heat pump system using R32

heat pump system using R32

International Journal of Thermal Sciences 68 (2013) 103e109 Contents lists available at SciVerse ScienceDirect International Journal of Thermal Scie...

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International Journal of Thermal Sciences 68 (2013) 103e109

Contents lists available at SciVerse ScienceDirect

International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts

Experiment study of an enhanced vapor injection refrigeration/heat pump system using R32 Xu Shuxue*, Ma Guoyuan, Liu Qi, Liu Zhongliang Beijing University of Technology, Beijing 100124, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 31 May 2012 Received in revised form 22 December 2012 Accepted 23 December 2012 Available online 10 February 2013

R32, with an ozone depletion potential (ODP) of zero and a global warming potential (GWP) of 675, may be an acceptable working fluid for refrigeration/heat pump systems to replace HFCs. The performance of an enhanced vapor injection refrigeration/heat pump system (EVI system) was experimentally investigated using R32. The results show that this system reduces the discharge temperatures for both cooling and heating, with the heating capacity of the EVI system using R32 3 e 9% higher than that of the singlestage system. The cooling capacity, cooling EER and heating COP depend on the refrigerant intermediate pressure and the operating conditions so they can be bigger or smaller than for the single-stage system. The best range of relative vapor injection mass is 12 e 16% for the best overall cooling and heating performance. Vapor injection changes the systems operating conditions, and increases both the evaporating and condensing temperatures by 0.8 e 1  C. Ó 2013 Elsevier Masson SAS. All rights reserved.

Keywords: R32 Enhanced vapor injection Heat pump Refrigeration

1. Introduction HFC refrigerant mixtures with favorable thermodynamic properties, such as R410A and R407C are recognized as the best alternatives for R22, but they still have high global warming potentials (GWP from 1700 to 2000, even higher than 1700 for R22), and will be phased out in the future. Hydrocarbons have a zero ozone depletion potential (ODP) and an extremely low GWP. From the technical and thermodynamic points of view, hydrocarbons such as R290 and R1270 are good alternatives for R22, but they are not safe. According to the ASHRAE 34 and prEN 378 standards, R290 is a highly flammable (class 3) refrigerant. R32, the main component of R410A, with zero ODP and a relatively low GWP (675), has similar thermodynamic properties with R410A but is less expensive and has been recognized as an attractive short term candidate to replace R22 [1]. Many researchers have studied the performance of systems using refrigerant mixtures with R32 as a component. These mixtures have lower flammability and improved cycle performance. M.H, Barley, et al. [2] reported vaporeliquid equilibrium data for binary mixtures of R32/R125, R32/R143a and R32/Rl34a for temperatures down to at least 30  C. Yu, J.L et al. [3] performed thermodynamic analyses of the performance of transcritical cycles

* Corresponding author. Tel./fax: þ86 10 67391613. E-mail addresses: [email protected], [email protected] (X. Shuxue). 1290-0729/$ e see front matter Ó 2013 Elsevier Masson SAS. All rights reserved. http://dx.doi.org/10.1016/j.ijthermalsci.2012.12.014

using R32/R290 with a 70/30 mass fraction in small heat pumps with the results showing that the system can produce hot water at temperatures up to 90  C with a big heating COP. There have been many studies of the performance of the binary non-azeotropic mixture R32/R134a [4e7], analyzed a ternary non-azeotropic mixture of R32/R125/R161 as an alternative refrigerant to R407C with the experimental results showing that for different operating conditions, the pressure ratio and power consumption of this refrigerant are lower than those of R407C and its cooling capacity and EER are superior to those of R407C. Ref. [8] presented an experimental study of R152a and R32 to replace R134a in domestic refrigerators with their results showing an average EER of R32 which is 8.5% lower than that of R134a with the performance of R152a in the domestic refrigerator consistently better than that of R134a and R32. Ref. [9] reported on a ternary blend of R152a/R125/ R32 with a mass ratio of 48/18/34 as a potential alternative to R22. The flammability of the ternary blend was also studied with an explosion apparatus to prove that it could be used safely. An enhanced vapor injection system (EVI system) can effectively improve the cooling/heating performance of vapor compression refrigeration/heat pump systems by increase the cooling/heating performance coefficients and reducing the discharge temperature in cold climates. Many papers have been published on EVI systems, including system types, injection with different kinds of compressors, and the effects of the injection refrigerant state on the system performance [10e14], reviewed much of the research on refrigerant injection and showed that an appropriate flash tank design

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X. Shuxue et al. / International Journal of Thermal Sciences 68 (2013) 103e109

Nomenclature di e h l le m p pk pm po P Qk Qo Re

t tk to u w x EER COP Dp

inner diameter of pipe (m) absolute roughness of inner tube (m) enthalpy (kJ/kg) length of pipe (m) equivalent lengths (m) mass flow rate (kg/s) pressure (MPa) condensing pressure (MPa) intermediate pressure (MPa) evaporating pressure (MPa) power input (kW) heating capacity (kW) cooling capacity (kW) Reynolds number (dimensionless)

3

le r

Subscripts 1, 2, 20 state points shown in the figures

plays a vital role in improving EVI system performance and that the compressor design can be improved to optimize the refrigerant injection performance. For the R22 EVI system, compared with SS system, the heating capacity can increase 10 e 34% and heating EER increase 5 e 10%, discharge temperature decreases 15 e 20  C, cooling capacity and COP improvement were about 5% and 15% [15]. Used R410A as the working fluid to experimentally investigate an EVI scroll compressor with the results showing that the heating capacity was increased about 30% and the COP was increased about 20% at an ambient temperature of 17.8  C. Ref. [16] did CO2 vapor injection research and the heating capacity and COP of EVI were improved by 45% and 24%, cooling COP can be enhanced by 16.5%. This paper describes an experimental investigation of the performance of an EVI refrigeration/heat pump system that originally operated with R32. The main aim is to evaluate the EVI system performance using R32 under the cooling and heating condition in domestic refrigerating/heat pumping systems. This study provides useful data for the development of R32 systems.

where m is the refrigerant mass flow rate [kg/s], p is the pressure [MPa], P is the power input [kW], h is the enthalpy [kJ/kg], 3 is relative vapor injection mass [dimensionless], and 1, 2.6, are the state points in Fig. 1. As shown in Fig. 1, when the EVI system is running, the vapor flashing must absorb heat from the liquid in the bottom, thus, the liquid in the tank must be cooled and enthalpy decreases, specific data can be seen in Table 1. For example, p3 ¼ 2.48 MPa and t3 ¼ 35  C, when vapor injection pressure (p4) decrease from 2.1 MPa to 1.4 MPa, the liquid enthalpy from 262.0 kJ/kg decreases to 232.6 kJ/kg; p3 ¼ 2.80 MPa and t3 ¼ 40  C, when vapor injection pressure (p4) from 2.3 MPa to 0.9 MPa, the liquid enthalpy from 269.3 kJ/kg decreases to 205.6 kJ/kg. The maximum relative vapor injection mass increases with the vapor injection pressure decrease, for example, p3 ¼ 2.48 MPa and t3 ¼ 35  C, when vapor injection pressure (p4) from 2.1 MPa to 1.4 MPa, 3 increases from 1.3% to 12.9%. That is because the dryness fraction of saturation refrigerant (x) increases with the vapor injection pressure decrease. The vapor injection mass flow rate can be calculated as:

2. EVI system The operating fundamentals of the EVI system are shown in Fig. 1. The system has a flash-tank with the system compressor having supplementary inlets. The high pressure refrigerant from the condenser flows into the expansion valve 1 and its pressure drops to intermediate pressure, and then enters into flash-tank. In the flash-tank, the refrigerant is separated into pure liquid and saturated vapor. On one hand, the liquid refrigerant from the bottom of the flash-tank flows into expansion valve 2 and its pressure drops to the evaporating pressure, and then enters into the evaporator; on the other hand, the saturated vapor leaving from the top of the flash-tank is injected into the compressor with suitable pressure adjusted by expansion valve 3. The mass and energy conservation equations for the compressor can be written as:

m2 ¼ m1 þ m6

temperature ( C) condensing temperature ( C) evaporating temperature ( C) flow velocity (m/s) compressor work (kJ/kg) dryness fraction cooling performance heating performance pressure difference (MPa) relative vapor injection mass frictional resistance coefficient of inner pipe (dimensionless) density of vapor (kg/m3)

(1)

m6 ¼

1 2 pd ru 4 i

where, di is the inner diameter of the pipe [m]; r is the density of vapor injected into the compressor [kg/m3]; and u is the flow velocity of the vapor [m/s].

2 Condenser

3

2

(2)

m4 h4 ¼ m5 h5 þ m6 h6

(3)

3

¼

m6 m  m5 ¼ 4 m5 m5

Scroll compressor Expansion valve 3 1

Expansion valve 1 4 6

m4 ¼ m5 þ m6

(5)

Expansion valve 2 7 5 Evaporator

Flash-tank (4) Fig. 1. EVI system.

X. Shuxue et al. / International Journal of Thermal Sciences 68 (2013) 103e109 Table 1 The variation of

3

with vapor injection pressure.

p3 ¼ 2.48 MPa, t3 ¼ 35  C, h3 ¼ 265.1 kJ/kg

p3 ¼ 2.80 MPa, t3 ¼ 40  C, h3 ¼ 275.3 kJ/kg

p4 (MPa)

x4 (%)

h5 [kJ/kg]

3

2.1 2.0 1.9 1.8 1.7 1.6 1.5 1.4 2.3 2.1 1.9 1.7 1.5 1.3 1.1 0.9

1.2 2.7 4.2 5.6 7.0 8.5 9.9 11.4 2.4 5.3 8.1 10.8 13.6 16.4 19.4 22.5

262.0 258.1 254.2 250.2 246.0 241.7 237.3 232.6 269.3 262.0 254.2 246.0 237.3 227.8 217.4 205.6

1.3 2.8 4.3 5.9 7.6 9.3 11.0 12.9 2.5 5.6 8.8 12.1 15.7 19.7 24.0 29.0

(%)

But the vapor injection velocity is depended on the difference in pressure between point 6 and point 20 , Dp, and it can be calculated according to the following equations:

Dp ¼ p6  p2’ ¼ le 2

l þ le ru2 di 2



e 106 le ¼ 0:005541 þ 20000 þ Re di

(6) 13

3 5

compressor), and these accessories flow resistance were shown as “le” in equation (8). The injection pressure was regulated by the manually-operated expansion valve. In equations (7) and (8), le is frictional resistance coefficient of inner pipe [dimensionless]; l is length of pipe [m]; e is absolute roughness of inner pipe [m]; and Re is Reynolds number [dimensionless]. Because the maximum relative vapor injection mass increases with the vapor injection pressure decrease, that is say, when m6 is small and Dp is large, and m6 is large with Dp small. So a pressure regulation device must be set in the vapor injection pipe line to regulate the vapor flow mass by changing the resistance characteristics of pipe and further, changing the pressure difference of Dp. Low enthalpy vapor is injected into the compressor to reduce the discharge temperature and compressor power consumption, and the effect of the vapor injection on the EVI system performance depends on whether the system is operating in cooling or heating mode. For the cooling mode, the vapor injection can decrease the enthalpy of the liquid entering the main expansion valve, which increases the unit cooling capacity. However, the vapor injection also decreases appreciably the refrigerant mass flow rate through the evaporator when opening angle of the main expansion valve was fixed. For the heating mode, the vapor injection can increase the refrigerant mass flow rate through the condenser and the heating capacity. Therefore, the influence of vapor injection on the EVI system performance depends on the operating mode, whether cooling or heating, as well as the vapor injection characteristics.

(7) 3. Experimental setup and procedures

Combining equations (5) and (6), the following equation was obtained.

1 m6 ¼ pd2i 4

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2rDp di $ le l þ le

(8)

The parts arousing flow resistance of the line include pipeline and its accessories (valve, elbows, reducer, etc, hole structure of the

This study analyzes the performance of a prototype heat pump using R32 measured using the experimental apparatus described by [12]. As seen in Fig. 2, the system has a water-cooled condenser and a glycol-water solution heated evaporator. A scroll compressor originally designed for R410A with two manually controlled expansion valves used to regulate the mass flow rate. The heating capacity of the condenser and the cooling capacity of the evaporator were calculated by the enthalpy difference multiplying the

t 6 p6

t5 p5

Drier-filter Flash-tank Cooling tower

t7 p7

t13

t8 p8

Mass flow rate meter t12

t4 p4

t11

One-way valve

Condenser

t9 p9

t10 Backwater pump Mass flow rate meter

t 3 p3

t1 p1

Evaporator

t2 p2

Watersupply pump

Scroll compressor

Electric heating coil

Shutoff valve

105

Manually controlled expansion valve

Glycol pump

Electric heating coil Pressure sensor

Fig. 2. Schematic diagram of the experimental system.

Temperature sensor

106

X. Shuxue et al. / International Journal of Thermal Sciences 68 (2013) 103e109 Table 2 Specifications of the prototype.

Table 4 Water temperatures and flow rates for the tests.

Parameters

Values

Power supply Voltage Frequency Compressor Type Displacement Water heat exchanger Type Area Glycol heat exchanger Type Area Expansion valve

Operation mode

Temperature entering the condenser ( C)

Flowrate entering the condenser (m3/h)

Temperature entering the evaporator ( C)

Flowrate entering the evaporator (m3/h)

Cooling Heating

30 32

7.1 6.9

25 15

1.9 1.9

380 V 50 Hz Scroll 80 cm3 Shell and tube 3 m2 Plate 3 m2 Manual

mass flow rate of the secondary fluid through them, respectively. And the mass flow rate of the refrigerant through the condenser or the evaporator was calculated by its capacity dividing by the enthalpy difference of the refrigerant. The temperatures and pressures of the fluids at the inlet and outlet of the condenser or evaporator were measured by the sensors or transducers, and the enthalpy can been obtained from the measured data. Table 2 shows the specifications of the prototype; the specifications and uncertainties of each sensor for measuring data was shown in Table 3. When the prototype was steadily running more than 1 h under the selected operating mode, the all measured data were recorded only if their fluctuation was within 2%. The test conditions were condensing temperatures, tk, of 40  C and 45  C and a suction superheat of 10  C, a degree of liquid sub cooling of 5  C. For the cooling conditions, the evaporating temperature, to, was set to 5  C. For the heating conditions, to was set to 10  C, 5  C or 0  C. To make the system operate close to practical operating conditions, the tests used a fixed supply water temperature and the flow rates listed in Table 4.

the single stage system, 19.4 kW, if 3 is more than 7.8%, the maximum EVI system Qo is about 3.2% bigger than that of the single stage system. Thus, the EVI system performs better when tk is relatively high. This demonstrates that the cooling performance of the EVI system improves greatly at higher tk and higher 3. This is because the pressure ratio becomes relatively high when tk is high so that it cause the compressor efficiency decreasing and discharge temperature rising. Under these operation conditions, to inject some refrigerant vapor with low enthalpy into the compressor chambers can markedly improve their compressing process. As discussed in Section 2, on one hand, the sub-cooling degree of the refrigerant liquid entering the main expansion valve increases as the vapor leaving from flash-tank to inject into the compressor, so the increment of the cooling capacity depends on the amount of vapor injected into the compressor. On the other hand, the mass of vapor injected into the compressor can not increase without limit, as the injection vapor pressure must higher than that in the compressor chambers which was depended on the suction pressure. 4.2. Heating performance The variations of the heating capacity, Qk, and COP of the EVI system with 3 are shown in Fig. 4. As 3 increases, both Qk and COP

(a)

4. Results and discussions

24 23

The variations of the cooling capacity, Qo, and EER with the relative intermediate pressure, 3 , are shown in Fig. 3. Both Qo and EER increase with increasing 3 . For example, when to is 5  C and tk is 40  C, 3 varies from 2% to 11.3%, Qo increases from 22.22 kW to 23.13 kW, about 4.0%, and the cooling EER increases from 3.42 to 3.65, about 6.7%. When to is 5  C and tk is 40  C, the cooling EER of the EVI system are all less than that of a single stage system with a maximum difference of 15%. For tk is 45  C, the cooling capacity, which depends on the intermediate pressure and the EVI system operating conditions, can be bigger or smaller than that of the single stage system. As shown in Fig. 3, if 3 is lower than 7.8%, the minimum EVI system Qo is 19.2 kW, about 1.1% lower than that of

22

QO / kW

4.1. Cooling performance

EVI, tk=40

SS, tk=45

EVI, tk=45 to=5

21 20 19 18 0

2

4

6

(b)

8 10 /%

SS, tk=40 SS, tk=45

4.2

12

14

Accuracy

Full scale

Model

Temperature Pressure transducer Flow meter Currency acquisition unit Power acquisition unit Data logger Heating capacity Heating COP Cooling capacity Cooling EER

0.2  C 0.2% of 0.2% of 0.2% of 0.2% of 0.2% of 2.2% 3.5% 2.2% 3.5%

e 2.5/4.5 MPa 2.5 kg/s e 10 kW e e e e e

Pt100 Huba LZB-50 DZFC-1 DZFC-1 HP34970A e e e e

scale scale scale scale scale

EER

Sensor

16

EVI, tk=40 EVI, tk=45 to=5

3.8

Table 3 Uncertainties of experimental parameters.

full full full full full

SS, tk=40

3.4 3.0 2.6 2.2 0

2

4

6

8 10 /%

12

Fig. 3. Cooling performance variation with

3

14

16

X. Shuxue et al. / International Journal of Thermal Sciences 68 (2013) 103e109

(a)

SS, to=0 SS, to=-5 SS, to=-10

24 23

115

EVI tk=40

EVI tk=45

SS tk=40

SS tk=45 to=5

110

tk=40

22

105

21

td ( )

Qk / kW

(a)

EVI, to=0 EVI, to=-5 EVI, to=-10

107

20

100

19

95

18

90

17

85

16 0

2

4

6

8

10 12

14 16

18 20

22

/%

0

2

4

6

(b)

8 10 /%

12

14

16

EVI to=-10 EVI to=-5

(b)

SS, to=0 SS, to=-5 SS, to=-10

3.8

EVI, to=0 EVI, to=-5 EVI, to=-10

3.6

td ( )

tk=40

3.4 COP

3.2 3.0 2.8

130 125 120 115 110 105 100

tk=40

EVI to=0

95 90

2.6

2

2.4 2.2 0

2

4

6

8

10

Fig. 4. Heating performance variation with

3

12 /%

14

16

18

20

22

(a) heating capacity (b) heating COP.

are gradually increases. For example, when to is 0  C, Qk increases from 22.1 to 23.1 kW while 3 varies from 4% to 15.4%, an increase of only 4.5%. The increase is about 8.6% when to was reduced to 10  C. This is because the heating capacity goes up with increase of the mass flow rate of the injection vapor and its enthalpy. For the conditions with lower evaporating temperature, the relative improvement of heating capacity increases with decrease of to as the enthalpy of injected vapor is relatively higher compared to that of the vapor in the compressor chambers. When to varies from 10  C to 0  C and tk is 40  C, the EVI system Qk is 3 e 9% bigger than that of the single stage system. When the evaporating temperature is relatively high, the EVI system COP is generally lower than that of the single stage system, but increases and becomes even better as the evaporating temperature decreases. For example, for an evaporating temperature of 10  C and 3 higher than 17%, the EVI system COP is 7.4% bigger than that of the single stage system. For a condensing temperature of 45  C, the discharge temperature rapidly increases and exceeds 130  C within a few minutes, even if the manually controlled expansion valve in the vapor injection line is fully opened, so there is no test data for these conditions. 4.3. Discharge temperature The variations of the compressor discharge temperature with 3 are shown in Fig. 5. For cooling condition, as with the single stage system, the EVI system discharge temperature is quite high for both

4

6

8

10

Fig. 5. Discharge temperature variation with condition.

12 /% 3

14

16

18

20

(a) cooling condition (b) heating

high or low tk, but is 5 e 10  C lower than that of the single stage system. For the EVI system, the discharge temperature remains constant for all the testing conditions and did not exceed 110  C. For heating conditions, the discharge temperature is 15 e 20  C higher than for cooling conditions although the variations are similar. Therefore, the discharge temperature for heating conditions must be carefully selected when designing EVI systems using R32. For EVI systems, the discharge temperature can be controlled to not exceed 125  C and the system can run safely for a long time with evaporating temperatures below 0  C and condensing temperatures of 40  C or 45  C. The results in Figs. 5 and 6 show 3 must keep large to increase the heating capacity and reduce the discharge temperature, but should be smaller to increase the heating COP. 4.4. Fixed supply water temperatures and flow rates In a real air conditioner system, the ambient temperature is fixed, but the pressure, temperature of evaporator and condenser, compressor operating condition must be changed with vapor injected into the compressor, and further, the whole performance of the system must be changed, so the fixed water supply temperature and the flow rates condition were provided in Table 4, and experimental results are shown in Fig. 6. The results in Fig. 6a show that the Qo and EER for the EVI system are bigger than that of the single stage system when 3 exceeds the range from 12% to 16%. From Fig. 6b, it can be seen that both Qk and COP increase as 3 increases, and Qk is about 7% bigger than that of the single stage system and the COPs of EVI system are very close to that of SS system when 3 reaches to 16%.

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X. Shuxue et al. / International Journal of Thermal Sciences 68 (2013) 103e109

(a)

SS, Qo SS, EER

24.0

3.9

tk=40

23.5 23.0

3.8 EER

QO / kW

EVI, Qo EVI, EER

22.5 22.0

3.7

21.5 21.0

3.6 0.0

11.3

(b)

13.4 /%

15.7

SS, Qk SS, COP

23.0

18.4

EVI, Qk EVI, COP

3.70

22.5

3.65

22.0

3.60

21.5

3.55

21.0

COP

Qk / kW

tk=40

3.50 0.0

13.1

13.9

15.0

16.0

5. Conclusions

/% Fig. 6. Cooling/heating performance variation with temperature and flow rate.

From Fig. 3, it can be seen that the favorable range of 3 should be 7.8e15% in cooling condition. From Fig. 4, the EVI system can achieve better heating performance when 3 was between 14% and 19% and better both cooling and heating performance when 3 was between 12% and 16%. The pressure distributions of the main components for the constant water temperature and the various flow rates are shown in Fig. 7. For both the EVI and single stage systems, the overall variations of the pressure distributions for the two testing conditions are very similar, but the pressures of the main components are always slightly higher after starting the vapor injection. For example, the discharge pressure (approximately equal to the condensing pressure) rises from 2.46 MPa to 2.53 MPa and the condensing temperature, tk, increases from 39.7  C to 40.8  C. The suction pressure (approximately equal to the evaporating pressure) increases from 0.96 to 0.98 MPa while the evaporating temperature, to, increases from 5.2  C to 6.0  C. These changes occur because the refrigerant discharge mass flow rate increases when vapor is injected into the compressor, so that the amount of refrigerant in the condenser increases. Since the condenser size is fixed, more refrigerant in the condenser increases the condensing pressure. Since the expansion valve size is also fixed, the evaporating pressure and temperature also increase. The prototype EVI system runs at relatively high evaporating and condensing temperatures. Thus, the size of the liquid receiver or the sizes of the evaporator and the condenser should be increased to avoid increasing the EVI system working pressure.

3

and to for fixed supply water

An experimental prototype of the enhanced vapor injection refrigeration/heat pump system (EVI system) using R32 was developed and it was tested under three different operation conditions: cooling, heating and the fixed water supply temperature and flow rate conditions. Comparing to the single-stage system, the EVI system using R32 can remarkably lower the discharge temperature of the compressor, and the cooling and heating performance, depending on its vapor injection parameters and operation conditions, can be improved or deteriorated. 1) The EVI system discharge temperature can be significantly reduced by 10 e 20  C and the system can run safely for a long time for cooling with relatively high evaporating temperatures and for heating with relatively low evaporating temperatures. 2) The cooling EER of an optimized EVI system can be close to and the cooling capacity can be 4% bigger than that of a single stage system. The heating capacity is 4 e 6% bigger and the heating COP is 3% bigger than that of a single stage system 3) When the EVI system is run with a constant water supply temperature and various flow rates to the evaporator and condenser, both the evaporating and condensing temperatures are 0.8 e 1  C higher than for the single stage system, and the heating capacity is increased by about 5%, while the cooling capacity, EER and heating COP are comparable. The size of the liquid receiver or the sizes of the evaporator and condenser should be increased in an EVI system. 4) 3 should be 12% e 16% to give the best cooling and heating rates for the EVI system. Acknowledgments

Fig. 7. Pressure distribution with vapor injection (a) cooling (b) heating.

This project was supported by the Beijing Postdoctoral Research Foundation (Grant No. Q6005014201102) and the China Postdoctoral Science Foundation funded projects (Grant No.

X. Shuxue et al. / International Journal of Thermal Sciences 68 (2013) 103e109

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