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Journal of Power Sources 562 (2023) 232752
Contents lists available at ScienceDirect
Journal of Power Sources
journal homepage: www.elsevier.com/locate/jpowsour
Performance evaluation and off-design strategy of a high temperature
proton exchange membrane fuel cell turbine-less hybrid system for low
pressure ratio and Mach number aircraft
Fafu Guo , Xinyan Xiu , Chenghao Li , Kunlin Cheng , Jiang Qin *
School of Energy Science and Engineering, Harbin Institute of Technology, Harbin, 150001, China
H I G H L I G H T S
• A HT-PEMFC turbine-less hybrid system for aircraft is proposed for the first time.
• Exergetic and exergoeconomic analysis models are built to study system performance.
• The impact and comparison of four off-design strategies are investigated in detail.
• The new system reduces specific fuel consumption by 24.90% compared to a turbojet.
• Strategy 2 is an economic option as it produces the minimum of total system cost.
A R T I C L E I N F O
A B S T R A C T
Keywords:
High temperature proton exchange membrane
fuel cell
Turbine-less
Plate reformer
Exergetic
Exergoeconomic
Off-design strategy
The aviation industry is moving towards low-carbon and environment-friendly electric propulsion. This paper
presents for the first time a high temperature proton exchange membrane fuel cell turbine-less hybrid system for
low pressure ratio and Mach number aircraft. It is a new electric propulsion engine in which a plate reformer is
used to supply hydrogen to the fuel cell. To investigate its performance and off-design strategies, thermody­
namic, exergetic and exergoeconomic analyses models are established. Firstly, the thermodynamic performance
is described and compared with that of a turbojet. Then, exergetic and exergoeconomic performances are
revealed. Finally, the impact and comparison of four off-design strategies are studied in detail. The results show
that the system can reduce specific fuel consumption by 24.90%. The burner, core nozzle and high temperature
proton exchange membrane fuel cell need further development due to their low exergy efficiencies and high
irreversibility ratios. The system has an exergoeconomic factor of 11.32%, relative cost difference of 24.65%,
carbon dioxide mass specific emissions of 2.70 kg/(kW⋅h), and total system cost of 82.50 $/h. Strategy 2 is an
economic option as it produces the minimum of specific fuel consumption, carbon dioxide mass specific emis­
sions and total system cost.
1. Introduction
In an era of energy revolution, the global aviation industry is grad­
ually moving towards low-carbon and environment-friendly electric
propulsion. Among all types of airborne power supply systems, fuel cell
propulsion systems have attracted widespread attention from academia
and industry for their zero pollution, low noise, high efficiency, and high
energy density characteristics, and have become a potential develop­
ment direction for green and low-carbon aviation [1].
The fuel cell propulsion system consists of a fuel cell system and
other auxiliary power units, which in turn usually contain an air
compressor, battery, and nozzles, as well as other components. At pre­
sent, fuel cell propulsion systems are mainly used in drones and small
aircraft. Researchers at the University of Michigan developed a solid
oxide fuel cell (SOFC) powered unmanned aerial vehicle (UAV) and
successfully conducted a 10 h test flight experiment [2]. The US Naval
Research Laboratory (NRL) developed the Ion Tiger UAV using proton
exchange membrane fuel cells (PEMFC), which created a flight record of
26 h with gaseous hydrogen [3,4]. Lockheed Martin designed the Stalker
XE UAV using SOFCs with a flight time of over 8 h [5]. Boeing Research
& Technology Europe (BRTE) developed a fuel cell UAV powered by
* Corresponding author.
E-mail address: qinjiang@hit.edu.cn (J. Qin).
https://doi.org/10.1016/j.jpowsour.2023.232752
Received 6 December 2022; Received in revised form 19 January 2023; Accepted 29 January 2023
Available online 8 February 2023
0378-7753/© 2023 Elsevier B.V. All rights reserved.
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Journal of Power Sources 562 (2023) 232752
Nomenclature
A
Alt
c
C
CEPCI
Cj
DL
E
Ex
f
F
F
H
in
j
j0
jL
jleak
KE
m
Ma
MSE
n
p
P
Q
r
R
rf
RH
Rrec
S
SCR
SFN
t
T
TSFC
u
U
Uf
V
W
X
y
Z
Zp
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Subscript
act
an
blow
ca
comb
comp
con
D
fc
I
inta
mem
nozz
O
ohm
over
prop
refo
rev
ther
Area, m2
Altitude, km
Specific exergoeconomic rate, $/GJ
Exergoeconomic rate, $/h
Cost index
Equipment cost, $
Doping level
Potential, V
Exergy, kW
Exergoeconomic factor
Faraday constant, 96,485 C/mol
Thrust, N
Enthalpy, kJ
Nominal interest rate
Current density, A/m2
Exchange current density, A/m2
Limiting current density, A/m2
Leakage current density, A/m2
Kinetic energy, kW
Mass flow rate, kg/s
Mach number
Mass specific emissions, kg/(kW⋅h)
Molar flow, mol/s, system lifetime, year
Pressure, bar
Power, kW
Thermal energy, kW
Relative cost difference
Universal gas constant, 8.314 J/(mol⋅K)
Inflation rate
Relative humidity
Recirculation ratio
Entropy, J/(mol⋅K), Selectivity
Steam to carbon ratio
Specific thrust, N/kg
Thickness, m
Temperature, K
Specific fuel consumption, g/(kN⋅s)
Velocity, m/s
Output voltage, V
Fuel utilization
Volume, m3
Work energy, kW
Conversion rate
Irreversibility ratio
Total investment cost rate, $/h
Purchase equipment cost, $
Greek
α
ε
η
π
σ
τ
φ
ψ
Activation
Anode
Blower
Cathode
Combustor
Compressor
Concentration
Destruction
Fuel cell
Input
Intake
Membrane
Nozzle
Output
Ohmic
Overall
Propulsive
Reformer
Reversible
Thermal
Charge transfer coefficient, excess air coefficient
Ratio of total output exergy to total input exergy
Efficiency
Pressure ratio
Pressure recovery coefficient, proton conductivity
Operational hours in a year, h
Velocity coefficient, maintenance factor
Exergy efficiency
Acronym
BN
Bypass nozzle
BRTE
Boeing Research & Technology Europe
CAB
Catalytic combustion chamber
CEA
Chemical Equilibrium with Applications
CN
Core nozzle
CRF
Capital recovery factor
HT-PEMFC High temperature proton exchange membrane fuel cell
LT-PEMFC Low temperature proton exchange membrane fuel cell
NASA
National Aeronautics and Space Administration
NRL
Naval Research Laboratory
PEMFC Proton exchange membrane fuel cell
SOFC
Solid oxide fuel cell
UAV
Unmanned aerial vehicle
solid-state PEMFCs and lithium batteries for low-altitude reconnaissance
missions [6].
Ly proposed a fuel cell propulsion system, called a turbine-less en­
gine, in which the compressor is driven by the fuel cell [7]. In our pre­
vious study, an SOFC turbine-less hybrid system was proposed [8–11].
The results showed that it outperformed the traditional turbojet engine
in terms of specific thrust and specific impulse. SOFCs belong to high
temperature fuel cells, and operate at 873–1273 K. Therefore, SOFCs can
be combined with other power units to make full use of exhaust heat
[12]. Initially, in an SOFC gas turbine hybrid system, SOFCs were used
to replace the combustor and generator [13]. However, in the studies of
hybrid systems, such as mathematical modeling [14], safe operation
[15–17] and fuel adaptation [18–20], burners were added to utilize the
unused fuel in the SOFC exhaust. In the SOFC turbine-less hybrid system,
the exhaust heat from the SOFC is not fully utilized because the turbine
is removed. However, at low pressure ratios and Mach numbers, the air
temperature at the compressor outlet is relatively low, which is difficult
to match with the SOFC operating temperature.
Thus, in this study, a high temperature proton exchange membrane
fuel cell (HT-PEMFC) turbine-less hybrid system is proposed for low
pressure ratio and Mach number aircraft. PEMFC is widely regarded as
one of the most promising fuel cells [21,22]. It has the advantages of
high power density, fast start-up and switching, and convenient opera­
tion, which is suitable for portable devices and transportation equip­
ment [23]. Recently, several papers have reported successful flight tests
of light aircraft powered by fuel cells [24–26]. Renau designed a
HT-PEMFC powered UAV with a flight altitude of 10 km [27–29].
HT-PEMFC has improved kinetics, reduced catalyst poisoning, and
2
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Journal of Power Sources 562 (2023) 232752
better thermal management than that of conventional PEMFCs. The
operating temperature range is 373–473 K and no humidification of the
reactant gas is required [30]. These properties provide the possibility of
practical operation at high altitudes and with open cathode structures
(in combination with an air compressor).
Fuel cell performance is heavily dependent on the feed gas. If the
hydrogen flow rate is low, the stack will not perform fully. If the CO
content is too high, the anode catalyst will be poisoned [31]. Due to the
low mass density of high-pressure gaseous hydrogen storage and the low
volumetric energy density of liquid hydrogen storage [32], on-site
hydrogen production is a better option for aircraft. Methanol, the
feedstock for on-site hydrogen production, is widely available, easily
stored and renewable, with low conversion temperatures and fairly
mature catalyst technology [33].
This study is novel as it is the first scheme of a HT-PEMFC turbineless hybrid system for low pressure ratio and Mach number aircraft using
methanol as fuel, in which a plate reformer is used to supply hydrogen to
the HT-PEMFC. The mathematical models, including jet engine, HTPEMFC, plate reformer, exergetic analysis, and exergoeconomic anal­
ysis models, are established to investigate the performance evaluation
and off-design strategy. The thermodynamic performance is described
and compared with that of a turbojet. Further, the exergetic and exer­
goeconomic performances of the system are revealed. Then, four offdesign strategies are proposed for this system. The effects of different
strategies on system performance and the comparison between them are
studied in detail to obtain the most economic strategy.
driven by an electric motor, which is powered by a HT-PEMFC. Some
compressed air enters the core duct, where the reformer, catalytic
combustion chamber (CAB), HT-PEMFC and conventional burner are
arranged. The remaining compressed air goes directly into the bypass
duct. The bypass duct is added to regulate the amount of air required by
the HT-PEMFC. By adjusting the bypass ratio, the HT-PEMFC can work
at a suitable air ratio.
Fig. 1 (b) shows the process flow of the HT-PEMFC turbine-less
hybrid system. In this study, a plate reformer is chosen, where a strong
exothermic reaction and a strong endothermic reaction are organically
coupled by indirect heat transfer. The combustion and reforming cata­
lysts are loaded on each side of the plate. First, air from the environment
is compressed in the intake and compressor in turn. Next, the highpressure air is split into two parts: one that enters the CAB where it
undergoes a catalytic combustion reaction with the anode recirculation
gas and another that feeds the HT-PEMFC cathode. The exhaust gas from
the CAB flows into the conventional burner. Meanwhile, methanol and
water undergo a reforming reaction in the reformer, and the resulting
hydrogen-rich gas is passed to the HT-PEMFC anode. Then, an electro­
chemical reaction occurs in the HT-PEMFC, and the electricity generated
is used to drive the compressor. Some of the anode exhaust gas partic­
ipates in the recirculation while the rest enters the burner with the
cathode exhaust gas. Subsequently, a violent redox reaction occurs in
the burner, releasing heat. Finally, the high temperature and pressure
combustion gases are accelerated in the nozzle and discharged into the
atmosphere, creating a thrust on the system in the opposite direction to
its own flow. In particular, the fuel and water need to pass through the
cooling channels inside the fuel cell before use.
2. System description
The schematic diagram of the HT-PEMFC turbine-less hybrid system
is shown in Fig. 1 and the layout is shown in Fig. 1 (a). The compressor is
Fig. 1. (a) Configuration and (b) detailed diagram of the HT-PEMFC turbine-less hybrid system.
3
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3. Mathematical models
Erev = Er0 +
The following assumptions are adopted for modeling the HT-PEMFC
turbine-less hybrid system in this study:
(1)
(2)
(3)
(4)
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ΔS
= − 18.449 − 0.01283T
n
The jet engine models including an intake, a compressor, a burner, a
core nozzle (CN) and a bypass nozzle (BN) model are from the GasTurb
software, which was validated in engine model applications in previous
studies [34]. The mathematical equations for each component can be
found in our previous work [35]. Table 1 shows the operating param­
eters of the burner and nozzles.
Assuming that there is no flow separation in the intake, the intake
pressure recovery coefficient is only related to the Mach number [36].
(1)
σ inta = 1 − 0.075(Ma − 1)1.35 (Ma > 1)
(2)
where α is the charge transfer coefficient with a value of 0.5 [45], jleak is
the leakage current density with a value of 50 A/m2 [46], and j0 is the
exchange current density.
The anode exchange current density is given as follows [45]:
[
(
)]
16900
1
1
j0,an = 0.072 × 104 exp
−
(13)
R
433.15 T
The cathode exchange current density is given as follows [45]:
[
(
)]
72400
1
1
j0,ca = 1.315 × 10− 4 exp
−
(14)
R
423.15 T
The adiabatic efficiency of the compressor is expressed as follows
[37]:
(
)/
ηcomp = 0.91 − π comp − 1 300
(3)
The concentration overpotential can be calculated by the following
equation [48]:
(
)
(
)
1 RT
jL
Econ = 1 +
ln
(15)
α nF
jL − j
3.2. HT-PEMFC model
where j is the operating current density, and jL is the limiting current
density with a value of 20,000 A/m2 [45].
The ohmic overpotential can be calculated by the following equation
[41]:
The HT-PEMFC consists of a cathode, an anode and an electrolyte.
When the HT-PEMFC is operating, hydrogen enters the anode and air
enters the cathode. The hydrogen reacts at the anode to form protons
and electrons, which then pass through the proton exchange membrane
and an external load into the cathode, respectively. Oxygen reacts with
protons and electrons to form H2O at the cathode. The electrochemical
reaction equations are as follows [38]:
Anode reaction : H2 →2H+ +2e−
(4)
1
Cathode reaction : 2H+ + O2 +2e− → H2 O + heat
2
(5)
Eohm = j
Membrane : H3 PO4 +PBI =
+
H2 PO−4
σ mem =
(6)
(7)
Cathode : PBI⋅H = PBI + H
(8)
+
+ PBI⋅H
For the HT-PEMFC, the reversible potential can be given as follows
[41,42]:
Table 1
Operating parameters of the burner and nozzles [10].
Component
Symbol
Value
Combustion efficiency
Burner pressure recovery coefficient
Nozzle velocity coefficient
ηcomb
σcomb
0.98
0.99
0.95
φnozz
(16)
bact
A0 B0 − RT
e
T
(17)
A0 = 68DL3 − 6324DL2 + 65750DL + 8460
(18)
⎧
⎨ 1 + (0.01704T − 4.767)RH 373.15 K ≤ T ≤ 413.15 K
B0 = 1 + (0.1432T − 56.89)RH 413.15 K < T ≤ 453.15 K
⎩
1 + (0.7T − 309.2)RH 453.15 K < T ≤ 473.15 K
(19)
bact = − 619.6DL + 21750
(20)
where DL is the doping level of the electrolyte with a value of 6 [38,40],
and RH is the relative humidity of the electrolyte with a value of 3.8%
[46].
Finally, the output voltage, power, and energy efficiency, respec­
tively, of the HT-PEMFC are as follows [45]:
(9)
+
tmem
σmem
The proton conductivity of the polybenzimidazole (PBI) membrane
depends on the relative humidity, polyaniline (PA) doping level and
operating temperature [47,49] and is calculated by the following ex­
pressions [38]:
In contrast to the low temperature proton exchange membrane fuel
cell (LT-PEMFC), phosphoric acid replaces water in the HT-PEMFC. The
mass transfer principle of the anode, cathode and membrane can be
expressed as [39]:
Anode : H2 PO−4 +H+ = H3 PO4
(11)
The Tafel equation is introduced to calculate the activation over­
potential [44]:
)
(
RT
j + jleak
Eact =
(12)
ln
αnF
j0
3.1. Jet engine model
σ inta = 1 (Ma ≤ 1)
(10)
where E0r is the ideal standard potential with a value of 1.185 V. The
standard molar entropy change is related to the operating temperature
by the following equation [43]:
The gaseous working fluids are considered as ideal gases.
The system is in steady state operation.
The air contains 21% oxygen and 79% nitrogen.
All system components are adiabatic.
1
Total reaction : H2 + O2 → H2 O + heat + electricity
2
)
(
pH2 p0.5
ΔS
RT
O2
ln
(T − T0 ) +
nF
nF
p H2 O
U = Erev − Eact − Econ − Eohm
(21)
Pfc = jAU
(22)
ηfc =
4
Pfc
− ΔH
(23)
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Journal of Power Sources 562 (2023) 232752
3.3. Plate reformer model
Platinum is chosen as the catalyst for combustion because of its high
activity, and carbon nanotubes are used as the carrier material [52]. The
following definitions are used to describe the reformer performance.
The plate reformer organically couples the strong exothermic reac­
tion and the strong endothermic reaction by means of indirect heat
transfer. The combustion catalyst and reforming catalyst are respec­
tively loaded on both sides of the plate, and the heat generated from the
CAB is transferred to the steam reformer through the plate, to make full
use of the reaction heat and improve the energy efficiency of the system
[50–54]. The plate reformer structure chosen for this study is shown in
Fig. 2. Silicon wafer is selected as a substrate of the steam reformer due
to high thermal conductivity that enhances the heat-exchange between
the reformer and combustor. The plate length l1 = 48 cm, the channel
length l2 = 4.8 mm, the shell length l3 = 8 mm, the shell height τ1 = 6
mm, the channel height τ2 = 4.8 mm, the plate height τ3 = 1.2 mm, the
chamber height τ4 = 6 mm, and the shell height τ5 = 6 mm. Its width is
equal to the length of the adjacent side. The mixture of methanol and
water enters the steam reforming chamber from the top, while the
mixture of hydrogen and air flows into the CAB at the bottom. Both the
reforming and catalytic combustion reactions are assumed to be in
equilibrium. The equilibrium parameters are solved using the Chemical
Equilibrium with Applications (CEA) program from the National Aero­
nautics and Space Administration (NASA).
The following reactions are contained in the reforming chamber:
o
CH3 OH + H2 O ↔ 3H2 +CO2 , ΔH298
= +49.4kJ/mol
(24)
o
= +92.0kJ/mol
CH3 OH ↔ 2H2 + CO, ΔH298
(25)
o
CO + H2 O ↔ H2 + CO2 , ΔH298
= − 41.1kJ/mol
(26)
XMeOH =
(28)
SH2 =
H2,out
H2,out + COout + CO2,out
(29)
SCO =
COout
H2,out + COout + CO2,out
(30)
3.4. Exergetic analysis model
The total exergy of working medium includes flow exergy, thermal
exergy, work exergy and kinetic exergy. Under a steady-state condition,
the exergy balance of each component is expressed in a general form of
the second law of thermodynamic equations as follows:
∑
∑
Q
KE
W
Exi + Exj,in
+ ExW
Exe + ExQj,out + Exj,out
+ ExKE
j,in + Exj,in =
j,out + ExD
i,j
e,j
(31)
Table 2 shows the input and output exergies of the system compo­
nents. The difference between the input and output exergy is defined as
destruction exergy ExD,j. The irreversibility ratio yj is defined as the ratio
of destruction exergy of a component to the total destruction exergy
[55]. The exergy efficiency of a component ψ j is expressed as the ratio of
the output to the input exergy, while the exergy efficiency of the system
ψ t is expressed as the ratio of the propulsion work to the total fuel
exergy, as follows:
Eq. (24) is the algebraic sum of Eqs. (25) and (26). Eq. (25) repre­
sents the methanol decomposition reaction and Eq. (26) represents the
water gas shift reaction. The main products of these reactions are H2 and
CO2 while a small amount of CO is also produced. Commercial Cu/ZnO/
Al2O3 is selected as the catalyst for reforming due to its reactivity and
selectivity [52].
The ratio of the anode recirculation flow to the total anode outlet
flow is called the recirculation ratio Rrec. During steady-state operation,
the residual hydrogen in the anode recirculation flow is used as fuel in
the CAB. The reaction equation is expressed as follows:
H2 +0.5O2 ↔ H2 O
COout + CO2,out
CH3 OHin
ExD,j = ExI,j − ExO,j
(32)
∑
ExO,j
ExD,j
ExO,j
F⋅u
yj = ∑
, ψj =
, εt = ∑
,ψ =
ExD,j
ExI,j t Exf
ExI,j
(33)
3.5. Exergoeconomic analysis model
The specific exergy costing consists of three basic steps: the identi­
fication of exergy streams, definition of input and output, and imple­
mentation of cost equations [56]. The exergy costing is defined as the
cost rate associated with each exergy stream. The cost rate can be
written as follows:
(27)
Ci = ci Exi
(34)
Ce = ce Exe
(35)
CQ = cQ ExQ
(36)
CW = cW ExW
(37)
The cost balance is expressed as follows:
Table 2
Input exergy and output exergy of system components.
Components
Input exergy
Output exergy
Intake
Ex1 + ExKE
inta,in
Ex2
Ex4 + ExW
blow,in
Ex5
Compressor
Blower
CAB
Reformer
HT-PEMFC
Bruner
CN
BN
Fig. 2. Schematic diagram of the plate reformer [52].
5
Ex2 + ExW
comp,in
Ex3
Ex5 + Ex6
Ex7 + ExQ
CAB,out
Ex10
Ex8 + Ex9 +
Ex10 + Ex12
ExQ
refo,in
Ex7 + Ex15 + Ex16
Ex17
Ex19
W
Ex11 + Ex13 + ExQ
fc,out + Exfc,out
Ex17
Ex18 + ExKE
CN.out
Ex20 + ExKE
BN,out
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Journal of Power Sources 562 (2023) 232752
∑
∑
Ce + CjW =
Ci + CjQ + Zj
out
Table 3
System component cost equations.
(38)
in
Zj = ZjCI + ZjOM = ZjCI × φ =
Zp,j × CRF × φ
τ
Components
(39)
Compressor
The CRF is the capital recovery factor, which depends on the interest
rate and estimated equipment lifetime, and can be estimated as:
CRF =
i(1 + i)n
(1 + i)n − 1
1 + i = (1 + in )
/(
1 + rf
)
Blower
(40)
CAB
(41)
Reformer
The Zp,j is the purchase equipment cost of a component in 2020. It is
estimated by the cost equation [57,58] of a component in a reference
year and adjusted by the cost index (CEPCI), as follows:
Zp,j = Cref
CEPCI2020
CEPCIref
HT-PEMFC
Bruner
(42)
where, the CEPCI in 2020 is 608 [57].
The number of unknown exergoeconomic costs is greater than the
number of exergy cost equations, so enough auxiliary equations need to
be formulated:
cI,j =
CI,j
ExI,j
(43)
CO,j
ExO,j
(44)
cO,j =
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CD,j = cI,j ExD,j
(45)
CO,j = CI,j + Zj
(46)
(49)
rj =
cO,j − cI,j
cI,j
(50)
(51)
cCO2 = 0.02086$/kgCO2
(52)
(53)
Finally, the total system cost is expressed as follows:
Ctotal = CF,total + Ztotal + CD,total + CCO2
402
[57]
2000
394
[58]
2005
468
[57]
2005
468
[57]
1998
2003
390
402
[58]
[57]
Components
Cost balance
Auxiliary Equations
Intake
Compressor
C1 + Zinta = C2
C2 + C W
comp + Zcomp = C3
Zinta = 0, c1 = c2 = 0
cw,comp = cw,fc
Blower
The CO2 mass specific emissions can be calculated as:
3600mCO2
MSECO2 =
Pnet
2003
Table 4
Component cost balance and associated auxiliary equations.
The CO2 emissions cost, related to the environmental impact caused,
is a function of the unit cost of environmental damage [59].
CCO2 = cCO2 mCO2
Ref.
Fig. 3 shows the calculation process of the HT-PEMFC turbine-less
hybrid system proposed in this paper and the system analysis process is
given in Fig. 3 (a). Based on the thermodynamic and exergetic analysis,
the exergoeconomic analysis is performed to obtain the total exergetic
cost, exergoeconomic factor and relative cost difference.
According to the mathematical models established, the calculation
process for thermodynamic analysis is shown in Fig. 3 (b). The solution
depends on a series of pre-selected parameters such as flight, engine, HTPEMFC and temperature conditions. After the parameters are initialized,
the calculation modules such as the intake, compressor, reformer, HTPEMFC, blower, CAB, burner, BN and CN are solved in turn. There are
two iterations: the red part is the HT-PEMFC operating temperature
iteration, while the blue part is the power matching iteration. The
iterative process of HT-PEMFC operating temperature is included in that
of power matching. The end condition for the loop iterations is that the
absolute value of the difference between the calculated and assumed
power is less than an acceptable error. Finally, the performance pa­
rameters such as efficiencies, power, specific thrust (SFN), specific fuel
consumption (TSFC), methanol conversion, hydrogen selectivity and
carbon monoxide selectivity are obtained.
The off-design strategies implemented in this paper are shown in
Fig. 3 (c). The common off-design principle for fuel cell systems is to
keep the excess air coefficient or cathode air flow rate constant.
The exergoeconomic evaluation is carried out using two parameters:
the exergoeconomic factor (fj), which is the ratio of the total investment
cost rate to the exergy destruction cost rate, and the relative cost dif­
ference (rj), which refers to the difference between the specific exergetic
cost of output and input. They are described as
Zj
Zj + CD,j
3240(Vrefo )0.4 + 21280.5Vrefo
Zfc = 1219.7Pfc
)[
(
46.08ma
1+
Zburn =
0.995 − pout /pin
exp(0.018Tin − 26.4)]
CEPCI
4. Methods
(48)
fj =
3240(VCAB )0.4 + 21280.5VCAB
)
(
Arefo 0.78
Zrefo = 130
+
0.093
Year
considered as zero. The component cost balance and associated auxiliary
equations are listed in Table 4. The economic data applied for the pre­
sent study are shown in Table 5.
The total specific exergetic cost of input and output can be defined as
follows:
∑
CI,j
cI,t = ∑
(47)
ExI,j
∑
CO,j
cO,t = ∑
ExO,j
PEC equation
)(
) (
)
(
44.71ma
pout
pout
ln
Zcomp =
0.95 − ηcomp
pin
pin
Zblow =
(
) (
)
Pblow 0.26 1 − ηblow 0.5
2100
10000
ηblow
)
(
ACAB 0.78
ZCAB = 130
+
0.093
(54)
The system component cost equations are presented in Table 3. The
intake, CN and BN are hollow tubes, and these three component costs are
6
C4 + CW
blow + Zblow = C5
CAB and
reformer
C5 + C6 + C8 + C9 + ZCAB + Zrefo =
C7 + C10
HT-PEMFC
C10 + C12 + Zfc = C11 + C13 + CW
fc
Bruner
C7 + C15 + C16 + Zburn = C17
CN
BN
C17 + ZCN = C18
C19 + ZBN = C20
C5 + C6 + ZCAB = C7 + CQ
CAB
C8 + C9 + CQ
refo + Zrefo = C10
cw,blow = cw,fc , c4 = c12 =
c15
c8 = 24.69$/GJ [58]
c9 = 0
cq,refo = 2.08$/GJ [55]
Q
CQ
CAB = Crefo
c10 = c11
c12 = c13
c16 = 24.69$/GJ [58]
C15 = C13 + C14
ZCN = 0
ZBN = 0, c3 = c6 = c12 =
c19
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and 3, respectively. The fuel utilization is 0.75, the current density is
3000 A/m2, and the recirculation ratio is 0.5. The reforming tempera­
ture is set to 523 K, and the fuel cell operating temperature is 473 K.
Table 8 shows the thermodynamic analysis results. The design con­
ditions for the turbojet, which consist of flight and engine conditions, are
the same as those for the HT-PEMFC turbine-less hybrid system. In
addition, for comparison purposes, the combustion temperature is
adjusted so that the specific thrust of the turbojet matches that of the HTPEMFC turbine-less hybrid system. As can be seen, compared to the
turbojet, the HT-PEMFC turbine-less hybrid system has greater advan­
tages in specific fuel consumption, thermal efficiency and overall effi­
ciency, and only slightly lags behind in propulsive efficiency. In
particular, the HT-PEMFC turbine-less hybrid system reduces the spe­
cific fuel consumption by 24.90%.
Table 5
Economic data applied for the present study [57].
Parameters
Value
Nominal interest rate, in
Inflation rate, rf
System lifetime, n (year)
Maintenance factor, φ
Operational hours in a year, τ (h)
Methanol cost ($/GJ)
12%
3%
20
1.06
5110
24.69
Therefore, four off-design strategies can be derived for the HT-PEMFC
turbine-less hybrid system. In strategy 1, the excess air coefficient is
held constant, and the system performance varies with the fuel cell
output power, which varies with the pressure ratio. In strategy 2, the
excess air coefficient is also held constant, while the difference is that the
fuel cell output power varies with the inlet air flow rate. In strategy 3,
the cathode air flow rate remains constant, and the fuel cell output
power varies with the pressure ratio. In strategy 4, the cathode air flow
rate also remains constant, but the fuel cell output power varies with the
inlet air flow rate.
6.2. Exergetic analysis results
The data results of the state points are shown in Table 9, including
mass flow rate, temperature, pressure, exergy flow rate, specific exer­
getic cost and exergetic cost rate. Table 10 displays the exergetic results
of all components used in the HT-PEMFC turbine-less hybrid system. The
output power for the HT-PEMFC is 94.37 kW. The required powers for
the compressor and blower are 93.66 kW and 0.72 kW, respectively.
Additionally, the required heat for the reformer is 36.91 kW from the
CAB. The released heat from the HT-PEMFC through the cooling chan­
nels is 56.19 kW. Most components have an exergy efficiency above
90%, while those with an exergy efficiency below this value include
82.18% for the HT-PEMFC, 74.64% for the burner, 69.80% for the CN
and 58.73% for the CAB. The highest irreversibility ratio is 32.91% to
operate the burner followed by 29.26% for the CN, then 23.75% for the
HT-PEMFC, and less than 10% for the rest. The components (the burner,
CN and HT-PEMFC) with a low exergy efficiency and a high irrevers­
ibility ratio need to be further developed, and the improvement of their
performance is of great significance to the performance of the whole
system.
The Sankey diagram for the exergy flow rates is shown in Fig. 5. The
air enters at an exergy rate of 4.05 kW and leaves the intake at the same
exergy rate. Furthermore, a portion of fuel enters the reformer at 8 with
a mass flow rate of 13.99 g/s and an exergy rate of 301.64 kW to be
reacted with water. The remaining fuel enters the burner at 16 with a
mass flow rate of 10 g/s and an exergy rate of 215.54 kW to be com­
busted with air which exits the HT-PEMFC. The exhaust flow of 10 has
the highest exergy flow of 314.44 kW. The exhaust gases exit the CN at
physical and kinetic exergy rates of 50.75 kW and 134.72 kW, respec­
tively, while the physical and kinetic exergy rates of the exhaust gases
discharged from the BN are 0.12 kW and 35.08 kW, respectively.
5. Model validation
Because the proposed system is a new one, and no data have been
published for it, validation is done for key subsystems such as the HTPEMFC and methanol reformer to ensure the validity of the developed
model for the whole system.
5.1. Validation for the HT-PEMFC
The HT-PEMFC model is validated against the experimental data [40,
45], as shown in Fig. 4. Fig. 4 (a) compares the predicted model voltage
and experimental data [40] under different operating temperatures. The
output voltages under different current densities are compared between
the simulation results and experimental results [45] in Fig. 4 (b). As can
be seen, a satisfactory agreement for the output voltage between the
simulation and experimental values from different sources, proving that
the HT-PEMFC model presents validated accuracies.
5.2. Validation for the methanol reformer
To verify the accuracy of the CEA method applied to analyze the
methanol reformer in this study, simulated data and experimental data
reported in the relevant literature [58,60,61] are employed. The com­
parison results are shown in Table 6. The simulated results obtained
from this work are very close to those presented in Refs. [58,60].
Comparing the simulated results with the experimental data, there is a
good agreement, except for a relatively large difference between the
molar fraction of CO obtained and the corresponding experimental data.
Considering the lower temperature for the reformer, this discrepancy
diminishes. Therefore, the accuracy of the methanol reformer model can
meet the requirements of system-level performance calculations.
6.3. Exergoeconomic analysis results
To conduct exergoeconomic analysis, it is first necessary to evaluate
the capital cost and annual levelized investment cost of components in
the HT-PEMFC turbine-less hybrid system, as shown in Table 11. Some
economic data are considered as follows: the nominal interest rate is
12%, the inflation rate is 3%, the system lifetime is 20 years, the
maintenance factor is 1.06, the annual operating hours of flight are
5110 h/year, and the methanol cost is 24.69 $/GJ. The highest cost is for
the HT-PEMFC which is 115,106 $ which increase to 179,447 $ because
of the maintenance and 2020 CEPCI (608). The total levelized invest­
ment cost of the HT-PEMFC turbine-less hybrid system is 4.4408 $/h. Of
all the components, the HT-PEMFC is the most critical because its annual
levelized investment cost is 4.0018 $/h, accounting for 90.11%.
In addition, the exergoeconomic results of components are shown in
Table 12. The total input exergetic cost rate is 181.10 $/h, while the
total output exergetic cost rate is 185.54 $/h, resulting in a total
destruction exergetic cost rate of 34.77 $/h. Thus, the overall specific
exergetic cost of input and output are 32.65 and 40.70 $/GJ,
6. Results and discussion
This section shows the results of thermodynamic, exergetic, and
exergoeconomic analyses for the HT-PEMFC turbine-less hybrid system.
Additionally, the effects of four off-design strategies are explained based
on these analyses.
6.1. Thermodynamic analysis results and comparison
Table 7 lists the design conditions of the HT-PEMFC turbine-less
hybrid system. The flight altitude is 10 km, and the flight Mach number
is 0.3. The inlet air flow rate and the compressor pressure ratio are 1 kg/s
7
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Fig. 3. Calculation process for the HT-PEMFC turbine-less hybrid system.
8
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Fig. 4. Validation of the HT-PEMFC model (p = 1 bar, DL = 5.6, RH = 3.8%).
Table 6
Validation of the model used for methanol steam reformer.
Molar
fraction
(%)
Simulated
data in
present study
SCR = 1.5, Trefo = 513 K
H2
74.70
CO
1.21
CO2
24.09
SCR = 1.5, Trefo = 533 K
H2
74.59
CO
1.63
CO2
23.78
Table 9
Stream data of the HT-PEMFC turbine-less hybrid system.
Simulated
data in
Ref. [58]
Simulated
data in
Ref. [60]
Experimental
data in Ref. [61]
74.69
1.21
24.09
74.69
1.21
24.1
70.1
0.172
24.4
74.59
1.63
23.77
74.61
1.63
23.78
71.6
0.365
24.8
Table 7
Design conditions of the HT-PEMFC turbine-less hybrid system.
Parameters
Values
Flight altitude, Alt (km)
Flight Mach number, Ma
Inlet air flow rate, ma (kg/s)
Compressor pressure ratio, πcomp
Fuel utilization, Uf
Current density, j (A/m2)
Recirculation ratio, Rrec
Reforming temperature, Trefo (K)
Fuel cell operating temperature, Tfc (K)
10
0.3
1
3
0.75
3000
0.5
523
473
Specific thrust, SFN (N/kg)
Specific fuel consumption, TSFC (g/
(kN⋅s))
Thermal efficiency, ηther (%)
Propulsive efficiency, ηprop (%)
Overall efficiency, ηover (%)
Turbojet
488.04
49.16
488.04
65.46
36.67
26.51
9.72
24.79
27.79
6.89
m (g/s)
T (K)
p (bar)
Ex (kW)
c ($/GJ)
C ($/h)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1000
1000
1000
11.92
11.92
11.89
23.81
13.99
11.78
25.78
23.85
561.80
563.73
11.92
575.66
10.00
609.47
609.47
426.31
426.31
223.15
227.16
319.81
473.15
511.68
319.81
627.16
298.15
298.15
523.15
473.15
319.81
473.15
473.15
473.15
298.15
840.24
464.04
319.81
234.56
0.2644
0.2814
0.8442
0.8273
1.0540
0.8442
0.8273
0.8442
0.8442
0.8273
0.8273
0.8442
0.8273
0.8273
0.8273
0.8273
0.8190
0.2644
0.8442
0.2644
4.05
4.05
91.23
42.80
43.43
1.08
6.78
301.64
1.64
314.44
85.59
51.25
90.89
42.80
133.70
215.54
265.73
185.47
38.89
35.20
0.00
0.00
50.23
23.89
24.37
50.23
160.69
24.69
0.00
23.89
23.89
50.23
50.23
23.89
41.80
24.69
45.34
64.97
50.23
55.51
0.00
0.00
16.50
3.68
3.81
0.20
3.92
26.81
0.00
27.04
7.36
9.27
16.44
3.68
20.12
19.16
43.38
43.38
7.03
7.03
Fig. 7 illustrates the Sankey diagram for the exergoeconomic flow
rates. The inlet air at 1 is free. Additionally, the inlet water at 9 is free.
The exergoeconomic flow rates of fuel methanol at 8 and 16 are 26.81
and 19.16 $/h, respectively. The highest exergoeconomic flow rate is
43.38 $/h to exit the burner due to the high exergetic cost rates of the
inlet gases. The exergetic cost rates of the input power are 16.39 $/h for
the compressor, and 0.13 $/h for the blower, while the exergetic cost
rate of the output power is 16.52 $/h for the HT-PEMFC. The exhaust
gases at the CN and BN are 11.87 $/h for physical exergy rate and 31.51
$/h for kinetic exergy rate, and 0.02 $/h for physical exergy rate and
7.01 $/h for kinetic exergy rate, respectively.
Table 8
Performance parameters and comparison of the HT-PEMFC turbine-less hybrid
system and turbojet.
HT-PEMFC turbine-less hybrid
system
No.
6.4. Off-design analysis results
This section discusses the impact of the off-design strategies 1 to 4 on
thermodynamic performance, exergetic performance, and exer­
goeconomic performance. A comparison of output results for the four
off-design strategies is also performed.
Fig. 8 (a) shows the operating temperature for HT-PEMFC and inlet
fuel flow rate for burner. The operating temperature range of the HTPEMFC studied in this paper is 373–473 K. In this study, the design
operating temperature of the HT-PEMFC is set to the maximum tem­
perature of 473 K. When the HT-PEMFC output power is lower than the
design power, the HT-PEMFC operating temperature is reduced due to
the reduction of heat release, while the inlet fuel flow rate for the burner
is set to be constant. When the HT-PEMFC output power is higher than
respectively. The HT-PEMFC turbine-less hybrid system has an exer­
goeconomic factor of 11.32% and a relative cost difference of 24.65%.
The highest exergoeconomic factor is 38.21% to operate the HT-PEMFC
followed by 33.08% for the blower, and less than 10% for the rest. The
highest relative cost difference is 73.45% to operate the CAB followed by
43.28% for the CN, then 35.09% for the HT-PEMFC, and 34.53% for the
burner. Finally, the CO2 mass specific emissions and total system cost are
2.70 kg/(kW⋅h) and 82.50 $/h, respectively. Fig. 6 illustrates the
composition and share of the total system cost.
9
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Table 10
Exergetic results of components in the HT-PEMFC turbine-less hybrid system.
Component
Wj (kW)
Qj (kW)
ExI (kW)
ExO (kW)
ExD (kW)
ψ (%)
y (%)
Intake
Compressor
Blower
CAB
Reformer
HT-PEMFC
Burner
CN
BN
0
93.66
0.72
0
0
94.37
0
0
0
0
0
0
36.91
36.91
56.19
0
0
0
4.05
97.71
43.51
44.52
324.44
365.69
356.02
265.73
38.89
4.05
91.23
43.43
26.15
314.44
300.53
265.73
185.47
35.20
0
6.48
0.08
18.37
10.01
65.16
90.29
80.26
3.70
100
93.37
99.81
58.73
96.91
82.18
74.64
69.80
90.49
0.00
2.36
0.03
6.70
3.65
23.75
32.91
29.26
1.35
Fig. 5. Sankey diagram for the exergy flow rates [kW].
than the design power, strategy 1 achieves a higher SFN with a lower
TSFC, as opposed to strategy 4.
Fig. 8 (c) displays the total exergy rates for input, output, and
destruction. When the output power is lower than the design power, the
total exergy rates of input, output, and destruction are relatively close
despite changing the strategies. When the output power is higher than
the design, strategy 3 has the maximum total exergy rates of input,
output, and destruction, followed by strategy 4, then strategy 1, and
finally strategy 2. The ratio of total output exergy to total input exergy,
and exergy efficiency of the whole system are shown in Fig. 8 (d). These
two parameters have maximum values at the design point. When the
output power is lower than the design power, the two parameters in­
crease monotonically and are relatively close under different strategies.
The values of these two parameters decrease when the output power is
higher than the design power. In particular, the ratio of total output
exergy to total input exergy for strategy 4 shows a different trend at the
end, because there is an excess of fuel in the burner.
Fig. 8 (e) illustrates the total exergoeconomic rates for input, output,
and destruction. The strategies are ranked from largest to smallest, like
the total exergy rates. However, the total exergoeconomic rate of output
is slightly higher than that of input. Additionally, the total exer­
goeconomic rate of destruction is much smaller than that of input and
Table 11
Capital cost and annual levelized investment cost of components in the HTPEMFC turbine-less hybrid system.
Component
Cj ($)
Zp,j ($)
Zj ($/h)
Intake
Compressor
Blower
CAB
Reformer
HT-PEMFC
Burner
CN
BN
Total
0
3158
101
2590
2586
115,106
5307
0
0
128,848
0
4776
156
3365
3360
179,447
8027
0
0
199,131
0
0.1065
0.0035
0.0751
0.0749
4.0018
0.1790
0
0
4.4408
the design power, the fuel must be increased to absorb excess heat and
prevent the HT-PEMFC from overheating due to increased heat release.
The highest variations of these two parameters are in strategy 3 followed
by strategy 4, then strategy 1, and finally strategy 2. The specific thrust
SFN and specific fuel consumption TSFC are shown in Fig. 8 (b). When
the output power is lower than the design power, strategies 2 and 4 have
much higher SFNs with similar TSFCs. When the output power is higher
Table 12
Exergoeconomic results of components in the HT-PEMFC turbine-less hybrid system.
Component
CW
j ($/h)
CQ
j ($/h)
CI ($/h)
CO ($/h)
CD ($/h)
cI ($/GJ)
cO ($/GJ)
f (%)
r (%)
Intake
Compressor
Blower
CAB
Reformer
HT-PEMFC
Burner
CN
BN
Total
0
16.39
0.13
0
0
16.52
0
0
0
–
0
0
0
0.16
0.16
0
0
0
0
–
0
16.39
3.81
4.01
26.97
36.31
43.20
43.38
7.03
181.10
0
16.50
3.81
4.08
27.04
40.32
43.38
43.38
7.03
185.54
0
1.09
0.01
1.65
0.83
6.47
10.96
13.10
0.67
34.77
0
46.60
24.30
25.00
23.09
27.58
33.70
45.34
50.23
32.65
0
50.23
24.37
43.36
23.89
37.26
45.34
64.97
55.51
40.70
–
8.93
33.08
4.34
8.26
38.21
1.61
0
0
11.32
–
7.80
0.28
73.45
3.47
35.09
34.53
43.28
10.51
24.65
10
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power under the different strategies. The CO2 mass specific emissions
and total system cost are shown in Fig. 8 (h). When the output power is
less than the design power, the CO2 mass specific emissions and total
system cost are relatively close, despite changing the strategies. When
the output power is greater than the design power, strategy 3 has the
greatest CO2 mass specific emissions and total system cost, followed by
strategy 4, then strategy 1, and finally strategy 2. Notably, the total fuel
cost accounts for approximately half of the total system cost.
7. Conclusion
This study proposes a HT-PEMFC turbine-less hybrid system for low
pressure ratio and Mach number aircraft. Additionally, the performance
evaluation and off-design strategy of the HT-PEMFC turbine-less hybrid
system are investigated based on three key types of analyses: thermo­
dynamic, exergetic, and exergoeconomic using methanol fuel. The
following conclusions can be drawn:
● Compared to the turbojet, the HT-PEMFC turbine-less hybrid system
has advantages in specific fuel consumption, thermal efficiency and
overall efficiency, and only slightly lags in propulsive efficiency. The
HT-PEMFC turbine-less hybrid system reduces the specific fuel con­
sumption by 24.90%.
● The components (the burner, CN and HT-PEMFC) with a low exergy
efficiency and a high irreversibility ratio need to be further devel­
oped, and the improvement of their performance is of great signifi­
cance to the performance of the whole system.
● Some fuel enters the reformer at 8 with a mass flow rate of 13.99 g/s
and an exergy rate of 301.64 kW to be reacted with water. The rest of
the fuel enters the burner at 16 with a mass flow rate of 10 g/s and an
exergy rate of 215.54 kW to be combusted with air which exits the
HT-PEMFC. The exhaust flow of 10 has the highest exergy flow of
314.44 kW.
● The total levelized investment cost of the HT-PEMFC turbine-less
hybrid system is 4.4408 $/h. Of all the components, the HT-PEMFC is
the most critical because its annual levelized investment cost is
4.0018 $/h, accounting for 90.11%.
● The total input exergetic cost rate is 181.10 $/h, while the total
output exergetic cost rate is 185.54 $/h, resulting in a total
destruction exergetic cost rate of 34.77 $/h. Thus, the overall specific
exergetic cost of input and output are 32.65 and 40.70 $/GJ,
respectively. The HT-PEMFC turbine-less hybrid system has an
exergoeconomic factor of 11.32% and a relative cost difference of
24.65%. The CO2 mass specific emissions and total system cost are
2.70 kg/(kW⋅h) and 82.50 $/h, respectively.
● System performance tends to be significantly different for HT-PEMFC
output powers below and above the design power, even under the
same strategy. Strategy 2 is an economic option, because it produces
the minimum of specific fuel consumption, CO2 mass specific
Fig. 6. Composition and share of the total system cost.
output. The overall specific exergetic cost of input and output are pre­
sented in Fig. 8 (f). The overall specific exergetic costs of input for
strategies 1 and 2 have a maximum value at the design output power,
while those for strategies 3 and 4 decrease monotonically over the range
of output powers studied. However, the overall specific exergetic costs
of output for strategies 1–4 all have a minimum value at the design
output power. When there is excess fuel in the burner, the overall spe­
cific exergetic cost of output decreases rapidly. As shown in Eqs. (47)
and (48), the overall specific exergetic costs are related to the total
exergoeconomic rates and the total exergy rates. Compared with the
other three strategies, strategy 3 has the highest inlet fuel flow rate for
the burner. After 120 kW for strategy 3, there is excess fuel in the burner
and some fuel is not utilized, resulting in an accelerated increase in the
total exergy rate of output. However, the total exergoeconomic rates of
input and output, and total exergy rate of input increase at a uniform
rate, respectively. Thus, the overall specific exergetic cost of input drops
sharply after 120 kW for strategy 3, while the overall specific exergetic
cost of output still decreases at a uniform rate. The exergoeconomic
factor and relative cost difference are demonstrated in Fig. 8 (g). The
exergoeconomic factor is a maximum in the design output power despite
changing the strategies. The HT-PEMFC turbine-less hybrid system has
the highest exergoeconomic factors to implement strategy 2, followed by
strategy 1, then strategy 4, and finally strategy 3. It shows that in
strategy 2, the total exergoeconomic rate of destruction for the system is
the smallest relative to the total annual levelized investment cost.
However, the relative cost difference is a minimum in the design output
Fig. 7. Sankey diagram for the exergoeconomic flow rates [$/h].
11
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Fig. 8. Off-design analysis results.
emissions and total system cost, as well as the maximum of system
exergy efficiency.
● Compared to turbojet engines, the HT-PEMFC turbine-less hybrid
system has a heavier mass, which is one of the characteristics of
electric propulsion systems. However, due to its advantage of low
12
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Fig. 8. (continued).
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Journal of Power Sources 562 (2023) 232752
Fig. 8. (continued).
fuel consumption rate, it is still very attractive for aircraft with a
flight time of over 2 h.
Acknowledgments
This work was supported by the National Natural Science Foundation
of China (No. 52076051). The authors thank the reviewers for their
valuable advice on this paper.
CRediT authorship contribution statement
Fafu Guo: Conceptualization, Methodology, Software, Validation,
Formal analysis, Investigation, Writing – original draft, Visualization.
Xinyan Xiu: Investigation, Writing – review & editing. Chenghao Li:
Investigation, Data curation. Kunlin Cheng: Software, Validation.
Jiang Qin: Resources, Writing – review & editing, Supervision.
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Data availability
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