Analysis of a CO2 Transcritical Refrigeration Cycle with a Vortex Tube Expansion

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Article Analysis of a CO2 Transcritical Refrigeration Cycle with a Vortex Tube Expansion

Yefeng Liu *, Ying Sun and Danping Tang

University of Shanghai for Science and Technology, Shanghai 200093, China; [email protected] (Y.S.); [email protected] (D.T.) * Correspondence: [email protected]; Tel.: +86-21-55272320; Fax: +86-21-55272376

Received: 25 January 2019; Accepted: 19 March 2019; Published: 4 April 2019

Abstract: A carbon dioxide (CO2) refrigeration system in a transcritical cycle requires modifications to improve the coefficient of performance (COP) for energy saving. This modification has become more important with the system’s more and more widely used applications in heat pump water heaters, automotive air conditioning, and space heating. In this paper, a single vortex tube is proposed to replace the expansion valve of a traditional CO2 transcritical refrigeration system to reduce irreversible loss and improve the COP. The principle of the proposed system is introduced and analyzed: Its mathematical model was developed to simulate and compare the system performance to the traditional system. The results showed that the proposed system could save energy, and the vortex tube inlet temperature and discharge pressure had significant impacts on COP improvement. When the vortex tube inlet temperature was 45 ◦C, and the discharge pressure was 9 MPa, the COP increased 33.7%. When the isentropic efficiency or cold mass fraction of the vortex tube increased, the COP increased about 10%. When the evaporation temperature or the cooling water inlet temperature of the desuperheater decreased, the COP also could increase about 10%. The optimal discharge pressure correlation of the proposed system was established, and its influences on COP improvement are discussed.

Keywords: carbon dioxide transcritical refrigeration cycle; energy saving; vortex tube; COP; optimal discharge pressure

1. Introduction In recent years, the ever-increasing menace of ozone layer depletion and global warming has caused a great deal of attention to be paid by environmental protection and energy-saving refrigerant insiders. The natural refrigerant CO2, which is a probable replacement for conventional refrigerants such as HCFCs (R22) or HFCs (R134a and R404A), is environmentally friendly (ODP (Ozone Depletion Potential) = 0, GWP (Global Warming Potential) = 1), nonflammable, and nontoxic. At a given saturation temperature and pressure, the surface tension, liquid viscosity, and ratio of liquid to vapor density of CO2 are the lowest [1]. CO2 also has excellent heat transfer coefficients and compatibility with the materials of refrigeration systems. As an environmentally friendly refrigerant that replaces traditional refrigerants, CO2 has been popularized in heat pump water heaters, automotive air conditioners, and heating applications [2]. However, CO2 has a relatively high operating pressure due to its low critical temperature (31.1 ◦C) and high critical pressure (7.38 MPa): A transcritical cycle system is usually adopted. When an expansion valve is used for isenthalpic expansion, the irreversible loss it causes is as high as 40%, which is higher than that of a compressor [3]. Therefore, the coefficient of performance (COP) of a CO2 transcritical refrigeration system is usually low, and reducing cycle irreversible loss becomes an important way to improve the COP of a CO2 system. There are many

Sustainability 2019, 11, 2021; doi:10.3390/su11072021 www.mdpi.com/journal/sustainability Sustainability 2019, 11, 2021 2 of 14 ways to improve performance, such as a vortex tube, multistaging, an internal heat exchanger, or an expansion turbine and ejector [3–8]. A vortex tube is a mechanical device operating as a refrigerating machine without any moving parts, using the Ranque–Hilsch effect to separate a compressed gas stream into a low total temperature region and a high one. Currently, most vortex tube research is generally about compressed air [9–14]: There are a few studies on refrigerants such as CO2 existing in a gas–liquid phase transition, but they are not comprehensive enough. In 2000, Li et al. [4] ﬁrst proposed the use of vortex tubes instead of expansion valves to reduce irreversible losses. A simple thermodynamic analysis and calculation under the same operation conditions to compare the irreversible loss of the expansion valve, vortex tube, and turbine expander as throttle devices of a CO2 transcritical refrigeration cycle were performed by Li and Groll et al. [4,5]. The research showed that the use of a vortex tube as an expansion device in a CO2 transcritical cycle is a promising cycle modiﬁcation in improving a system performance COP. These articles focused on the performance of a system under a given operation condition and not under various operation conditions. As is known, due to the particular characteristics of CO2 transcritical refrigeration cycles, there is an optimal discharge pressure under which the COP is at a maximum, and the optimal discharge pressure is a function of the system operation conditions. For CO2 transcritical refrigeration systems with an expansion valve, the optimal discharge pressure correlation has been studied [15]. However, for the proposed system, the optimal discharge pressure correlation is more complex and has not been studied. In addition, the effects of vortex tube characteristics on CO2 transcritical refrigeration cycles need further research. Based on a thermodynamic analysis and a performance simulation, a CO2 transcritical refrigeration system with a vortex tube (i.e., the proposed system) was studied, and the COP improvement of the proposed system compared to a CO2 transcritical refrigeration system with an expansion valve (i.e., a basic system) was analyzed for this paper. The optimal discharge pressure correlation of the proposed system was established, and COP improvement under the optimal discharge pressure was studied.

2. Materials and Methods

2.1. CO2 Transcritical Refrigeration System with an Expansion Valve (i.e., a Basic System)

In traditional CO2 transcritical refrigeration systems, one expansion valve is used, as shown in Figure1. From Figure1, it can be seen that high-pressure and high-temperature CO 2 is discharged from the compressor (state 2b), and after a nonphase change heat release process (state 2b to state 3) via a gas cooler, CO2 enters the expansion valve and is expanded from a supercritical state to a vapor–liquid two-phase state (state 3b). Then, it enters the evaporator to absorb heat. Finally, CO2 returns to the compressor.Sustainability 2019, 11, 2021 3 of 16

FigureFigure 1. 1.Schematic Schematic of of aa basicbasic CO CO2 2transcriticaltranscritical refrigeration refrigeration system system with an with expansion an expansion valve. valve.

2.2. CO2 Transcritical Refrigeration System with a Vortex Tube (i.e., the Proposed System) A conventional vortex tube mainly contains an inlet nozzle, a vortex chamber, a cold-end orifice, a hot-end control valve, and a tube. It converts a gas flow initially homogeneous in temperature into two separate flows of differing temperatures. Due to the expansion of high-pressure CO2 through the vortex tube nozzle into the vapor–liquid two-phase zone, the vortex tube in this paper adds a saturated liquid outlet compared to the conventional vortex tube, as shown in Figure 2. The saturated liquid is collected in a ring inside the vortex tube (100% separation efficiency). The basic cycle and the proposed cycle of CO2 transcritical refrigeration systems (in a pressure (P)–enthalpy (h) diagram) are shown in Figure 3, and each state point code corresponds to the states of systems in Figure 1 and Figure 2. In Figure 3, states 2s and 3s indicate the states when the compression process and the expansion process are isentropic processes, respectively.

Figure 2. Schematic of the proposed CO2 transcritical refrigeration system with a vortex tube. Sustainability 2019, 11, 2021 3 of 16

Figure 1. Schematic of a basic CO2 transcritical refrigeration system with an expansion valve.

2.2. CO2 Transcritical Refrigeration System with a Vortex Tube (i.e., the Proposed System)

SustainabilityA conventional2019, 11, 2021 vortex tube mainly contains an inlet nozzle, a vortex chamber, a cold-end ori3fi ofce, 14 a hot-end control valve, and a tube. It converts a gas flow initially homogeneous in temperature into two separate flows of differing temperatures. Due to the expansion of high-pressure CO2 through the vortex2.2. CO 2tubeTranscritical nozzle into Refrigeration the vapor–liquid System with two-ph a Vortexase Tube zone, (i.e., the the vortex Proposed tube System) in this paper adds a saturatedA conventional liquid outlet vortex compared tube mainly to the conventional contains an inlet vortex nozzle, tube, aas vortex shown chamber, in Figure a 2. cold-end The saturated orifice, liquida hot-end is collected control valve,in a ring and inside a tube. the It vortex converts tube a gas(100% flow separation initially homogeneous efficiency). in temperature into The basic cycle and the proposed cycle of CO2 transcritical refrigeration systems (in a pressure two separate flows of differing temperatures. Due to the expansion of high-pressure CO2 through (theP)–enthalpy vortex tube (h) nozzlediagram) into are the shown vapor–liquid in Figure two-phase 3, and each zone, state thepoint vortex code tube corresponds in this paper to the adds states a ofsaturated systems liquid in Figure outlet 1 compared and Figure to the 2. conventionalIn Figure 3, vortexstates tube,2s and as 3s shown indicate in Figure the 2states. The saturatedwhen the compressionliquid is collected process in aand ring the inside expansion the vortex process tube are (100% isentropic separation processes, efficiency). respectively.

Figure 2. Schematic of the proposed CO2 transcritical refrigeration system with a vortex tube. Figure 2. Schematic of the proposed CO2 transcritical refrigeration system with a vortex tube.

The basic cycle and the proposed cycle of CO2 transcritical refrigeration systems (in a pressure (P)–enthalpy (h) diagram) are shown in Figure3, and each state point code corresponds to the states of systems in Figures1 and2. In Figure3, states 2s and 3s indicate the states when the compression Sustainability 2019, 11, 2021 4 of 16 process and the expansion process are isentropic processes, respectively.

Figure 3. Pressure (P)–enthalpy (h) diagram of the proposed cycle and the basic cycle. Figure 3. Pressure (P)–enthalpy (h) diagram of the proposed cycle and the basic cycle. From Figures2 and3, it can be seen that CO 2 is expanded from discharge pressure P (i.e., the gas coolerFrom Figure outlet 2 pressure) and Figure to evaporation3, it can be seen pressure that COPe2 isand expanded divided from into discharge three fractions, pressure including P (i.e., the gas cooler outlet pressure) to evaporation pressure Pe and divided into three fractions, including saturated liquid (state 4), which is collected by a groove inside the vortex tube; saturated vapor (state C); and superheated gas (state H). The saturated liquid and saturated vapor are mixed again (state 6) and go through the evaporator to give a useful cooling effect. The superheated gas is cooled in the desuperheater to state 5 and then mixed with the gas from the evaporator (state 7) to be state 1 before entering the compressor. The cycle processes of a basic CO2 transcritical refrigeration system and the proposed system can also be described as shown in Figure 4. It can be seen from Figure 3 that the enthalpy of the outlet of the vortex tube nozzle (state 3´) is lower than that of the expansion valve outlet (state 3b), and state 3´ is closer to the isentropic state 3s than state 3b. This is due to the higher isentropic effect of the vortex tube nozzle, which reduces the irreversible loss of the CO2 transcritical refrigeration cycle. At the same time, the superheated gas CO2 (state H) separated by the vortex tube is cooled by the desuperheater (state 5) to further reduce the suction temperature of the compressor and improve the system performance COP.

(a) Cycle process of the basic system (b) Cycle process of the proposed system

Figure 4. Cycle processes of the basic system and the proposed system: (a) Cycle process of the basic system; (b) Cycle process of the proposed system.

2.3. Mathematical Models and Assumptions The coefficient of performance of a refrigeration system is the ratio of the cooling capacity provided over the input power of the compressor. According to Figure 3, the calculation of COPb for a basic system with an expansion valve is the following: Sustainability 2019, 11, 2021 4 of 16

Figure 3. Pressure (P)–enthalpy (h) diagram of the proposed cycle and the basic cycle.

From Figure 2 and Figure 3, it can be seen that CO2 is expanded from discharge pressure P (i.e., the gas cooler outlet pressure) to evaporation pressure Pe and divided into three fractions, including saturated liquid (state 4), which is collected by a groove inside the vortex tube; saturated vapor (state C); and superheated gas (state H). The saturated liquid and saturated vapor are mixed again (state 6) and go through the evaporator to give a useful cooling effect. The superheated gas is cooled in the desuperheater to state 5 and then mixed with the gas from the evaporator (state 7) to be state 1 before Sustainability 2019, 11, 2021 4 of 14 entering the compressor. The cycle processes of a basic CO2 transcritical refrigeration system and the proposed system cansaturated also be liquiddescribed (state as 4),shown which in Figure is collected 4. by a groove inside the vortex tube; saturated vapor (stateIt C);can and be seen superheated from Figure gas 3 (state that the H). enthalpy The saturated of the liquid outlet andof the saturated vortex tube vapor nozzle are mixed (state again3´) is lower(state 6)than and that go of through the expansion the evaporator valve outlet to give (state a useful 3b), cooling and state effect. 3´ is The closer superheated to the isentropic gas is cooled state 3s in thanthe desuperheater state 3b. This is to due state to 5the and higher then mixedisentropic with effect the gasof the from vortex the evaporatortube nozzle, (state which 7) reduces to be state the 1 irreversiblebefore entering loss of the the compressor. CO2 transcritical refrigeration cycle. At the same time, the superheated gas CO2 (stateThe H) separated cycle processes by the of vortex a basic tube CO2 istranscritical cooled by refrigerationthe desuperheate systemr (state and the5) to proposed further reduce system the can suctionalso be temperature described as of shown the compressor in Figure4. and improve the system performance COP.

(a) Cycle process of the basic system (b) Cycle process of the proposed system

FigureFigure 4. 4. CycleCycle processes processes of of the the basic basic system system and and the the pr proposedoposed system: system: (a) (a) Cycl Cyclee process process of of the the basic basic system; (b) Cycle processsystem; of the proposed (b) Cycle system.process of the proposed system.

2.3. MathematicalIt can be seen Models from and Figure Assumptions3 that the enthalpy of the outlet of the vortex tube nozzle (state 3 0) is lower than that of the expansion valve outlet (state 3b), and state 30 is closer to the isentropic state 3s The coefficient of performance of a refrigeration system is the ratio of the cooling capacity than state 3b. This is due to the higher isentropic effect of the vortex tube nozzle, which reduces the provided over the input power of the compressor. According to Figure 3, the calculation of COPb for irreversible loss of the CO transcritical refrigeration cycle. At the same time, the superheated gas CO a basic system with an expansion2 valve is the following: 2 (state H) separated by the vortex tube is cooled by the desuperheater (state 5) to further reduce the suction temperature of the compressor and improve the system performance COP.

2.3. Mathematical Models and Assumptions The coefﬁcient of performance of a refrigeration system is the ratio of the cooling capacity provided over the input power of the compressor. According to Figure3, the calculation of COPb for a basic system with an expansion valve is the following:

(h7 − h3b) COPb = . (1) (h2b − h7)

The vortex tube nozzle outlet enthalpy h30 at given nozzle efﬁciency ηn can be calculated by

h30 = h3 − ηn × (h3 − h3s). (2)

Then, the vapor quality is found (x = x (Pe, h30 )) by using the thermodynamic property code in Refprop [16]. The deﬁnition of the cold mass fraction y can be calculated by m y = C . (3) mH + mC

Assuming that the refrigerant mass flow rate entering the vortex tube is 1 kg/s, and the liquid (1 − x) kg is separated from the vortex tube, then the total mass flow rate from the cold end at state C and from the hot end at state H is x, i.e., mH + mC = x. (4) Solving Equations (3) and (4), the fraction of saturated vapor is separated as saturated gas at the cold end, mC = x × y, and the rest absorbs all the kinetic energies and is separated as superheated gas at the hot end: mH = x × (1 − y), as shown in Figure2. Based on the first law of thermodynamics, the enthalpy of the superheated gas hH is given by Sustainability 2019, 11, 2021 5 of 14

h 0 − (1 − x) × h − x × y × h h = 3 4 C . (5) H x × (1 − y)

State 6 is the mixing point of state 4 and state C, so h6 can be found by

(1 − x) × h + x × y × h h = 4 7 . (6) 6 (1 − x + x × y)

State 5 can be found by using the effectiveness of desuperheater ε,

t5 = tH − ε × (tH − twi). (7)

State 1 is the mixing point of state 5 and state 7, so enthalpy at state 1 is found by

h1 = x × (1 − y) × h5 + (1 − x + x × y) × h7. (8)

For given compressor efﬁciency and compressor discharge pressure P, enthalpy at state 2 can be found by h2 = h1 + ηc × (h2s − h1). (9)

Based on the above calculation, the COPv of the proposed system is obtained by

(1 − x + x × y) × (h7 − h6) COPv = . (10) h2 − h1

The code “Imcop” is utilized to describe the COP improvement of the proposed system over the basic system, and it is calculated using the following equation,

Imcop = (COPv − COPb) × 100%/COPb. (11)

The following assumptions are made to simulate the system’s performance:

• The heat transfer effectiveness of the desuperheater is 0.8;

• The CO2 compressor isentropic efﬁciency is 0.8.

The vortex tube characteristics that influence the COP include the vortex tube isentropic efficiency ηn and the cold mass fraction y. The main thermodynamic parameters that influence the COP include the vortex tube inlet temperature T3 (i.e., the gas cooler outlet temperature), the discharge pressure P, the water inlet temperature of the desuperheater Twi, and the evaporation temperature T6. The setting of these parameters is shown in Table1. The reference values also mean the typical values of the variables. In the following simulation, when the impact of one variable is simulated, the other variables are reference values.

Table 1. Parameter settings for the performance simulation.

Parameters Reference Value Variation Range ◦ Vortex tube inlet temperature T3, C 40 25–45 ◦ Evaporation temperature T6, C 0 −10–10 Vortex tube isentropic efﬁciency ηn 80% 0%–100% Cold mass fraction y 0.5 0.3–0.8 Water inlet temperature of the ◦ 25 10–35 desuperheater Twi, C Discharge pressure P, MPa 9 8–12

All thermophysical properties of the refrigerant were calculated using the Refprop database [16]. Sustainability 2019, 11, 2021 6 of 14

3. Results and Discussions

3.1. Effects of Vortex Tube Characteristics and Thermodynamic Parameters on COP Improvement

3.1.1. Results Figure5 shows the variation in the COPs of the two systems and the COP improvement (i.e.,

Imcop) of theSustainability proposed 2019, 11 system, 2021 with the vortex tube inlet temperature. 7 of 16

Figure 5. VariationsFigure 5. Variations in coefﬁcients in coefficients of performanceof performance (C (COPs)OPs) and and COP COPimprovement improvement with vortex with tube vortex tube inlet temperature T3. inlet temperature T3.

From FigureFigure5, it6 shows can be the seen variation that in the COPs COP and of CO theP improvement basic system with and evaporation the proposed temperature system T6. decreased It can be seen that COP improvement increased gradually with a decrease in evaporation with an increasetemperature. in vortex When tubethe evaporation inlet temperature. temperature was However, −5 ℃, the COP COP increased improvement from 1.61 increased to 1.76, and significantly, ◦ ◦ especiallythe when COP the improvement vortex tube was inlet9.3%. The temperature reason was thatT3 wasthe quality higher of the than CO 402 fromC. the When nozzleT of3 was the 45 C, the COP of thevortex basic tube system (state waspoint 0.86,3’) increased and the when COP the ofevaporation the proposed temperature system decreased, was 1.15. and then Therefore, more the COP CO2 hot gas (state H) entered the desuperheater and was cooled, which led to a lower enthalpy of improvement was 33.7%. The reason was that when the vortex tube inlet temperature was higher, the CO2 (state 1) before entering the compressor. So, the input power of the compressor decreased and quality ofcaused the CO a higher2 at the COP. outlet of the vortex tube was higher, which caused a more efficient energy separation effect by the vortex tube and benefited COP improvement. Figure6 shows the variation in COPs and COP improvement with evaporation temperature T6. It can be seen that COP improvement increased gradually with a decrease in evaporation temperature. When the evaporation temperature was −5 ◦C, the COP increased from 1.61 to 1.76, and the COP improvement was 9.3%. The reason was that the quality of the CO2 from the nozzle of the vortex tube (state point 3’) increased when the evaporation temperature decreased, and then more CO2 hot gas (state H) entered the desuperheater and was cooled, which led to a lower enthalpy of CO2 (state 1) before entering the compressor. So, the input power of the compressor decreased and caused a higher COP. The isentropic efficiency of a vortex tube changes with different vortex tube geometries. In order to design a vortex tube, it is necessary to investigate the impact of the isentropic efficiency of a vortex tube on a system’s COP. Figure7 shows the variation in COPs and COP improvement with vortex tube isentropic efficiency. It can be seen that COP improvement increased obviously with an increase in the vortex tube isentropic efficiency ηn. COP improvement was 11.6% when the expansion in the vortex tube was an isentropic process. Therefore, increasing vortex tube isentropic efficiency was an Figure 6. Variation in COPs and COP improvement with evaporation temperature T6. important way to improve COP, too. Figure8 showsThe isentropic the variation efficiency inof a COPs vortex tube and change COPs improvement with different vortex with tube cold geometries. mass fraction.In order It can be to design a vortex tube, it is necessary to investigate the impact of the isentropic efficiency of a vortex seen that COPv gradually increased with an increase in cold mass fraction y. When the cold mass tube on a system’s COP. Figure 7 shows the variation in COPs and COP improvement with vortex fraction y was 0.8, the COP of the proposed system was 11.5% higher than that of the basic system. tube isentropic efficiency. It can be seen that COP improvement increased obviously with an increase When the coldin themass vortex fraction tube isentropicy increased, efficiency the ηn. COP hot gasimprovement (state H) was temperature 11.6% when the increased, expansion and in the heat capacity was rejected from the desuperheater increases, too. Therefore, the temperature and enthalpy of CO2 at the inlet of compress (state 1) decreased, which benefited COP improvement. Sustainability 2019, 11, 2021 7 of 16

Figure 5. Variations in coefficients of performance (COPs) and COP improvement with vortex tube

inlet temperature T3.

Figure 6 shows the variation in COPs and COP improvement with evaporation temperature T6. It can be seen that COP improvement increased gradually with a decrease in evaporation temperature. When the evaporation temperature was −5 ℃, the COP increased from 1.61 to 1.76, and the COP improvement was 9.3%. The reason was that the quality of the CO2 from the nozzle of the vortex tube (state point 3’) increased when the evaporation temperature decreased, and then more CO2 hot gas (state H) entered the desuperheater and was cooled, which led to a lower enthalpy of SustainabilityCO2 (state2019 1) ,before11, 2021 entering the compressor. So, the input power of the compressor decreased and7 of 14 caused a higher COP.

Sustainability 2019, 11, 2021 8 of 16

vortex tube was an isentropic process. Therefore, increasing vortex tube isentropic efficiency was an important way to improve COP, too.

Sustainability 2019, 11, 2021 8 of 16

vortex tube was an isentropic process. Therefore, increasing vortex tube isentropic efficiency was an important way to improve COP, too. FigureFigure 6. 6.Variation Variation in in COPs COPs andand COPCOP improvement with with evaporation evaporation temperature temperature T6T. 6.

The isentropic efficiency of a vortex tube changes with different vortex tube geometries. In order to design a vortex tube, it is necessary to investigate the impact of the isentropic efficiency of a vortex tube on a system’s COP. Figure 7 shows the variation in COPs and COP improvement with vortex tube isentropic efficiency. It can be seen that COP improvement increased obviously with an increase in the vortex tube isentropic efficiency ηn. COP improvement was 11.6% when the expansion in the

Figure 7. Variation in COPs and COP improvement with vortex tube isentropic efficiency ηn.

Figure 8 shows the variation in COPs and COP improvement with cold mass fraction. It can be seen that COPv gradually increased with an increase in cold mass fraction y. When the cold mass fraction y was 0.8, the COP of the proposed system was 11.5% higher than that of the basic system. When the cold mass fraction y increased, the hot gas (state H) temperature increased, and heat capacity was rejected from the desuperheater increases, too. Therefore, the temperature and enthalpy 2 η of CO Figure atFigure the 7.inlet 7.Variation Variation of compress in in COPs COPs (state andand 1) COPCOP decreased, improvement which wi with benefitedth vortex vortex tube tubeCOP isentropic isentropic improvement. efficiency efﬁciency ηn. n.

Figure 8 shows the variation in COPs and COP improvement with cold mass fraction. It can be seen that COPv gradually increased with an increase in cold mass fraction y. When the cold mass fraction y was 0.8, the COP of the proposed system was 11.5% higher than that of the basic system. When the cold mass fraction y increased, the hot gas (state H) temperature increased, and heat capacity was rejected from the desuperheater increases, too. Therefore, the temperature and enthalpy of CO2 at the inlet of compress (state 1) decreased, which benefited COP improvement.

Figure 8. Variation in COPs and COP improvement with cold mass fraction y. Figure 8. Variation in COPs and COP improvement with cold mass fraction y.

Similarly, when the inlet water temperature of the desuperheater decreased, COP improvement increased due to more heat rejection. When Twi was 10 ℃, COP improvement was 12.0%, as shown in Figure 9.

Figure 8. Variation in COPs and COP improvement with cold mass fraction y.

Similarly, when the inlet water temperature of the desuperheater decreased, COP improvement increased due to more heat rejection. When Twi was 10 ℃, COP improvement was 12.0%, as shown in Figure 9. Sustainability 2019, 11, 2021 8 of 14

Similarly, when the inlet water temperature of the desuperheater decreased, COP improvement ◦ increased due to more heat rejection. When Twi was 10 C, COP improvement was 12.0%, as shown Sustainability 2019, 11, 2021 9 of 16 inSustainability Figure9. 2019, 11, 2021 9 of 16

Figure 9. Variation in COPs and COP improvement with inlet water temperature of the FigureFigure 9. 9. Variation Variation in in COPs COPs and and COP COP improvement improvement with with inlet inlet water water temperature temperature of of the the desuperheater desuperheater desuperheater Twi. TTwiwi. . Figure 10 shows the variation in COPs and COP improvement with discharge pressure. It can be FigureFigure 10 10 shows shows the the variation variation in in COPs COPs and and COP COP improvement improvement with with discharge discharge pressure. pressure. It It can can seen that the COPs of both the basic system and the proposed system increased and then decreased bebe seen seen that that the the COPs COPs of of both both the the basic basic system system an andd the the proposed proposed system system increased increased and and then then decreased decreased with discharge pressure increases, and there were optimal discharge pressures with maximum cooling withwith dischargedischarge pressurepressure increases,increases, andand therethere werewere optimaloptimal dischargedischarge pressurespressures withwith maximummaximum COPs for the two systems. However, COP improvement decreased signiﬁcantly with discharge coolingcooling COPsCOPs forfor thethe twotwo systems.systems. However,However, COPCOP improvementimprovement decreaseddecreased significantlysignificantly withwith pressure increases, especially when the discharge pressure was lower than 9 MPa. When the discharge dischargedischarge pressure pressure increases, increases, especially especially when when th thee discharge discharge pressure pressure was was lower lower than than 9 9 MPa. MPa. When When pressure was 8.4 MPa, COP improvement increased by 25.3%. thethe discharge discharge pressure pressure was was 8.4 8.4 MPa, MPa, COP COP improvement improvement increased increased by by 25.3%. 25.3%.

Figure 10. Variation in COPs and COP improvement with discharge pressure P. FigureFigure 10. 10. Variation Variation in in COPs COPs and and COP COP improv improvementement with with discharge discharge pressure pressure P P. .

3.1.2.3.1.2. Discussions Discussions FromFrom the the above above results, results, it it can can be be found found that that th thee discharge discharge pressure pressure was was a a critical critical thermodynamic thermodynamic parameterparameter for for COP COP improvement. improvement. Therefore, Therefore, it it wa wass extremely extremely important important and and necessary necessary to to research research thethe optimal optimal discharge discharge pressure pressure for for the the optimal optimal design design of of the the proposed proposed CO CO2 2transcritical transcritical refrigeration refrigeration Sustainability 2019, 11, 2021 9 of 14

3.1.2. Discussions From the above results, it can be found that the discharge pressure was a critical thermodynamic parameter for COP improvement. Therefore, it was extremely important and necessary to research the optimal discharge pressure for the optimal design of the proposed CO2 transcritical refrigeration system with a vortex tube. Therefore, research on the optimal pressure correlation for the proposed system,Sustainability and its effects2019, 11, 2021 on COPs and COP improvement, is developed in the following sections.10 of 16

3.2. Regressionsystem with of Optimal a vortex Dischargetube. Therefore, Pressure research Correlation on the foroptimal the Proposed pressure System correlation with for aVortex the proposed Tube and a COP Improvementsystem, and its Investigation effects on COPs under and Optimal COP improvement, Discharge Pressure is developed in the following sections.

As3.2. is Regression known, due of Optimal to the Discharge particular Pressure characteristics Correlation of for CO the2 Proposedtranscritical System refrigeration with a Vortex Tube cycles, and there a is an optimalCOP Improvement discharge pressure Investigation under under which Optimal the Discharge COP is atPressure a maximum. For a basic system, the optimal discharge pressureAs is known, correlation due to the has particular already characteristics been researched of CO and2 transcritical given. It is refrigeration a function ofcycles, the gasthere cooler outletis temperature an optimal discharge and theevaporation pressure under temperature, which the COP and is it canat a bemaximum. described For as a thebasic following system, the [15 ]: optimal discharge pressure correlation has already been researched and given. It is a function of the gas cooler outlet temperaturePb,opt = (2.778 and −the0.0157 evaporatio× T6n)T temperature,3 + (0.381T 6and− 9.34).it can be described as the (12) following [15]: Similarly, there is also an optimal discharge pressure for the proposed system with a vortex tube. Because the proposed systemPb,opt = is(2.778 more−0.0157 complex×T6) T than3+(0.381T the6− basic9.34). system, the influence(12) factors include not only the vortex tube inlet temperature T and the evaporation temperature T , but also Similarly, there is also an optimal discharge pressure3 for the proposed system with a vortex6 the characteristictube. Because parameters the proposed of system the vortex is more tube, comp suchlex than as cold the basic mass system, fraction they influence, vortex tubefactors isentropic η efficiencyincluden ,not and only water the vortex inlet temperaturetube inlet temperature of the desuperheater T3 and the evaporationTwi. Thus, temperature the optimal T6, but discharge pressurealso is the the characteristic function Pv,opt parameters= ƒ(T3,T of6, ythe,ηn vortex,Twi). tube, such as cold mass fraction y, vortex tube Inisentropic order to efficiency simplify theηn, and correlation, water inlet some temperature of the parameters of the desuperheater are given asTwi the. Thus, following the optimal assumptions: discharge pressure is the function Pv,opt = ƒ(T3,T6,y,ηn,Twi). • The coldIn order mass to simplify fraction they is correlation, 0.5; some of the parameters are given as the following • Theassumptions: vortex tube isentropic efficiency ηn is 0.8;  The cold mass fraction y is 0.5; ◦ • The water inlet temperature of the desuperheater Twi is 25 C.  The vortex tube isentropic efficiency ηn is 0.8; Based The on water the mathematical inlet temperature models of the in desuperheater Section2, the T optimalwi is 25 ℃ discharge. pressures were calculated for the proposedBased on systemthe mathematical under different models in inletSection temperatures 2, the optimal ofdischarge the vortex pressures tube were and calculated evaporation temperatures,for the proposed and the optimalsystem under discharge different pressures inlet te ofmperatures the basic systemof the vortex were alsotube calculated,and evaporation as shown in Figuretemperatures, 11. From and Figure the optimal11, it can discharge be seen pressures that there of the were basic slightly system differenceswere also calculated, between as the shown optimal in Figure 11. From Figure 11, it can be seen that there were slightly differences between the optimal discharge pressure values for the proposed system and the basic system. Therefore, the vortex tube discharge pressure values for the proposed system and the basic system. Therefore, the vortex tube did not much affect the values of the optimal discharge pressure. did not much affect the values of the optimal discharge pressure.

(a) T6 = −10℃

Figure 11. Cont. Sustainability 2019, 11, 2021 10 of 14 Sustainability 2019, 11, 2021 11 of 16

(b) T6 = 0℃

FigureFigure 11. 11.Variation Variation inin optimaloptimal discharge pressures pressures with with the theinlet inlet temperature temperature of the of vortex the vortex tube/expansiontube/expansion valve valve T T3 3 andand evaporationevaporation temperature temperature T6 Tfor6 forthe theproposed proposed system system and the and basic the basic ◦ ◦ ◦ system:system:. (a)T (a)6 = T6− =10 −10℃,C, ((b)b)T T6 == 0 0℃,C, (c) ( cT)T6 = 610=℃ 10. C.

BasedBased on on the the simulation simulation results, results, thethe values of of the the optimal optimal discharge discharge pressure pressure for the for proposed the proposed CO2COtranscritical2 transcritical refrigeration refrigeration system system with a a vortex vortex tu tubebe were were regressed regressed in terms in terms of vortex of vortex tube inlet tube inlet temperaturetemperature and and evaporation evaporation temperature, temperature, and th thee correlation correlation was was obtained obtained as the as following: the following:

Pv,opt = 2.4895−0.027T6+0.0985T3+0.00229T32. (13) Pv,opt = 2.4895 − 0.027T6 + 0.0985T3 + 0.00229T32. (13)

Apart from the conditions (y = 0.5, ηn = 0.8, Twi = 25℃) set for this correlation, a range in the Apart from the conditions (y = 0.5, η = 0.8, T = 25 ◦C) set for this correlation, a range in the vortex tube inlet temperature T3 from 30 ℃n to 50 ℃wi and the evaporation temperature T6 from ◦ ◦ vortex−10 tube ℃ to inlet 10 ℃ temperature was also required.T3 from It is worth 30 C mentioni to 50 Cng and that the the evaporation coefficient of determination temperature RT26 from −10 ◦ ◦ C towas 10 99.8%,C was and also the required. average deviati It is worthon was mentioningless than 5%, thatwhich the indicated coefficient that ofthe determination relationship R2 was 99.8%,between and the the average discharge deviation pressure wasPv,opt less, vortex than tube 5%, whichinlet temperature indicated thatT3, and the evaporation relationship between the dischargetemperature pressure T6 were highlyPv,opt, vortexpositively tube correlated. inlet temperature Moreover, theT3 value, and of evaporation the F significant temperature statistic T6 were highly positively correlated. Moreover, the value of the F significant statistic was 2.75 × 10−15, which was far less than the significance level of 0.05, showing a significant regression effect of this regression equation. Sustainability 2019, 11, 2021 11 of 14

According to Equations (12) and (13), the optimal discharge pressures of the basic system and the proposed system could be calculated with various T3 and T6. Then, based on the above mathematical models,Sustainability the COPs 2019 and, 11,COP 2021 improvement were obtained, as shown in Figure 12. 13 of 16

(a) T6 = −10 ℃

(b) T6 = 0 ℃

Figure 12.FigureVariation 12. Variation in COPs in COPs and and COP COP improvement improvement under under an an optimaloptimal discharge discharge pressure pressure with with an an inlet temperature of the vortex tube/expansion valve T3 and evaporation temperature T6. inlet temperature of the vortex tube/expansion valve T3 and evaporation temperature T6.

From FigureFrom Figure 12, it 12, can it be can seen be seen that that the the COPs COPs of of the the proposed proposed systemsystem were were higher higher than than those those of of the basic system. COP improvement increased gradually with an increase in the vortex tube inlet the basic system. COP improvement increased gradually with an increase in the vortex tube inlet Sustainability 2019, 11, 2021 12 of 14

temperature T3 and decreased slightly with an increase in the evaporation temperature T6. It should be noted that COP improvement increased obviously when the vortex tube inlet temperature T3 ◦ ◦ was higher than 40 C. When the vortex tube inlet temperature T3 was −10 C and the evaporation ◦ temperature T6 was 45 C, COP improvement was 7.1%. Based on the above results, when the gas cooler outlet temperature is high, utilizing a vortex tube in a CO2 transcritical refrigeration system can be more beneﬁcial in terms of reducing irreversible loss and improving the COP.

4. Conclusions

A CO2 transcritical refrigeration system with a vortex tube expansion was proposed in this paper. In the proposed system, one vortex tube is used to replace the expansion valve in order to reduce irreversible loss and improve system performance COP. The inﬂuences of various parameters on the COP improvement of the proposed system were simulated and analyzed. The optimal discharge pressure correlation of the proposed CO2 transcritical refrigeration system with a vortex tube was regressed and obtained. The following conclusions were drawn:

• The COP of the proposed system with a vortex tube was higher than that of the basic system with an expansion valve; • The critical inﬂuence factors of COP improvement were the inlet temperature of the vortex tube (i.e., the outlet temperature of the gas cooler) and the discharge pressure. The higher the inlet temperature of the vortex tube, the higher COP improvement was. The lower the discharge pressure, the higher COP improvement was. When the inlet temperature of the vortex tube was 45 ◦C, the discharge pressure was 9 MPa, and the COP increased by 33.7%; • The higher the isentropic efﬁciency of the vortex tube, the higher the COP improvement was. COP improvement could be up to 11.6%; • The more the cold mass fraction of the vortex tube, the higher the COP improvement was. When the cold mass fraction was 0.8, COP improvement was 11.5%; • The lower the evaporation temperature, the higher COP improvement was. When the evaporation temperature was −5 ◦C, COP improvement was 9.2%; • The lower the inlet water temperature of the desuperheater, the higher COP improvement was. When the inlet water temperature of the desuperheater was 10 ◦C, COP improvement was 12.0%; • Under optimal discharge pressures, COP improvement increased gradually with an increase in vortex tube inlet temperature and decreased slightly with an increase in evaporation temperature. When the vortex tube inlet temperature was −10 ◦C, and the evaporation temperature was 45 ◦C, COP improvement was 7.1%.

The effects of the vortex tube inlet temperature and discharge pressure on COP improvement were more signiﬁcant compared to the isentropic efﬁciency, evaporation temperature, desuperheater water inlet temperature, and cold mass fraction of the vortex tube in the proposed system. Therefore, the application of a vortex tube is highly recommended when a higher vortex tube inlet temperature and lower discharge pressure are required. These research results provide a theoretical basis for the following design and experimental research of a CO2 transcritical refrigeration system with a vortex tube.

Author Contributions: Funding acquisition, Y.L.; investigation, Y.S. and D.T.; methodology, Y.L.; validation, Y.S.; writing—original draft, Y.S.; writing—review and editing, Y.L. Funding: This research was funded by Shanghai Committee of Science and Technology of China, grant number 17PJ1407200. Acknowledgments: The authors gratefully acknowledge the Shanghai Committee of Science and Technology of China (Shanghai Pujiang Program, grant number 17PJ1407200). Conﬂicts of Interest: The authors declare no conﬂicts of interest. Sustainability 2019, 11, 2021 13 of 14

Nomenclature

English letters COP coefﬁcient of performance

COPb COP of the basic system COPv COP of the proposed system h specific enthalpy (kJ/kg) Imcop COP improvement of the proposed system over the basic system (%) P discharge pressure (MPa) T temperature (◦C) x quality y cold mass fraction m mass flow rate (kg/s) Greek letters ε heat exchanger effectiveness η isentropic efficiency Subscript b basic system with expansion valve c compressor or cold end of vortex tube H hot end of vortex tube s isentropic process n vortex tube nozzle wi water inlet of desuperheater v the proposed system with vortex tube expansion opt optimal

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