Enhancing the performance of a CO2 refrigeration system with the use of an absorption chiller

International Journal of Refrigeration 108 (2019) 37–52

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Enhancing the performance of a CO2 refrigeration system with the use of an absorption chiller Evangelos Bellos∗, Christos Tzivanidis Thermal Department, School of Mechanical Engineering, National Technical University of Athens, Zografou, Heroon Polytechniou 9, 15780 Athens, Greece

a r t i c l e

i n f o

Article history: Received 13 May 2019 Revised 2 September 2019 Accepted 12 September 2019 Available online 14 September 2019 Keywords: Absorption chiller Subcooling CO2 refrigeration Transcritical CO2 cycle R744

a b s t r a c t The objective of this work is to examine a transcritical CO2 refrigeration system coupled to a single-effect absorption chiller. The role of the absorption machine is to create a subcooling after the gas-cooler in order to increase the COP. The absorption system is fed by waste heat after the CO2 compressor and so there is not any need for any external energy source. The analysis is conducted with a validated numerical model which is developed in Engineering Equation Solver. The system is studied and optimized for different heat rejection temperatures from 35 °C up to 50 °C and for different refrigeration temperatures from -35 °C up to 5 °C. It is found that there is COP enhancement in all the operating scenarios and especially in the cases with higher heat-rejection temperature and lower refrigeration temperature. The mean COP enhancement is about 23.4% which is an important enhancement for designing more efficient systems. © 2019 Elsevier Ltd and IIR. All rights reserved.

Amélioration des performances d’un système frigorifique au CO2 à l’aide d’un refroidisseur à absorption Mots-clés: Refroidisseur à absorption; Sous-refroidissement; Froid au CO2 ; Cycle au CO2 transcritique; R744

1. Introduction The use of natural refrigerants in the refrigeration systems is an effective way to face important environmental issues such as global warming (Khanmohammadi et al., 2018, Purohit et al., 2018). Many regulations have been developed in this direction (for example EU F-Gas Regulation 517/2014 (European Commission, 2014)) in order to start the substitution of the older and harmful refrigerants with the refrigerants of the new generation. The most usual natural refrigerants are CO2 , propane, butane, ammonia, air but among them CO2 is the only one which is nontoxic, non-flammable, stable and it has low-cost (Purohit et al., 2017; Ciconkov, 2018). So, the CO2 refrigeration systems have been examined by many researchers. The goal of the studies about the CO2 refrigeration systems aims to increase the system coefficient of performance because

∗

Corresponding author. E-mail address: [email protected] (E. Bellos).

https://doi.org/10.1016/j.ijrefrig.2019.09.009 0140-7007/© 2019 Elsevier Ltd and IIR. All rights reserved.

this parameter has generally low values with the CO2 compared to other conventional refrigerants. The reason for this result is mainly the low-critical point of the CO2 (31.1 °C) which makes the compression to need high amounts of electricity consumption. This problem is more intense in the warm climates where the refrigeration cycle has to operate in transcritical mode and so the performance is reduced (Tsamos et al., 2017; Gullo et al., 2016). Many ideas have been studied in order to enhance CO2 refrigeration systems performance. Firstly, the optimization of the high pressure in the transcritical mode had been studied by Kauf (1999) and Liao et al. (20 0 0). The use of an internal heat exchanger for subcooling after the gas cooler has been studied by various researchers such as Chen and Gu (2005), Torrella et al. (2011), etc. and COP enhancements up to 10% have been found. Moreover, the uses of a two-stage compression system (Lorentzen, 1994; Kauf, 1999) and of parallel compression (Liao et al., 20 0 0; Brown et al., 2002) have been found to be more effective choices for increasing the COP. Other configurations include ejector devices

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Nomenclature COP h m p Q r T Tc T0 Pel Wpump X

coefficient of performance, specific enthalpy, kJ kg−1 K−1 mass flow rate, kg s−1 pressure, bar heat rate, kW pressure ratio, temperature, °C heat rejection temperature, °C reference temperature, K electricity consumption in the CO2 compressor, kW electricity consumption in the solution pump, kW LiBr concentration in the solution, %

Greek Symbols α high-pressure optimization parameter, Tsc subcooling temperature difference, °C ηex exergy efficiency, ηhex,g generator heat exchanger effectiveness, ηhex,s solution heat exchanger effectiveness, ηis isentropic efficiency of the compressor, Subscripts and superscripts a absorber ach absorption chiller con condenser (absorption chiller) CO2 carbon dioxide crit critical exp experimental e evaporator (CO2 cycle) e,ach evaporator of the absorption chiller g generator gc gas cooler high high is isentropic low low max maximum min minimum opt optimum r refrigerant (water) sc subcooling str strong solution sim simulation w weak solution Abbreviations Symbols ACH Absorption chiller EES Engineering Equation Solver M-SC System with mechanical subcooling

(Nakagawa et al., 2011; Chen et al., 2017), expanders (Yang et al., 2007; Megdouli et al., 2017), as well as cascade systems, have been studied in the literature (Sanchez et al., 2017; Megdouli et al., 2017; Ma et al., 2014). However, the use of an external device for creating a dedicated subcooling after the gas cooler has been found as an ideal choice for increasing a lot the COP (Llopis et al., 2018) with enhancements around 30%. So, the use of a dedicated subcooling method is an interesting and effective idea for enhancing the performance of the refrigerator. Practically, the subcooling after the gas cooler is viable for the system in order to increase the cooling capacity and also it is able to reduce a bit the optimum high pressure. In the literature, there are two main categories for creating a dedicated subcooling; the use of an external mechanical compression

refrigeration systems and the use of an external thermal compression refrigeration system. In the mechanical refrigeration systems, usually R134a and R290 are the used refrigerants; the first one as a typical choice and the second one as a natural refrigerant but with high flammability (A3 ASHRAE safety group). The thermal compression can be done with an absorption chiller or with a thermoelectrical device. Firstly, the studies about mechanical subcooling (M-SC) are presented. Llopis et al., 2015; Llopis et al., 2016) examined the use of R134a as the working fluids in the (M-SC) system and they found enhancements in the COP up to 30%. Gullo et al. (2016) studied the use of the same refrigerant and they calculated the total equivalent warming impact to be reduced compared to a supermarket booster system about 10% for Greece and 25% for Spain climate. Nebot-Andres et al. (2017) studied the use of R1234yf in the (M-SC) system and they found also an enhancement in the refrigeration system. Dai et al. (2018) investigated the utilization of zeotropic mixtures in the (M-SC) system in order to reduce the exergy distraction during the heat transfer process and they found 35% COP enhancement compared to the conventional configuration. Bellos and Tzivanidis (2019), in a comparative study, stated that the use of a mechanical subcooling system is able to increase the system COP up to 75% compared to the simple system. The use of a thermoelectrical subcooling device is another usual technique in the literature. Schoenfield et al. (2012) stated that this idea increases 3% the COP and 8% the refrigeration production of the system. Sarkar (2013) calculated a COP enhancement of 25% compared to the conventional system, while Jamali et al. (2017) stated that the enhancement is about 19%. Moreover, Dai et al. (2017) found that the combination of a thermoelectrical subcooling device with an expander is able to enhance the COP about 38%. Liu et al. (2019) found that the COP can increase up to 40% in a system with thermoelectrical subcooling and elector. Moreover, Astrain et al. (2019) compared the use of the thermoelectrical subcooling with the use of an internal heat exchanger for subcooling and they concluded that the first method increases the COP 25% and the second one 12%. The last part of the literature studies about the subcooled systems regards the use of absorption chillers. Heat input from solar systems, waste heat or biomass boiler can be used in these systems in order to feed the absorption machine. Salajeghe and Ameri (2016) examined the incorporation of an absorption chiller which operates with LiBr-H2 O for subcooling purposes. The heat input in the chiller is given by a solid oxide fuel cell and they also studied the use an internal heat exchanger in the system. They concluded that the use of the dedicated subcooling with the absorption chiller is a more effective method than the use of the internal heat exchanger for subcooling. However, the combination of the two methods is found to be a totally optimum scenario. In another study, Bellos and Tzivanidis (2019) compared the use of an absorption chiller and of a mechanical compression system as the subcooling devices in a CO2 refrigeration system. They found that the use of the absorption chiller is able to reduce the electricity consumption up to 84% while the use of the (M-SC) up to 41%, but the use of the absorption chiller needs an extra heat source input. Hojjat Mohammadi (2018) studied different configurations of the CO2 refrigeration systems coupled to absorption machines. They tried to produce refrigeration in temperature levels from −80 °C up to −30 °C and so they suggested some novel designs. They examined the use of two-stage machines in order to reduce the compressor work due to the huge pressure ratio. They fed the absorption machines with the waste heat after the compressors. They found that the COP of the examined configurations can be increased up to 200% in some cases. Lastly, it has to be said that the use of an absorption machine in the high-stage of

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Fig. 1. The examined refrigeration configuration with CO2 compression system and absorption chiller for subcooling.

a CO2 cascade system has been studied in Mohammadi and McGowan (2019), Cyklis (2014). Moreover, the incorporation of absorption machines in CO2 power cycles has been studied in Li et al. (2018), Arora et al. (2011). Another effective method for enhancing the CO2 refrigeration system is the use of a vortex tube expansion device after the gas cooler. This system has been studied by Sarkar (2009) and enhancements up to 18% have been found. The previous literature review makes clear that there is a lot of interest in the use of subcooling methods for enhancing the performance of the CO2 refrigerators in the transcritical mode. On this direction, this work comes to study this idea with the use of an absorption machine because there are only a few studies with this subcooling method. The examined idea is the optimum use of the waste heat after the compressor and to feed the absorption chiller totally with this waste heat. A similar idea had been studying in Hojjat Mohammadi (2018) but in this work, the examined configurations are totally different and the system is studied for refrigeration production in temperatures from −35 °C up to 5 °C, while in the reference Hojjat Mohammadi (2018) the system had examined in lower refrigeration temperatures. The examined temperature levels of this study are different than the other literature work and the present temperature levels cover the applications of supermarket refrigeration (low-temperature or medium temperature evaporators), as well as the cooling applications. Moreover, an extra novelty of this work is the detailed optimization of the examined configuration which is studied for various heat rejection temperatures. Furthermore, the present work includes a financial analysis about the evaluation of the viability of the examined idea and so it is the only literature work which studies the use of an absorption chiller as a subcooling device from the financial point of view. The incorporation of the absorption chiller in the CO2 is able to increase the system performance without any extra heat source and so the obtained results can clearly present a novel and highly efficient system. The analysis is conducted with a developed model in Engineering Equation Solver (EES) (F-Chart Software 2015) which is validated with literature results.

2. Material and methods 2.1. The examined configuration In this work, a novel refrigeration system with CO2 as the main refrigerant is studied. Fig. 1 depicts the investigated configuration which contains a conventional one-stage CO2 system and an absorption chiller (ACH). The absorption chiller is used for subcooling the CO2 after the gas cooler. The subcooling is performed by the produced refrigeration in the evaporator of the absorption chiller. The absorption chiller is fed by heat in the generator. The hot CO2 after the compressor goes into the generator and it gives heating in this device. The CO2 with reduced temperature after the generator goes to the gas cooler in order to be further cooled. The refrigeration load (Qe ) is assumed to be 100 kW in all the cases and the refrigeration temperature (Te ) is examined from −35 °C up to 5 °C. The absorption chiller includes a generator where the heat input is given, an evaporator where the subcooling is produced and two other devices (condenser and absorber) which reject heat to the environment. The working pair is LiBr-H2 O with the water to be the refrigerant and the solution LiBr-H2 O to be the absorbent substance. The refrigeration in the evaporator of the absorption chiller is produced at Te,ach = 10 °C which is a typical temperature for this machine. This value has a small impact on the results. Generally, it can be ranged from 5 °C up to 15 °C in the studied system and the value of 10 °C is a selected as an intermediate one in order to have relatively sufficient performance and to give a proper margin for low CO2 temperature in the subcooler outlet. The minimum temperature of the subcooled CO2 is assumed to be 5 °C higher than the respective temperature in the ACH evaporator (Bellos and Tzivanidis, 2019) and so the minimum temperature of the subcooled CO2 is equal to 15 °C in this work. The heat transfer in the generator is performed with a heat exchange effectiveness (ηhex,g ) of 70% which is a typical value (Bellos et al., 2018). The effectiveness of the solution heat exchanger (ηhex,s ) of the 70% (Bellos and Tzivanidis, 2017). It is useful to state that in this work,

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Fig. 2. The pressure – specific enthalpy (p-h) depiction of the examined cycle about the CO2 subsystem.

the temperature of the subcooled CO2 is calculated by the energy balance in the evaporator of the ACH. So, the approach temperature in this device is variable but there is the constraint of minimum 5 °C approach temperature. The heat rejection temperature (Tc ) is the same for both sub-cycles in this work. The condenser temperature (Tcon ) and the temperature in the gas cooler outlet (T3 ) are assumed to be the same as the parameter (Tc ). The heat rejection temperature (Tc ) is examined parametrically in this work from 35 °C up to 50 °C because this study investigates the transcritical operation. Fig. 2 shows the pressure-specific enthalpy (p-h) diagram of the refrigeration cycle of the CO2 . It is a simple depiction which shows that the process (2→23) is the heat rejection to the generator, the process (23→3) is the heat rejection to the ambient through the gas cooler and the process (3→34) is the subcooling process which rejects heat to the absorption chiller evaporator. 2.2. Mathematical formulation

In this work, the isentropic efficiency (ηis ) is calculated as below (Brown et al., 2002):

ηis = 0.9343 − 0.04478 · r The pressure ratio (r) is defined as:

r=

phigh plow

Qg = mco2 · (h2 − h23 )

ηhex,g =

T2 − T23 T2 − Tg

Qsc = mco2 · (h3 − h34 )

Pel = mco2 · (h2 − h1 )

The isentropic efficiency (ηis ) of the compressor is defined as below:

ηis =

h2,is − h1 h2 − h1

(3)

(8)

The heat rejection in the evaporator of the absorption chiller for subcooling reasons (Qsc ) can be written as:

(9)

The process in the throttling valve is assumed to be ideal and so the enthalpy is the same between inlet and outlet:

h4 = h34 (2)

(7)

In this work, the (ηhex,g ) parameter is assumed to be 70% (Bellos et al., 2018) which is a typical value. The heat rejection in the gas cooler (Qgc ) can be written as:

2.2.1. Modeling of the CO2 refrigeration cycle The refrigeration load in CO2 evaporator (Qe ) can be written as below:

The electricity consumption (Pel ) can be calculated as:

(6)

The heat exchange effectiveness in the generator (ηhex,g ) can be written as below:

Qgc = mco2 · (h23 − h3 )

(1)

(5)

The heat rejection in the generator (Qg ) can be written as:

This subsection includes the main equations of the developed mathematical modeling. These equations have been inserted in the EES which are solved all together iteratively.

Qe = mco2 · (h1 − h4 )

(4)

(10)

The system coefficient of performance (COP) is defined as:

COP =

Qe Qe ≈ Pel + Wpump Pel

(11)

Practically, the pumping work demand in the solution pump of the absorption chiller (Wpump ) is extremely low compared to the

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electricity consumption in the CO2 compressor (Pel ) and thus it is neglected in the present work. More specifically, the calculations of this work indicate that the pumping work demand is around to 1 W while the electricity consumption in the compressor is around 80,0 0 0 W. The heat input of the absorption chiller is not taken into consideration because it is taken by the waste heat after the compressor outlet. The exergy efficiency (ηex ) of the cycle is defined as:

ηex =

Qe ·



T0 273.15+Te



−1

Pel

(12)

The reference temperature (T0 ) in the previous expression is equal to 298.15 K. 2.2. Modeling of the absorption chiller The heat input in the absorption chiller evaporator (Qsc ) is defined as below:



Qsc = mr · h j − hi



hd − he hd − hb

(15)

(16)

(18)

The work consumption in the circulation pump is neglected and thus it can be said:

hb = ha

(19)

The enthalpy does not be reduced in the throttling valves and thus it can be said:

h f = he

(20)

hi = hh

(21)

The heat rejection temperature levels in the absorber and the condenser are the same and so it can be said:

Tcon = Ta

(22)

The balance of the total mass flow rate in the absorber is given below:

mw = mstr + mr

(23)

The balance of the LiBr substance mass flow rate in the absorber is given below:

Xw · mw = Xstr · mstr

(24)

Furthermore, it has to be stated that the state point “j” is assumed to be saturated vapor. The absorption chiller coefficient of performance (COPach ) is defined as:

COPach =

Qsc Qg

(26)

The high-pressure ratio takes values from 1.02 to 2.00 in the optimization procedure. The “dimensionless generator temperature” is defined as below:

Tg − Tg,min Tg,max − Tg,min

Tg,min = 1.71779 + 2.20727 · Tcon − 1.21801 · Te,ach

(25)

(27)

(28)

The maximum generator temperature (Tg,max ) is approximated by the following formula (R2 =99.9%):

Tg,max = 49.2038 + 1.20560 · Tcon + 0.237967 · Te,ach (17)

In this work, the (ηhex,s ) parameter is assumed to be 70% (Bellos and Tzivanidis, 2017) which is a typical value. The energy balance in the heat exchanger is given below:

mw · (hc − hb ) = mstr · (hd − he )

phigh pcrit

This parameter takes values from 0.00 up to 1.00 in this study and practically this parameter makes the generator temperature (Tg ) to be ranged in all the proper region in every case. The minimum generator temperature (Tg,min ) is approximated by the following formula (R2 =99.9%):

The solution heat exchanger effectiveness (ηhex,s ) definition is given below:

ηhex,s =

a=

(14)

The energy balance in the condenser is given below:

Qcon = mr · (hh − hg )

In this study, a novel CO2 refrigeration system is studied for different refrigeration temperatures (Te ) from −35 °C up to 5 °C with a step of 10 °C and for different heat rejection temperature (Tc ) from 35 °C up to 50 °C with step 5 °C. Totally 20 different cases are studied and in every case, the system is optimized. The optimization is conducted by using two optimization variables in order to maximize the system COP. The optimization variables are the highpressure ratio (α ) and the dimensionless generator temperature. The “high-pressure ratio” and it is the ratio of the maximum pressure (phigh ) to the critical pressure of the CO2 (pcrit ) which is 73.77 bar:

ηg =

The energy balance in the absorber is given below:

Qa = mr · h j + mstr · h f − mw · ha

2.3. Followed methodology

(13)

The energy balance in the generator is given below:

Qg = mr · hg + mstr · hd − mw · hc

41

(29)

The previous expressions give the limits of the generator temperature for different operating conditions. These equations have been created by using the developed model for making various tests. More specifically, the maximum generator temperature is the maximum temperature level which does not create crystallization problems in the system. The minimum generator temperature is the one which corresponds to the temperature level of the weak solution at the high-pressure level. The Eqs. (28) and (29) are valid for the following conditions:

5oC ≤ Te,ach ≤ 15oC 30oC ≤ Tcon ≤ 50oC Tcon = Ta The optimization procedure is conducted by using the conjugate directions method or “Powell’s method” which is supported by EES (F-Chart Software 2015). This procedure is an iterative method which assumes some initial values for the optimization variables and it tries to find the values which lead to the optimum solution by using the gradient values of the objective function. In this study, the relative convergence tolerance has been chosen at 10−8 and the maximum number of iterations (function calls) at 30 0 0. The goal of the optimization procedure is the maximization of the system COP which is equivalent the maximization of the system exergy efficiency or the minimization of the electricity consumption in the compressor. The optimization variables are the high-pressure ratio (α ) which is ranged from 1.02 up to 2.0 and the dimensionless generator temperature which is ranged from 0% up to 100%. About the pressure ratio parameter, the selected range is a suitable one in order to have an intermediate optimum value in all the examined cases.

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Table 1 Main parameter of the present work. Parameter

Symbol

Value

Refrigeration capacity Generator heat exchanger effectiveness Solution heat exchanger effectiveness Reference temperature Refrigeration temperature Heat rejection temperature Evaporation temperature in the ACH

Qe

100 kW 70% 70% 298.15 K −35 °C up to 5 °C 35 °C up to 50 °C 10 °C

ηhex,g ηhex,s T0 Te Tc Te,ach

Table 2 Validation of the CO2 refrigeration cycle with Reference (Llopis et al., 2016). Te (°C)

Phigh (bar)

Tc (°C)

COPexp (-)

COPsim (-)

Deviation (%)

0.0 0.0 0.0 −10.0 −10.0 −10.0

82.8 89.6 102.6 77.6 82.5 101.9

28.36 33.51 41.69 27.00 32.79 41.09

2.57 1.93 1.32 1.91 1.44 0.98

2.612 2.063 1.372 1.897 1.477 0.933

1.63% 6.89% 3.94% 0.68% 2.57% 4.80%

The found results are compared with the respective results for the reference system which has not subcooling in order to determine the COP enhancement in every case. Lastly, the most important assumptions of this work are summarized below (Llopis et al., 2016; Dai et al., 2018; Gullo et al., 2016; Bellos et al., 2017) and the main parameters of this work are included in Table 1. • • •

• •

•

•

The analysis is conducted in steady-state conditions. There are no pressure losses in the devices and in the tubes. There is no superheating in the evaporator outlets for the main cycle and for the absorption cycle. There is no subcooling in the absorption chiller condenser. The expansion of the fluids in the throttling valves is ideal and so the enthalpy of the outlet is the same as in the inlet. The heat rejection temperature level is the same in the CO2 system and in the absorption chiller. The minimum approach temperature difference in the subcooler is 5 °C. This constraint has been checked in all the examined cases.

3. Results and discussion 3.1. Preliminary analysis Section 3.1 includes some preliminary results of the present work which regards the performance of the simple cycles (CO2 and absorption chillers), as well as the validation evidence of the developed models. These results are given in order to present an initial analysis of the examined sub-systems before the investigation of the new configuration in the followings sections.

The first part of the preliminary analysis regards the validation of the developed model about the CO2 . The experimental results of the Reference (Llopis et al., 2016) about a simple cycle without subcooling are used in order to test the developed model. Table 2 includes the comparison results and it is obvious that there are relatively low deviations in the COP. The mean deviation is about 3.4% which is an acceptable value. So, the developed model about the CO2 cycle can be adopted as a reliable one. The next step is the validation of the developed model about the absorption chiller by using the results of Reference Gogoi and Konwar (2016) about LiBr-H2 O. The validation shows relatively low deviations about the COP and the LiBr concentrations. More specifically, Table 3 indicates that the mean COP deviation is 0.76%, the mean weak solution concentration deviation is 0.11% and the mean strong solution concentration is 0.23%. The obtained deviations are low and so the developed model about the absorption chiller can be adopted as a valid one. Fig. 3 shows the performance of the simple CO2 refrigeration cycle without subcooling. The COP and the exergy efficiency are given for different refrigeration temperatures and heat rejection temperatures. It can be said that the COP increases for higher refrigeration temperatures and lower heat rejection temperatures. Moreover, the exergy efficiency increase with the increase of the evaporate temperature up to −10 °C where it maximized after this point has a decreasing rate with the refrigeration temperature increase. Moreover, the increase of the heat rejection temperature has a negative impact on the exergy efficiency of the CO2 refrigeration system. Moreover, the preliminary analysis includes a simple parametric study about the COP of the absorption chiller for different heat rejection temperatures and generation temperatures. Fig. 4 shows the absorption chiller COP for evaporator temperature at −10 °C, as in the present work. It is obvious that higher generator temperature leads to a higher COP. Moreover, the COP is higher when the heat rejection temperature is decreased.

3.2. The impact of the optimization parameters on the performance Section 3.2 is devoted in order to present the impact of the optimization parameters on the system performance. Practically this section is a parametric study in order to check how the dimensionless generator temperature (ηg ) and the high-pressure ratio parameter (α ) impact on the system performance. The results of this section explain why these parameters have selected as the optimization variables and also it is made clear how the system performs in different design scenarios. The results of Section 3.2 are created for the operating scenario (Te = −25 °C & Tc = 40 °C), while the optimum results for all the operating scenarios are given in Section 3.3 which follows. Firstly, the impact of the (ηg ) on system performance is depicted in Figs. 5 and 6 for a high-pressure ratio parameter equal to 1.4. This value (α = 1.4) is a typical value which can be used

Table 3 Validation of the absorption chiller with the Reference (Gogoi and Konwar, 2016). Te

Tg

Tcon

Ta

Literature

(°C)

(°C)

(°C)

(°C)

COP

Xw

Xstr

COP

Xw

Xstr

COP

Xw

Xstr

4 4 5 6 8 8 9

70 69 66 72 63 85 66

31 31 28 33 25 46 28

31 35 35 37 37 39 34

0.794 0.697 0.769 0.730 0.819 0.585 0.837

0.578 0.573 0.575 0.576 0.578 0.565 0.575

0.536 0.559 0.552 0.557 0.543 0.555 0.520

0.7886 0.6954 0.7628 0.7252 0.8152 0.5989 0.8357

0.5780 0.5733 0.5755 0.5766 0.5777 0.5673 0.5755

0.5376 0.5587 0.5528 0.5572 0.5453 0.5557 0.5227

0.68% 0.23% 0.81% 0.66% 0.46% 2.38% 0.16%

0.00% 0.05% 0.09% 0.10% 0.05% 0.41% 0.09%

0.30% 0.05% 0.14% 0.04% 0.42% 0.13% 0.52%

This study

Deviation

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43

Fig. 3. COP and exergy efficiency of the simple CO2 cycle without subcooling.

Fig. 4. COP of the absorption chiller for different heat rejection temperatures and generator temperatures with the evaporator temperature at 10 °C.

for the present parametric study and it is close to the global optimum choice, as it will be presented in Section 3.3. This parameter practically is associated with the generator temperature (Tg ) and higher values of the (ηg ) mean higher values of (Tg ). Fig. 5 shows that the increase of the (ηg ) increases the COP of the absorption chiller which is a reasonable result. However, the heat input in the generator is reduced because higher (ηg ) means higher (Tg ) and so lower amounts of heat can be given in the generator because the temperature (T2 ) is the same in all the cases of Fig. 5. The result is the maximization of the subcooling heat transfer for intermediate values of the (ηg ) close to 0.15. The subcooling heat transfer rate is the same as the cooling production in the absorption chiller which is practically the product of the absorption chiller COP and of the generator heat input (Qsc = Qe = COPach ·Qg ). Fig. 6 shows the impact of the (ηg ) on the system COP. Higher values of the (ηg ) lead to higher enthalpy gain in the CO2 evaporator (h1 –h4 ), while the enthalpy difference in the compressor is the same (h2 –h1 ). So, the system COP increases with the increase

of the difference (h1 –h4 ). At this point, it would be useful to state that by combing the Eqs. (1), (2) and (11), it can be said:

COP =

h1 − h4 h2 − h1

(30)

The previous formula makes clear that the depicted enthalpy differences directly influence on the system COP. The maximum COP is found for (ηg ) close to 0.15 which is near to the optimum values of Fig. 5 about the subcooling heat transfer. Practically, the enthalpy difference (h1 –h4 ) is included by the subcooling heat transfer because higher subcooling leads to lower values of (h4 ) and consequently to greater (h1 –h4 ) values. The existence of the optimum value of the (ηg ), which maximizes the system COP, in an intermediate value of the examined range indicates the need for a detailed optimization procedure. The next step in this analysis is the investigation of the high-pressure ratio (α ) impact on the system performance. Figs. 7 to 11 give the respective results for the case (Te = −25 °C

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Fig. 5. The impact of the dimensionless generator temperature on the absorption chiller performance for α =1.4 and (Te = −25 °C & Tc = 40 °C).

Fig. 6. The impact of the dimensionless generator temperature on the system performance for α =1.4 and (Te = −25 °C & Tc = 40 °C).

& Tc = 40 °C). In Figs. 8 to 11, the (ηg ) is examined parametrically, while in Fig. 7 (ηg = 0.50) which is an intermediate value and it can be used for a simple parametric depiction. Fig. 7 shows the impact of the (α ) on the enthalpy differences (h1 –h4 ) and (h2 – h1 ). Both these enthalpy differences increase with the values of the (α ) but the COP is maximized for an intermediate value of (α ) around 1.4, the fact that proves the need for an optimization procedure. Fig. 8 shows the COP of the total system for different combinations of (α ) and (ηg ). It is obvious that the global maximum is found for (ηg = 0.25) and generally the optimum values of (α ) are in the range of 1.4 to 1.5. So, it can be said, that a detailed optimization is needed but in any case, a small variation of the optimization parameters does not lead to extremely high deviations of the COP. This fact proves that there is a general optimal region, in terms of (α ) and (ηg ), where the COP has values close to the global maximum one. The maximum COP is around 1.277, according to the results of Fig. 8.

Fig. 9 shows the exergy efficiency which has practically similar behavior with the COP, as Fig. 8 indicates the maximum value of the exergy efficiency is about 25.7% which is a relatively satisfactory value for a refrigeration system with CO2 . For the depicted cases, eth worst efficiency is found, both for COP and exergy efficiency, for the higher value of the (ηg ). This fact indicates that a high value of the generator temperature is not beneficial because it restricts the heat transfer amount to the generator and also it does not make an important increase in the absorption chiller COP. The last figures of this section regard the electricity consumption (Fig. 10) and the subcooling degree (Fig. 11). The electricity consumption has a reverse behavior of the COP (see Fig. 8) because the following expression can be written Pel = Qe /COP (see Eq. (11)) and the refrigeration production is constant in this work (Qe = 100 kW). The minimum electricity consumption is about 78 kW and it regards the case of maximum COP. Fig. 10 illustrates the subcooling degree in the examined cases. Higher high-pressure leads to higher subcooling degree which is an

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Fig. 7. The impact of the high-pressure ratio parameter on the system performance for ηg =0.5 and (Te = −25 °C & Tc = 40 °C).

Fig. 8. System COP for different combinations of high-pressure ratio parameter and of dimensionless generator temperature for (Te = −25 °C & Tc = 40 °C).

interesting result. Practically, higher pressure after the compressor increases the temperature level of the CO2 after the compressor (T2 ) and so there is greater potential for heat input in the generator. Higher heat input in the generator leads to higher cooling production in the absorption chiller which means higher heat transfer in the subcooling process. So, the subcooling degree (Tsc = T3 – T34 ) increases. The parameter (ηg ) has a small impact on the subcooling degree compared to the pressure ratio parameter. The maximum subcooling is found for the case (ηg = 0.25) which is the value for COP maximization. So, it can be said that for a specific high pressure, higher subcooling degree leads to higher system COP values. 3.3. Optimum performance of the examined system Section 3.3 includes the results of the optimum system design for the different operating conditions. Different combinations of refrigeration temperature (Te ) and heat rejection temperature

(Tc ) are studied in this section. The optimization variables are the high-pressure parameter and the dimensions generator temperature. Figs. 12–18 depict the system performance in the optimum design and Table 4 shows briefly the respective values. Fig. 12 shows the COP values of the examined systems and the enhancement compared to the system without subcooling. The COP is higher for greater refrigeration temperatures and fro lower heat rejection temperatures. On the other hand, the enhancements compared to the reference system are greater for lower refrigeration temperatures and higher heat rejection temperatures. Enhancement is found in all the cases with the maximum value to be 74.93% for (Te = −35 °C & Tc = 50 °C) and the minimum to be 0.39% for (Te = 5 °C & Tc = 35 °C). The mean COP enhancement is 23.35% which is a relatively satisfactory value which indicates that the examined idea has great enhancement potential. Fig. 13 depicts the exergy efficiency which is greater for lower heat rejection temperatures, while it is maximized for refrigeration production around −20 °C. The enhancements of the exergy

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Fig. 9. Exergy efficiency for different combinations of high-pressure ratio parameter and of dimensionless generator temperature (Te = −25 °C & Tc = 40 °C).

Fig. 10. Electricity consumption for different combinations of high-pressure ratio parameter and of dimensionless generator temperature (Te = −25 °C & Tc = 40 °C).

efficiency are similar to the enhancements of the COP compared to the reference system. Higher enhancements are found for lower refrigeration temperatures and greater heat rejection temperatures. Practically both the COP and exergy efficiency enhancements are higher when there is a greater temperature difference between the heat rejection temperature level and the refrigeration temperature level (Tc –Te ). In these cases, the pressure ratio in the compressor is higher and this fact increases the temperature (T2 ), as it is obvious from Fig. 18. This fact creates a higher potential for heat input in the generator and so higher subcooling can be achieved. The higher subcooling leads generally to greater COP as it has been explained in Section 3.2. The temperature difference (T2 –T23 ) which is given in Fig. 14 proves that higher values of the (T2 ) give higher temperature difference in the heat exchanger of the generator about the CO2 stream. Another interesting point that has to be discussed is the curve’s trends of the new system with subcooling (see Figs. 12 and 13)

compared to the reference system (see Fig. 3). The COP curves have similar trends, while the exergy efficiency curves have an important difference. For the novel system, the optimum exergy efficiency is found for refrigeration temperature close to −20 °C, while for the reference system around −10 °C. This fact indicates that the increase of the COP gives the potential for refrigeration production in lower temperatures with high performance. The next step in this analysis is the presentations of the optimization variables values in the optimum designs. Fig. 15 exhibits the optimum high-pressure ratio parameter and its increase compared to the reference system. Generally, the pressure ratio presents a small increase for greater refrigeration temperatures, while it has an important increase with higher heat rejection temperatures. Generally, the optimum high-pressure ratio parameter and consequently the high-pressure level (phigh ) is greater than the reference system with increases up to 10%, while the mean increase is 6%. These increases are reasonable because the higher

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Fig. 11. Subcooling degree values for different combinations of high-pressure ratio parameter and of dimensionless generator temperature (Te = −25 °C & Tc = 40 °C).

Fig. 12. COP of the optimized system and the enhancement compared to the reference system without subcooling. Table 4 Summary of the results for the optimized cases. Tc (°C)

Te (°C)

COP (-)

COP increase

ηex

α opt (-)

Tg,opt (°C)

Tsc

(-)

(°C)

Pel (kW)

Qg (kW)

COPach (-)

T2 (°C)

35 35 35 35 35 40 40 40 40 40 45 45 45 45 45 50 50 50 50 50

−35 −25 −15 −5 5 −35 −25 −15 −5 5 −35 −25 −15 −5 5 −35 −25 −15 −5 5

1.196 1.539 1.981 2.588 3.491 1.004 1.280 1.624 2.070 2.681 0.856 1.081 1.356 1.696 2.134 0.740 0.923 1.146 1.412 1.736

41.12% 24.13% 14.03% 6.75% 0.39% 50.31% 28.67% 16.55% 8.30% 1.54% 61.32% 33.52% 19.11% 9.66% 2.29% 74.93% 39.02% 21.63% 10.86% 2.89%

30.14% 31.01% 30.69% 28.95% 25.10% 25.29% 25.79% 25.16% 23.15% 19.27% 21.56% 21.78% 21.00% 18.98% 15.34% 18.63% 18.61% 17.75% 15.80% 12.48%

1.230 1.243 1.236 1.224 1.216 1.412 1.442 1.449 1.434 1.412 1.591 1.644 1.667 1.660 1.645 1.768 1.848 1.891 1.903 1.893

70.30 68.76 67.25 67.02 67.00 83.05 81.03 79.53 78.08 78.05 95.98 93.45 91.60 89.90 89.09 109.10 106.00 103.70 101.80 100.20

16.60 8.95 4.55 1.94 0.31 20.35 11.05 6.04 2.80 0.63 24.84 13.37 7.49 3.69 1.15 30.52 16.01 8.99 4.64 1.63

83.59 64.97 50.49 38.65 28.65 99.62 78.13 61.60 48.32 37.30 116.90 92.50 73.77 58.95 46.86 135.20 108.30 87.30 70.81 57.61

35.45 24.37 16.07 8.65 1.75 41.88 28.85 19.33 11.43 3.24 48.78 33.51 22.63 13.81 5.34 56.34 38.59 26.12 16.29 7.27

0.834 0.817 0.790 0.784 0.783 0.815 0.797 0.775 0.740 0.739 0.800 0.781 0.758 0.723 0.698 0.788 0.767 0.742 0.708 0.656

169.60 129.70 103.70 84.88 70.24 199.80 151.40 122.20 100.80 83.73 232.30 173.50 140.00 116.40 98.13 269.20 196.70 157.80 131.90 111.90

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Fig. 13. Exergy efficiency of the optimized system and the enhancement compared to the reference system without subcooling.

Fig. 14. CO2 temperature level before the generator (T2 ) and CO2 temperature decrease in the generator [T2 - T23 ] for the optimized system.

pressure level in the new system leads to higher temperatures after the compressor (T2 ) and so there is a potential for heat recovery in the generator and more subcooling production. The next optimization variable is the dimensionless generator temperature which is given in Fig. 16. The generator temperature is also given in this figure and it is an important parameter of the system design. Higher refrigeration temperatures reduce the optimum generator temperature and the (ηg ) parameter. Moreover, the optimum generator temperature is lower for lower heat rejection temperatures. Practically, the optimum generator temperature is lower when the refrigeration production is easier (lower heat rejection temperature and higher refrigeration production which is a reasonable conclusion. The maximum generator temperature is 109.1 °C and the lowest 67.0 °C. Fig. 17 shows the electricity demand and the subcooling degree for optimum cases. The electricity production has a reverse behavior compared to the COP, as it has been discussed in Section 3.2. The optimum subcooling degree is lower when the refrigeration

temperature increases and when the heat rejection temperature decreases. The maximum subcooling degree is found to be 30.52 °C and the minimum 0.31 °C. Fig. 18 shows the heat input in the generator and the absorption chiller COP. The heat input in the generator is lower in the cases with smaller (T2 ) which means in the cases with higher refrigeration temperature and lower heat rejection temperature. The absorption chiller COP has a small variation with the refrigeration production which is not always monotonic, something that is a result of the optimization procedure and the non-linear equation which are solved. The higher heat rejection temperature leads to lower absorption chiller COP in all the cases. Moreover, it has to be said that all the presented parameters of this section are included in Table 4. The COP enhancement values of the optimized cases compared to the conventional one are given this table and they are ranged from 0.39% up to 74.93%. At this point, it is useful to give some details about the exergy performance of the system. For the typical case (Te = −25 °C & Tc = 40 °C), the exergy efficiency is 25.79% and the other part

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Fig. 15. High-pressure ratio parameter of the optimized system and the increase compared to the reference system without subcooling.

Fig. 16. Optimum generator temperature and optimum dimensionless generator temperature for the optimized system.

Fig. 17. Electricity consumption and subcooling degree for the optimized system.

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Fig. 18. Heat input in the generator and absorption chiller COP for the optimized system.

Fig. 19. Simple payback period of the examined idea for different operating scenarios.

(74.21%) regards the exergy loss and the exergy destruction together. This part which regards the not utilized exergy is separated in the following terms: 19.86% in the gas cooler, 25.71% in the evaporator, 18.32% in the CO2 valve, 1.95% in the subcooler, 4.08% in the generator, 1.66% in the absorber, 1.48% in the condenser and 1.14% in the other devices of the absorption chiller. It is obvious that the greater exergy losses are found in the CO2 system and not in the absorption chiller. So, there is a need for improvement of this cycle by adding internal heat exchanger or using a two-stage compression cycle for example. The last step in this section is a simple financial analysis of the examined idea. Fig. 19 shows the simple payback period of the examined idea for different operating scenarios. These results have been found by assuming absorption chiller cost at 10 0 0 € /kWcool (Shirazi et al., 2016), electricity cost at 0.20 €/kWh (Bellos and Tzivanidis, 2018) and 20 0 0 h yearly operation at transcritical mode (Bellos and Tzivanidis, 2019). The results indicate that the invest-

ment is always viable with relatively low payback periods. However, the investment is extremely viable with payback period up to 4 years for the cases with the refrigeration production up to −15 °C. For the case with refrigeration production at 5 °C, the investment is not so viable with payback period about 10 years and more. For the typical case (Te = −25 °C & Tc = 40 °C), the simple payback period is found at 2.57 years which is a satisfying value. Generally, the investment is more viable in the cases with lower refrigeration production temperature and greater heat rejection temperature because in these cases there is a greater enhancement margin compared to the reference case. In the future, more detailed financial works can be performed and the system can be optimized financially. Moreover, another interesting idea for future work is the optimization of the system devices by minimizing the exergy destruction in every device. So, a detailed exergetic analysis (conventional or advanced) can be performed in this system for all the examined cases.

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4. Conclusions The objective of this work is the investigation of a novel transcritical CO2 refrigeration system. The examined configuration includes an absorption chiller for subcooling the CO2 after the gas cooler. The absorption chiller is driven by the waste heat of the compressor outlet and so there is not any need for any external heat source. The study is performed with a developed model in EES which is validated with literature data. The most important conclusions of this work are summarized below: •

•

•

•

•

•

The examined system with the subcooling is more efficient than the reference system without subcooling in all the examined cases. Both COP and exergy efficiency are enhanced. The mean COP enhancement is 23.35% while the maximum is 74.93%. The enhancement is greater in the cases with higher heat rejection temperature and lower refrigeration production temperature. The optimum high pressure of the new system is a bit higher than the optimum temperature of the reference system with a mean increase of 6%. The maximum subcooling degree is up to 30.52 °C for refrigeration production at −35 °C and heat rejection to the ambient at 50 °C. The simple payback period for the case (Te = −25 °C & Tc = 40 °C) is found at 2.57 years. The examined system is a promising choice for the CO2 refrigeration system because it is able to have higher performance in all the operating cases without the use of an external heat source. The only drawback of the examined system is the higher investment cost due to the use of an absorption chiller.

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