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Applying mechanical subcooling to ejector refrigeration cycle for improving the coefficient of performance
Energy Conversion and Management 48 (2007) 1193–1199 www.elsevier.com/locate/enconman
Applying mechanical subcooling to ejector refrigeration cycle for improving the coefficient of performance Jianlin Yu *, Yunfeng Ren, Hua Chen, Yanzhong Li Institute of Refrigeration and Cryogenics Engineering, Xi’an Jiaotong University, Xi’an 710049, China Received 2 September 2005; accepted 8 October 2006 Available online 29 November 2006
Abstract This paper describes a new ejector refrigeration system with mechanical subcooling which uses an auxiliary liquid–gas ejector to enhance subcooling for the refrigerant from condenser. The new system can have larger subcooling degree when circulating pump consumes a little more power compared with conventional ejector refrigeration system. Based on the built mathematical model, the performance of the new ejector refrigeration system was discussed and compared with that of a conventional ejector refrigeration system for refrigerant R142b. Theoretical analyzing results show that the new system can efficiently improve the coefficient of performance (COP) of ejector refrigeration. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Mechanical subcooling; Ejector refrigeration; Ejector
1. Introduction Ejector refrigeration system (ERS) powered by lowgrade energy has been studied since the mid-1950s. Compared with other refrigeration systems, ERS has some special advantages such as the simplicity in construction, high reliability and low cost. However, the coefficient of performance for the conventional ERS is significantly lower than that for other refrigeration systems. This has restricted its wide applications. In recent years, people have tried to find wider application for ejector refrigeration systems in refrigeration and air conditioning field by directly utilizing low-grade thermal energy, such as solar energy and waste heat. Chunnanond and Aphornratana provides a literature review on ejectors and their applications in refrigeration [1]. The literature review showed that in many studies the pre-cooler and the pre-heater are installed to the conventional system, in order to improve the system efficiency. Cizungu, Groll conducted the research on performance comparison of vapor jet refrig*
Corresponding author. Tel.: +86 29 82668738; fax: +86 29 82668725. E-mail address: [email protected] (J. Yu).
0196-8904/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2006.10.009
eration system with environment friendly working fluids R123, R134a, R152a and R717 [2]. The results suggest that the system efficiency depends mainly on the ejector geometry and the compression ratio. Chang and Chen investigated a steam-jet refrigerator using petal nozzle and results indicated it might elevate the performance of an ejector [3]. Eames and Aphornratana conducted the research on a small-scale steam-jet refrigerator, in which an ejector with movable primary nozzle was used [4,5]. Sun’s studies showed that the use of variable-geometry ejector might achieve optimum performance under various operating condition [6]. A combined ejector-vapor compression refrigeration systems as a mechanically efficient way to increase the COP of ERS was also proposed and studied [7–10]. Despite of the higher COP in this combined cycle, additional compressor actually makes systems more complicated and higher cost due to compressor itself. To significantly improve the COP of ERS, a new integrated mechanical-subcooling ejector refrigeration system is proposed in this paper. In the new ERS (NERS) an auxiliary liquid–gas ejector is used to construct an additional subcooling loop in a conventional ejector refrigeration system (CERS). This subcooling loop can make the liquid
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Nomenclature COP Ex h m_ P Pb Q s t T T0 u g l
coefficient of performance exergy (kW) enthalpy (kJ/kg) mass flow rate (kg/s) pressure (Pa) backpressure (Pa) heat load (kW) entropy ( kJ/Kg K) temperature (°C) thermodynamic temperature (K) ambient temperature (K) velocity (m/s) efficiency entrainment ratio (m_ sf =m_ pf )
Subscripts c condenser d diffuser section of ejector e evaporator g generator m mixing section of ejector mf mixed fluid n nozzle n1 inlet of nozzle n2 outlet of nozzle p pump pf primary fluid s isentropic process sf secondary fluid
Fig. 1 shows a basic CERS. It mainly consists of a generator, an evaporator, a condenser, expansion device, ejector and circulating pump. In this system, the vapor (primary fluid) from the generator at high pressure flows through the nozzle of the ejector and entrains the vapor (secondary fluid) from evaporator at low pressure. The primary fluid and secondary fluid then mix in the mixing section and recover a pressure in the diffuser. The combined fluid flows to condenser where it condenses. And then the
condensate is divided into two parts; one is pumped back to the generator, and the other flows through the expansion device and enters the evaporator, where it is evaporated to vapor. The vapor is finally entrained into the ejector again, thus finishing the ejector refrigeration cycle. Within one cycle, when the system obtains heat from heat source in the generator and work input from the pump, it produces the cooling effect in the evaporator and dissipates the heat to the environment through the condenser. The ejector is the key component in the ejector refrigeration cycle. The ejector generally consists of four parts: a nozzle section for a primary flow and a suction chamber for the secondary flow, a mixing section for the primary flow and secondary flow to mix, a throat section (constant area section) in which the mixed fluid normally undergoes a transverse shock and a pressure rise, and a diffuser section for the mixed fluid to recompress to the back pressure. Fig. 2 shows the schematic configuration of an ejector and the variation of pressure in the ejector. The COP of the CERS is highly dependent on the entrainment of ejector (the ratio of secondary flow rate
Fig. 1. A conventional ejector refrigeration system.
Fig. 2. An ejector and the variation of pressure in ejector.
refrigerant from the condenser to be further subcooled with increasing a little more circulating pump power. The new system can utilize solar energy or waste-heat more effectively and elevate the coefficient of performance (COP) of ejector refrigeration in some extent. A general description of the new system is presented and further analysis on its performance is conducted based on mathematical model. And the comparison between NERS and the CERS was also made. 2. General system description
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the one-dimensional constant pressure flow model used by most researchers studying ejector refrigeration systems. The basic principle of the model was introduced by Keenan et al. [14] based on gas dynamics, and developed by Huang et al. and Ouzzane et al. [15,16]. For simplicity, the theory is also applied to liquid–gas ejector although two–phase mixing flow through the liquid–gas ejector is more complicated. The following assumptions are made for the analysis:
Fig. 3. A new ejector refrigeration system.
to primary flow rate). The entrainment is relative to the primary flow inlet state, secondary flow inlet state and mixing outlet state of the ejector. The three primary, secondary and back pressures, are main factors which affect the entrainment. Some research results showed the entrainment increases with the decreasing backpressure when primary pressure and secondary pressure are constant [11–13]. These pressures are, respectively, the functions of condensing temperature, generating temperature and evaporating temperature. Usually these temperatures depend on the operating condition and are fixed within a range. The optimum operating condition could not make more improvement for COP. The NERS developed by author is shown in Fig. 3. The new integrated mechanical subcooling ejector refrigeration system consists of two simple cycles coupled to each other via a subcooler which functions as the evaporator in the subcooling cycle. The main cycle is similar to the CERS. In the subcooling cycle, the liquid (primary fluid) from pump at high pressure flows through the nozzle of the liquid–gas ejector and entrains the vapor (secondary fluid) from subcooler at low pressure. Then the combined fluid from liquid–gas ejector flows to condenser where it condenses. And then the condensate is divided into two parts; one is pumped back to liquid–gas ejector, and the other flows through the expansion device and enters the subcooler, where it is evaporated to vapor. The vapor is finally entrained into the liquid–gas ejector again, thus finishing the subcooling cycle. In the main cycle, the working process is the same as that introduced in the previous sections. The new system can have larger subcooling degree compared with conventional ejector refrigeration system. Details of new cycle performance analysis are discussed as follows. 3. Simulation mathematical model In the present system, the main ejector is a common vapor–vapor ejector and the auxiliary ejector is a type of liquid–vapor ejector. They have similar structure and working process. In the present study, the vapor–vapor ejector performance simulation is carried out based on
(1) The flow inside the ejectors is in steady state and onedimensional. (2) The compression and expansion process in ejectors are isentropic or friction losses are defined in terms of the isentropic efficiency in the nozzle, mixing section, diffuser and circulating pump. (3) Mixing in the mixing section of ejectors occurs at constant pressure and complying with the conversation of energy and momentum; the inner walls of ejectors are adiabatic, namely no heat losses. (4) A homogenous two-phase flow mixing is idealized for the liquid–gas ejector inside. Based on the above assumptions, the mass, momentum and energy equations are applied to sections for both the ejector and the jet pump and then the following equations are obtained. In the nozzle section, the energy conservation equation for the adiabatic and steady primary flow is given as: hpf;n2 þ u2pf;n2 =2 ¼ hpf;n1 þ u2pf;n1 =2
ð1Þ
Compared with the exit velocity of primary flow upf,n2, the inlet velocity of primary flow upf,n1 could be negligible. According to Eq. (1), the exit velocity of primary flow upf,n2 is expressed as: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi upf;n2 ¼ 2ðhpf;n1 hpf;n2 Þ ð2Þ The nozzle efficiency is given as: gn ¼
hpf;n1 hpf;n2 hpf;n1 hpf;n2;s
hence upf;n2 ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2gn ðhpf;n1 hpf;n2;s Þ
ð3Þ
ð4Þ
where hpf;n1 ¼ f ðT pf;n1 ; P pf;n1 Þ
ð5Þ
spf;n1 ¼ f ðT pf;n1 ; P pf;n1 Þ spf;n2;s ¼ spf;n1
ð6Þ ð7Þ
P pf;n2;s ¼ P m hpf;n2;s ¼ f ðspf;n2;s ; P pf;n2;s Þ
ð8Þ ð9Þ
The entrainment ratio of ejector is given as: l¼
m_ sf m_ pf
ð10Þ
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In the mixing section, the momentum conservation equation is m_ pf upf;n2 þ m_ sf usf;n2 ¼ ðm_ pf þ m_ sf Þumf;m;p
ð11Þ
hence umf;m;p
hmf;d ¼ hmf;m þ u2mf;m =2 upf;n2 þ l usf;n2 ¼ 1þl
ð12Þ
where usf;n2
ð13Þ
The mixing efficiency is given as: u2mf;m u2mf;m;p
ð15Þ
The average velocity of mixed flow umf,m is written according to Eqs. (14) and (15) as: pffiffiffiffiffiffi umf;m ¼ upf;n2 gm =ð1 þ lÞ ð16Þ The energy conservation equation for the mixing section is m_ pf
u2pf;n2 hpf;n2 þ 2
! þ m_ sf hsf;n2 þ
u2mf;m ¼ ðm_ pf þ m_ sf Þ hmf;m þ 2
u2sf;n2
ð17Þ
ð18Þ
where hsf ¼ f ðT sf ; P sf Þ
ð19Þ
smf;m ¼ f ðhmf;m ; P mf;m Þ
ð20Þ
In diffuser section, the mixed fluid converts the kinetic energy into pressure energy. Assuming the compression process is isentropic, then the energy equation for the diffuser section is ð21Þ
The actual energy equation for the diffuser section is
hmf;d;s hmf;m hmf;d hmf;m
ð26Þ ð27Þ
smf;d;s ¼ smf;m
ð28Þ
It is known the performance of ejectors are evaluated by their entrainment ratio l. Based on above Eqs. 4,16,25, it can be derived as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l ¼ gn gm gd ððhpf;n1 hpf;n2;s Þ=ðhmf;d;s hmf;m ÞÞ 1 ð29Þ When the inlet state parameters of primary fluid, secondary fluid and back pressure are given, the value of entrainment ratio l could be found using iteration calculation. For the whole cycle performance, the basic equations obtained from the conversation law for energy are written as follows:
ð30Þ
Qg ¼ m_ g ðh1 h4 Þ
ð31Þ
For condenser:
The enthalpy of mixed flow is written according to Eqs. (2,13,17) as:
gd ¼
hmf;d;s ¼ f ðsmf;d;s ; P mf;d;s Þ P mf;d;s ¼ P b
For generator:
!
1 2 ðu u2mf;d Þ ¼ hmf;d hmf;m 2 mf;m The diffuser efficiency is given as:
where
Qe ¼ m_ e ðh6 h5 Þ
2
1 2 ðu u2mf;d;s Þ ¼ hmf;d;s hmf;m 2 mf;m
ð25Þ
For evaporator:
!
hmf;m ¼ ðhpf;n1 þ lhsf Þ=ð1 þ lÞ u2mf;m =2
ð24Þ
In addition, according to Eq. (23), the actual exit enthalpy of the mixed fluid is also expressed as: hmf;d ¼ hmf;m þ ðhmf;d;s hmf;m Þ=gd
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 2ðhsf hsf;n2 Þ
Compared with the primary flow velocity upf,n2, the velocity of secondary flow usf,n2 is negligible. Then the Eq. (12) becomes upf;n2 umf;m;p ¼ ð14Þ 1þl
gm ¼
Compared with the velocity umf,m, the exit velocity of the mixed fluid umf,d is negligible, the actual exit enthalpy of the mixed fluid hmf,d is written according to energy Eq. (22) as:
ð22Þ
ð23Þ
Qc ¼ m_ c ðh2 h3 Þ
ð32Þ
For circulating pump: W ¼ m_ P ðh4 h3 Þ
ð33Þ
The system performance is evaluated by the coefficient of performance COP, which is the ratio of the cooling capacity to the gross energy input of the cycle. It is written as follows: COP ¼ Qe =ðQg þ W Þ
ð34Þ
4. Simulation results and discussion The refrigerants thermodynamics properties are calculated by using NIST database and subroutines [17]. And the calculating program is written with Fortran. Language. Some selected refrigerants, such as R134a, R152a and R142b are applied to the above computation models for simulating the ejector and CERS cycle performance, and the simulation results are in very good agreement with the research results from Sun’s study [18] under the same operating conditions, shown in Fig. 4.
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considering the grade of input energy. The input exergy is described as follows: Ex ¼ ExQg þ W
ð35Þ
where ExQg ¼ ð1 T 0 =T g Þ Qg ;
ðT 0 ¼ 298:15 KÞ
ð36Þ
4.1. The evaluation of mechanical subcooling
Fig. 4. Comparison of the present simulation results with the Sun’s research results. tg = 90 °C, tk = 35 °C, to = 5 °C
In present study, R142b is singled out as working refrigerant for simulating the NERS cycle performance. For the following simulation calculation, the points 1, 3, 6 and 7R are assumed to be at saturated states shown in Fig. 5, which are corresponding to Fig. 3 and the points 1 0 , 2 0 , 4 0 , 8 0 are states in the ejectors. Here the outlet temperature difference for subcooler is given as t3R t7R = 5 °C, thus mechanical subcooling degree is DtC = t3 t3R = tk t7R 5 °C. Isentropic efficiencies of the ejectors are assumed to be gn = 0.85, gd = 0.85, gm = 0.95. Considering the important function of the circulating pump in the new system, pump efficiency has also been taken into account in the simulation by assuming isentropic efficiency gp = 0.75. Usually, evaporating temperature and condensing temperature depend on refrigeration request and cooling fluid temperature, but generating temperature depends on the temperature of heat resource. The former two temperatures can only vary in a limited range but the latter one can change more widely. Therefore, in the following analysis, we lay emphasis on the variation of the performance of the new cycle with generator temperature and mechanical subcooling degree, and on the comparison of the performances of the NERS with CERS. These systems consume both low-grade heat energy and high-grade electric power, thus exergy concept is used in the following analysis when
Fig. 5. P–h chart of the new ejector refrigeration cycle.
Obviously, mechanical subcooling is realized through increasing the power input of circulating pump. For illustrating the effectiveness of mechanical subcooling, the comparison of cooling capacity increment and pump power increment is made by simulation calculation. Here the simulation conditions are given as: condensing temperature is tk = 35 °C, evaporating temperature is to = 5 °C, generating temperature is tg = 100 °C. The following results are obtained when the mass flow rate of refrigerant flowing through evaporator is constant. Fig. 6 shows the variation of DQe/DW with mechanical subcooling degree DtC. Where cooling capacity increment is DQe ¼ m_ e ðh6 h3R Þ m_ e ðh6 h3 Þ ¼ m_ e ðh3 h3R Þ caused by mechanical subcooling, and pump power increment is DW ¼ m_ 9 ðh4 h3 Þ. As DtC rises, DQe/DW decrease. The values of DQe/ DW are more than one when DtC varies in the range of 5–20 °C. It can be seen that cooling capacity increment DQe is greater than pump power increment DW. This indicates that adding a mechanical-subcooling loop in a conventional ejector refrigeration system is feasible, and can improve the COP of ERS. But it should be noticed that the value of DQe/DW is to be less than one when DtC is close to 25 °C. It is obvious that adding a mechanical-subcooling in a CERS is infeasible when the value of DQe/DW is less than one. 4.2. Effect of generating temperature on the performance of NERS Simulation conditions are given as: condensing temperature is tk = 35 °C, evaporating temperature is to = 5 °C, mechanical subcooling degree is DtC = 15 °C.
Fig. 6. Variation of DQe/DW with DtC.
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The following results are obtained under the condition that the cooling capacity of NERS is 1000 W. Fig. 7 shows the variation of entrainment ratio l with generating temperature tg. As tg rises, both entrainment ratio l0 of ejector and entrainment ratio l1 of liquid–gas ejector increase. This is because that generating pressure rises with tg rising, and then the performance of ejector (or liquid–gas ejector ) is improved. Fig. 8 shows the variation of pump power W with tg. As tg rises, pump power W increases for the CERS, and it decreases firstly and then increases for the NERS. In addition, Fig. 8 shows that pump power W for the NERS is higher than that for the CERS. To realize mechanical subcooling, it is necessary that pump power W for the NERS is slightly higher than that for the CERS. Fig. 9 shows the variation of input exergy Ex with tg. As tg rises, for the NERS or the CERS, Ex decreases. NERS can save about 7%Ex. Fig. 10 shows the variation of COP with tg. As tg rises, COP increases. From Fig. 10, we know the new system can efficiently improve the COP. Generally, NERS’ COP is about 10% more than CERS’ when generating temperature is in the range of 80–120 °C.
Fig. 9. Variation of Ex with tg.
4.3. Effect of mechanical subcooling degree on the performance of NERS Simulation conditions are given as: condensing temperature tk = 35 °C, evaporating temperature t0 = 5 °C, generating temperature tg = 100 °C.
Fig. 10. Variation of COP with tg.
Fig. 7. Variation of entrainment ratio l with tg.
The following results are obtained under the condition that the cooling capacity of ERS is 1000 W. Because mechanical subcooling degree is DtC = t3 t3R = tk t7R 5 °C, t7R = tk 5 °C DtC = 30 °C DtC, and then t7R drops with DtC rising. Fig. 11 shows the variation of entrainment ratio l with mechanical subcooling degree DtC. As DtC rises, t7R drops, and the entrained fluid pressure of liquid–gas ejector drops. And then entrainment ratio l1 of liquid–gas ejector decreases. Because ejector has nothing to do with t7R, entrainment ratio l0 keeps invariable. Fig. 12 shows the variation of pump power W with DtC. As DtC rises, W of NERS increases. W of NERS is approximately equal to that of CERS when DtC = 5 °C. W of NERS increases remarkably when DtC varies in the range of 20–25 °C.
Fig. 8. Variation of W with tg.
Fig. 11. Variation of entrainment ratio l with DtC.
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5. Conclusion
Fig. 12. Variation of W with DtC.
A new mechanical subcooling ejector refrigeration cycle was proposed. From the foregoing analysis, we can see the new cycle is feasible and there is an obvious improvement in COP. NERS’ COP is about 10% more than CERS’ for R142b when condensing temperature tk = 35 °C, evaporating temperature t0 = 5 °C, mechanical subcooling degree DtC = 15 °C and generating temperature is in the range of 80–120 °C. And as tg rises further, COPof NERS tend to increase by much more. As mechanical subcooling degree DtC rises, COP of NERS increases firstly and then decreases for R142b. This also indicates there should exist an optimum DtC for different refrigerant and operating conditions. References
Fig. 13. Variation of Ex with DtC.
Fig. 13 shows the variation of input exergy Ex with DtC. As DtC rises, Ex of NERS decreases firstly and then increases. NERS can save about 7%Ex when DtC 15 °C. In addition, it can be noticed that Ex of NERS is more than Exof CERS when the value of DtC is greater than about 22 °C. This indicates that NERS for R142b is unfit to run under the condition that DtC is very large. From the above discussion in view point of Ex, we make a conclusion the performance of NERS for R142b is best when DtC 15 °C. Fig. 14 shows the variation of COP with DtC. As DtC rises, COPof NERS increases firstly and then decreases. COP of NERS is maximal and about 13% more than that of CERS when DtC 20 °C.
Fig. 14. Variation of COP with DtC.
[1] Chunnanond K, Aphornratana S. Ejector: applications in refrigeration technology. Renew Sust Energy Rev 2004;8:129–55. [2] Cizungu K, Mani A, Groll M. Performance comparison of vapour jet refrigeration system with environment friendly working fluids. Appl Therm Eng 2001;21:585–98. [3] Chang YJ, Chen YM. Enhancement of a steam-jet refrigerator using a novel application of the petal nozzle. Exp Therm Fluid Sci 2000;22: 203–11. [4] Eames IW, Aphornratana S, Haider H. A theoretical and experimental study of a small-scale steam jet refrigerator. Int J Refrig 1995;18(6):378–86. [5] Aphornratana S, Eames IW. A small capacity steam-ejector refrigerator: experimental investigation of a system using ejector with movable primary nozzle. Int J Refrig 1997;20(5):352–8. [6] Sun DW. Variable geometry ejectors and their applications in ejector refrigeration systems. Energy 1996;21(10):919–29. [7] Hernandez JI, Dorantes RJ, Best R, Estrada CA. The behaviour of a hybrid compressor and ejector refrigeration system with refrigerants 134a and 142b. Appl Therm Eng 2004;24:1765–83. [8] Sokolov M, Hershgal D. Enhanced ejector refrigeration cycles powered by low-grade heat, part I: system characterization. Int J Refrig 1990;13:351–6. [9] Sokolov M, Hershgal D. Enhanced ejector refrigeration cycles powered by low-grade heat, part II: design procedures. Int J Refrig 1990;13:357–63. [10] SokolovM,HershgalD.Enhancedejectorrefrigerationcyclespoweredby low-grade heat, part III: experimental results. Int J Refrig 1991;14:24–31. [11] Rogdakis ED, Alexis GK. Investigation of ejector design at optimum operating condition. Energy Convers Manag 2000;41:1841–9. [12] Khattab NM, Barakat MH. Modeling the design and performance characteristics of solar steam-jet cooling for comfort air conditioning. Solar Energy 2002;73(4):257–67. [13] Aly NH, Karameldin A, Shamloul MM. Modelling and simulation of steam jet ejectors. Desalination 1999;123:1–8. [14] Keenan H, Neumann EP, Lustwerk F. An investigation of ejector design by analysis and experiment. J Appl Mech Trans ASME 1950;72:299–309. [15] Huang BJ, Chang JM, Wang CP, Petrenko VA. A 1-D analysis of ejector performance. Int J Refrig 1999;22:354–64. [16] Ouzzane M, Aidoun Z. Model development and numerical procedure for detailed ejector analysis and design. Appl Therm Eng 2003;23: 2337–51. [17] NIST Standard Reference Database 23, NIST thermodynamics and transport properties of refrigerants and refrigerant mixtures, 1998, REFPROP, Version 6.01. [18] Da-wen Sun. Comparative study of the performance of an ejector refrigeration cycle operating with various refrigerants. Energy Convers Manag 1999;40:873–84.
Applying mechanical subcooling to ejector refrigeration cycle for improving the coefficient of performance Jianlin Yu *, Yunfeng Ren, Hua Chen, Yanzhong Li Institute of Refrigeration and Cryogenics Engineering, Xi’an Jiaotong University, Xi’an 710049, China Received 2 September 2005; accepted 8 October 2006 Available online 29 November 2006
Abstract This paper describes a new ejector refrigeration system with mechanical subcooling which uses an auxiliary liquid–gas ejector to enhance subcooling for the refrigerant from condenser. The new system can have larger subcooling degree when circulating pump consumes a little more power compared with conventional ejector refrigeration system. Based on the built mathematical model, the performance of the new ejector refrigeration system was discussed and compared with that of a conventional ejector refrigeration system for refrigerant R142b. Theoretical analyzing results show that the new system can efficiently improve the coefficient of performance (COP) of ejector refrigeration. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Mechanical subcooling; Ejector refrigeration; Ejector
1. Introduction Ejector refrigeration system (ERS) powered by lowgrade energy has been studied since the mid-1950s. Compared with other refrigeration systems, ERS has some special advantages such as the simplicity in construction, high reliability and low cost. However, the coefficient of performance for the conventional ERS is significantly lower than that for other refrigeration systems. This has restricted its wide applications. In recent years, people have tried to find wider application for ejector refrigeration systems in refrigeration and air conditioning field by directly utilizing low-grade thermal energy, such as solar energy and waste heat. Chunnanond and Aphornratana provides a literature review on ejectors and their applications in refrigeration [1]. The literature review showed that in many studies the pre-cooler and the pre-heater are installed to the conventional system, in order to improve the system efficiency. Cizungu, Groll conducted the research on performance comparison of vapor jet refrig*
Corresponding author. Tel.: +86 29 82668738; fax: +86 29 82668725. E-mail address: [email protected] (J. Yu).
0196-8904/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2006.10.009
eration system with environment friendly working fluids R123, R134a, R152a and R717 [2]. The results suggest that the system efficiency depends mainly on the ejector geometry and the compression ratio. Chang and Chen investigated a steam-jet refrigerator using petal nozzle and results indicated it might elevate the performance of an ejector [3]. Eames and Aphornratana conducted the research on a small-scale steam-jet refrigerator, in which an ejector with movable primary nozzle was used [4,5]. Sun’s studies showed that the use of variable-geometry ejector might achieve optimum performance under various operating condition [6]. A combined ejector-vapor compression refrigeration systems as a mechanically efficient way to increase the COP of ERS was also proposed and studied [7–10]. Despite of the higher COP in this combined cycle, additional compressor actually makes systems more complicated and higher cost due to compressor itself. To significantly improve the COP of ERS, a new integrated mechanical-subcooling ejector refrigeration system is proposed in this paper. In the new ERS (NERS) an auxiliary liquid–gas ejector is used to construct an additional subcooling loop in a conventional ejector refrigeration system (CERS). This subcooling loop can make the liquid
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J. Yu et al. / Energy Conversion and Management 48 (2007) 1193–1199
Nomenclature COP Ex h m_ P Pb Q s t T T0 u g l
coefficient of performance exergy (kW) enthalpy (kJ/kg) mass flow rate (kg/s) pressure (Pa) backpressure (Pa) heat load (kW) entropy ( kJ/Kg K) temperature (°C) thermodynamic temperature (K) ambient temperature (K) velocity (m/s) efficiency entrainment ratio (m_ sf =m_ pf )
Subscripts c condenser d diffuser section of ejector e evaporator g generator m mixing section of ejector mf mixed fluid n nozzle n1 inlet of nozzle n2 outlet of nozzle p pump pf primary fluid s isentropic process sf secondary fluid
Fig. 1 shows a basic CERS. It mainly consists of a generator, an evaporator, a condenser, expansion device, ejector and circulating pump. In this system, the vapor (primary fluid) from the generator at high pressure flows through the nozzle of the ejector and entrains the vapor (secondary fluid) from evaporator at low pressure. The primary fluid and secondary fluid then mix in the mixing section and recover a pressure in the diffuser. The combined fluid flows to condenser where it condenses. And then the
condensate is divided into two parts; one is pumped back to the generator, and the other flows through the expansion device and enters the evaporator, where it is evaporated to vapor. The vapor is finally entrained into the ejector again, thus finishing the ejector refrigeration cycle. Within one cycle, when the system obtains heat from heat source in the generator and work input from the pump, it produces the cooling effect in the evaporator and dissipates the heat to the environment through the condenser. The ejector is the key component in the ejector refrigeration cycle. The ejector generally consists of four parts: a nozzle section for a primary flow and a suction chamber for the secondary flow, a mixing section for the primary flow and secondary flow to mix, a throat section (constant area section) in which the mixed fluid normally undergoes a transverse shock and a pressure rise, and a diffuser section for the mixed fluid to recompress to the back pressure. Fig. 2 shows the schematic configuration of an ejector and the variation of pressure in the ejector. The COP of the CERS is highly dependent on the entrainment of ejector (the ratio of secondary flow rate
Fig. 1. A conventional ejector refrigeration system.
Fig. 2. An ejector and the variation of pressure in ejector.
refrigerant from the condenser to be further subcooled with increasing a little more circulating pump power. The new system can utilize solar energy or waste-heat more effectively and elevate the coefficient of performance (COP) of ejector refrigeration in some extent. A general description of the new system is presented and further analysis on its performance is conducted based on mathematical model. And the comparison between NERS and the CERS was also made. 2. General system description
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the one-dimensional constant pressure flow model used by most researchers studying ejector refrigeration systems. The basic principle of the model was introduced by Keenan et al. [14] based on gas dynamics, and developed by Huang et al. and Ouzzane et al. [15,16]. For simplicity, the theory is also applied to liquid–gas ejector although two–phase mixing flow through the liquid–gas ejector is more complicated. The following assumptions are made for the analysis:
Fig. 3. A new ejector refrigeration system.
to primary flow rate). The entrainment is relative to the primary flow inlet state, secondary flow inlet state and mixing outlet state of the ejector. The three primary, secondary and back pressures, are main factors which affect the entrainment. Some research results showed the entrainment increases with the decreasing backpressure when primary pressure and secondary pressure are constant [11–13]. These pressures are, respectively, the functions of condensing temperature, generating temperature and evaporating temperature. Usually these temperatures depend on the operating condition and are fixed within a range. The optimum operating condition could not make more improvement for COP. The NERS developed by author is shown in Fig. 3. The new integrated mechanical subcooling ejector refrigeration system consists of two simple cycles coupled to each other via a subcooler which functions as the evaporator in the subcooling cycle. The main cycle is similar to the CERS. In the subcooling cycle, the liquid (primary fluid) from pump at high pressure flows through the nozzle of the liquid–gas ejector and entrains the vapor (secondary fluid) from subcooler at low pressure. Then the combined fluid from liquid–gas ejector flows to condenser where it condenses. And then the condensate is divided into two parts; one is pumped back to liquid–gas ejector, and the other flows through the expansion device and enters the subcooler, where it is evaporated to vapor. The vapor is finally entrained into the liquid–gas ejector again, thus finishing the subcooling cycle. In the main cycle, the working process is the same as that introduced in the previous sections. The new system can have larger subcooling degree compared with conventional ejector refrigeration system. Details of new cycle performance analysis are discussed as follows. 3. Simulation mathematical model In the present system, the main ejector is a common vapor–vapor ejector and the auxiliary ejector is a type of liquid–vapor ejector. They have similar structure and working process. In the present study, the vapor–vapor ejector performance simulation is carried out based on
(1) The flow inside the ejectors is in steady state and onedimensional. (2) The compression and expansion process in ejectors are isentropic or friction losses are defined in terms of the isentropic efficiency in the nozzle, mixing section, diffuser and circulating pump. (3) Mixing in the mixing section of ejectors occurs at constant pressure and complying with the conversation of energy and momentum; the inner walls of ejectors are adiabatic, namely no heat losses. (4) A homogenous two-phase flow mixing is idealized for the liquid–gas ejector inside. Based on the above assumptions, the mass, momentum and energy equations are applied to sections for both the ejector and the jet pump and then the following equations are obtained. In the nozzle section, the energy conservation equation for the adiabatic and steady primary flow is given as: hpf;n2 þ u2pf;n2 =2 ¼ hpf;n1 þ u2pf;n1 =2
ð1Þ
Compared with the exit velocity of primary flow upf,n2, the inlet velocity of primary flow upf,n1 could be negligible. According to Eq. (1), the exit velocity of primary flow upf,n2 is expressed as: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi upf;n2 ¼ 2ðhpf;n1 hpf;n2 Þ ð2Þ The nozzle efficiency is given as: gn ¼
hpf;n1 hpf;n2 hpf;n1 hpf;n2;s
hence upf;n2 ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2gn ðhpf;n1 hpf;n2;s Þ
ð3Þ
ð4Þ
where hpf;n1 ¼ f ðT pf;n1 ; P pf;n1 Þ
ð5Þ
spf;n1 ¼ f ðT pf;n1 ; P pf;n1 Þ spf;n2;s ¼ spf;n1
ð6Þ ð7Þ
P pf;n2;s ¼ P m hpf;n2;s ¼ f ðspf;n2;s ; P pf;n2;s Þ
ð8Þ ð9Þ
The entrainment ratio of ejector is given as: l¼
m_ sf m_ pf
ð10Þ
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In the mixing section, the momentum conservation equation is m_ pf upf;n2 þ m_ sf usf;n2 ¼ ðm_ pf þ m_ sf Þumf;m;p
ð11Þ
hence umf;m;p
hmf;d ¼ hmf;m þ u2mf;m =2 upf;n2 þ l usf;n2 ¼ 1þl
ð12Þ
where usf;n2
ð13Þ
The mixing efficiency is given as: u2mf;m u2mf;m;p
ð15Þ
The average velocity of mixed flow umf,m is written according to Eqs. (14) and (15) as: pffiffiffiffiffiffi umf;m ¼ upf;n2 gm =ð1 þ lÞ ð16Þ The energy conservation equation for the mixing section is m_ pf
u2pf;n2 hpf;n2 þ 2
! þ m_ sf hsf;n2 þ
u2mf;m ¼ ðm_ pf þ m_ sf Þ hmf;m þ 2
u2sf;n2
ð17Þ
ð18Þ
where hsf ¼ f ðT sf ; P sf Þ
ð19Þ
smf;m ¼ f ðhmf;m ; P mf;m Þ
ð20Þ
In diffuser section, the mixed fluid converts the kinetic energy into pressure energy. Assuming the compression process is isentropic, then the energy equation for the diffuser section is ð21Þ
The actual energy equation for the diffuser section is
hmf;d;s hmf;m hmf;d hmf;m
ð26Þ ð27Þ
smf;d;s ¼ smf;m
ð28Þ
It is known the performance of ejectors are evaluated by their entrainment ratio l. Based on above Eqs. 4,16,25, it can be derived as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l ¼ gn gm gd ððhpf;n1 hpf;n2;s Þ=ðhmf;d;s hmf;m ÞÞ 1 ð29Þ When the inlet state parameters of primary fluid, secondary fluid and back pressure are given, the value of entrainment ratio l could be found using iteration calculation. For the whole cycle performance, the basic equations obtained from the conversation law for energy are written as follows:
ð30Þ
Qg ¼ m_ g ðh1 h4 Þ
ð31Þ
For condenser:
The enthalpy of mixed flow is written according to Eqs. (2,13,17) as:
gd ¼
hmf;d;s ¼ f ðsmf;d;s ; P mf;d;s Þ P mf;d;s ¼ P b
For generator:
!
1 2 ðu u2mf;d Þ ¼ hmf;d hmf;m 2 mf;m The diffuser efficiency is given as:
where
Qe ¼ m_ e ðh6 h5 Þ
2
1 2 ðu u2mf;d;s Þ ¼ hmf;d;s hmf;m 2 mf;m
ð25Þ
For evaporator:
!
hmf;m ¼ ðhpf;n1 þ lhsf Þ=ð1 þ lÞ u2mf;m =2
ð24Þ
In addition, according to Eq. (23), the actual exit enthalpy of the mixed fluid is also expressed as: hmf;d ¼ hmf;m þ ðhmf;d;s hmf;m Þ=gd
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 2ðhsf hsf;n2 Þ
Compared with the primary flow velocity upf,n2, the velocity of secondary flow usf,n2 is negligible. Then the Eq. (12) becomes upf;n2 umf;m;p ¼ ð14Þ 1þl
gm ¼
Compared with the velocity umf,m, the exit velocity of the mixed fluid umf,d is negligible, the actual exit enthalpy of the mixed fluid hmf,d is written according to energy Eq. (22) as:
ð22Þ
ð23Þ
Qc ¼ m_ c ðh2 h3 Þ
ð32Þ
For circulating pump: W ¼ m_ P ðh4 h3 Þ
ð33Þ
The system performance is evaluated by the coefficient of performance COP, which is the ratio of the cooling capacity to the gross energy input of the cycle. It is written as follows: COP ¼ Qe =ðQg þ W Þ
ð34Þ
4. Simulation results and discussion The refrigerants thermodynamics properties are calculated by using NIST database and subroutines [17]. And the calculating program is written with Fortran. Language. Some selected refrigerants, such as R134a, R152a and R142b are applied to the above computation models for simulating the ejector and CERS cycle performance, and the simulation results are in very good agreement with the research results from Sun’s study [18] under the same operating conditions, shown in Fig. 4.
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considering the grade of input energy. The input exergy is described as follows: Ex ¼ ExQg þ W
ð35Þ
where ExQg ¼ ð1 T 0 =T g Þ Qg ;
ðT 0 ¼ 298:15 KÞ
ð36Þ
4.1. The evaluation of mechanical subcooling
Fig. 4. Comparison of the present simulation results with the Sun’s research results. tg = 90 °C, tk = 35 °C, to = 5 °C
In present study, R142b is singled out as working refrigerant for simulating the NERS cycle performance. For the following simulation calculation, the points 1, 3, 6 and 7R are assumed to be at saturated states shown in Fig. 5, which are corresponding to Fig. 3 and the points 1 0 , 2 0 , 4 0 , 8 0 are states in the ejectors. Here the outlet temperature difference for subcooler is given as t3R t7R = 5 °C, thus mechanical subcooling degree is DtC = t3 t3R = tk t7R 5 °C. Isentropic efficiencies of the ejectors are assumed to be gn = 0.85, gd = 0.85, gm = 0.95. Considering the important function of the circulating pump in the new system, pump efficiency has also been taken into account in the simulation by assuming isentropic efficiency gp = 0.75. Usually, evaporating temperature and condensing temperature depend on refrigeration request and cooling fluid temperature, but generating temperature depends on the temperature of heat resource. The former two temperatures can only vary in a limited range but the latter one can change more widely. Therefore, in the following analysis, we lay emphasis on the variation of the performance of the new cycle with generator temperature and mechanical subcooling degree, and on the comparison of the performances of the NERS with CERS. These systems consume both low-grade heat energy and high-grade electric power, thus exergy concept is used in the following analysis when
Fig. 5. P–h chart of the new ejector refrigeration cycle.
Obviously, mechanical subcooling is realized through increasing the power input of circulating pump. For illustrating the effectiveness of mechanical subcooling, the comparison of cooling capacity increment and pump power increment is made by simulation calculation. Here the simulation conditions are given as: condensing temperature is tk = 35 °C, evaporating temperature is to = 5 °C, generating temperature is tg = 100 °C. The following results are obtained when the mass flow rate of refrigerant flowing through evaporator is constant. Fig. 6 shows the variation of DQe/DW with mechanical subcooling degree DtC. Where cooling capacity increment is DQe ¼ m_ e ðh6 h3R Þ m_ e ðh6 h3 Þ ¼ m_ e ðh3 h3R Þ caused by mechanical subcooling, and pump power increment is DW ¼ m_ 9 ðh4 h3 Þ. As DtC rises, DQe/DW decrease. The values of DQe/ DW are more than one when DtC varies in the range of 5–20 °C. It can be seen that cooling capacity increment DQe is greater than pump power increment DW. This indicates that adding a mechanical-subcooling loop in a conventional ejector refrigeration system is feasible, and can improve the COP of ERS. But it should be noticed that the value of DQe/DW is to be less than one when DtC is close to 25 °C. It is obvious that adding a mechanical-subcooling in a CERS is infeasible when the value of DQe/DW is less than one. 4.2. Effect of generating temperature on the performance of NERS Simulation conditions are given as: condensing temperature is tk = 35 °C, evaporating temperature is to = 5 °C, mechanical subcooling degree is DtC = 15 °C.
Fig. 6. Variation of DQe/DW with DtC.
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The following results are obtained under the condition that the cooling capacity of NERS is 1000 W. Fig. 7 shows the variation of entrainment ratio l with generating temperature tg. As tg rises, both entrainment ratio l0 of ejector and entrainment ratio l1 of liquid–gas ejector increase. This is because that generating pressure rises with tg rising, and then the performance of ejector (or liquid–gas ejector ) is improved. Fig. 8 shows the variation of pump power W with tg. As tg rises, pump power W increases for the CERS, and it decreases firstly and then increases for the NERS. In addition, Fig. 8 shows that pump power W for the NERS is higher than that for the CERS. To realize mechanical subcooling, it is necessary that pump power W for the NERS is slightly higher than that for the CERS. Fig. 9 shows the variation of input exergy Ex with tg. As tg rises, for the NERS or the CERS, Ex decreases. NERS can save about 7%Ex. Fig. 10 shows the variation of COP with tg. As tg rises, COP increases. From Fig. 10, we know the new system can efficiently improve the COP. Generally, NERS’ COP is about 10% more than CERS’ when generating temperature is in the range of 80–120 °C.
Fig. 9. Variation of Ex with tg.
4.3. Effect of mechanical subcooling degree on the performance of NERS Simulation conditions are given as: condensing temperature tk = 35 °C, evaporating temperature t0 = 5 °C, generating temperature tg = 100 °C.
Fig. 10. Variation of COP with tg.
Fig. 7. Variation of entrainment ratio l with tg.
The following results are obtained under the condition that the cooling capacity of ERS is 1000 W. Because mechanical subcooling degree is DtC = t3 t3R = tk t7R 5 °C, t7R = tk 5 °C DtC = 30 °C DtC, and then t7R drops with DtC rising. Fig. 11 shows the variation of entrainment ratio l with mechanical subcooling degree DtC. As DtC rises, t7R drops, and the entrained fluid pressure of liquid–gas ejector drops. And then entrainment ratio l1 of liquid–gas ejector decreases. Because ejector has nothing to do with t7R, entrainment ratio l0 keeps invariable. Fig. 12 shows the variation of pump power W with DtC. As DtC rises, W of NERS increases. W of NERS is approximately equal to that of CERS when DtC = 5 °C. W of NERS increases remarkably when DtC varies in the range of 20–25 °C.
Fig. 8. Variation of W with tg.
Fig. 11. Variation of entrainment ratio l with DtC.
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5. Conclusion
Fig. 12. Variation of W with DtC.
A new mechanical subcooling ejector refrigeration cycle was proposed. From the foregoing analysis, we can see the new cycle is feasible and there is an obvious improvement in COP. NERS’ COP is about 10% more than CERS’ for R142b when condensing temperature tk = 35 °C, evaporating temperature t0 = 5 °C, mechanical subcooling degree DtC = 15 °C and generating temperature is in the range of 80–120 °C. And as tg rises further, COPof NERS tend to increase by much more. As mechanical subcooling degree DtC rises, COP of NERS increases firstly and then decreases for R142b. This also indicates there should exist an optimum DtC for different refrigerant and operating conditions. References
Fig. 13. Variation of Ex with DtC.
Fig. 13 shows the variation of input exergy Ex with DtC. As DtC rises, Ex of NERS decreases firstly and then increases. NERS can save about 7%Ex when DtC 15 °C. In addition, it can be noticed that Ex of NERS is more than Exof CERS when the value of DtC is greater than about 22 °C. This indicates that NERS for R142b is unfit to run under the condition that DtC is very large. From the above discussion in view point of Ex, we make a conclusion the performance of NERS for R142b is best when DtC 15 °C. Fig. 14 shows the variation of COP with DtC. As DtC rises, COPof NERS increases firstly and then decreases. COP of NERS is maximal and about 13% more than that of CERS when DtC 20 °C.
Fig. 14. Variation of COP with DtC.
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