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Thermodynamic design and simulation of a CO2 based transcritical vapour compression refrigeration system with an ejector
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 7 e1 8 8
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Thermodynamic design and simulation of a CO2 based transcritical vapour compression refrigeration system with an ejector Md. Ezaz Ahammed, Souvik Bhattacharyya*, M. Ramgopal Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
article info
abstract
Article history:
A two phase ejector suitable as an expansion device in a CO2 based transcritical vapour
Received 24 March 2014
compression refrigeration system is designed by extending the thermodynamic analysis
Received in revised form
and by interfacing with the system simulation model. A converging diverging nozzle is
9 June 2014
considered as primary nozzle of the ejector. For both design and parametric analyses, the
Accepted 12 June 2014
efficiencies of nozzles and diffuser have been assumed to be 85% each. Further, choked
Available online 21 June 2014
condition in the primary C-D nozzle and constant pressure mixing are assumed. Parameters such as COP, entrainment ratio, pressure lift and cooling capacity were obtained for
Keywords:
varying motive inlet and evaporator conditions. Motive inlet is found to be crucial for both
Carbon dioxide
performance and range of feasible application. Results show a COP improvement of 21%
Refrigeration cycle
compared to an equivalent conventional CO2 system. A comprehensive exergy analysis of
Thermodynamic analysis
the system establishes the justification of replacement of throttle valve by ejector in such
Ejector dimensions
systems.
Constant pressure mixing
© 2014 Elsevier Ltd and IIR. All rights reserved.
me Conception et simulation thermodynamiques d'un syste compression de vapeur au CO2 transcritique frigorifique a jecteur avec un e jecteur ; Me lange a pression constante Mots cles : Dioxyde de carbone ; Cycle frigorifique ; Analyse thermodynamique ; Dimensions de l'e
* Corresponding author. E-mail address: [email protected] (S. Bhattacharyya). http://dx.doi.org/10.1016/j.ijrefrig.2014.06.010 0140-7007/© 2014 Elsevier Ltd and IIR. All rights reserved.
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Nomenclature A a COP CRC RCE G h M _ m P Pc Pd d IHX Pe Ps Q s u W x
1.
area, m2 sonic velocity, m s1 coefficient of performance conventional refrigeration cycle refrigeration cycle with ejector mass flux, kg m2 s1 enthalpy, J kg1 Mach number mass flow rate, kg s1 pressure, Pa inlet pressure to compressor, Pa discharge pressure of compressor, Pa diameter internal heat exchanger evaporator pressure, Pa suction pressure of secondary stream, Pa heat transfer, W entropy, J kg1 K1 velocity, m s1 work transfer, W dryness fraction
Introduction
Carbon dioxide is an eco-friendly natural refrigerant with no ODP 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 suitably 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, modification 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 optimisations 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 modifications 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 expansion device with optimum design and operating conditions where the performance was reported to be marginally better
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 total
with higher gas cooler exit temperature. More recently, several studies have been reported on performance enhancing expansion devices and the ejector has shown promising potential as an expansion device characterized by absence of moving 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, mathematical models on ejectors have progressed as thermodynamic models and dynamic models which are further subdivided to single phase and two phase flow models. Dynamic models have higher prediction precision yielding greater information (He et al., 2009). Li and Groll (2005) implemented a thermodynamic analysis at different operating conditions for an assumed entrainment ratio and pressure 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 reporting 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
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and 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 velocity and critical mass flux. They varied diameter of the convergingediverging (CeD) nozzle and other geometrical parameters to test their sensitivity with respect to performance 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 cycle was reported and performance was higher for the constant pressure mixing ejector. Nakagawa et al. (2011) reported experimental results on a two phase ejector refrigeration system. They used an ejector comprising a C-D motive 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 CO2 as working fluids. The detailed literature survey, presented above, shows that even 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 primary 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 comprehensively evaluated for the given geometry of ejector.
2.
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Fig. 1 e Schematic diagram of refrigeration system with ejector.
motive fluid decreases in the primary nozzle of ejector from 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,
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 consists 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 primary 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 increases 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 (CD) nozzle is used as the primary nozzle, in which the primary fluid or motive fluid expands from the super-critical, single phase region to a sub-critical pressure, that is less than or equal to the evaporator pressure. The static enthalpy of the
Fig. 2 e P-h diagram of the CO2 based refrigeration system with ejector.
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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:
m¼
ms
mp
(1)
However, for all operating conditions, the vapour fraction at the exit of ejector may not be exactly equal to the required _ p =ðm _pþm _ s Þ, which leads to a mass imbalance value of x7 ¼ m in 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 þ m) x7 > 1 is satisfied. It may be noted that if the exit vapour fraction is less than that of the required value stated above, then the cycle will not be realized as the above modification in the cycle can take care of excess vapour at ejector exit only. The feedback throttle is required for system simulation; however, in an actual system, the system will adjust automatically to a new balanced condition, even without the feedback throttle valve. In Fig. 2, the lines 3e90 and 10e20 represent the expansion and compression process in a conventional transcritical cycle with a throttle valve and without any recovery during the expansion process, and 10e20 e3e90 represents the corresponding 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 section is an important part in the design of an ejector. Constant
pressure mixing is adopted in the present study since it leads to superior performance compared to constant area mixing as is evident from the literature (Keenan et al., 1950). Mixing section length (Xm) is greater than zero for constant pressure mixing whereas Xm ¼ 0 for constant area mixing (Fig. 3). The performance of the ejector and the system can be specified in terms of pressure lift and cooling COP, given by: Pressure lift ; Plift ¼ Pc Ps COPcooling ¼ m
h10 h9 h2 h1
(2)
(3)
3. Thermodynamic analysis of the ejector based refrigeration cycle The following simplifying assumptions have been made for the thermodynamic analysis: i. Steady one dimensional homogeneous equilibrium flow. ii. Pressure drop in gas cooler and evaporator are negligibly small. iii. No heat interaction with surrounding in all the components 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 feedback mass for 1 Ton cooling capacity. Isentropic efficiency for
Fig. 3 e Schematic diagram of the ejector with a convergingediverging nozzle.
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compressor hcomp has been calculated from the following correlation given by Robinson and Groll (1998): 2
Qgc ¼
3
hcomp ¼ 0:815 þ 0:022ðPc =Pd Þ 0:0041ðPc =Pd Þ þ 0:0001ðPc =Pd Þ
(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 ¼ f ðh3 ; h4s ; hnoz1 Þ u4 ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ðh3 h4 Þ
(5)
u5 ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ðh10 h5 Þ
(7) (8)
Both fluids are assumed to mix at constant pressure. Therefore, the momentum and energy equations for the mixing process are: ð1 þ mÞu6 ¼ u4 þ mu5 ð1 þ mÞ h6 þ u26 2 ¼ h4 þ u24 2 þ m h5 þ u25 2
(9) (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 ¼ f ðPs ; h6 Þ
(11)
h7 ¼ f Pc ; h7s ; hdiff
(12)
hdiff ¼
h7s h6 h7 h6
(13)
Applying overall energy balance to the ejector, ð1 þ mÞh7 ¼ h3 þ mh10
Wcomp ¼
1 _ tot ðh2 h1 Þm 1þm
(19)
(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)).
(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 ¼ f ðh10 ; h5s ; hnoz2 Þ
1 _ tot ðh3 h2 Þm 1þm
181
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, _ p Þ, secondary h ¼ 0.85 in the nozzles. Primary mass flow rate ðm _ s Þ and ‘Pc’ are the outcome of the thermomass flow rate ðm dynamic analysis at 110 bar discharge pressure and 35 C gas cooler exit temperature keeping evaporator temperature 2 C for 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 condition 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 ¼
_p m G4
(21)
A5 ¼
_s m G5
(22)
_s _p þm m G6
(23)
(14)
Vapour quality at the exit of diffuser of ejector is expressed as: x7 ¼ f ðPc ; h7 Þ
(15)
A6 ¼
ð1 þ mÞx7 ¼ 1
(16)
Fig. 4 shows the mass flux (G) variation with 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,
Saturated liquid from separator is throttled to evaporator through expansion valve in an isenthalpic process yielding: h8 ¼ h9
(17)
The expression for refrigeration effect, gas cooler heat rejection and compressor work are as follows: Qevap ¼
m _ tot ðh10 h9 Þm 1þm
(18)
M ¼ u=a
(24)
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dA dr du þ þ ¼0 A r u
(30)
Energy equation, dh þ udu ¼ 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 a motive stream pressure of 110 bar and the saturated suction stream at 2 C.
5. System simulation at different operating conditions with designed ejector
Fig. 4 e Pressure variation with mass flux for isentropic and non-isentropic expansion.
a¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s
ffi vP vr s¼c
(25)
The condition for choking is given by, dG ¼0 dP
(26)
Suitable stage efficiency (hstage) for elemental pressure drop is chosen by iteration such that it matches the end state point 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 ¼
hstage;com
ðdhÞ ðdhÞiso
ðdhÞiso ¼ dh
(27)
(28)
Properties such as enthalpy, entropy, velocity, Mach number 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 ¼
The transcritical CO2 cycle with ejector is simulated to study the effect of operating parameters on the system performance. 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:
_p m 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 pressure 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,
i. Choked condition for primary nozzle ii. Feedback mass is such that the difference in vapour fraction variation is below 2% of total mass flow rate. Critical mass flux is determined from the motive input of pressure (P3 ¼ Pd) and temperature, T3 for the given path of expansion and primary mass flow rate is determined for the designed throat area (At). Gmax ¼ f ðPd ; T3 ; hnoz1 Þ
(32)
_ p ¼ Gmax At m
(33)
Secondary pressure drop (DPsec) is assumed in the iteration loop. P5 ¼ Pe DPsec
(34)
Secondary mass flow rate for the small expansion DPsec is expressed as: G5 ¼ f ðPe ; Ps ; hnoz2 Þ
(35)
_ s ¼ G5 A5 m
(36)
Table 1 e Dimension (mm) and mass flow rates (kg s¡1) of the designed ejector. _p m 0.024
_s m
dt
d4
d5
d6
d7
0.016
0.67
0.89
3.2
1.85
5.43
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‘P5’ is the back pressure for the diverging part of C-D nozzle. Fluid in primary nozzle may exit with underexpansion 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: ½ru ¼ 0
(37)
p þ ru2 ¼ 0
(38)
h þ u2 2 ¼ 0
(39)
_pþm _s¼m _ tot m Momentum conservation equation, ðP þ P6 Þ _ s u5 þ P4 A4 þ P5 A5 5 _ p u4 þ m ðA4 þ A5 A6 Þ m 2 _ tot u6 þ P6 A6 ¼m
(40)
(41)
Energy conservation equation,
u2 u2 u2 _ s h5 þ 5 ¼ m _ tot h6 þ 6 _ p h4 þ 4 þ m m 2 2 2
(42)
Mass flux at the exit of diffuser, G7 ¼
_ tot m A7
(43)
Pressure and other thermodynamic properties at the exit of diffuser are obtained for the given path and designed area A7. Pc ¼ f G7 ; hdiff
h7 ¼ f G7 ; hdiff
Values of P6 and the pressure drop across the secondary nozzle, DPsec were adjusted till convergence was 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 0 0 corresponding conventional transcritical cycle 10e2 39 10 (Fig. 2). COPconv ¼
6.
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 _ p Þ and secondary employed to solve the problem. Primary ðm _ s Þ are mixed in converging mixing zone and the mass ðm stream 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 equations as expressed below. Mass conservation equation,
(44)
(45)
x7 ¼ f ðPc ; h7 Þ
(46)
ð1 þ mÞx7 1
(47)
h10 h3 h20 h10
(48)
(49)
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 temperature were assumed to be 110 bar and 35 C, respectively while the evaporator temperature was taken as 2 C. It is assumed that the system studied is suitable for the application of comfort air conditioning, hence the refrigerated space temperature (Tw) for evaporator is assumed to be 25 C, while the reference temperature (To) is 32 C.
6.1.
Exergy analysis of conventional cycle
_ 0 ðs20 s10 Þ Exergy destruction in compressor; Ic ¼ mT Exergy destruction in gas cooler;
h20 h3 _ 0$ Igc ¼ m$T ðs20 s3 Þ T0
(50)
_ 0 ðs90 s3 Þ Exergy destruction in expansion valve; Iv ¼ mT
(52)
Exergy destruction in evaporator;
h10 h90 _ T0 ðs10 s90 Þ Ievap ¼ m Tw
(53)
6.2.
(51)
Exergy analysis of cycle with ejector
_ p T0 ðs2 s1 Þ Exergy destruction in compressor; Ic ¼ m
(54)
Exergy destruction in gas cooler;
h2 h3 _ p $T0 $ Igc ¼ m ðs2 s3 Þ T0
(55)
_ p T0 ðs4 s3 Þ Exergy destruction in primary nozzle; Inoz1 ¼ m (56) _ s T0 ðs5 s10 Þ Exergy destruction in secondary nozzle; Inoz2 ¼ m
To allow feedback mass expressed in Eq. (47), the evaporator capacity equation changes to: _ s h10 ð1 x7 Þ m _ p þm _ s h9 ðx7 ð1=ð1 þ mÞÞÞ m _ p þm _ s ah1 Qevap ¼ m
183
(57) Exergy destruction in mixing section; _ p s4 þ m _ s s5 _ tot s6 m Imix ¼ T0 m
(58)
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_ tot T0 ðs7 s6 Þ Exergy destruction in diffuser section; Idiff ¼ m (59) Exergy destruction in separator; Isep _ tot ðh7 T0 s7 Þ m _ p ðh1 T0 s1 Þ þ m _ s ðh8 T0 s1 Þ ¼m
(60)
_ s T0 ðs9 s8 Þ Exergy destruction in expansion valve; Iv ¼ m
(61)
Exergy destruction in evaporator;
h10 h9 _ s T0 ðs10 s9 Þ Ievap ¼ m Tw
(62)
Second law efficiency; h2nd ¼
7.
P
I 1 Wcomp
(63)
Results and discussions
Behaviour of refrigeration system with ejector at different operating parameters is investigated and performance parameters 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 conditions. For example, it can be seen from Fig. 5 that when the evaporator temperature is maintained below 4 C, for high pressure 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 refrigeration system.
7.1.
Fig. 5 e Effect of gas cooler exit pressure and temperature on primary nozzle exit pressure, and evaporator pressure at corresponding temperature.
reasonably 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 no major role as the expansion is kept low for all cases and hence is kept fixed at 65% in the simulation. Isentropic efficiencies for diffuser are
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 numerical 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 the ejector components, the primary nozzle efficiency is varied from 65% to 70% for the purpose of validation so that a
Fig. 6 e Comparison between numerical and experimental values.
185
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Table 2 e Values for varying motive inlet pressure at T3 ¼ 35 C, Te ¼ 2 C. P3 (bar) 95 100 105 110
Pc (kPa)
P6 (kPa)
P4 (kPa)
Ps (kPa)
_ p (kg s1) m
_ s (kg s1) m
u6 (m s1)
4119 4201 4275 4349
3766 3730 3689 3643
2933 3256 3486 3643
3658 3653 3648 3643
0.0185 0.0208 0.0229 0.0248
0.0120 0.0138 0.0154 0.0169
70.18 80.30 88.88 97.07
also kept between 65% and 70%. Feedback mass 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 predicted mass 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 quantitative 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 pressure with the use of ejector. Difference between compressor pressure and secondary suction pressure has been termed as
Fig. 7 e (a). Effect of P3 on Pressure lift and entrainment ratio. (b). Effect of P3 on COP and cooling capacity. (c). Effect of P3 on COP for different motive inlet temperature.
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pressure 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 primary mass and secondary mass are increasing with increase in P3 the ratio between them does not change significantly. Furthermore, secondary fluid exit pressure Ps does not vary much 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, high momentum leads to low exit pressure after mixing. In the second part of pressure lift which occurs in diffuser, the same high 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 refrigeration 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 evaporator 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 P3 is 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 increase with 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 depends 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 decreases which also causes lower secondary mass. This leads to low momentum at the exit of mixing section or in other words at the inlet of diffuser section. Therefore, lower pressure lift occurs in diffuser. Entrainment ratio significantly decreases at higher gas cooler exit temperature in this condition. Lower cooling capacity 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 than the design value (3.517 kW), either design value for T3 should be taken higher or design value of cooling load should be set
(a) μ
μ
186
(b)
Fig. 8 e (a). Effect of T3 on Pressure lift and entrainment ratio. (b). Effect of T3 on COP and cooling capacity. 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, entrainment 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 temperature 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 ratio show slight variation. Increasing evaporator temperature also has marginal effect on cooling capacity but
187
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 7 e1 8 8
4 T 3 =35°C T e=2°C
COP
3.5
3
2.5
Ejector based cycle Conventional cycle
2 90
95
100
105
110
Gas Cooler Exit Pressure (P3 ,bar) Fig. 10 e COP of ejector based and conventional transcritical CO2 system at varying P3.
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 system performance enhancement. Exergy destruction rates are estimated (Fig. 11) at a gas cooler pressure and exit temperature of 110 bar and 35 C for evaporator temperature of 2 C and 1 Ton cooling capacity for both refrigeration cycle with ejector (RCE) and conventional refrigeration cycle (CRC). Exergy destruction rate in the evaporator of both the cycles are Fig. 9 e (a) Effect of Te on Pressure lift and entrainment ratio. (b). Effect of varying Te on COP and cooling capacity. 350
200 150 100 50
or ra t
er us
pa Se
in
2
g D iff
M ix
N oz
1 oz N
va
lv
e
le r p. Ex
co o
so
as G
pr es
om
or
at
or
r
0
C
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 conventional 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.
Irreversibility (Watt)
Comparison with conventional cycle
250
ap
7.5.
RCE CRC
300
Ev
decreased 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).
Fig. 11 e Exergy destruction in different components of conventional and ejector based cycle.
188
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 7 e1 8 8
almost the same for the given operating conditions and cooling capacity. The secondary nozzle of ejector and separator 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 conventional and cycles with ejector. The resulting second law efficiencies obtained are 6.6% and 7.52% for conventional and systems with ejector, respectively, under the given conditions.
8.
Conclusion
An ejector has been designed for choked condition based on a thermodynamic model, solved numerically employing MATLAB 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. Results 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 condition in case of the system with ejector. Additionally, a comprehensive exergy analysis was implemented to identify component level deficiencies and it establishes the justification of replacement of throttle valve by an ejector as an expansion device in a CO2 based transcritical vapour compression refrigeration system.
Acknowledgement 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 demonstration unit of carbon dioxide based transcritical refrigeration system”.
references
Agrawal, N., Bhattacharyya, S., 2008. Optimized transcritical CO2 heat pumps: performance comparison of capillary tubes against expansion valves. Int. J. Refrigeration 31, 388e395. Casson, V., Cecchinato, L., Corradi, M., Fornasieri, E., Girotto, S., Minetto, S., Zamboni, L., Zilio, C., 2003. Optimisation of the throttling system in a CO2refrigerating machine. Int. J. Refrigeration 26 (8), 926e935. Deng, J., Jiang, P., Lu, Tao, Lu, W., 2007. Particular characteristics of transcritical CO2 refrigeration cycle with an ejector. App. Therm. Engg 27, 381e388. Elbel, S., Hrnjak, P., 2004. Flash gas bypass for improving the performance of transcritical R744 systems that use microchannel evaporators. Int. J. Refrigeration 27 (7), 724e735. He, S., Li, Y., Wang, R.Z., 2009. Progress of mathematical modeling on ejectors. Renew. Sustain. Energy Rev. 13, 1760e1780. Henry, E.R., Fauske, H.K., 1971. The two phase critical flow of onecomponent mixtures in nozzles, orifices and short tubes. J. Heat. Transf., 179e187. Kauf, F., 1999. Determination of the optimum high pressure for transcritical CO2 refrigeration cycles. Int. J. Therm. Sci. 38 (4), 325e330. Keenan, J.H., Neumann, E.P., Lustwerk, F., 1950. An investigation of ejector design by analysis and experiment. J. Appl. Mech. Tran. ASME 72, 299e309. Kim, M., Pettersen, J., Bullard, C.W., 2004. Fundamental process and system design issues in CO2 vapor compression systems. Prog. Energy Comb. SC. 30 (2), 119e174. Kornhauser, A.A., 1990. The use of an Ejector as a Refrigerant Expander. Proceedings of USNC/IIR-Purdue refrigeration conference. USA, 10e19. Lee, J.S., Kim, M.S., Kim, M.S., 2011. Experimental study on the improvement of CO2 air conditioning system performance using an ejector. Int. J. Refrigeration 34, 1614e1625. Li, D., Groll, E.A., 2005. Transcritical CO2 refrigeration cycle with ejector expansion device. Int. J. Refrigeration 28, 766e773. Liao, S.M., Zhao, T.S., Jakobsen, A., 2000. A correlation of optimal heat rejection pressures in transcritical carbon dioxide cycles. Appl. Therm. Engg. 20 (9), 831e841. Liu, F., Groll, E.A., 2008. Analysis of a two phase flow Ejector for the Transcritical CO2 Cycle. International Refrigeration and Air Conditioning Conference, Purdue. Lorentzen, G., 1994. Revival of carbon dioxide as a refrigerant. Int. J. Refrigeration 17 (5), 292e301. Nakagawa, M., Marasigan, A.R., Matsukawa, T., Kurashina, A., 2011. Experimental investigation on the effect of mixing length on the performance of two-phase ejector for CO2 refrigeration cycle with and without heat exchanger. Int. J. Refrigeration 34, 1604e1613. Robinson, D.M., Groll, E.A., 1998. Efficiencies of transcritical CO2 cycles with and without an expansion turbine. Int. J. Refrigeration 21 (7), 577e589. Sarkar, J., 2012. Ejector enhanced vapor compression refrigeration and heat pump systems e a review. Renew. Sustain. Energy Rev. 16, 6647e6659. Sarkar, J., Bhattacharyya, S., Ramgopal, M., 2004. Optimization of a transcritical CO2 heat pump cycle for simultaneous cooling and heating application. Int. J. Refrigeration 27, 830e838. Sumeru, K., Nasution, H., Ani, F.N., 2012. A review on two-phase ejector as an expansion device in vapor compression refrigeration cycle. Renew. Sustain. Energy Rev. 16, 4927e4937.
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journal homepage: www.elsevier.com/locate/ijrefrig
Thermodynamic design and simulation of a CO2 based transcritical vapour compression refrigeration system with an ejector Md. Ezaz Ahammed, Souvik Bhattacharyya*, M. Ramgopal Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
article info
abstract
Article history:
A two phase ejector suitable as an expansion device in a CO2 based transcritical vapour
Received 24 March 2014
compression refrigeration system is designed by extending the thermodynamic analysis
Received in revised form
and by interfacing with the system simulation model. A converging diverging nozzle is
9 June 2014
considered as primary nozzle of the ejector. For both design and parametric analyses, the
Accepted 12 June 2014
efficiencies of nozzles and diffuser have been assumed to be 85% each. Further, choked
Available online 21 June 2014
condition in the primary C-D nozzle and constant pressure mixing are assumed. Parameters such as COP, entrainment ratio, pressure lift and cooling capacity were obtained for
Keywords:
varying motive inlet and evaporator conditions. Motive inlet is found to be crucial for both
Carbon dioxide
performance and range of feasible application. Results show a COP improvement of 21%
Refrigeration cycle
compared to an equivalent conventional CO2 system. A comprehensive exergy analysis of
Thermodynamic analysis
the system establishes the justification of replacement of throttle valve by ejector in such
Ejector dimensions
systems.
Constant pressure mixing
© 2014 Elsevier Ltd and IIR. All rights reserved.
me Conception et simulation thermodynamiques d'un syste compression de vapeur au CO2 transcritique frigorifique a jecteur avec un e jecteur ; Me lange a pression constante Mots cles : Dioxyde de carbone ; Cycle frigorifique ; Analyse thermodynamique ; Dimensions de l'e
* Corresponding author. E-mail address: [email protected] (S. Bhattacharyya). http://dx.doi.org/10.1016/j.ijrefrig.2014.06.010 0140-7007/© 2014 Elsevier Ltd and IIR. All rights reserved.
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Nomenclature A a COP CRC RCE G h M _ m P Pc Pd d IHX Pe Ps Q s u W x
1.
area, m2 sonic velocity, m s1 coefficient of performance conventional refrigeration cycle refrigeration cycle with ejector mass flux, kg m2 s1 enthalpy, J kg1 Mach number mass flow rate, kg s1 pressure, Pa inlet pressure to compressor, Pa discharge pressure of compressor, Pa diameter internal heat exchanger evaporator pressure, Pa suction pressure of secondary stream, Pa heat transfer, W entropy, J kg1 K1 velocity, m s1 work transfer, W dryness fraction
Introduction
Carbon dioxide is an eco-friendly natural refrigerant with no ODP 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 suitably 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, modification 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 optimisations 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 modifications 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 expansion device with optimum design and operating conditions where the performance was reported to be marginally better
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 total
with higher gas cooler exit temperature. More recently, several studies have been reported on performance enhancing expansion devices and the ejector has shown promising potential as an expansion device characterized by absence of moving 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, mathematical models on ejectors have progressed as thermodynamic models and dynamic models which are further subdivided to single phase and two phase flow models. Dynamic models have higher prediction precision yielding greater information (He et al., 2009). Li and Groll (2005) implemented a thermodynamic analysis at different operating conditions for an assumed entrainment ratio and pressure 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 reporting 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
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and 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 velocity and critical mass flux. They varied diameter of the convergingediverging (CeD) nozzle and other geometrical parameters to test their sensitivity with respect to performance 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 cycle was reported and performance was higher for the constant pressure mixing ejector. Nakagawa et al. (2011) reported experimental results on a two phase ejector refrigeration system. They used an ejector comprising a C-D motive 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 CO2 as working fluids. The detailed literature survey, presented above, shows that even 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 primary 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 comprehensively evaluated for the given geometry of ejector.
2.
179
Fig. 1 e Schematic diagram of refrigeration system with ejector.
motive fluid decreases in the primary nozzle of ejector from 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,
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 consists 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 primary 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 increases 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 (CD) nozzle is used as the primary nozzle, in which the primary fluid or motive fluid expands from the super-critical, single phase region to a sub-critical pressure, that is less than or equal to the evaporator pressure. The static enthalpy of the
Fig. 2 e P-h diagram of the CO2 based refrigeration system with ejector.
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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:
m¼
ms
mp
(1)
However, for all operating conditions, the vapour fraction at the exit of ejector may not be exactly equal to the required _ p =ðm _pþm _ s Þ, which leads to a mass imbalance value of x7 ¼ m in 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 þ m) x7 > 1 is satisfied. It may be noted that if the exit vapour fraction is less than that of the required value stated above, then the cycle will not be realized as the above modification in the cycle can take care of excess vapour at ejector exit only. The feedback throttle is required for system simulation; however, in an actual system, the system will adjust automatically to a new balanced condition, even without the feedback throttle valve. In Fig. 2, the lines 3e90 and 10e20 represent the expansion and compression process in a conventional transcritical cycle with a throttle valve and without any recovery during the expansion process, and 10e20 e3e90 represents the corresponding 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 section is an important part in the design of an ejector. Constant
pressure mixing is adopted in the present study since it leads to superior performance compared to constant area mixing as is evident from the literature (Keenan et al., 1950). Mixing section length (Xm) is greater than zero for constant pressure mixing whereas Xm ¼ 0 for constant area mixing (Fig. 3). The performance of the ejector and the system can be specified in terms of pressure lift and cooling COP, given by: Pressure lift ; Plift ¼ Pc Ps COPcooling ¼ m
h10 h9 h2 h1
(2)
(3)
3. Thermodynamic analysis of the ejector based refrigeration cycle The following simplifying assumptions have been made for the thermodynamic analysis: i. Steady one dimensional homogeneous equilibrium flow. ii. Pressure drop in gas cooler and evaporator are negligibly small. iii. No heat interaction with surrounding in all the components 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 feedback mass for 1 Ton cooling capacity. Isentropic efficiency for
Fig. 3 e Schematic diagram of the ejector with a convergingediverging nozzle.
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 7 e1 8 8
compressor hcomp has been calculated from the following correlation given by Robinson and Groll (1998): 2
Qgc ¼
3
hcomp ¼ 0:815 þ 0:022ðPc =Pd Þ 0:0041ðPc =Pd Þ þ 0:0001ðPc =Pd Þ
(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 ¼ f ðh3 ; h4s ; hnoz1 Þ u4 ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ðh3 h4 Þ
(5)
u5 ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ðh10 h5 Þ
(7) (8)
Both fluids are assumed to mix at constant pressure. Therefore, the momentum and energy equations for the mixing process are: ð1 þ mÞu6 ¼ u4 þ mu5 ð1 þ mÞ h6 þ u26 2 ¼ h4 þ u24 2 þ m h5 þ u25 2
(9) (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 ¼ f ðPs ; h6 Þ
(11)
h7 ¼ f Pc ; h7s ; hdiff
(12)
hdiff ¼
h7s h6 h7 h6
(13)
Applying overall energy balance to the ejector, ð1 þ mÞh7 ¼ h3 þ mh10
Wcomp ¼
1 _ tot ðh2 h1 Þm 1þm
(19)
(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)).
(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 ¼ f ðh10 ; h5s ; hnoz2 Þ
1 _ tot ðh3 h2 Þm 1þm
181
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, _ p Þ, secondary h ¼ 0.85 in the nozzles. Primary mass flow rate ðm _ s Þ and ‘Pc’ are the outcome of the thermomass flow rate ðm dynamic analysis at 110 bar discharge pressure and 35 C gas cooler exit temperature keeping evaporator temperature 2 C for 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 condition 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 ¼
_p m G4
(21)
A5 ¼
_s m G5
(22)
_s _p þm m G6
(23)
(14)
Vapour quality at the exit of diffuser of ejector is expressed as: x7 ¼ f ðPc ; h7 Þ
(15)
A6 ¼
ð1 þ mÞx7 ¼ 1
(16)
Fig. 4 shows the mass flux (G) variation with 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,
Saturated liquid from separator is throttled to evaporator through expansion valve in an isenthalpic process yielding: h8 ¼ h9
(17)
The expression for refrigeration effect, gas cooler heat rejection and compressor work are as follows: Qevap ¼
m _ tot ðh10 h9 Þm 1þm
(18)
M ¼ u=a
(24)
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dA dr du þ þ ¼0 A r u
(30)
Energy equation, dh þ udu ¼ 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 a motive stream pressure of 110 bar and the saturated suction stream at 2 C.
5. System simulation at different operating conditions with designed ejector
Fig. 4 e Pressure variation with mass flux for isentropic and non-isentropic expansion.
a¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s
ffi vP vr s¼c
(25)
The condition for choking is given by, dG ¼0 dP
(26)
Suitable stage efficiency (hstage) for elemental pressure drop is chosen by iteration such that it matches the end state point 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 ¼
hstage;com
ðdhÞ ðdhÞiso
ðdhÞiso ¼ dh
(27)
(28)
Properties such as enthalpy, entropy, velocity, Mach number 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 ¼
The transcritical CO2 cycle with ejector is simulated to study the effect of operating parameters on the system performance. 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:
_p m 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 pressure 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,
i. Choked condition for primary nozzle ii. Feedback mass is such that the difference in vapour fraction variation is below 2% of total mass flow rate. Critical mass flux is determined from the motive input of pressure (P3 ¼ Pd) and temperature, T3 for the given path of expansion and primary mass flow rate is determined for the designed throat area (At). Gmax ¼ f ðPd ; T3 ; hnoz1 Þ
(32)
_ p ¼ Gmax At m
(33)
Secondary pressure drop (DPsec) is assumed in the iteration loop. P5 ¼ Pe DPsec
(34)
Secondary mass flow rate for the small expansion DPsec is expressed as: G5 ¼ f ðPe ; Ps ; hnoz2 Þ
(35)
_ s ¼ G5 A5 m
(36)
Table 1 e Dimension (mm) and mass flow rates (kg s¡1) of the designed ejector. _p m 0.024
_s m
dt
d4
d5
d6
d7
0.016
0.67
0.89
3.2
1.85
5.43
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 7 e1 8 8
‘P5’ is the back pressure for the diverging part of C-D nozzle. Fluid in primary nozzle may exit with underexpansion 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: ½ru ¼ 0
(37)
p þ ru2 ¼ 0
(38)
h þ u2 2 ¼ 0
(39)
_pþm _s¼m _ tot m Momentum conservation equation, ðP þ P6 Þ _ s u5 þ P4 A4 þ P5 A5 5 _ p u4 þ m ðA4 þ A5 A6 Þ m 2 _ tot u6 þ P6 A6 ¼m
(40)
(41)
Energy conservation equation,
u2 u2 u2 _ s h5 þ 5 ¼ m _ tot h6 þ 6 _ p h4 þ 4 þ m m 2 2 2
(42)
Mass flux at the exit of diffuser, G7 ¼
_ tot m A7
(43)
Pressure and other thermodynamic properties at the exit of diffuser are obtained for the given path and designed area A7. Pc ¼ f G7 ; hdiff
h7 ¼ f G7 ; hdiff
Values of P6 and the pressure drop across the secondary nozzle, DPsec were adjusted till convergence was 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 0 0 corresponding conventional transcritical cycle 10e2 39 10 (Fig. 2). COPconv ¼
6.
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 _ p Þ and secondary employed to solve the problem. Primary ðm _ s Þ are mixed in converging mixing zone and the mass ðm stream 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 equations as expressed below. Mass conservation equation,
(44)
(45)
x7 ¼ f ðPc ; h7 Þ
(46)
ð1 þ mÞx7 1
(47)
h10 h3 h20 h10
(48)
(49)
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 temperature were assumed to be 110 bar and 35 C, respectively while the evaporator temperature was taken as 2 C. It is assumed that the system studied is suitable for the application of comfort air conditioning, hence the refrigerated space temperature (Tw) for evaporator is assumed to be 25 C, while the reference temperature (To) is 32 C.
6.1.
Exergy analysis of conventional cycle
_ 0 ðs20 s10 Þ Exergy destruction in compressor; Ic ¼ mT Exergy destruction in gas cooler;
h20 h3 _ 0$ Igc ¼ m$T ðs20 s3 Þ T0
(50)
_ 0 ðs90 s3 Þ Exergy destruction in expansion valve; Iv ¼ mT
(52)
Exergy destruction in evaporator;
h10 h90 _ T0 ðs10 s90 Þ Ievap ¼ m Tw
(53)
6.2.
(51)
Exergy analysis of cycle with ejector
_ p T0 ðs2 s1 Þ Exergy destruction in compressor; Ic ¼ m
(54)
Exergy destruction in gas cooler;
h2 h3 _ p $T0 $ Igc ¼ m ðs2 s3 Þ T0
(55)
_ p T0 ðs4 s3 Þ Exergy destruction in primary nozzle; Inoz1 ¼ m (56) _ s T0 ðs5 s10 Þ Exergy destruction in secondary nozzle; Inoz2 ¼ m
To allow feedback mass expressed in Eq. (47), the evaporator capacity equation changes to: _ s h10 ð1 x7 Þ m _ p þm _ s h9 ðx7 ð1=ð1 þ mÞÞÞ m _ p þm _ s ah1 Qevap ¼ m
183
(57) Exergy destruction in mixing section; _ p s4 þ m _ s s5 _ tot s6 m Imix ¼ T0 m
(58)
184
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 7 e1 8 8
_ tot T0 ðs7 s6 Þ Exergy destruction in diffuser section; Idiff ¼ m (59) Exergy destruction in separator; Isep _ tot ðh7 T0 s7 Þ m _ p ðh1 T0 s1 Þ þ m _ s ðh8 T0 s1 Þ ¼m
(60)
_ s T0 ðs9 s8 Þ Exergy destruction in expansion valve; Iv ¼ m
(61)
Exergy destruction in evaporator;
h10 h9 _ s T0 ðs10 s9 Þ Ievap ¼ m Tw
(62)
Second law efficiency; h2nd ¼
7.
P
I 1 Wcomp
(63)
Results and discussions
Behaviour of refrigeration system with ejector at different operating parameters is investigated and performance parameters 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 conditions. For example, it can be seen from Fig. 5 that when the evaporator temperature is maintained below 4 C, for high pressure 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 refrigeration system.
7.1.
Fig. 5 e Effect of gas cooler exit pressure and temperature on primary nozzle exit pressure, and evaporator pressure at corresponding temperature.
reasonably 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 no major role as the expansion is kept low for all cases and hence is kept fixed at 65% in the simulation. Isentropic efficiencies for diffuser are
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 numerical 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 the ejector components, the primary nozzle efficiency is varied from 65% to 70% for the purpose of validation so that a
Fig. 6 e Comparison between numerical and experimental values.
185
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 7 e1 8 8
Table 2 e Values for varying motive inlet pressure at T3 ¼ 35 C, Te ¼ 2 C. P3 (bar) 95 100 105 110
Pc (kPa)
P6 (kPa)
P4 (kPa)
Ps (kPa)
_ p (kg s1) m
_ s (kg s1) m
u6 (m s1)
4119 4201 4275 4349
3766 3730 3689 3643
2933 3256 3486 3643
3658 3653 3648 3643
0.0185 0.0208 0.0229 0.0248
0.0120 0.0138 0.0154 0.0169
70.18 80.30 88.88 97.07
also kept between 65% and 70%. Feedback mass 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 predicted mass 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 quantitative 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 pressure with the use of ejector. Difference between compressor pressure and secondary suction pressure has been termed as
Fig. 7 e (a). Effect of P3 on Pressure lift and entrainment ratio. (b). Effect of P3 on COP and cooling capacity. (c). Effect of P3 on COP for different motive inlet 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 7 e1 8 8
pressure 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 primary mass and secondary mass are increasing with increase in P3 the ratio between them does not change significantly. Furthermore, secondary fluid exit pressure Ps does not vary much 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, high momentum leads to low exit pressure after mixing. In the second part of pressure lift which occurs in diffuser, the same high 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 refrigeration 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 evaporator 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 P3 is 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 increase with 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 depends 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 decreases which also causes lower secondary mass. This leads to low momentum at the exit of mixing section or in other words at the inlet of diffuser section. Therefore, lower pressure lift occurs in diffuser. Entrainment ratio significantly decreases at higher gas cooler exit temperature in this condition. Lower cooling capacity 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 than the design value (3.517 kW), either design value for T3 should be taken higher or design value of cooling load should be set
(a) μ
μ
186
(b)
Fig. 8 e (a). Effect of T3 on Pressure lift and entrainment ratio. (b). Effect of T3 on COP and cooling capacity. 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, entrainment 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 temperature 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 ratio show slight variation. Increasing evaporator temperature also has marginal effect on cooling capacity but
187
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 7 e1 8 8
4 T 3 =35°C T e=2°C
COP
3.5
3
2.5
Ejector based cycle Conventional cycle
2 90
95
100
105
110
Gas Cooler Exit Pressure (P3 ,bar) Fig. 10 e COP of ejector based and conventional transcritical CO2 system at varying P3.
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 system performance enhancement. Exergy destruction rates are estimated (Fig. 11) at a gas cooler pressure and exit temperature of 110 bar and 35 C for evaporator temperature of 2 C and 1 Ton cooling capacity for both refrigeration cycle with ejector (RCE) and conventional refrigeration cycle (CRC). Exergy destruction rate in the evaporator of both the cycles are Fig. 9 e (a) Effect of Te on Pressure lift and entrainment ratio. (b). Effect of varying Te on COP and cooling capacity. 350
200 150 100 50
or ra t
er us
pa Se
in
2
g D iff
M ix
N oz
1 oz N
va
lv
e
le r p. Ex
co o
so
as G
pr es
om
or
at
or
r
0
C
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 conventional 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.
Irreversibility (Watt)
Comparison with conventional cycle
250
ap
7.5.
RCE CRC
300
Ev
decreased 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).
Fig. 11 e Exergy destruction in different components of conventional and ejector based cycle.
188
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 7 e1 8 8
almost the same for the given operating conditions and cooling capacity. The secondary nozzle of ejector and separator 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 conventional and cycles with ejector. The resulting second law efficiencies obtained are 6.6% and 7.52% for conventional and systems with ejector, respectively, under the given conditions.
8.
Conclusion
An ejector has been designed for choked condition based on a thermodynamic model, solved numerically employing MATLAB 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. Results 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 condition in case of the system with ejector. Additionally, a comprehensive exergy analysis was implemented to identify component level deficiencies and it establishes the justification of replacement of throttle valve by an ejector as an expansion device in a CO2 based transcritical vapour compression refrigeration system.
Acknowledgement 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 demonstration unit of carbon dioxide based transcritical refrigeration system”.
references
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