (Fig. 8), resulting in the decrease of the water (Fig. 7(b)) and the temperature inside the membrane. Consequently, the hydrogen crossover decreased due to reducing the membrane swelling. In terms of the diffusion coefficient of oxygen crossover, the outlet species concentration is directly proportional to the stoichiometric flow ratio [27]. Therefore, when the stoichiometric flow ratio rose, the species concentration at CL/membrane interface increased, which, finally, increased oxygen crossover rate through the membrane. In addition, the water flowing from the cathode side to the anode side of the membrane by the back diffusion increases because the species concentration gradient the between the cathode and anode sides was enlarged. In consequence, as shown in Fig. 7(a), the amount of oxygen dissolving in the water and diffusing through the membrane to the anode side increased.

the density of elements on the boundary. At each step, which is the distance between each element, the equations for calculating different phenomena are fully combined and computed with the boundary conditions following the schematic as shown in Fig. 2. Initial values were given to each parameter at the first attempt, which, then, were followed by iterative processes until the calculation error is smaller than 10−4. The list of the parameters and constants used in this work is depicted in Table 3. Results and discussion Model validation The two-phase algorithm implemented on FreeFem++ was validated by the polarization curve of the numerical and experimental results at an inlet gas flow rate of 0.3 NL/min, cell temperature of 80 °C, relative humidity (RH) of 80%, ambient outlet pressure, and the current density in the range from 0 to 0.5 A/cm2. Fig. 3 shows that the numerical results of single-phase model [9] and two-phase model were comparable with the experimental data [9]. It is obvious that the trend of numerical results was similar to that of experimental results. Although, the experimental data agreed better with two-phase results than single-phase results at high current density because of the effect of liquid water in PEM fuel cell, however, a little gap between the experimental results and two-phase results still existed. This distinction can result from the assumptions of the two-phase model as well as the neglecting of the interfacial contact resistance.

Effect of membrane parameter on gas crossover through the membrane As a membrane is thicker, the membrane transport resistance increases and proton conductivity of the membrane decreases [28]. As shown in Fig. 9(b), because the number of protons taken part in the ORR at the cathode CL reduced, the performance of cell and generated water reduced, which decreased the water absorption into membrane. Therefore, size of ionic pores in the Nafion® was smaller, which prevents the permeating of gas through the membrane. Consequently, the diffusion coefficient of gas crossover through the membrane decreases with increasing membrane thickness as shown in Fig. 9(a) under the operating condition at 80 °C, 80% RH, 1 atm, and Iave = 1.0 A/cm2. The equivalent weight (EW) of Nafion®, determined as the weight of dry Nafion® in grams (g) per mole sulfonic acid (SO3) groups, is accounted by the mean distance between the side chains along the hydrophobic Teflon backbone [20]. Therefore, ion exchange capacity as well as water absorption capacity of the membrane decrease as increasing EW [29]. As a consequence, the cell performance and water content decreased with increasing EW (Fig. 10(b)), and the diffusion coefficient of gas crossover through the membrane (Fig. 10(a)), decreased with increasing EW at operating condition 80 °C, 80% RH,

Effect of operating conditions on gas crossover through the membrane The crossover mechanism of hydrogen and oxygen through the membrane have been investigated by several researchers [8,18,19]. The gases permeating through the membrane involves ionic clusters as well as amorphous part of the hydrophobic backbone regions of Nafion®. Due to the strong hydrophilic nature of the terminal SO3 group, the Nafion® membrane considerably swelled as exposed to humid environments [20]. Water absorbed by the dry membrane to solvate the acid groups and form inverted micelles in the polymer matrix. With more water absorbed, these clusters grew and formed interconnections. The ionic pores were 1.5 nm diamater spheres in the dry membrane, expanded to bigger pores of ~4 nm diameter, and connected with each other by the ~1 nm channels in the fully hydrated membrane [20,21], where gas permeation could occur. In addition, according to Michaels and Bixler [22], the volumetric coefficient of thermal expansion for the amorphous phase was greater than that for the crystalline phase in the temperature range from 5 to 55 °C, which led to a decrease in the tensile strength of Nafion® when the temperature increases [23]. The above analyses show that increasing the relative humidity and temperature will increase the size of the ion clusters and the amorphous regions, respectively, hence leading to the higher diffusion coefficient of gas crossover through the membrane as the results shown in Figs. 4 and 5 at high current density (Iave = 0.3 A/cm2) with channel length Ly = 2 cm. However, according to Michaels and Bixler [22], and Huang et al. [24] reported that the volume fraction of crystalline region in Nafion® increased with increasing the temperature. Consequently, the diffusion coefficient of gas crossover through the Nafion® was reduced at higher temperature since the gas do not permeate through the crystalline region. The results in Figs. 4 and 5 also show that the diffusion coefficient of gas crossover proportionally increased with operating pressure. It can be explained that the reactant gas concentration at CL increases with the increase of the species partial pressure, which results from the increase of the inlet pressure [25,26]. Consequently, the hydrogen molar fraction at the anode CL for the HOR and oxygen molar fraction at the cathode CL for the ORR also increased. Therefore, water will be generated more at higher pressure, leading to more water content in the

Fig. 3. Two-phase model validation with experimental data. 5

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Fig. 4. Effect of (a) temperature and (b) relative humidity on the diffusion coefficient of hydrogen crossover.

Fig. 5. Effect of (a) temperature and (b) relative humidity on the diffusion coefficient of oxygen crossover.

Fig. 6. Membrane water content versus pressure with different operating conditions of (a) temperature and (b) relative humidity.

Fig. 7. Effect of stoichiometric flow ratio on (a) the gas crossover diffusion coefficient and (b) the water content and cell performance at various channel length.

1 atm, and 1.0 A/cm2.

the concentration of reactant gas at CL/membrane interface is decreased. In addition, the liquid water saturation increases significantly (Fig. 11) as increasing the GDL thickness since the liquid water accumulated in the cathode side, preventing oxygen diffusion to the CL. Consequently, the diffusion coefficient of oxygen crossover decreases when the GDL thickness increased (Fig. 12(a)).

Effect of GDL parameter on gas crossover through the membrane In a thicker GDL, the reactant gas is supplied at a lower velocity because the GDL transport resistance increases [30]. Which resulting in 6

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Fig. 8. Liquid water saturation in the cathode channel, GDL and CL of (a) Ly = 2 cm and (b) Ly = 14.8 cm at various cathode stoichiometric flow ratios.

Fig. 9. Effect of membrane thickness on (a) the gas crossover diffusion coefficient and (b) the water content and cell performance at various channel length.

Fig. 10. Effect of equivalent weight on (a) the gas crossover diffusion coefficient and (b) the water content and cell performance at various channel length.

Fig. 11. Liquid water saturation in the cathode channel, GDL and CL of (a) Ly = 2 cm and (b) Ly = 14.8 cm at various GDL thickness.

7

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Fig. 12. Effect of GDL thickness on (a) the gas crossover diffusion coefficient and (b) the water content and cell performance at various channel length.

Fig. 13. Effect of GDL porosity on (a) the gas crossover diffusion coefficient and (b) the water content and cell performance at various channel length.

fuel cell with the various operating conditions, material physical properties and morphological structure of PEM fuel cell’s components. The results at high current density show that the diffusion coefficient of gas crossover increased with increasing the operating temperature or relative humidity, which results from the increasing ion clusters size and amorphous volume fraction inside the membrane. Increasing the operating pressure improved considerably the cell performance, however the membrane will be degraded faster due to an increase in gas crossover through the membrane. The results also indicated that increasing the stoichiometric flow ratio and channel length improved slightly the cell performance and moderately reduced the gas crossover diffusion coefficient because the accelerated removal rate of liquid water out of the outlet channel. In a thicker membrane, the diffusion coefficient of gas crossover significantly decreased, however the cell performance will be decreased dramatically due to proton transfers hardly through the membrane. As a GDL is thicker, the oxygen crossover diffusion coefficient considerably decreased because the liquid water accumulated in the cathode side and prevented oxygen diffusion to the CL. Similarly, the diffusion coefficient of gas crossover minimally decreased as increasing GDL porosity due to the produced water easily passes out of the PEM fuel cell. Furthermore, the results show that the gas crossover phenomenon dramatically decreases with higher equivalent weight of Nafion® while the cell performance was reduced negligibly.

For hydrogen crossover, due to the increase of membrane water content with increasing GDL thickness (Fig. 12(b)), the diffusion coefficient of hydrogen crossover increases as illustrated in Fig. 12(a). The effect of GDL thickness on the gas crossover investigated at 80 °C, 80% RH, 1 atm, and Iave = 1.0 A/cm2 condition. The GDL with the highest porosity value of 0.8 had a low mass transfer resistance of reactants to the reaction sites because of the big pores in the GDL. This situation resulted in an increased reactant concentration due to providing adequate space for the reactants to diffuse into the reaction sites. In addition, at higher porosity, hydrogen and oxygen gases are more uniformly distributed and easier to diffuse into the catalyst layer. Therefore, the performance of PEM fuel cell is improved, and more water is generated, hence increasing dissolved water in the membrane. However, a high GDL porosity value facilitates the water management because the produced water easily passes out of the PEM fuel cell, which, in turn, decreases the dissolved water in the membrane. In this work, the water production rate was lower than the removal rate, thus, as GDL porosity increased, the total dissolved water in the membrane caused by two above phenomena is reduced, as shown in Fig. 13(b). Consequently, the diffusion coefficient of gas crossover decreased. However, as shown in Fig. 13(a), change in the gas crossover diffusion coefficients are negligible at 80 °C, 80% RH, 1 atm, and Iave = 1.0 A/cm2 condition.

Conclusions Declaration of Competing Interest A mathematical model, using an open source software FreeFem++ bridging micro-scale heterogeneous surface electrochemical reaction with macro-scale two-phase and non-isothermal transport, has been successfully developed and solved in two-dimensions for a single PEM

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 8

Sustainable Energy Technologies and Assessments 37 (2020) 100584

T.-T. Nguyen and K. Fushinobu

References

[16] Cao TF, et al. Numerical investigation of the coupled water and thermal management in PEM fuel cell. Appl Energy 2013;112:1115–25. [17] Lampinen MJ, Fomino M. Analysis of free energy and entropy changes for half-cell reactions. J Electrochem Soc 1993;140–12:3537–46. [18] Schalenbach M, et al. Gas permeation through Nafion. Part 1: measurements. J Physical Chemistry 2015;119:25145–55. [19] Weber AZ, Newman J. Transport in polymer-electrolyte membranes: I. Physical model. Electrochem Soc 2003;150–7:A1008–15. [20] Dorenbos G, Suga Y. Simulation of equivalent weight dependence of Nafion morphologies and predicted trends regarding water diffusion. J Membr Sci 2009;330:5–20. [21] Mauritz KA, Moore RB. State of understanding of Nafion. Chem Rev 2004;104:4535–85. [22] Michaels AS, Bixler HJ. Solubility of gases in polyethylene. J Polym Sci L 1961:393–412. [23] Yoshitake M, et al. Studies of perfluorinated ion exchange membranes for polymer electrolyte fuel cells. Denki Kagaku 1996;64–6:727–36. [24] Huang C, et al. XRD and XPS analysis of the degradation of the polymer electrolyte in H2–O2 fuel cell. Chem Phys Lett 2003;371:80–5. [25] Shan J, et al. Local resolved investigation of hydrogen crossover in polymer electrolyte fuel cell. Energy 2017;128:357–65. [26] Baik KD, et al. Effects of operating parameters on hydrogen crossover rate through Nafion membranes in polymer electrolyte membrane fuel cells. Renew Energy 2013;57:234–9. [27] Kulikovsky AA. The effect of stoichiometric ratio on the performance of a polymer electrolyte fuel cell. Electrochim Acta 2004;49:617–25. [28] Kientiz B, et al. Interfacial water transport effects in proton exchange membranes. J Fuel Cell Sci Technol 2011;8:1–7. [29] Basura VI, et al. Effect of equivalent weight on electrochemical mass transport properties of oxygen in proton exchange membranes based on sulfonated ß, ß-trifluorostyrene (BAM®) and sulfonated styrene-(ethylene-butylene)-styrene triblock (DAIS-analytical) copolymers. J Electroanal Chem 2001;501:77–88. [30] Lin G, Nguyen TV. Effect of thickness and hydrophobic polymer content of the gas diffusion layer on electrode flooding level in a PEMFC. Electrochem Soc 2005;152–10:A1942–8.

[1] Shah AA, et al. Modeling and simulation of the degradation of perfluorinated ionexchange membranes in PEM fuel cells. J Electrochem Soc 2009;156–4:B465–84. [2] Zaton M, et al. Current understanding of chemical degradation mechanisms of perfluorosulfonic acid membranes and their mitigation strategies: a review. Sustain Energy Fuels 2017;1:409–38. [3] Nam J, et al. Numerical analysis of gas crossover effects in polymer electrolyte fuel cells (PEFCs). Appl Energy 2010;87:3699–709. [4] Chippar P, Ju H. Numerical modeling and investigation of gas crossover effects in high temperature proton exchange membrane (PEM) fuel cells. Int J Hydrogen Energy 2013;38:7704–14. [5] Schalenbach M, et al. Pressurized PEM water electrolysis: efficiency and gas crossover. Int J Hydrogen Energy 2013;38:14921–33. [6] Seddiq M, et al. Numerical analysis of gas crossover through the membrane in a proton exchange membrane fuel cell. J Power Sour 2006;161:371–9. [7] Ito H, et al. Properties of Nafion membranes under PEM water electrolysis conditions. Int J Hydrogen Energy 2011;36:10527–40. [8] Ogumi Z, et al. Gas permeation in SPE method - II. Oxygen and hydrogen permeation through Nafion. J Electrochem Soc 1985;132–11:2601–5. [9] Nguyen TT, et al. Numerical and experimental investigation on the reactant gas crossover in a PEM fuel cell. Int J Heat Mass Transf 2018;127:447–56. [10] Hecht, F., FreeFem++, v.3.41, 2015. [Online]. Available: http://www.freefem. org/ff++/. [11] Ye Q, Nguyen TV. Three-dimensional simulation of liquid water distribution in a PEMFC with experimentally measured capillary functions. Electrochem Soc 2007;154–12:B1242–51. [12] Jung C-Y, et al. Investigations of the temperature distribution in proton exchange membrane fuel cells. Appl Energy 2012;93:733–41. [13] Xing L, et al. A two-phase flow and non-isothermal agglomerate model for a proton exchange membrane (PEM) fuel cell. Energy 2014;73:618–34. [14] Kocha SS, et al. Characterization of gas crossover and its implications in PEM fuel cells. AIChE J 2006;52–5:1916–25. [15] Tsai SW, Chen YS. A mathermatical model to study the energy efficiency of a proton exchange membrane fuel cell with a dead-ended anode. Appl Energy 2017;188:151–9.

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