applications in energy and combustion science

Applications in Energy and Combustion Science 17 (2024) 100239
Available online 30 December 2023
2666-352X/© 2024 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-
nc-nd/4.0/).
Enhancing water hydration in air-cooled proton exchange membrane fuel
cell using a staggered tapered slotted flow field
Jianfei Zhang, Wei Li, Guobin Zhang, Hongwei Bai, Zhiguo Qu *
MOE Key Laboratory of Thermo-Fluid Science and Engineering, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China
A R T I C L E I N F O
Keywords:
Air-cooled proton exchange membrane fuel cell
Flow field
UAVS
Membrane hydration
3D modeling
A B S T R A C T
Air-cooled proton exchange membrane fuel cell (AC-PEMFC) is widely considered as a promising power source
for unmanned aerial vehicles (UAVs) due to its merits such as high energy density, short refueling time, and
simple auxiliary system. However, the performance of AC-PEMFC is not satisfactory due to the poor membrane
hydration caused by the large air supply for heat dissipation demand. This study proposes a staggered tapered
slotted flow field (STSF) configuration to address this issue, which has higher contact area between the airflow
and the bipolar plate by arranging tapered and slotted sections in the channels along the airflow direction,
aiming to enhance the cooling effect and improve the membrane water hydration. Utilizing a three-dimensional
(3D) multiphase non-isothermal model verified against experimental data, it was found that the STSF configu
ration reduces the internal temperature of the cell by about 14.2–28.3 K and increases the water content in the
membrane by about 35.1–85.7 % compared with traditional straight channels. In addition, the STSF configu
ration can enhance mass transfer by inducing cross-flow, reducing concentration losses, which takes more effect
for UAVs working at high altitude. Moreover, the slotted sections reduced the volume and weight of the bipolar
plates, contributing to an additional power density improvement. Finally, the pressure drop within the flow
channels and net power was compared. Due to the increased contact area between the cooling airflow and the
bipolar plates, the STSF configuration inevitably results in a higher pressure drop within the channels, but the net
power of PEMFC with STSF still increased under severe conditions by 0.080 W.
Introduction
The excessive consumption of fossil fuels has led to the continuous
deterioration of the global environment. Many countries are tran
sitioning towards renewable and clean energy sources to address this
problem [1,2]. Hydrogen-fueled proton exchange membrane fuel cell
(PEMFC) is a prominent candidate due to its high energy density and
zero emissions [3,4]. PEMFC is widely used in automobiles, power
generation, unmanned aerial vehicles (UAVs) applications, etc. Specif
ically, for UAVs, considering the requirements of long endurance and
quick refueling characteristics, PEMFC has been considered a competi
tive alternative power source to Li-ion batteries, and its energy density is
usually three to five times higher than Li-ion batteries [5,6]. Addition
ally, air-cooled proton exchange membrane fuel cell (AC-PEMFC) can
improve endurance by reducing self-weight and parasitic power. This
makes it a more promising power source for small-scale UAVs applica
tions [7,8].
The internal heat sources within the PEMFC consist of the heat
generated from electrochemical reactions and Ohmic heating. As the
current density increases, the electrochemical reactions accelerate,
increasing heat generation. If this heat is not promptly dissipated, it may
lead to non-uniform temperature distribution within the PEMFC [9].
Additionally, it may give rise to localized hotspots, potentially causing
irreversible damage to the components [10,11]. Furthermore, elevated
internal temperatures can accelerate water evaporation, reducing
membrane hydration and increasing proton conduction losses [12,13].
Therefore, it becomes imperative to promptly implement measures for
dissipating excess heat generated within the PEMFC under high current
density conditions. In the case of AC-PEMFC that employ air as the
cooling medium, it is worth noting that the lower thermal conductivity
and specific heat capacity of air compared to liquid water necessitate a
Abbreviations: AC-PEMFC, Air Cooled Proton Exchange Membrane Fuel Cell; BP, Bipolar Plate; CCM, Catalyst Coated Membrane; CH, Channel; CL, Catalyst Layer;
GDL, Gas Diffusion Layer; PEM, Proton Exchange Membrane; PEMFC, Proton Exchange Membrane Fuel Cell; STSF, Staggered Tapered Slotted Flow Field; UAVs,
Unmanned Aerial Vehicles.
* Corresponding author.
E-mail address: zgqu@mail.xjtu.edu.cn (Z. Qu).
Contents lists available at ScienceDirect
Applications in Energy and Combustion Science
journal homepage: www.sciencedirect.com/journal/applications-in-energy-and-combustion-science
https://doi.org/10.1016/j.jaecs.2023.100239
Received 10 June 2023; Received in revised form 11 October 2023; Accepted 26 December 2023

2
higher airflow rate to maintain the AC-PEMFC temperature within an
acceptable range [3]. Generally, a cathode stoichiometric ratio of up to
50 or higher is required to effectively cool the PEMFC [14]. On the
contrary, if airflow rates are too high, which implies a higher water
evaporation rate, can potentially lead to membrane dehydration again
[15,16]. Although pre-humidifying the air before it enters the cathode
side can mitigate some of these issues, practical applications of
AC-PEMFC, such as those in UAVs, often find using a humidifier
impractical. The literature review reveals that achieving an ideal bal
ance between effective heat dissipation and optimal water retention in
AC-PEMFC is challenging. The conflict between heat dissipation and
water retention may be resolved by achieving superior cooling perfor
mance at lower airflow rates. Moreover, it is well known that the specific
power of air-cooled systems is lower than that of water-cooled systems.
Therefore, enhancing power density by reducing the system’s mass is
essential to broaden the scope of AC-PEMFC applications [17].
The bipolar plate (BP) is a fundamental component of a PEMFC,
accounting for approximately 60–80 % of the fuel cell’s weight and
30–50 % of the stack manufacturing cost [18,19]. The cathode flow field
located in the BP needs to provide the cooling medium and the oxygen
simultaneously, which significantly impacts oxidant supply, water
removal, and operating temperature control [20,21]. Optimizing the
cathode BP and flow field to some extent could address the contradiction
between thermal management and membrane dehydration [22–24]. Yin
et al. [25] designed a novel stack with additional air-cooling edge
channels in both bipolar plates to improve performance and reduce
weight. The results show that additional cooling channels can improve
the performance of the fuel cell stack by improving membrane hydration
and temperature distribution uniformity. Lee et al. [26] proposed an
innovative cathode flow field configuration separating the reactant and
cooling air. They supplied more air to the cooling channels to improve
water-retaining capability when excess dry air is supplied. Simulation
results demonstrated that the new cathode flow field configuration
performed better than the cell with a straight flow channel configura
tion. Peng et al. [27] proposed novel cathode flow field configurations
by inserting porous media into the gas channel to alter the flow rate
between reactant air and cooling air. The design was found to improve
the performance of AC-PEMFC and alleviate the performance reduction
with the increase in altitude. Many researchers have also proposed
numerous novel designs to enhance the performance of AC-PEMFC
[28–30].
Under UAV operation conditions, flight altitude causes ambient
temperature, pressure, relative humidity, and oxygen concentration
variations [31–33]. These parameters significantly impact the
Nomenclature
C Molar concentration (mol m− 3
)
CP Heat capacity (J kg− 1
K− 1
)
D Diffusion coefficient (m2
s− 1
)
E Voltage(V) or Activation energy (J mol− 1
)
F The Faraday’s constant (96,487 C mol− 1
)
I Current density (A m− 2
)
M Molar mass (kg mol− 1
)
p Pressure (Pa)
pc Capillary pressure (Pa)
R Universal gas constant (J mol− 1
K− 1
)
Rion Resistance of the ionomer membrane
S Source term (kg m− 3
s− 1
or mol m− 3
s− 1
)
Sp Source term of membrane water caused by pressure
difference (mol m− 3
s− 1
)
T Temperature (K)
Yi Gas species mass fraction
a Water activity
h Latent heat of water (J mol− 1
)
iad,cd Reference exchange current density per unit active area
(A m− 2
)
iref
Reference exchange current density at reference
temperature (A m− 2
)
j Volumetric reaction rate (A m− 3
)
k Relative permeability
s Water saturation
ΔS Entropy change (J mol− 1
K− 1
)
u Velocity vector (m s− 1
)
K Intrinsic permeability (m2
) or thermal conductivity
(W m− 1
K− 1
)
Greek letters
α Transfer coefficient
γ Phase change coefficient (s− 1
) or concentration index
δ Thickness (m)
ε Porosity
ζ Specific active area (m− 1
)
η Overpotential (V)
θ Contact angle (◦
)
λ Membrane water content
μ Dynamic viscosity (kg m− 1
s− 1
)
ξ Stoichiometric ratio
ρ Density (kg m− 3
)
σele Electric conductivity (S m− 1
)
σion Ionic conductivity (S m− 1
)
τ Surface tension coefficient (N m− 1
)
ϕele Electric potential (V)
ϕion Ionic potential (V)
Subscripts and superscripts
0 Standard state or base condition
H2 Hydrogen
H2O Water
O2 Oxygen
act Activation state
ad Anode
cd Cathode
d Membrane water
d − l Membrane water to liquid
eff Effective
ele Electrical
eq Equivalent state
g Gas phase
i Gas species
in Inlet
ion Ionic
l Liquid phase
m Mass
mem Membrane
mw Membrane water
ref Reference state
rev Reversible
sat Saturation state
u Momentum
v − l Vapor to liquid phase
J. Zhang et al.

3
performance of PEMFC [34,35]. Jung et al. [36] investigated the effects
of humidity and temperature on PEMFC and found that higher humidity
is essential for PEMFC to prevent the membrane from drying out at high
ambient temperatures. The work by Al-Zeyoudi et al. [37] also arrived at
similar conclusions. So, the performance of AC-PEMFC will inevitably
fluctuate with altitude changes as AC-PEMFC’s cathode flow comes from
the atmosphere. At high altitudes, AC-PEMFC is affected by two main
factors: inefficient cooling efficiency and insufficient oxygen supply due
to the reduction in atmospheric pressure. The inefficient cooling leads to
a decrease in water content. The inadequate oxygen supply results in
high mass transportation losses, often overlooked in AC-PEMFC. How
ever, in extreme altitude conditions, these mass transportation losses
can become crucial and significantly contribute to the overpotential.
Hordé et al. [38] investigated the effect of altitude on PEMFC perfor
mance through numerical and experimental analysis. Their results
showed a sharp drop in performance with increasing altitude due to
water flooding in the channel, where the air compressor efficiency drops
as the ambient pressure decreases. They also suggested increasing the
cathode stoichiometry factor to alleviate the performance drop. Espa
sandín et al. [39] studied the effect of atmospheric conditions on PEMFC
and found that the impact of flight altitude on PEMFC is more significant
than that of direct methanol fuel cells. Some researchers proposed so
lutions to this problem. Renau et al. [40] successfully controlled the
stack temperature at 160 ◦
C by applying high-temperature PEMFC
technology with phosphoric acid doped polybenzimidazole membrane
for high-altitude UAVs missions through air cooling. Peng et al. [27]
proposed a flow field configuration that can improve the performance of
AC-PEMFC and alleviate the performance degradation problem with
increasing altitude by adding porous media into the cathode gas
channel. To address the issue of membrane dehydration in PEMFC,
Werner et al. [41] suggested reducing the fuel cell stack temperature and
cathode stoichiometry ratio when operating at low working pressures. In
addition to the increased challenge of balancing heat dissipation and
water retention at high altitudes, the issue of inadequate oxygen supply
has also emerged as a significant concern. Currently, there is limited
research addressing these two critical issues effectively.
Resolving the conflict between cooling and water management poses
a challenge for AC-PEMFC. Additionally, considering the application
scope of AC-PEMFC, reducing the weight of the fuel cell to enhance its
power density is highly necessary. Although many new flow field de
signs have been proposed, few have been specifically designed for
applying AC-PEMFC in the field of UAVs mentioned above. This study
proposes a cathode staggered tapered slotted flow field (STSF) config
uration suitable for AC-PEMFC, as depicted in Fig. 1. The structure en
hances heat dissipation without increasing the cathode airflow rate by
improving the contact area between the cooling airflow and the bipolar
plate by arranging tapered and slotted sections. Specifically, the stag
gered placement of the tapered sections along the flow direction gen
erates cross-flow between adjacent channels, thereby improving mass
transfer. The slotted sections ultimately increase power density by
reducing the weight of the bipolar plate.
Model development
Computational domain
The computational domain and related size of the fuel cell used in
this study are shown in Fig. 2, including the BPs, flow channels (CHs),
Fig. 1. Schematic of the proposed STSF configuration to improve the cooling capacity by increasing the contact area between airflow and BP.
Fig. 2. Schematic of the computational domain.
J. Zhang et al.

4
gas diffusion layers (GDLs), catalyst layers (CLs), and proton exchange
membrane (PEM). The catalyst coated membrane (CCM) comprises PEM
with anode and cathode CLs. To reduce computational burden while
ensuring the effectiveness of the new configuration, the number of
channels is chosen to three, with six uniform tapered and slotted sections
arranged along the direction of airflow in each channel. It is worth
noting that the slotted sections coincide with the tapered on both sides of
the flow channels. To better analyze the effect of the new configuration
on the performance of AC-PEMFC, as a comparison, this study also
calculated the performance of an AC-PEMFC with a traditional straight
flow field configuration using the identical geometric size. Specific
geometric parameters can be found in Table 1.
Governing equations
The three-dimensional (3D) multiphase non-isothermal model of AC-
PEMFC consists of a series of governing equations, as shown in Table 2
[23,42]. The model adopts a two-fluid model to describe the two-phase
flow of gas and liquid, where the gas phase and liquid phase water
equations are separated, and the condensation/evaporation terms are
included in the source terms. The gas flow is described by mass and
momentum equations, and a species equation describes the gas species
transport. The liquid flow in porous structures such as GDLs and CLs is
mainly driven by capillary pressure, which is described by the liquid
pressure equation. The electron and proton potential equations describe
the transport of electrons and protons, respectively. The heat generation
of the fuel cell is considered a source term in the energy equation. The
source terms and their computational domains are shown in Table 3 [26,
43], and the relevant physical properties are given in Table 4 [27,43].
The model and material parameters are presented in Table 5 [43,44].
The following equations calculated the electrochemical reaction
rate:
jad = ζadiad
(
CH2
Cref
H2
)γad [
exp
(
Fαad
RT
ηad
)
− exp
(
−
Fαcd
RT
ηcd
)]
(1)
jcd = ζcdicd
(
CO2
Cref
O2
)γcd [
− exp
(
Fαad
RT
ηcd
)
+ exp
(
−
Fαcd
RT
ηcd
)]
(2)
where ζ (m− 1
) is the specific activity area, Cref
(mol m− 3
) is the reference
concentration, γ represents the concentration index, F (96,487C mol− 1
)
represents the Faraday’s constant and E (J mol− 1
K− 1
) means the uni
versal gas constant, α is the transfer coefficient, iad,cd (A m− 2
) is the
reference exchange current density per unit active surface area, which is
calculated by:
ix = ix(T) = iref
x exp
[
−
Ex
R
(
1
T
−
1
Tref
x
)]
, x = ad, cd (3)
Table 1
Geometric parameters.
Parameters Values
MEA area (mm2
) 490
Channel length (mm) 70
Channel depth (mm) Anode: 0.5, Cathode: 1.0
Channel width (mm) Anode: 1.0, Cathode: 1.0
Rib width(mm) 1.0
BP height (mm) 1.25
Thickness (μm) (PEM, ACL, CCL, GSL) 13, 7, 10, 200
Number of tapered and slotted sections 6
Tapered section length (mm) 5
Contraction angle in the tapered section (
˚
) 45
Contraction distance in the tapered section (mm) 0.25
Slotted section length (mm) 4
Table 2
Governing equations [23,42].
Description Equations Components
Mass (gas phase) ∇⋅(ερgug) = Sm CH, GDL, CL
Momentum (gas
phase)
∇⋅(ερgugug) = − ε∇pg + ∇⋅(εμug) + Su CH, GDL, CL
Gas species ∇⋅(ερgugYi) = ∇⋅(ρgD
eff
i ∇Yi) + Si
CH, GDL, CL
Liquid water
0 = ∇⋅
(
ρl
Kkl
μl
∇pl
)
+ Sl
GDL, CL
Membrane water
content
∇⋅
(
− σ∇ϕion
nd
F
MH2O
)
= ∇⋅(MH2ODd∇λ) +
Smw
MEM, CL
Electric potential ∇⋅(σele∇ϕele) + Sele = 0 BP, GDL, CL
Ionic potential ∇⋅(σion∇ϕion) + Sion = 0 MEM, CL
Energy ∇⋅(εsρlCp,lulT + ε(1 − s)ρgCp,gugT) =
∇⋅(Keff
∇T) + ST
All
components
Table 3
Source terms of the governing equations [26,43].
Source terms Expressions
Hydrogen (kg m− 3
s− 1
)
SH2
= −
MH2
2F
jad ACL
Oxygen (kg m− 3
s− 1
)
SO2 = −
MO2
4F
jcd CCL
Water vapor (kg m− 3
s− 1
)
SH2O =
⎧
⎨
⎩
− Sv− l GDL
− SV− L + Sd− v ACL
− Sv− l + Sd− v CCL
Liquid water (kg m− 3
s− 1
) Sl = Sv− l CH,GDL,CL
Gas mixture (kg m− 3
s− 1
)
Sg =
⎧
⎨
⎩
− Sv− l + Sd− v − jadMH2 /2F ACL
− Sv− l + Sd− v − jcdMO2 /4F CCL
− Sv− l CH, GDL
Water evaporation and
condensation (kg m− 3
s− 1
)
Sv− l =
{
γv− lε(1 − s)(CH2O − Csat)MH2O CH2 O > Csat
γl− vεs(CH2O − Csat)MH2O CH2 O < Csat
Momentum (N m− 3
) Su = −
μg
kg
ug GDL,ACL,CCL
Electric and ionic potential
(A m− 3
)
Sele =
{
− jad ACL
jcd CCL
Sion = {
jad ACL
− jcd CCL
Membrane water content
(mol m− 3
s− 1
)
Smw =
{
− Sd− v/MH2O − Sp ACL
− Sd− v/MH2 O + MH2 Ojcd/2F + Sp CCL
Membrane water absorption
and release (kg m− 3
s− 1
)
Sd− v = γd− vρmem/EW(λ − λeq)MH2O
Membrane water caused by
pressure (mol m− 3
s− 1
)
Sp =
ρlKmem(plad − plcd)
μlMH2 OδmemδCL
Energy (W m− 3
)
ST =
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎩
‖ ∇ϕele||2
σeff
e BP
‖ ∇ϕele||2
σeff
e + Sv− lh GDL
jad|ηad
act|+ ‖ ∇ϕele||2
σeff
e + ‖ ∇ϕion||2
σeff
ion
+jad
ΔSadT
2F
+ (Sv− l − Sd− v)h
ACL
jcd|ηcd
act|+ ‖ ∇ϕele||2
σeff
e + ‖ ∇ϕion||2
σeff
ion
+jcd
ΔSadT
4F
+ (Sv− l − Sd− v)h
CCL
‖ ∇ϕion||2
σeff
ion MEM
Sv− lh CH
J. Zhang et al.

5
where iref
(A m− 2
) represents the reference exchange current density at
the reference temperature Tref
(K), while E (J mol− 1
) denoting the acti
vation energy. The equation for calculating the overpotential η (V) is:
ηad = ϕele − ϕion (4)
ηcd = ϕele − ϕion − Erev (5)
where ϕele(V) and ϕion(V) mean the electric and proton potential. The
open-circuit voltage Erev (V) is calculated using the Nernst equation
corrected by the temperature effect.
Boundary conditions
The inlet boundary condition is set as a mass flow rate boundary
condition while specifying the mass fraction of the relevant gas species
[43]:
mad =
ρad
g IξadAact
2FCH2,in
(6)
mcd =
ρcd
g IξcdAact
4FCO2,in
(7)
CH2,in =
pad
g,in − RHadpsat
RT
(8)
CO2,in =
0.21
(
pcd
g,in − RHcdpsat
)
RT
(9)
Cad,cd
H2O =
RHad,cdpsat
RT
= RHad,cdCsat
H2O (10)
Yi =
MiCi
∑
MiCi
(11)
The outlet is set as a pressure outlet boundary condition, and the
walls in contact with the environment are set as adiabatic walls. The
model uses a constant current density condition, with the anode end
voltage set to 0 V, and the cathode end set to the corresponding current
density value.
Numerical implementation
The 3D multiphase model was implemented using the FUEL CELL
MODULE in the commercial CFD software ANSYS FLUENT. The fuel cell
simulations were performed on a small workstation equipped with 12
processors (12th Gen Intel(R) Core (TM) i7–12,700 @2.10 GHz) and
32GB DDR RAM. The geometry model meshed using ICEM, and struc
tured hexahedral meshes were employed for all mesh types. To perform
mesh independence analysis, six different meshing schemes with grid
Table 4
Physical and transport properties [27,43].
Parameters Equations
Gas diffusivities (m2
s− 1
)
D
eff
i = ε1.5
(1 − s)2.5
D0
i
(101325
p
)
( T
300
)1.5
Diffusion coefficient of membrane water (m2
s− 1
)
Dd =
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎩
3.1 × 10− 7
λ(e0.28λ
− 1)e
− 2346
T
ρPEM
EW
0 < λ < 3
4.17 × 10− 8
λ(161e− λ
+ 1)e
− 2346
T
ρPEM
EW
3 ≤ λ < 17
4.1 × 10− 10
(
λ
25
)0.15(
1 + tanh
(
λ − 2.5
1.4
))
ρPEM
EW
λ ≥ 17
Equilibrium membrane water content
λeq =
{
0.043 + 17.81a − 39.85a2
+ 36.0a3
0 ≤ a ≤ 1
14.0 + 1.4(a − 1.0) 1 < a ≤ 3
Water activity in CL a = CH2ORT/psat
Water saturation pressure (Pa) log10
( psat
101325
)
= − 2.1794 + 0.02953(T − 273.15) − 9.1837 × 10− 5
(T − 273.15)2
+ 144.54 × 10− 7
(T − 273.15)3
Proton conductivity in PEM and CL (S m− 1
)
σion = σion(λ,T) = (0.5139λ − 0.326)exp
[
1268
( 1
303
−
1
T
)]
Leverett-J function
pc = τcos
(
θ
K
)2
J(s)
J(s) =
{
1.42(1 − s) − 2.12(1 − s)2
+ 1.26(1 − s)3
θ < 90∘
1.42s − 2.12ss
+ 1.26s3
θ > 90∘
Relative permeability kg = (1 − s)3.0
, kl = s3.0
Effective thermal conductivity (W m− 1
K− 1
) Keff
= sKl + (1 − s)[εKg + (1 − s)Ksolid]
Open-circuit voltage(V)
Erev = 1.229 − 0.9 × 10− 3
(T − 298.15) +
RT
2F
(
lnpin
H2
+
1
2
lnpin
O2
)
Table 5
Fuel cell and model parameters [43,44].
Parameters Values
Permeability (m2
) (GDL, MPL, CL,
Membrane)
2.0 × 10− 12
,1.0 × 10− 13
,2.0 ×
10− 20
Reference hydrogen concentration
(mol m− 3
)
56.4
Reference oxygen concentration (mol m− 3
) 3.39
Transfer coefficient 0.5
Dry membrane density (kg m− 3
) 1980
Membrane equivalent weight (kg kmol− 1
) 1.1
Latent heat of water
evaporation (J mol− 1
)
44,900
Liquid density (kg m− 3
) 982
Faraday’s constant (C mol− 1
) 96,487
Universal gas constant (J mol− 1
K− 1
) 8.314
Thermal conductivity (W m− 1
K− 1
)
(BP, CL, PEM)
150, 10, 2
GDL thermal conductivity (W m− 1
K− 1
) In-plane: 31, Through-plane: 1.7
Anode stoichiometric ratio 2
Operating pressure (Pa) 101,325
Inlet relative humidity Anode: 0.4, Cathode: 0
Inlet Temperature (K) 298
Reference current density (A cm− 2
) Anode: 6000, Cathode: 6
Porosity in GDL 0.5
Porosity in CL 0.4
Electronic conductivity in CL (S m− 1
) 3500
Electronic conductivity in GDL (S m− 1
) In-plane: 3500, Through-plane: 350
J. Zhang et al.

6
numbers ranging from 520,000 to 1170,000 were used to calculate at
the current density of 0.7A cm− 2
. When the calculation reached a steady
state, the variations in the fuel cell output voltage and the temperature
at the cathode GDL-CL interface with respect to the mesh number are
shown in Fig. 3. It can be observed that the influence of the mesh number
on the calculation results can be neglected when the mesh number ex
ceeds 660,000. In order to save computational time and resources, the
meshing strategy with a grid number of 660,000 was adopted for the
geometry model meshing.
Results and discussion
In order to investigate the effect of the STSF configuration on the
performance of AC-PEMFC, including output voltage, cooling capacity,
water retention capacity, and reaction gas transfer ability, mathematical
simulations are performed for AC-PEMFC with both STSF and traditional
cathode flow field configurations.
Model validation
The model was validated against the experimental data from refer
ence [45], which investigated the effects of different cathode flow
channel widths. Four sets of experimental data from reference [45] with
flow channel widths of 1.5, 1.3, 1.1 and 0.9 mm were used to validate
the model. The validation results are shown in Fig. 4, which indicates
good agreement between the simulation and experimental results.
Overall performance
The IV curve is a major performance indicator for PEMFC. It is
affected by various factors, such as the cell’s internal temperature, the
membrane’s water content, and the oxygen concentration at the GDL-CL
interface. In order to comprehensively analyze the performance of the
STSF configuration, we conducted simulations under various operating
conditions. As mentioned earlier, the cathode airflow rate influences the
performance of AC-PEMFC. Therefore, we considered three different
cathode stoichiometric ratios: 50, 80, and 100. The altitude changes that
occur during the operation of UAVs will cause variations in atmospheric
physical properties, such as inlet temperature and pressure. The pressure
and temperature would inevitably cause the gas diffusion coefficient or
latent heat of vaporization of water to vary, but here, we investigate how
the temperature and pressure vary with altitudes affect performance
directly. This study selected three altitude levels of 0, 4, and 8 km for
simulation calculations. The atmospheric temperature Tatmo and pres
sure patmo were calculated according to the International Standard At
mosphere (ISA) model [31,32] as follows:
Tatmo = T0 − 6.5 × hL (12)
patmo = p0
[
1 −
(
6.5 ×
hL
T0
)]5.2561
(13)
where T0 (K) is the temperature at sea level, set to 298, hL (km) is the
altitude, p0(Pa) is the atmospheric pressure at sea level, set to 101,325.
As indicated by Eq. (12), the temperature decreases with increasing
altitude. Consequently, the temperature difference between the atmo
sphere and the inside of the fuel cell increases with higher altitudes,
resulting in improved cooling efficiency. Therefore, the cathode stoi
chiometric ratio decreases with increasing altitude to maintain the same
cooling effectiveness. According to literature [34], if the altitude in
creases from sea level to 4 kms, the required cathode stoichiometric
ratio for maintaining cooling effectiveness decreases from 110 to 22.
Taking into account the practical considerations mentioned above, the
method for determining the cathode stoichiometric ratio at different
altitudes in this study is as follows: Using the traditional parallel channel
flow field as the reference, when the current density is 0.7A cm− 2
, and
the temperature at the GDL-CL interface reaches 320 K at steady-state
conditions, the cathode stoichiometric ratio is determined for various
altitudes. Using this approach, the cathode stoichiometric ratio is 80 at
sea level, 45 at an altitude of 4 km, and 45 at an altitude of 8 km. During
the simulation, the basic operating condition is set at a cathode stoi
chiometric ratio of 80 and an altitude of 0.
Fig. 5(a) shows the IV curve and the mass-specific power density and
Fig. 5(b) is the performance improvement rate under different operating
conditions. The range for calculating current density varies under
different operating conditions. The specific strategy for determining
these ranges is explained in the following section on the analysis of in
ternal temperature in the PEMFC. Generally, compared to the traditional
configuration, the STSF configuration with tapered and slotted sections
improves the performance of the AC-PEMFC. The factors contributing to
performance improvement under different operating conditions differ.
For basic conditions, the performance improvement is more pronounced
at higher current densities. The heat generation rate increases with the
current density, the advantage of the STSF configuration in enhancing
heat dissipation is highlighted in the high current density region. At a
current density of 1.1 A cm− 2
, the output voltage is improved by 11.1 %,
and the mass-specific power density is improved by 15.2 %. The latter is
larger because arranging the slotted sections significantly reduce the
Fig. 3. Schematic of the grid independent test.
Fig. 4. Comparison of the polarization density of the present numerical model
with the experimental data of Zhao et al. [45].
J. Zhang et al.

7
Fig. 5. Polarization curve and mass-specific power density for traditional and STSF configurations under different (a1) altitudes and (a2) cathode stoichiometric ratio
and (b) mass-specific power density improvement rate of the STSF configuration compared with the traditional configuration under different operating conditions.
The abbreviation ‘Trad’ means traditional configuration. The character 0 means the basic condition with a cathode stoichiometric ratio of 80 and altitude 0. S50 and
S100 means 50 and 100 for the cathode stoichiometric ratio. The cathode stoichiometric ratios for 4 and 8 km are both 45.
J. Zhang et al.

8
cell’s mass, further improving the mass-specific power density.
Considering the impact of cathode stoichiometric ratio on output
voltage, as shown in Fig. 5(a2), the voltage of both configurations de
creases when the cathode stoichiometric ratio adopts 50. Because a
decreased cathode flow rate means a decrease in heat dissipation effi
ciency, which leads to a decrease in membrane water content. However,
when the cathode stoichiometric ratio is increased to 100, there is no
significant improvement in performance. Because excessive cathode
flow rate can also take away a large amount of water. Additionally, the
oxygen concentration is adequate at the reaction sites under the basic
and cathode stoichiometric ratio for 100 conditions, so increasing the
airflow rate does not benefit reducing concentration losses. As expected,
the performance of both configurations decreases with increasing alti
tude, as shown in Fig. 5(a1). At current densities of 1.1A cm− 2
with the
traditional cathode flow field configuration, the mass-specific power
density drops by 9.2 and 16.8 % at 4 and 8 km altitudes. A similar trend
is observed for the STSF configuration with decreases of 6.5 and 11.2 %.
The performance degradation can be attributed to two primary factors.
The cooling effect weakens as altitude increases and the oxygen partial
pressure decreases with altitude which leads to higher concentration
losses in both configurations under high current density regions. How
ever, the performance decrease is smaller for the AC-PEMFC using the
STSF configuration. The mass-specific power density of the fuel cell
using the new cathode flow field configuration is improved by 15.2 to
23.6 % for the five operating conditions studied under a current density
of 1.1A cm− 2
. As shown in Fig. 5(b), the STSF configuration proposed in
this study is more effective in improving performance under adverse
conditions, such as low cathode flow rate and high altitudes conditions.
Distribution characteristics of multiple physical fields
The average temperature within the fuel cell using different flow
field configurations is analyzed, as shown in Fig. 6. For both configu
rations, internal temperature increases with current density as a higher
current density means a faster heat production rate. The internal tem
perature of the cell is greatly reduced when the STSF configuration is
adopted. For instance, when operating under the basic condition, the
average temperature drops from 335.3 to 319.4 K for a current density of
1.1A cm− 2
. The tapered and slotted sections in the STSF configuration
increase the contact area between the cooling airflow and the bipolar
plate by 29.18 %, which is the reason for the improved heat dissipation
capacity. As expected, the cathode stoichiometric ratio heavily in
fluences the cell temperature, with the temperature rising as the cathode
stoichiometric ratio decreases. For the traditional and STSF configura
tions under a lower cathode stoichiometric ratio of 50, the average cell
temperature increases by 15.9 and 10.6 K under a current density of
1.1A cm− 2
. Fig. 6-a illustrates the relationship between the average in
ternal temperature of the fuel cell and the current density at different
altitudes. In general, higher current densities result in greater heat
generation within the fuel cell, leading to higher internal temperatures.
For example, under the baseline operating conditions with a traditional
flow field, as the current density increases from 0.3 to 1.5A cm− 2
, the
internal temperature of the fuel cell rises from 309 K to 354 K. It’s worth
noting that when the temperature reaches 100 ◦
C, liquid water begins to
boil, rendering the fuel cell unable to operate properly. Therefore, the
maximum operating current density is limited by this factor. The vari
ation in altitude affects two factors simultaneously: atmospheric tem
perature and pressure. Temperature decreases with increasing altitude,
which is favorable for heat dissipation. On the other hand, the reduction
in atmospheric pressure with higher altitudes leads to a decrease in air
intake, which is unfavorable for cooling efficiency. Consequently, the
changes in atmospheric temperature and pressure have opposing effects
on cooling efficiency. The dominant factor varies under different elec
trical density conditions. Under low current density conditions, the fuel
cell generates relatively less heat, and the cathode flow rate is sufficient
to carry away excess heat. However, at high altitudes, the lower atmo
spheric temperature increases the convective heat transfer coefficient,
enhancing heat dissipation. The decrease in air intake temperature due
to higher altitudes becomes the dominant factor affecting performance.
Taking the traditional flow field configuration as an example, at a cur
rent density of 0.3A cm− 2
, as the altitude increases from sea level to 4
km, the internal temperature of the fuel cell decreases from 309 K to 299
K. When the altitude rises to 8 km, it further decreases to 296 K. How
ever, when operating in a high current density range, the increased heat
generation in the fuel cell begins to reduce the cooling efficiency due to
insufficient air intake. Using the traditional flow field as an example
again, at a current density of 1.1A cm− 2
, as the altitude increases from
sea level to 4 km, the internal temperature of the fuel cell increases from
335 K to 351 K. At an altitude of 8 km, the internal temperature further
rises to 371 K, nearing the limited operating temperature. Therefore,
when unmanned aerial vehicles require high current density operation
Fig. 6. Average temperature at the interface of the cathode GDL-CL for traditional and STSF configurations under different (a) altitudes and (b) cathode stoi
chiometric ratio. The abbreviation ‘Trad’ means traditional configuration. The character 0 means the basic condition with a cathode stoichiometric ratio of 80 and
altitude 0. S50 and S100 means 50 and 100 for the cathode stoichiometric ratio. The cathode stoichiometric ratios for 4 and 8 km are both 45.
J. Zhang et al.

9
to output high power, there is a risk of overheating with the traditional
flow field. In this context, adopting the new flow field proposed in this
study can effectively address this issue. As shown in Fig. 6-(a), under the
same current density condition of 1.1A cm− 2
, at an altitude of 4 km, the
average internal temperature of the fuel cell using the new flow field is
327 K, which is 24 K lower than that of the traditional flow field. At an
altitude of 8 km, the temperature is 343 K, which is 28 K lower than that
of the traditional flow field. This enables the fuel cell to operate within a
reasonable temperature range. The deteriorating cooling conditions at
high altitudes underscore the advantages of the STSF configuration in
terms of heat dissipation. For the traditional configuration, at an altitude
of 8 km, when the current density reaches 1.1A cm− 2
, the maximum
temperature in the cell exceeds 100 ◦
C, which is beyond the normal
operating temperature range of PEMFC. Therefore, the calculation range
for both flow field configurations is limited to between 0 and 1.1A cm− 2
for this altitude. A similar range selection strategy is applied for the 4 km
altitude condition, with the calculation range chosen as 0 to 1.3A cm− 2
.
The calculation range is set at 0 to 1.5A cm− 2
for the basic and variable
cathode stoichiometric ratio conditions. It’s important to emphasize that
the aforementioned current density determination strategy is based on
the perspective of the traditional configuration. When using the STSF,
cooling efficiency is improved, and the operating range of the fuel cell is
expanded. However, for the purpose of facilitating a comparison be
tween the two flow field configurations, the same current density
calculation range as the traditional flow field design is applied to the
new flow field design.
The distribution of internal temperature in a PEMFC is ultimately
reflected in the water content of the membrane. Fig. 7 illustrates the
average water content of the membrane under various working condi
tions. Firstly, for all conditions, the average water content is always
below ten for both configurations. This falls into the low water content
region, which is determined by the characteristics of AC-PEMFC and is
the problem this study aims to solve. The adoption of the STSF config
uration significantly increases the value of water content. For the basic
condition, the 4 km and 8 km altitude, the cathode stoichiometric ratio
50 and 100 working conditions, the average water content of the PEM is
increased by 49.0, 67.9, 85.7, 35.1, and 65.7 % under a current density
of 1.1A cm− 2
. This conclusion aligns with that mentioned in the previous
section, where the STSF configuration is beneficial to heat dissipation
and reducing the internal temperature of the cell. The working condi
tions affect the water content by influencing the internal temperature.
Under lower cathode airflow rate condition, the membrane water con
tent drops by 28.6 and 20.5 % for traditional and STSF configurations.
Water content drops less in the STSF configuration than in the tradi
tional one. It should be noted that when the cathode stoichiometric ratio
is increased to 100, the temperature is significantly reduced. However,
the exceeded airflow takes away a large amount of water along with the
heat, which prevents the membrane’s water content from increasing.
Under high altitudes, the water content of AC-PEMFC significantly drops
from low current density to high current density. The reason is, as
mentioned above, the result of the combined effect of atmospheric
temperature and pressure. For the two configurations, water content is
reduced by 28.6 and 10.9 % in the 4 km altitude conditions. And in the
altitude of 8km, these value increase to 42.9 and 35.6 %. And the STSF
configuration alleviates the worsening trend with the increase of
altitude.
The transportation of reactant gases to the CCM is critical for the
performance of fuel cells. At high current densities, most of the losses in
PEMFC are due to concentration losses resulting from the inadequate
oxygen supply. This effect is particularly noticeable at high altitudes.
Fig. 8 shows the gas velocity in the middle plane of the cathode GDL for
different configurations while the current density is adopted to 1.1
A cm− 2
. For the traditional configuration, the velocity at the middle
plane of the GDL gradually decreases from the inlet to the outlet vicinity
as oxygen is consumed with the flow resistance of the channel wall.
However, for STSF configuration, the maximum velocity appears
downstream of the channel due to the staggered arrangement of the
tapered sections, which create a pressure difference between adjacent
channels and induces cross-flow in the GDL as shown in Fig. 8(f). The
biggest velocity improvement for STSF configuration is 37.3 times, as
shown in Fig. 8(e) for the cathode stoichiometric ratio of 100. And the
minimum rate of improvement in velocity has also reached 11.8 times,
corresponding to an 8 km altitude condition as shown in Fig. 8(c). The
STSF configuration’s slotted sections allow adjacent channels to
Fig. 7. Average membrane water content for traditional and STSF configurations under different (a) altitudes and (b) cathode stoichiometric ratio. The abbreviation
‘Trad’ means traditional configuration. The character 0 means the basic condition with a cathode stoichiometric ratio of 80 and altitude 0. S50 and S100 means 50
and 100 for the cathode stoichiometric ratio. The cathode stoichiometric ratios for 4 and 8 km are both 45.
J. Zhang et al.

10
Fig. 8. Comparison of the velocity distribution in the middle plane of the cathode GDL for the traditional configuration (left) and the STSF configuration (right)
under current density 1.1A cm− 2
at (a) basic condition with a cathode stoichiometric ratio of 80 and altitude 0, altitude of (b) 4 and (c) 8 km, cathode stoichiometric
ratio of (d) 50 and (e) 100 with (f) enlarged partial view.
J. Zhang et al.

11
exchange reactants, alleviating the problem of uneven reactant distri
bution between channels caused by cross-flow while enhancing the
turbulence intensity. The operating conditions significantly impact the
velocity in the middle plane of the GDL. The velocity is higher when the
larger cathode stoichiometric ratio is adapted. Altitude indirectly affects
the velocity by affecting atmospheric pressure, with higher altitude
leading to slower velocity.
Fig. 9 illustrates the oxygen concentration distribution at the cathode
GDL-CL interface under a current density 1.1A cm− 2
. The STSF config
uration leads a significantly higher oxygen concentration at the cathode
GDL-CL interface and a more uniform distribution of oxygen. The largest
average oxygen concentration at the reaction site increased by up to
39.0 %, corresponding to the cathode stoichiometric ratio of 100, as
shown in Fig. 9(e). This increment is consistent with the increase of
airflow velocity in the middle of the GDL under different operating
conditions. However, compared with the basic condition, the larger
cathode flow rate may not mean a significant decrease in concentration
losses since the oxygen is abundant under these operating conditions.
When the cathode stoichiometric ratio decreases from 80 to 50, as
depicted in Fig. 9(d), the oxygen concentration is decreased for both
configurations. At this condition, the STSF configuration improves the
oxygen concentration by 17.0 %. According to ISA model, the oxygen
partial pressure decreases with altitude by 30.1 and 66.7 % compared to
sea level at altitudes of 4 km and 8 km. This will significantly decrease
the cathode flow rate, ultimately leading to insufficient oxygen supply.
Taking the traditional flow field configuration as an example, under the
conditions of 4 and 8 km altitude, the oxygen concentration at the re
action sites decreases by 8.8 and 15.8 %, respectively. Nevertheless, the
STSF configuration still plays a promoting role in oxygen conduction.
For the two high altitude conditions investigated in this study, adopting
the STSF configuration leads to an increase in oxygen concentration by
7.7 and 4.2 %.
In the context of PEMFC flow field design, apart from considering the
influence of different flow field structures on the cell’s heat and mass
transfer performance, the pressure drop within the flow field is a crucial
performance indicator that cannot be overlooked. This is because pres
sure drop is linked to pump power, which, in turn, affects the cell’s ef
ficiency. Fig. 10 compares the pressure drops under various operating
conditions between the STSF and the traditional one. The STSF config
uration results in a somewhat increased pressure drop due to its more
intricate internal structure. As depicted in Fig. 10, the extent of this
increase depends on the operating conditions. The corresponding intake
air flow rate is low at a low cathode stoichiometric ratio and high alti
tude, so the pressure drop in the channel is small and the increase caused
by the STSF is also minor. For current density 1.1A cm− 2
, compared with
traditional, using STSF configuration under altitudes of 4 and 8 km and
low cathode stoichiometric ratio of 50, the pressure drop increased by
867, 515 and 416 Pa, respectively. As shown in Fig. 10-(c), under high
altitudes and low cathode stoichiometric ratios, considering the increase
of PEMFC output power is significant with the increase of pump power is
slight, the net power has a significant increase. Under the current den
sity of 1.1A cm− 2
, the net power increased by 0.080 and 0.060 W for
altitudes 8 and 4 km, and the value is 0.013 W for the cathode stoi
chiometric ratio of 50. However, when the PEMFC operates under less
severe conditions, such as a high stoichiometric ratio of 100, the cell’s
performance is not significantly improved by STSF. At the same time,
due to the large cathode flow, the pump power increases more promi
nently when using STSF, so the net power decreases. However, when the
Fig. 9. Comparison of the oxygen concentration distribution at the interface of the cathode GDL-CL for the traditional configuration (left) and the STSF configuration
(right) under current density 1.1A cm− 2
at (a) basic condition with a cathode stoichiometric ratio of 80 and altitude 0, altitude of (b) 4 and (c) 8 km, cathode
stoichiometric ratio of (d) 50 and (e) 100.
J. Zhang et al.

12
cell operates under a high current density of 1.5A cm− 2
, the advantages
of STSF are highlighted, and the net power is raised by 0.068 W with
STSF.
Conclusion
This study proposes an STSF configuration to address the thermal
and water management issues of AC-PEMFC. Its performance fluctua
tions at different altitudes during UAVs operation are investigated and
compared with the traditional straight configuration. The design
concept of this STSF configuration is to increase the contact area be
tween the cooling airflow and the bipolar plate by arranging tapered and
slotted sections to enhance the cooling ability. Based on numerical
simulations, the internal temperature distribution, membrane water
content distribution, oxygen concentration distribution, and overall
performance of the fuel cell are discussed. The following conclusions can
be drawn.
By increasing the water content and the oxygen concentration, the
STSF configuration significantly reduces ohmic and concentration losses
in the AC-PEMFC. Under the base operating conditions, the mass-
specific power density increases by 15.2 %. Under 4 km and 8 km alti
tude conditions, the mass-specific power density increases by 19.1 and
23.6 %. With a smaller cathode stoichiometric ratio of 50 and a larger
stoichiometric ratio of 100, the mass-specific power density increases by
18.9 and 15.5 %. The performance enhancement with the STSF
configuration is more significant in harsh environments.
After adopting the STSF configuration, the internal temperature of
the cell is significantly reduced without increasing the cathode
Fig. 10. Comparison of pressure drop of the two configurations under different conditions (a) various altitudes, (b) various cathode stoichiometric ratios, and (c) the
net power increment of PEMFC with STSF compared with traditional configuration under various conditions.
J. Zhang et al.

13
stoichiometric ratio. Taking an example of a cathode stoichiometric
ratio of 80, the average temperature decreases by 15.9 K and the
advantage of the STSF configuration for heat dissipation becomes more
prominent under more severe operating conditions. As the temperature
inside the cell decreases, the water content increases. For the basic case,
with a cathode stoichiometric ratio of 80 and at sea level, the average
membrane water content increases by 49.0 %.
The STSF configuration induces cross-flow to promote oxygen
diffusion towards the reaction site, which is critical for enhancing the
performance of AC-PEMFC under oxygen-deficient conditions like high
altitudes. For example, at altitudes of 4 and 8 km, the oxygen concen
tration at the reaction site increased by 7.7 and 4.2 %, respectively.
Ultimately, a thorough evaluation of pressure losses within the flow
channels for both the STSF and the conventional flow field was under
taken. The heightened contact area between the cooling airflow and the
bipolar plates in the STSF design invariably leads to elevated pressure
drops within the channels. Further investigation into the impact of STSF
on pump power shows that the net power of PMEFC with STSF still
raised significantly under tough conditions.
Declaration of competing interest
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.
Data availability
Data will be made available on request.
Acknowledgment
This work is supported by the National Natural Science Foundation
of China (No. 52206112), the Foundation for Innovative Research
Groups of the National Natural Science Foundation of China (No.
51721004), and the Fundamental Research Funds for the Central Uni
versities (No. xhj032021001-01 and No. xpt012023029).
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