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Performance analysis of a combined vapor compression cycle and ejector cycle for refrigeration cogeneration
Accepted Manuscript Title: Performance analysis of a combined vapor compression cycle and ejector cycle for refrigeration cogeneration Author: K. Megdouli, B.M. Tashtoush, E. Nahdi, M. Elakhdar, A. Mhimid, L. Kairouani PII: DOI: Reference:
S0140-7007(16)30415-7 http://dx.doi.org/doi: 10.1016/j.ijrefrig.2016.12.003 JIJR 3495
To appear in:
International Journal of Refrigeration
Received date: Revised date: Accepted date:
27-7-2016 5-12-2016 7-12-2016
Please cite this article as: K. Megdouli, B.M. Tashtoush, E. Nahdi, M. Elakhdar, A. Mhimid, L. Kairouani, Performance analysis of a combined vapor compression cycle and ejector cycle for refrigeration cogeneration, International Journal of Refrigeration (2016), http://dx.doi.org/doi: 10.1016/j.ijrefrig.2016.12.003. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Performance analysis of a combined vapor compression cycle and ejector cycle for refrigeration cogeneration K. Megdouli1, 3,*, B. M. Tashtoush2, E. Nahdi1, M. Elakhdar1, A. Mhimid3 and L. Kairouani1 1
Unité de Recherche Energétique et Environnent, Ecole National d’ingénieur de Tunis 37 Le Belvédère Tunis, Tunisie. 2
Mechanical Engineering Department, Jordan University of Science and Technology, Irbid, Jordan
3
Laboratoire d’Études des Systèmes Thermiques et Énergétiques Ecole National d’ingénieur de Monastir Avenue Ibn El Jazzar, 5019 Monastir, Tunisie
Highlights:
Waste heat utilization can reduce emissions of carbon dioxide.
A hybrid vapor compression refrigeration system (HVCR) with CO2 is proposed.
The effects of some thermodynamic parameters on the cycle performance are evaluated.
The work shows that the HVCR system is quite promising.
ABSTRACT: A hybrid vapor compression refrigeration (HVCR) system, which combines a vapor compression refrigeration (VCR) system and an ejector refrigeration (ER) system, was developed. The waste heat energy from the gas cooler in the VCR system is applied as driven source towards ER system. Thermodynamic investigations on the performance of the HVCR system, using CO2 as a refrigerant, are performed with energetic and exergetic methods, and the comparative analyses with the VCR system are conducted. Comprehensive effects of key operating parameters on the system performance are also studied. The results indicate that for the same cooling * Corresponding author. Tel: +216 22507488 E-mail address: [email protected] (K. Megdouli)
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capacity, the coefficient of performance (COP) of the HVCR system shows 25 % higher COP and the total mechanical power consumption is reduced by 20 % than that of conventional VCR system, respectively. The performance characteristics of the proposed cycle show its application potential in cooling and air-conditioning. Keywords: Thermodynamic analysis; Ejector; energy; Exergy; waste heat
Nomenclature COP
Coefficient of performance
Exdes
Exergy destruction rate (kW)
h
Specific enthalpy (kJkg-1)
m
Mass flow rate (kgs-1)
P
Pressure (MPa)
Q
Heat load rate (kW)
s
Specific entropy (kJ(kg.K)-1)
SL
Second law efficiency (%)
T
Temperature (°C or K)
T0
Environmental temperature (K)
Tr
The temperature of secondary fluid in the evaporator (K)
U
Entrainment ratio
W
Mechanical power (kW)
Subscripts 0
Reference environment
1, 2, 3 …
Cycle location
bo
Booster
c
Compressor
cd
Condenser
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3
ej
Ejector
e
Evaporator
exp
Expansion valve
gc
Gas cooler
is
Isentropic process
pu
Pump
sys
System
tot
Total
'
Primary fluid (or motive fluid)
' '
Secondary fluid (or entrained aspirated)
Greek symbol Φ
Area ratio between mixing tube and primary nozzle throat (d3/dt)
ξ
Driving pressure ratio (P7/P9)
r
The pressure lift ratio (P9/P6)
η
Efficiency (%)
Introduction: Due to the environmental concerns about ozone depletion and global warming, CFC, HCHC and HFC refrigerants are now being regulated. Adopting appropriate natural refrigerant such as CO2, is one of the advanced methods of enhancing system performance and reducing ozone depletion and global warming. Carbon dioxide as a refrigerant has attracted the interest of researchers because of its unique thermal characteristics, such as low viscosity, excellent heat transfer coefficient, no toxicity and no inflammability. At the same time, CO2 has zero ODP (Ozone depletion potential), negligible GWP (Global warming potential) and very low cost. However, in common refrigeration conditions, the refrigeration system using CO2 needs to be operated with a transcritical cycle mode because of the lower critical temperature of CO2
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which results in a lower first and second law efficiency. Large amount of efforts were devoted to enhance the performance of these cycles. For thermodynamic reasons, the working fluid exiting the compressor (Usually at 100- 200 °C for CO2) should be cooled down to about 35- 55 °C in the gas cooler providing a large amount of energy and exergy, which will be rejected to the environment. This is an ideal thermal energy source to be utilized to increase the refrigeration system performance. In order to improve the system performance of the CO2 VCR system and obtain dualtemperature refrigeration function, an ejector cooling cycle driven by low grade heat energy is considered to be combined with the transcritical refrigeration cycle in the present paper. It is hoped that the obtained results could provide some guidelines for refrigeration system designers. Therefore, as well known, an ejector cooling system, that utilizes natural or renewable thermal energy, offers several advantages. The distinctive characteristic of ejector refrigeration system is its ability to utilize low grade heat energy which can be easily acquired from automobile waste gas, solar radiation, industrial process and geothermal energy. Moreover, because of the application of ejector, the system possesses many advantages, such as passive device (no moving components), durable life span, and little maintenance cost and high reliable. Several research work on ejector cooling technology driven by low-grade energy was carried out extensively in the past decades. A great effort was devoted to theoretical and experimental evaluation of the ejector cycle performance (Chen et al., 2011, 2014, 2015; Huang et al., 2001, 2014; Manjili and Yavari, 2012; Pridasawas and Lundqvist, 2006; Shuxue and Guoyuan, 2011; Megdouli, et al., 2015;Tashtoush, et al., 2015; Wang, et al., 2016; Yan, et al., 2016). The technology is becoming mature for commercialization. The main restriction of prevalence of ejector refrigeration system is its relative low efficiency compared to vapor compression system. Their typically low COP of around 0.5 (Huang and Chang, 1999a; Huang et al., 1999b) can be improved substantially when combined with other systems such as absorption or vapor compression. For example, (Sun, 1998) studied a combined ejector compression refrigeration system in which an inner heat exchanger was used to combine the ejector cycle and the vapor compression cycle. (Huang, et al., 2001) proposed a combined cycle refrigeration system (CCRS) that combines a conventional refrigeration and air conditioning by using a mechanical compressor and an ejector cooling cycle. The system performance was significantly increased and the improvement in the coefficient of performance (COP) can be as high as 18.4% for evaporating temperature at −5 °C. (Hernandez, et al., 2004) developed a theoretical analysis on the thermodynamics of a
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hybrid ejector compression refrigeration system. The effects of the working fluid and operation conditions on the hybrid system performance were analyzed. (Zhu and Jiang, 2012) studied a combined ejector compression refrigeration system. The results show that the COP is improved by 9.1% for R22 system. By considering the published literature, there be no doubt that use of combined ejector compression refrigeration (CECR) systems would exhibit a reasonable performance. Although, CECR systems have been studied from different angles, but a use of an ejector refrigeration (ER) system as a way to improve the performance of CO 2 transcritical refrigeration system have not yet been performed and needs to be considered. In order to do so, a hybrid vapor compression refrigeration (HVCR) system with carbon dioxide refrigerant with dual cooling temperature that combines a basic vapor compression refrigeration (VCR) system with an ejector refrigeration (ER) system is described in this paper. The ER system is driven thermally by the gas cooler waste heat from the CO2 transcritical system. The HVCR system can be used as a support system to favour the implantation of transcritical system and reduce the consumption of limited fuel supplies. In order to deeply evaluate thermodynamic performances of the proposed cycle, energetic and exergetic methods are used in this paper. A parametric study of a combined ejector compression refrigeration system have been performed. The results are compared with a basic refrigeration system.
1. Cycle description: Figure 1 shows the basic VCR system and its p-h diagram. The layout and pressure-enthalpy diagrams of the HVCR system are shown in Figure 2. The proposed system consists of two cycles. It includes the basic refrigeration cycle and a heat driven ejector cooling cycle. The cycle working principle is described as follows: the superheated gas discharge by the compressor (state 2) enters the gas cooler and leaves at (state 3). In gas cooler, the compressed gas rejects heat to the fluid coming from the condenser. This heat is used to drive the ER system. The gas from state 3 enters a throttling device (Exp A), where the pressure and temperature are reduced and enters evaporator (A) at state 4, where it evaporates and absorbs the heat in evaporator (A). After this, the working fluid enters the compressor as saturated vapor (state 1), and the cycle continues. The ER system is driven thermally by waste heat of the VCR system. The heat transfer between these two cycles is linked through the gas cooler. The high temperature and pressure refrigerant vapor (the primary flow, state 7) enters the ejector through a convergent-divergent nozzle, which accelerates the primary flow
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from subsonic to supersonic velocity and creates a low pressure region at the nozzle exit. This entrains the low temperature, low-pressure vapor (the secondary flow, state 5) from the evaporator (B) outlet. The secondary flow from the evaporator (B) is first compressed to a relatively high pressure in the booster and then enters the ejector at (state 6). The primary and secondary flows mix in the ejector and then the mixture is discharged to condenser (state 8). After the condensation, the refrigerant at state (9) is divided into two streams; the first one is directed through a pump to gas cooler at state (10) and the second one is directed through an expansion valve (B) (state 11) and into the evaporator (B). The liquid vapor refrigerant mixture evaporates in the evaporator (B) and the ER system thus provides an additional cooling capacity.
2. System modeling: In order to analyze the HVCR system, the energetic and the exergetic models based on the first and the second law of thermodynamics are established.
2.1. Ejector model : Ejector is the critical component in the ejector enhanced refrigeration cycles and its performance is closely related to the system performance and energy efficiency. Therefore, establishing a valid simulation model plays a significant role in the prediction and analysis of the operating characteristics of the ejector enhanced system. A typical ejector construction comprises four distinct parts: a convergent– divergent nozzle, a suction chamber attached to a constant area duct and a diffuser, Figure 3. The typical processes inside an ejector begin with high temperature and pressure stream from the generator entering the ejector through the convergent–divergent nozzle. This stream is accelerated and expanded to a supersonic speed at the nozzle exit where it creates an aerodynamic duct to entrain the low pressure and low temperature secondary stream into the mixing chamber. The secondary stream is accelerated to a sonic velocity and mixes with the primary stream in the constant area duct. The region of supersonic flow is terminated by a normal shock wave further down the duct or in the diffuser. Across the shock, pressure increases but Mach number (velocity) reduces to a subsonic value. The mixed stream then enters the subsonic diffuser where it undergoes a re-compression process to reach the back-pressure (gas cooler pressure) at near zero velocity. In the past decades, various ejector models have been developed for the theoretical and experimental analyses on the ejector cycles. From the open
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literature on the thermodynamic modeling for ejector cycle, it could be found that ejectors are classified into two types depending on the position of the nozzle; constant-pressure mixing ejector and constant-area mixing ejector. In the constant-pressure mixing ejector the exit plane of the nozzle is located within the suction zone upstream of the constant area section, the static pressure throughout the mixing zone is assumed constant. In the constant- area mixing ejector, the primary nozzle exit is located in the constant area section, where the mixing of the primary and secondary flows occurs and the pressures of the two streams are not equal (He, et al., 2009). In order to simplify the ejector modeling process, the constant-area mixing model is adopted in the present work. The ejector operates in three different modes, the critical, subcritical and back flow modes. Critical modes are more favorable in terms of high entrainment ratio and enhanced ejector performance. For this reason, we will analyze the ejector in critical mode. The previous published paper (Kairouani, et al., 2009) contains a useful appendix, which explains additional steps in the model derivation. The model was validated in our previously published data (Megdouli, et al., 2016).
2.2. Energetic model : The energetic analysis as a fundamental method is widely used to analyze the operating performance of thermodynamic cycles. In present paper, the energetic model is developed to assess the energy utilization on the basis of the first law of thermodynamics. For simplicity, some assumptions are made as follows: 1- The system is simulated under steady state conditions. 2- The refrigerant leaving evaporators are assumed to be at saturated vapor state. 3- The enthalpy before and after the expansion valve remains constant. 4- The compression processes in the liquid pump, the booster and the compressor are adiabatic and non-isentropic. 5- The total cooling capacity Q of the system, is kept to be 100 kW for both HVCR and VCR system. 6- A temperature difference of 5°C is assumed in the gas cooler (∆T = T2-T7) (Wang, et al., 2010). 7- Ambient condition is specified as 1.01 bar and 25 °C. Based on these assumptions, the governing equations are based on conservation of energy and mass for each component in HVCR system. The simulation code written by FORTRAN is developed to investigate the effect of different operating parameters on the HVCR system
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performance, where the thermodynamic properties of CO2 is taken from the NIST database and subroutines (Lemmon, et al., 2010) For the compressor, the input power can be calculated as: W c m 1 ( h 2 , s h1 ) / is
(1) Where is represents the isentropic efficiency of the compressor (Yari and Mahmoudi, 2011): is 0 .9 3 4 3 0 .0 4 4 7 8(
P2
)
P1
(2) The input power of the liquid pump is calculated by isentropic efficiency method (Yu and Du, 2010; Dai, et al., 2009; Ben, et al., 2014), expressed as, W pu m ( h10 , s h9 ) / pu
(3) Where p u represents the isentropic efficiency of the liquid pump and is assumed to be constant. For a real non-isentropic efficiency of the compression process the input power to the booster can be expressed as (Zhu and Jiang, 2012): W bo m ( h 6 , s h5 ) / bo
(4) Where bo represents the isentropic efficiency of booster and is assumed to be constant. The total power input the system can be given as: W W c W pu W bo
(5) For the evaporator A in the VCR system, the cooling capacity is: Q e _ A m 1 ( h1 h 4 )
(6) For the evaporator B in the ER system, the cooling capacity is: Q e _B m ( h5 h11 )
(7) The total cooling capacity of the HVCR system is:
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(8) The heat flow rate at the gas cooler is: Q g c m 1 ( h 2 h3 )
(9) Using the ideal heat exchange condition and from an energy balance principle, it follows that (Tan, et al., 2015): m1 ( h2 h3 ) m ( h7 h10 )
(10) The heat flow rate at the condenser is: Q cd m tot ( h9 h8 )
(11) Where:
m tot m m (12) For expansion valves:
h 4 h3 (13)
h11 h9 (14) For ejector:
m tot h8 m h6 m h7 (15) Entrainment ratio also is an important parameter that describes the ER system performance. This parameter is related to the cooling capacity and directly depends on the refrigeration type and ejector geometry. The entrainment ratio is the ratio between the mass flow rate of the secondary flow and the mass flow rate of the primary flow, given as: U
m m
(16)
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Where m and m represent the mass flow rates of the secondary and the primary flow, respectively. The coefficient of performance of the HVCR system, COP is: COP
Q sys W
(17) For comparison, the coefficient of performance of the VCR system, C OPbasic is: C O Pbasic
Qe _ A Wc
(18) The ER system performance can be evaluated based on the coefficient of performance, C O Pej , C O Pej
Q e _B W pu W bo Q gc
(19) Another criterion is the COP improvement C O Pim p which could be used to compare the performance of HVCR system with this of the conventional VCR system, is given as follows: C O Pim p (% ) (
C O P C O Pb a sic
) *100
C O Pb a sic
(20)
2.3.Exergetic model : Exergy is defined as the maximum work potential of a material or of a form of energy in relation to its environment. Exergy based analyses help determine the entropy generation and quantify the inefficiencies of a given energy conversion process and the reduction of value of the energy utilized in the system working process. In this section, the exergetic model is built to assess the energy utilization of the HVCR system. According to the definition of exergy and exergy balance at steady operation, the exergy at any point and exergy destruction in a component can be expressed as follows (Joybari, et al., 2013): Ex m ( h h0 ) T0 ( s s 0 )
(21)
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E x des E x in E x out
T0 in
Q (1 T
T0 Q (1 T out
W
in
W out
(22) Where, T0 is a reference temperature maintained at 25 °C and the reference pressure is set at 0.101 MPa throughout this study to obtained the reference enthalpy h0 and entropy s 0 . In eq. (22), the first term represents the exergy destruction resulting from the fluid flow, the second term represents the exergy destructions caused by the heat transfers, and the last term represents the exergy destruction by the mechanical and/or electrical work transfer through the component. Based on the definition of exergy and exergy destruction mentioned above, the exergy destruction in each component of HVCR system can be derived as follows: For the compressor, the exergy destruction rate can be expressed as:
Ex c T0 m1 (s 2 s1 ) (23) For gas cooler the exergy destruction rate can be calculated by: E x gc T 0 ( m 1 (s 3 s 2 ) m (s 7 s10 ))
(24) For condenser the exergy destruction rate can be calculated by: Ex cd m tot (h 8 h9 T0 (s 8 s 9 ))
(25) For ejectors exergy destruction rate can be expressed as: E x ej T0 ( m tot s 8 m s 7 m s 6 )
(26) For expansion valve A: E x exp_A T0 m 1 (s 4 s 3 )
(27) For expansion valve B: E x exp_B T0 m (s 11 s 9 )
(28) For evaporator A:
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E x e_A T 0 m 1 ((s 1 s 4 )
(h 4 h1 )
)
Tr 1
(29) For evaporator B: E x e_B T 0 m ((s 5 s11 )
(h 11 h5 )
)
Tr 2
(30) For pump: E x pu T0 m (s 10 s 9 )
(31) For booster:
Ex bo T0 m (s 6 s 5 ) (32) The total exergy destruction rate of the HVCR system is the sum of the exergy destruction rate in each component: E x des E x c E x pu E x bo E x e _ A E x e _B E x gc E x cd E x ej E x exp_ A E x exp_B
(33) The parameter used to measure the performance of the cycle based on the second law thermodynamic, is the second-law efficiency. The second-law efficiency of the HVCR system is written as follows: Qe _ A ( SL
T0 Tr 1
1) Q e _B (
T0
1)
Tr 2
W
(34) Where, T0 is a reference temperature maintained at 25 °C, T r 1 Te _ A Te and T r 2 Te _B Te . It can be expressed as follows for the conventional VCR system: Qe _ A ( SLbasic
T0
1)
Tr 1
Wc
(35) The system exergy efficiency improvement of the HVCR system over the conventional VCR system is evaluated by:
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S L im p (% ) (
S L S L b a sic
) *100
S L b a sic
(36)
3. RESULTS AND DISCUSSION : Results are obtained from the developed model. Initially, for specified temperatures ( T e _A = 20 °C, T e _ B = 0°C, T gc = 45°C) the effect of varying gas cooler pressure on the performance of a CO2 HVCR system is reported. Optimum values of performance parameters (1st and 2nd law efficiency) at different gas cooler pressure for the HVCR system are compared with those of the VCR baseline system. During the entire analysis the cooling capacity of the HVCR system is assumed to be the same as the basic VCR system and both are assumed to be 100 kW.
3.1. Energy analysis: Table 1 summarizes the basic assumptions and input parameter values in the simulation of two considered cycles. Tables 2 and 3 show the thermodynamic properties of each state point under the standard operating condition of simulation for VCR and HVCR system, respectively. It is given in terms of pressure, temperature, enthalpy, entropy, flow rate and exergy destruction rate under the standard operating condition: the gas cooler exit temperature is 45°C, the evaporating temperatures T e _ A and T e _B are -20 °C and 0 °C, respectively.
The highest COP value
corresponds to a gas cooler pressure of 11.4 MPa as shown in Figure 4, indicating that this is an optimum value for the gas cooler pressure. It should be mentioned that the mass flow rate of each state points is obtained by applying the principle of mass and energy conversation.
3.1.1. Effects of gas cooler outlet pressure : The effect of varying gas cooler pressure Pgc on the COP and the total mechanical power consumption for the HVCR and the VCR systems are shown in Figure 4. According to references (Liao, et al., 2000; Kauf, 1999; Joneydi, et al., 2016), there exists an optimal value for gas cooler pressure to reach the maximum COP in a carbon dioxide refrigeration cycle. In this respect, it can be observed in Figure. 4, that the corresponding optimum gas cooler pressure is 11.4 MPa that maximizes the COP of both systems at the given operating condition.
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As can be seen (Figure 4), the total mechanical work consumption W, of both cycles drops first and then increases. For this reason, the system COP rises first and then decreases as previously noted. Since the cooling capacity is the same for the two refrigeration systems, the performance improvement appears in terms of lower mechanical power consumption. The main reason for this is that the large temperature in the gas cooler is utilized to drive an ejector cooling cycle. In this case, the HVCR system exhibits a reasonable value of COP. In order to illustrate the energy saving potential and advantages of excellent cooling performances, the energetic performance comparisons between HVCR and VCR systems using CO2 are carried out at the specific operating condition and for the same cooling capacity. It can be observed that the HVCR system has more advantages than the VCR system in terms of system COP. Under the given operating condition and at the optimum gas cooler pressure, the HVCR system shows 25 % higher COP and the total mechanical power consumption W sys is reduced by 20 %. Therefore, it could be concluded that the use of the waste heat from the gas cooler in the VCR system to drive the ejector cooling system could significantly improve the system performance. This indicates that applying HVCR system to obtain better performance with lower energy consumption is feasible. The variation of the entrainment ratio U and the ejector cycle COP with the gas cooler pressure Pgc are presented in Figure 5. It is clear from Figure 5 that the entrainment ratio increases with the gas cooler pressure Pgc and vary in the range of 0.43-0.57. It is also demonstrated that the C O Pej is low in compare to the VCR system COP, the ejector cycle improve the COP because the heat energy utilized in the ejector cycle is waste heat from the gas cooler.
3.1.2. Effects of gas cooler outlet temperature on cycle performance: The following results were obtained by varying the gas cooler temperature from 40°C to 50°C. Figure 6 shows the effect of Tgc on the HVCR system COP and the total mechanical power consumption. As shown in Figure 6, increasing gas cooler temperature results in an increase of the optimum gas cooler pressure. The optimum gas cooler pressure varies from 9.8 to 12 MPa when the gas cooler temperature varies from 40 to 50°C. The COPsys of the HVCR system decreases as the gas cooler temperature increases because the enthalpy of the CO 2 at state 3 increases as the gas cooler temperature increases, which leads to an increase in the total mechanical power consumption, W , as shown in Figure 6. Increasing gas cooler outlet temperature will significantly decrease the system performance.
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3.1.3. Effects of evaporator outlet temperature on cycle performance: Figure 7 shows the effect of the evaporator outlet temperature on the COP and the mechanical work consumption, W. The COP increases as the evaporating temperature Te_A increases. The maximum COP increases with the evaporating temperature Te_A when the evaporating temperature Te_A ranges from -25°C to -15°C, the COP is higher at the optimum gas cooler pressure. As it can be seen from Figure 7, the mechanical work consumption, W, decreases as the evaporating temperature Te_A increases. This is because of the decrease in difference between the gas cooler and evaporator temperatures. It is observed that for each evaporating temperature an optimum gas cooler pressure exists for which W is a minimum.
The variations of the ejector system COP and the entrainment ratio with T e_A are presented in Figure 8. It can be seen that COPej and the entrainment ratio U increase with increasing Te_A. Refereeing to Figure 8, as the evaporating temperature increases, the entrainment ratio is raised. This is justified by the fact that the compressor exit temperature increase results in more vapors generated to drive the ejector refrigeration system. The increase in the entrainment ratio will increase the value of COPej as depicted in Figure 8.
3.2. Exergy analysis: 3.2.1. Effects of gas cooler outlet pressure : The results are obtained with the operating condition kept at T e _A = -20 °C, T e _ B = 0°C, T gc = 45°C and Φ=7. Figure 9 compares the total exergy destruction rate and the second law efficiency of the VCR and the HVCR system in which both of them depict the same trend with minimum amount of exergy destruction rate according to the optimum Pgc which is approximately 11.4 MPa. However, the EXdest of the HVCR system is 22 % lower in compare to the VCR system, as can be seen from Table 4. Table 4 outlines the exergy destruction rates in different components of the systems at T e _A = 20°C, T e _ B = 0°C, T gc = 45°C and Φ=7. As indicated in Table 4, the main irreversibility of VCR system occurring in the compressor, gas cooler and expansion valve are lower for HVCR system. Figures 9 shows that the maximum second law efficiency of 15.6 % and 14.9 % for HVCR and VCR system are obtained. The optimal gas cooler pressure of approximately 11.4 MPa is
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attained. It can be deduced that the HVCR system represents approximately 4.7 % increase as compared to the conventional one. The maximization of second law efficiency with the gas cooler pressure can be justified if we note that an increase in the gas cooler pressure causes a reduction in the total exergy destruction rate when the Pgc is inferior to 11.4 MPa as shown in Figure 9. Further, the integration of the ER system with the conventional VCR system leads to an improvement in total system exergy destruction rate.
3.2.2. Effects of condenser outlet temperature on cycle performance: The effect of gas cooler temperature on second-law efficiency and the total exergy destruction rate are discussed in Figure 10. Referring to Figure 10, when the Tgc varies from 40 °C to 50°C it could be observed that as the increasing gas cooler temperature, SL and EXdest.tot increases. The main reason for this variation tendency of the SL is that for a fixed cooling capacity, when Pgc increases the total mechanical power consumption, W increases (as shown in Figure 6) and this leads a reduction in SL (Eq. 34). In addition, the exergy destruction in gas cooler increases as the Pgc increases due to the increased temperature level (energy quality) of the fluid.
3.2.3. Effects of evaporator outlet temperature on cycle performance: Figure 11 shows the variation of second law efficiency and total exergy destruction rate with the evaporating temperature ranging from -25°C to -15°C when Tgc = 45°C and Φ = 7. It could be found that as the increasing evaporating temperature, the SL increases while the total exergy destruction rate shows a remarkable decreases. The main reason for this is that the compression ratio of decreases with the increasing evaporating temperature which, leads a remarkable exergy destruction in the compressor. The exergy destruction occurring in the compressor is reduced, causing the decrease in the system total exergy destruction rate.
Conclusion: A proposed hybrid vapor compression refrigeration system (HVCR) is proposed in this paper. Energetic and exergetic analyses are conducted on the thermodynamic performances of this system with CO2. The principal operating parameters including gas cooler temperature, gas cooler pressure and evaporating temperature on the system performance are discussed theoretically in detail and then compare to the conventional vapor compression refrigeration system (VCR). The simulation results indicated that HVCR exhibits significant cooling
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performance improvement with respect to COP and second law efficiency over the conventional VCR system. It is also found that exergy destruction in the compressor, the gas cooler and the ejector accounted for large percentage in total exergy destruction and thus more effective methods to reduce these exergy destructions should be developed to enhance system performance. Furthermore, the results showed that the HVCR system is proposed to be a candidate system in the cooler applications. Therefore, further theoretical and experimental investigations on the operating characteristics of HVCR system is required in the future study to confirm the practical usefulness of this system.
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Huang, B., Chang, J., Wang, C., Petrenko, V., 1999b. A 1D analysis of ejector performance. Int. J. Refrig. 22, 354–64.
Joneydi, O.S., Abolhassani, S.S., Rahmani, M., Nejad, M.Z., 2016. Comparison of transcritical CO2 refrigeration cycle with expander and throttling valve including/excluding internal heat exchanger: Exergy and energy points of view. Applied Thermal Engineering 93, 779-787.
Joybari, M.M., Hatamipour, M.S., Rahimi, A., Modarres, F.G., 2013. Exergy analysis and optimization of R600a as a replacement of R134a in a domestic refrigerator system. Int. J. Refrig. 36:1233-42.
Kairouani, L., Elakhdar, M., Nehdi, E., Bouaziz, N., 2009. Use of ejectors in a multievaporator refrigeration system for performance enhancement. International Journal of Refrigeration 32, 1173-85.
Kauf, F., 1999. Determination of the optimum high pressure for transcritical CO2 refrigeration cycles. Int. Therm. Sci 38 (4) 325-330.
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Lemmon, E.W., McLinden, M.O., Huber, M.L., 2010. NIST standard reference database 23: reference fluid thermodynamic and transport properties- REFPROP, version 9.0. National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, USA.
Liao, S.M., Zhao, T.S., Jakobsen, A., 2000. A correlation of optimal heat rejection pressures in transcritical carbon dioxide cycles. Applied Thermal Engineering 20 (9) 831-841.
Manjili, F.E., Yavari, M.A., 2012. Performance of a new two-stage multi-intercooling transcritical CO2 ejector refrigeration cycle. Appl. Therm. Eng. 40, 202–209.
Megdouli, K., Tashtoush, B.M., Nahdi, E., Elakhdar, M., Kairouani, L., Mhimid, A., 2016. Thermodynamic analysis of a novel ejector-cascade refrigeration cycles for freezing process applications and air conditioning. International Journal of Refrigeration 70, 108-118.
Megdouli, K., Elakhdar, M., Nahdi, E., Kairouani, L., Mhimid, A., 2015. Performance evaluation of a solar ejector-vapour compression cycle for cooling application. Journal of Physics: Conference Series 596, 012004.
Pridasawas, W., 2006. Solar-driven refrigeration systems with focus on the ejector cycle. In: Royal Institute of Technology, Stockholm.
Shuxue, X., Guoyuan, M., 2011. Research on air-source heat pump coupled with economized vapor injection scroll compressor and ejector. Int. J. Refrig. 34, 1587–1595.
Sun, D.W., 1998. Evaluation of a combined ejector vapour compression refrigeration system. Int. J. Energy Res. 22, 333-342.
Tan, Y., Wang, L., Liang, K., 2015. Thermodynamic performance of an auto-cascade ejector refrigeration cycle with mixed refrigerant R32+ R236fa, Applied Thermal Engineering, doi: 10.1016/j.applthermaleng.2015.03.047.
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Tashtoush, B., Alshare, A., Alrifai, S., 2015. Performance study of ejector cooling cycle at critical mode under superheated primary flow. Energy Conversion and Management 94, 300– 310.
Wang, H., Cai, W., Wang, Y., Yan, J., Wang, L., 2016. Experimental study of the behavior of a hybrid ejector-based air-conditioning system with R134a. Energy Conversion and Management 112, 31–40.
Wang, J., Sun. Z., Dai, Y., Ma, S., 2010. Parametric optimization design for supercritical CO2 power cycle using genetic algorithm and artificial neural network. Applied Energy 87: 131724.
Yan, G., Bai, T., Yu, J., 2016. Energy and exergy efficiency analysis of solar driven ejector– compressor heat pump cycle. Solar Energy 125, 243–255.
Yari, M., Mahmoudi, S.M.S., 2011. Thermodynamic analysis and optimization of novel ejector-expansion TRCC (transcritical CO2) cascade refrigeration cycles (Novel transcritical CO2 cycle). Energy 36, 6839-6850. Yu, J., Du, Z., 2010. Theoretical study of a transcritical ejector refrigeration cycle with refrigerant R143a. Renew. Energy 35, 2034–2039.
Zhu, Y., Jiang, P., 2012. Hybrid vapor compression refrigeration system with an integrated ejector cooling cycle. International Journal of Refrigeration 35, 68-78.
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Figure 1. (a) Schematic of a VCR system. (b) P-h diagram of a VCR Figure 2. (a) Schematic of a HVCR system. (b) P-h diagram of a HVCR Figure 3. Schematic of an ejector (Huang, et al., 1999b) Figure 4. The effect of the gas cooler pressure on the COP end the mechanical power consumption of two systems under specified operation conditions Figure 5. Variation of the ejector COP and the entrainment ratio with the gas cooler pressure Figure 6. Variation of the COP and the mechanical power consumption of the HVCR system with the gas cooler temperature Tgc Figure 7. Variation of the COP and the mechanical power consumption of the HVCR system with the evaporating temperature Te_A Figure 8. Variation of the ejector COP and the entrainment ratio with the evaporating temperature Te_A Figure 9. Variation of the of second-law efficiency and the total exergy destruction rate of HVCR and VCR systems with gas cooler pressure Figure 10. Variation of the second law efficiency and the exergy destruction rate of the HVCR system with the gas cooler temperature Tgc Figure 11. Variation of the second law efficiency and the exergy destruction rate of the HVCR system with the evaporator temperature Te_A
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Table 1. Condition of simulation for HVCR system Parameters
Values
Ambient temperature, T0 [°C]
25
Evaporating temperature, Te_A [°C]
-25 to -15 °C
Evaporating temperature, Te_B [°C]
0
Gas cooler temperature, Tgc [°C]
40 to 50
Condenser temperature Tcd [°C]
T0 + 5
Gas cooler pressure, Pgc [MPa]
9 to14
∆T [°C] = T2 -T7
5
Liquid pump efficiency, ηpu [%]
0.8
Booster efficiency, ηbo [%]
0.8
Table 2. Parameters of state points for the VCR system at optimum gas cooler pressure s (kJkg-1K-1)
m (kgs )
Ex (kW)
253.15 436.89
1.9485
0.85
142.6
11.4
417.54 557.49
2.045
0.85
221.2
3
11.4
318.15 320.35
1.3723
0.85
190
4
1.96
253.15 320.15
1.48
0.85
160.4
State point
P (MPa)
T (K)
1
1.96
2
h ( kJkg-1)
-1
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Table 3. Parameters of state points for the HVCR system at optimum gas cooler pressure State point
P (MPa)
T (K)
h ( kJkg-1) s (kJkg-1K1
-1
m (kgs )
Ex (kW)
)
1
1.96
253.15
436.89
1.9485
0.59
98.78
2
11.4
417.54
557.49
2.045
0.59
153.23
3
11.4
318.15
320.35
1.3723
0.59
131.62
4
1.96
253.15
320.35
1.48
0.59
111.09
5
3.48
273.15
430.8
1.8452
0.24
46.5
6
6.03
316.42
456.91
1.8592
0.24
51.63
7
11.4
412.54
550.8
2.0439
0.59
151.58
8
7.21
371.31
523.45
2.058
0.83
190.78
9
7.21
303.15
304.55
1.4288
0.83
179.08
10
11.4
316.07
312.84
1.4421
0.59
130.89
11
3.48
273.15
304.55
1.5
0.24
49.31
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Table 4. Exergy destruction rate and their ratio to the total values for HVCR and VCR systems (Under standard operating conditions) Process
Rate of exergy destruction Rate of exergy destruction (kW) (kW) of VCR system
of HVCR system
Compressor
24.86
17
Evaporator A
2.28
1
Gas cooler
31.21
0.92
Expansion valve A
29.63
20
Evaporator B
-
0.60
Booster
-
1.19
Ejector
-
12.43
Condenser
-
11.7
Pump
-
0.92
Expansion valve B
-
2.85
Total
87.9
68.64
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Figure 1.
Page 25 of 35
26
Figure 2.
Page 26 of 35
27
Figure 3.
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28
220 1.2 200 1.1 180 160
COP
0.9
140
0.8
W(kW)
1.0
120
0.7 0.6
100
0.5
80 9
10
11
12
13
14
Pgc[MPa]
Figure 4.
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29
0.28 0.60 0.27 0.26
0.55
U
COP ej
0.25 0.50
0.24 0.23
0.45
0.22 0.21
0.40 9
10
11
12
13
14
Pgc[MPa]
Figure 5.
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30
1.6 200 1.4
180 160 140
1.0
120 0.8
W(kW)
COP
1.2
100 0.6
80 60
0.4 9
10
11
12
13
14
Pgc[MPa]
Figure 6.
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31
150
1.4 1.3
140
1.2 130
1.1 1.0
COP
0.8
110
0.7 0.6
W(kW)
120
0.9
100
0.5 90
0.4 0.3
80
0.2 0.1
70
0.0 9
10
11
12
13
14
Pgc[MPa]
Figure 7.
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32
1.6
0.32 0.30
1.4
0.28 0.26
1.2
0.22
1.0
U
COP ej
0.24
0.20 0.18
0.8
0.16 0.14
0.6
0.12 0.10
0.4 9
10
11
12
13
14
Pgc[MPa]
Figure 8.
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33
200
16
180
15
2
nd
160
13 140
12 11
120
10
Ex des (kW)
law efficiency (%)
14
100
9 8
80
7 60 9
10
11
12
13
14
Pgc[MPa]
Figure 9.
Page 33 of 35
34
20
200 180
2
nd
160 140
10
120
Ex des (kW)
law efficiency (%)
15
100 5 80 60 0 9
10
11
12
13
14
Pgc[MPa]
Figure 10.
Page 34 of 35
2
nd
16
130
15
120
14
110
13
100
12
90
11
Ex des (kW )
law efficiency (% )
35
80
10 70 9 60 8 9
10
11
12
13
14
Pgc[MPa]
Figure 11.
Page 35 of 35
S0140-7007(16)30415-7 http://dx.doi.org/doi: 10.1016/j.ijrefrig.2016.12.003 JIJR 3495
To appear in:
International Journal of Refrigeration
Received date: Revised date: Accepted date:
27-7-2016 5-12-2016 7-12-2016
Please cite this article as: K. Megdouli, B.M. Tashtoush, E. Nahdi, M. Elakhdar, A. Mhimid, L. Kairouani, Performance analysis of a combined vapor compression cycle and ejector cycle for refrigeration cogeneration, International Journal of Refrigeration (2016), http://dx.doi.org/doi: 10.1016/j.ijrefrig.2016.12.003. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
1
Performance analysis of a combined vapor compression cycle and ejector cycle for refrigeration cogeneration K. Megdouli1, 3,*, B. M. Tashtoush2, E. Nahdi1, M. Elakhdar1, A. Mhimid3 and L. Kairouani1 1
Unité de Recherche Energétique et Environnent, Ecole National d’ingénieur de Tunis 37 Le Belvédère Tunis, Tunisie. 2
Mechanical Engineering Department, Jordan University of Science and Technology, Irbid, Jordan
3
Laboratoire d’Études des Systèmes Thermiques et Énergétiques Ecole National d’ingénieur de Monastir Avenue Ibn El Jazzar, 5019 Monastir, Tunisie
Highlights:
Waste heat utilization can reduce emissions of carbon dioxide.
A hybrid vapor compression refrigeration system (HVCR) with CO2 is proposed.
The effects of some thermodynamic parameters on the cycle performance are evaluated.
The work shows that the HVCR system is quite promising.
ABSTRACT: A hybrid vapor compression refrigeration (HVCR) system, which combines a vapor compression refrigeration (VCR) system and an ejector refrigeration (ER) system, was developed. The waste heat energy from the gas cooler in the VCR system is applied as driven source towards ER system. Thermodynamic investigations on the performance of the HVCR system, using CO2 as a refrigerant, are performed with energetic and exergetic methods, and the comparative analyses with the VCR system are conducted. Comprehensive effects of key operating parameters on the system performance are also studied. The results indicate that for the same cooling * Corresponding author. Tel: +216 22507488 E-mail address: [email protected] (K. Megdouli)
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capacity, the coefficient of performance (COP) of the HVCR system shows 25 % higher COP and the total mechanical power consumption is reduced by 20 % than that of conventional VCR system, respectively. The performance characteristics of the proposed cycle show its application potential in cooling and air-conditioning. Keywords: Thermodynamic analysis; Ejector; energy; Exergy; waste heat
Nomenclature COP
Coefficient of performance
Exdes
Exergy destruction rate (kW)
h
Specific enthalpy (kJkg-1)
m
Mass flow rate (kgs-1)
P
Pressure (MPa)
Q
Heat load rate (kW)
s
Specific entropy (kJ(kg.K)-1)
SL
Second law efficiency (%)
T
Temperature (°C or K)
T0
Environmental temperature (K)
Tr
The temperature of secondary fluid in the evaporator (K)
U
Entrainment ratio
W
Mechanical power (kW)
Subscripts 0
Reference environment
1, 2, 3 …
Cycle location
bo
Booster
c
Compressor
cd
Condenser
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3
ej
Ejector
e
Evaporator
exp
Expansion valve
gc
Gas cooler
is
Isentropic process
pu
Pump
sys
System
tot
Total
'
Primary fluid (or motive fluid)
' '
Secondary fluid (or entrained aspirated)
Greek symbol Φ
Area ratio between mixing tube and primary nozzle throat (d3/dt)
ξ
Driving pressure ratio (P7/P9)
r
The pressure lift ratio (P9/P6)
η
Efficiency (%)
Introduction: Due to the environmental concerns about ozone depletion and global warming, CFC, HCHC and HFC refrigerants are now being regulated. Adopting appropriate natural refrigerant such as CO2, is one of the advanced methods of enhancing system performance and reducing ozone depletion and global warming. Carbon dioxide as a refrigerant has attracted the interest of researchers because of its unique thermal characteristics, such as low viscosity, excellent heat transfer coefficient, no toxicity and no inflammability. At the same time, CO2 has zero ODP (Ozone depletion potential), negligible GWP (Global warming potential) and very low cost. However, in common refrigeration conditions, the refrigeration system using CO2 needs to be operated with a transcritical cycle mode because of the lower critical temperature of CO2
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which results in a lower first and second law efficiency. Large amount of efforts were devoted to enhance the performance of these cycles. For thermodynamic reasons, the working fluid exiting the compressor (Usually at 100- 200 °C for CO2) should be cooled down to about 35- 55 °C in the gas cooler providing a large amount of energy and exergy, which will be rejected to the environment. This is an ideal thermal energy source to be utilized to increase the refrigeration system performance. In order to improve the system performance of the CO2 VCR system and obtain dualtemperature refrigeration function, an ejector cooling cycle driven by low grade heat energy is considered to be combined with the transcritical refrigeration cycle in the present paper. It is hoped that the obtained results could provide some guidelines for refrigeration system designers. Therefore, as well known, an ejector cooling system, that utilizes natural or renewable thermal energy, offers several advantages. The distinctive characteristic of ejector refrigeration system is its ability to utilize low grade heat energy which can be easily acquired from automobile waste gas, solar radiation, industrial process and geothermal energy. Moreover, because of the application of ejector, the system possesses many advantages, such as passive device (no moving components), durable life span, and little maintenance cost and high reliable. Several research work on ejector cooling technology driven by low-grade energy was carried out extensively in the past decades. A great effort was devoted to theoretical and experimental evaluation of the ejector cycle performance (Chen et al., 2011, 2014, 2015; Huang et al., 2001, 2014; Manjili and Yavari, 2012; Pridasawas and Lundqvist, 2006; Shuxue and Guoyuan, 2011; Megdouli, et al., 2015;Tashtoush, et al., 2015; Wang, et al., 2016; Yan, et al., 2016). The technology is becoming mature for commercialization. The main restriction of prevalence of ejector refrigeration system is its relative low efficiency compared to vapor compression system. Their typically low COP of around 0.5 (Huang and Chang, 1999a; Huang et al., 1999b) can be improved substantially when combined with other systems such as absorption or vapor compression. For example, (Sun, 1998) studied a combined ejector compression refrigeration system in which an inner heat exchanger was used to combine the ejector cycle and the vapor compression cycle. (Huang, et al., 2001) proposed a combined cycle refrigeration system (CCRS) that combines a conventional refrigeration and air conditioning by using a mechanical compressor and an ejector cooling cycle. The system performance was significantly increased and the improvement in the coefficient of performance (COP) can be as high as 18.4% for evaporating temperature at −5 °C. (Hernandez, et al., 2004) developed a theoretical analysis on the thermodynamics of a
Page 4 of 35
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hybrid ejector compression refrigeration system. The effects of the working fluid and operation conditions on the hybrid system performance were analyzed. (Zhu and Jiang, 2012) studied a combined ejector compression refrigeration system. The results show that the COP is improved by 9.1% for R22 system. By considering the published literature, there be no doubt that use of combined ejector compression refrigeration (CECR) systems would exhibit a reasonable performance. Although, CECR systems have been studied from different angles, but a use of an ejector refrigeration (ER) system as a way to improve the performance of CO 2 transcritical refrigeration system have not yet been performed and needs to be considered. In order to do so, a hybrid vapor compression refrigeration (HVCR) system with carbon dioxide refrigerant with dual cooling temperature that combines a basic vapor compression refrigeration (VCR) system with an ejector refrigeration (ER) system is described in this paper. The ER system is driven thermally by the gas cooler waste heat from the CO2 transcritical system. The HVCR system can be used as a support system to favour the implantation of transcritical system and reduce the consumption of limited fuel supplies. In order to deeply evaluate thermodynamic performances of the proposed cycle, energetic and exergetic methods are used in this paper. A parametric study of a combined ejector compression refrigeration system have been performed. The results are compared with a basic refrigeration system.
1. Cycle description: Figure 1 shows the basic VCR system and its p-h diagram. The layout and pressure-enthalpy diagrams of the HVCR system are shown in Figure 2. The proposed system consists of two cycles. It includes the basic refrigeration cycle and a heat driven ejector cooling cycle. The cycle working principle is described as follows: the superheated gas discharge by the compressor (state 2) enters the gas cooler and leaves at (state 3). In gas cooler, the compressed gas rejects heat to the fluid coming from the condenser. This heat is used to drive the ER system. The gas from state 3 enters a throttling device (Exp A), where the pressure and temperature are reduced and enters evaporator (A) at state 4, where it evaporates and absorbs the heat in evaporator (A). After this, the working fluid enters the compressor as saturated vapor (state 1), and the cycle continues. The ER system is driven thermally by waste heat of the VCR system. The heat transfer between these two cycles is linked through the gas cooler. The high temperature and pressure refrigerant vapor (the primary flow, state 7) enters the ejector through a convergent-divergent nozzle, which accelerates the primary flow
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from subsonic to supersonic velocity and creates a low pressure region at the nozzle exit. This entrains the low temperature, low-pressure vapor (the secondary flow, state 5) from the evaporator (B) outlet. The secondary flow from the evaporator (B) is first compressed to a relatively high pressure in the booster and then enters the ejector at (state 6). The primary and secondary flows mix in the ejector and then the mixture is discharged to condenser (state 8). After the condensation, the refrigerant at state (9) is divided into two streams; the first one is directed through a pump to gas cooler at state (10) and the second one is directed through an expansion valve (B) (state 11) and into the evaporator (B). The liquid vapor refrigerant mixture evaporates in the evaporator (B) and the ER system thus provides an additional cooling capacity.
2. System modeling: In order to analyze the HVCR system, the energetic and the exergetic models based on the first and the second law of thermodynamics are established.
2.1. Ejector model : Ejector is the critical component in the ejector enhanced refrigeration cycles and its performance is closely related to the system performance and energy efficiency. Therefore, establishing a valid simulation model plays a significant role in the prediction and analysis of the operating characteristics of the ejector enhanced system. A typical ejector construction comprises four distinct parts: a convergent– divergent nozzle, a suction chamber attached to a constant area duct and a diffuser, Figure 3. The typical processes inside an ejector begin with high temperature and pressure stream from the generator entering the ejector through the convergent–divergent nozzle. This stream is accelerated and expanded to a supersonic speed at the nozzle exit where it creates an aerodynamic duct to entrain the low pressure and low temperature secondary stream into the mixing chamber. The secondary stream is accelerated to a sonic velocity and mixes with the primary stream in the constant area duct. The region of supersonic flow is terminated by a normal shock wave further down the duct or in the diffuser. Across the shock, pressure increases but Mach number (velocity) reduces to a subsonic value. The mixed stream then enters the subsonic diffuser where it undergoes a re-compression process to reach the back-pressure (gas cooler pressure) at near zero velocity. In the past decades, various ejector models have been developed for the theoretical and experimental analyses on the ejector cycles. From the open
Page 6 of 35
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literature on the thermodynamic modeling for ejector cycle, it could be found that ejectors are classified into two types depending on the position of the nozzle; constant-pressure mixing ejector and constant-area mixing ejector. In the constant-pressure mixing ejector the exit plane of the nozzle is located within the suction zone upstream of the constant area section, the static pressure throughout the mixing zone is assumed constant. In the constant- area mixing ejector, the primary nozzle exit is located in the constant area section, where the mixing of the primary and secondary flows occurs and the pressures of the two streams are not equal (He, et al., 2009). In order to simplify the ejector modeling process, the constant-area mixing model is adopted in the present work. The ejector operates in three different modes, the critical, subcritical and back flow modes. Critical modes are more favorable in terms of high entrainment ratio and enhanced ejector performance. For this reason, we will analyze the ejector in critical mode. The previous published paper (Kairouani, et al., 2009) contains a useful appendix, which explains additional steps in the model derivation. The model was validated in our previously published data (Megdouli, et al., 2016).
2.2. Energetic model : The energetic analysis as a fundamental method is widely used to analyze the operating performance of thermodynamic cycles. In present paper, the energetic model is developed to assess the energy utilization on the basis of the first law of thermodynamics. For simplicity, some assumptions are made as follows: 1- The system is simulated under steady state conditions. 2- The refrigerant leaving evaporators are assumed to be at saturated vapor state. 3- The enthalpy before and after the expansion valve remains constant. 4- The compression processes in the liquid pump, the booster and the compressor are adiabatic and non-isentropic. 5- The total cooling capacity Q of the system, is kept to be 100 kW for both HVCR and VCR system. 6- A temperature difference of 5°C is assumed in the gas cooler (∆T = T2-T7) (Wang, et al., 2010). 7- Ambient condition is specified as 1.01 bar and 25 °C. Based on these assumptions, the governing equations are based on conservation of energy and mass for each component in HVCR system. The simulation code written by FORTRAN is developed to investigate the effect of different operating parameters on the HVCR system
Page 7 of 35
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performance, where the thermodynamic properties of CO2 is taken from the NIST database and subroutines (Lemmon, et al., 2010) For the compressor, the input power can be calculated as: W c m 1 ( h 2 , s h1 ) / is
(1) Where is represents the isentropic efficiency of the compressor (Yari and Mahmoudi, 2011): is 0 .9 3 4 3 0 .0 4 4 7 8(
P2
)
P1
(2) The input power of the liquid pump is calculated by isentropic efficiency method (Yu and Du, 2010; Dai, et al., 2009; Ben, et al., 2014), expressed as, W pu m ( h10 , s h9 ) / pu
(3) Where p u represents the isentropic efficiency of the liquid pump and is assumed to be constant. For a real non-isentropic efficiency of the compression process the input power to the booster can be expressed as (Zhu and Jiang, 2012): W bo m ( h 6 , s h5 ) / bo
(4) Where bo represents the isentropic efficiency of booster and is assumed to be constant. The total power input the system can be given as: W W c W pu W bo
(5) For the evaporator A in the VCR system, the cooling capacity is: Q e _ A m 1 ( h1 h 4 )
(6) For the evaporator B in the ER system, the cooling capacity is: Q e _B m ( h5 h11 )
(7) The total cooling capacity of the HVCR system is:
Page 8 of 35
9 Q sys Q e _ A Q e _ B
(8) The heat flow rate at the gas cooler is: Q g c m 1 ( h 2 h3 )
(9) Using the ideal heat exchange condition and from an energy balance principle, it follows that (Tan, et al., 2015): m1 ( h2 h3 ) m ( h7 h10 )
(10) The heat flow rate at the condenser is: Q cd m tot ( h9 h8 )
(11) Where:
m tot m m (12) For expansion valves:
h 4 h3 (13)
h11 h9 (14) For ejector:
m tot h8 m h6 m h7 (15) Entrainment ratio also is an important parameter that describes the ER system performance. This parameter is related to the cooling capacity and directly depends on the refrigeration type and ejector geometry. The entrainment ratio is the ratio between the mass flow rate of the secondary flow and the mass flow rate of the primary flow, given as: U
m m
(16)
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Where m and m represent the mass flow rates of the secondary and the primary flow, respectively. The coefficient of performance of the HVCR system, COP is: COP
Q sys W
(17) For comparison, the coefficient of performance of the VCR system, C OPbasic is: C O Pbasic
Qe _ A Wc
(18) The ER system performance can be evaluated based on the coefficient of performance, C O Pej , C O Pej
Q e _B W pu W bo Q gc
(19) Another criterion is the COP improvement C O Pim p which could be used to compare the performance of HVCR system with this of the conventional VCR system, is given as follows: C O Pim p (% ) (
C O P C O Pb a sic
) *100
C O Pb a sic
(20)
2.3.Exergetic model : Exergy is defined as the maximum work potential of a material or of a form of energy in relation to its environment. Exergy based analyses help determine the entropy generation and quantify the inefficiencies of a given energy conversion process and the reduction of value of the energy utilized in the system working process. In this section, the exergetic model is built to assess the energy utilization of the HVCR system. According to the definition of exergy and exergy balance at steady operation, the exergy at any point and exergy destruction in a component can be expressed as follows (Joybari, et al., 2013): Ex m ( h h0 ) T0 ( s s 0 )
(21)
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E x des E x in E x out
T0 in
Q (1 T
T0 Q (1 T out
W
in
W out
(22) Where, T0 is a reference temperature maintained at 25 °C and the reference pressure is set at 0.101 MPa throughout this study to obtained the reference enthalpy h0 and entropy s 0 . In eq. (22), the first term represents the exergy destruction resulting from the fluid flow, the second term represents the exergy destructions caused by the heat transfers, and the last term represents the exergy destruction by the mechanical and/or electrical work transfer through the component. Based on the definition of exergy and exergy destruction mentioned above, the exergy destruction in each component of HVCR system can be derived as follows: For the compressor, the exergy destruction rate can be expressed as:
Ex c T0 m1 (s 2 s1 ) (23) For gas cooler the exergy destruction rate can be calculated by: E x gc T 0 ( m 1 (s 3 s 2 ) m (s 7 s10 ))
(24) For condenser the exergy destruction rate can be calculated by: Ex cd m tot (h 8 h9 T0 (s 8 s 9 ))
(25) For ejectors exergy destruction rate can be expressed as: E x ej T0 ( m tot s 8 m s 7 m s 6 )
(26) For expansion valve A: E x exp_A T0 m 1 (s 4 s 3 )
(27) For expansion valve B: E x exp_B T0 m (s 11 s 9 )
(28) For evaporator A:
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E x e_A T 0 m 1 ((s 1 s 4 )
(h 4 h1 )
)
Tr 1
(29) For evaporator B: E x e_B T 0 m ((s 5 s11 )
(h 11 h5 )
)
Tr 2
(30) For pump: E x pu T0 m (s 10 s 9 )
(31) For booster:
Ex bo T0 m (s 6 s 5 ) (32) The total exergy destruction rate of the HVCR system is the sum of the exergy destruction rate in each component: E x des E x c E x pu E x bo E x e _ A E x e _B E x gc E x cd E x ej E x exp_ A E x exp_B
(33) The parameter used to measure the performance of the cycle based on the second law thermodynamic, is the second-law efficiency. The second-law efficiency of the HVCR system is written as follows: Qe _ A ( SL
T0 Tr 1
1) Q e _B (
T0
1)
Tr 2
W
(34) Where, T0 is a reference temperature maintained at 25 °C, T r 1 Te _ A Te and T r 2 Te _B Te . It can be expressed as follows for the conventional VCR system: Qe _ A ( SLbasic
T0
1)
Tr 1
Wc
(35) The system exergy efficiency improvement of the HVCR system over the conventional VCR system is evaluated by:
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S L im p (% ) (
S L S L b a sic
) *100
S L b a sic
(36)
3. RESULTS AND DISCUSSION : Results are obtained from the developed model. Initially, for specified temperatures ( T e _A = 20 °C, T e _ B = 0°C, T gc = 45°C) the effect of varying gas cooler pressure on the performance of a CO2 HVCR system is reported. Optimum values of performance parameters (1st and 2nd law efficiency) at different gas cooler pressure for the HVCR system are compared with those of the VCR baseline system. During the entire analysis the cooling capacity of the HVCR system is assumed to be the same as the basic VCR system and both are assumed to be 100 kW.
3.1. Energy analysis: Table 1 summarizes the basic assumptions and input parameter values in the simulation of two considered cycles. Tables 2 and 3 show the thermodynamic properties of each state point under the standard operating condition of simulation for VCR and HVCR system, respectively. It is given in terms of pressure, temperature, enthalpy, entropy, flow rate and exergy destruction rate under the standard operating condition: the gas cooler exit temperature is 45°C, the evaporating temperatures T e _ A and T e _B are -20 °C and 0 °C, respectively.
The highest COP value
corresponds to a gas cooler pressure of 11.4 MPa as shown in Figure 4, indicating that this is an optimum value for the gas cooler pressure. It should be mentioned that the mass flow rate of each state points is obtained by applying the principle of mass and energy conversation.
3.1.1. Effects of gas cooler outlet pressure : The effect of varying gas cooler pressure Pgc on the COP and the total mechanical power consumption for the HVCR and the VCR systems are shown in Figure 4. According to references (Liao, et al., 2000; Kauf, 1999; Joneydi, et al., 2016), there exists an optimal value for gas cooler pressure to reach the maximum COP in a carbon dioxide refrigeration cycle. In this respect, it can be observed in Figure. 4, that the corresponding optimum gas cooler pressure is 11.4 MPa that maximizes the COP of both systems at the given operating condition.
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As can be seen (Figure 4), the total mechanical work consumption W, of both cycles drops first and then increases. For this reason, the system COP rises first and then decreases as previously noted. Since the cooling capacity is the same for the two refrigeration systems, the performance improvement appears in terms of lower mechanical power consumption. The main reason for this is that the large temperature in the gas cooler is utilized to drive an ejector cooling cycle. In this case, the HVCR system exhibits a reasonable value of COP. In order to illustrate the energy saving potential and advantages of excellent cooling performances, the energetic performance comparisons between HVCR and VCR systems using CO2 are carried out at the specific operating condition and for the same cooling capacity. It can be observed that the HVCR system has more advantages than the VCR system in terms of system COP. Under the given operating condition and at the optimum gas cooler pressure, the HVCR system shows 25 % higher COP and the total mechanical power consumption W sys is reduced by 20 %. Therefore, it could be concluded that the use of the waste heat from the gas cooler in the VCR system to drive the ejector cooling system could significantly improve the system performance. This indicates that applying HVCR system to obtain better performance with lower energy consumption is feasible. The variation of the entrainment ratio U and the ejector cycle COP with the gas cooler pressure Pgc are presented in Figure 5. It is clear from Figure 5 that the entrainment ratio increases with the gas cooler pressure Pgc and vary in the range of 0.43-0.57. It is also demonstrated that the C O Pej is low in compare to the VCR system COP, the ejector cycle improve the COP because the heat energy utilized in the ejector cycle is waste heat from the gas cooler.
3.1.2. Effects of gas cooler outlet temperature on cycle performance: The following results were obtained by varying the gas cooler temperature from 40°C to 50°C. Figure 6 shows the effect of Tgc on the HVCR system COP and the total mechanical power consumption. As shown in Figure 6, increasing gas cooler temperature results in an increase of the optimum gas cooler pressure. The optimum gas cooler pressure varies from 9.8 to 12 MPa when the gas cooler temperature varies from 40 to 50°C. The COPsys of the HVCR system decreases as the gas cooler temperature increases because the enthalpy of the CO 2 at state 3 increases as the gas cooler temperature increases, which leads to an increase in the total mechanical power consumption, W , as shown in Figure 6. Increasing gas cooler outlet temperature will significantly decrease the system performance.
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3.1.3. Effects of evaporator outlet temperature on cycle performance: Figure 7 shows the effect of the evaporator outlet temperature on the COP and the mechanical work consumption, W. The COP increases as the evaporating temperature Te_A increases. The maximum COP increases with the evaporating temperature Te_A when the evaporating temperature Te_A ranges from -25°C to -15°C, the COP is higher at the optimum gas cooler pressure. As it can be seen from Figure 7, the mechanical work consumption, W, decreases as the evaporating temperature Te_A increases. This is because of the decrease in difference between the gas cooler and evaporator temperatures. It is observed that for each evaporating temperature an optimum gas cooler pressure exists for which W is a minimum.
The variations of the ejector system COP and the entrainment ratio with T e_A are presented in Figure 8. It can be seen that COPej and the entrainment ratio U increase with increasing Te_A. Refereeing to Figure 8, as the evaporating temperature increases, the entrainment ratio is raised. This is justified by the fact that the compressor exit temperature increase results in more vapors generated to drive the ejector refrigeration system. The increase in the entrainment ratio will increase the value of COPej as depicted in Figure 8.
3.2. Exergy analysis: 3.2.1. Effects of gas cooler outlet pressure : The results are obtained with the operating condition kept at T e _A = -20 °C, T e _ B = 0°C, T gc = 45°C and Φ=7. Figure 9 compares the total exergy destruction rate and the second law efficiency of the VCR and the HVCR system in which both of them depict the same trend with minimum amount of exergy destruction rate according to the optimum Pgc which is approximately 11.4 MPa. However, the EXdest of the HVCR system is 22 % lower in compare to the VCR system, as can be seen from Table 4. Table 4 outlines the exergy destruction rates in different components of the systems at T e _A = 20°C, T e _ B = 0°C, T gc = 45°C and Φ=7. As indicated in Table 4, the main irreversibility of VCR system occurring in the compressor, gas cooler and expansion valve are lower for HVCR system. Figures 9 shows that the maximum second law efficiency of 15.6 % and 14.9 % for HVCR and VCR system are obtained. The optimal gas cooler pressure of approximately 11.4 MPa is
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attained. It can be deduced that the HVCR system represents approximately 4.7 % increase as compared to the conventional one. The maximization of second law efficiency with the gas cooler pressure can be justified if we note that an increase in the gas cooler pressure causes a reduction in the total exergy destruction rate when the Pgc is inferior to 11.4 MPa as shown in Figure 9. Further, the integration of the ER system with the conventional VCR system leads to an improvement in total system exergy destruction rate.
3.2.2. Effects of condenser outlet temperature on cycle performance: The effect of gas cooler temperature on second-law efficiency and the total exergy destruction rate are discussed in Figure 10. Referring to Figure 10, when the Tgc varies from 40 °C to 50°C it could be observed that as the increasing gas cooler temperature, SL and EXdest.tot increases. The main reason for this variation tendency of the SL is that for a fixed cooling capacity, when Pgc increases the total mechanical power consumption, W increases (as shown in Figure 6) and this leads a reduction in SL (Eq. 34). In addition, the exergy destruction in gas cooler increases as the Pgc increases due to the increased temperature level (energy quality) of the fluid.
3.2.3. Effects of evaporator outlet temperature on cycle performance: Figure 11 shows the variation of second law efficiency and total exergy destruction rate with the evaporating temperature ranging from -25°C to -15°C when Tgc = 45°C and Φ = 7. It could be found that as the increasing evaporating temperature, the SL increases while the total exergy destruction rate shows a remarkable decreases. The main reason for this is that the compression ratio of decreases with the increasing evaporating temperature which, leads a remarkable exergy destruction in the compressor. The exergy destruction occurring in the compressor is reduced, causing the decrease in the system total exergy destruction rate.
Conclusion: A proposed hybrid vapor compression refrigeration system (HVCR) is proposed in this paper. Energetic and exergetic analyses are conducted on the thermodynamic performances of this system with CO2. The principal operating parameters including gas cooler temperature, gas cooler pressure and evaporating temperature on the system performance are discussed theoretically in detail and then compare to the conventional vapor compression refrigeration system (VCR). The simulation results indicated that HVCR exhibits significant cooling
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performance improvement with respect to COP and second law efficiency over the conventional VCR system. It is also found that exergy destruction in the compressor, the gas cooler and the ejector accounted for large percentage in total exergy destruction and thus more effective methods to reduce these exergy destructions should be developed to enhance system performance. Furthermore, the results showed that the HVCR system is proposed to be a candidate system in the cooler applications. Therefore, further theoretical and experimental investigations on the operating characteristics of HVCR system is required in the future study to confirm the practical usefulness of this system.
Reference:
Ben Mansour, R., Ouzzane, M., Aidoun, Z., 2014. Numerical evaluation of ejector-assisted mechanical compression systems for refrigeration applications. Int. J. Refrig. 43, 36–49.
Chen, X., Zhou, Y., Yu, J., 2011. A theoretical study of an innovative ejector enhanced vapor compression heat pump cycle for water heating application. Energy Build. 43, 3331–3336.
Chen, J., Havtun, H., Palm, B., 2014. Investigation of ejectors in refrigeration system: optimum performance evaluation and ejector area ratios perspectives. Appl. Therm. Eng. 64, 182–191.
Chen, J., Havtun, H., Palm, B., 2015. Conventional and advanced exergy analysis of an ejector refrigeration system. Appl. Energy 144, 139–151.
Dai, Y., Wang, J., Gao, L., 2009. Exergy analysis, parametric analysis and optimization for a novel combined power and ejector refrigeration cycle. Appl. Therm. Eng. 29, 1983–1990.
He, S., Li, Y., Wang, R.Z., 2009. Progress of mathematical modeling on ejectors. Renew. Sustain. Energy Rev. 13, 1760–1780.
Hernandez, J.I., Dorantes, R.J., Best, R., Estrada, C.A., 2004. The behaviour of a hybrid compressor and ejector refrigeration system with refrigerants 134a and 142b. Appl. Therm. Eng. 24, 1765-1783.
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Huang, B.J., Petrenko, V.A., Chang, J.M., Lin, C.P., Hu, S.S., 2001. A combined-cycle refrigeration system using ejector-cooling cycle as the bottom cycle. International Journal of Refrigeration 24, 391-399.
Huang, B.J., Ton, W.Z., Wu, C.C., Ko, H.W., Chang, H.S., Hsu, H.Y., Liu, J.H., Wu, J. H., Yen, R.H., 2014. Performance test of solar assisted ejector cooling system. Int. J. Refrig. 39, 172–185.
Huang, B.J., Chang, J.M., 1999a. Empirical correlation for ejector design. Int. J. Refrig. 22, 379–88.
Huang, B., Chang, J., Wang, C., Petrenko, V., 1999b. A 1D analysis of ejector performance. Int. J. Refrig. 22, 354–64.
Joneydi, O.S., Abolhassani, S.S., Rahmani, M., Nejad, M.Z., 2016. Comparison of transcritical CO2 refrigeration cycle with expander and throttling valve including/excluding internal heat exchanger: Exergy and energy points of view. Applied Thermal Engineering 93, 779-787.
Joybari, M.M., Hatamipour, M.S., Rahimi, A., Modarres, F.G., 2013. Exergy analysis and optimization of R600a as a replacement of R134a in a domestic refrigerator system. Int. J. Refrig. 36:1233-42.
Kairouani, L., Elakhdar, M., Nehdi, E., Bouaziz, N., 2009. Use of ejectors in a multievaporator refrigeration system for performance enhancement. International Journal of Refrigeration 32, 1173-85.
Kauf, F., 1999. Determination of the optimum high pressure for transcritical CO2 refrigeration cycles. Int. Therm. Sci 38 (4) 325-330.
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Lemmon, E.W., McLinden, M.O., Huber, M.L., 2010. NIST standard reference database 23: reference fluid thermodynamic and transport properties- REFPROP, version 9.0. National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, USA.
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Manjili, F.E., Yavari, M.A., 2012. Performance of a new two-stage multi-intercooling transcritical CO2 ejector refrigeration cycle. Appl. Therm. Eng. 40, 202–209.
Megdouli, K., Tashtoush, B.M., Nahdi, E., Elakhdar, M., Kairouani, L., Mhimid, A., 2016. Thermodynamic analysis of a novel ejector-cascade refrigeration cycles for freezing process applications and air conditioning. International Journal of Refrigeration 70, 108-118.
Megdouli, K., Elakhdar, M., Nahdi, E., Kairouani, L., Mhimid, A., 2015. Performance evaluation of a solar ejector-vapour compression cycle for cooling application. Journal of Physics: Conference Series 596, 012004.
Pridasawas, W., 2006. Solar-driven refrigeration systems with focus on the ejector cycle. In: Royal Institute of Technology, Stockholm.
Shuxue, X., Guoyuan, M., 2011. Research on air-source heat pump coupled with economized vapor injection scroll compressor and ejector. Int. J. Refrig. 34, 1587–1595.
Sun, D.W., 1998. Evaluation of a combined ejector vapour compression refrigeration system. Int. J. Energy Res. 22, 333-342.
Tan, Y., Wang, L., Liang, K., 2015. Thermodynamic performance of an auto-cascade ejector refrigeration cycle with mixed refrigerant R32+ R236fa, Applied Thermal Engineering, doi: 10.1016/j.applthermaleng.2015.03.047.
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Tashtoush, B., Alshare, A., Alrifai, S., 2015. Performance study of ejector cooling cycle at critical mode under superheated primary flow. Energy Conversion and Management 94, 300– 310.
Wang, H., Cai, W., Wang, Y., Yan, J., Wang, L., 2016. Experimental study of the behavior of a hybrid ejector-based air-conditioning system with R134a. Energy Conversion and Management 112, 31–40.
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Yari, M., Mahmoudi, S.M.S., 2011. Thermodynamic analysis and optimization of novel ejector-expansion TRCC (transcritical CO2) cascade refrigeration cycles (Novel transcritical CO2 cycle). Energy 36, 6839-6850. Yu, J., Du, Z., 2010. Theoretical study of a transcritical ejector refrigeration cycle with refrigerant R143a. Renew. Energy 35, 2034–2039.
Zhu, Y., Jiang, P., 2012. Hybrid vapor compression refrigeration system with an integrated ejector cooling cycle. International Journal of Refrigeration 35, 68-78.
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Figure 1. (a) Schematic of a VCR system. (b) P-h diagram of a VCR Figure 2. (a) Schematic of a HVCR system. (b) P-h diagram of a HVCR Figure 3. Schematic of an ejector (Huang, et al., 1999b) Figure 4. The effect of the gas cooler pressure on the COP end the mechanical power consumption of two systems under specified operation conditions Figure 5. Variation of the ejector COP and the entrainment ratio with the gas cooler pressure Figure 6. Variation of the COP and the mechanical power consumption of the HVCR system with the gas cooler temperature Tgc Figure 7. Variation of the COP and the mechanical power consumption of the HVCR system with the evaporating temperature Te_A Figure 8. Variation of the ejector COP and the entrainment ratio with the evaporating temperature Te_A Figure 9. Variation of the of second-law efficiency and the total exergy destruction rate of HVCR and VCR systems with gas cooler pressure Figure 10. Variation of the second law efficiency and the exergy destruction rate of the HVCR system with the gas cooler temperature Tgc Figure 11. Variation of the second law efficiency and the exergy destruction rate of the HVCR system with the evaporator temperature Te_A
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Table 1. Condition of simulation for HVCR system Parameters
Values
Ambient temperature, T0 [°C]
25
Evaporating temperature, Te_A [°C]
-25 to -15 °C
Evaporating temperature, Te_B [°C]
0
Gas cooler temperature, Tgc [°C]
40 to 50
Condenser temperature Tcd [°C]
T0 + 5
Gas cooler pressure, Pgc [MPa]
9 to14
∆T [°C] = T2 -T7
5
Liquid pump efficiency, ηpu [%]
0.8
Booster efficiency, ηbo [%]
0.8
Table 2. Parameters of state points for the VCR system at optimum gas cooler pressure s (kJkg-1K-1)
m (kgs )
Ex (kW)
253.15 436.89
1.9485
0.85
142.6
11.4
417.54 557.49
2.045
0.85
221.2
3
11.4
318.15 320.35
1.3723
0.85
190
4
1.96
253.15 320.15
1.48
0.85
160.4
State point
P (MPa)
T (K)
1
1.96
2
h ( kJkg-1)
-1
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Table 3. Parameters of state points for the HVCR system at optimum gas cooler pressure State point
P (MPa)
T (K)
h ( kJkg-1) s (kJkg-1K1
-1
m (kgs )
Ex (kW)
)
1
1.96
253.15
436.89
1.9485
0.59
98.78
2
11.4
417.54
557.49
2.045
0.59
153.23
3
11.4
318.15
320.35
1.3723
0.59
131.62
4
1.96
253.15
320.35
1.48
0.59
111.09
5
3.48
273.15
430.8
1.8452
0.24
46.5
6
6.03
316.42
456.91
1.8592
0.24
51.63
7
11.4
412.54
550.8
2.0439
0.59
151.58
8
7.21
371.31
523.45
2.058
0.83
190.78
9
7.21
303.15
304.55
1.4288
0.83
179.08
10
11.4
316.07
312.84
1.4421
0.59
130.89
11
3.48
273.15
304.55
1.5
0.24
49.31
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Table 4. Exergy destruction rate and their ratio to the total values for HVCR and VCR systems (Under standard operating conditions) Process
Rate of exergy destruction Rate of exergy destruction (kW) (kW) of VCR system
of HVCR system
Compressor
24.86
17
Evaporator A
2.28
1
Gas cooler
31.21
0.92
Expansion valve A
29.63
20
Evaporator B
-
0.60
Booster
-
1.19
Ejector
-
12.43
Condenser
-
11.7
Pump
-
0.92
Expansion valve B
-
2.85
Total
87.9
68.64
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Figure 1.
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26
Figure 2.
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27
Figure 3.
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28
220 1.2 200 1.1 180 160
COP
0.9
140
0.8
W(kW)
1.0
120
0.7 0.6
100
0.5
80 9
10
11
12
13
14
Pgc[MPa]
Figure 4.
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29
0.28 0.60 0.27 0.26
0.55
U
COP ej
0.25 0.50
0.24 0.23
0.45
0.22 0.21
0.40 9
10
11
12
13
14
Pgc[MPa]
Figure 5.
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1.6 200 1.4
180 160 140
1.0
120 0.8
W(kW)
COP
1.2
100 0.6
80 60
0.4 9
10
11
12
13
14
Pgc[MPa]
Figure 6.
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31
150
1.4 1.3
140
1.2 130
1.1 1.0
COP
0.8
110
0.7 0.6
W(kW)
120
0.9
100
0.5 90
0.4 0.3
80
0.2 0.1
70
0.0 9
10
11
12
13
14
Pgc[MPa]
Figure 7.
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32
1.6
0.32 0.30
1.4
0.28 0.26
1.2
0.22
1.0
U
COP ej
0.24
0.20 0.18
0.8
0.16 0.14
0.6
0.12 0.10
0.4 9
10
11
12
13
14
Pgc[MPa]
Figure 8.
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33
200
16
180
15
2
nd
160
13 140
12 11
120
10
Ex des (kW)
law efficiency (%)
14
100
9 8
80
7 60 9
10
11
12
13
14
Pgc[MPa]
Figure 9.
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20
200 180
2
nd
160 140
10
120
Ex des (kW)
law efficiency (%)
15
100 5 80 60 0 9
10
11
12
13
14
Pgc[MPa]
Figure 10.
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2
nd
16
130
15
120
14
110
13
100
12
90
11
Ex des (kW )
law efficiency (% )
35
80
10 70 9 60 8 9
10
11
12
13
14
Pgc[MPa]
Figure 11.
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