Energy Conversion and Management 217 (2020) 112998
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Energy Conversion and Management
journal homepage: www.elsevier.com/locate/enconman
Thermodynamic modeling and analysis of a novel PEMFC-ORC combined
power system
T
Guokun Liua, Yanzhou Qina, , Jianchao Wangb, Can Liua,c, Yifan Yina,c, Jian Zhaod, Yan Yina,
Junfeng Zhanga, Obed Nenyi Otooa
⁎
a
State Key Laboratory of Engines, Tianjin University, Tianjin, China
Tianjin Internal Combustion Engine Research Institute, Tianjin, China
c
School of Automotive Studies, Tongji University, Shanghai, China
d
Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, Canada
b
A R T I C LE I N FO
A B S T R A C T
Keywords:
PEMFC
ORC
Cooling system
Waster heat recovery
Thermodynamic modeling
Exergy analysis
In this study, a novel proton exchange membrane fuel cell (PEMFC) system is proposed, which uses organic
working fluid to cool the fuel cell stack directly and recovers the waste heat by combining with an Organic
Rankine Cycle (ORC) system. A thermodynamic model of each component and subsystem is established for the
combined PEMFC-ORC system. The influence of the PEMFC stack inlet temperature and current density, the ORC
working fluid, superheat temperature and saturation pressure on the system performance is studied. The flow
and distribution of energy and exergy in the whole PEMFC-ORC system are analyzed comprehensively. It is
found that the system performance indicators reach the optimum when the stack inlet temperature is about
343.15 K. Lower current density improves the system efficiency, but reduces the system power density. R245fa
shows the best performance among the five organic working fluids investigated for the designed ORC system.
Higher superheat temperature and saturation pressure of the organic working fluid in the cycle improves the
ORC efficiency. The PEMFC stack has the largest exergy loss in the system, and the cathode side heater and air
compressor also contribute much to the large power and exergy loss. The optimization of these components
should be the focus of system performance improvement.
1. Introduction
Fuel cell is recognized as a promising technology in the context of
decreasing oil resource consumption and greenhouse gas emissions. As
the most popular type of fuel cell, proton exchange membrane fuel cell
(PEMFC) has some key advantages such as low operating temperature,
high power density and long operating life [1]. There have been a lot of
researches on PEMFC in recent years, and most of them are focused on
the key components of the PEMFC stack, such as the cooling plate [2],
gas flow channel [3,4], microporous layers [5,6] and bipolar plates [7].
As many fundamental technical obstacles overcoming, the PEMFC becomes viable for many applications and is being commercialized [8,9].
The PEMFC stack needs equipping with a series of auxiliary
equipment during the operation, such as air compressor, humidifier,
heat exchanger, hydrogen recirculating device, to form a complete
power system. All these auxiliary equipment in the system consume a
considerable amount of power and reduce the overall system efficiency
[10]. Besides, the waste heat generated by the PEMFC stack is nearly
⁎
equal to its power output under normal operating operations, so the
electric efficiency of vehicular PEMFC stack is usually limited to 50%.
Therefore, the recovery and utilization of the PEMFC stack’s waste heat
has great potential to improve the efficiency of the PEMFC system [11].
There are some researches on waste heat recovery of fuel cells and the
most common method is through combined heat and power (CHP)
systems. Kwan et al. [12] applied a thermoelectric generator (TEG) to
the PEMFC system and made an optimization investigation based on the
genetic algorithm. Hwang et al. [13,14] integrated a novel heat recovery unit into a PEMFC cogeneration system, and the maximum efficiency of the proposed CHP system is near 81% according to their
results. Shabani et al. [15] experimentally studied the potential of extracting thermal energy and electric energy from PEMFC, and improved
the economy of providing energy for remote homes by using computer
simulation. Chen et al. [16] proposed a combined cooling, heating and
power system (CCHP) of PEMFC, which can provide electric power,
space heating/cooling and hot water for apartment simultaneously, and
carried out a multi-criteria assessment study on it. Guo et al. [17]
Corresponding author.
E-mail address: qinyanzhou@tju.edu.cn (Y. Qin).
https://doi.org/10.1016/j.enconman.2020.112998
Received 5 February 2020; Received in revised form 3 May 2020; Accepted 17 May 2020
0196-8904/ © 2020 Elsevier Ltd. All rights reserved.
Energy Conversion and Management 217 (2020) 112998
G. Liu, et al.
Nomenclature
A
Cp
e
Ex
F
g
h
H
I
J
∙
m
M
N
P
Q
RH
S
s
T
V
W
1,2,i
a
ac
ah
air
ave
c
cnd
ch
e
H2
hc
in
loss
net
orc
O2
out
output
p
Q, q
stack
system
tn
v
w
Effective working area, cm2
Specific heat at constant pressure, J kg−1 K−1
Specific exergy, J kg−1
Exergy, W
Faraday constant, C mol−1
Mass fraction
Specific enthalpy, J kg−1
Enthalpy, J
Current, A
Current density, A cm−2
Mass flow rate, kg s−1
Relative molecular mass, kg mol−1
Number of single cells
Pressure, Pa
Heat, J
Relative humidity
Stoichiometric ratio
Specific entropy, J kg−1 K−1
Temperature, K
Voltage, V
Power, W
Greek letters
γ
η
χ
Adiabatic coefficient
Isentropic efficiency
Mole fraction
Superscripts
ch
ph
Subscripts
0
Indexes
Anode
Air compressor
Anode side heater
Air
Average
Cathode
Condenser
Cathode side heater
Expander
Hydrogen
Hydrogen circulating compressor
Inlet
Loss
Net
Organic Rankine Cycle
Oxygen
Outlet
Output
Pump
Heat
PEMFC stack
System
Thermoneutral
Vapor
Work
Chemical
Physical
Ambient condition
challenges in its waste heat recovery and conversion to electric power.
The Organic Rankine Cycle (ORC) system has an excellent performance
in recovering and utilizing low-temperature waste heat to produce
electricity. It has wide usage in the generation of seawater temperature
difference power, geothermal power plant and recycling of energy from
heat engine exhaust gas [18,19]. Wang et al. [20] studied the
proposed a new general model of an integrated system consisting of a
high-temperature PEMFC, a regenerator and an absorption cycle for
waste heat recovery which can be functioned as either an absorption
heat pump for heating or an absorption refrigerator for cooling.
However, due to the low operating temperature and design requirement of the PEMFC stack, there are still numerous technical
Fig. 1. Schematic of a typical ORC system applied for PEMFC [26].
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Energy Conversion and Management 217 (2020) 112998
G. Liu, et al.
both the “quantity” and “quality” of energy and provide more reference
indexes for performing fuel cell system analysis [28,29]. Therefore,
energy and exergy analysis should be both used for the system performance analysis to achieve a more comprehensive understanding of the
influence of the system design and operating parameters. In addition,
the effectiveness of heat transfer between the cooling water and organic
working fluid is still poor in the conventional ORC system. The volume
of heat exchanger has to be large to solve this problem, which accounts
for a large amount of investment cost and makes it difficult for the
organic working fluid to reach enough temperature.
In this study, a novel design of PEMFC-ORC system is proposed, in
which the ORC working fluid is used to cool the PEMFC stack and absorb heat generated by PEMFC directly, rather than from the cooling
water of the conventional PEMFC-ORC system shown in Fig. 1. This
novel design is expected to achieve more efficient heat exchange between PEMFC and ORC system, as well as a simpler system structure. It
also considers waste heat recovery from the PEMFC cathode exhaust
gases through water/heat exchangers. The thermodynamic model of the
PEMFC-ORC system is established, and the combined energy and exergy
analysis methods are established. By varying the operating parameters
of the PEMFC-ORC system, the system performance is analyzed, the
system optimization scheme is proposed and the future direction of
PEMFC-ORC system research and design is pointed out.
thermodynamic properties and environmental influence of 9 different
organic working fluids based on ORC to recover low-grade waste heat,
and selection of the best working ORC fluid to achieve optimal control
of ORC. Gao et al. [21] analyzed the influence of different working
fluids on supercritical ORC efficiency based on the values of net power
output, exergy efficiency, thermal efficiency and other indexes. Ebrahimi et al. [22] combined with the characteristics of solid oxide fuel cell
(SOFC), micro gas turbine and ORC in the SOFC system. They used ORC
for waste heat recovery and studied the ORC cycle efficiency by
changing design parameters. The ORC system has been successfully
used for waste heat recovery in SOFCs [23,24] and molten carbonate
fuel cells [25], hence it is recognized as a feasible method to recover
and utilize waste heat of PEMFC to improve the system efficiency.
However, there are few studies on the use of ORC in waste heat recovery of low-temperature PEMFC. A typical ORC system applied for
PEMFC is described in Fig. 1. The heat generated by PEMFC is firstly
absorbed by the cooling water, and an evaporator is needed to transfer
the heat from cooling water to the ORC working fluid.
Zhao et al. [27] carried out a parametric analysis of a PEMFC-ORC
hybrid power system and some meaningful results were obtained.
However, the power consumption of the PEMFC’s auxiliary equipment
is not included in their model, and only the conventional energy analysis method is applied. Different from the conventional energy analysis
method studying the energy’s “quantity” distribution in the system, the
exergy analysis based on the second law of thermodynamics can reflect
Fig. 2. Schematic of the proposed PEMFC-ORC system (AC: air compressor; EX: water/heat exchanger; HE: heater; HU: humidifier; HC: hydrogen circulating
compressor; E: expander; C: condenser; P: pump; G: generator).
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Energy Conversion and Management 217 (2020) 112998
G. Liu, et al.
2. System description
3. Thermodynamic model
The schematic of the PEMFC-ORC system investigated is shown in
Fig. 2. The arrows represent the direction of fluid flow in the system and
the numbers in the circle represent a state of the fluid. This PEMFC
system uses hydrogen and air as anode fuel and cathode oxidizer, respectively, and it mainly includes water/heat exchanger, heater, humidifier, hydrogen circulating compressor and air compressor. And
other pieces of auxiliary equipment that have little influence on the
thermodynamic analysis are not shown in the diagram.
To provide sufficient reaction fuels for the cells, the amount of
hydrogen supplied to the anode should be larger than the actual reaction requirement. The excessive wet hydrogen at the anode outlet is
recovered by a hydrogen recirculating compressor and remixed with
the fresh hydrogen, which can not only improve the fuel utilization
efficiency but also play a certain role in heating and humidifying the
fresh hydrogen. To ensure that the fuel cell stack operates under appropriate conditions, the hydrogen and air are usually preheated and
humidified before entering the fuel cell stack. This system adopts the
method of external spray humidification, i.e., a humidifier is set outside
the fuel cell stack to inject liquid water mist into the gas. Electric heater
is adopted to heat the incoming gases before entering the humidifier.
The exhaust air of cathode has a higher temperature and relative humidity, the waste energy is recycled to elevate the temperature and
relative humidity of the input gases through water/heat exchanger, as
shown in Fig. 2. The water/heat exchanger can be a porous plate,
permeable film or enthalpy wheel.
The biggest challenge to apply the ORC system in practice is to
balance its cost and benefit. The evaporator has to be large to ensure the
heat transfer efficiency between the cooling water and organic working
fluid in the conventional ORC system. Still, it would increase the
amount of investment cost. On the other hand, the relatively complex
system structure with many apparatuses also greatly affects the system
cost and reliability. In order to simplify the system and improve the
heat transfer efficiency, the cooling water system and evaporator are
eliminated in this novel PEMFC-ORC hybrid system. The ORC organic
working fluid is directly fed into the cooling passage of the PEMFC stack
to cool the fuel cell stack and meanwhile absorb heat. Because the organic working fluid mainly goes through a phase-change heat transfer
process in the cooling passage, it can not only directly and efficiently
absorb the heat from the stack, but also help to maintain the uniformity
of the temperature in the stack, which is beneficial to the PEMFC stack
performance.
The following assumptions are made to simplify the analysis of the
system.
3.1. PEMFC stack
The PEMFC stack performance is obtained from a validated PEMFC
stack model based on our previous study with the same design and
operating parameters [32]. Given the working current density, the individual cell voltages can be obtained. Then, the electric power output
of the stack is:
Wstack = N ·Vave·J ·A
(1)
where N is the number of single cells, Vave is the average output voltage
of single cells, J is the current density of the stack and A is the effective
working area of a single cell.
The heat generated by the fuel cell stack is expressed as:
Qstack = N ·(Vtn − Vave )·J ·A
(2)
where Vtn is the thermoneutral voltage of PEMFC, and its value is
1.482 V.
The hydrogen mass flow rate required in the operation of the fuel
cell stack can be obtained by:
∙
m = Sa·MH2·
H2
N ·A·J
N ·I
= Sa·MH2·
2F
2F
(3)
whereF is the Faraday constant, and the value is 96,350 C mol−1. Sa is
the anode stoichiometric ratio. Similarly, the air mass flow rate required by the stack can be obtained by:
∙
∙
m=
air
mO 2
n·A·J
n·I
= Sc ·MO2·
= Sc ·MO2·
4F ·gO2
4F ·gO2
gO2
(4)
where gO2 is the mass fraction of oxygen in the air, Sc is the cathode
stoichiometric ratio.
3.2. Auxiliary equipment
The hydrogen circulating compressor is adopted to recover excessive hydrogen from the anode and pressurize it to reach the stack
inlet pressure. The air is from the environment and pressurized by the
air compressor to reach the stack inlet pressure. The thermodynamic
processes of hydrogen circulating compressor and air compressor are
basically the same, they both consume power for the gas compression,
and can be recognized as isentropic compression processes. The power
consumed by hydrogen circulating compressor and air compressor is,
respectively, expressed as:
∙
Whc =
(1) All the equipment in the system are in steady-state, and the heat
loss and pressure loss are neglected.
(2) The ambient air temperature is 298.15 K, the pressure is 101 kPa
and the relative humidity is 50%.
(3) The temperature difference of the gases between the inlet and outlet
of the stack is 5 K and the relative humidity of the air at the cathode
outlet is 100%.
(4) The isentropic efficiency of the air compressor, hydrogen circulating compressor, expander and ORC fluid pump is 78%, 78%, 85%
and 85%, respectively [30].
(5) The humidity of the hydrogen or air at the outlet of the water/heat
exchanger is 95% and the temperature is 5 K lower than the exhaust
air [31].
(6) The temperature of fresh hydrogen entering the system is 298.15 K
and the pressure is the same with the stack inlet pressure.
γ−1
m6 Cp,6 T6 ⎛ P7 γ
⎞
− 1⎟
⎜ P6
ηhc
⎝
⎠
∙
Wac =
(5)
γ−1
m8 Cp,8 T8 ⎛ P9 γ
⎞
− 1⎟
⎜ P8
ηac
⎠
⎝
(6)
where Cp is the specific heat at constant pressure, ηhc and ηac are the
isentropic efficiency of hydrogen circulating compressor and air compressor, respectively, P and T are the pressure and temperature of the
gas, respectively. The numbers of subscripts correspond to the state of
the fluid in the system block diagram as described above.
After pressurized by hydrogen circulating compressor or air compressor, the temperature of the gas is:
p
T7 = T6·⎛⎜ 7 ⎞⎟
⎝ p6 ⎠
p
T9 = T8·⎜⎛ 9 ⎞⎟
⎝ p8 ⎠
γ−1
γ
(7)
γ−1
γ
(8)
The unconsumed hydrogen recovered by the hydrogen circulating
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Energy Conversion and Management 217 (2020) 112998
G. Liu, et al.
operating temperature of the stack. This thermodynamic process is similar to the mixing process of hydrogen, which is assumed to be
adiabatic condition and follows the energy conservation. For the humidifier of anode side:
∙
∙
∙
m4 Cp,4 T4 + m19 Cp,19 T19 = m5 Cp,5 T5
(18)
For the humidifier of cathode side:
∙
∙
∙
m11 Cp,11 T11 + m20 Cp,20 T20 = m12 Cp,12 T12
(19)
The power consumption of the heaters on the anode and cathode
sides can be calculated according to energy conservation. For the heater
of anode side:
∙
Wah = mCp,3 (T4 − T3)
3
Fig. 3. Ideal ORC cycle temperature-entropy diagram.
(20)
For the heater of cathode side:
∙
compressor is mixed with the fresh hydrogen. The heat loss is neglected
and the gas pressure before and after mixing remains unchanged. Hence
the process is considered to be a constant pressure and adiabatic process. According to the conservation of energy, the mixed gas temperature is:
∙
T2 =
Wch = mCp,10 (T11 − T10)
10
3.3. ORC system
∙
(m1 Cp,1 T1 + m7 Cp,7 T7 )
∙
m2 Cp,2
The temperature-entropy diagram of an ideal ORC cycle is shown in
Fig. 3. The numbers correspond to the state of fluids in the system
schematic diagram. Process 24-21 is the heat absorption process of the
working fluid under constant pressure condition. The organic working
fluid fully absorbs heat in the stack’s cooling passage, gradually evaporates from the liquid state, and finally flows out of the stack in the
form of superheated steam. Process 21-22 is the isentropic expansion
process. The superheated organic working fluid steam enters the expander driving the generator to generate electricity. Process 22-23 is an
isobaric condensation process. The organic working fluid is gradually
liquefied from the superheated steam state and finally reaches the saturated liquid state. Process 23-24 is an isentropic compression process.
The pump pressurizes the working fluid to the required pressure.
In the calculation, it is assumed that the superheat temperature of
the organic working fluid is 5 K, and the condensation temperature is
298.15 K. Since Process 24-21 and Process 22-23 are isobaric and
Process 21-22 and Process 23-24 are isentropic, the relationship of
pressure and entropy of the organic fluid can be expressed as:
(9)
The water/heat exchangers shown in Fig. 2 allow the transfer of
water and heat between the wet waste air and the dry intake gases, and
consume little or no power. The process of heat transfer is similar to an
adverse current heat exchanger. The relative humidity of hydrogen or
air at the outlet of the water/heat exchangers is 95% and the temperature is 5 K lower than the exhaust air according to the assumptions,
which can be expressed as:
RH3 = RH10 = 0.95
(10)
T3 = T10 = T13 − 5K
(11)
The heat and mass transfer process in water/heat exchangers is
adiabatic, so there is no heat loss, and the enthalpy of the inlet gases is
equal to that of the outlet gases.
For water/heat exchanger of anode side:
H2 + H16 = H3 + H17
(12)
For water/heat exchanger of cathode side:
H9 + H14 = H15 + H10
(21)
(13)
In the calculation, it needs to assume the temperature of the exhaust
air flowing out of the water/heat exchangers (T15, T17), and use the
iteration method to obtain the correct temperature values based on the
above relationships. The results need further verification: the temperature and water content of the moist hot gas should be higher than
the dry cold gas, to ensure of the correct heat and water transfer direction in the water/heat exchanger:
p21 = p24
(22)
p22 = p23
(23)
S21 = S22
(24)
S23 = S24
(25)
Compared with the conventional ORC system, the fuel cell stack of
this system replaces the evaporator and directly provides heat for the
organic working fluid. That way the organic working fluid directly
absorbs heat from the fuel cell rather than the cooling water realizing
more direct and efficient heat absorption. Assuming that the heat
generated by the stack is completely absorbed by the organic working
fluid, the flow rate of the organic working fluid can be obtained:
T17 ⩾ T2
(14)
T15 ⩾ T9
(15)
χv,17 ⩾ χv,2
(16)
orc
χv,15 ⩾ χv,9
(17)
where h is the specific enthalpy of the organic working fluid. Thermal
energy is converted into mechanical energy in the expander. It is necessary to ensure that the organic fluid comes out of the expander in an
overheated state to prevent damage to impellers. The output power of
the steam expander is:
∙
m=
where χv is the mole fraction of water vapor in the gas. If the results do
not meet this condition, it indicates that the guessed temperatures are
wrong, and it is necessary to re-assume the gas temperatures at the
outlet of the water/heat exchanger.
Spray humidification is adopted in the system, and water mist is
injected into the inlet gas after the heating. The water mist is vaporized
and mixed with the gas to reach the required inlet humidity. The
temperature of humidified gases should be exactly the required
Qstack
(h21 − h24 )
(26)
∙
We = m ·(h21 − h22)·ηe
orc
(27)
where ηe is the isentropic efficiency of the expander. The working
fluid changes from a gaseous state to a liquid state in the condenser, and
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Energy Conversion and Management 217 (2020) 112998
G. Liu, et al.
the heat dissipates into the environment. The heat ejected from the
organic working fluid to the environment is:
Table 1
Standard molar chemical exergy of several substances [30].
∙
Qcnd = m (h22 − h23)
orc
The isentropic compression process of organic working fluid occurs
in the pump, and the organic fluid pressure increases. The power consumed by the pump is:
Wp =
∙
morc (h24 − h23 )
ηp
Substances
Standard chemical exergy (kJ kmol−1)
H2
O2
N2
CO2
H2O (vapor)
Else components in dry air
H2O (liquid)
R245fa
236,100
3948
693
20,108
9500
11,649
900
1062
(28)
(29)
where ηp is the isentropic efficiency of the ORC fluid pump.
The net output work of ORC system is:
Worc = We − Wp
⎡
T
e ph = CP T0 ⎢
T
⎢ 0
(30)
⎣
The thermal efficiency of ORC cycle is:
ηorc =
We − Wp
Worc
=
Qstack
Qstack
(31)
e ch =
(37)
∑ χn ·ench Mn + RT0 ∑ χn ·ln χn
M
(38)
(39)
3.5. Performance indicators
Based on the thermodynamic modeling and exergy analysis, many
parameters of the PEMFC-ORC system can be obtained, of which the net
system output power, energy efficiency, exergy loss, exergy efficiency
and ecological function are selected as evaluation indexes of system
performance.
The sum of the power output of fuel cell stack and ORC system is the
total power output of the system, and the power consumed by auxiliary
equipment (air compressor, hydrogen circulating compressor, anode
side heater, cathode side heater) should be deducted. The net output
power of the system can be expressed as:
(32)
Wnet , system = Wstack + Worc − Whc − Wac − Wah − Wch
(40)
The net output power of the system reflects the system's ability to
provide external power under certain operating conditions, and is an
important indicator for system performance evaluation.
The energy efficiency reflects the system’s ability to make full use of
fuel energy. The higher the energy efficiency is, the more energy converted by the system under the same hydrogen consumption, the more
energy saved by the system. The energy efficiency of the system can be
expressed as:
(33)
(34)
(35)
ηenergy =
The kinetic energy and potential energy are neglected.
The specific physical exergy of fluid can be expressed as follows:
e ph = (h − h 0) − T0 (s − s0)
⎥
⎥
⎦
where Ex , in and Ex , out are the mass flow exergy of incoming and outgoing fluids, Woutput and Ex , heat are the output work (power) and the
exergy of heat and Ex , loss is the exergy loss.
where e is the specific exergy of fluid, and it is the sum of specific
physical exergy and specific chemical exergy of fluid:
e = e ch + e ph
⎟
Ex , in = Ex , out + Woutput + Ex , heat + Ex , loss
The mass flow exergy of fluid can be calculated as:
∙
⎜
exergy of the component, Mn and M are the relative molecular mass of
the component and the relative molecular mass of the mixture, respectively. The standard chemical exergy of several substances is shown
in Table 1:
For a certain thermodynamic process in the system, the exergy
balance equation is:
The exergy of heat can be deduced from the Carnot cycle. If a Carnot
engine works between a heat source with the high-temperature T and
the environment with the low-temperature T0, and the heat absorbed
from the heat source is Q and the output work is W, then the exergy of
this heat source is:
Ex = m · e
⎟
where χn is the mole fraction of a component, ench the standard chemical
In order to completely evaluate the thermodynamic performance of
the PEMFC-ORC system, the exergy analysis is necessary to be applied
based on the second law of thermodynamics. When a completely reversible change (heat transfer, mass transfer, chemical reaction, etc.)
takes place between a given form of energy or a given state of a substance and the environment, and finally it is in complete equilibrium
with the environment, the work done by this process is exergy. The
exergy can be expressed as Ex. In exergy analysis, a standard environmental state should be defined first. In this study, the standard environmental state is set as 298.15 K and 101 kPa.
As defined above, exergy belongs to energy or matter, so it is divided into energy flow exergy and mass flow exergy. In this system,
energy exists in the form of heat and work, so there are exergy of heat
and exergy of work. The exergy of mass flow can be divided into
physical exergy and chemical exergy, which respectively reflect the
imbalance of physical state and chemical composition between the fluid
and the environment.
According to the definition of exergy, the exergy of work is equal to
the work itself:
T
Ex , q = W = ⎛1 − 0 ⎞ Q
T⎠
⎝
⎜
γ−1
γ ⎤
Chemical exergy is the exergy due to the chemical composition
difference between the system and the environment, which can be expressed as:
3.4. Exergy analysis
Ex , w = W
T
P
− 1 − ln ⎛ ⎞ + ln ⎛ ⎞
T
P
0
⎝ 0⎠
⎝ ⎠
Wnet , system Vave
·
Wstack
Vtn
(41)
where Vave Vtn is the electrical energy conversion efficiency of the fuel
cell stack, which multiplies the ratio of Wnet , system Wstack results in the
combined PEMFC-ORC system efficiency.
Through the exergy balance equation, the exergy loss of each
component in the system can be calculated. The total exergy loss of the
system is the sum of the exergy loss of all equipment. The magnitude of
(36)
where h 0 and s0 are the enthalpy and entropy of the fluid at standard
environmental state, respectively.
With the assumption of ideal gas and constant isobaric specific heat
capacity, the physical exergy of the fluid can be expressed as:
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Energy Conversion and Management 217 (2020) 112998
G. Liu, et al.
region, although the absorbed heat decreases with temperature, the
increase of temperature increases the ORC efficiency more notably, so
the ORC output power increases. However, when the stack inlet temperature is further increased, the output voltage of the stack increases,
which leads to a more obvious reduction in the waste heat generated
and the absorbed heat, so the total heat recovered by the ORC system
decreases, even if the ORC efficiency is improved.
exergy loss reflects the unbalanced loss of the system, which is of great
significance to the evaluation of system performance. The exergy efficiency definition is similar to the energy efficiency. In this system, it is
the ratio of the net system output power to the exergy of input hydrogen:
ηexergy =
Wnet , system
Ex ,1
(42)
4.2. Effect of stack current density
Angulo-brown [33] derived the concept of ecological function according to Newton’s heat transfer law when studying heat engines. The
ecological function is defined as the difference between the system
output power and system exergy loss. It is a performance indicator that
optimizes the tradeoff between the output power and the entropy
production, which aims to increase output power and reduce exergy
loss simultaneously. The ecological function is expressed as:
E = Wnet , system − Ex , loss, system
Simulation is carried out for the system with different stack current
densities. Five different current densities were selected, namely
0.6 A cm−2, 0.7 A cm−2, 0.8 A cm−2, 0.9 A cm−2, and 1.0 A cm−2, and
the corresponding average cell voltages are 0.723 V, 0.703 V, 0.678 V,
0.655 V and 0.634 V, respectively. The trends of the system indicators
obtained by simulation are shown in Fig. 6.
It can be seen from Fig. 6 that, with the increase of the stack current
density, the net output power and exergy loss of the system increase
continuously, and the output power increases from the lowest
16291.14 W to the maximum 24054.50 W, with an increasing range of
nearly 50%. Energy efficiency and exergy efficiency decrease continuously, from 48.95% and 59.11% to 43.37% and 52.37%, respectively, and the magnitude of decline reach more than 5%.
Increasing the current density of the stack can effectively improve
the power density of the system, and an appropriately large stack current density is most desirable when the system layout space is limited,
such as in the vehicular application where it is a critical design parameter. This can also downsize fuel cell stack for a designed power requirement, decreasing the cost. From the perspective of efficiency, in
order to pursue higher energy utilization, it is necessary to keep the
current density smaller to reduce the electric potential loss of fuel cells,
such as application in the distributed power plant.
Fig. 7 shows the trends of ORC system output power and efficiency
under different stack current densities. The increase of current density
not only increases the output power of the PEMFC stack, but also increases the waste heat generated by the stack, which increases the ORC
output power. The efficiency of the ORC system remains unchanged at
7.01%, indicating that the efficiency of the ORC cycle is only affected
by temperature and pressure in the cycle process, and the change of
current density has no significant impact on its efficiency.
(43)
where Ex , loss, system is the total exergy loss of the system.
4. Results and discussion
The influence of different operating parameters on the system performance is studied. Different stack inlet gas temperatures, working
current densities, ORC working fluids, superheat temperatures and saturation pressures are applied to the model, and the system performances are evaluated. The basic parameters of the system are listed in
Table 2, and all subsequent calculation and analysis are based on these
parameters. When a certain parameter is changed to analyze its influence, other parameters remain unchanged.
4.1. Effect of stack inlet temperature
The system performance is simulated at the stack inlet temperature
of 333.15 K, 338.15 K, 343.15 K, 348.15 K and 353.15 K, and the
corresponding average cell voltages are 0.678 V, 0.693 V, 0.705 V,
0.712 V, and 0.717 V, respectively. The variation trends of various
system performance evaluation indexes are shown in Fig. 4.
From the variation trend of indicators, it can be clearly seen that
when the stack inlet temperature is 343.15 K, all indicators reach the
optimal values, the system net power reaches 20849.83 W, and the
energy efficiency reaches 46.99%, the total effective energy loss of the
system is 15478.54 W, the effective exergy efficiency is 56.74%, and the
ecological function is 5371.29 W.
The average cell voltage is low at low stack inlet temperature due to
large activation loss, which reduces the electric power output of the
stack. Therefore, increasing the stack inlet temperature at the low
temperature region can improve the overall performance of the system.
However, when the stack inlet temperature exceeds 348.15 K, all the
evaluation indexes of the system decline significantly. When the inlet
temperature is 353.15 K, the energy efficiency and exergy efficiency are
only 43.68% and 52.75%, respectively, both reduced by over 3%
compared with the maximum values at the stack inlet temperature of
343.15 K. The system net power is 19382.98 W which is 1085.66 W
lower than the optimal value. As the temperature increases, the average
cell voltage increases and hence the output power of stack increases.
Therefore, the decline of indicators at higher temperatures is caused
mainly by the increase of the auxiliary equipment power consumption
and decrease of ORC system power generation.
Fig. 5 shows the output power and thermal efficiency of the ORC
system at different stack inlet temperatures. It can be seen that with the
increase of the stack inlet temperature, the thermal efficiency of ORC
system continues to improve, which is mainly because the rise of
temperature improves the grade of thermal energy and enhances the
ORC recovery on thermal energy. With the increase of stack inlet
temperature, the power output of the ORC system decreases after
slightly increasing at low temperature. At low stack inlet temperature
4.3. Effect of ORC working fluid
The efficiency of ORC is largely determined by the thermal and
physical properties of the selected working fluid and many researchers
Table 2
Basic parameters of the system [34].
7
Equipment
Parameter
Value
PEMFC stack
Number of single cells
Anodic stoichiometry
Relative humidity at anode inlet
cathode stoichiometry
Relative humidity at cathode inlet
Anode inlet pressure
Cathode inlet pressure
Anode outlet pressure
Cathode outlet pressure
Width of effective area
Length of effective area
Stack inlet gas temperature
Stack outlet gas temperature
Current density
Average cell voltage
120
1.05
100%
2.0
100%
120 kPa
120 kPa
1 atm
1 atm
339 mm
92 mm
333.15 K
338.15 K
0.8 A cm−2
0.678 V
ORC system
Working fluid
Superheat degree
Superheat temperature
R245fa
5K
333.15 K
Energy Conversion and Management 217 (2020) 112998
G. Liu, et al.
Fig. 4. Variation trends of the system performance with the stack inlet temperature.
Fig. 7. Variation trends of the ORC performance with the stack current density.
Fig. 5. Variation trends of the ORC performance with the stack inlet temperature.
needs to meet the following requirements: the critical temperature is
higher than the maximum temperature in the ORC cycle; strong vaporization ability, easy to vaporize in the evaporation process; high
decomposition temperature, not easy to decompose during evaporation
heating; high molecular weight; non-toxic and non-corrosive; nonflammable; low cost.
According to the above selection principles, five common organic
working fluids, R245fa, R11, R134a, R123 and isobutane, are selected
for simulation. The basic physical parameters of these working fluids
are shown in Table 3.
The slope of the saturated vapor curve is an important thermodynamic index of OCR working fluids. If the slope is negative, the fluid
is wet fluid, and the expansion process may end in a two-phase region
where the fluid can be in the liquid state, which may easily damage the
blade of the expander with a high rotation speed. So the dry fluid
(positive slope) or isentropic fluid (vertical slope) should be selected as
the ORC working fluid. Compared with isentropic fluid, the dry fluid is
safer because it is unlikely to be liquid during the expansion process.
The ORC performance with different organic working fluids is
shown in Fig. 8. The order of the output power and efficiency is:
R245fa > R11 > R123 > Isobutane > R134a. The maximum
difference of efficiency among the working fluids is 1.08%, and the
maximum difference of output power is 173.26 W. During the ORC
cycle, the heat absorbed from the PEMFC stack by different working
fluids is basically the same. The difference between the output power
and thermal efficiency is mainly caused by the enthalpy difference
before and after the expansion process. Under the operating temperature and pressure conditions investigated, R245fa has the maximum
enthalpy difference in the expansion due to its thermodynamic properties, so it shows the best thermodynamic performance with the ORC
efficiency close to 8%.
The environmental characteristics of working fluids are also important nowadays. In these five working fluids investigated, the GWP
and ODP values of R11 are extremely high, which may destroy the
atmosphere ozone layer seriously, so it is not suitable for practical
application. The ODP of R245fa is 0, which is relatively friendly to the
environment, and it is a dry working fluid and has the best thermodynamic performance, so the R245fa is selected for the ORC system.
Fig. 6. Variation trends of the system performance with the stack current
density.
4.4. Effect of superheat temperature
The superheat temperature of the working fluid varies by changing
the mass flow rate, design of stack cooling passage and etc. Different
superheat temperatures of the organic working fluid are selected for
simulation, and the results are shown in Fig. 9.
Fig. 9 shows the trends of the system performance indicators as the
have explored the organic working fluids available for ORC system. In
general, the choice of the ORC working fluid varies under different heat
sources and temperatures, and it may exist multiple choices of organic
working fluid for a specific situation. The ORC working fluid basically
8
Energy Conversion and Management 217 (2020) 112998
G. Liu, et al.
Table 3
The basic physical parameters of the working fluids.
Organic working fluid
R245fa
R11
R134a
R123
Isobutane
Chemical formula
Molecular weight
Critical temperature (°C)
Critical pressure (MPa)
Ozone Depletion Potential (ODP)
Global Warming Potential (GWP, 100 yr)
Slope of saturated vapor curve (dT/ds)
CF3CH2CHF2
134
154
3.65
0
950
>0
CCl3F
137
198
4.40
1
4600
>0
CH2FCF3
102
101
4.07
0
1300
≈0
CF3CHCl2
156
184
3.67
0.012
120
≈0
CH3CH(CH3)CH3
58
135
3.65
0
0
>0
significantly with the superheat temperature, from 619.61 W to
1276.21 W, with an increment rate of more than 100%, and its efficiency also increases from 3.85% to 7.93%.
Through the above analysis, it reveals that the ORC superheat
temperature has a significant impact on the improvement of ORC performance, as well as the overall performance of the PEMFC-ORC
system. Therefore, in the practical application, the design of the stack
cooling passage should be optimized carefully, to make sure that the
ORC working fluid and PEMFC stack can fully exchange heat, reaching
high superheat temperature at the stack outlet.
4.5. Effect of saturation pressure
Under the basic parameters set in this study, the superheat temperature of ORC working fluid is 333.15 K with a superheat degree of
5 K, so the ORC working fluid evaporating temperature is 328.15 K and
the corresponding saturation pressure is 400.05 kPa. In this section, the
ORC working fluid saturation pressure is varied from 200 kPa to
400 kPa to explore its influence on the system performance. It is worth
noting that, since the superheat temperature remains constant, the superheat degree varies with the saturation pressure and is no longer
maintained at 5 K.
Fig. 11 shows the variations of system performance indicators with
the ORC working fluid saturation pressure. It is found that all the
performance indicators of the system continue to improve as the saturation pressure rises from 200 kPa to 400 kPa. The system net power
increases from 19696.64 W to 20468.49 W, and the system energy efficiency and exergy efficiency increases from 44.39% and 53.39% to
46.13% and 55.69%, respectively. The system exergy loss is decreased
by 771.86 W and the ecological function is increased by 1543.74 W.
The combined PEMFC-ORC system performance is mainly affected
by the improvement of ORC system performance. Fig. 12 shows the
variation of ORC system performance with the saturation pressure. For
Fig. 8. ORC performance with different organic working fluids.
Fig. 9. Variation trends of the system performance with the superheat temperature.
superheat temperature rises from 318.15 K to 338.15 K. With the increase of the superheat temperature, the system energy efficiency and
exergy efficiency continue to improve. When the superheat temperature
reaches 338.15 K, which is basically equal to the stack operating temperature, the energy efficiency and exergy efficiency reach 46.46% and
56.10%, respectively; while when the superheat temperature is
318.15 K, 20 K lower than the stack operating temperature, the two
efficiencies are decreased to 44.98% and 54.31%, respectively. System
net power, exergy loss and ecological function are also constantly improved with the increase of superheat temperature. However, the improvement of system net power is not very significant, bacuase the ORC
system output power is relatively small compared with the system
power output.
Fig. 10 shows the influence of superheat temperature on the ORC
system performance. The output power of ORC system increases
Fig. 10. Variation trends of the ORC performance with the superheat temperature.
9
Energy Conversion and Management 217 (2020) 112998
G. Liu, et al.
hydrogen circulating compressor and ORC fluid pump consume a relatively small amount of power in all operating conditions.
By comparing the power of each component at different stack inlet
temperatures, it is found that the power consumption of most auxiliary
components (hydrogen circulating compressor, anode side heater and
cathode side heater) increases with temperature, except for the air
compressor and ORC fluid pump. The increment rate of cathode heater
power consumption is accelerated with temperature, which leads to the
greater increment rate of the total parasitic power loss. The output
power of the expander decreases with the stack inlet temperature, due
to higher fuel cell stack efficiency and less heat generation. When the
temperature is lower than 343.15 K, the increase of the stack power is
dominant, and the system output power increases with temperature.
However, when the temperature is higher than 343.15 K, the increase
of parasitic power and decrease of expander power is dominant, and
resulting in the decrease of the system output power with temperature.
With the increase of the stack current density, the power of all
components in the system increases. This is because the increase of
current density increases the flow rate of reaction gases, so the energy
distributed in the system increases proportionally. The increase of the
PEMFC stack power is much greater than that of the auxiliary equipment, so the system net power is also significantly increased.
According to the exergy analysis method, the exergy distribution of
the PEMFC-ORC system is investigated. Fig. 13 shows the exergy distribution of each component in the system based on the basic operating
parameters. The black numbers represent the exergy value of the fluids,
and the red numbers represent the exergy loss of the components. The
maximum exergy loss occurs in the fuel cell stack, with a value of
15041.51 W, accounting for 93.73% of the total exergy loss of the
system. This is caused by various irreversible reactions in the stack,
which is consistent with the results of Ye et al [30]. The exergy loss of
the stack is mainly in the form of waste heat dissipation, so it is of great
significance to find an efficient way of waste heat recovery to reduce
the exergy loss of the system.
Among other components, the cathode side heater, the expander,
the cathode side water/heat exchanger and the air compressor have
relatively large exergy loss, accounting for 2.36%, 1.26%, 0.65% and
0.59% of the exergy loss of the system, respectively, indicating that
there are more irreversible loss of these components. The airflow rate
on the cathode side of the stack is 21.47 g s−1, and the hydrogen flow
rate on the anode side is 0.33 g s−1. The larger flow rate takes more
energy to compress, preheat or expand it, so the exergy loss is higher.
As for the exergy of the fluids, the exergy of the hydrogen supply
side is very large, because the hydrogen has a great amount of chemical
energy. In actual system design, the hydrogen loss should be avoided as
much as possible, which plays an important role in improving system
efficiency.
Table 6 shows the exergy loss of five major components at different
stack inlet temperatures, and the exergy loss of other components is
small which is not listed. The exergy loss of the PEMFC stack decreases
from 15042 W to 13248 W with the stack inlet temperature varying
from 333.15 K to 353.15 K. As the temperature increases, the average
cell voltage increases from 0.678 V to 0.717 V, and the overpotential
decreases, so the exergy is greatly reduced. The exergy loss of the
Fig. 11. Variation trends of the system performance with the saturation pressure.
Fig. 12. Variation trends of the ORC performance with the saturation pressure.
the ORC system, its efficiency increases from 2.21% to 7.01%, and its
output power increases from 355.65 W to 1127.51 W with the saturation pressure investigated. The ORC system performance improvement
range is very significant.
By comparing the variation characteristics of the system performance influenced by the saturation pressure and superheat temperature, it can be seen that the variation trends are basically the same. The
performance of the ORC system is significantly improved by increasing
the superheating temperature and saturation pressure, which improves
the performance of the PEMFC-ORC system. Therefore, in practical
application, high ORC superheat temperature and saturation pressure
should be maintained.
4.6. The energy distribution of the system
Table 4
Power of each component at different stack inlet temperatures.
Tables 4 and 5 show the power of each component under different
stack inlet temperatures and current densities, respectively. The positive values represent the power output and the negative values represent the power consumed. By comparison, it can be found that the
cathode side heater and air compressor consume the largest amount of
power, and they are the main contribution to the system parasitic
power loss. To reduce the parasitic power consumption and further
improve the system efficiency, the design and operating of the air
compressor should be carefully considered; and preheating and humidifying the fresh reactants by waste heat should be utilized. The
Component (Power:W)
PEMFC stack
Expander
Hydrogen circulating
compressor
Air compressor
Heater (anode side)
Heater (cathode side)
ORC fluid pump
10
333.15 K
20,300
1144
−9
338.15 K
20,749
1189
−10
343.15 K
21,108
1152
−11
348.15 K
21,318
962
−14
353.15 K
21,467
390
−17
−425
−81
−443
−16
−425
−112
−584
−18
−425
−159
−795
−19
−425
−230
−1123
−17
−425
−351
−1672
−8
Energy Conversion and Management 217 (2020) 112998
G. Liu, et al.
Table 5
Power of each component at different stack current densities.
Component (power:W)
PEMFC stack
Expander
Hydrogen circulating compressor
Air compressor
Heater (anode side)
Heater (cathode side)
ORC fluid pump
0.6 A cm−2
16,235
786
−7
−319
−61
−332
−11
0.7 A cm−2
18,417
954
−8
−372
−71
−388
−14
cathode side heater and water/heat exchanger increases with the stack
inlet temperature. When the inlet temperature reaches 353.15 K, the
exergy loss of these two components account for 8.26% and 3.50% of
the exergy loss of the system, respectively, which is the main reason for
the increase of the system exergy loss at high temperature.
Table 7 shows the exergy loss of these five components at different
stack current densities. It is found that the exergy loss of all components
increases with the current density, which can be explained similarly
with the power variation trends. The increase of the exergy loss is
mainly caused by the increase of the fluid flow in the system, and the
exergy loss increases relatively slowly, compared with the influence of
temperature. The exergy loss of the stack increases with the current
density, which is not only caused by the increase of reactant flow rate,
but also owing to the stack polarization law: the output voltage of the
0.8 A cm−2
20,300
1144
−9
−425
−81
−443
−16
0.9 A cm−2
22,062
1342
−10
−478
−92
−498
−19
1.0 A cm−2
25,375
1430
−12
−531
−102
−554
−20
Table 6
Exergy loss of each component at different stack inlet temperatures.
Component (Exergy
loss:W)
PEMFC stack
Heater (cathode side)
Expander
Water/heat exchanger
(cathode side)
Air compressor
333.15 K
338.15 K
343.15 K
348.15 K
353.15 K
15,042
380
202
105
14,483
491
210
141
14,021
654
203
207
13,673
901
169
328
13,248
1303
69
552
95
95
95
95
95
Fig. 13. Exergy distribution (Unit: W) of the PEMFC-ORC system (AC: air compressor; EX: water/heat exchanger; HE: heater; HU: humidifier; HC: hydrogen
circulating compressor; E: expander; C: condenser; P: pump; G: generator).
11
Energy Conversion and Management 217 (2020) 112998
G. Liu, et al.
Table 7
Exergy loss of each component at different stack current densities.
Component (Exergy loss:W)
PEMFC stack
Heater (cathode side)
Expander
Water/heat exchanger (cathode side)
Air compressor
0.6 A cm−2
10,355
285
139
79
71
0.7 A cm−2
12,561
332
168
92
83
0.8 A cm−2
15,042
380
202
105
95
0.9 A cm−2
17,632
427
237
118
107
1.0 A cm−2
18,802
474
252
131
119
Acknowledgement
stack decreases with the current density, and the irreversibility of the
reaction increases.
This work is financially supported by the National Natural Science
Foundation of China (Grant No. 51706153).
5. Conclusions
References
A novel PEMFC-ORC system is proposed, in which the ORC system
can simultaneously absorb heat and recover energy from the PEMFC
stack, and the waste energy of PEMFC cathode exhaust gas is also used
to preheat and humidify the dry inlet gases. On the basis of this novel
design, the thermodynamic model of the system is established and simulated, and the performance of the system under different operating
conditions is obtained. The components in the system (PEMFC stack,
expander, heater, air compressor, etc.) are also analyzed. Based on the
analysis of the results, the following conclusions can be drawn:
[1] Chen X, Chen L, Guo J, Chen J. An available method exploiting the waste heat in a
proton exchange membrane fuel cell system. Int J Hydrog Energy
2011;36(10):6099–104.
[2] Mandavi A, Ranjbar AA, Gorji M, Rahimi-Esbo M. Numerical simulation based design for an innovative PEMFC cooling flow field with metallic bipolar plates. Appl
Energy 2018;228:656–66.
[3] Qin Y, Yin Y, Jiao K, Du Q. Effects of needle orientation and gas velocity on water
transport and removal in a modified PEMFC gas flow channel having a hydrophilic
needle. Int J Energy Res 2019;43(7):2538–49.
[4] Yin Y, Wang X, Zhang J, Xiang S, Qin Y. Influence of sloping baffle plates on the
mass transport and performance of PEMFC. Int J Energy Res 2019;43(7):2643–55.
[5] Wong AKC, Ge N, Shrestha P, Liu H, Fahy K, Bazylak A. Polytetrafluoroethylene
content in standalone microporous layers: tradeoff between membrane hydration
and mass transport losses in polymer electrolyte membrane fuel cells. Appl Energy
2019;240:549–60.
[6] Shrestha P, Banerjee R, Lee J, Ge N, Muirhead D, Liu H, et al. Hydrophilic microporous layer coatings for polymer electrolyte membrane fuel cells operating without
anode humidification. J Power Sources 2018;402:468–82.
[7] Yi P, Li X, Yao L, Fan F, Peng L, Lai X. A lifetime prediction model for coated
metallic bipolar plates in proton exchange membrane fuel cells. Energy Conserv
Manage 2019;183:65–72.
[8] Sharaf OZ, Orhan MF. An overview of fuel cell technology: fundamentals and applications. Renew Sust Energ Rev 2014;32:810–53.
[9] Zhang H, Qin Y, Li X, Liu X, Yan J. Power Management Optimization in Plug-In
Hybrid Electric Vehicles Subject to Uncertain Driving Cycles. eTransportation.
DOI:10.1016/j.etran.2019.100029.
[10] Paul B, Andrews J. PEM unitised reversible/regenerative hydrogen fuel cell systems: state of the art and technical challenges. Renew Sustain Energy Rev
2017;79:585–99.
[11] Zhang J, Xie Z, Zhang J, Tanga Y, Song C, Navessin T, et al. High temperature PEM
fuel cells. J Power Sources 2006;160(2):872–91.
[12] Kwan TH, Wu X, Yao Q. Multi-objective genetic optimization of the thermoelectric
system for thermal management of proton exchange membrane fuel cells. Appl
Energy 2018;217:314–27.
[13] Hwang J, Zou M. Development of a proton exchange membrane fuel cell cogeneration system. J Power Sources 2010;195(9):2579–85.
[14] Hwang J, Zou M, Chang W, Su A, Weng F, Wu W. Implementation of a heat recovery
unit in a proton exchange membrane fuel cell system. Int J Hydrog Energy
2010;35(16):8644–53.
[15] Shabani B, Andrews J. An experimental investigation of a PEM fuel cell to supply
both heat and power in a solar-hydrogen RAPS system. Int J Hydrog Energy
2011;36(9):5442–52.
[16] Chen X, Zhou H, Li W, Yu Z, Gong G, Yan Y, et al. Multi-criteria assessment and
optimization study on 5 kW PEMFC based residential CCHP system. Energy Conserv
Manage 2018;160:384–95.
[17] Guo X, Zhang H, Zhao J, Wang F, Wang J, Miao H, et al. Performance evaluation of
an integrated high-temperature proton exchange membrane fuel cell and absorption
cycle system for power and heating/cooling cogeneration. Energy Conserv Manage
2019;181:292–301.
[18] Ziviani D, Beyene A, Venturini M. Advances and challenges in ORC systems modeling for low grade thermal energy recovery. Appl Energy 2014;121:79–95.
[19] Mahmoudi A, Fazli M, Morad MR. A recent review of waste heat recovery by
Organic Rankine Cycle. Appl Therm Eng 2018;143:660–75.
[20] Wang E, Zhang H, Fan B, Ouyang M, Zhao Y, Mu Q. Study of working fluid selection
of organic Rankine cycle (ORC) for engine waste heat recovery. Energy
2011;36(5):3406–18.
[21] Gao H, Liu C, He C, Xu X, Wu S, Li Y. Performance analysis and working fluid
selection of a supercritical Organic Rankine Cycle for low grade waste heat recovery. Energies 2012;5(9):3233–47.
[22] Ebrahimi M, Moradpoor I. Combined solid oxide fuel cell, micro-gas turbine and
organic Rankine cycle for power generation (SOFC-MGT-ORC). Energy Conserv
Manage 2016;116:120–33.
[23] Ghirardo F, Santin M, Traverso A, Massardo A. Heat recovery options for onboard
fuel cell systems. Int J Hydrog Energy 2011;36(13):8134–42.
[24] Buonomano A, Calise F, d'Accadia MD, Palombo A, Vicidomini M. Hybrid solid
(1) The system performance can be improved by increasing the stack
inlet temperature within a certain range. The system performance
indicators are optimal when the stack inlet temperature is about
343.15 K for the PEMFC-ORC system studied.
(2) The stack current density has a great influence on the system performance. When the current density increases, the system output
power and power density increase, but the efficiency decreases with
the current density. It should be considered comprehensively in
practical application balancing the efficiency and power density
requirements.
(3) The type of ORC working fluid has a certain influence on the system
performance. When selecting ORC fluid, some basic requirements
should be satisfied, as well as its effect on the system performance
improvement. R245fa shows the best performance among several
ORC fluids investigated.
(4) Increasing the superheat temperature can significantly improve the
ORC system performance. The PEMFC stack cooling passage should
be carefully designed, in order to achieve efficient heat transfer
between the ORC working fluid and PEMFC stack, increasing the
superheat temperature.
(5) Among the auxiliary equipment of the system, the power consumed
by the cathode side heater and air compressor accounts for a large
proportion of the system parasitic power loss. To reduce system
parasitic power consumption and further improve the system efficiency, the performance of the air compressor should be optimized
and preheating and humidifying the fresh gases by the stack waste
energy should be enhanced.
(6) Through the analysis of the energy distribution of the system, it is
found that the power and exergy loss of the PEMFC stack is much
larger than the other components of the system. The cathode side
heater and air compressor process the largest exergy loss in the
auxiliary components. In order to improve the performance of the
system, emphasis should be given to the performance improvement
of these components.
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.
12
Energy Conversion and Management 217 (2020) 112998
G. Liu, et al.
analyses of a proton exchange membrane fuel cell (PEMFC) system and the feasibility evaluation of integrating with a proton exchange membrane electrolyzer
(PEME). Energy Conserv Manage 2019;186:487–99.
[30] Ye L, Jiao K, Du Q, Yin Y. Exergy analysis of high-temperature proton exchange
membrane fuel cell systems. Int J Green Energy 2015;12(9):917–29.
[31] Ruan W, Qu M, Horton WT. Modeling analysis of an enthalpy recovery wheel with
purge air. Int J Heat Mass Transf 2012;55(17–18):4665–72.
[32] Qin Y, Liu G, Chang Y, Du Q. Modeling and design of PEM fuel cell stack based on a
flow network method. Appl Therm Eng 2018;144:411–23.
[33] Angulo-Brown F. An ecological optimization criterion for finite-time heat engines. J
Appl Phys 1991;69:7465.
[34] Qin Y, Du Q, Fan M, Chang Y, Yin Y. Study on the operating pressure effect on the
performance of a proton exchange membrane fuel cell power system. Energy
Conserv Manage 2017;142:357–65.
oxide fuel cells-gas turbine systems for combined heat and power: a review. Appl
Energy 2015;156:32–85.
[25] Sanchez D, de Escalona JMM, Monje B, Chacartegui R, Sanchez T. Preliminary
analysis of compound systems based on high temperature fuel cell, gas turbine and
Organic Rankine Cycle. J Power Sources 2011;196(9):4355–63.
[26] He T, Shi R, Peng J, Zhuge W, Zhang Y. Waste heat recovery of a PEMFC system by
using Organic Rankine Cycle. Energies 2016;9(4):15.
[27] Zhao P, Wang J, Gao L, Dai Y. Parametric analysis of a hybrid power system using
organic Rankine cycle to recover waste heat from proton exchange membrane fuel
cell. Int J Hydrog Energy 2012;37(4):3382–91.
[28] Sarabchi N, Mahmoudi SMS, Yari M, Farzi A. Exergoeconomic analysis and optimization of a novel hybrid cogeneration system: high-temperature proton exchange
membrane fuel cell/Kalina cycle, driven by solar energy. Energy Conserv Manage
2019;190:14–33.
[29] Chitsaz A, Haghghi MA, Hosseinpour J. Thermodynamic and exergoeconomic
13