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Performance analysis of an advanced ejector-expansion autocascade refrigeration cycle
Accepted Manuscript Performance analysis of an advanced ejector-expansion autocascade refrigeration cycle
Ye Liu, Jianlin Yu PII:
S0360-5442(18)31997-2
DOI:
10.1016/j.energy.2018.10.016
Reference:
EGY 13913
To appear in:
Energy
Received Date:
13 May 2018
Accepted Date:
03 October 2018
Please cite this article as: Ye Liu, Jianlin Yu, Performance analysis of an advanced ejectorexpansion autocascade refrigeration cycle, Energy (2018), doi: 10.1016/j.energy.2018.10.016
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ACCEPTED MANUSCRIPT Performance analysis of an advanced ejector-expansion autocascade refrigeration cycle Ye Liu, Jianlin Yu Department of Refrigeration & Cryogenic Engineering, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China
Abstract In this paper, an advanced ejector-expansion autocascade refrigeration cycle (AEARC) using hydrocarbon mixture R290/R170 for applications in low-temperature freezers is proposed. In the AEARC, a two-phase flow driven ejector is introduced with new cycle configuration to reduce the thermodynamic loss in throttling process and lift the suction pressure of compressor significantly. The performances of the AEARC and traditional autocascade refrigeration cycle (ARC) are compared using energy and exergy analysis methods, and several important parameters for AEARC are also discussed in detail. The results indicate that AEARC is feasible and there are obvious performances improvements in the COP , volumetric refrigeration capacity and exergic efficiency. Especially, in AEARC, the COP and volumetric refrigeration capacity increase by 80.0% and 78.5% at most compared to that of ARC, respectively. In general, the AEARC can provide significant performance improvement and produce better actual operation benefit. The potential practical advantages may be worth further attention in future research. Keywords Hydrocarbon mixture; Ejector; Autocascade refrigeration cycle; Performance improvement
Corresponding author. Tel.:+86-29-82668738. Fax:+86-29-82668725. Email: [email protected] 1
ACCEPTED MANUSCRIPT Nomenclature COP
cooling coefficient of performance
h
specific enthalpy ( kJ kg -1 )
m
mass flow rate ( kg s -1 )
p
pressure ( kPa )
Q e
cooling capacity ( kW )
E xd
exergy destruction ( kW )
s
specific entropy( kJ kg -1 K 1 )
x
vapor quality
T
Kelvin temperature ( K )
t
Celsius temperature (℃)
W
compressor input power ( kW )
rpj
pressure lift ratio
rp
pressure ratio of compressor
specific volume( m 3 kg -1 )
qv
volumetric refrigeration capacity( kJ m -3 )
ex
specific exergy( kJ kg -1 )
w
velocity ( m s -1 )
z
mass fraction of R290 in the mixture
Greek letters
efficiency
entrainment ratio 2
ACCEPTED MANUSCRIPT
exergy destruction percentage
Subscripts 0
reference state
n
nozzle section of ejector
d
diffuser section of ejector
m
mixing section of ejector
ex
exergy
exd
exergy destruction
cm
compressor
con
condenser
eva
evaporator
tot
total exergy destruction
is
isentropic procedure
sf
secondary flow
pf
primary flow
mf
mixing flow
1 - 12
state points of refrigerant
1. Introduction Autocascade refrigeration systems are very effective for producing low temperature cooling over a span of temperatures [1, 2]. In an autocascade system, the autocascade refrigeration cycle (ARC) usually employs a single compressor and a zeotropic refrigerant mixture comprising the low boiling and high boiling refrigerants, along with a series of vapor-liquid separators and cascade heat exchangers, which makes it possible for the system to reach low temperature. 3
ACCEPTED MANUSCRIPT Autocascade refrigeration systems offer many benefits, such as a relatively low compression ratio and high volumetric efficiency. These features have led to the popularity of ARC system application for low temperature freezers and natural gas liquefaction [3, 4]. Actually, there are other ways to reach effective deep refrigeration, such as the mixed refrigerant (gas) cycle (MRC). The MRC is a single refrigerant circuit with one compressor and without phase separators, which is also known as the Joule–Thomson cycles using mixed refrigerant [5, 6]. In the MRC, multi-component mixtures are usually in use in order to achieve demanded low temperatures and obtain enhanced performance [7]. Previous studies have shown that these two typical cycle configurations ARC and MRC can be used for providing low temperature refrigeration. Their performances depend strongly on the composition of mixtures, and different cycle configuration has different optimal mixture composition. In the cases of optimal mixtures, both cycles can provide approximately equal performance [8]. Overall, many studies on ARC and MRC systems have been conducted over the past years. Early, Kim et al. [9] investigated the performance of an autocascade refrigeration system using zeotropic refrigerant mixtures of R744/R134a and R744/R290. Performance test and simulation indicate that the ARC system has a merit of low operating pressure, but lower coefficient of performance (COP) is a disadvantage. Du et al. [10] experimentally studied the cycle characteristics of an auto-cascade refrigeration system with R23/R134a mixed refrigerants, and showed that High COP of the ARC system may be acquired when the charging concentration is around 30% (wt). Wang et al. [11] simulated an auto-cascade refrigerator operating with two vapor-liquid separators, and found that the main factors affecting COP include the pressure ratio, the composition of mixed refrigerants, the main stream ratio and the pressure. Recently, Sivakumar and Somasundaram [12] conducted exergy and energy analysis on three stage ARC system, and revealed that environmentally benign refrigerant mixture of R290/R23/R14 with the specified mass fraction was performing better at very low evaporating temperature. Zhang et al. [13] applied a fractionation heat exchanger in the R744/R290 auto-cascade refrigerator, and showed that it can 4
ACCEPTED MANUSCRIPT effectively improve the separation efficiency of R744/R290, and then lower the evaporating temperature. Rui et al. [14] carried out experimental investigation of the performance of a single-stage auto-cascade refrigerator for 190 K applications, and demonstrated the feasibility of the proposed R600a/R23/R14 ternary mixture for ARC systems. In addition, the composition behaviors of zeotropic mixtures in ARC systems were also studied by few researchers [15, 16]. Generally, the ARC has received more and more attention to deeply investigate its performance and develop its applications. As known, traditional throttling devices such as expansion valves and capillary tubes are usually used in conventional ARCs. From a thermodynamics point of view, the use of these throttling devices is main reason for lower COP of a conventional ARC due to the large irreversibilities in the throttling process. To recover this thermodynamic loss, an ejector as the expansion device can be used in the throttling process. Ejector expansion method is a technique that involves expansion work recovery, and it has proven to be effective in improving the performance of vapor compression systems [17]. Ejector expansion techniques for various vapor compression systems have rapidly developed in recent years owing to their outstanding performance enhancement potential [18-21]. For an example, some researchers have been focused on the ejector application to conventional single-stage vapor compression cycle for household refrigerator-freezers and air conditioners [2224]. Therefore, based on the knowledge about conventional ARCs, using an ejector as expansion device is also one of the alternative ways of improving cycle performance. In the authors' previous publications [25-27], three different designs of the ARCs with an ejector have been proposed. Overall, these cycle configurations showed a comparable performance improvement over the baseline cycle. Principally, a modified cycle design employing ejector needs to be able to improve the performance by as much as possible over a conventional cycle. Therefore, we further propose a new cycle, i.e. an advanced EARC in this paper. The major advantage of this cycle configuration is the ability to sufficiently recover the expansion work in the throttling processes. This is because in the ejector enhanced ARC of the authors' previous study 5
ACCEPTED MANUSCRIPT [26], only the liquid phase flow from the separator is supplied to the ejector as primary flow, the enthalpy value and the flow rate is relative low. On the other hand, the vapor phase flow from the separator is condensed and then expanded through the evaporative condenser and throttling valve, and is fed into the evaporator for refrigeration. Obviously, the potential expansion work in this flow circuit is not recovered. In the advanced EARC (AEARC), however, the primary flow of ejector comes from the condenser entirely. It has high enthalpy value and large flow rate. Thus, the ejector in AEARC could recover more expansion work and provide high pressure lifting ratio, and resulting in much more significant performance improvement. Furthermore, using the two-phase flow driven ejector in the AEARC provides very promising potential to yield a more efficient system in comparison to the conventional MRC system, because the main disadvantage of the MRC cycle is the very large thermodynamic loss in its throttling process (isenthalpic expansion). In general, the pressure ratio in the compressor of AEARC can be significantly reduced compared with MRC, thus increasing its efficiency due to reduced compressor power consumption. The purpose of the current research is to theoretically investigate thermodynamic performances of the proposed cycle using energetic and exergetic methods. And the performance of the novel cycle is compared to the conventional cycle. 2. Cycle description and modeling 2.1 Cycle description Fig. 1 (a) show the schematic diagram of the conventional single stage ARC system that mainly consists of a vapor compressor, a condenser, a vapor-liquid separator, a cascade heat exchanger (CHEX), two throttling devices, and an evaporator. On the basis of the ARC, a modified ARC that includes an additional ejector at the condenser exit is proposed, where it is named as advanced ejectorexpansion ARC (AEARC), as shown in Fig. 1(b). In this novel cycle configuration, the two-phase refrigerant mixture is used to drive the ejector which lifts the compressor suction pressure through expansion work recovery. For this reason, the AEARC has a higher potential to improve the system than the ARC. Fig. 1(c) shows 6
ACCEPTED MANUSCRIPT the P-h diagram of the AEARC. The working principle of the AEARC is as follows: the zeotropic refrigerant mixture vapor discharged from the compressor (Point 2) flows through the condenser and then enters the ejector as a primary flow (Point 3, two-phase state). The vapor exiting from the CHEX (Point 9) is entrained as a secondary flow by the ejector. The two-phase mixture of the primary and secondary flows leaves the ejector to the separator (Point 4) and is then separated into liquid (Point 6) and vapor phases (Points 5, 1). A portion of the vapor mixture with more low-boiling point component returns to the suction of the compressor (Point 1) for the next cycle. At the same time, another portion of the vapor mixture (Point 5) passes through the CHEX and then is condensed to liquid (Point 10), which is expanded in the first throttling device (Point 11) and then evaporated in the evaporator (Point 12) by the heat received from the cooled objects. The saturated liquid mixture with more high-boiling point component (Point 6) passes through the second throttling device and then mixes the vapor from the evaporator (Points 7, 12 and 8). The mixing two-phase stream is passed the CHEX and then evaporated to vapor (Point 9), and it forms a complete cycle. It should be noted that in the AEARC, although the separation process is shifted from the high pressure location downstream of the condenser to a lower pressure location, this will still provide sufficient potential for the autocascade to work. The reason is that the outlet refrigerant mixture of the condenser is fed into the ejector as primary flow, and it entrains the vapor refrigerant mixture coming from the CHEX. In this case, the outlet refrigerant mixture of the ejector is still in two phase state, and is then separated into liquid and vapor phase streams through the separator. Thermodynamically, the concentrations of the vapor phase stream of the refrigerant mixture from the separator still has more low-boiling point component, which is the same as the concentrations of the refrigerant mixture from the condenser. This could ensure the evaporator to provide cooling at lowest possible temperature with the sufficient low boiling temperature component. On the other hand, the AEARC also could recover more expansion work and provide high pressure lifting ratio, and result in reaching lower temperatures. 7
ACCEPTED MANUSCRIPT
Fig. 1 (a). The schematic diagram for ARC system
Fig. 1 (b). The schematic diagram for AEARC system;
8
ACCEPTED MANUSCRIPT Fig. 1 (c). The schematic P-h diagram for the AEARC The performances of AEARC are theoretically evaluated based on the energetic and exergetic methods. The following assumptions are made to simplify the analysis: (1) All components are assumed to be a steady-state and steady-flow process. (2) The compression process in the compressor is irreversible and has variable isentropic efficiency which is related to the compression ratio. (3) The flow through the ejector is one-dimensional, steady state and adiabatic. (4) The velocities of the refrigerant are negligible at the primary fluid inlet, secondary fluid inlet and the outlet of ejector. (5) Flow losses in the ejector are defined in terms of isentropic efficiencies in the nozzle, mixing section and diffuser that are assumed to be constant. (6) Mixing in the ejector occurs at constant pressure and in a constant-area section. (7) The expansion processes in throttling devices are isenthalpic. (8) The vapor and liquid from the phase separator are both saturated. (9) The refrigerant outlet flow is considered as a saturated state in the evaporator, condenser and CHEX. (10)Refrigerant pressure drop and heat losses in the cycle are neglected.
Fig. 2 The schematic of the ejector 2.2 Mathematical models According to the above assumptions, the mathematical model of the ejector is obtained by employing the steady flow energy equations and mass, momentum balance equations. The schematic of the ejector is shown in Fig. 2. Note that there are
9
ACCEPTED MANUSCRIPT two models can be used to simulate the ejector. One is the constant-area mixing model and the other one is the constant-pressure mixing model. Literature review indicates that the constant-pressure mixing ejector provides better performance than the constant-area mixing ejector, which was widely used by many researchers [11, 12, 28].
Thus, the 1-D constant-pressure mixing model and the homogeneous flow
model are applied in this paper. The entrainment ratio is key parameter to evaluate the ejector’s performance, and it can be defined as:
m sf / m pf
(1)
where m sf and m pf is the mass flow rate of the second flow and primary flow, respectively. It should be noted that the detailed principal of ejector is not described in this paper, as it is already a matured knowledge. The detailed ejector modelling can be obtained in the author’s published papers [25-27]. Based on the mass, momentum and energy conservation, the ejector entrainment ratio can be found. Under the assumption that the kinetic energy of refrigerant at the outlet of the ejector can be negligible, so the entrainment ratio of the ejector as an important performance parameter can be obtained as follow:
n m d ((h3,n1 h3,n 2,is ) /(h4,d ,is h4,m2 )) 1
(2)
For the compressor, the input power can be expressed as
Wc m 1 (h2 h1 ) m 1 (h2,is h1 ) / cm
(3)
where m 1 is the mass flow rate of the compressor inlet, h1 is the refrigerant specific enthalpy at the compressor inlet, h2,is is the refrigerant specific enthalpy at the outlet of the compressor under the isentropic compression processes, cm is compressor isentropic efficiency, which can be obtained [26, 29], 10
ACCEPTED MANUSCRIPT cm 0.874 0.0135rp 0.874 0.0135( P2 / P1 )
(4)
where rp the pressure lift ratio of the compressor, P1 and P2 is the refrigerant pressure at the inlet and outlet of the compressor, respectively. 2.3 system performance For the condenser, the amount of heat rejected by the condenser is given by:
Q c m 1 (h2 h3 )
(5)
For the evaporator, the refrigeration capacity is calculated using the following equation:
Q e m 11 (h12 h11 )
(6)
where m 11 is the mass flow rate of the evaporator, h11 is the refrigerant specific enthalpy at the evaporator inlet, h12 is the refrigerant specific enthalpy at the outlet of the evaporator. Volumetric refrigeration capacity based on the specific suction volume of the compressor is given by:
qv Q e / m 111 (h12 h11 ) / 1
(7)
where 1 is suction specific volume of the compressor. The coefficient of performance (COP) for is calculated by:
COP Q e / W
(8)
The basic equation obtained from the conservation law of energy in the CHEX is written as:
m 5 (h5 h10 ) m 9 (h9 h8 )
(9)
where m 5 and m 9 are the mass flow rates in the CHEX, h5 , h10 , h8 and h9 are the refrigerant specific enthalpies at the CHEX inlets and outlets, respectively. The mass balance equations for the ejector and separator can be written as:
m 3 m 9 m 4
(10) 11
ACCEPTED MANUSCRIPT m 4 m 1 m 5 m 6
(11)
Based on the definitions of entrainment ratio in equation (1) and vapor quality, the entrainment ratio of the ejector and the ejector outlet quality are expressed by:
m 9 / m 3
(12)
x4 (m 1 m 5 ) / m 4
(13)
To evaluate the exergy destructions in the AEARC system, the exergy analysis is further conducted in this study [30]. When the kinetic and potential energies are neglected, the specific exergy of refrigerant at any state point can be defined as [31, 33]:
ex (h h0 ) T0 ( s s0 )
(14)
where h0 and s0 are the enthalpy and entropy of the refrigerant at ambient temperature T0 . The exergy destruction in each component is calculated by the equation:
E xd m i exi m o exo Q (1 T0 / T ) W
(15)
where the first term on the right-hand side is the sum of the exergy input, the second term is the sum of the exergy output, the third term is the exergy of heat transferred (Note that the output heat in condenser is considered negative, and the input heat in evaporator is considered positive), while the last term is the exergy of the mechanical work added to the cycle system which is also considered positive. Based on the above equation, the exergy destruction in each component can be written as follows: Compressor:
E xdcom m 1T0 ( s2 s1 )
(16)
Condenser:
E xdcon m 1 ((h2 h3 ) T0 ( s2 s3 )) Qc (1 T0 / Tc )
(17)
Ejector:
E xdejc m 1 (h3 T0 s3 ) m 9 (h9 T0 s9 ) m 4 (h4 T0 s4 ) 12
(18)
ACCEPTED MANUSCRIPT CHEX:
E xdche m 5 ((h5 h10 ) T0 ( s5 s10 )) m 9 ((h8 h9 ) T0 ( s8 s9 ))
(19)
Evaporator:
E xdeva m 5 ((h11 h12 ) T0 ( s11 s12 )) Q e (1 T0 / Te )
(20)
Throttling devices:
E xd thr1 m 6T0 ( s7 s6 )
(21)
E xd thr2 m 5T0 ( s11 s10 )
(22)
The total exergy destruction in the system is the sum of exergy destruction in different components of the cycle system and is given by:
E xd tot E xdcom E xdcon E xdejc E xdche E xdeva E xd thr1 E xd thr2
(23)
Exergetic efficiency for the AEARC system is given by the following equation:
ex 1 E xd tot / W cm
(24)
The exergy destruction percentage for each component with respect to total input exergy is given by:
exd E xd /W cm
(25)
Based on the above theoretical model of AEARC, the simulation program has been developed to investigate the effect of different operating parameters on cycle performances. The refrigerant thermodynamic properties are calculated by using NIST database and subroutines [33]. In addition, note that the modeling for the ARC cycle without the ejector is not presented here for simplicity, whereas the relevant simulations are also conducted for performance comparison. 3. Simulation and results discussion In 2014, the Directive 517/2014 [34] was introduced by European Parliament to reduce the use of high-GWP greenhouse gases in order to limit global climate change. Thus the widely used refrigerants with high GWP values should be gradually phased out and replaced by low-GWP alternatives. Therefore, in the following simulations, the zeotropic refrigerant mixture R290/R170 is selected as a working fluid for 13
ACCEPTED MANUSCRIPT evaluating the performances of AEARC and ARC. The following operating conditions are assumed: the condenser outlet temperature tc ranges from 30 to 50℃, the vapor quality at the condenser outlet x3 is in the range of 0.465 to 0.615, the evaporator outlet temperature te varies from -65 to -40°C. The mass composition of R290 in the mixture R290 / R170 z1 is varied from 0.42 to 0.65. The working fluid flow in the ejector is very complicated, therefore, the ejector component efficiencies are usually used to consider the irreversibility losses in the working process. In addition, From the open literature studies, it could be found that the constant component efficiencies are widely used, due to that, the ejector in this study is assumed to have the following efficiencies: n 0.8 , m 0.95 and d 0.8 [26, 35]. The refrigerant mass flow rate at the compressor inlet is assumed to be
0.1 10-2 kg / s . The simulation results of AEARC and ARC under typical operating conditions are listed in Table 1, where tc 40℃ , te 50℃ , x3 0.5 , z1=0.5. The calculated thermodynamic properties for the AEARC in the operating condition are shown in Table 2. Table 1 The comparison between ARC and AEARC
parameters Coefficient of performance Volumetric refrigeration capacities (kJ/m3) Pressure ratio of compressor Pressure lift ratio of ejector Overall exergy destruction (W) Exergic efficiency Isentropic efficiency of compressor
ARC 0.349 328.1 17.6 / 241.8 0.182 0.64
Values AEARC 0.456 496.1 9.9 2.11 139.2 0.233 0.74
From the Table 1, it can be seen that the AEARC achieves better performances than ARC. The results indicate that the coefficient of performance (COP) and 14
ACCEPTED MANUSCRIPT volumetric refrigeration capacities qv of AEARC increase by 30.7% and 51.2% compared to those of ARC, respectively. Meanwhile, AEARC could increases the exergic efficiency by up to 28%, and decreases the overall exergy destruction by up to 42.4%. The results also shows that the pressure ratio of compressor in AEARC is reduced by 43.8% than that in ARC, and resulting in 15.6% higher compressor isentropic efficiency. It is obvious that the cycle configuration of AEARC could be considered as a promising modification to improve the conventional auto-cascade cycle performance. In the authors' previous publications, different designs of the ARCs with an ejector also have been proposed. It can be found that the novel auto-cascade refrigeration cycle (NARC) which is proposed in reference [25] improves the COP by 3.9-17.4% compared to the ARC for the given operating conditions, and the ejector enhanced auto-cascade refrigeration cycle (EARC) in reference [26] provides 8.4218.02% improvement in COP to that of ARC. However, according to the simulation results, the COP of the AEARC could offer 33.2% improvement to that of ARC according to Table 1 for the given conditions. Obviously, the AEARC could obtain much higher performance improvement than those of the previous two cycles because this cycle configuration has the ability to sufficiently recover the expansion work in the throttling processes. Table 2 The thermodynamic properties for the AEARC
State points 1 2 3 4 5 6 7 8 9 10
Temperature (℃) -32.4 96.2 40.0 -33.4 -32.4 -32.4 -49.7 -53.1 -45.7 -52.3
Pressure (kPa) 312.8 3101.4 3101.4 312.8 312.8 312.8 148.2 148.2 148.2 312.8 15
Vapor quality 1.00 1.00 0.50 0.86 1.00 0 0.10 0.57 1.0 0
mass fraction of R290 0.50 0.50 0.50 0.53 0.50 0.84 0.84 0.62 0.62 0.50
ACCEPTED MANUSCRIPT 11 12
-69.4 -50.0
148.2 148.2
0.09 1.00
0.50 0.50
Typical operating conditions: tc=40℃,te=-50℃,x3=0.5,z1=0.5
In order to explain the reason for the exergy efficiency improvement in AEARC, the exergy destruction of each component in both cycles under typical operating condition is displayed in Fig. 3. As it can be seen, most components of the AEARC exhibit a lower level of exergy destruction than those of ARC. This is because the use of ejector lifts the suction pressure, and thus reduces the pressure ratio and discharge temperature of the compressor. As a result, the exergy destructions of the compressor, the condenser and the cascade condenser of AEARC are 55.7%, 76.2% and 92.5% lower than those of ARC, respectively. Furthermore, the exergy destructions of the two throttling valves of AEARC are reduced by 98.3% and 98.6% compared to those of ARC. This fact indicates that the introduction of an ejector can effectively reduce the exergy destruction in the expansion process. Thus, the exergy efficiency of the AEARC can be improved by using the ejector due to smaller overall exergy destruction.
Fig. 3 The exergy destruction comparison for the components of two cycles To indicate the performance enhancement of the AEARC, the comparisons of COPs and volumetric refrigeration capacities between the ARC and AEARC under
various evaporating and condensing temperatures are shown in Figs. 4 and 5. Fig. 4 16
ACCEPTED MANUSCRIPT shows the variation of COPs and qv with t e in two cycles. It can be seen that as t e increases, both the COP and qv in two cycles rise. Clearly, the AEARC cycle outperforms the ARC in the COP within the whole evaporating temperature range. The COPs of AEARC range from 0.267 to 0.554, and they show 8.6% to 80.1% higher than those of the ARC. This is because that the introduction of ejector in AEARC significantly lifts the compressor suction pressure, and resulting in lower consumption power of compressor. For this reason, the COP of AEARC can achieve higher value, especially at a lower evaporating temperature. Also, the AEARC achieves improvement in the volumetric refrigeration capacities. According to Fig. 4, it can be found that qv of AEARC is 24.9% to 78.5% higher than that in ARC as t e increases. Fig. 5 displays the COP and qv tendencies of both the AEARC and ARC cycles versus t c . In order to ensure the simulation results to be reasonable, the selected t c of AEARC and ARC ranges from 35~50℃ and 30~45℃, respectively. From the results it can be seen that COPs in two cycles are all decreased as t c rises. As
expected,
AEARC
gives
a
higher
COP
and
a
higher
volumetric
refrigeration capacity under given condensing temperatures. In general, AEARC can achieve obvious COP and volumetric refrigeration capacity improvement.
17
ACCEPTED MANUSCRIPT
Fig. 4 The variation of COP and qv with evaporating temperature t e
Fig. 5 The variation of COP and qv with condensing temperature t c To further reveal the exergic performance enhancement of the AEARC, the comparisons of ex and E xd tot between the two cycles under different evaporating and condensing temperatures are shown in Figs. 6 and 7, respectively. It can be seen from Fig. 6 that as t e increases, the ex values of both the AEARC and ARC increase, 18
ACCEPTED MANUSCRIPT and the ex of AEARC is changed from 0.119 to 0.215. Moreover, the ex of AEARC is increased by 11.5% to 55.2% over the ARC. On the other hand, the E xd tot for two cycles are decreased with increasing t e . For the ARC, E xd tot varies from 179.9 to 603.5 W, which is nearly 38.6-68.7% greater than that for the AEARC. Furthermore, it also can be seen that the E xd tot of ARC attains higher value than that of AEARC under lower evaporating temperatures. Fig. 7 shows the variations of ex and E xd tot with different t c in two cycles. It can be seen that as t c rises, the ex and E xd tot in AEARC display uptrend, although the E xd tot shows a small increase. However, the
E xd tot of ARC increases obviously, it also leads to a decline in ex values. Therefore, the results of the study reveal that from an exergetic point of view, the performance of the AEARC is better than that of the ARC.
Fig. 6 The variation of ex and E xd tot with evaporating temperature t e
19
ACCEPTED MANUSCRIPT
Fig. 7 The variation of ex and E xd tot with condensing temperature t c Note that the vapor mass quality at state point 3, x3 , and the mass fraction of the mixture at state point 1, z1 , are important parameters for cycle performance evaluation. Figs. 8 and 9 display the COP and qv variation tendencies of both the AEARC and ARC cycles versus x3 and z1 , respectively. In Fig. 8, it can be seen that as x3 rises, the COP and qv of the AEARC both are decreased, but the COP and qv of the ARC are increased. Nevertheless, the qv of AEARC still are 14.8% to 53.9% higher than those of ARC. In addition, it can also be seen from Fig. 8 that the COP of AEARC is higher than that of ARC as x3 increased from 0.465 to 0.562
but it
appears to be lower that of ARC as the x3 increased further. This is due to that under the constant evaporating and condensing temperature, a higher x3 means there are more refrigerant flowed into the evaporator of ARC. However, in AEARC, the higher
x3 leads to the lower condensing pressure, and causes the entrainment ratio of the ejector and the refrigerant flow rate to drop. As a result, the COP of AEARC is decreased. Even so, in general, the AEARC can achieve better performance 20
ACCEPTED MANUSCRIPT improvement under appropriate operation parameters especially for the vapor mass quality of condenser outlet.
Fig.8 Variation of COP and qv in two cycles with x3
Fig. 9 Variation of COP and qv in two cycles with z1 Fig. 9 shows the variation of COP and qv in two cycles with z1 . It can be found that as z1 rises, the COPs of the two cycles are all increased. However, the qv of the 21
ACCEPTED MANUSCRIPT two cycles decrease with increasing z1 . The reason is that as z1 increased, the evaporating pressure is reduced with increasing the R290 mass fraction of the mixture in the evaporator, as a result, the qv is declined. On the other hand, the cooling capacity and the compressor input work of two cycles are decreased with increasing R290 mass fraction of the mixture. Meanwhile, the compressor input work is decreased more rapidly than the cooling capacity. In this case, the COP variation tendencies as shown in Fig. 8 are observed. The entrainment ratio
and the pressure lift ratio rpj are important
performance parameters of an ejector. In this work, the variations of and rpj with
t e are shown in Fig. 10, where tc 40℃ , x3 0.534 , z1 0.45 . It can be seen that as t e increases, the rises from 0.297 to 0.396. Meanwhile, the pressure lift ratio rpj is reduced from 3.06 to 1.89. From the results it can be seen that the rpj values are much greater than 1 in the whole range of given evaporating temperatures since the two-phase flow from the condenser is used to drive the ejector. Obviously, this is beneficial to the reductions of pressure ratio and power consumption of compressor. Therefore, the higher pressure lift ratio of ejector also gives rise to the COP improvement of AEARC. In addition, the ejector component efficiencies also influence the cycle performances. The variations of COP and rp with t e for different ejector component efficiencies are shown in Fig. 11, where tc 40℃ , x3 0.534 , z1 0.45 . The three ejector component efficiencies are assumed to have the same values, which is selected as 0.8, 0.85, and 0.9, respectively. It can be seen that when increasing the efficiencies, the COP of the AEARC is increased at the given conditions. The COP can be improved by 15.2-84.9% when the ejector component efficiencies are varied from 0.8 to 0.9. Meanwhile, the higher ejector component efficiencies also result in the decrease of the compressor pressure ratio due to the increased ejector. Therefore, higher ejector component efficiencies are conductive to recover more expansion work 22
ACCEPTED MANUSCRIPT and improve the COP, which could be beneficial for cycle performances.
Fig. 10 Variation of and rpj in two cycles with t e
Fig. 11 Variation of COP and rp in AEARC with t e
4. Conclusions This paper presents an advanced ejector-expansion autocascade refrigeration cycle using hydrocarbon mixture R290/R170 for applications in low-temperature freezers. In the proposed cycle, an ejector is introduced to reduce the thermodynamic 23
ACCEPTED MANUSCRIPT loss in throttling process and lift the suction pressure of compressor significantly. Energy and exergy analysis for the AEARC are conducted theoretically and compared with ARC under various operating conditions. From the foregoing analysis results, it can be concluded that AEARC is meaningful and there are significant performances improvements in COP , volumetric refrigeration capacity and exergic efficiency. Main operating parameters, including the evaporating and condensing temperatures, mass composition of R290, condenser outlet vapor quality and ejector efficiencies, have different extent effects on the performance improvements. Overall, the COP can achieve higher improvement at lower evaporating temperatures. In the given range of operating conditions, it is found that compared to the ARC, the AEARC has a COP improvement of 78.5% and a volumetric capacity improvement of 80.0% under the condition of tc 40℃ , te 65℃ , x3 0.534 , z1 0.45 . Thus, the application of ejector to this novel cycle configuration is more effective for improving the performance of the autocascade refrigeration cycle under reasonable operation conditions. And the new developed cycle could offer advantages for its applications in low-temperature freezers. Of course, further theoretical and experimental work for the AEARC based system will be necessary in the next step.
Acknowledgements The work presented in this paper is financially supported by National Natural Science Foundation of China (NSFC) under the grant No. 51776147. The authors would like to thank NSFC for the sponsorship.
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ACCEPTED MANUSCRIPT 33: 565-575. [4] Nayak HG, Venkatarathnam G. Performance of an auto refrigerant cascade refrigerator operating in gas refrigerant supply (GRS) mode with nitrogen– hydrocarbon and argon–hydrocarbon refrigerants. Cryogenics. 2009, 49: 350359. [5] Walimbe NS, Narayankhedkar KG, Atrey MD. Experimental investigation on mixed refrigerant Joule–Thomson cryocooler with flammable and non-flammable refrigerant mixtures. Cryogenics. 2010, 50:653-659. [6] Tzabar N. Binary mixed-refrigerants for steady cooling temperatures between 80 K and 150 K with Joule–Thomson cryocoolers. Cryogenics. 2014, 64: 70-76. [7] Gong MQ, Wu JF, Cheng QW, et al. Development of a 186 C cryogenic preservation chamber based on a dual mixed-gases Joule-Thomson refrigeration cycle. Applied Thermal Engineering. 2012. 36: 188-192. [8] Gong MQ, Wu JF, Luo EG. Performances of the mixed-gases Joule–Thomson refrigeration cycles for cooling fixed-temperature heat loads. Cryogenics. 2004, 44: 847-857. [9] Kim SG, Kim MS. Experiment and simulation on the performance of an autocascade refrigeration system using carbon dioxide as a refrigerant. International Journal of Refrigeration. 2002, 25: 1093-1101. [10]Du K, Zhang SQ, Xu WR, Niu XF. A study on the cycle characteristics of an auto-cascade refrigeration system. Experimental Thermal and Fluid Science. 2009, 33: 240-245. [11]Wang Q, Li DH, Wang JP, Sun TF, Han XH, Chen GM. Numerical investigations on the performance of a single-stage auto-cascade refrigerator operating with two vapor–liquid separators and environmentally benign binary refrigerants. Applied Energy. 2013,112: 949-955. [12]Sivakumar M, Somasundaram P. Exergy and energy analysis of three stage auto refrigerating
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ACCEPTED MANUSCRIPT [23]Li H, Cao F, Bu X, Wang L, Wang X. Performance characteristics of R1234yf ejector expansion refrigeration cycle. Applied Energy. 2014, 121:96-103. [24]Jeon Y, Jung J, Kim D, et al. Effects of ejector geometries on performance of ejector-expansion
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ACCEPTED MANUSCRIPT No. 517/2014 of the European Parliament and of the Council on fluorinated greenhouse gases and repealing Regulation (EC) No. 842/2006. Official Journal of the European Union. 2014. [35]Liu F, Groll EA. Study of ejector efficiencies in refrigeration cycles. Applied Thermal Engineering. 2013, 52: 360-370.
28
ACCEPTED MANUSCRIPT Highlights: An advanced ejector-expansion autocascade refrigeration cycle is presented. Energy and exergy analysis are applied. The performances of the presented cycle are compared with those of the basic cycle. The presented cycle shows obvious COP, volumetric refrigeration capacity and exergic efficiency improvements.
Ye Liu, Jianlin Yu PII:
S0360-5442(18)31997-2
DOI:
10.1016/j.energy.2018.10.016
Reference:
EGY 13913
To appear in:
Energy
Received Date:
13 May 2018
Accepted Date:
03 October 2018
Please cite this article as: Ye Liu, Jianlin Yu, Performance analysis of an advanced ejectorexpansion autocascade refrigeration cycle, Energy (2018), doi: 10.1016/j.energy.2018.10.016
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.
ACCEPTED MANUSCRIPT Performance analysis of an advanced ejector-expansion autocascade refrigeration cycle Ye Liu, Jianlin Yu Department of Refrigeration & Cryogenic Engineering, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China
Abstract In this paper, an advanced ejector-expansion autocascade refrigeration cycle (AEARC) using hydrocarbon mixture R290/R170 for applications in low-temperature freezers is proposed. In the AEARC, a two-phase flow driven ejector is introduced with new cycle configuration to reduce the thermodynamic loss in throttling process and lift the suction pressure of compressor significantly. The performances of the AEARC and traditional autocascade refrigeration cycle (ARC) are compared using energy and exergy analysis methods, and several important parameters for AEARC are also discussed in detail. The results indicate that AEARC is feasible and there are obvious performances improvements in the COP , volumetric refrigeration capacity and exergic efficiency. Especially, in AEARC, the COP and volumetric refrigeration capacity increase by 80.0% and 78.5% at most compared to that of ARC, respectively. In general, the AEARC can provide significant performance improvement and produce better actual operation benefit. The potential practical advantages may be worth further attention in future research. Keywords Hydrocarbon mixture; Ejector; Autocascade refrigeration cycle; Performance improvement
Corresponding author. Tel.:+86-29-82668738. Fax:+86-29-82668725. Email: [email protected] 1
ACCEPTED MANUSCRIPT Nomenclature COP
cooling coefficient of performance
h
specific enthalpy ( kJ kg -1 )
m
mass flow rate ( kg s -1 )
p
pressure ( kPa )
Q e
cooling capacity ( kW )
E xd
exergy destruction ( kW )
s
specific entropy( kJ kg -1 K 1 )
x
vapor quality
T
Kelvin temperature ( K )
t
Celsius temperature (℃)
W
compressor input power ( kW )
rpj
pressure lift ratio
rp
pressure ratio of compressor
specific volume( m 3 kg -1 )
qv
volumetric refrigeration capacity( kJ m -3 )
ex
specific exergy( kJ kg -1 )
w
velocity ( m s -1 )
z
mass fraction of R290 in the mixture
Greek letters
efficiency
entrainment ratio 2
ACCEPTED MANUSCRIPT
exergy destruction percentage
Subscripts 0
reference state
n
nozzle section of ejector
d
diffuser section of ejector
m
mixing section of ejector
ex
exergy
exd
exergy destruction
cm
compressor
con
condenser
eva
evaporator
tot
total exergy destruction
is
isentropic procedure
sf
secondary flow
pf
primary flow
mf
mixing flow
1 - 12
state points of refrigerant
1. Introduction Autocascade refrigeration systems are very effective for producing low temperature cooling over a span of temperatures [1, 2]. In an autocascade system, the autocascade refrigeration cycle (ARC) usually employs a single compressor and a zeotropic refrigerant mixture comprising the low boiling and high boiling refrigerants, along with a series of vapor-liquid separators and cascade heat exchangers, which makes it possible for the system to reach low temperature. 3
ACCEPTED MANUSCRIPT Autocascade refrigeration systems offer many benefits, such as a relatively low compression ratio and high volumetric efficiency. These features have led to the popularity of ARC system application for low temperature freezers and natural gas liquefaction [3, 4]. Actually, there are other ways to reach effective deep refrigeration, such as the mixed refrigerant (gas) cycle (MRC). The MRC is a single refrigerant circuit with one compressor and without phase separators, which is also known as the Joule–Thomson cycles using mixed refrigerant [5, 6]. In the MRC, multi-component mixtures are usually in use in order to achieve demanded low temperatures and obtain enhanced performance [7]. Previous studies have shown that these two typical cycle configurations ARC and MRC can be used for providing low temperature refrigeration. Their performances depend strongly on the composition of mixtures, and different cycle configuration has different optimal mixture composition. In the cases of optimal mixtures, both cycles can provide approximately equal performance [8]. Overall, many studies on ARC and MRC systems have been conducted over the past years. Early, Kim et al. [9] investigated the performance of an autocascade refrigeration system using zeotropic refrigerant mixtures of R744/R134a and R744/R290. Performance test and simulation indicate that the ARC system has a merit of low operating pressure, but lower coefficient of performance (COP) is a disadvantage. Du et al. [10] experimentally studied the cycle characteristics of an auto-cascade refrigeration system with R23/R134a mixed refrigerants, and showed that High COP of the ARC system may be acquired when the charging concentration is around 30% (wt). Wang et al. [11] simulated an auto-cascade refrigerator operating with two vapor-liquid separators, and found that the main factors affecting COP include the pressure ratio, the composition of mixed refrigerants, the main stream ratio and the pressure. Recently, Sivakumar and Somasundaram [12] conducted exergy and energy analysis on three stage ARC system, and revealed that environmentally benign refrigerant mixture of R290/R23/R14 with the specified mass fraction was performing better at very low evaporating temperature. Zhang et al. [13] applied a fractionation heat exchanger in the R744/R290 auto-cascade refrigerator, and showed that it can 4
ACCEPTED MANUSCRIPT effectively improve the separation efficiency of R744/R290, and then lower the evaporating temperature. Rui et al. [14] carried out experimental investigation of the performance of a single-stage auto-cascade refrigerator for 190 K applications, and demonstrated the feasibility of the proposed R600a/R23/R14 ternary mixture for ARC systems. In addition, the composition behaviors of zeotropic mixtures in ARC systems were also studied by few researchers [15, 16]. Generally, the ARC has received more and more attention to deeply investigate its performance and develop its applications. As known, traditional throttling devices such as expansion valves and capillary tubes are usually used in conventional ARCs. From a thermodynamics point of view, the use of these throttling devices is main reason for lower COP of a conventional ARC due to the large irreversibilities in the throttling process. To recover this thermodynamic loss, an ejector as the expansion device can be used in the throttling process. Ejector expansion method is a technique that involves expansion work recovery, and it has proven to be effective in improving the performance of vapor compression systems [17]. Ejector expansion techniques for various vapor compression systems have rapidly developed in recent years owing to their outstanding performance enhancement potential [18-21]. For an example, some researchers have been focused on the ejector application to conventional single-stage vapor compression cycle for household refrigerator-freezers and air conditioners [2224]. Therefore, based on the knowledge about conventional ARCs, using an ejector as expansion device is also one of the alternative ways of improving cycle performance. In the authors' previous publications [25-27], three different designs of the ARCs with an ejector have been proposed. Overall, these cycle configurations showed a comparable performance improvement over the baseline cycle. Principally, a modified cycle design employing ejector needs to be able to improve the performance by as much as possible over a conventional cycle. Therefore, we further propose a new cycle, i.e. an advanced EARC in this paper. The major advantage of this cycle configuration is the ability to sufficiently recover the expansion work in the throttling processes. This is because in the ejector enhanced ARC of the authors' previous study 5
ACCEPTED MANUSCRIPT [26], only the liquid phase flow from the separator is supplied to the ejector as primary flow, the enthalpy value and the flow rate is relative low. On the other hand, the vapor phase flow from the separator is condensed and then expanded through the evaporative condenser and throttling valve, and is fed into the evaporator for refrigeration. Obviously, the potential expansion work in this flow circuit is not recovered. In the advanced EARC (AEARC), however, the primary flow of ejector comes from the condenser entirely. It has high enthalpy value and large flow rate. Thus, the ejector in AEARC could recover more expansion work and provide high pressure lifting ratio, and resulting in much more significant performance improvement. Furthermore, using the two-phase flow driven ejector in the AEARC provides very promising potential to yield a more efficient system in comparison to the conventional MRC system, because the main disadvantage of the MRC cycle is the very large thermodynamic loss in its throttling process (isenthalpic expansion). In general, the pressure ratio in the compressor of AEARC can be significantly reduced compared with MRC, thus increasing its efficiency due to reduced compressor power consumption. The purpose of the current research is to theoretically investigate thermodynamic performances of the proposed cycle using energetic and exergetic methods. And the performance of the novel cycle is compared to the conventional cycle. 2. Cycle description and modeling 2.1 Cycle description Fig. 1 (a) show the schematic diagram of the conventional single stage ARC system that mainly consists of a vapor compressor, a condenser, a vapor-liquid separator, a cascade heat exchanger (CHEX), two throttling devices, and an evaporator. On the basis of the ARC, a modified ARC that includes an additional ejector at the condenser exit is proposed, where it is named as advanced ejectorexpansion ARC (AEARC), as shown in Fig. 1(b). In this novel cycle configuration, the two-phase refrigerant mixture is used to drive the ejector which lifts the compressor suction pressure through expansion work recovery. For this reason, the AEARC has a higher potential to improve the system than the ARC. Fig. 1(c) shows 6
ACCEPTED MANUSCRIPT the P-h diagram of the AEARC. The working principle of the AEARC is as follows: the zeotropic refrigerant mixture vapor discharged from the compressor (Point 2) flows through the condenser and then enters the ejector as a primary flow (Point 3, two-phase state). The vapor exiting from the CHEX (Point 9) is entrained as a secondary flow by the ejector. The two-phase mixture of the primary and secondary flows leaves the ejector to the separator (Point 4) and is then separated into liquid (Point 6) and vapor phases (Points 5, 1). A portion of the vapor mixture with more low-boiling point component returns to the suction of the compressor (Point 1) for the next cycle. At the same time, another portion of the vapor mixture (Point 5) passes through the CHEX and then is condensed to liquid (Point 10), which is expanded in the first throttling device (Point 11) and then evaporated in the evaporator (Point 12) by the heat received from the cooled objects. The saturated liquid mixture with more high-boiling point component (Point 6) passes through the second throttling device and then mixes the vapor from the evaporator (Points 7, 12 and 8). The mixing two-phase stream is passed the CHEX and then evaporated to vapor (Point 9), and it forms a complete cycle. It should be noted that in the AEARC, although the separation process is shifted from the high pressure location downstream of the condenser to a lower pressure location, this will still provide sufficient potential for the autocascade to work. The reason is that the outlet refrigerant mixture of the condenser is fed into the ejector as primary flow, and it entrains the vapor refrigerant mixture coming from the CHEX. In this case, the outlet refrigerant mixture of the ejector is still in two phase state, and is then separated into liquid and vapor phase streams through the separator. Thermodynamically, the concentrations of the vapor phase stream of the refrigerant mixture from the separator still has more low-boiling point component, which is the same as the concentrations of the refrigerant mixture from the condenser. This could ensure the evaporator to provide cooling at lowest possible temperature with the sufficient low boiling temperature component. On the other hand, the AEARC also could recover more expansion work and provide high pressure lifting ratio, and result in reaching lower temperatures. 7
ACCEPTED MANUSCRIPT
Fig. 1 (a). The schematic diagram for ARC system
Fig. 1 (b). The schematic diagram for AEARC system;
8
ACCEPTED MANUSCRIPT Fig. 1 (c). The schematic P-h diagram for the AEARC The performances of AEARC are theoretically evaluated based on the energetic and exergetic methods. The following assumptions are made to simplify the analysis: (1) All components are assumed to be a steady-state and steady-flow process. (2) The compression process in the compressor is irreversible and has variable isentropic efficiency which is related to the compression ratio. (3) The flow through the ejector is one-dimensional, steady state and adiabatic. (4) The velocities of the refrigerant are negligible at the primary fluid inlet, secondary fluid inlet and the outlet of ejector. (5) Flow losses in the ejector are defined in terms of isentropic efficiencies in the nozzle, mixing section and diffuser that are assumed to be constant. (6) Mixing in the ejector occurs at constant pressure and in a constant-area section. (7) The expansion processes in throttling devices are isenthalpic. (8) The vapor and liquid from the phase separator are both saturated. (9) The refrigerant outlet flow is considered as a saturated state in the evaporator, condenser and CHEX. (10)Refrigerant pressure drop and heat losses in the cycle are neglected.
Fig. 2 The schematic of the ejector 2.2 Mathematical models According to the above assumptions, the mathematical model of the ejector is obtained by employing the steady flow energy equations and mass, momentum balance equations. The schematic of the ejector is shown in Fig. 2. Note that there are
9
ACCEPTED MANUSCRIPT two models can be used to simulate the ejector. One is the constant-area mixing model and the other one is the constant-pressure mixing model. Literature review indicates that the constant-pressure mixing ejector provides better performance than the constant-area mixing ejector, which was widely used by many researchers [11, 12, 28].
Thus, the 1-D constant-pressure mixing model and the homogeneous flow
model are applied in this paper. The entrainment ratio is key parameter to evaluate the ejector’s performance, and it can be defined as:
m sf / m pf
(1)
where m sf and m pf is the mass flow rate of the second flow and primary flow, respectively. It should be noted that the detailed principal of ejector is not described in this paper, as it is already a matured knowledge. The detailed ejector modelling can be obtained in the author’s published papers [25-27]. Based on the mass, momentum and energy conservation, the ejector entrainment ratio can be found. Under the assumption that the kinetic energy of refrigerant at the outlet of the ejector can be negligible, so the entrainment ratio of the ejector as an important performance parameter can be obtained as follow:
n m d ((h3,n1 h3,n 2,is ) /(h4,d ,is h4,m2 )) 1
(2)
For the compressor, the input power can be expressed as
Wc m 1 (h2 h1 ) m 1 (h2,is h1 ) / cm
(3)
where m 1 is the mass flow rate of the compressor inlet, h1 is the refrigerant specific enthalpy at the compressor inlet, h2,is is the refrigerant specific enthalpy at the outlet of the compressor under the isentropic compression processes, cm is compressor isentropic efficiency, which can be obtained [26, 29], 10
ACCEPTED MANUSCRIPT cm 0.874 0.0135rp 0.874 0.0135( P2 / P1 )
(4)
where rp the pressure lift ratio of the compressor, P1 and P2 is the refrigerant pressure at the inlet and outlet of the compressor, respectively. 2.3 system performance For the condenser, the amount of heat rejected by the condenser is given by:
Q c m 1 (h2 h3 )
(5)
For the evaporator, the refrigeration capacity is calculated using the following equation:
Q e m 11 (h12 h11 )
(6)
where m 11 is the mass flow rate of the evaporator, h11 is the refrigerant specific enthalpy at the evaporator inlet, h12 is the refrigerant specific enthalpy at the outlet of the evaporator. Volumetric refrigeration capacity based on the specific suction volume of the compressor is given by:
qv Q e / m 111 (h12 h11 ) / 1
(7)
where 1 is suction specific volume of the compressor. The coefficient of performance (COP) for is calculated by:
COP Q e / W
(8)
The basic equation obtained from the conservation law of energy in the CHEX is written as:
m 5 (h5 h10 ) m 9 (h9 h8 )
(9)
where m 5 and m 9 are the mass flow rates in the CHEX, h5 , h10 , h8 and h9 are the refrigerant specific enthalpies at the CHEX inlets and outlets, respectively. The mass balance equations for the ejector and separator can be written as:
m 3 m 9 m 4
(10) 11
ACCEPTED MANUSCRIPT m 4 m 1 m 5 m 6
(11)
Based on the definitions of entrainment ratio in equation (1) and vapor quality, the entrainment ratio of the ejector and the ejector outlet quality are expressed by:
m 9 / m 3
(12)
x4 (m 1 m 5 ) / m 4
(13)
To evaluate the exergy destructions in the AEARC system, the exergy analysis is further conducted in this study [30]. When the kinetic and potential energies are neglected, the specific exergy of refrigerant at any state point can be defined as [31, 33]:
ex (h h0 ) T0 ( s s0 )
(14)
where h0 and s0 are the enthalpy and entropy of the refrigerant at ambient temperature T0 . The exergy destruction in each component is calculated by the equation:
E xd m i exi m o exo Q (1 T0 / T ) W
(15)
where the first term on the right-hand side is the sum of the exergy input, the second term is the sum of the exergy output, the third term is the exergy of heat transferred (Note that the output heat in condenser is considered negative, and the input heat in evaporator is considered positive), while the last term is the exergy of the mechanical work added to the cycle system which is also considered positive. Based on the above equation, the exergy destruction in each component can be written as follows: Compressor:
E xdcom m 1T0 ( s2 s1 )
(16)
Condenser:
E xdcon m 1 ((h2 h3 ) T0 ( s2 s3 )) Qc (1 T0 / Tc )
(17)
Ejector:
E xdejc m 1 (h3 T0 s3 ) m 9 (h9 T0 s9 ) m 4 (h4 T0 s4 ) 12
(18)
ACCEPTED MANUSCRIPT CHEX:
E xdche m 5 ((h5 h10 ) T0 ( s5 s10 )) m 9 ((h8 h9 ) T0 ( s8 s9 ))
(19)
Evaporator:
E xdeva m 5 ((h11 h12 ) T0 ( s11 s12 )) Q e (1 T0 / Te )
(20)
Throttling devices:
E xd thr1 m 6T0 ( s7 s6 )
(21)
E xd thr2 m 5T0 ( s11 s10 )
(22)
The total exergy destruction in the system is the sum of exergy destruction in different components of the cycle system and is given by:
E xd tot E xdcom E xdcon E xdejc E xdche E xdeva E xd thr1 E xd thr2
(23)
Exergetic efficiency for the AEARC system is given by the following equation:
ex 1 E xd tot / W cm
(24)
The exergy destruction percentage for each component with respect to total input exergy is given by:
exd E xd /W cm
(25)
Based on the above theoretical model of AEARC, the simulation program has been developed to investigate the effect of different operating parameters on cycle performances. The refrigerant thermodynamic properties are calculated by using NIST database and subroutines [33]. In addition, note that the modeling for the ARC cycle without the ejector is not presented here for simplicity, whereas the relevant simulations are also conducted for performance comparison. 3. Simulation and results discussion In 2014, the Directive 517/2014 [34] was introduced by European Parliament to reduce the use of high-GWP greenhouse gases in order to limit global climate change. Thus the widely used refrigerants with high GWP values should be gradually phased out and replaced by low-GWP alternatives. Therefore, in the following simulations, the zeotropic refrigerant mixture R290/R170 is selected as a working fluid for 13
ACCEPTED MANUSCRIPT evaluating the performances of AEARC and ARC. The following operating conditions are assumed: the condenser outlet temperature tc ranges from 30 to 50℃, the vapor quality at the condenser outlet x3 is in the range of 0.465 to 0.615, the evaporator outlet temperature te varies from -65 to -40°C. The mass composition of R290 in the mixture R290 / R170 z1 is varied from 0.42 to 0.65. The working fluid flow in the ejector is very complicated, therefore, the ejector component efficiencies are usually used to consider the irreversibility losses in the working process. In addition, From the open literature studies, it could be found that the constant component efficiencies are widely used, due to that, the ejector in this study is assumed to have the following efficiencies: n 0.8 , m 0.95 and d 0.8 [26, 35]. The refrigerant mass flow rate at the compressor inlet is assumed to be
0.1 10-2 kg / s . The simulation results of AEARC and ARC under typical operating conditions are listed in Table 1, where tc 40℃ , te 50℃ , x3 0.5 , z1=0.5. The calculated thermodynamic properties for the AEARC in the operating condition are shown in Table 2. Table 1 The comparison between ARC and AEARC
parameters Coefficient of performance Volumetric refrigeration capacities (kJ/m3) Pressure ratio of compressor Pressure lift ratio of ejector Overall exergy destruction (W) Exergic efficiency Isentropic efficiency of compressor
ARC 0.349 328.1 17.6 / 241.8 0.182 0.64
Values AEARC 0.456 496.1 9.9 2.11 139.2 0.233 0.74
From the Table 1, it can be seen that the AEARC achieves better performances than ARC. The results indicate that the coefficient of performance (COP) and 14
ACCEPTED MANUSCRIPT volumetric refrigeration capacities qv of AEARC increase by 30.7% and 51.2% compared to those of ARC, respectively. Meanwhile, AEARC could increases the exergic efficiency by up to 28%, and decreases the overall exergy destruction by up to 42.4%. The results also shows that the pressure ratio of compressor in AEARC is reduced by 43.8% than that in ARC, and resulting in 15.6% higher compressor isentropic efficiency. It is obvious that the cycle configuration of AEARC could be considered as a promising modification to improve the conventional auto-cascade cycle performance. In the authors' previous publications, different designs of the ARCs with an ejector also have been proposed. It can be found that the novel auto-cascade refrigeration cycle (NARC) which is proposed in reference [25] improves the COP by 3.9-17.4% compared to the ARC for the given operating conditions, and the ejector enhanced auto-cascade refrigeration cycle (EARC) in reference [26] provides 8.4218.02% improvement in COP to that of ARC. However, according to the simulation results, the COP of the AEARC could offer 33.2% improvement to that of ARC according to Table 1 for the given conditions. Obviously, the AEARC could obtain much higher performance improvement than those of the previous two cycles because this cycle configuration has the ability to sufficiently recover the expansion work in the throttling processes. Table 2 The thermodynamic properties for the AEARC
State points 1 2 3 4 5 6 7 8 9 10
Temperature (℃) -32.4 96.2 40.0 -33.4 -32.4 -32.4 -49.7 -53.1 -45.7 -52.3
Pressure (kPa) 312.8 3101.4 3101.4 312.8 312.8 312.8 148.2 148.2 148.2 312.8 15
Vapor quality 1.00 1.00 0.50 0.86 1.00 0 0.10 0.57 1.0 0
mass fraction of R290 0.50 0.50 0.50 0.53 0.50 0.84 0.84 0.62 0.62 0.50
ACCEPTED MANUSCRIPT 11 12
-69.4 -50.0
148.2 148.2
0.09 1.00
0.50 0.50
Typical operating conditions: tc=40℃,te=-50℃,x3=0.5,z1=0.5
In order to explain the reason for the exergy efficiency improvement in AEARC, the exergy destruction of each component in both cycles under typical operating condition is displayed in Fig. 3. As it can be seen, most components of the AEARC exhibit a lower level of exergy destruction than those of ARC. This is because the use of ejector lifts the suction pressure, and thus reduces the pressure ratio and discharge temperature of the compressor. As a result, the exergy destructions of the compressor, the condenser and the cascade condenser of AEARC are 55.7%, 76.2% and 92.5% lower than those of ARC, respectively. Furthermore, the exergy destructions of the two throttling valves of AEARC are reduced by 98.3% and 98.6% compared to those of ARC. This fact indicates that the introduction of an ejector can effectively reduce the exergy destruction in the expansion process. Thus, the exergy efficiency of the AEARC can be improved by using the ejector due to smaller overall exergy destruction.
Fig. 3 The exergy destruction comparison for the components of two cycles To indicate the performance enhancement of the AEARC, the comparisons of COPs and volumetric refrigeration capacities between the ARC and AEARC under
various evaporating and condensing temperatures are shown in Figs. 4 and 5. Fig. 4 16
ACCEPTED MANUSCRIPT shows the variation of COPs and qv with t e in two cycles. It can be seen that as t e increases, both the COP and qv in two cycles rise. Clearly, the AEARC cycle outperforms the ARC in the COP within the whole evaporating temperature range. The COPs of AEARC range from 0.267 to 0.554, and they show 8.6% to 80.1% higher than those of the ARC. This is because that the introduction of ejector in AEARC significantly lifts the compressor suction pressure, and resulting in lower consumption power of compressor. For this reason, the COP of AEARC can achieve higher value, especially at a lower evaporating temperature. Also, the AEARC achieves improvement in the volumetric refrigeration capacities. According to Fig. 4, it can be found that qv of AEARC is 24.9% to 78.5% higher than that in ARC as t e increases. Fig. 5 displays the COP and qv tendencies of both the AEARC and ARC cycles versus t c . In order to ensure the simulation results to be reasonable, the selected t c of AEARC and ARC ranges from 35~50℃ and 30~45℃, respectively. From the results it can be seen that COPs in two cycles are all decreased as t c rises. As
expected,
AEARC
gives
a
higher
COP
and
a
higher
volumetric
refrigeration capacity under given condensing temperatures. In general, AEARC can achieve obvious COP and volumetric refrigeration capacity improvement.
17
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Fig. 4 The variation of COP and qv with evaporating temperature t e
Fig. 5 The variation of COP and qv with condensing temperature t c To further reveal the exergic performance enhancement of the AEARC, the comparisons of ex and E xd tot between the two cycles under different evaporating and condensing temperatures are shown in Figs. 6 and 7, respectively. It can be seen from Fig. 6 that as t e increases, the ex values of both the AEARC and ARC increase, 18
ACCEPTED MANUSCRIPT and the ex of AEARC is changed from 0.119 to 0.215. Moreover, the ex of AEARC is increased by 11.5% to 55.2% over the ARC. On the other hand, the E xd tot for two cycles are decreased with increasing t e . For the ARC, E xd tot varies from 179.9 to 603.5 W, which is nearly 38.6-68.7% greater than that for the AEARC. Furthermore, it also can be seen that the E xd tot of ARC attains higher value than that of AEARC under lower evaporating temperatures. Fig. 7 shows the variations of ex and E xd tot with different t c in two cycles. It can be seen that as t c rises, the ex and E xd tot in AEARC display uptrend, although the E xd tot shows a small increase. However, the
E xd tot of ARC increases obviously, it also leads to a decline in ex values. Therefore, the results of the study reveal that from an exergetic point of view, the performance of the AEARC is better than that of the ARC.
Fig. 6 The variation of ex and E xd tot with evaporating temperature t e
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Fig. 7 The variation of ex and E xd tot with condensing temperature t c Note that the vapor mass quality at state point 3, x3 , and the mass fraction of the mixture at state point 1, z1 , are important parameters for cycle performance evaluation. Figs. 8 and 9 display the COP and qv variation tendencies of both the AEARC and ARC cycles versus x3 and z1 , respectively. In Fig. 8, it can be seen that as x3 rises, the COP and qv of the AEARC both are decreased, but the COP and qv of the ARC are increased. Nevertheless, the qv of AEARC still are 14.8% to 53.9% higher than those of ARC. In addition, it can also be seen from Fig. 8 that the COP of AEARC is higher than that of ARC as x3 increased from 0.465 to 0.562
but it
appears to be lower that of ARC as the x3 increased further. This is due to that under the constant evaporating and condensing temperature, a higher x3 means there are more refrigerant flowed into the evaporator of ARC. However, in AEARC, the higher
x3 leads to the lower condensing pressure, and causes the entrainment ratio of the ejector and the refrigerant flow rate to drop. As a result, the COP of AEARC is decreased. Even so, in general, the AEARC can achieve better performance 20
ACCEPTED MANUSCRIPT improvement under appropriate operation parameters especially for the vapor mass quality of condenser outlet.
Fig.8 Variation of COP and qv in two cycles with x3
Fig. 9 Variation of COP and qv in two cycles with z1 Fig. 9 shows the variation of COP and qv in two cycles with z1 . It can be found that as z1 rises, the COPs of the two cycles are all increased. However, the qv of the 21
ACCEPTED MANUSCRIPT two cycles decrease with increasing z1 . The reason is that as z1 increased, the evaporating pressure is reduced with increasing the R290 mass fraction of the mixture in the evaporator, as a result, the qv is declined. On the other hand, the cooling capacity and the compressor input work of two cycles are decreased with increasing R290 mass fraction of the mixture. Meanwhile, the compressor input work is decreased more rapidly than the cooling capacity. In this case, the COP variation tendencies as shown in Fig. 8 are observed. The entrainment ratio
and the pressure lift ratio rpj are important
performance parameters of an ejector. In this work, the variations of and rpj with
t e are shown in Fig. 10, where tc 40℃ , x3 0.534 , z1 0.45 . It can be seen that as t e increases, the rises from 0.297 to 0.396. Meanwhile, the pressure lift ratio rpj is reduced from 3.06 to 1.89. From the results it can be seen that the rpj values are much greater than 1 in the whole range of given evaporating temperatures since the two-phase flow from the condenser is used to drive the ejector. Obviously, this is beneficial to the reductions of pressure ratio and power consumption of compressor. Therefore, the higher pressure lift ratio of ejector also gives rise to the COP improvement of AEARC. In addition, the ejector component efficiencies also influence the cycle performances. The variations of COP and rp with t e for different ejector component efficiencies are shown in Fig. 11, where tc 40℃ , x3 0.534 , z1 0.45 . The three ejector component efficiencies are assumed to have the same values, which is selected as 0.8, 0.85, and 0.9, respectively. It can be seen that when increasing the efficiencies, the COP of the AEARC is increased at the given conditions. The COP can be improved by 15.2-84.9% when the ejector component efficiencies are varied from 0.8 to 0.9. Meanwhile, the higher ejector component efficiencies also result in the decrease of the compressor pressure ratio due to the increased ejector. Therefore, higher ejector component efficiencies are conductive to recover more expansion work 22
ACCEPTED MANUSCRIPT and improve the COP, which could be beneficial for cycle performances.
Fig. 10 Variation of and rpj in two cycles with t e
Fig. 11 Variation of COP and rp in AEARC with t e
4. Conclusions This paper presents an advanced ejector-expansion autocascade refrigeration cycle using hydrocarbon mixture R290/R170 for applications in low-temperature freezers. In the proposed cycle, an ejector is introduced to reduce the thermodynamic 23
ACCEPTED MANUSCRIPT loss in throttling process and lift the suction pressure of compressor significantly. Energy and exergy analysis for the AEARC are conducted theoretically and compared with ARC under various operating conditions. From the foregoing analysis results, it can be concluded that AEARC is meaningful and there are significant performances improvements in COP , volumetric refrigeration capacity and exergic efficiency. Main operating parameters, including the evaporating and condensing temperatures, mass composition of R290, condenser outlet vapor quality and ejector efficiencies, have different extent effects on the performance improvements. Overall, the COP can achieve higher improvement at lower evaporating temperatures. In the given range of operating conditions, it is found that compared to the ARC, the AEARC has a COP improvement of 78.5% and a volumetric capacity improvement of 80.0% under the condition of tc 40℃ , te 65℃ , x3 0.534 , z1 0.45 . Thus, the application of ejector to this novel cycle configuration is more effective for improving the performance of the autocascade refrigeration cycle under reasonable operation conditions. And the new developed cycle could offer advantages for its applications in low-temperature freezers. Of course, further theoretical and experimental work for the AEARC based system will be necessary in the next step.
Acknowledgements The work presented in this paper is financially supported by National Natural Science Foundation of China (NSFC) under the grant No. 51776147. The authors would like to thank NSFC for the sponsorship.
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ACCEPTED MANUSCRIPT Highlights: An advanced ejector-expansion autocascade refrigeration cycle is presented. Energy and exergy analysis are applied. The performances of the presented cycle are compared with those of the basic cycle. The presented cycle shows obvious COP, volumetric refrigeration capacity and exergic efficiency improvements.