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: souvik.iit@gmail.com (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