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Energy Conversion and Management
journal homepage: www.elsevier.com/locate/enconman
Performance analysis and exergoeconomic evaluation of a TRC system
enhanced by a dedicated mechanical subcooling
Ali Zahedi Mirana
, Arash Nematib
, Mortaza Yarib,⁎
a
Department of Mechanical Engineering, University College of Nabi Akram, Tabriz, Iran
b
Faculty of Mechanical Engineering, University of Tabriz, 29th Bahman Blvd., Tabriz, Iran
A R T I C L E I N F O
Keywords:
Exergy
Exergoeconomic
Mechanical subcooling
Transcritical refrigeration
A B S T R A C T
In the present study, a transcritical refrigeration cycle’s performance with dedicated mechanical subcooling (MS)
is investigated from the energy, exergy and exergoeconomic viewpoints. Three different refrigerants containing
CO2 (R744), N2O (R744A) and ethane (R170) are considered as the transcritical cycle’s refrigerant. A thorough
parametric study is carried out on the system and finally, the effect of dedicated subcooling system is checked
out on the energy, exergy and exergoeconomic perimeters. Based on the results, value of the COP and exergy
performance for N2O, unlike the CO2, is the highest. In other words, the CO2 refrigerant shows the best economic
performance. By comparing the system with and without subcooling cycle, it can be concluded that utilizing
subcooler improves performance of the system and increases the unit product cost. However, the unit product
cost increment is much lower than COP improvement which makes the subcooling an effective and economical
way to improve the refrigeration system’s performance. Application of subcooler leads to an enhancement of
30.74%, 26.48% and 36.1% in COP for CO2, N2O, and ethane, respectively while the unit product cost increment
is 9.04%, 8.37% and 10.63% for the mentioned refrigerants, respectively.
1. Introduction
Extensive use of synthetic refrigerants in the field of air-con-
ditioning and refrigeration in recent decades, such as CFCs, HCFCs, and
HFCs, is one of the main causes of average global temperature rise [1].
Hence, natural fluids such as CO2, N2O, and ethane have received great
attention as refrigerants [2]. Carbon dioxide (R744) as a natural re-
frigerant has many advantages [3] such as no toxicity, no combust-
ibility, and high volume capacity with the compact system, better heat
transfer specifications, low pressure ratio, full adaptability with con-
ventional lubricants, easy access and low price [4]. The use of CO2 as a
refrigerant has been discussed in automotive air-conditioning [5], heat
pump, and environmental control unit [6]. In addition, CO2 can be used
as a refrigerant in low-temperature applications such as quick-freezing
systems and frozen food storage. Due to the low critical temperature of
R744 (31.1 °C) which is usually less than air-conditioning and heat
pump systems usual temperature, the supercritical vapor compression
cycle (VCC) can be used instead of conventional vapor compression
cycle for this refrigerant [7]. Nitrous oxide (N2O) and ethane has si-
milar thermodynamic properties to those of CO2 and also are promising
natural refrigerant [8]. Therefore, many researchers have worked on
the analysis of CO2 transcritical cycles (TRCs). However, N2O and
ethane systems have not been well studied.
An ejector-expansion refrigeration cycle using nitrous oxide (N2O)
was examined by Aghazadeh Dokandari et al [9]. The results show that
their proposed cycle has a maximum coefficient of performance and
exergy efficiency of 12% and 15% relative to the internal heat ex-
changer cycle, respectively. They found that total exergy destruction for
the N2O ejector-expansion cycle was 63% and 53% lower than the in-
ternal heat exchanger cycle and vapor compression cycle, respectively.
Also, it was concluded that the highest COP for the three types of
carbon dioxide refrigeration system was equal to the pressure side of
8.4 MPa. A vortex tube can be used instead of an expansion valve to
improve the performance of the refrigeration cycle for useful energy
losses. Jain et al. [10] studied a used vortex tube in a vapor compres-
sion cycle as an expansion device, with using nitrous oxide (N2O) to
improve the COP, also the results of the transcritical cycle with ex-
pansion valve were compared. They found that the coefficient of per-
formance of the transcritical cycle with the vortex tube improved from
1.72% to 27.01% relative to the transcritical cycle with the expansion
valve. Comparison of the performance of N2O and CO2 in the tran-
scritical cycle with the vortex tube shows that, as the optimal pressure
required for N2O is less than CO2, also its maximum cooling coefficient
of performance is higher than that of CO2. In another study, Jain et al.
https://doi.org/10.1016/j.enconman.2019.111890
Received 29 May 2019; Received in revised form 29 July 2019; Accepted 30 July 2019
⁎
Corresponding author.
E-mail address: myari@tabrizu.ac.ir (M. Yari).
Energy Conversion and Management 197 (2019) 111890
0196-8904/ © 2019 Elsevier Ltd. All rights reserved.
T

2. [11] investigated the performance characteristics of the two-stage
transcritical cycle using N2O with vortex tubes. In their study, they used
a two-stage transcritical cycle with a vortex tube instead of the ex-
pansion valve with N2O as the refrigerant. They also compared their
results with a two-stage transcritical cycle with an expansion valve.
They optimize the pressure of gascooler and intercooler at the same
time to achieve maximum performance. The results show that COP of
the TSTCVT system in comparison to TSTCEV system improves by
1.97% up to 27.19%. Also, the comparison of refrigerants N2O and CO2
in TSTCVT system shows that N2O exhibits higher efficiencies under the
considered operating conditions such as COP, second law efficiency.
Subcooling (SC) is one of the practical methods for improvement of
refrigeration systems’ performance. This method is widely used in
medium- and low-temperature cooling systems in which a simple vapor
compression cooling system is utilized [12]. Subcooling technologies
including (a) environmental subcooling; (b) the use of heat exchangers
as heat sink; (c) mechanical subcooling; and (d) systems with external
heat sinks. Among these, mechanical subcooling is thoroughly in-
vestigated [13]. Mechanical subcooling is a practical way to improve
cooling capacity and it is likely to be a way to save energy. Energy
analysis for dedicated and integrated mechanical subcooling carbon
dioxide boosters for supermarket applications was carried out by Cat-
alán-Gil et al. [14] with using thermodynamic models close to reality.
Due to the state-of-the-art of the CO2 booster system, they concluded
that both systems with parallel compressors and flash gas by-pass would
reduce energy consumption, while its performance is highly dependent
on environmental conditions. They found that the dedicated mechan-
ical cooling system offers an annual reduction of energy for temperate
regions from 1.5 to 2.9% while an integrated subcooling system offers a
reduction for these areas from 1.4 to 2.9%. They concluded that the IMS
system uses subcooling for the entire evaluation range, while the DMS
system was only for temperatures higher than 8.15 °C.
In dedicated MS, both the main cycle and the subcooling processes
have their own specific condenser. One of the main advantages of the
SC system is the reduction of main pressure, same as temperature. She
et al. [12] presented a new subcooling method based on expansion
power recovery for the vapor compression cycle. The thermodynamic
analysis led to discussing the effects of parameters on system perfor-
mance. Results show that when R744 is used as working fluid in the
main cooling cycle, the proposed system has a much higher COP
compared to the base conventional compression refrigeration cycle.
Llopis et al. [13] experimentally demonstrate the improved energy in
using a mechanical subcooling in combination with a supercritical
carbon dioxide refrigeration cycle. According to the results, at the op-
timal operating conditions, capacity and coefficient of performance
(COP) increase about 55.7% and 30.3%, respectively. A new config-
uration of the CO2 refrigeration cycle with a thermoelectric subcooler
and ejector was proposed by Liu et al [15]. In the transcritical CO2
refrigeration cycle with an ejector, they installed a thermoelectric
subcooler after the gascooler. The results showed that, as compared to
the base cycle, the maximum COP of the TES + EJE cycle would in-
crease by 39.34% and the optimal discharge pressure would be reduced
by 8.01% under the given operating conditions. Llopis et al. [16] the-
oretically examined the ability to boost the energy performance of the
CO2 TRC using a mechanical subcooling cycle. Their results showed
that the proposed cycle is more appropriate for ambient temperatures
above 25 °C and it has been observed that a cycle combination can
increase the coefficient of performance up to a maximum of 20% and
raises the Qe to a maximum of 28.8%, while both increases at high
evaporation levels. Xing et al. [17] proposed a novel VCC using a MS to
enhance the performance of the system. Their results indicate that the
ejector-SC cycle performance is better than the basic cycle. The new
proposed cycle improved the COP by 9.5% for R404A and 7.0% for the
R290. They also found that improving COP and Qe of the new cycle
greatly belongs to the ejector operating pressure. Gullo et al. [18]
compared different configurations of R744 refrigeration systems
Nomenclature
A Area [m2
]
amb Ambient
app Approach
COP Coefficient of performance
ci Cost per exergy unit [$ GJ−1
]
Ci Cost flow rate [$ s−1
]
CRF Capital Recovery Factor
E Exergy rate [kW]
Ei
PH
Exergy rate of the stream
e Electrical
ei
PH
Specific Physical Exergy of State
ex Specific Exergy [kJ kg−1
]
f Exergoeconomic factor
h Specific enthalpy [kJ kg−1
]
m Mass flow rate [kg s−1
]
Acronyms
Comp Compressor
C1 Compressor
Cond Condenser
EV Expansion Valve
Evap Evaporator
GC Gas Cooler
SC Sub Cooler
ε Exergy efficiency
F Maintenance factor
tot Total
rev Reversible
m Mechanical
n Lifecycle
N Annual operating hours
P Pressure (MPa)
Ph High Pressure
Qe Evaporator Cooling Capacity (kW)
s Specific entropy [kJ kg−1
K−1
]
T Temperature [°C]
U Overall heat-transfer coefficient [W m−2
C−1
)]
w Specific work
W Power [kJ s−1
]
x Quality
Zi Purchased equipment cost
Zi Levelized cost
Subscripts
0 Reference environment state
1,2, … Cycle State
Ch Chemical
D Destruction
env Environmental
F Fuel
I Irreversibility
in Inlet
is Isentropic process
out Outlet
ph Physical
A.Z. Miran, et al. Energy Conversion and Management 197 (2019) 111890
2

3. energetically and environmentally. They concluded that the mechanical
subcooling should be run at part load conditions and implementing the
control system would be difficult at variable subcooler outlet
temperature. Song and Cao [19] performed an experimental and the-
oretical study on an R744 transcritical heat pump equipped with an
R134a subcooling device. They found a correlation to predict the op-
timum medium temperature under various operating conditions of the
system. She et al. [20] carried out an experimental study on a novel
subcooling method for vapor-compression refrigeration cycles based on
liquid desiccant dehumidification. They concluded that the payback
period for the proposed system is about 2.4 to 3.2 years for different
electricity tariffs. In addition, the investment savings ratio is about 1.3
and 2.1, which clarifies that the proposed system is profitable.
Exergoeconomic is a promising method that combines the concept
of exergy with those that depend on economic analysis [21]. Ex-
ergoeconomic analysis helps to check the cost of the irreversibilities of
system. In this way, the goal is either to reduce the cost of the units in
the system for the constant output product or to maximize output for
the entire system cost. The exergoeconomic model includes cost bal-
ances and component’s auxiliary equations [22]. Siddiqui et al. [23]
studied a 5 kW refrigeration cycle with a hybrid storage system from the
exergoeconomic viewpoint. They carried out this analysis based on
initial and irreversible costs to compare the components of the re-
frigeration cycle. Also, they presented an analysis of semi-fixed exergy
and exergoeconomic for a summer day in the Dhahran area. According
to their results, the system product cost should be minimized by opti-
mization of the system’s design variables to achieve a cost-effective
operating condition. Gullo and Cortella [24] compared the cost of the
final product of a different CO2 refrigeration system, with a particular
emphasis on the existence of a two-stage ejector as an expansion device.
The results showed that using such technology reduces the product cost
during basic single-stage solution for the average cooling temperature.
Mehrpooya and Ansarinasab [25] performed an advanced ex-
ergoeconomic analysis in three processes of multi-stage liquid-mixtures
of refrigerants. They found avoidable/inevitable and endogenous/exo-
genous exergy destructions and related costs segments’ components.
They found that the components’ interactions are not significant be-
cause the investment cost and the exergy destruction in many of them
are endogenous. Wu et al. [26] performed the analysis of the carbon
dioxide Brayton-absorption cycle based on energy, exergy and ex-
ergoeconomic perspectives. They found the absorber as the most sig-
nificant component in the absorption refrigeration cycle from the ex-
ergoeconomic viewpoint. Commercial refrigeration units are widely
used to meet various human needs and play an important role in
modern society. Thus, Gullo [27] examined the thermodynamic per-
formance of a transcritical R744 booster supermarket refrigeration
system equipped with a dedicated mechanical subcooling with R290
refrigerant using advanced exergy analysis. The results showed that the
improvement priority should be attributed to the production of high-
efficiency compressors and then to enhancement the gas cooler/con-
denser, the medium temperature evaporators, the R290 compressor,
and the low-temperature evaporators.
Fig. 1. Schematic and T-s and P-h diagram of TRC with MS. (a) Overall system.
(b) T-s diagram (c) P-h diagram.
Table 1
Parameters used to simulate the system.
Parameters Value
Tamb [°C] 30
Tevap [°C] −30~0
Tgc [°C] 30~50
T0 [K] 300
Tr [°C] Tgc − 5
Pgc [MPa] 7~14
P0 [MPa] 0.1
ΔTWater [°C] 8
ΔTSC, Pinch [°C] 10
ΔTCond, Pinch [°C] 10
ΔTGC, App [°C] 8
ηm [%] 0.9
ηe [%] 0.9
A.Z. Miran, et al. Energy Conversion and Management 197 (2019) 111890
3

4. By surveying the mentioned literature and to the best of the author’s
knowledge, comprehensive energy, exergy and exergoeconomic ana-
lyses on the effect of mechanical subcooling application by utilizing
different refrigerants have not investigated yet. Hence, three potential
candidates to work in the transcritical condition, R744, R744A, and
R170 are selected as refrigerant of the TRC and compared in terms of
energy, exergy, and exergoeconomic and the best refrigerants are of-
fered from various viewpoints. Also, R152a is utilized as the dedicated
subcooling cycle’s refrigerant. A constant value of Qe for overall cycle is
considered for all refrigerants and all of the results are obtained by
optimizing coefficient of performance subject to subcooling tempera-
ture difference and compressor discharge pressure. Finally, the effect of
subcooler utilization in a transcritical refrigeration cycle is investigated
and the results are compared for the systems with and without sub-
cooler for all of the refrigerants.
Table 2
Energy, and exergy relations for main and subcooling cycles.
Subsystems Energy relations Exergy relations
Compressor 1 =
W m h h
( )/( . )
C Main m e
1 2 1 =
I m T s s
. . ( )
C Main
,1 0 2 1
Compressor 2 =
W m h h
( )/( . )
C MS m e
2 7 6 =
I m T s s
. . ( )
C MS
,2 0 7 6
Gas Cooler =
Q m h h
( )
GC Main 2 3 =
I m h h T s s
. ( . ( ))
GC 2 2 3 0 2 3
Sub Cooler =
m h h m h h
( ) ( )
Main MS
3 4 6 9 = +
I T m s s m s s
( . ( ) . ( ))
SC Main MS
0 4 3 6 9
Expansion Valve 1 =
h h
4 5 =
I m T s s
. . ( )
EV Main
,1 0 5 4
Expansion Valve 2 =
h h
9 8 =
I m T s s
. . ( )
EV MS
,2 0 9 8
Evaporator =
Q m h h
( )
e Main 1 5 = +
( )
I m T s s
. .
Evap
h h
Tr
5 0 1 5
5 1
Condenser =
Q m h h
( )
Cond MS 7 8 =
I m h h T s s
. ( . ( ))
Cond 6 7 8 0 7 8
Table 3
Definitions of fuel and product for components of transcritical refrigeration
cycle with mechanical subcooling.
Component Fuel Product
Compressor 1 m w
. C
2 1 E E
PH PH
2 1
Compressor 2 m w
. C
6 2 E E
PH PH
7 6
Gas Cooler E E
PH PH
2 3 E E
PH PH
23 22
Expansion Valve 1 E
PH
4 E
PH
5
Expansion Valve 2 E
PH
8 E
PH
9
Sub Cooler E E
PH PH
9 6 E E
PH PH
3 4
Evaporator E E
PH PH
5 1 E E
PH PH
25 24
Condenser E E
PH PH
7 8 E E
PH PH
27 26
Table 4
Cost equilibrium and auxiliary equations for exergoeconomic analysis.
Component Cost balance equation Auxiliary equation
Compressor 1 + + =
C C Z C
W C C
1 , 1 1 2 =
C c W
.
W C W C C Main
, 1 , 1 ,
Compressor 2 + + =
C C Z C
W C C
6 , 2 2 7 =
C c W
.
W C W C C MS
, 2 , 2 ,
Gas Cooler + + = +
C C Z C C
GC
2 22 3 23 =
c c
2 3
Expansion Valve 1 – =
c c
4 5
Expansion Valve 2 – =
c c
9 8
Sub Cooler + + = +
C C Z C C
SC
3 9 6 4 =
c c
3 4
Evaporator + + = +
C C Z C C
Evap
5 24 1 25 =
c c
5 1
Condenser + + = +
C C Z C C
Cond
7 26 8 27 =
c c
8 7
Table 5
Properties of candidate refrigerants.
Refrigerant Critical
temperature
(K)
Critical
pressure
(MPa)
ODP GWP Toxicity
(ppm)
Safety
classification
CO2 304.13 7.377 0 1 5000 A1
Ethane 305.32 4.872 0 5.5 1000 A3
N2O 309.52 7.245 0.017 298 1000 A1
R152a 386.41 4.520 0 124 1000 A2
Fig. 2. Property diagrams of the candidate refrigerants a) T-s diagram b) P-h
diagram.
A.Z. Miran, et al. Energy Conversion and Management 197 (2019) 111890
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5. 2. Cycle modeling
2.1. Cycle description
Fig. 1 shows a schematic and T-s diagram of a transcritical re-
frigerant cycle. The 1-2-3-5′-1 cycle shown in Fig. 1b is a simple tran-
scritical refrigeration cycle consisting of a gas cooler, a compressor, an
expansion valve, and an evaporator. While the 1-2-3-4-5-1 is the main
cycle, which is combined with a dedicated subcooling cycle. The cycle
6-7-8-9-6 is the subcooling cycle, which is a VCC. This cycle consists of
a compressor, a condenser, an expansion valve, and a subcooler. The
subcooler links the main and subcooling cycles. This part acts as an
evaporator in the subcooling cycle, and a subcooler for the main cycle.
In the subcooling cycle, the evaporation process (9–6) absorbs heat
from the main cycle refrigerant that comes from the gas cooler.
2.2. Dedicated mechanical subcooling system (MS cycle)
Two criteria can be utilized to fix the evaporation level:
Temperature difference between the evaporation process and the pro-
duced outlet cold stream, and the other is constant average temperature
of transcritical cycle working fluid. The mentioned criteria offer better
results, but in some cases, the evaporator temperature is not in the
operating range of the compressors. Furthermore, the mechanical sub-
cooling evaporating temperature can reach the high-temperature
compressors’ maximum operating pressure. The second criteria is se-
lected in this study because it's closer to reality. Moreover, a fixed
amount of cooling capacity is considered in all studied cases.
2.3. Assumptions
The following assumptions are considered for calculations [7,8]:
(1) The system operates at the steady-state condition.
(2) The pressure drops and heat losses in the subcooler and other pi-
pelines are neglected.
(3) Expansion processes in both cycles are isenthalpic;
(4) For the subcooling cycle, the outlet temperature of the condenser is
8 °C above the gas cooler temperature.
(5) For the subcooler, the approach temperature is selected equal to
10 °C.
(6) The isentropic efficiency of main and subcooling cycle compressors
depends on the compression ratio.
(7) The gas cooler outgoing temperature (Tgc) is supposed to be be-
tween 30 °C and 50 °C, and evaporating temperature (Te) varies
from −30 °C and 0 °C.
(8) The electrical and mechanical efficiency of compressors are taken to
be 90%.
(9) The value of Qe for whole system is constant and taken to be
200 kW.
It is assumed that for cooling a space some specific cooling capacity
is needed and it is produced by different refrigerants under various
operating conditions.
2.4. Energy and exergy analysis
In the subcooling cycle, the thermodynamic properties at the states
are calculated by repeating method. Additionally, the depletion pres-
sure and the subcooling degree are also calculated using the repetition
for the main cycle. In addition, the properties of the refrigerant and
water are calculated using engineering equation solver (EES) [28].
Single-stage transcritical refrigeration cycle:
2.4.1. Main Cycle
The net consumed work of the compressor in the main cycle is given
as:
=
W m h h
( )/( . )
comp Main Main m e
, 2 1 (1)
Moreover, the isentropic efficiency of the compressor in the main
cycle is expressed as [29]:
= + +
P P P P P P
0.815 0.022( / ) 0.0041( / ) 0.0001( / )
is Main
, 2 1 2 1
2
2 1
3
(2)
= h h h h
( )/( )
is Main s
, 2 1 2 1 (3)
According to fixed cooling capacity of the evaporator, mass flow
Table 6
Comparison of results from the present model with those reported by Ref. [29].
CO2 With: Evaporator Temperature −15 −10 −5 0 5 10
Maximum COP R600a Dai 2018 1.7551 1.94898 2.17857 2.44898 2.77551 3.17347
Present Study 1.746 1.945 2.174 2.445 2.772 3.175
Err % 0.518% 0.204% 0.210% 0.163% 0.126% −0.048%
R152a Dai 2018 1.776 1.97 2.204 2.48 2.796 3.209
Present Study 1.756 1.955 2.184 2.455 2.782 3.185
Err % 1.126% 0.761% 0.907% 1.008% 0.501% 0.748%
R1234yf Dai 2018 1.71939 1.91837 2.14286 2.41327 2.7398 3.13265
Present Study 1.723 1.919 2.146 2.413 2.736 3.134
Err % −0.210% −0.033% −0.147% 0.011% 0.139% −0.043%
Optimum high pressure [MPa] R600a Dai 2018 9.41071 9.41071 9.40476 9.3869 9.375 9.36905
Present Study 9.426 9.426 9.42 9.4 9.387 9.38
Err % −0.162% −0.162% −0.162% −0.140% −0.128% −0.117%
R152a Dai 2018 9.387 9.387 9.381 9.369 9.351 9.345
Present Study 9.42 9.421 9.413 9.404 9.385 9.38
Err % −0.352% −0.362% −0.341% −0.374% −0.364% −0.375%
R1234yf Dai 2018 9.42857 9.42857 9.42262 9.41071 9.39881 9.39286
Present Study 9.443 9.444 9.438 9.43 9.414 9.408
Err % −0.153% −0.164% −0.163% −0.205% −0.162% −0.161%
Optimum subcooling degree [°C] R600a Dai 2018 22.4581 20.4469 18.4916 16.4804 14.4693 12.4581
Present Study 22.25 20.29 18.4 16.47 14.36 12.35
Err % 0.927% 0.767% 0.495% 0.063% 0.755% 0.868%
R152a Dai 2018 23.464 21.397 19.218 17.151 15.028 13.017
Present Study 23.07 20.96 18.94 16.97 14.76 12.88
Err % 1.679% 2.042% 1.447% 1.055% 1.783% 1.052%
R1234yf Dai 2018 20.838 18.9944 17.1508 15.2514 13.352 11.5084
Present Study 21 19.2 17.3 15.42 13.65 11.65
Err % −0.777% −1.082% −0.870% −1.105% −2.232% −1.230%
A.Z. Miran, et al. Energy Conversion and Management 197 (2019) 111890
5

6. Fig 3. Validation of the present TRC mechanical subcooling cycle with pre-
viously published data by Ref. [29].
Fig. 4. Effect of subcooling temperature on (a) COP and (b) Performance
parameters for different working fluids.
Fig. 5. Variation of COP by changing compressor discharge pressure for dif-
ferent working fluids.
A.Z. Miran, et al. Energy Conversion and Management 197 (2019) 111890
6

7. rate of the main cycle is calculated as follows:
=
m
h h
Q
Main
C Main
1 5
, (4)
Also, the main cycle coefficient of performance is given as follow:
=
COP Q W
/
Main c Main Comp Main
, , (5)
2.4.2. Subcooling cycle
=
W m h h
( )/( . )
comp MS MS m e
, 7 6 (6)
= + P P
0.874 0.0135( / )
is MS
, 7 6 (7)
= h h h h
( )/( )
is MS s
, 7 6 7 6 (8)
=
m h h m h h
( ) ( )
MS Main
6 9 3 4 (9)
=
Q m h h
( )
C MS MS
, 6 9 (10)
=
COP Q W
/
MS c MS Comp MS
, , (11)
2.4.3. Overall cycle
The input net power and COP of the entire cycle can be calculated
by the following equations:
= +
W W W
comp comp Main comp MS
. . (12)
=
Q m h h
( )
e Main 1 5 (13)
Overall performance of the system with thermal efficiency is ex-
amined as given [30]:
=
COP Q W
/
Overall e Comp (14)
= +
W w I
comp rev Total (15)
where Qe is the cooling capacity of the overall system.
The main assumptions and considered parameters of the simulation
are shown in Table 1.
Also, the main energy and exergy relations are presented in Table 2
for analyzing the system components.
Exergy is the optimal theoretical available work in regards to the
second law of thermodynamics and it also defines as the least beneficial
work needed to form an amount of material from the environment and
transforms the substance into a particular condition [21]. A powerful
methodology for accurately determining the type and quantity of ex-
ergy destruction in each component of the energy system is called ex-
ergy analysis [31]. This work has been investigated for quantitative
evaluation of causes of thermodynamic failure of the process under
investigation. The following equilibrium represents the exergy balance:
= +
E E E
in
i
Out
j D
(16)
E
in i, E
Out j and ED are the input, output and the rate of system
exergy destruction, respectively. Also, the exergy of each state point can
be calculated from the following:
=
E m h h T s s
[ ( )]
i i i o i o
0 (17)
Neglecting the kinetics and possible changes of the exergy, the
stream’s specific exergy is the sum of specific chemical (ech) and phy-
sical (eph) exergies [32]:
= +
e e e
i i
Ph
i
Ch
(18)
The specific physical exergy of the flow belongs to its temperature
and pressure, also the reference environment conditions [33,34]:
=
e h h T s s
( )
i
Ph
i o i o
0 (19)
The following presumptions are constructed for calculating the ex-
ergy of each state point:
(a) Kinetic and potential exergies of materials are ignorable.
(b) Only physical exergies are considered for the gas and vapor flows.
(c) Chemical exergies of the substances are neglected.
the heat stream exergy and the work exergy can be defined as follows
[35]:
=
E Q
T
T
1
q
0
(20)
=
E W
w (21)
The exergy efficiency and exergy destruction of system’s compo-
nents can be obtained as follows [36]:
=
E E E
D k F k P k
. . . (22)
=
E
E
k
P k
F k
.
. (23)
where, ED k
, , EF k
, , EP k
, and k are exergy destruction, fuel exergy, product
exergy, and exergy efficiency, respectively and product and fuel ex-
ergies for each component have been defined in Table 3.
The overall system’s exergy efficiency can be calculated by [7]:
Fig. 6. Variation of COP and exergy efficiency with compressor discharge
pressure for CO2 as main working fluid at different subcooling temperature.
Fig. 7. Variation of COP with compressor discharge pressure for CO2 as main
working fluid at different subcooling temperatures.
A.Z. Miran, et al. Energy Conversion and Management 197 (2019) 111890
7

8. =
E
W
II
qe
in (24)
here, Eqeis the product exergy of the system.
2.5. Exergoeconomic analysis
Exergoeconomic in a system is the combination of the economic and
exergy analyses. To evaluate the effectiveness of a refrigeration cycle,
exergoeconomic can be considered as a useful methodology. The ex-
ergoeconomic results are carried out by exergy or economic analyses,
simultaneously. This methodology’s main purpose is the unit cost of
product determination.
In the present work, the SPECO which is defined as specific exergy
costing method is used to evaluate exergoeconomic parameters such as
total product cost, exergy destruction cost, and exergoeconomic factor
[37].
2.5.1. Exergoeconomic evaluation
To evaluate each component of the single-stage TRC with the me-
chanical subcooling as a control volume, by designating the SPECO
method to the mentioned system, the following steps are accomplished
[38]:
I. The exergy amounts for each state point in the system are calculated
by thermodynamic properties;
II. Product and fuel are defined for components of the system;
III. Cost and auxiliary equations are identified for each component of
the system.
2.5.2. Cost balance
Writing the cost balance is determined as input and output equili-
brium for the kth
component and can be written as following [39]:
+ = + +
C C C C Z
e
e k w k q k
i
i k k
, , , ,
(25)
=
C c E
j j j (26)
In Eq. (25), i and e indices define the inlet and outlet streams for the
kth
component. Zk is the levelized cost rate associated with capital in-
vestment, operation, and maintenance.
The time-based capital cost investment of each component can be
calculated as following [40]:
= ×
×
×
Z CRF
N
Z
3600
k
r
k
(27)
here, r, N andZkare the maintenance factor equals to 1.06 and the
annual operating hours, and purchased equipment cost of the system
component, respectively.
CRF known as the capital recovery factor can be defined by [41]:
=
+
+
CRF
i i
i
(1 )
(1 ) 1
n
n
(28)
here, i designate the interest rate and n indicate the system's operation
years which are considered as 15% and 20 years, respectively. The
consumption power cost of the compressor is supposed as $10 per GJ
[42].
By considering the cost equilibrium associated with auxiliary
equations of each component, according to Table 4, for exergoeconomic
analysis, a computer program is developed by the EES software.
Fig. 8. COP of different refrigerants versus evaporator and gascooler temperatures.
A.Z. Miran, et al. Energy Conversion and Management 197 (2019) 111890
8

9. There are some key parameters in the exergoeconomic analysis such
as unit product cost (cP k
, ), unit fuel cost (cF k
, ), exergy destruction cost
(CD k
, ), and the exergoeconomic factor (fk). The mentioned parameters
can be defined as follows [43,44].
=
C c E
D k F k D k
, , , (29)
=
c
C
E
F k
F k
F k
,
,
, (30)
=
+
f
Z
Z C
k
k
k D k
, (31)
=
c
C
E
P k
P k
P k
,
,
, (32)
As shown in Eq. (31), a greater amount of exergy destruction or
exergy loss costs leads to a decrease in the value of fk, and in order to
improve the economic performance of the system, we need to focus on
the structure of component that needs to increase the initial cost of
investment.
The overall exergy destruction cost rate (CD overall
, ) and overall fk are
determined as follows:
=
=
C C
D Tot
i
n
D k
,
1
,
k
(33)
=
+
f
Z
Z C
k tot
Tot
Tot D Tot
,
, (34)
2.5.3. Selection of refrigerant
The candidate refrigerants for the supercritical refrigeration cycle
with mechanical subcooling are presented in Table 5. In addition, some
of the environmental-related parameters, for example, the toxicity,
safety grade, global warming and ozone depletion potentials of re-
frigerants are listed in Table 5. As it is obvious, R744A includes the
highest and R744 has the lowest GWPs that are about 298 and 1, re-
spectively.
Subcritical fluids are utilized in the auxiliary cycle as working fluid.
R152a is an HFC refrigerant, but the first issue to comment on is its
GWP value which is 124. Also, R152a is a refrigerant with a reduced
price compared to other HFC and HFO refrigerants and is included in
the A2 safety group following the ASHRAE Std32 [ASHRAE (2013)]
designation. In addition, R152 has a negative slope saturation vapor
line (wet fluid), and higher operating pressures. This means that R152a
is beyond the scope of the new regulations related to F-Gases, so no
reductions, replacements, prohibitions or taxes should be applied to this
fluid. In addition, R152a is available and it is known for its high-per-
formance. Therefore, the cycle performance is analyzed and discussed
based on the use of R152a as the subcooling cycle refrigerant (Fig. 2).
Fig.9. Effects of exergy efficiency on different refrigerants versus evaporator and gascooler temperatures.
A.Z. Miran, et al. Energy Conversion and Management 197 (2019) 111890
9

10. 3. Results
3.1. Model validation
In order to validate the thermodynamic model developed for the
proposed system, the performance of transcritical CO2 refrigeration
cycles with mechanical subcooling [29] is validated using data reported
in the literature for single stage part. Table 6 compares the results
obtained for TRC with mechanical subcooling cycle in the present work
with those reported by Dai et al. [29]. Also, a comparison of results
obtained from the present work and those reported by them for the
system is shown in Fig. 3. Referring to Table 6 and Fig. 3, there is a
good agreement between the results.
The effects of chosen parameters on the energy performance of the
transcritical refrigeration cycle with a dedicated subcooling system as
well as exergy performance are investigated in this section. Also,
comparing the energy and exergy of a simple and subcooling cycle, an
exergoeconomic analysis is performed. Three main output parameters,
namely, energy and exergy efficiencies, and overall unit product cost
are specified as optimization goals, while Ph and ΔTsub are considered as
decision variables that the SC cycle performance depends on.
3.2. Parametric study
Fig. 4-a shows the overall COP of the system under various amounts
of subcooling temperature difference for CO2, N2O and Ethane re-
frigerants. As can be seen, the COP of the system is optimized by
variation of the subcooling temperature. Furthermore, the COP for CO2
refrigerant is higher than those of the N2O and ethane. Moreover, the
range of subcooling temperature, which maximizes the COP for ethane,
is higher than CO2 and N2O. The optimum COP values for carbon di-
oxide, nitrous oxide, and ethane are 2.833, 2.711 and 2.158 at sub-
cooling temperature difference of 15 °C, 16.55 °C and 21.72 °C, re-
spectively.
Fig. 4-b shows the thermal performance changes in the carbon di-
oxide subcooling cycle. The parameters studied are cycle's coefficient of
performance, total power consumption, the input net-work of main
cycle compressor and the input work of the auxiliary cycle compressor.
It can be seen that the compressor energy consumption of main cycle
decreases with increasing subcooling temperature because the gas-
cooler output flow rate reduces by increasing the TSub. By increasing
the TSub, the energy consumption of the main cycle and auxiliary cycle
decreases and increases, respectively. Therefore, the overall consumed
energy in the compressors has a minimum value. As a result, due to the
constant value of cooling capacity, the overall COP primarily increased
and then reduced and the maximum COP is obtained at an optimal
temperature for subcooling.
The overall COP variation by change in the compressor pressure is
depicted in Fig. 5. According to this figure, the COP amount at first
increases dramatically with increasing the compressor pressure and
then gradually decreases. In this section, ΔTSub has a constant value and
therefore, the value of COP depends on compressor discharging pres-
sure changes. By increasing the compressor outlet pressure, the main
cycle compressor’s work increases, while the auxiliary cycle consumed
Fig. 10. Changing the optimum compressor pressure by gascooler and evaporator temperatures variation for different refrigerants.
A.Z. Miran, et al. Energy Conversion and Management 197 (2019) 111890
10

11. work decreases intensely, especially in the lower amounts of com-
pressor pressure which leads to a minimum value for the overall con-
sumed power in the system and maximization of COP. As shown in this
figure, the optimum COP for nitrous oxide is higher than that of others
at the same condition. Furthermore, the amount of compressor pressure
that maximizes the COP for ethane is lower than CO2 and N2O. In ad-
dition, the optimum value of COP for CO2, N2O and ethane is 2.763,
3.09 and 2.752 at compressor discharge pressure of 8.372, 7.067 and
5.374 MPa, respectively.
The COP and second law efficiency variation by a change in the
compressor pressure of the main cycle and the subcooler temperature
are illustrated in Fig. 6. Referring to this figure, increasing the com-
pressor pressure at first leads to increasing and then decreasing the COP
and II amount. As shown in this figure, the optimum COP and II in-
crease by increasing the subcooler temperature difference.
Fig. 7 shows the COP variation of transcritical refrigeration cycle
with using dedicated mechanical subcooling versus compressor dis-
charge pressure at Te = 0 °C and gascooler temperature of 35 °C by
utilizing CO2 as main working fluid and R152a as the auxiliary working
fluid. It can be seen that the COP is not only subject to discharge
pressure, but also associated with the temperature of subcooling. In
general, COP rises dramatically, and then gradually decreases with
discharge pressure and subcooling temperature. Specifically, the max-
imum COP of 2.75 and ηII of 40.73% has been obtained at discharge
pressure of 8.40 MPa and subcooling temperature of 13.01 °C, which
can be considered as an optimal discharge pressure and subcooling
temperature. According to the analytical results, there is an optimal
favorable discharge pressure when the gascooler outlet temperature is
fixed. The analyzes in the next sections are performed based on oper-
ating conditions with the highest COP at the optimum discharge pres-
sure and subcooling temperature.
Fig. 8, illustrates the variation of overall COP for CO2, N2O, and
Ethane with gascooler and evaporator temperature. As shown in Fig. 8-
a, COPOverall increases considerably with increasing the evaporator
temperature. Moreover, the COPOverall of nitrous oxide is always higher
than the COP of ethane and carbon dioxide by changing the evaporator
temperature from −30 to 0 °C. Fig. 8-b shows the variations in max-
imum yield of COP for the overall cycle with gascooler and evaporator
temperature for CO2, N2O, and Ethane. As shown in Fig. 8-b, the CO-
POverall decreases considerably with increasing gas cooler temperature.
The COPOverall of nitrous oxide is always higher than the COP of ethane
and carbon dioxide by changing the gascooler temperature from 30 to
50 °C. For instance, the maximum COP of N2O at Tevap = 0 °C and
Tgc = 30 °C is about 10.55% and 9.74% higher than CO2 and ethane,
respectively.
Fig. 8-c and 8-d show the gascooler and evaporator outgoing tem-
perature at maximum overall COP of the cycle in optimum conditions
for ethane-CO2 and ethane-N2O, respectively. Reducing the tempera-
ture of gascooler and increasing the evaporating temperature will result
in an increment of the maximum amount of COP, and as it can be seen,
the change in COP amount with Te changes is more than gas cooler
temperature. Because the same amount is considered for Qe, value of the
Fig. 11. Variation of compressor outgoing temperature versus gascooler and evaporating temperatures for CO2, N2O, and Ethane.
A.Z. Miran, et al. Energy Conversion and Management 197 (2019) 111890
11

12. COP is only associated with the compressor power consumption. The
consumed power relates to the specific work and mass flow rate value.
Compressor net power consumption is reduced by increasing the eva-
porator temperature, which results in COP increment. Also, the special
work of the compressor is related to the thermodynamic properties of
the refrigerant and level of operating pressure. In other words, ac-
cording to Fig. 8-c and 8-d, maximum COP values for nitrous oxide as a
refrigerant are higher than that of others.
The second law efficiency (ηII) variation with changing the eva-
poration and gascooler temperature for CO2, N2O, and Ethane are
shown in Fig. 9. The exergy efficiency (ηII) changes with variations of
the compressor consumption and entire cycle irreversibility values.
Also, compressor energy consumption increases with rising discharge
pressure. Therefore, WComp and ITotal increments lead to increasing the
value of ηII. As it is obvious in Fig. 9-a, increasing Te leads to a decrease
in the value of ηII. Also, as can be seen in Fig. 9-b, the amount of ηII is
decreasing with rising the gas cooler outlet temperature. According to
this figure, increment in the gas cooler temperature decreases the ex-
ergy efficiency. ηII variation with changing gas cooler and evaporator
temperature are shown in Fig. 9-c and 9-d. Referring to this figure,
decreasing both gas cooler and evaporator temperature will result in
raising the second law efficiency of cycle and in exergy analysis view-
point nitrous oxide is more efficient than the same for CO2 and ethane
in operating conditions of Tevap = 0 °C, and Tgc = 35 °C about 2.23%
and 2.13%, respectively.
Fig. 10-a, depicts the optimal discharge pressure changing with
evaporating temperature and it is almost constant because compressor
discharge pressure for refrigerants is not influenced by the variation of
Te. Fig. 10-b shows the optimal discharge pressure variations with
changing gas cooler temperature. It rises linearly with increasing the
gascooler temperature. However, the effect of evaporator temperature
is not significant.
The High discharge pressure of the compressor variables with both
gascooler and evaporator outgoing temperature are shown in Fig. 10-c
and 10-d. As can be seen, high discharge pressure rises with increasing
the gascooler temperature; however, it is almost constant by increasing
the evaporating temperature. Moreover, according to Fig. 10-c and 10-
d, in each value of gas cooler temperature, the high discharging pres-
sure for CO2 is higher than that of others and this is mainly due to
differences in their critical pressures (Table 5). With increasing dis-
charge pressure, the COP value is reduced, so the lower the compressor
discharging pressure, the system works better.
Fig. 11 reveals the effect of gascooler and evaporator temperature
on compressors discharging temperature for different refrigerants.
Fig. 11-a shows the variation of discharge temperature with changing
evaporator outgoing temperature in different gas cooler temperatures.
By increasing evaporator temperature, from −30 to 0 °C, discharge
temperature decreases linearly. Also, according to Fig. 11-b, by gas
cooler temperature increment, the high-temperature rises linearly. The
value of T2 for CO2 is higher than that for other working fluids at the
same condition. Effect of the gas cooler and evaporator temperature on
the high temperature is illustrated in Fig. 11-c. By increasing gascooler
Fig. 12. Total exergy destruction cost rate for different refrigerants changing with gascooler and evaporator temperatures.
A.Z. Miran, et al. Energy Conversion and Management 197 (2019) 111890
12

13. temperature and decreasing evaporator temperature, the maximum
amount of compressor outlet temperature increases. Also, R170 and
R744 have the lowest and highest compressor outlet temperature, re-
spectively. Meanwhile, the mentioned temperature has a considerable
influence on compressor performance, also its decrement will increase
the compressor life-time. As shown in Fig. 11-a, the value of T2 for
ethane at Te = −30 °C has the highest difference at Tgc = 50 °C about
46.32 °C and 42.32 °C lower than that for CO2 and N2O, respectively.
3.3. Exergoeconomic analysis
In this section, the primary economic parameters includingCD Overall
. ,
fk and unit product cost of the system have been investigated and the
results are shown in the graphs below. Changes in total exergy de-
struction cost (CD Overall
. ) are shown in Fig. 12 by reflecting the eva-
porator and gascooler temperatures for different refrigerants. Rising the
evaporating temperature and reducing the temperature of gascooler
will reduce the value ofCD Overall
. . Also, the amount of CD Overall
. is directly
relevant to the amount of ED that reduces with increasing Te and de-
creasing Tgc. Compared to refrigerants, CO2 and N2O have the highest
and lowest amount of CD Overall
. , respectively.
As already mentioned, the fk shows the relative significance of ca-
pital components cost in comparison with the cost of exergy destruc-
tion. The effect of the units such as evaporator and gas-cooler tem-
perature on the exergoeconomic coefficient is shown in Fig. 13.
According to this figure, for an extensive variety of operational condi-
tions, the fk value is less than 50% and demonstrates that CD Overall
. has a
significant role in the system exergoeconomic efficiency. So, replacing
cycle equipment with more efficacious and high-cost ones can enhance
the economic efficiency in the overall system. CO2 has the least fk be-
tween the studied refrigerants. The amount of fk for CO2 is lower than
ethane and nitrous oxide about 3.1% and 1.51% at Te of 0 °C and Tgc of
30 °C, respectively. This means CO2 cycle has the highest capacity for
improvement by replacing the more effective and expensive compo-
nents. Moreover, according to this figure, fk decreases by rising gas
cooler temperature, while its amount rises by increasing the tempera-
ture of the evaporator.
The main goal of a refrigeration cycle is to have a secondary flow or
a cooling part that called the primary product of the system. The cost of
exergy destruction is an important parameter that can be obtained by
conventional exergoeconomic analysis.
Fig. 14 shows the total product cost rate effected by variation of the
gas cooler and evaporator temperature. According to this figure, the
variation of cProduct has a linear form. The overall cost rate, in con-
junction with exergy destruction of the system, is reduced about 2 $/h
with an evaporation temperature increasing of 5 °C at a constant gas
cooler temperature. The cooling process in subcooler alters the exergy
of a cooled stream or the substance. According to Fig. 14, by rising
evaporator temperature, the total unit product cost decreases, as well as
reducing gas cooler temperature. In addition, the average highest and
lowest unit product costs (the average amount of cProduct for
Tgc = 30 ~ 50 °C) at Te = −20 °C, belongs to ethane and carbon di-
oxide by 23.05 and 23.44 $ GJ−1
, respectively. The same value for N2O
Fig. 13. Variation of the total exergoeconomic factor with gascooler and evaporator temperatures.
A.Z. Miran, et al. Energy Conversion and Management 197 (2019) 111890
13

14. is approximately 23.22 $ GJ−1
in the same operating conditions which
is between two other refrigerants. This factor makes the CO2 re-
frigerants more economically privileged than other refrigerants.
Fig. 14-c and 14-d show the total product cost rate variation with
changing gascooler and evaporator temperature in optimum conditions
for ethane-N2O and N2O-CO2, respectively. As it is depicted, cProduct
decreases with increasing both gascooler and evaporating temperature.
4. Comprehensive comparison of subcooled and simple cycles
A comprehensive comparison between the transcritical refrigeration
cycle using dedicated mechanical subcooling and the simple cycle is
accomplished in this section. The COP, second law efficiency, ex-
ergoeconomic factor, and unit product cost between cycles with or
without subcooling are compared for different refrigerants (CO2, N2O,
and ethane) at Tgc = 35 °C and Te = −20 °C, at optimum conditions.
Fig. 15.a shows a comparison of COP between simple cycle and cycle
with subcooler for different refrigerants. As can be seen, the amount of
COP for subcooling cycle is higher than that for a simple cycle and its
value for N2O is the highest in both systems. The difference between
simple and subcooling cycle's COP for CO2, N2O, and Ethane is about
0.422, 0.403 and 0.482, respectively. In fact, utilizing the subcooling
cycle increases the COP amount for CO2, N2O, and Ethane about
30.74%, 26.48%, and 36.1%, respectively which illustrates that sub-
cooling is more efficient for ethane cycle. Fig. 15.b illustrates a com-
parison of II between simple and subcooling cycle for different re-
frigerants. According to this figure, the amount of II is enhanced for
subcooling cycle in comparison with the simple cycle. The highest value
of II belongs to N2O and its value in the subcooling cycle is about
14.96% more than the simple cycle. Also, the amount of second law
efficiency for CO2 and Ethane in the cycle with subcooler is higher than
a simple cycle of about 16.59% and 19.24%, respectively. Comparison
of exergoeconomic factor between simple and subcooling cycle for CO2,
N2O, and Ethane, is displayed in Fig. 15.c and Ethane has the highest
value in both systems among other refrigerants. Value of fOverall for CO2,
N2O and ethane in subcooling cycle is about 18.27, 14.62 and 14.91%
higher than simple cycle. Fig. 15.d shows a comparison of unit product
cost between simple and subcooling cycle for different refrigerants.
According to this figure, the amount of cProduct for subcooling cycle is
higher than that for simple cycle due to more components used in the
cycle with subcooler. The highest value of unit product cost belongs to
Ethane following with N2O and CO2. The value of cProduct for the sub-
cooling cycle for CO2, N2O and Ethane is about 9.04, 8.37 and 10.63%
more than the simple cycle, respectively. The comparison of the ob-
tained results for COP and cProduct in this section reveals an important
point. Based on the mentioned results, utilizing the dedicated sub-
cooling cycle for performance improvement of the transcritical cycle,
the unit cost of the product increases less than the COP of system. This
means using subcooler can be considered as an effective and econom-
ical way for the system’s performance improvement.
5. Conclusion
In this paper, the influences of dedicated subcooling cycle on a
Fig. 14. Evaporator and gascooler temperature effects on the unit product cost.
A.Z. Miran, et al. Energy Conversion and Management 197 (2019) 111890
14

15. transcritical refrigeration cycle are investigated based on energy, ex-
ergy, and exergoeconomic analysis. A parametric study is thoroughly
investigated on the system and finally, the performance of the system
with and without subcooler is compared. All the acquired results are
surveyed by optimizing the coefficient of performance subject to sub-
cooling temperature difference, and compressor discharge pressure.
The main conclusions obtained from the presented study can be sum-
marized as follow:
• The COP and exergy efficiency are optimized by subcooling tem-
perature difference and compressor discharge pressure. The op-
timum ΔTSub for ethane is higher than that of CO2 and N2O.
• In similar conditions, the maximum and minimum COP and exergy
efficiency belong to N2O and CO2, respectively.
• The compressor discharge pressure, which maximizes the COP, has
the highest and lowest values for CO2 and ethane. The same trend
can be observed for the gas cooler inlet temperature. These para-
meters have a significant effect on the compressor lifetime, which
makes the ethane an appropriate refrigerant from this point of view.
For Te = 0 °C and Tgc = 30 °C, the compressor discharge pressure of
ethane refrigerant is 32.44% and 55.02% lower than that of N2O
and CO2. In the same operating conditions, the difference of the gas
cooler inlet temperature between ethane-N2O and ethane-CO2 is
44.42% and 48.61%, respectively.
• The CO2 refrigerant is the best case based on economic evaluations
among the analyzed refrigerants, due to its lowest CD Overall
. and
cProduct. The average unit product cost in Te = −20 °C for CO2, N2O
and ethane is 23.44, 23.22 and 23.05 $ GJ−1
, respectively.
• According to the obtained results from comparing the system with
and without subcooling cycle, utilizing subcooler improves perfor-
mance of the system, while it increases the unit product cost. It is
worth mentioning that, the unit product cost increment is much
lower than COP improvement. This means using subcooler can be
considered as an effective and economical way for the refrigeration
system’s performance improvement. The COP enhancement for CO2,
N2O, and ethane is 30.74%, 26.48%, and 36.1%, respectively and
the unit product cost increment is 9.04%, 8.37% and 10.63% for the
mentioned refrigerants, respectively.
Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influ-
ence the work reported in this paper.
Fig. 15. Comparison of main performance parameters between simple and subcooling cycle for different refrigerants a) COP, b) II, c) foverall and d) cProduct.
A.Z. Miran, et al. Energy Conversion and Management 197 (2019) 111890
15

16. Appendix A
The purchased equipment costs associated with evaporator, heat exchanger (Sub Cooler), condenser and gascooler can be calculated, considering
each of them as a simple heat exchanger in the form of a power-law relation as:
=
Z Z
A
A
.
k R k
k
R
,
0.6
(A1)
It should be noted that, ZR k
, is the reference cost which is listed in Table A-1, and is the reference size of each mentioned heat exchangers which is
considered to be 100 m2
. Furthermore, Ak is the heat exchanger area which is a function of operating condition and refrigerant. The subscript ‘R’
represents the reference component of a particular type and size. The cost of electrical energy used for the motors of compressors is considered $10
per GJ [42].
Also, the purchased equipment cost for the case of compressors is considered as follows [45,46]:
= ×
Z W
10167.5
C C
1 1
0.46
(A2)
= ×
Z W
10167.5
C C
2 2
0.46
(A3)
In the above-mentioned equations, WC1
0.46
and WC2
0.46
represent the consumed power by compressor 1 and 2, respectively.
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