Thermodynamics analysis of a modified dual-evaporator CO2 transcritical refrigeration cycle with two-stage ejector

Energy xxx (2015) 1e11

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Thermodynamics analysis of a modified dual-evaporator CO2 transcritical refrigeration cycle with two-stage ejector Tao Bai, Gang Yan*, Jianlin Yu Department of Refrigeration and Cryogenic Engineering, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 26 September 2014 Received in revised form 18 January 2015 Accepted 28 February 2015 Available online xxx

In this paper, a modified dual-evaporator CO2 transcritical refrigeration cycle with two-stage ejector (MDRC) is proposed. In MDRC, the two-stage ejector are employed to recover the expansion work from cycle throttling processes and enhance the system performance and obtain dual-temperature refrigeration simultaneously. The effects of some key parameters on the thermodynamic performance of the modified cycle are theoretically investigated based on energetic and exergetic analyses. The simulation results for the modified cycle show that two-stage ejector exhibits more effective system performance improvement than the single ejector in CO2 dual-temperature refrigeration cycle, and the improvements of the maximum system COP (coefficient of performance) and system exergy efficiency could reach 37.61% and 31.9% over those of the conventional dual-evaporator cycle under the given operating conditions. The exergetic analysis for each component at optimum discharge pressure indicates that the gas cooler, compressor, two-stage ejector and expansion valves contribute main portion to the total system exergy destruction, and the exergy destruction caused by the two-stage ejector could amount to 16.91% of the exergy input. The performance characteristics of the proposed cycle show its promise in dualevaporator refrigeration system. © 2015 Published by Elsevier Ltd.

Keywords: Transcritical cycle Exergy Dual-evaporator Ejector Carbon dioxide Performance

1. Introduction Currently, vapor-compression refrigeration systems are extensively used in residential and commercial refrigerating applications, which account for large proportion of the social energy consumption [1]. The crucial influence of the refrigeration industry on global warming and ozone depletion has become an increasingly obvious issue. The proper choice of cycle configuration and environmental friendly refrigerants for these refrigeration systems has positive effect on energy savings and greenhouse emission reduction. The natural working fluid such as CO2 can be an alternative refrigerant to replace CFCs and HCFCs due to its environmental friendly characteristic and excellent heat transfer coefficients [2]. However, in the 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, and the coefficient of performance (COP) of these systems is lower than

* Corresponding author. Tel.: þ86 29 82668738; fax: þ86 29 82668729. E-mail address: [email protected] (G. Yan).

that of conventional cycle using CFCs and HCFCs refrigerants due to huge expansion losses [3]. Therefore, a large amount of efforts such as employing the expander [4,5] or additional ejector [6e8] have been made by researchers to recover the throttling losses in the systems. In recent years, ejectors has been getting more attention due to its obvious features, such as no moving parts, low cost, simple structure, low maintenance requirements and high performance improvement potential. Therefore, lots of theoretical and experimental literatures about ejector enhanced transcritical CO2 refrigeration and heat pump cycle have been made recently. And the research results show that use of ejector as an expansion device in transcritical CO2 cycle is considered to be a promising cycle modification to improve the system performance [9e14]. As well known, multi-temperature refrigeration systems have gained greater popularity due to their potential applications in a wide range of cooling temperature. Besides widely used refrigerator-freezer for households, the two-stage compression CO2 refrigeration cycle with different temperatures also has been getting increasing concern. Sharma et al. [15] presented an optimizing analysis on the various multi-temperature transcritical cycles including cascaded and secondary loop refrigeration cycle systems which are becoming popular in the supermarket applications. Ge

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Nomenclature COP Ex h m_ P Q qv rP s T u v W

coefficient of performance exergy flow rate, kW specific enthalpy, kJ/kg mass flow rate, kg/s pressure, MPa refrigeration capacity, kW volumetric refrigeration capacity, kJ/m3 pressure lift ratio of ejector entropy, kJ/kg$K temperature,  C fluid velocity, m/s specific volume, m3/kg compressor power, kW

Greek symbols h efficiency m entrainment ratio f refrigeration capacity ratio b mass flow rate allocation ratio

and Tassou [16] investigated a typical two-stage compression dualtemperature CO2 refrigeration system applied in supermarket through thermodynamic analysis and derived a function for optimal discharge pressure with the variables consisting of ambient air temperature, effectiveness of suction line heat exchanger and compressor efficiency. Shin et al. [17] modeled the two-stage compression CO2 refrigeration cycle with two different evaporating temperatures by taking into account of frost growth condition and investigated the effects of frost growth on the system performances. Generally, in a multi-temperature refrigeration system large thermodynamic losses in throttling processes can be generated if conventional expansion devices are used. From a viewpoint of exergy, however, the system performance still has large potential improvement. An effective method of improving the system performance is to recover the expansion work in the throttling processes. In the past years, various cycle configurations employing ejector have been developed for the energy saving purpose [18e24]. The specialized literatures generally are concentrated on the single ejector enhanced multi-evaporator refrigeration cycles to recover the expansion losses. Elakdhar et al. [18] theoretically analyzed an ejector enhanced dual-temperature refrigerator with several different refrigerants, and the results show that ejection cycle can reach higher coefficient of performance compared with standard cycle. Liu et al. [19] presented three different connecting forms of single ejector enhanced refrigeration cycles and found the energy consumption could be reduced by 7.75%. Sarkar [25] firstly performed two new layouts of dualevaporator transcritical CO2 refrigeration cycle with single ejector and found the new ejector cycles has higher COP than that of the conventional cycle. On the other hand, some other researchers proposed that multiple ejectors may be utilized to recover the expansion losses sufficiently. Kairouani et al. [20] theoretically analyzed a three cooling temperatures refrigeration cycle with twostage ejector, and pointed out that the two-stage ejector are efficient to recover pressure loss in the multi-evaporator refrigeration system. Lin et al. [21e23] experimentally evaluated the performance of three-circuit refrigeration system with the adjustable ejectors. Zhou et al. [24] presented a two-circuit refrigeration cycle with a novel dual-nozzle ejector and found the COP could be improved by 22.9e50.8%. Jaruwongwittaya et al. [26] proposed new layout of a two-stage ejector enhanced refrigeration cycle used

Subscripts a ambient Com compressor d diffuser des exergy destruction Eje ejector Ev expansion valve Gc gas cooler HT high temperature evaporator i inlet is isentropic process LT low temperature evaporator mix mixing chamber n nozzle o outlet opt optimum value p primary fluid s secondary fluid 1e10 state point

in bus, and indicated that the two stage ejector cooling system has higher COP than that of the single-stage ejector cooling system. Hafner et al. [27] theoretically investigated efficiency and capacity of the CO2 supermarket layouts with multi-ejector and heat recovery under different climate conditions and the achieved system efficiency improvement could be up to 30%. Based on the published literatures mentioned above, we can see that little attention has been paid to the CO2 transcritical dualevaporator refrigeration cycle with a two-stage ejector. In this paper, we propose a modified dual-evaporator refrigeration cycle with two-stage ejector. The main advantage of this cycle configuration could sufficiently recover the expansion work by utilizing the existing large pressure differences between gas cooler and two evaporators in the system and obtain dual-temperature refrigeration function. In order to deeply evaluate the thermodynamic performances of the proposed cycle, energetic and exergetic methods are applied in this paper. 2. Cycle system description The layout of a conventional dual-evaporator CO2 refrigeration cycle (CDRC) is shown in Fig. 1. The CDRC system includes a compressor, a gas cooler, three expansion valves and two

Fig. 1. The schematic diagram of CDRC cycle.

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evaporators. The thermodynamic processes of CDRC feature the compression, heat rejection, expansion and evaporation. It is recognized that the isenthalpic expansion processes in this cycle lead to lower system performance owing to the higher irreversibility of the three expansion valves. In this case, it should be a better solution to use ejector as expansion device to improve the thermodynamic performances of CDRC, because ejector can effectively recover the expansion work to lift the suction pressure and enhance the system performance. Undoubtedly, an appropriate ejector configuration with better pressure lifting performance must be desired. Based on CDRC described above, the cycle layout and pressureenthalpy diagram of a modified dual-evaporator transcritical CO2 refrigeration cycle with two-stage ejector (MDRC) are shown in Figs. 2 and 3, respectively. The MDRC system consists of a compressor, a gas cooler, a separator, two expansion valves, two evaporators and two ejectors. The saturated vapor from the separator is compressed to gas cooler pressure. The vapor leaving the compressor at state 2 enters the gas cooler where it cools to state 3 by rejecting heat to surroundings. The fluid leaving gas cooler (state 3) is split into two streams. One of them directly enters the nozzle of the first stage ejector 1, the other stream enters high-temperature evaporator after a pressure reduction in the expansion valve 2 and gives useful cooling effect. The vapor from high-temperature evaporator outlet (state 5) as the primary flow of the second stage ejector 2 entrains the two-phase fluid (state 10) coming from the ejector 1 and then the mixed fluid enters the separator (state 6). The two-phase refrigerant from separator is separated into two parts: the saturated vapor refrigerant (state 1) is returned to the compressor and the liquid refrigerant (state7) through expansion valve 1 enters lowtemperature evaporator and gives a relatively low temperature level cooling effect. The saturated vapor (state 9) from lowtemperature evaporator enters the suction chamber of ejector 1, and then mixes with the primary flow from gas cooler. The mixed flow is going to the constant pressure mixing and diffuser sections of ejector 1. The two-phase refrigerant comes out from ejector 1 then enters the suction chamber of ejector 2 again. In this way, the MDRC cycle is completed. Obviously, compared to MDRC cycle, the main cycle configuration feature of MDRC cycle is the employing of two-stage ejector. The fluid at lower evaporating pressure could be lifted by first stage

3

Fig. 3. The pressure-enthalpy diagram of MDRC cycle.

ejector to be at intermediary pressure first, then the fluid from the first stage ejector is entrained by the second stage ejector utilizing the higher evaporating pressure fluid. In this case, the expansion losses associated with the throttling processes could be gradually recovered by the two-stage ejector, and then the suction pressure of compressor could achieve a larger lift, which would promote the improvement of system performance. 3. Mathematical modeling and simulation 3.1. Ejector model Ejector is a critical component in ejector refrigeration system, and the proper simulation model for ejector plays significant role to exhibit cycle performance. In the past decades, the thermodynamic analyses of ejector refrigeration cycles are mainly based on two approaches, the mixing of the primary flow and the secondary flow either at constant pressure or constant area model [28]. For simplicity in this modeling, the ejector performance simulation is carried out based on the one-dimensional constant pressure mixing model [29e32], in which the mixing process of primary flow and secondary flow occurs at a constant pressure. It has been used as a common thermodynamic cycle analysis method to develop an ejector mathematical model. For simulation, additional assumptions are made for ejector as follows [24,33]: (1) The flow inside the ejector is steady state. (2) The kinetic energy of refrigerant of inlet and outlet are negligible. (3) The efficiencies of the ejector are considered as constant values. (4) Mixing process in the ejector occurs at constant pressure and complies with the conservation of energy, mass and momentum. (5) The ejector does not exchange heat with surroundings.

Fig. 2. The schematic diagram of MDRC cycle.

Based on the above assumptions, steady flow energy equations and mass balance equations have been employed. As well known, the ejector performance can be evaluated by entrainment ratio which is defined as,

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m¼

m_ s m_ p

(1)

where m_ s is the mass flow rate of secondary flow, m_ p is the mass flow rate of primary flow. Thus, the entrainment ratio of the twostage ejector configuration mt and the entrainment ratio of individual ejector (m1 ,m2 ) are given as,

!2

hm ¼

umix u0mix

umix ¼

un:o pffiffiffiffiffiffiffi hm 1þm

(10)

(11)

mt ¼

m_ s1 m_ p1 þ m_ p2

(2)

By employing the energy conservation equation in the mixing chamber, the specific enthalpy of the mixed flow which is also considered to be the inlet flow of the diffuser can be derived as:

m1 ¼

m_ s1 þ m_ p1 m_ s1 ; m ¼ m_ p1 2 m_ p2

(3)

hd:i ¼

where m_ p1 and m_ p2 are the mass flow rate of the primary fluid in ejector 1 and ejector 2, respectively. And m_ s1 and m_ s2 are the mass flow rate of secondary fluid in ejector 1 and ejector 2, respectively. Meanwhile, the entrainment ratio of the two-stage ejector configuration can also be deduced by Eqs. (1)e(3) as,

mt ¼

m1 m2 1 þ m1 þ m2

(4)

In the simulations, the mass flow rate ratio b for the primary fluid is introduced to adjust the refrigeration capacity allocation between the high and low temperature evaporators, which is defined as:

b¼

m_ p1 m_ p2 ; 1b¼ m_ p1 þ m_ p2 m_ p1 þ m_ p2

(5)

On the basis of the constant pressure mixing theory, the detailed computational process of each ejector is expressed as, In the nozzle section, the nozzle isentropic efficiency is defined as follow,

hn ¼

hn:i  hn:o hn:i  hn:is:o

(6)

where, hn:i and hn:o are the inlet and outlet specific enthalpy of the primary flow at the nozzle, hn:is:o is the ideal exiting specific enthalpy through an isentropic expansion in the nozzle. When inlet velocity of the primary flow is ignored, the velocity of primary fluid leaving the nozzle can be derived from the energy conservation,

un:o ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2hn ðhn:i  hn:is:o Þ  1000

(7)

In the mixing section, neglecting the inlet pressure drop of the secondary flow, the momentum conservation in the mixing chamber can be expressed as,

u0mix ¼

1 m un:o þ u 1þm 1 þ m s:i

(8)

where, u0mix represents the ideal velocity of the mixed flow at the mixing chamber, which is obtained without considering the energy dissipation in the mixing process. The us:i represents the inlet velocity of the secondary flow. When the us:i is neglected, the ideal mixing velocity u0mix can be derived as,

u0mix ¼

un:o 1þm

(12)

where hs:i is the inlet specific enthalpy of the secondary flow. In the diffuser section, the mixed flow converts the kinetic energy into pressure energy. Neglecting the exit velocity of the mixed flow and taking diffuser efficiency into account, the exit enthalpy of the mixed flow hd:o can be calculated as:

hd:o ¼

hn:i þ mhs:i 1þm

(13)

The isentropic efficiency of the diffuser hd is defined as,

hd ¼

hd:is:o  hd:i hd:o  hd:i

(14)

where, hd:i and hd:o are the inlet and outlet specific enthalpy of the mixed flow at the diffuser. And the hd:is:o is the ideal exiting specific enthalpy through an isentropic compression in the diffuser, which can be calculated by,

hd:is:o ¼ hd:i þ ðhd:o  hd:i Þhd

(15)

When the entrainment ratio and inlet state parameters are specified initially, the state parameters of the exit flow for the ejector can also be obtained by using Eqs. (6)e(15). In addition, when the state parameters of inlet and exit flows of the ejector are given under the selected operating conditions, the entrainment ratio for the individual ejector can be derived as follow using Eqs. (6)e(15) described above.

m¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hn hm hd ðhn:i  hn:is:o Þ=ðhd:is:o  hd:i Þ  1

(16)

Besides the entrainment ratio, the pressure lift ratio of ejector is also a key parameter that plays significant role in the system performance improvements. Therefore, a pressure lift ratio is introduced to evaluate the pressure lifting performance of each ejector, which can be expressed as,

rPj ¼

Pd:o Ps:i

(17)

where Ps:i and Pd:o represent the inlet pressure of secondary flow and the exit pressure of the mixed flow, respectively. For the MDRC cycle, the pressure lift ratio of the two-stage ejector configuration is defined as the ratio of exit pressure of ejector 2 to the inlet pressure of secondary flow of ejector 1, which can be expressed as,

(9)

Taking into account of the friction loss for the mixing process in the mixing chamber, the mixing efficiency hm [13] is introduced to derive the velocity of the mixed fluid.

  hn:i þ mhs:i 1 2 umix  1000 2 1þm

rPt ¼

P1 P9

(18)

It is noted that the detailed calculation steps for an ejector are given in the Appendix A.

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3.2. Energetic analysis Energetic analysis based on the first law thermodynamics is a fundamental method for the cycle performance evaluation. In order to simplify the cycle simulation, some assumptions are also considered [34]: (1) The system operates at a steady state, and pressure drop in pipe and heat losses to ambient in gas cooler, evaporator and separator are negligible. (2) The compression process is adiabatic and non-isentropic. (3) The throttling process through expansion devices are isenthalpic. (4) The vapor and liquid flow from the separator are both saturated fluids. (5) The exiting fluid of evaporator is saturated vapor. Based on these assumptions, the conservation equations of energy and mass conservations in each component can be obtained as follows: For the compressor, the compressor power can be expressed as,

    h h1 W ¼ m_ p1 þ m_ p2 ðh2 h1 Þ ¼ m_ p1 þ m_ p2 2s his



P2 P1



  0:0041

P2 P1

2

 3 P þ 0:0001 2 P1 (20)

For evaporators, the refrigeration capacities are given as,

QHT ¼ m_ p2 ðh5 h4 Þ QLT

¼ m_ s1 ðh9 h8 Þ

(21) (22)

In addition, the refrigeration capacity ratio f is introduced as,

Q f ¼ HT QLT

(23)

Q  m_ p1 þ m_ p2 v1

(25)

COP  COPCDRC COPCDRC

  Exdes:Com ¼ m_ p1 þ m_ p2 Ta ðs2  s1 Þ

(30)

The exergy destruction in evaporators can be given as,

 Exdes:HT ¼ m_ p2 Ta ðs5  s4 Þ  ðh5  h4 Þ

Ta THT þ DTe

Ta TLT þ DTe

(31)

(32)

  Exdes:Gc ¼ m_ p1 þ m_ p2 ½ðh2  h3 Þ  Ta ðs2  s3 Þ

(33)

The exergy destructions in the two ejectors can be given as,

(26)

The improvement of COP for MDRC compared with CDRC is defined as,

DCOP ¼

where, T0 is a reference temperature maintained at 298.15 K and the reference pressure is set at 0.101 MPa throughout this study to obtained the reference enthalpy h0 and entropy s0. In the Eq. (29), 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 MDRC cycle can be derived as follows: The exergy destruction in compressor can be given as,

The exergy destruction in gas cooler can be given as,

where v1 is the suction specific volume of the compressor. The refrigeration COP of the MDRC can be calculated by,

Q COP ¼ W

(28)

  X  X  T T Exdes ¼ Exin  Exout þ Q 1 0  Q 1 0 T T in out X X þ Win  Wout

(24)

The volumetric refrigeration capacity is given as,

qv ¼ 

_ Ex ¼ m½ðh  h0 Þ  T0 ðs  s0 Þ

 Exdes:LT ¼ m_ s1 Ta ðs9  s8 Þ  ðh9  h8 Þ

The total refrigeration capacity can be obtained as,

Q ¼ QHT þ QLT

work potential which can be produced by a system when it becomes equilibrium with a reference environment. Exergetic analysis is often used to determine the maximum performance of system and identify the locations where exergy destruction occurs, and indicate the direction for potential thermodynamic improvement [36]. And the exergetic analysis can provide more realistic and accurate assessments than energetic analysis. Thus, in order to have deeper insights into the thermodynamic performance, exergetic analysis is applied in our studies. Therefore, applying the assumptions mentioned already, the system exergetic models are established as follows [37e39]: 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 [40],

(29) (19)

where the isentropic efficiency of the compressor his is calculated as follow [35],

his ¼ 0:815 þ 0:022

5

 Exdes:Eje1 ¼ Ta m_ p1 ð1 þ m1 Þs10  m_ p1 s3  m_ s1 s9

(34)

 Exdes:Eje2 ¼ Ta m_ p2 ð1 þ m2 Þs6  m_ p2 s5  m_ s2 s10

(35)

The total exergy destruction caused by the two expansion valves can be given as

Exdes:Ev ¼ m_ s1 Ta ðs8  s7 Þ þ m_ p2 Ta ðs4  s3 Þ (27)

3.3. Exergetic analysis In a real cycle system, the system includes various exergy destructions in each component. Exergy represents its maximum

(36)

Based on the exergy destructions in all components of the system above, the cycle total exergy destruction can be obtained as,

Exdes:tot ¼ Exdes:Com þ Exdes:Gc þ Exdes:Eje1 þ Exdes:Eje2 þ Exdes:Ev þ Exdes:HT þ Exdes:LT (37)

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The overall exergy efficiency of MDRC can be evaluated by the ratio of the effective exergy output to the rate of exergy input, and the effective exergy output can be gained by subtracting the total exergy destruction from effective exergy input. Thus the exergetic (second law) efficiency of system can be given as,

hEx ¼ 1 

Exdes:tot W

(38)

The system exergy efficiency improvement of the MDRC over the CDRC is evaluated by,

DhEx ¼

hEx  hEx:CDRC hEx:CDRC

(39)

In addition, the percentage of the exergy destruction in each component is defined by the ratio of the exergy destruction of each component to the work input of the system. Based on the theoretical model described above, the simulation code written by Fortran is developed to investigate the effect of different operating parameters on MDRC system performance, where the thermodynamic properties of CO2 are calculated by using REFPROP 7.1 [41]. It should be noted that the entrainment ratios m1 , m2 and the quality of the ejector 2 outlet refrigerant x2 have to satisfy the relationships x2 ¼ 1=ð1 þ m1 bÞ and m1 ¼ m2 ð1  bÞ=b  1 due to the mass conservation constrain for a steady-state operation of the cycle, and mass flow rate allocation ratio b has to be adjusted to match the specified refrigeration capacity ratio f. Therefore, we designed efficient iteration procedures, and the relative convergence tolerance of the iteration is set at 0.01%. The flowchart for MDRC simulation model is shown in Fig. 4. What is more, for illustrating the effectiveness of the two-stage ejector configuration to improve the system performance, the simulation model for conventional dual-evaporator refrigeration cycle shown in Fig. 1 is also established. 4. Results and discussion To investigate the performance characteristic of the modified cycle, the simulation conditions are given as follows: the gas cooler exit temperature TGc:o ranges from 35 to 50  C, the high evaporating temperature THT ranges from 5 to 5  C, the low evaporating temperature TLT ranges from 35 to 15  C, the temperature difference between refrigerant and cooled space is taken as a constant DTe ¼ 5  C, the discharge pressure Pdis varies from 8.5 to 12 MPa. Although the ejector component efficiencies vary with the operating conditions, for simplicity, the ejector efficiencies are assumed to be hn ¼ hd ¼ 0:8,and hm ¼ 0:85 by making reference to literatures [24,37,42]. In addition, the mass flow rate cross the compressor is assumed to be per unit mass flow rate, and the refrigeration capacity ratio f of the two evaporators is set in the range from 0.2 to 2.0. In the following analysis, effects of discharge pressure, evaporating temperature, gas cooler exit temperature and the refrigeration capacity ratio on the system performances are studied, respectively.

Fig. 4. Flowchart for MDRC simulation model.

12 MPa, the pressure lift ratio rPt and entrainment ratio mt vary in the ranges of 1.58e1.31 and 0.111e0.265, respectively. The MDRC cycle applying two-stage ejector configuration has the thermodynamic improvement potential due to the high pressure lift ratio. In order to show the system performance improvement potential of the two-stage ejector in dual-temperature CO2 transcritical cycle, the performance comparison between the two-stage ejector cycle (MDRC), single-stage ejector cycle (EDRC1 by Sarkar

4.1. Effect of discharge pressure Fig. 5 shows the effects of discharge pressure Pdis on the COP, exergy efficiency hex, pressure lift ratio rPt ð¼ P1 =P9 Þ and entrainment ratio mt . It can be observed that there exists an optimum discharge pressure where the both system COP and exergy efficiency hEx reach the maximum values at the given operating condition. The pressure lift ratio rPt decreases with the increasing discharge pressure, and the entrainment ratio mt shows opposite variation tendency. When the gas cooler pressure varies from 8.5 to

Fig. 5. Variation of system performance with the discharge pressure.

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7

Table 1 Performance comparison among different cycles at optimum discharge pressure. Cycles Two-stage ejector Single-stage ejector Without ejector

MDRC EDRC1 [25] EDRC2 [19] CDRC

COPmax

Pdis.opt/MPa

Tdis/ C

rPt

mt

COP improvements (%)

1.749 1.539 1.378 1.271

10.15 10.05 10.75 10.80

100.5 108.3 117.6 129.9

1.492 1.281 1.119 e

0.244 0.362 0.919 e

37.61% 21.09% 8.42% e

Operating conditions: Tgc.o ¼ 40  C, THT ¼ 5  C, TLT ¼ 20  C, f ¼ 1; Ejector model presented by Ref. [25]: the pressure drop through secondary nozzle is taken into account and fixed at 0.03 MPa, ejector efficiencies are assumed to be hn ¼ hd ¼ 0:8, hm ¼ 1, compressor efficiency is hc ¼ 0:75.

[25] and EDRC2 by Liu [19]) and the baseline cycle (CDRC) at optimum discharge pressure under the given operating condition are carried out, and the detail data are listed in Table 1. Here, it should be mentioned that the optimum discharge pressure is searched with a calculation step size of 0.05 MPa with respect to the maximum COP value when other operating parameters are fixed. Obviously shown in Table 1, the ejector enhanced cycles all exhibit higher system COP over CDRC. Under the given operating condition, the system COP of MDRC, EDRC1 and EDRC2 cycles are 37.61%, 21.09% and 8.42% higher than that of CDRC. In addition, the MDRC outperforms EDRC1 and EDRC2 in term of system COP, pressure lift ratio rPt and discharge temperature. Compared with EDRC1 and EDRC2, the system COP of MDRC cycle is improved by 13.64% and 26.92%, and the pressure lift ratio is enhanced by 16.47% and 33.3%, respectively. The main reason for this is that the large pressure drop between gas cooler and low-level temperature evaporator is utilized by the first stage ejector to get much more expansion work recovery. In this case, the MDRC exhibits a higher pressure lift ratio rPt and system COP. Therefore, it could be concluded that the twostage ejector used in two different temperature levels (pressure drop) refrigeration cycle could recover the expansion work more efficiently and exhibits higher system performance than the cycle using a single ejector. Fig. 6 shows the variation of exergy destruction percentage in each component with discharge pressure. It can be seen that the exergy destruction percentage in gas cooler has a remarkable increase with the increasing discharge pressure and accounts for the largest percentage (29.23%) at optimum discharge pressure. The main reason is that the heat from gas cooler is rejected to surroundings that cannot be effectively utilized in this system. Thus, if the high grade heat from gas cooler could be used for air heating or water heating, the exergy destruction in gas cooler could be obviously reduced, and the system exergy efficiency may be significantly enhanced. The exergy destruction in compressor slightly

Fig. 6. Variation of exergy destruction percentages with the discharge pressure.

changes with the variation of discharge pressure, and the exergy destruction accounts relatively large percentage of the total exergy input due to the low isentropic efficiency of compressor. The exergy destruction percentage in the individual ejector shows opposite variation tendency with the increasing discharge pressure, and the sum exergy destruction of the two ejectors at optimum discharge pressure is the third largest exergy destruction (16.91%). Therefore, it needs to use advanced design technique to reduce the exergy destruction in ejector in practical applications. The throttling processes cause the fourth largest exergy destruction. The exergy destructions in high temperature evaporator and low temperature evaporator are relatively minor and have slight changes with increasing discharge pressure. This is because the effective temperature difference between refrigerant and cooled space in evaporator is assumed to be at a fixed value (DTe ¼ 5  C), which results in the slight changes of exergy destructions in the two evaporators. The detailed exergy comparisons between CDRC and MDRC are shown in Fig. 7 and Table 2, when the operating condition is kept as THT ¼ 5  C, TLT ¼ 20  C and the optimum discharge pressure is specified to be 10.15 MPa. It can be noted that MDRC shows 25.39% higher exergy output than that of CDRC under the given operating condition. In addition, it can be seen that the largest exergy destruction occur in the expansion valves for CDRC (39.01%) due to the large throttling pressure difference, while exergy destruction from the cooling process in gas cooler for MDRC contributes about 29.23% to the total exergy input. In this case, we could infer that the expansion losses in the expansion valves could be effectively recovered by adopting the two-stage ejector in MDRC.

Fig. 7. Grassmann diagram depicting the exergy destructions in CDRC and MDRC cycles.

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Table 2 Exergy input, destructions and output at optimum discharge pressure.

Exergy input Exergy destructions

Components

MDRC

CDRC

Compressor Gas cooler Compressor Two-stage ejector Expansion valves LT Evaporator HT Evaporator

100% 29.23% 20.25% 16.91% 11.59% 2.05% 1.65% 18.32%

100% 30.38% 13.08% e 39.01% 1.60% 1.32% 14.61%

Exergy output

Operating conditions: Pdis.opt ¼ 10.15 MPa, Tgc.o ¼ 40  C, THT ¼ 5  C, TLT ¼ 20  C,

f ¼ 1.

Table 3 shows the detailed thermodynamic data of all the state points of MDRC in terms of pressure, temperature, enthalpy, entropy and exergy flow rate under the given condition: the gas cooler exit temperature is 40  C, the high and low-level evaporating temperatures are 5 and 20  C, respectively, and the corresponding optimum discharge pressure is 10.15 MPa. It should be mentioned that the mass flow rate of each state points is obtained by applying the principle of mass and energy conversation based on the assumption that the mass flow rate through the compressor is considered to be per unit mass flow rate. Based on the analysis of discharge pressure on system performance above, it can be conclude that the discharge pressure significantly affects the system performance. Therefore, the flowing analysis for other operating parameters on system operating characteristic are all based on the optimum discharge pressure. 4.2. Effect of evaporating temperatures The effects of the evaporating temperatures THT and TLT on the performances of the modified cycle at optimum discharge pressure are shown in Fig. 8. It can be seen that COPmax increases as an increasing of THT and TLT . Furthermore, the influence of the lowlevel evaporating temperature TLT on the variation of COPmax is more obvious than that of the high-level evaporating temperature THT . When THT is set at 5  C, TLT varies from 35 to 15  C, the COPmax is improved by 50.5%. In addition, the exergy efficiency hEx gets higher value at lower THT and reaches the maximum values at an optimum low-level evaporating temperature TLT as shown in Fig. 8. When THT is 5  C, the maximum exergetic efficiency hex reaches 18.69%.

Fig. 8. Variation of COPmax and exergy efficiency with the evaporating temperatures.

Fig. 9 shows the variation of pressure lift ratios and entrainment ratios with the evaporating temperatures THT and TLT . For the twostage ejector configuration, as the increasing low-level evaporating temperature TLT , the pressure lift ratio rPt decreases and the entrainment ratio mt increases accordingly. When THT is 5  C and TLT varies from 35 to 15  C, the pressure lift ratio rPt is reduced by 15.8% and entrainment ratio mt is increased by 10.4%. For the individual ejector, it has been proved that the ejector performance has a direct relationship with the pressure ratio between the primary flow and secondary flow. As well known, the optimum discharge pressure reduces as the increasing evaporating temperature for transcritical CO2 refrigeration cycle [34], and the similar variation tendency has been obtained as increasing the THT and TLT for MDRC. Therefore, increasing the TLT at a specified high-level evaporating temperature THT leads to a decrease of the expansion ratio of ejector 1 ðPdis:opt =P9 Þ due to the decreasing Pdis:opt . Consequently, the pressure lift ratio rP1 ð¼ P10 =P9 Þ and the exit pressure P10 of ejector 1 decrease, and the expansion ratio ðP5 =P10 Þ and the pressure lift ratio rP2 ð¼ P1 =P10 Þ of ejector 2 decrease accordingly, as shown in Fig. 9. Therefore, the pressure lift ratio of the two-stage ejector rPt decreases as the increasing THT . By employing similar analysis principle, it could be found that the proposed cycle shows higher rPt and rP2 and obtains lower rP1 at higher THT under the given low-level evaporating temperature TLT . 4.3. Effect of gas cooler exit temperature

Table 3 Parameters of state points for the cycle at optimum discharge pressure. State points

P (MPa)

T ( C)

h (kJ/kg)

s(kJ/kg K)

m_ (kg/s)

Ex (kW)

1 2 3 30 4 5 50 6 60 7 8 9 10 100

2.75 10.15 10.15 1.97 3.97 3.97 2.59 2.75 2.59 2.75 1.97 1.97 2.59 1.97

8.7 104.3 40.0 20.0 5.0 5.0 10.7 8.7 10.7 8.7 20.0 20.0 10.7 20.0

434.75 509.45 310.92 290.23 310.92 427.48 415.74 385.24 383.09 179.42 179.42 436.89 353.63 344.59

1.892 1.942 1.349 1.369 1.397 1.816 1.828 1.705 1.703 0.926 0.931 1.949 1.591 1.579

1 1 1 0.47 0.53 0.53 0.53 1.24 1.24 0.24 0.24 0.24 0.71 0.71

180.81 240.52 218.93 90.11 108.57 104.12 96.11 232.13 230.06 51.32 50.96 39.95 134.44 129.48

Cycle operating conditions: Pdis.opt ¼ 10.15 MPa, Tgc.o ¼ 40  C, THT ¼ 5  C, TLT ¼ 20  C, f ¼ 1. Ejector operating conditions: Ejector 1: Pn.i ¼ 10.15 MPa, Tn.i ¼ 40  C, Ps.i ¼ 1.97 MPa, Ts.i ¼ 20  C, Pd.o ¼ 2.59 MPa. Ejector 2: Pn.i ¼ 3.97 MPa, Tn.i ¼ 5  C, Ps.i ¼ 2.59 MPa, Ts.i ¼ 10.7  C, Pd.o ¼ 2.75 MPa.

The effects of gas cooler exit temperature on the performance are shown in Fig. 10. It can be seen that COPmax and exergy efficiency hEx all decrease with the increasing gas cooler exit temperature. When gas cooler exit temperature TGc:o ranges from 35 to 50  C, COPmax and hEx are decreased by 36.4% and 36.7%, respectively. It means that the increasing gas cooler exit temperature would significantly decrease the system COP. Fig. 11 shows the variation of the pressure lift ratios and entrainment ratios of the individual ejector and the two-stage ejector. It can been seen that the pressure lift ratio of the twostage ejector rPt increases as the increasing gas cooler exit temperature, while the entrainment ratio mt shows an opposite tendency. When the gas cooler exit temperature TGc:o varies from 35 to 50  C, the pressure lift ratio rPt and entrainment ratio mt of the twostage ejector varies in the ranges of 1.287e1.424 and 0.255e0.214, respectively. For the individual ejector, as the increasing gas cooler exit temperature TGc:o , the pressure lift ratio of ejector 1 rP1 increases from 1.217 to 1.356, and the pressure lift ratio of ejector 2

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Fig. 9. Variation of pressure lift ratios and entrainment ratios with evaporating temperatures.

Fig. 10. Variation of COPmax and exergy efficiency with gas cooler exit temperature at optimum discharge pressure.

rP2 shows a slightly decrease from 1.058 to 1.047, and m1 and m2 vary in the ranges of 1.359e1.271 and 0.546e0.459, respectively. The main reason for the variation tendency of pressure lift ratio with the increasing gas cooler exit temperature is that the pressure lift ratio has direct relationship with the available expansion ratio between the primary flow and secondary flow. The increasing gas cooler exit temperature result in an increase of the optimum discharge pressure, and this variation characteristic is indicated from the comprehensive simulation investigations for MDRC cycle, which is also proved to be similar to the conclusion from the published works about CO2 transcritical refrigeration cycle [34]. In this case, the expansion ratio of ejector 1 ðPdis:opt =P9 Þ increases as the increasing gas cooler exit temperature TGc:o due to the increasing optimum discharge pressure, which leads to increase the pressure lift ratio rP1 and the exit pressure of ejector 1 P10. Accordingly, the expansion ratio of ejector 2 ðP5 =P10 Þ decreases due to the increase of P10 under the specified high-level temperature (evaporating pressure), and the pressure lift ratio rP2 slightly decreases consequently as shown in Fig. 11. Ultimately, the pressure lift ratio of the two-stage ejector rPt is increased with the increasing gas cooler exit temperature. 4.4. Effect of refrigeration capacity ratio

Fig. 11. Variation of pressure lit ratios and entrainment ratios with the gas cooler exit temperature at optimum discharge pressure.

As know, the refrigeration capacity ratio f of dual-temperature refrigeration system often varies with the practical operating conditions. Hence, the effect of refrigeration capacity ratio on the system performance should be investigated. Fig. 12 shows the variation of specific refrigeration capacity q ð¼ Q =ðm_ p1 þ m_ p2 ÞÞ, and pressure lift ratio with the refrigeration capacity ratio. And the specific refrigeration capacity q hardly has any changes, while the high-temperature refrigeration capacity qHT increases and the lowtemperature refrigeration capacity qLT decreases with the increasing f. It should be noted that in the cycle simulation, the refrigeration capacity ratio f is obtained by adjusting the mass flow rate allocation ratio b. When f is selected at a higher value, the mass flow rate of low-temperature evaporator as secondary flow entrained by the two-stage ejector configuration is reduced accordingly. Thus the pressure lift ratio of the two-stage ejector rPt actually increases, as shown in Fig. 12.

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32.6% and the exergy efficiency improvement DhEx of the MDRC over the CDRC varies in the range of 23.5e31.9%. Furthermore, the variation of exergy destruction percentage in the individual component with f is shown in Fig. 14. As the mass flow rate through each component varies, the exergy destruction varies correspondingly. The exergy destructions caused by compressor and gas cooler can be basically considered to maintain invariable. The exergy destruction contributions of the two evaporators show opposite variation tendency as the increasing f due to the inverse mass flow rate variation characteristic in the two evaporators. The same trend of exergy destruction contributions in ejector 1 and ejector 2 can also be observed in Fig. 14. However, the exergy destruction caused by expansion valves shows a remarkable increase with the increasing f due to the increasing mass flow rate through the two expansion valves. This may be the main reason for decreasing exergy efficiency hEx as shown in Fig. 13. Fig. 12. Variation of specific refrigeration capacity and pressure lift ratio with refrigeration capacity ratio.

Fig. 13. Effect of refrigeration capacity ratio on the exergetic performance of MDRC.

Fig. 13 shows the variation of the system exergy efficiency and its improvements DhEx over CDRC cycle with refrigeration capacity ratio. It could be observed that hEx decreases with the increasing f, whereas, the exergy efficiency improvement shows opposite variation tendency. When f varies from 0.2 to 2.0, hEx is reduced by

5. Conclusion A modified two-stage ejector enhanced dual-evaporator transcritical CO2 refrigeration is proposed in this paper. Energetic and exergetic analysis are conducted on the thermodynamic performances of this cycle. The effects of key operating parametric on performance are discussed. From the discussion above, the modified cycle could simultaneously obtain dual cooling temperatures with higher COP and exergy efficiency. Meanwhile the modified cycle has more advantages in terms of optimum discharge pressure and discharge temperature due to the efficient expansion work recovery effect of the two-stage ejector. It is also found that amount of exergy destruction in the gas cooler compressor and two-stage ejector accounts for large percentage in total exergy destruction. Thus, effective methods for reducing these exergy destructions are further required to enhance system performance. What is more, the parametric study shows that discharge pressure, low-level evaporating temperature and gas cooler exit temperature have significant effects on system COP and exergy efficiency. It should be mentioned that although the computational model developed for the ejector is relatively simple in respect of its practical application in real system, it is hoped that the proposed cycle could provide useful guidance to the development of dual-evaporator transcritical CO2 refrigeration. Thus, it should be emphasized that further studies, especially experimental studies, are needed to confirm the practical usefulness of this cycle. Appendix A. Calculation steps for an ejector

Fig. 14. Variation of exergy destruction percentages with refrigeration capacity ratio.

Under the specified ejector efficiencies (hn ,hm , and hd ) as well as the given ejector working condition including the inlet and outlet state parameters (Tn:i ,Pn:i ,Ts:i Ps:i and Pd:o ), the detailed thermodynamic calculation steps for the entrainment ratio m of an ejector are presented as follows: (ⅰ) The inlet properties of the primary and secondary flows are obtained by using the property subroutines at given Tn:i ,Pn:i ,Ts:i and Ps:i . The exit velocity at the nozzle un:o is calculated by using Eq. (7), in which hn:is:o ¼ f ðPn:o ¼ Ps:i ; sn:is:o ¼ sn:i Þ. (ⅱ) Some initial guess values of m are assumed for the iterations. (ⅲ) Using Eqs. (9)e(11) to calculate the mixing velocity umix. And then the specific enthalpies of the mixed fluid entering and leaving the diffuser (i.e. hd:i and hd:o ) are obtained by using Eqs. (12) and (13) and thus other properties like sd:i can be calculated. (ⅳ) Using Eq. (15) to calculate the ideal exiting specific enthalpy of the mixed flow hd:is:o. And then the back pressure 0 Pd:o ¼ f ðhd:is:o ; sd:is:o ¼ sd:i Þ could be obtained. 0 (ⅴ) If the condition Pd:o ¼ Pd:o is not satisfied, steps (ii)e(iv) will pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi be repeated by using a new value of m ðm ¼ hn hm hd

Please cite this article in press as: Bai T, et al., Thermodynamics analysis of a modified dual-evaporator CO2 transcritical refrigeration cycle with two-stage ejector, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.02.104

T. Bai et al. / Energy xxx (2015) 1e11

ðhn:i  hn:is:o Þ=ðhd:is:o  hd:i Þ  1Þ until the condition is satisfied. Then the properties of the exit fluid, entrainment ratio m and pressure lift ratio rP of the ejector are obtained. It should be mentioned that if the inlet parameters and entrainment ratio (Tn:i ,Pn:i ,Ts:i ,Ps:i and m) of the ejector are known under the specified ejector efficiencies (hn ,hm , and hd ), the iteration calculation would not be needed, and the exit property parameters can be calculated directly by following the steps (i), (iii) and (iv) mentioned above. References [1] Radermacher R, Kim K. Domestic refrigerators: recent developments. Int J Refrig 1996;19:61e9. [2] Sarkar J, Bhattacharyya S, Ram Gopal M. Transcritical CO2 heat pump systems: exergy analysis including heat transfer and fluid flow effects. Energy Convers Manag 2005;46:2053e67. [3] Liu F, Groll EA. Study of ejector efficiencies in refrigeration cycles. Appl Therm Eng 2013;52:360e70. [4] Lu Y, He W, Wu Y, Ji W, Ma C, Guo H. Performance study on compressed air refrigeration system based on single screw expander. Energy 2013;55:762e8. [5] Yang JL, Ma YT, Liu SC. Performance investigation of transcritical carbon dioxide two-stage compression cycle with expander. Energy 2007;32:237e45. [6] Chunnanond K, Aphornratana S. Ejectors: applications in refrigeration technology. Renew Sustain Energy Rev 2004;8:129e55. [7] Chen X, Omer S, Worall M, Riffat S. Recent developments in ejector refrigeration technologies. Renew Sustain Energy Rev 2013;19:629e51. [8] Groll EA, Kim J-H. Review article: review of recent advances toward transcritical CO2 cycle technology. HVAC&R Res 2007;13:499e520. [9] Liu JP, Chen JP, Chen ZJ. Thermodynamic analysis on trans-critical R744 vapor compression/ejection hybrid refrigeration cycle. In: Proceedings of the fifth IIR-GUSTAV Lorentzen conference on natural working fluids, Guangzhou,China; 2002. [10] Sun FT, Ma YT. Thermodynamic analysis of transcritical CO2 refrigeration cycle with an ejector. Appl Therm Eng 2011;31:1184e9. [11] Elbel S, Hrnjak P. Experimental validation of a prototype ejector designed to reduce throttling losses encountered in transcritical R744 system operation. Int J Refrig 2008;31:411e22. [12] Li DQ, Groll EA. Transcritical CO2 refrigeration cycle with ejector-expansion device. Int J Refrig 2005;28:766e73. [13] Manjili FE, Yavari MA. Performance of a new two-stage multi-intercooling transcritical CO2 ejector refrigeration cycle. Appl Therm Eng 2012;40:202e9. [14] Yari M, Sirousazar M. Cycle improvements to ejector-expansion transcritical CO2 two-stage refrigeration cycle. Int J Energy Res 2008;32:677e87. [15] Sharma V, Fricke B, Bansal P. Comparative analysis of various CO2 configurations in supermarket refrigeration systems. Int J Refrig 2014;46:86e99. [16] Ge YT, Tassou SA. Thermodynamic analysis of transcritical CO2 booster refrigeration systems in supermarket. Energy Convers Manag 2011;52: 1868e75. [17] Shin E, Park C, Cho H. Theoretical analysis of performance of a two-stage compression CO2 cycle with two different evaporating temperatures. Int J Refrig 2014;47:164e75. [18] Elakdhar ENM, Kairouani L. Analysis of a compression-ejection cycle for domestic refrigeration. Ind Eng Chem Res 2007;46:3639e44. [19] Liu Y, Xin T, Cao L, Wan C, Zhang M. Compression-injection hybrid refrigeration cycles in household refrigerators. Appl Therm Eng 2010;30:2442e7.

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Please cite this article in press as: Bai T, et al., Thermodynamics analysis of a modified dual-evaporator CO2 transcritical refrigeration cycle with two-stage ejector, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.02.104