Thermodynamic design and simulation of a CO2
Article history:
ritiqueavec un ejecteur
e a pression constante
* Corresponding author.
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i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 7 7e1 8 8E-mail address: [email protected] (S. Bhattacharyya).Mots cles : Dioxyde de carbone ; Cycle frigorifique ; Analyse thermodynamique ; Dimensions de l'ejecteur ; Melangfrigorifique a compression de vapeur au CO2 transc
Conception et simulation thermodynamiques d'un systemeReceived 24 March 2014
Received in revised form
9 June 2014
Accepted 12 June 2014
Available online 21 June 2014
Keywords:
Carbon dioxide
Refrigeration cycle
Thermodynamic analysis
Ejector dimensions
Constant pressure mixinghttp://dx.doi.org/10.1016/j.ijrefrig.2014.06.0100140-7007/ 2014 Elsevier Ltd and IIR. All rigA two phase ejector suitable as an expansion device in a CO2 based transcritical vapour
compression refrigeration system is designed by extending the thermodynamic analysis
and by interfacing with the system simulation model. A converging diverging nozzle is
considered as primary nozzle of the ejector. For both design and parametric analyses, the
efficiencies of nozzles and diffuser have been assumed to be 85% each. Further, choked
condition in the primary C-D nozzle and constant pressure mixing are assumed. Param-
eters such as COP, entrainment ratio, pressure lift and cooling capacity were obtained for
varying motive inlet and evaporator conditions. Motive inlet is found to be crucial for both
performance and range of feasible application. Results show a COP improvement of 21%
compared to an equivalent conventional CO2 system. A comprehensive exergy analysis of
the system establishes the justification of replacement of throttle valve by ejector in such
systems.
2014 Elsevier Ltd and IIR. All rights reserved.a r t i c l e i n f o a b s t r a c tbased transcritical vapour compressionrefrigeration system with an ejector
Md. Ezaz Ahammed, Souvik Bhattacharyya*, M. Ramgopal
Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, Indiahts reserved.
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 7 7e1 8 8178Carbon dioxide is an eco-friendly natural refrigerant with no expansion devices and the ejector has shown promising po-
tential as an expansion device characterized by absence of1. Introduction
Nomenclature
A area, m2
a sonic velocity, m s1
COP coefficient of performance
CRC conventional refrigeration cycle
RCE refrigeration cycle with ejector
G mass flux, kg m2 s1
h enthalpy, J kg1
M Mach number_m mass flow rate, kg s1
P pressure, Pa
Pc inlet pressure to compressor, Pa
Pd discharge pressure of compressor, Pa
d diameter
IHX internal heat exchanger
Pe evaporator pressure, Pa
Ps suction pressure of secondary stream, Pa
Q heat transfer, W
s entropy, J kg1 K1
u velocity, m s1
W work transfer, W
x dryness fractionODP and low GWP. Moreover, it is inexpensive, weakly toxic,
abundantly available and has the potential to be an ideal
refrigerant, provided the cycle and design are modified suit-
ably for achieving competitive performance (Lorentzen, 1994).
Interestingly, the high system operating pressures which
rendered it to be unpopular earlier, turns out to be beneficial
as it leads to a compact system. However, relatively lower COP
of the CO2 based refrigeration cycle compared to basic vapour
compression refrigeration cycle has been cited to be a major
drawback or area where developments are required.
Enhancement in performance of CO2 transcritical cycle has
been attained through optimization of parameters, modifica-
tion of basic cycle, replacement and addition of components
in system etc. Optimization of discharge pressure in CO2 cycle
has been done for air conditioning applications and various
methods have been proposed as well to control optimum high
pressure (Kauf, 1999; Liao et al., 2000; Casson et al., 2003).
Sarkar et al. (2004) presented energetic and exergetic optimi-
sations of a heat pump for simultaneous cooling and heating.
It is shown that compared to other components, exergy losses
in the throttle valve are the highest. Various cycle modifica-
tions have been studied such as multi-staging and flash gas
bypass to improve the system performance (Kim et al., 2004;
Elbel and Hrnjak, 2004). Internal heat exchanger and work
producing expander were employed to avoid high throttling
loss (Kim et al., 2004; Robinson and Groll, 1998). Agrawal and
Bhattacharyya (2008) employed a capillary tube as an expan-
sion device with optimum design and operating conditions
where the performance was reported to be marginally betterwith higher gas cooler exit temperature. More recently,
several studies have been reported on performance enhancing
Greek symbols
h efficiency
r density
m entrainment ratio
Subscripts
comp compressor
com compression
Diff diffuser
E equilibrium
evap evaporator
exp expansion
gc gas cooler
i ith state, number
is isentropic
max maximum
noz1 primary nozzle
noz2 secondary nozzle
p primary
s secondary, isentropic
sec secondary
t throat
tot totalmoving parts, low cost and low maintenance. The use of
ejector in vapour compression refrigeration system was first
introduced by Kornhauser (1990) through a numerical analysis
using R12 as a refrigerant reporting 21% improvement in COP.
Thereafter, a good body of research has been reported on
various ejector based refrigeration systems with different
working substances, which is well documented in two review
papers of Sumeru et al. (2012) and Sarkar (2012). Along with
empirical and semi empirical modelling of ejector, mathe-
matical models on ejectors have progressed as thermody-
namic models and dynamic models which are further
subdivided to single phase and two phase flow models. Dy-
namic models have higher prediction precision yielding
greater information (He et al., 2009). Li and Groll (2005)
implemented a thermodynamic analysis at different oper-
ating conditions for an assumed entrainment ratio and pres-
sure drop in the suction section of the ejector for a
transcritical CO2 refrigeration cycle and reported a 16% COP
improvement over the basic transcritical CO2 cycle. They
added a feedback fraction of vapour throttled to evaporator in
the cycle to satisfy mass balance constraint at the ejector exit.
Deng et al. (2007) also presented a theoretical analysis for a
transcritical CO2 ejector expansion refrigeration cycle report-
ing a 22% improvement in COP at working conditions and
11.5% at conditions for the maximum cooling COP. Liu and
Groll (2008) developed a simulation model of a two phase
flow ejector with converging nozzle as the motive nozzle and
employed it along with test data to obtain the adjusted nozzle
2The detailed literature survey, presented above, shows that
h3 to h4 (Fig. 2) as it gets converted into to kinetic energy. For
the operation of the system to be feasible, the primary and
secondary fluids should enter the ejector in such a ratio that,
i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 7 7e1 8 8 179even though several authors carried out thermodynamic
analysis of transcritical CO2 based refrigeration systems with
ejector as an expansion device, none of these studies included
the geometrical aspects of the ejector in the thermodynamic
system simulation. Also the second law analysis on these
systems did not estimate the individual contribution of pri-
mary and secondary nozzles, diffuser and mixing sections to
total system irreversibility.
This study supplements a thermodynamic approach to
design an ejector for a given operating condition employing
variable properties of the working fluid along with detailed
system simulation. Furthermore, effects of varying operating
conditions on the system simulation have been comprehen-
sively evaluated for the given geometry of ejector.
2. CO2 refrigeration system with an ejector
In the vapour compression refrigeration system with an
ejector, the ejector is used in place of the expansion valve
(Fig. 1). The ejector considered in the present analysis con-
sists of a primary nozzle, a secondary nozzle, a convergent
mixing section followed by a constant area section and a
diffuser section. In the ejector, the primary fluid (motive
fluid) from the gas cooler after expansion through the pri-
mary nozzle entrains refrigerant vapour from the evaporator
(secondary fluid). The primary and secondary fluid streams
are mixed in the mixing chamber and flow through the
diffuser. The pressure of the two-phase fluid mixture in-
creases as it flows through the diffuser. After diffuser vapour
and liquid are separated in separator. The saturated liquid
enters the evaporator through an expansion valve, while the
saturated refrigerant vapour is compressed in the
compressor. In the present study a converging-diverging (C-
D) nozzle is used as the primary nozzle, in which the primary
fluid or motive fluid expands from the super-critical, singleand mixing efficiencies while examining effect of operating
conditions and design parameters of the ejector. Lee et al.
(2011) designed a two phase ejector for their test facility
considering the non-equilibrium state to calculate sonic ve-
locity and critical mass flux. They varied diameter of the
convergingediverging (CeD) nozzle and other geometrical
parameters to test their sensitivity with respect to perfor-
mance leading to the optimal design of ejector for which the
Henry and Fauske (1971) model was employed. A 15%
improvement in COP over the conventional cyclewas reported
and performancewas higher for the constant pressuremixing
ejector. Nakagawa et al. (2011) reported experimental results
on a two phase ejector refrigeration system. They used an
ejector comprising a C-Dmotive nozzle, secondary nozzle and
diffuser of rectangular cross section and showed the effect of
mixing length on performance. With an optimum mixing
length size, 26% improvement in COP was obtained over
conventional system with IHX. It may be noted that most of
the theoretical analyses did not deal with geometrical features
and those which did employed only steam and refrigerants
other than CO as working fluids.phase region to a sub-critical pressure, that is less than or
equal to the evaporator pressure. The static enthalpy of themotive fluid decreases in the primary nozzle of ejector from
Fig. 1 e Schematic diagram of refrigeration system with
ejector.Fig. 2 e P-h diagram of the CO2 based refrigeration system
with ejector.
after mixing, the ejector is able to eject the mixed fluid in the
same ratio of vapour and liquid. The ratio of secondary to
primary mass flow rate is termed as entrainment ratio (m),
expressed as:
m ms
mp (1)
However, for all operating conditions, the vapour fraction
at the exit of ejector may not be exactly equal to the required
value of x7 _mp= _mp _ms, which leads to a mass imbalancein the system simulation for these conditions. To relax the
constraint, the modified cycle with a feedback throttle valve
(Figs. 1 and 2) proposed by Li and Groll (2005) has been
considered in the simulation. The purpose of the feedback
throttle (Fig. 1) is to return back the extra vapour to evaporator
so that the condition (1 m) x7 > 1 is satisfied. It may be notedthat if the exit vapour fraction is less than that of the required
value stated above, then the cycle will not be realized as the
abovemodification in the cycle can take care of excess vapour
at ejector exit only. The feedback throttle is required for sys-
tem simulation; however, in an actual system, the systemwill
pressure mixing is adopted in the present study since it leads
to superior performance compared to constant areamixing as
is evident from the literature (Keenan et al., 1950). Mixing
section length (Xm) is greater than zero for constant pressure
mixing whereas Xm 0 for constant area mixing (Fig. 3). Theperformance of the ejector and the system can be specified in
terms of pressure lift and cooling COP, given by:
Pressure lift ;Plift Pc Ps (2)
COPcooling m h10h9h2 h1 (3)
3. Thermodynamic analysis of the ejectorbased refrigeration cycle
The following simplifying assumptions have been made for
the thermodynamic analysis:
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 7 7e1 8 8180adjust automatically to a new balanced condition, even
without the feedback throttle valve.
In Fig. 2, the lines 3e90 and 10e20 represent the expansionand compression process in a conventional transcritical cycle
with a throttle valve and without any recovery during the
expansion process, and 10e20e3e90 represents the corre-sponding cycle.
In this study, based on the thermodynamic model, an
ejector has been designed for a refrigeration capacity of 1 Ton
operating at a gas cooler outlet pressure of 110 bar, outlet
temperature of 35 C and an evaporator temperature of 2 C.Mass flow rate for primary and secondary flow and Pc are
estimated from the thermodynamic analysis at the same
operating conditions with a zero feedback mass. Mixing sec-
tion is an important part in the design of an ejector. ConstantFig. 3 e Schematic diagram of the ejectori. Steady one dimensional homogeneous equilibrium flow.
ii. Pressure drop in gas cooler and evaporator are negli-
gibly small.
iii. No heat interaction with surrounding in all the com-
ponents except evaporator and gas cooler.
iv. Refrigerant exits evaporator as saturated vapour.
v. Constant pressure mixing occurs in the mixing section.
vi. Primary nozzle, secondary nozzle and diffuser have an
isentropic efficiency of 85%.
vii. Velocities at inlet to primary and secondary nozzle are
negligibly small.
Additionally, the secondary nozzle pressure drop (PeePs)
was assumed to be 0.3 bar (Li and Groll, 2005) and the gas
cooler exit temperature is kept at 35 C with zero feedbackmass for 1 Ton cooling capacity. Isentropic efficiency forwith a convergingediverging nozzle.
A5 _msG5
(22)
i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 7 7e1 8 8 181compressor hcomp has been calculated from the following
correlation given by Robinson and Groll (1998):
hcomp 0:815 0:022Pc=Pd 0:0041Pc=Pd2 0:0001Pc=Pd3(4)
Motive stream of fluid expands with the given isentropic
efficiency and gets accelerated to very high velocity. For the
exit of the primary nozzle:
h4 fh3;h4s; hnoz1 (5)
u4 2h3 h4
q(6)
The low pressure at the exit of primary nozzle causes
expansion of secondary stream through the secondary nozzle.
The enthalpy and velocity of secondary stream at the exit of
the secondary nozzle are:
h5 fh10;h5s;hnoz2 (7)
u5 2h10 h5
q(8)
Both fluids are assumed to mix at constant pressure.
Therefore, the momentum and energy equations for the
mixing process are:
1 mu6 u4 mu5 (9)
1 mh6 u262 h4 u242 mh5 u252 (10)In the diffuser section, the single fluid loses kinetic energy
and receives useful pressure lift before it is separated into
liquid and vapour fractions in the phase separator. For the
diffuser the applicable equations are:
s6 fPs;h6 (11)
h7 fPc;h7s; hdiff
(12)
hdiff h7s h6h7 h6 (13)
Applying overall energy balance to the ejector,
1 mh7 h3 mh10 (14)Vapour quality at the exit of diffuser of ejector is expressed
as:
x7 fPc;h7 (15)
1 mx7 1 (16)Saturated liquid from separator is throttled to evaporator
through expansion valve in an isenthalpic process yielding:
h8 h9 (17)The expression for refrigeration effect, gas cooler heat
rejection and compressor work are as follows:
Qevap m1 m h10 h9 _mtot (18)A6 _mp _msG6
(23)
Fig. 4 shows themass flux (G) variationwith pressure for an
adiabatic expansion process in the nozzle at different nozzle
efficiencies.
At choking condition, the fluid achieves sonic velocity at
the throat where the mass flux attains the maximum value
termed as critical mass flux (Gmax). Mach number (M) and
sonic velocity (a) are given by,
M u=a (24)Qgc 11 m h3 h2 _mtot (19)
Wcomp 11 m h2 h1 _mtot (20)
The above set of equations is solved in MATLAB while
interfacing with REFPROP 9.0 for thermodynamic state and
property calculation. Entrainment ratio (m) and diffuser exit
pressure (Pc) are iterated in loop to satisfy both energy balance
(Eq. (14)) and mass balance (Eq. (16)).
4. Ejector design
The design of ejector comprises design of primary nozzle,
secondary nozzle, mixing zone and diffuser. The important
geometrical factor is the throat diameter of primary nozzle
which is designed for choked condition. Secondary nozzle
experiences a very small expansion, and hence no choking is
expected to occur there. In the present study, homogeneous
equilibrium is considered for total expansion. Critical mass
flux and sonic velocity were obtained by interfacing REFPROP
9.0 with MATLAB and giving a particular path of expansion,
h 0.85 in the nozzles. Primarymass flow rate _mp, secondarymass flow rate _ms and Pc are the outcome of the thermo-dynamic analysis at 110 bar discharge pressure and 35 C gascooler exit temperature keeping evaporator temperature 2 Cfor a refrigeration capacity of 1 Ton. Pressure at exit of primary
nozzle has been taken as design pressure Ps to avoid shock in
the diverging section of nozzle as well as in the mixing
section.
The thermodynamic simulation for the above given con-
dition is extended to design the ejector. Exit area of primary
nozzle (A4), exit area of secondary nozzle (A5) and exit area of
constant pressure mixing zone (A6) are obtained from the
following set of equations:
A4 _mpG4
(21)
dAA
drr
duu
0 (30)
Energy equation,
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 7 7e1 8 8182a
vPvr
sc
s(25)
The condition for choking is given by,
dGdP
0 (26)
Suitable stage efficiency (hstage) for elemental pressure drop
is chosen by iteration such that it matches the end state point
Fig. 4 e Pressure variation with mass flux for isentropic
and non-isentropic expansion.and given isentropic efficiency (hnoz) while attaining the chosen
path of expansion. The simulation is run for the expansion
through small pressure drop steps keeping stage efficiency
constant for each step. Stage efficiencies are defined for
expansion and compression in Eq. (27) and Eq. (28), respectively.
hstage;exp dhdhiso
(27)
hstage;com dhisodh
(28)
Properties such as enthalpy, entropy, velocity, Mach num-
ber and mass flux are calculated at each step. For a given inlet
condition, the critical mass flux is fixed and thus the throat
area can be determined as per the required mass flow rate.
At _mp
Gmax(29)
Following mixing, fluid exits from the constant pressure
mixing zone with subsonic velocity and the state point of
diffuser inlet is the same as that of exit of the constant pres-
sure mixing zone. With respective inlet condition, outlet area
of diffuser is calculated satisfying the continuity equation,
energy equation, diffuser efficiency and the corresponding
exit pressure.
Continuity equation,
Secondary pressure drop (DPsec) is assumed in the iterationloop.
P5 Pe DPsec (34)Secondary mass flow rate for the small expansion DPsec is
expressed as:
G5 fPe;Ps;hnoz2 (35)
_ms G5A5 (36)
Table 1 eDimension (mm) andmass flow rates (kg s1) ofthe designed ejector.dh udu 0 (31)Diameters of the given ejector are obtained by solving
Equations 21e31 for the primary and secondary mass flow
rates calculated from the thermodynamic simulation at given
condition.
Table 1 shows the diameters of the designed ejector with
mass flow rate of both streams for amotive streampressure of
110 bar and the saturated suction stream at 2 C.
5. System simulation at different operatingconditions with designed ejector
The transcritical CO2 cycle with ejector is simulated to study
the effect of operating parameters on the system perfor-
mance. In the simulation it is assumed that the evaporator
and gas cooler are capable of transferring the required heat
transfer rates, and the compressor is able to compress the
required amount of refrigerant. Keeping the dimensions of
ejector fixed, the complete system is simulated at different
values of gas cooler exit pressure (P3), temperature (T3) and
different evaporator temperatures (Te) while adhering to the
chosen expansion path through elemental pressure drops.
The following simplifying assumptions are considered:
i. Choked condition for primary nozzle
ii. Feedback mass is such that the difference in vapour frac-
tion variation is below 2% of total mass flow rate.
Critical mass flux is determined from the motive input of
pressure (P3 Pd) and temperature, T3 for the given path ofexpansion and primary mass flow rate is determined for the
designed throat area (At).
Gmax fPd;T3;hnoz1 (32)
_mp GmaxAt (33)_mp _ms dt d4 d5 d6 d7
0.024 0.016 0.67 0.89 3.2 1.85 5.43
h20 h3
(51)
i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 7 7e1 8 8 183P5 is the back pressure for the diverging part of C-D
nozzle. Fluid in primary nozzle may exit with under-
expansion or over-expansion to back pressure or it may
exit at back pressure with a shock at its diverging section.
Shock exit pressure (PSE) is checked considering shock just
at the exit of primary nozzle. Assuming shock thickness to
be negligible, equations for the jump across shock are
included in the simulation to obtain thermo-physical
properties across shock at the exit end given by the
following equations:
ru 0 (37)
p ru2 0 (38)h u22 0 (39)The square bracket notation in the above Eq. (37)e(39)
imply jump across the shock. For the present range of cases,
solving Eq. 37e39 for the given geometry of primary nozzle
confirms about the irreversible over-expansion of primary exit
to back pressure P5. A simplified mixing model has been
employed to solve the problem. Primary _mp and secondarymass _ms are mixed in converging mixing zone and thestream exits at pressure P6 which is assumed in the iteration
loop and the thermodynamic state after mixing is calculated
satisfying mass, momentum and energy conservation equa-
tions as expressed below.
Mass conservation equation,
_mp _ms _mtot (40)Momentum conservation equation,
_mpu4 _msu5 P4A4 P5A5 P5 P62 A4 A5 A6 _mtotu6 P6A6 (41)
Energy conservation equation,
_mp
h4 u
24
2
_ms
h5 u
25
2
_mtot
h6 u
26
2
(42)
Mass flux at the exit of diffuser,
G7 _mtotA7
(43)
Pressure and other thermodynamic properties at the exit of
diffuser are obtained for the given path and designed area A7.
Pc fG7;hdiff
(44)
h7 fG7;hdiff
(45)
x7 fPc;h7 (46)
1 mx7 1 (47)To allow feedback mass expressed in Eq. (47), the evapo-
rator capacity equation changes to:
Qevap _msh101x7_mp _ms
h9x71=1m
_mp _ms
ah1(48)Igc _m$T0$ T0 s20 s3
Exergy destruction in expansion valve; Iv _mT0s90 s3 (52)
Exergy destruction in evaporator;
Ievap _mT0s10 s90
h10 h90
Tw
(53)
6.2. Exergy analysis of cycle with ejector
Exergy destruction in compressor; Ic _mpT0s2 s1 (54)
Exergy destruction in gas cooler;
Igc _mp$T0$
h2 h3T0
s2 s3
(55)
Exergy destruction in primary nozzle; Inoz1 _mpT0s4 s3(56)
Exergy destruction in secondary nozzle; Inoz2 _msT0s5 s10(57)
Exergy destruction in mixing section;
Imix T0_mtots6
_mps4 _mss5
(58)6.1. Exergy analysis of conventional cycle
Exergy destruction in compressor; Ic _mT0s20 s10 (50)Exergy destruction in gas cooler;6. Exergy analysis
Exergy calculations are carried out for both conventional and
ejector based cycles to have a clear view of losses occurring in
both the systems. The gas cooler exit pressure and tempera-
ture were assumed to be 110 bar and 35 C, respectively whilethe evaporator temperature was taken as 2 C. It is assumedthat the system studied is suitable for the application of
comfort air conditioning, hence the refrigerated space tem-
perature (Tw) for evaporator is assumed to be 25 C, while thereference temperature (To) is 32 C.Values of P6 and the pressure drop across the secondary
nozzle, DPsec were adjusted till convergencewas obtained. It is
to be noted that the nozzle is designed assuming a secondary
pressure drop of 0.3 bar. However, during simulation it is
calculated for each off-design condition iteratively.
To assess the performance of the optimally designed
refrigeration system with ejector, it is compared with the
corresponding conventional transcritical cycle 10e2039010
(Fig. 2).
COPconv h10 h3h20 h10 (49)
Fig. 5 e Effect of gas cooler exit pressure and temperature
on primary nozzle exit pressure, and evaporator pressure
at corresponding temperature.
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 7 7e1 8 8184Exergy destruction in diffuser section; Idiff _mtotT0s7 s6(59)
Exergy destruction in separator; Isep
_mtoth7 T0s7 _mph1 T0s1 _msh8 T0s1
(60)
Exergy destruction in expansion valve; Iv _msT0s9 s8 (61)
Exergy destruction in evaporator;
Ievap _msT0s10 s9
h10 h9
Tw
(62)
Second law efficiency;h2nd
1
PI
Wcomp
(63)
7. Results and discussions
Behaviour of refrigeration system with ejector at different
operating parameters is investigated and performance pa-
rameters such as pressure lift, entrainment ratio, COP and
cooling capacity are presented below.
The analysis shows that the system with an ejector
designed for a specific operating condition is constrained to
operate within a particular range only at off-design condi-
tions. For example, it can be seen from Fig. 5 that when the
evaporator temperature is maintained below 4 C, for highpressure and low gas cooler exit temperature conditions, the
primary nozzle exit pressure is above the evaporator pressure.
Since this condition is not practically feasible, the system
cannot operate under these conditions. Similarly for some
range of operating conditions, the solution fails to converge,
as feedback mass has been kept below 0.5% of the total mass.
It can be inferred that had the ejector been designed for a
different set of operating conditions, then the applicability
range would have been different from the present range. Thus
depending upon the range of operating conditions, one has to
choose the design conditions of the ejector for the refrigera-
tion system.
7.1. Validation of numerical results
To validate the simulation model, the geometry of ejector
presented by Nakagawa et al. (2011) for their experimental
work has been chosen. As per their study the gas cooler outlet
temperature T3 and evaporator temperature Te are taken as
42 C and 2 C, respectively. Fig. 6 shows comparison of nu-merical results with experimental data of Nakagawa et al.
(2011), for the case without internal heat exchanger and an
ideal mixing length of 15 mm.
The plots clearly show that though qualitatively there is a
good match between the theoretical and experimental results,
quantitatively, the difference is significant. However, it is seen
that the difference between the predicted and experimental
values is gradually narrowing towards the high pressure. Since
Nakagawa et al. (2011) do not specify the efficiencies of theejector components, the primary nozzle efficiency is varied
from 65% to 70% for the purpose of validation so that areasonably close match between the primary mass flow rate
from the simulation and experimental value is obtained. Then
fixing this efficiency, the other parameters are computed. It is
assumed that the secondary nozzle efficiency has nomajor role
as the expansion is kept low for all cases and hence is kept fixed
at 65% in the simulation. Isentropic efficiencies for diffuser areFig. 6 e Comparison between numerical and experimental
values.
also kept between 65% and 70%. Feedbackmass has been taken
to be zero. By doing so it is seen that the difference between the
predicted and experimental values for secondary mass flow
rate is high. Since the actual secondary mass flow rate is much
lower than the predictedmass flow rate, particularly at low gas
cooler pressure, the predicted COP and entrainment ratio are
much higher than that obtained from the experimental results.
A possible explanation for this could be that Nakagawa et al.
(2011) used an ejector of rectangular cross section fabricated
by piercing three plates stacked together. Hence, the secondary
nozzle path is restricted in their design leading probably to a
secondary flow that is much lower than that obtained from
simulations. At high pressure, secondary mass manages to
pass through the restricted passage and as a result there is a
better match between simulation predictions and reported test
values at higher pressures. In addition to this, in the simulation
the phase separator at the exit of the ejector is assumed to be
perfect. However, an examination of the experimental results
of Nakagawa shows that this is far from perfect in the actual
system. These and the usual frictional pressure drops and other
losses that exist in actual systems have resulted in the quan-
titative disagreement between the experimental and predicted
values.
It may be noted that for the given geometry and operating
condition, solutions are absent below 95 bar and above 105 bar
in simulation.
7.2. Effect of gas cooler exit pressure
Pressure lift or pressure recovery represents the rise in pres-
sure with the use of ejector. Difference between compressor
pressure and secondary suction pressure has been termed as
Table 2 e Values for varying motive inlet pressure at T3 35 C, Te 2 C.P3 (bar) Pc (kPa) P6 (kPa) P4 (kPa) Ps (kPa) _mp (kg s
1) _ms (kg s1) u6 (m s
1)
95 4119 3766 2933 3658 0.0185 0.0120 70.18
100 4201 3730 3256 3653 0.0208 0.0138 80.30
105 4275 3689 3486 3648 0.0229 0.0154 88.88
110 4349 3643 3643 3643 0.0248 0.0169 97.07
i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 7 7e1 8 8 185Fig. 7 e (a). Effect of P3 on Pressure lift and entrainment ratio. (b
COP for different motive inlet temperature.). Effect of P3 on COP and cooling capacity. (c). Effect of P3 on
momentum leads to low exit pressure after mixing. In the
second part of pressure lift which occurs in diffuser, the same
larger to fulfil the cooling capacity requirement even under
such adverse conditions.
7.4. Effect of evaporator temperature
Fig. 9(a) and (b) shows the effect of evaporator temperature on
system performance. Evaporator temperature variation
seems to have no significant effect on pressure lift, entrain-
ment ratio and cooling capacity.
Primary mass flow rate does not change for fixed motive
inlet condition. Secondary mass flow rate change is very
small. However, in actual conditions, since evaporator tem-
perature affects the cooling capacity of the compressor, the
balanced condition between the ejector and compressor need
to be obtained by including compressor characteristics in the
analysis. As shown in Fig. 9(a), pressure lift and entrainment
(b)
Fig. 8 e (a). Effect of T3 on Pressure lift and entrainment
ratio. (b). Effect of T3 on COP and cooling capacity.
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 7 7e1 8 8186high momentum gives rise to high pressure gain and thus a
reversal trend is found here due to larger gain in pressure than
that of the first phase lift. Thus, as shown in Fig. 7(a), pressure
lift increases with increase in gas cooler exit pressure. For the
given geometry, the primary exit pressure becomes lower for
low gas cooler exit pressure which causes a low value of
pressure lift.
Entrainment ratio is an important parameter in a refrig-
eration cycle with an ejector. Higher value of entrainment is
desirable as it reflects better performance of the ejector.
Fig. 7(a) shows that for a particular gas cooler exit and evap-
orator temperature there is negligible effect on entrainment
ratio when motive inlet pressure is varying. Cooling capacity,
work input and COP with variation of P3 are shown in Fig. 7(b).
It may be observed that cooling capacity and power input
decrease but COP increases marginally as P3 reduces.
In addition, at different values of T3, COP variation with P3is presented in Fig. 7(c). At some operating points, solutions
are not available due to issues related to convergence and
other reasons discussed previously. At lower gas cooler exit
temperature, effect of P3 on COP is not significant. However,
for higher gas cooler exit temperature, the COP is seen to in-
creasewith P3; this implies that the system should be operated
at higher P3 when T3 is high.
7.3. Effect of gas cooler exit temperature
Gas cooler exit temperature (T3) is a vital parameter as it de-
pends upon the available heat sink for a given gas cooler size.
Fig. 8(a) and (b) exhibit the adverse effect of increased value of
T3 on system performance. As T3 increases, primary mass
decreaseswhich also causes lower secondarymass. This leads
to low momentum at the exit of mixing section or in other
words at the inlet of diffuser section. Therefore, lower pres-
sure lift occurs in diffuser.
Entrainment ratio significantly decreases at higher gas
cooler exit temperature in this condition. Lower cooling ca-
pacity at higher gas cooler exit temperature lowers COP
drastically. Due to this it is advisable that since under adverse
ambient conditions, as the cooling load is much lower thanpressure lift. Supersonic primary fluid and secondary fluid are
combined in the mixing section which causes pressure rise
partly before entering the diffuser.
As the mixture flows, pressure rise occurs in the diffuser
section. Table 2 shows the values of pressure at the exit of
primary nozzle (P4), secondary nozzle (P5), mixing section (P6),
diffuser (Pc) and other values when the system is operated at
various gas cooler pressures. Table 2 exhibits that even
though primarymass and secondarymass are increasingwith
increase in P3 the ratio between them does not change
significantly. Furthermore, secondary fluid exit pressure Psdoes not varymuch for various input conditions. The first part
of pressure lift in mixing zone is dominated by momentum
(mtot u6) of mixed fluid at the exit of mixing section. Even
though primary exit pressure is higher at higher P3, highthe design value (3.517 kW), either design value for T3 should
be taken higher or design value of cooling load should be set
(a)ratio show slight variation. Increasing evaporator tempera-
ture also has marginal effect on cooling capacity but
2.5
3
3.5
4
CO
P
Ejector based cycle
T3=35CTe=2C
i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 7 7e1 8 8 187decreased compressor work gives higher COP for the system.
COP, cooling capacity and compressor work variation with
varying evaporator temperature are presented in Fig. 9(b).
7.5. Comparison with conventional cycle
Vapour compression cycle with an ejector is expected to yield
superior performance but that needs to be substantiated
through a systematic evaluation compared to conventional
systems. A comparison between cycle with ejector and con-
ventional CO2 transcritical cycle is presented in Fig. 10. While
generally the system with ejector exhibits greater benefit at
higher gas cooler exit pressures, as a specific example at
110 bar it yields a very significant 21% improvement in
performance.
90 95 100 105 1102
Conventional cycle
Fig. 9 e (a) Effect of Te on Pressure lift and entrainment
ratio. (b). Effect of varying Te on COP and cooling capacity.7.6. Exergy destruction rate at different components
Exergy analysis is typically carried out to identify component
level performance deficiencies so that remedial measures can
be undertaken for those identified components leading to
Gas Cooler Exit Pressure (P3 ,bar)Fig. 10 e COP of ejector based and conventional
transcritical CO2 system at varying P3.system performance enhancement. Exergy destruction rates
are estimated (Fig. 11) at a gas cooler pressure and exit tem-
perature of 110 bar and 35 C for evaporator temperature of2 C and 1 Ton cooling capacity for both refrigeration cyclewith ejector (RCE) and conventional refrigeration cycle (CRC).
Exergy destruction rate in the evaporator of both the cycles are
Comp
ressor
Evap
orator
Exp.
valve
Gas c
ooler
Noz1
Noz2
Diffu
ser
Separa
tor
Mixin
g 0
50
100
150
200
250
300
350
RCE CRC
Irre
vers
ibili
ty (W
att)
Fig. 11 e Exergy destruction in different components of
conventional and ejector based cycle.
almost the same for the given operating conditions and
cooling capacity. The secondary nozzle of ejector and sepa-
law efficiencies obtained are 6.6% and 7.52% for conventional
and systems with ejector, respectively, under the given
tion of replacement of throttle valve by an ejector as an
expansion device in a CO2 based transcritical vapour
compression refrigeration system.
r e f e r e n c e s
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 7 7e1 8 8188Acknowledgement
The work is supported by Science and Engineering Research
Board (SERB), Technology Bhawan, New Mehrauli Road, New
Delhi, for the project Design and development of a demon-
stration unit of carbon dioxide based transcritical refrigera-
tion system.conditions.
8. Conclusion
An ejector has been designed for choked condition based on a
thermodynamic model, solved numerically employing MAT-
LAB interfaced with REFPROP to derive refrigerant properties.
A converging-diverging nozzle is used as the primary nozzle
and a constant pressure mixing section is assumed. Effects of
varying operating conditions on the performance of the
designed refrigeration system with ejector were investigated.
Effort has been made with a viewpoint of exploring
geometrical features with simplified numerical analysis. Re-
sults confirm that design condition should be chosen as per
the range of application requirement. From the validation
results, it is evident that design of secondary nozzle has as
much significance as primary nozzle. Parametric variation
exhibits that at lower heat sink temperatures performance is
slightly better towards low gas cooler pressure but cooling
capacity significantly decreases, whereas at higher ambient
temperature high gas cooler pressure leads to notable
improvement in performance. It is inferred that motive inlet
is the deciding factor of performance and applicability. A
comparison is presented with conventional cycle which
yields as much as 21% improvement on COP for design con-
dition in case of the system with ejector. Additionally, a
comprehensive exergy analysis was implemented to identify
component level deficiencies and it establishes the justifica-rator contributes negligibly to system exergy destruction. It
may be noted that total exergy destruction in the entire ejector
(nozzle, mixing and diffuser) is around half of that in an
expansion valve of conventional cycle. Small pressure drop
during throttling in cycle with an ejector leads to a much
lower exergy destruction. At higher operating pressures such
as 110 bar, irreversibility in the gas cooler is high for both
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Thermodynamic design and simulation of a CO2 based transcritical vapour compression refrigeration system with an ejector1 Introduction2 CO2 refrigeration system with an ejector3 Thermodynamic analysis of the ejector based refrigeration cycle4 Ejector design5 System simulation at different operating conditions with designed ejector6 Exergy analysis6.1 Exergy analysis of conventional cycle6.2 Exergy analysis of cycle with ejector
7 Results and discussions7.1 Validation of numerical results7.2 Effect of gas cooler exit pressure7.3 Effect of gas cooler exit temperature7.4 Effect of evaporator temperature7.5 Comparison with conventional cycle7.6 Exergy destruction rate at different components
8 ConclusionAcknowledgementReferences
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