Performance optimization of transcritical CO2 cycle with parallel compression economization
ABSTRACT Being a low critical temperature fluid, CO2 transcritical system offers low COP for a given application. Parallel compression economization is one of the techniques to improve the COP for transcritical CO2 cycle. An optimization study of transcritical CO2 refrigeration cycle with parallel compression economization is presented in this paper. Further, performance comparisons of three different COP improvement techniques; parallel compression economization alone, parallel compression economization with recooler and multistage compression with flash gas bypass are also presented for chosen operating conditions. Results show that the parallel compression economization is more effective at lower evaporator temperature. The expression for optimum discharge pressure has been developed which offers useful guideline for optimal system design and operation. Study shows that the parallel compression with economizer is promising transcritical CO2 cycle modifications over other studied cycle configurations. A maximum improvement of 47.3% in optimum COP is observed by employing parallel compression economization for the studied ranges.

Conference Paper: A rapid algorithm for online and realtime ARMA modeling
[Show abstract] [Hide abstract]
ABSTRACT: We introduce a new practical method of online and realtime ARMA modeling. In this method a very high order AR model is used to approach the ARMA model. The multiplication of multi lower order AR models are used to replace the high order AR model, and the cascading linear systems are used to resolve the multiplication of the AR models. The lower order and linear algorithm can achieve the online and realtime resolution. The modeling experiments for some systems have proved that the method is effective, and the prediction based on the method also has higher precision. This method has been used to improve GPS positioning precision to achieve some better resultsSignal Processing Proceedings, 2000. WCCCICSP 2000. 5th International Conference on; 02/2000
Page 1
Performance optimization of transcritical CO2cycle with parallel
compression economization
Jahar Sarkara, Neeraj Agrawalb,*
aDepartment of Mechanical Engineering, Institute of Technology, B.H.U. Varanasi, UP221005, India
bDepartment of Mechanical Engineering, Dr. B. A. Technological University Lonere, MS402 103, India
a r t i c l e i n f o
Article history:
Received 15 May 2009
Received in revised form
28 November 2009
Accepted 1 December 2009
Available online 30 December 2009
Keywords:
Transcritical CO2cycle
Parallel compression economization
Optimization
Performance improvement
Comparison
a b s t r a c t
Being a low critical temperature fluid, CO2transcritical system offers low COP for a given application.
Parallel compression economization is one of the techniques to improve the COP for transcritical CO2
cycle. An optimization study of transcritical CO2refrigeration cycle with parallel compression econo
mization is presented in this paper. Further, performance comparisons of three different COP improve
ment techniques; parallel compression economization alone, parallel compression economization with
recooler and multistage compression with flash gas bypass are also presented for chosen operating
conditions. Results show that the parallel compression economization is more effective at lower evap
orator temperature. The expression for optimum discharge pressure has been developed which offers
useful guideline for optimal system design and operation. Study shows that the parallel compression
with economizer is promising transcritical CO2cycle modifications over other studied cycle configura
tions. A maximum improvement of 47.3% in optimum COP is observed by employing parallel compres
sion economization for the studied ranges.
? 2009 Elsevier Masson SAS. All rights reserved.
1. Introduction
While the synthetic refrigerants exhibit considerably high ODP
and GWP, lately the environment friendly natural refrigerant
carbon dioxide has gained considerable interest and identified as
a suitable alternative refrigerants owing to its excellent heat
transfer properties and it is nonflammable and nontoxic [1].
However, critical temperature for CO2is quite low (31.1?C). A fluid
with a lower critical temperature will tend to have a higher volu
metric capacity and a lower COP for a given application [2]. The
lower COP is related to high level of irreversibility because of the
superheated vapour horn and the throttling process [3,4]. A
significant amount of research has been carried out to improve the
COP of transcritical CO2 systems by cycle modification such as
employing internal heat exchanger, multistage compression,
expansion turbine, vortex tube and ejector expansion device [5].
Cecchinato et al. [6] carried out thermodynamic analysis on two
stage transcritical CO2cycles. It is shown that employing double
compression with intercooling improves the performance signifi
cantly and also governs the choice of optimum intermediate
pressure.
Parallel compression economization is one of the techniques
where refrigerant vapour is compressed to supercritical discharge
pressure in two separate nonmixing streams; one coming from an
economizer and the other coming from the main evaporator to
improve the performance of transcritical CO2refrigeration cycle.
The parallel compression system will have wide application for
automotive air conditioning, window air conditioners and small
water chillers where it is not appropriate to use screw or scroll
compressors [7]. Bell [8] has carried out theoretical and experi
mental study on parallel compression economization CO2refrig
eration cycle considering suction superheat. It is concluded that
parallel compression economization is more beneficial with CO2
transcritical system than similar hydrocarbon system in terms of
efficiency and capacity under the same conditions. However, this
simplified study did not include the optimization issue of the cycle.
In the present study an optimization of transcritical CO2
refrigeration cycle with parallel compression economization has
been carried out. Further, performance comparisons with other
similar cycle layouts (parallel compression with recooler [9,10] and
multistage with flash gas bypass [11]) are presented.
2. Mathematical modeling and simulation
The
flowdiagramandcorrespondingpressureeenthalpy
diagram of a transcritical CO2 cycle with parallel compression
* Corresponding author. Tel.: þ91 2140 275101; fax: þ91 2140 275142.
Email address: neeraj.titan@gmail.com (N. Agrawal).
Contents lists available at ScienceDirect
International Journal of Thermal Sciences
journal homepage: www.elsevier.com/locate/ijts
12900729/$ e see front matter ? 2009 Elsevier Masson SAS. All rights reserved.
doi:10.1016/j.ijthermalsci.2009.12.001
International Journal of Thermal Sciences 49 (2010) 838e843
Page 2
economization is shown in Fig.1. The liquid (state 5) and vapour (7)
are separated in economizer after the expansion of transcritical
fluid from states 3 to 4 in primary expansion valve V1. The liquid
from the separator is further expanded in expansion valve V2to
provide cooling effect in the evaporator (from states 6 to 1). The
saturated vapourfromevaporatorand economizer is compressed in
the compressor simultaneously to the states 2 and 8, respectively.
The mixed stream (state 9) enters to the gas cooler for heat rejec
tion to the external fluid (states 9e3). The entire system has been
modeled based on the energy balance of individual components of
the system. Steady flow energy equations based on first law of
thermodynamics have been employed in each case and specific
energy quantities are used. The following assumptions have been
made in the thermodynamic analysis:
? Heat transfer with the ambient is negligible
? Compression process is adiabatic but nonisentropic
? Evaporation and gas cooling processes are isobaric
? Separation and mixing processes are isobaric
? Refrigerant at evaporator outlet is saturated vapour
Further it is assumed that process in both the expansion valves
is isenthalpic which brings
h3¼ h4;
For unit total mass flow rate, the mass flow rates through the
economizing and main compressors are x4and 1 ? x4, respectively,
where, x4is given as:
h5¼ h6
(1)
x4¼ ðh4? h5Þ=ðh7? h5Þ
The isentropic efficiency of the compressor is given as:
(2)
his;comp¼h2s? h1
h2? h1
¼h8s? h7
h8? h7
(3)
Refrigerating effect of the evaporator:
qev ¼ ð1 ? x4Þðh1? h6Þ
Work input to the compressor:
(4)
wc ¼ x4ðh8? h7Þ þ ð1 ? x4Þðh2s? h1Þ
The cooling COP for parallel compression economization is
given by:
(5)
COP ¼ qev=wc
(6)
The cooling COP of corresponding basic cycle is given by:
COPb¼ ðh1? h3Þ=ðh2? h1Þ
(7)
A computer code has been developed for the steady state
simulation to evaluate the system performance of the proposed
parallel compression economization CO2 cycle under different
operating conditions. Subcritical and supercritical thermophysical
properties of CO2are estimated employing a precision property
code CO2PROP developed locally [12]. For the given evaporator and
gas cooler exit temperatures, and gas cooler and economizer
pressures, properties at states 1, 3, 5 and 7 are calculated. Properties
of states 4 and 6 are calculated employing Eq. (1) and then econ
omizing mass fraction is evaluated by Eq. (2). Compressor exit
conditions (2 and 8) are evaluated using compressor isentropic
efficiency relation (Eq. (3)). Further, state 9 is also calculated. Using
Eqs. (4)e(7), the performance parameters: cooling capacity,
compressor work, COP and COPbare calculated.
Specific enthalpy
Pressure
Evaporator
Compressor
Gas cooler
V1
2
1
3
1
93
4
4
7
9
8
6
5
7
5
6
V2
82
Fig. 1. Layout and peh diagram of CO2cycle with parallel compression economization.
Nomenclature
COP
GWP
h
_ m
ODP
pd;opt
q
t, T
V
w
x
3
coefficient of performance
Global warming potential
specific enthalpy (kJ kg?1)
mass flow rate of refrigerant (kg s?1)
Ozone depletion potential
optimum discharge pressure (bar)
refrigerating effect (kJ)
temperature (?C, K)
valve
compressor work (kJ)
vapour mass fraction
recooler effectiveness
Subscripts
1e10
b
c
co
ev
refrigerant state points
basic cycle
compressor
gas cooler exit
evaporator
70
90
110
130
150
170
3040 5060
Gas cooler exit temperature (oC)
) r a
b (
e r u
s
s
e r p
e
g r a
h
c
s i d
m
u
m
i t p
O
5
20
45
o
ev
o
ev
o
ev
tC
tC
tC
=
= −
= −
Fig. 2. Variation of optimum discharge pressure with gas cooler exit temperature.
J. Sarkar, N. Agrawal / International Journal of Thermal Sciences 49 (2010) 838e843
839
Page 3
3. Results and discussion
It is reported [11,12] that an optimum gas cooler pressure exists
for the transcritical CO2cycle where it exhibits the maximum COP
for a given gas cooler exit temperature. However, in case of two
stage compression transcritical CO2cycle, the intermediate pres
sure is also an influential parameter to decide the best COP along
with the gas cooler pressure [6,11]. It makes necessary to optimize
the gas cooler pressure and intermediate pressure simultaneously.
The performance of the optimized transcritical carbon dioxide
cycle with parallel compression economization on the basis of
maximum cooling COP are presented for various evaporator and
gas cooler exit temperatures. Isentropic efficiency depends on both
compressor design and pressure ratio. However, it is observed that
it has negligible effect on optimum pressures. Hence, the isentropic
efficiency for both main and economizing compressors is taken
a constant value of 75% to accommodate nonisentropic compres
sion. In the search for optimum gas cooler pressure and economizer
pressure, simultaneous variation of the gas cooler pressure and
economizer pressure with a step size of 0.2 bar was taken in
numerical simulation. Existence of the optimum economizer
pressure is mainly on account of the changing slope of saturation
curve while optimum discharge pressure is existed due to the
unique behavioural pattern of CO2properties around the critical
point where the slope of the isotherms is quite modest for a specific
pressure range; at pressure above and below this range, the
isotherms become much steeper. Improvement in COP and reduc
tion in discharge pressure are compared with optimized basic cycle
by keeping operating conditions the same.
Variation of optimum discharge pressure with gas cooler exit
temperature for three evaporator temperatures, tev¼ 5?C, ?20 C
and ?45
increases rapidly with gas cooler exit temperature. However, vari
ation of optimum economizer pressure is quite modest with gas
cooler exit temperature (Fig. 3). This can be attributed to the fact
that although the shape of isotherm changes with temperature, the
shape of saturation curve remains unaltered. Optimum economizer
pressure is comparatively more influenced by evaporator temper
ature than that of gas cooler exit temperature (Fig. 3). It is shown in
Fig. 2 thatevaporatortemperaturehas negligible effecton optimum
discharge pressure.
As discussed earlier that the liquid and vapour are separated in
economizer after the expansion of transcritical fluid in primary
expansion valve V1to minimize the vapour entry in the evaporator.
Fig. 4 exhibits the variation of mass fraction ‘x4’ goes in the econ
omizer with gas cooler exit temperature at various evaporator
temperatures. It can be seen that economizer mass fraction
increases with increase in cycle temperature lift (Fig. 4). This may
?C is shown in Fig. 2. Optimum discharge pressure
33
38
43
48
53
58
63
3040 5060
Gas cooler exit temperature (oC)
) r a
b ( e r u
s
s
e r p r e
z i
m
o
n
o
c
e
m
u
m
i t p
O
45o
ev tC
= −
20o
ev tC
= −
5o
ev tC
=
Fig. 3. Variation of optimum economizer pressure with gas cooler exit temperature.
0.29
0.34
0.39
0.44
0.49
0.54
0.59
304050 60
Gas cooler exit temperature (oC)
n
o i t c
a r f s
s
a
m
r e
z i
m
o
n
o
c
E
5
20
45
o
ev
o
ev
o
ev
tC
tC
tC
=
= −
= −
Fig. 4. Variation of optimum economizer mass fraction with gas cooler exit
temperature.
0.5
1.3
2.1
2.9
3.7
4.5
5.3
30405060
Gas cooler exit temperature (oC)
P
O
C
g
n i l o
o
c
m
u
m
i x
a
M
5
20
45
o
ev
o
ev
o
ev
tC
tC
tC
=
= −
= −
Fig. 5. Variation of maximum cooling COP with gas cooler exit temperature.
30405060
Gas cooler exit temperature (oC)
1
5
9
13
17
21
25
)
%
( n
o i t c
u
d
e r e r u
s
s
e r p e
g r a
h
c
s i
D
5o
ev tC
=
20o
ev tC
= −
45o
ev tC
= −
Fig. 6. Variation of percentage discharge pressure reduction in comparison with basic
optimum cycle with gas cooler exit temperature.
J. Sarkar, N. Agrawal / International Journal of Thermal Sciences 49 (2010) 838e843
840
Page 4
be due tothe fact that at high gas cooler exit temperature, optimum
discharge pressure is high while optimum economizer pressure
decreases with lowering the evaporatortemperature(Figs. 2 and 3).
With decrease in evaporator temperature, optimum economizer
pressure decreases, although difference increases which leads to
increase in quality at the evaporator inlet. Fig. 5 shows that
optimum cooling COP increases with decrease in temperature lift
similar to the basic CO2transcritical cycle. This implies that CO2
transcritical system should operate at lower gas cooler exit
temperature to have higher optimum cooling COP and lower
optimum discharge pressure.
Reduction in optimum discharge pressure improves the COP
[11]. One of the techniques to reduce the optimum discharge
pressure is by adopting parallel compression economization.
Percentage reduction (compare to optimum basic cycle) in
optimum discharge pressure and improvement in optimum cooling
COP with gas cooler exit temperature are shown in Figs. 6 and 7,
respectively. Results show that the percentage improvement in
cooling COP and percentage reduction in discharge pressure first
increase and then decrease with gas cooler exit temperature at all
the chosen evaporator temperatures with a peak value. The peak
value shifts towards higher gas cooler temperature as the evapo
rator temperature decreases. This may be attributed to the fact that
as the gas cooler temperature increases, initially vapour quality
increases with faster rate than that of later stages (due to unique
behaviour of isentropic and isotherm) and hence the compressor
work reduction increases initially at faster rate and then at slower
rate. Consequently, parallel compression cycle COP decreases at
slower rate initially than that of basic cycle COP and hence
percentage improvement of COP increases and then decreases.
Nevertheless there is gain in terms of reduction in optimum
discharge pressure and improvement in maximum cooling COP and
both increase with decrease in evaporator temperature. It may be
noted that gain in cooling COP is as high as 47.3% while reduction in
optimum discharge pressure in the range of 2e23% for the chosen
conditions. Hence, it may be concluded that parallel compression
economization is more profitable at lower evaporator temperature.
Fig. 8 shows the variations of discharge pressure, economizer
pressure, COP and COP improvement for pressure ratio dependent
compressor isentropic efficiency (correlation given in Ref. [12]).
Results show that the variation trends of all parameters are similar
to those of constant isentropic efficiency as shown above, whereas
absolute values are slightly different due to different isentropic
efficiency value ranges.
Performing a regression analysis on the data obtained from the
cycle simulation, the following relation are obtained to predict the
optimum discharge pressure for the parallel compression system
studied here for the chosen temperature ranges; tev¼ ?45?C to
5?C and tco¼ 30?Ce60?C.
1
5
9
13
17
21
30405060
Gas cooler exit temperature (oC)
)
%
( t n
e
m
e
v
o r p
m
i
P
O
C
,
P
O
C
57
78
99
120
141
162
Economizer pressure, discharge
) r a
b ( s
e r u
s
s
e r p
Cooling COP
COP improvement
Discharge pressure
Economizer pressure
5o
ev tC
=
Fig. 8. Variations of optimum parameters for variable compressor isentropic efficiency.
10
17
24
31
38
45
52
304050 60
Gas cooler exit temperature (oC)
)
%
( t n
e
m
e
v
o r p
m
i
P
O
C
g
n i l o
o
C
5o
ev tC
=
20o
ev tC
= −
45o
ev tC
= −
Fig. 7. Variation of percentage cooling COP improvement in comparison with basic
optimum cycle with gas cooler exit temperature.
Specific enthalpy
e r u
s
s
e r
P
Evaporator
Compressor
Gas cooler
V1
2
1
3
1
93
4
4
7
9
8
6
5
7
5
6
Subcooler
2
V2
Fig. 9. Layout and peh diagram of parallel compression cycle with recooler.
Specific enthalpy
e r u
s
s
e r
P
Evaporator
Compressor
Gas cooler
2
1
3
1
9
3
4
4
7
9
8
6
5
7
5
6
2
8
V1
V2
Fig. 10. Layout and peh diagram of twostage cycle with flash gas bypass.
J. Sarkar, N. Agrawal / International Journal of Thermal Sciences 49 (2010) 838e843
841
Page 5
pd;opt¼ 36:877 ? 0:00004tevþ 0:38234tcoþ 0:027667t2
where temperature in?C.
Effect of employing parallel compression with recooler and
multistage compression with flash gas bypass is also presented
here. Flow diagram and corresponding peh representation of
parallel compression cycle with recooler are shown in Fig. 9. The
exit transcritical vapour from gas cooler is recooled (3e5) in
recooler by the secondary stream (4e7) which is at lower pressure
and temperature due to expansion in the valve V1, prior to entry in
the recooler. The recooledliquid is furtherexpanded (5e6) invalve
V2 to provide useful cooling effect in the evaporator (6e1).
Compression processes are similar to parallel compression econo
mization cycle. It is assumed that exit state (7) of the cooling stream
in recooler is dry saturated, which can be maintained by the proper
splitting of refrigerant flow from gas cooler.
Properties at 5 can be found by using effectiveness of recooler,
which is taken as 0.8, given as:
co
(8)
T5¼ T3? 3ðT3? T7Þ
Applying energy conservation for recooler, the mass flow rate at
7 for unit total mass flow rate is given by:
(9)
_ m7¼ ðh3? h5Þ=ðh7? h5Þ
then performance of the recooler system is given as:
?1 ? _ m7
Flow diagram of twostage transcritical CO2system with flash
gas bypass is shown in Fig. 10 where vapour from low pressure
compressor (1e2) mixes with flash gas (state 7) and then
compressed (8e9) to gas cooler pressure. The cooling COP is given
as [11]:
(10)
COP ¼
?ðh1? h6Þ
ð1 ? _ m7Þðh2? h1Þ þ _ m7ðh8? h7Þ
(11)
COP ¼
ð1 ? x4Þðh1? h6Þ
ð1 ? x4Þðh2? h1Þ þ ðh9? h8Þ
where x4is the vapour mass fraction at state 4.
Performance comparisons in terms of cooling COP, percentage
reduction in discharge pressure and percentage improvement in
optimum COP of the three systems explained earlier are shown in
Figs. 11e13, respectively, for various evaporator and gas cooler exit
temperatures. Results show that the parallel compression cycles
with economizer and recooler are similar in terms of cooling COP,
discharge pressure reduction and COP improvement (Figs. 11e13).
However, use of parallel compression with economizer is more
profitable for lower temperature applications. Increase in recooler
effectiveness may give more COP improvement. Considering the
economics, parallel compression cycle with economizer is better
than that with recooler due to the lower cost of separator than
recooler. Figs. 11 and 13 exhibit that performance of the parallel
compression cycle with economizer is better than twostage cycle
with flash gas bypass. It can be said that employing parallel
compression economization in a simple transcritical CO2cycle is
the most effective way to improve the cycle performance.
(12)
4. Conclusions
A detailed optimization study of transcritical CO2cycle with
parallel compression economization is presented here. Further,
a comparative study of three systems; transcritical CO2systemwith
parallel compression economization, recooler and flash gas bypass
are also included. Discharge pressureand intermediatepressure are
simultaneously optimized based on cooling COP. Employing
parallel compression economization not only improves the
optimum cooling COP, but also brings down the optimum discharge
0
1
2
3
4
5
Maximum cooling COP
With economizer
With recooler
With flash gas bypass
5
30
o
o
C
C
5
60
o
o
C
C
55
30
o
o
C
C
−
55
60
o
o
C
C
−
ev
co
t
t
Fig. 11. Comparison based on maximum cooling COP.
0
5
10
15
20
25
Discharge pressure reduction (%)
With economizer
With recooler
With flash gas bypass
55
60
o
o
C
C
−
55
30
o
o
C
C
−
5
60
o
o
C
C
5
30
o
o
C
C
ev
co
t
t
Fig. 12. Comparison based on optimum discharge pressure reduction.
0
5
10
15
20
25
30
35
40
45
50
)
%
(
t n
e
m
e
v
o r p
m
i
P
O
C
g
n i l o
o
C
With economizer
With recooler
With flash gas bypass
55
60
o
o
C
C
−
55
30
o
o
C
C
−
5
60
o
o
C
C
5
30
o
o
C
C
ev
co
t
t
Fig. 13. Comparison based on maximum cooling COP improvement.
J. Sarkar, N. Agrawal / International Journal of Thermal Sciences 49 (2010) 838e843
842
Page 6
pressure. Optimum discharge pressure varies significantly with gas
cooler exit temperature. However, the optimum economizer pres
sure varies marginally, in contrast to the variation with evaporator
temperature with gas cooler pressure. The expression for optimum
discharge pressure has been developed which offers useful guide
line for optimal system design and operation. Usefulness of parallel
compression economization is more significant at lower evaporator
temperature. It is observed that cycle configuration is insignificant
in terms of maximum cooling COP. However, the cycle configura
tion is significant with respect to percentage improvement in COP.
Use of parallel compression with economizer is more profitable for
lower temperature applications. Employing parallel compression
economization improves the optimum COP of CO2 transcritical
refrigeration cycle by 47.3% for the chosen ranges over basis CO2
transcritical refrigeration cycle. Present study reveals that the
parallel compression with economizer is promising modifications
to improve the transcritical CO2cycle performance.
References
[1] M.H. Kim, J. Pettersen, C.W. Bullard, Fundamental process and system design
issues in CO2 vapor compression systems. Progress Energy Combustion
Science 30 (2) (2004) 119e174.
[2] S. Yana Motta, P.A. Domanski, Impact of elevated ambient temperature on
capacity and energy input to a vapour compression system e literature review,
Letter report for ARTI 21CR Research Project: 605e50010/60550015.
[3] G. Lorentzen, Revival of carbon dioxide as a refrigerant. International Journal
of Refrigeration 17 (5) (1994) 292e300.
[4] J. Sarkar, S. Bhattacharyya, M. Ramgopal, Transcritical CO2heat pump systems:
exergy analysis including heat transfer and fluid flow effects. Energy
Conversion and Management 46 (13e14) (2005) 2053e2067.
[5] E.A. Groll, J.H. Kim, Review of recent advances toward transcritical CO2cycle
technology. HVAC&R Research 13 (3) (2007) 499e520.
[6] L. Cecchinato, M. Chiarello, M. Corradi, E. Fornasieri, S. Minetto, P. Stringari,
C. Zilio, Thermodynamic analysis of different twostage transcritical cycles.
International Journal of Refrigeration 32 (5) (2008) 1058e1067.
[7] S.F. Pearson, Improved transcritical refrigeration cycle, European Patent
EP1498667 2005.
[8] I. Bell, Performance increase of carbon dioxide refrigeration cycle with the
addition of parallel compression economization, in: 6th IIR Gustav Lorentzen
Natural Working Fluid, Glasgow UK, 29e1 September 2004, p.2/A/4.30.
[9] E. Torrella, R. Llopis, R. Cabello, Experimental evaluation of the interstage
conditions of a twostage refrigeration cycle using a compound compressor.
International Journal of Refrigeration 32 (2009) 307e315.
[10] W.J. Zhang, C.L. Zhang, G.L. Ding, Transient modeling of an aircooled chiller
with economized compressor, part I: model development and validation.
Applied Thermal Engineering 29 (11e12) (2009) 2396e2402.
[11] N. Agrawal, S. Bhattacharyya, J. Sarkar, Optimization of twostage transcritical
carbon dioxide heat pump cycles. International Journal of Thermal Science 46
(2) (2007) 180e187.
[12] J. Sarkar, S. Bhattacharyya, M. Ramgopal, Optimization of a transcritical CO2
heat pump cycle for simultaneous cooling and heating applications. Interna
tional Journal of Refrigeration 27 (8) (2004) 830e838.
J. Sarkar, N. Agrawal / International Journal of Thermal Sciences 49 (2010) 838e843
843