Article Investigation on the Performances of Vuilleumier Cycle Pump Adopting Mixture Refrigerants

Yingbai Xie and Kai Zhong *

Department of Power Engineering, North China Electric Power University, Baoding 071000, China; [email protected] * Correspondence: [email protected]; Tel.: +86-312-752-2706; Fax: +86-312-752-2440

Received: 30 July 2017; Accepted: 24 August 2017; Published: 26 August 2017

Abstract: The performances of cycles are dependent on the properties of refrigerants. The performances of Vuilleumier (VM) cycle adopting mixture refrigerants are analyzed by MATLAB software using REFPROP programming. At given operating parameters and configuration, performances of the VM cycle adopting pure refrigerant, H2, He or N2 are compared. Thermodynamic properties of the four type mixtures, namely, He-H2, He-N2,H2-N2 and He-H2-N2, are obtained with total 16 mixing ratio, and the coefficient of performance and the exergy efficiency of these four mixture types in VM cycle heat pump are calculated. The results indicate that within the temperature of heat source 400–1000 K, helium is the best choice of pure refrigerant for VM cycle heat pump. The He-H2 mixture is the best among all binary refrigerant mixtures; the recommended proportion is 1:2. For trinary refrigerant mixture, suggested proportion of helium, hydrogen and nitrogen is 2:2:1. For these recommended mixtures, system COPs (coefficient of performances) are close to 3.3 and exergy efficiencies are about 0.2, which are close to pure refrigerant helium.

Keywords: VM cycle heat pump; coefficient of performance; exergy efficiency; pure refrigerant; mixture refrigerants

1. Introduction Vuilleumier (VM) cycle is a thermally driven reversible Stirling gas cycle [1,2]. Selection of heat sources is of great flexibility [3]; it can be fossil fuels such as natural gas, or renewable energy such as solar energy or even waste heat. The advantages of using VM cycle heat pump are small output, low noise, long life span, high efficiency, etc. [4,5]. It can provide cold or hot production, even with power product. The cyclic efficiency of the ideal VM cycle is the same as that of the [6]. However, the actual coefficient of performance of the VM cycle is only about 30~40% of the ideal cycle, due to the reciprocating flow of refrigerant in the VM cycle heat pump. The inevitable heat transfer and flow losses caused by the flowing of refrigerant account for more than half of the total losses [7], which has great influence on the performances of the VM cycle heat pump. Undoubtedly, different refrigerants have different characteristics in heat transfer and fluid flow. Therefore, the performances of the system vary under different working conditions with different working fluid [8]. Mixture refrigerants are good examples. Chakravarthy et al. obtained mixing criteria with a number of cycles within 4 K to 300 K, including the Stirling gas cycle [9]. Narasimhan and Venkatarathnam experimentally determined the mixture fraction that had the highest exergy efficiency of single-stage [10]. Asadnia and Mehrpooya [11] studied the application of mixture refrigerants, namely, nitrogen, helium and hydrogen in Joule Brayton refrigeration cycle. Results showed that the coefficient of performance using the new mixture refrigerants was 0.1710 and the exergy efficiency was 39.5%, both of them were higher than the existing refrigerant. Lee et al. [12] carried out optimum research of a cryogenic refrigeration cycle adopted nitrogen and argon mixture

Entropy 2017, 19, 446; doi:10.3390/e19090446 www.mdpi.com/journal/entropy Entropy 2017, 19, 446 2 of 14 as refrigerant, from the distribution of temperature and the working of compressor. He got the maximum coefficient of performance and the corresponding Carnot cycle efficiency. Lee et al. [13] researched the feasibility and effectiveness of helium-nitrogen mixture as refrigerant in the refrigeration cycle by Peng-Robinson . There are more literatures on the mixture refrigeration cycles. Zhejiang University, which owns the National Key Laboratory [14], used the operation pressure ratio method to optimize the cyclic performance for single-stage compression by adopting binary mixture. They also obtained that constituent and the concentration of mixture, the low side pressure of cycle, and the pressure ratio were factors that had an influence on the coefficient of cycle performance. Literature [15] tested a small capacity pre-cooled mixture cycle system, and established a chromatographic analysis method for mixture concentration optimization. REFPROP is used in these mixture properties investigations. Yin et al. [16] investigated mixtures of SF6-CO2 as working fluids for geothermal power plants by obtaining the thermophysical properties of the mixtures from National Institute of Standards and Technology (NIST) REFPROP software (Version 8.0). Seneviratne et al. [17] extended critical point literature data for methane and propane mixtures in a beta-version of REDPROP 9.2. Rivas et al. [18] measured a suitable doping agent in two CO2-rich, CO2 + SO2 mixtures with the same SO2 composition from 263.15 to 373.19 K and up to 190.10 MPa, and validated the modeling with the REFPROP 9 software. For VM cycle heat pump, gas hydrogen, helium or nitrogen are common working fluids, but all applications are single-refrigerant, few on the mixture. To know the performances of mixture, we set the given working condition and determine the configuration of all system parts. Using MATLAB and REFPROP software (Version 9.1) to simulate the variation of properties of pure refrigerant hydrogen, helium and nitrogen, calculate the coefficient of performance and exergy efficiency of the system. Then investigate the properties of four type mixtures, He-H2, He-N2,H2-N2 and He-H2-N2, separately. Finally, compare the system performances of mixture cycles at different mixture ratio with that of the pure refrigerant cycle.

2. Working Principle and Performances Calculation for VM Cycle Heat Pump

2.1. Working Principle Figure1 shows the schematic of VM cycle heat pump. The heat pump mainly contains two cylinders, a cold and a hot cylinder, two passing pistons, two regenerators and three heat exchangers. The two passing pistons are connected to the crankshaft by the driven connecting rod, and the pistons are moved following the rotation of the crankshaft. Between the hot passing piston and the top of hot cylinder is the hot space; while between the cold passing piston and the top of cold cylinder is the cold space. The between cold and hot cylinder which varies with the movement of the piston is called warm space. When the VM cycle heat pump is in heating condition, it absorbs the heat from both heat source and cold source via hot and cold cylinder, then supplies the heat to the user by the warm heat exchanger. While in refrigeration condition, it absorbs the heat of the user, lowers the temperature of the subject, and rejects the heat to the environment at room temperature. Theoretically, in heating or refrigeration mode, the total heat absorbed by the hot space and the cold space is equal to the heat released at the warm space. Entropy 2017, 19, 446 3 of 14 Entropy 2017, 19, 46 3 of 14

FigureFigure 1. 1. SchematicSchematic of of Vuilleumier Vuilleumier (VM) cycle heat pump.

2.2. Performances Performances Calculation Method Formulas used to calculate the performances of VM cycle heat pump are as follows [[19,20]:19,20]: (1) Travel volume ofof thethe coldcold cylinder:cylinder: 1 = 1π 22 VVDZcoco= πD coco Z (1)(1) 4 (2) Temperature ratioratio ofof thethe hothot andand coldcold space:space:

τ =TT (2) τ = Thcoh/Tco (2)

(3) Pressure angle: ωτ()− ϕ 1sinh θ = arctan ω(1 − τh) sin ϕ (3) θ = arctan ()()τωτ−−11cos − ϕ (3) (τcoco− 1) − ω(1 − hτh) cos ϕ

(4) Temperature ratioratio ofof thethe coldcold side:side: τ = coTT a co (4) τco = Ta/Tco (4) (5) Temperature ratio of hot side: (5) Temperature ratio of hot side: τ ==TTTa/T (5)(5) hhahh (6) Pressure parameter: q 222 22 2 (()()()()ττωτωττco −−+111) + ω (1 −− τh) −− 211cos2ω(τco −− 1)(1 −− τh) cosϕϕ δδ== co h co h (6)(6) (()()111++++τωττco) + ω(1 + τh) co h (7) Pressure ratio: P 1 + δ max = (7) +−δ PPminmax 11 δ = (7) (8) Maximum pressure: P 1−δ min r 1 + δ (8) Maximum pressure: Pmax = Pav (8) 1 − δ (9) Minimum pressure: 1+δ PP= r (8) max av 11−−δ δ P = P (9) min av 1 + δ (9) Minimum pressure:

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(10) Theoretical cooling capacity of cold cylinder:

πnδ sin θ Qco = PavVco  √  (10) 60 1 + 1 − δ2

(11) Theoretical heating absorption of hot cylinder:

τco − 1 Qh = Qco (11) 1 − τh

(12) Theoretical heating release of warm cylinder:

Qa = Qco + Qh (12)

(13) Theoretical coefficient of performance of heat pump:

Q COP = a (13) Qh

(14) Theoretical exergy efficiency of heat pump:     T0 T0 Qa 1 − − 1 − Ex,out − Ex,in Tout Tin ηe = =     (14) E + E T0 T0 x,h x,co Q 1 − + Qco − 1 h Th Tco

3. Performances of Pure Refrigerants in VM Cycle

3.1. Properties of Pure Refrigerants In order to get close to the ideal cycle, the actual VM cycle heat pump should choose the actual gas which is more similar to the . Therefore, helium, hydrogen and nitrogen are the most common pure refrigerant to be used in the VM cycle. Here are some of their physical properties: (1) Helium Helium is a colorless, odorless gas. Its chemical nature is pretty stable; it could not normally combine with any other element. What is more, helium is the most difficult gas to liquefy in nature owing to the extremely low critical temperature. And the conversion temperature of it is also very low; helium has the lowest boiling point among all gases. In terms of high specific , high thermal conductivity and low density, helium is only inferior to hydrogen. (2) Hydrogen Generally, hydrogen is also a colorless, odorless gas. It is extremely insoluble in water. It is also a gas with the lightest quality, the largest specific heat, the highest thermal conductivity, and the lowest viscosity of all gases. The conversion temperature of hydrogen is much lower than room temperature, for example, the maximum conversion temperature is only about 204 K. Therefore, in order to produce cold effect, hydrogen must be pre-cooled to 204 K firstly, and then throttled. It is noted that hydrogen belongs to flammable and explosive substances, there is a need for special attention to operate liquid hydrogen, and a need for rigorous control and gauging the purity of liquid hydrogen. (3) Nitrogen Similar to helium and hydrogen, nitrogen is also a colorless, odorless gas, it is slightly lighter than air and insoluble in water. The chemical nature of it is also stable, so it is frequently used as a protective gas. Furthermore, because it is non-toxic and has a lower boiling point than air, liquid nitrogen is the safest refrigerant in low-temperature research fields, but should be avoided of asphyxia. Entropy 2017, 19, 46 5 of 14 Entropy 2017, 19, 46 5 of 14 Similar to helium and hydrogen, nitrogen is also a colorless, odorless gas, it is slightly lighter Similar to helium and hydrogen, nitrogen is also a colorless, odorless gas, it is slightly lighter than air and insoluble in water. The chemical nature of it is also stable, so it is frequently used as a than air and insoluble in water. The chemical nature of it is also stable, so it is frequently used as a protectiveEntropy 2017, gas.19, 446 Furthermore, because it is non-toxic and has a lower boiling point than air, liquid5 of 14 protective gas. Furthermore, because it is non-toxic and has a lower boiling point than air, liquid nitrogen is the safest refrigerant in low-temperature research fields, but should be avoided of nitrogen is the safest refrigerant in low-temperature research fields, but should be avoided of asphyxia. Liquid nitrogen is also used as pre-cooling equipment in hydrogen or helium liquefaction asphyxia.Liquid nitrogen Liquid is nitrogen also used is as also pre-cooling used as pre-cooling equipment inequipment hydrogen in or hydrogen helium liquefaction or helium installations.liquefaction installations. To prevent explosions, storage of liquid nitrogen should be careful, avoiding long-time Toinstallations. prevent explosions, To prevent storage explosions, of liquid storage nitrogen of liquid should nitrogen be careful, shouldavoiding be careful, long-time avoiding contacting long-time contacting with hydrocarbons. withcontacting hydrocarbons. with hydrocarbons. 3.2. Properties Variationof Pure Refrigerants 3.2. Properties Variationof Pure Refrigerants The physical properties of three refrigerants, helium, hydrogen and nitrogen, are shown from The physical properties of three refrigerants, helium, hydrogen and nitrogen, are shown from Figures 22–4.–4. TheThe temperaturetemperature rangerange isis 400–1000400–1000 K.K. Figures 2–4. The temperature range is 400–1000 K.

0.5 0.5 0.5 He He HHe 0.4 H2 0.4 H2 ） 0.4 N2 ） N2 ） 2 N2 0.3

W/m·k 0.3

W/m·k 0.3 W/m·k （ （ （ 0.2 0.2

0.1 0.1 Therm.Cond. 0.1 Therm.Cond. Therm.Cond. 0.0 0.0 400 500 600 700 800 900 1000 400 500 600 700 800 900 1000 （ ） Temperature（K） Temperature（K） Figure 2. The thermal conductivity of three refrigerants. Figure 2. The thermal conductivity of three refrigerants.

50 · 50 · 50 · He 45 He 45 HHe 45 H2 H2 40 N2 40 2 40 N2 ） N2 ） 35 ） 35

Pa·s 35 Pa·s μ Pa·s

μ 30 μ （ 30 （ （ 25 25 20

Viscosity 20

Viscosity 20 Viscosity 15 15 10 10 400 500 600 700 800 900 1000 400 500 600 700 800 900 1000 （ ） Temperature（K） Temperature（K） Figure 3. The viscosity of three refrigerants. Figure 3. The viscosity of three refrigerants. 16 16 14 14 12 He 12 He HHe ） 10 H2

） 10 H2 ） 10 N2 N2 8 N2 8 2 kJ/kg·K

kJ/kg·K 6 kJ/kg·K （ 6

（ 6 （ Cp 4 Cp Cp 4 2 2 0 0 400 500 600 700 800 900 1000 400 500 600 700 800 900 1000 （ ） Temperature（K） Temperature（K） Figure 4. The constant pressure specific heat of three refrigerants. Figure 4. The constant pressure specific specific heat of three refrigerants. As illustrated in Figures 2–4: As illustrated in Figures 2–4: As illustrated in Figures2–4:

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(1) The constant pressure specific heat and thermal conductivity of helium and hydrogen are greater than that of nitrogen, which indicates that helium and hydrogen have advantages over nitrogen in absorbing heat from heat source. However, the loss of heat conduction and heat dissipation is also greater than that of nitrogen. (2) The viscosity of nitrogen is greater than hydrogen, so nitrogen has larger friction loss, further increasing the pressure loss. It has effect on the pressure ratio, and lower the refrigeration output than hydrogen. However, the viscosity of nitrogen is less than that of the helium. As a result, each refrigerant has different characteristics in terms of heat transfer and flow resistance. Hydrogen shows the best performance overall. When comparing helium with nitrogen, both of them have advantages in heat transfer and flow, respectively. For example, the flow resistance of nitrogen is smaller, but the heat transfer performance of helium is better.

3.3. Performances of Pure Refrigerants To make a clear comparison, the configuration and some operating parameters of the VM heat pump are given in Tables1 and2.

Table 1. Structure parameters of VM cycle heat pump [19–21].

Parameter Symbol, Formula, Basis, Introduction Value

Cylinder bore Dco 0.0699 m Distance of run Z 0.0312 m Phase angle of volume ϕ 90◦ The length of passing piston L 0.04359 m Radial clearance of passing piston σ 0.00015 m Diameter of regenerator DR 0.0226 m Length of regenerator LR 0.0226 m Filler of regenerator Mesh of stainless steel — Pressure parameter δ 0.3 Mode of driving Piston driving of single handle, dual power — Proportion of volume ω 10 Rotation rate n 600 rpm = 10 Hz

Table 2. Calculation parameters of VM cycle heat pump.

Parameter Symbol, Formula, Basis, Introduction Value

Temperature of hot space Th 500 K Temperature of warm space Ta 340 K Temperature of cold space Tco 300 K Ambient temperature T0 273 K Th+Tco Average temperature Tav = 2 400 K 6 Average pressure Pav 10.0 × 10 Pa Theoretical exergy efficiency ηe — Theoretical coefficient of COP — performance

As shown in Figure5, the COPs (coefficient of performances) of three working fluids increase with the elevation of the heat source temperature. It trends to go gentle at higher temperature. The COPs of heat pump adopting hydrogen and helium are very close, which are higher than that of the nitrogen. Figure6 shows the exergy efficiency to temperature of heat source of these three working fluids. Exergy efficiency of the VM cycle heat pump adopting hydrogen and helium decrease as the temperature of the heat source increases. The trends are opposite to that of the COP. While for nitrogen, the exergy efficiency variation trend is the same as that of the COP. They both increase as the temperature of heat source increases. Entropy 2017, 19, 46 7 of 14 Entropy 2017, 19, 446 7 of 14 nitrogen, the exergy efficiency variation trend is the same as that of the COP. They both increase as the temperature of heat source increases. Therefore, according to the system performances of the three pure refrigerants, helium and hydrogen are similar to each other, betterbetter than thatthat ofof thethe nitrogen.nitrogen. Considering the liable explosion problem ofof hydrogen, hydrogen, helium helium is theis the best best choice choice of working of working fluid forfluid VM for cycle VM heat cycle pump. heat For pump. economic For concern,economic nitrogen concern, should nitrogen be should introduced be introduc to lowered the to costlower of the the cost whole of facility.the whole facility.

3.5

3

2.5 COP COP 2 H 2 He 1.5 He N 2

1 400 500 600 700 800 900 1000 Temperature of heat source（K） Figure 5. The COP (coefficient of performance) for the three pure refrigerants. Figure 5. TheThe COP (coefficient (coefficient of performance) for the three pure refrigerants.

0.2 H 2 0.15 He N N2 0.1 2 Exergy efficiency Exergy Exergy efficiency Exergy 0.05

400 500 600 700 800 900 1000 （ ） Temperature of heat source（K） Figure 6. The exergy efficiency of three refrigerants. Figure 6. The exergy efficiency of three refrigerants.

4. Performances for Mixture Refrigerant in VM Cycle Giacobbe analyzed the heat transfer properties of of helium, hydrogen hydrogen and and other other inert inert gases gases [22]. [22]. Hosseinnejad et al. carried carried out out numerical numerical calculatio calculationsns of of transport transport properties properties on on the mixture of hydrogen andand inertinert gas gas [23 [23].]. For For security security and and economy economy reasons, reasons, four four kinds kinds of mixture of mixture refrigerants refrigerants were discussedwere discussed in this in paper, this paper, namely, namely, helium helium and hydrogen, and hydrogen, helium andhelium nitrogen, and nitrogen, hydrogen hydrogen and nitrogen, and helium,nitrogen, hydrogen helium, hydrogen and nitrogen. and nitrogen. 4.1. Properties of Mixture 4.1. Properties of Mixture In Figures7 and8, the thermal conductivity and viscosity of helium and hydrogen mixture In Figures 7 and 8, the thermal conductivity and viscosity of helium and hydrogen mixture increase as the elevation of heat source temperature. When at mixing proportion of 1:2, it has the increase as the elevation of heat source temperature. When at mixing proportion of 1:2, it has the maximum value of the thermal conductivity and the minimum value of viscosity. This could be maximum value of the thermal conductivity and the minimum value of viscosity. This could be explained by Figures2 and3, in which the thermal conductivity of hydrogen is the highest, but the explained by Figures 2 and 3, in which the thermal conductivity of hydrogen is the highest, but the viscosity is the lowest. Figure7 also indicates that there are a cross point of mixture proportion 2:1 and viscosity is the lowest. Figure 7 also indicates that there are a cross point of mixture proportion 2:1 1:1 when the heat source temperature is about 550 K. and 1:1 when the heat source temperature is about 550 K. Figures9 and 10 indicate that the thermal conductivity and viscosity of helium and nitrogen mixture also increase with the heat source temperature rise. In addition, the bigger the number of mole fractions of helium, the higher the value of thermal conductivity and viscosity. The curves for viscosity have the same variation, but the difference of viscosity values for the three mixing proportions is relatively small.

EntropyEntropy 20172017,, 1919,, 4646 88 ofof 1414

0.550.55 He:HHe:H=1:1=1:1 0.500.50 22 He:H =2:1 He:H22=2:1

） 0.45 ） 0.45 K

K He:H =1:2 He:H22=1:2 0.400.40 W/m· W/m· 0.350.35 （

Entropy 2017, 19, 446 （ 8 of 14 EntropyEntropy 20172017,, 1919,, 4646 0.300.30 88 ofof 1414 0.250.25 0.550.55 Therm.cond. Therm.cond. 0.200.20 He:H He:H=1:1=1:1 0.500.50 22 0.15 0.15 He:H He:H=2:1=2:1 400400 500 50022 600 600 700 700 800 800 900 900 100 10000 ） ） 0.450.45 K K He:H He:H=1:2=1:2 22Temperature（（K）） 0.400.40 Temperature K W/m· W/m· 0.350.35 （ FigureFigure 7.7.（ ThermalThermal conductivityconductivity forfor He-HHe-H22 mixture.mixture. 0.300.30 0.250.25 5050 Therm.cond. Therm.cond. 0.200.20 He:HHe:H=1:1=1:1 4545 22 He:H =2:1 0.150.15 He:H22=2:1 400400 500 500 600 600 700 700 800 800 900 900 100 10000 4040 He:HHe:H=1:2=1:2 ） 2 ） 2 TemperatureTemperature（（KK））

Pa·s 35

Pa·s 35 μ μ （ （ 3030 FigureFigure 7.7. ThermalThermal conductivityconductivity forfor He-HHe-H22 mixture.mixture. 2525 Viscosity Viscosity 20502050

He:H He:H2=1:1=1:1 154545 2 15 He:H He:H=2:1=2:1 400400 500 50022 600 600 700 700 800 800 900 900 1000 1000 4040 He:H He:H=1:2=1:2 ） ） 2Tem2Tempperatureerature（（KK））

Pa·s 35 Pa·s 35 μ μ （ FigureFigure（ 3030 8.8. ViscosityViscosity forfor He-HHe-H22 mixture.mixture.

2525 Viscosity FiguresFigures 99 andand 1010 indicateindicate thatthatViscosity thethe thermalthermal condconductivityuctivity andand viscosityviscosity ofof heliumhelium andand nitrogennitrogen 2020 mixturemixture alsoalso increaseincrease withwith thethe heatheat sourcesource tempertemperatureature rise.rise. InIn addition,addition, thethe biggerbigger thethe numbernumber ofof 1515 molemole fractionsfractions ofof helium,helium, thethe higherhigher thethe400400 valuevalue 500 500 of 600of 600 thermalthermal 700 700 800 800 conductivityconductivity 900 900 1000 1000 andand viscosity.viscosity. TheThe curvescurves forfor viscosityviscosity havehave thethe samesame variation,variation, butbut thethe differTemdifferTempperatureeratureenceence（（KK ） ）ofof viscosityviscosity valuesvalues forfor thethe threethree mixingmixing proportionsproportions isis rerelativelylatively small.small. FigureFigure 8.8. ViscosityViscosity forfor He-HHe-H22 mixture.mixture.

FiguresFigures 99 andand 1010 indicateindicate thatthat0.110.11 thethe thermalthermal condconductivityuctivity andand viscosityviscosity ofof heliumhelium andand nitrogennitrogen

He:NHe:N2=1:1=1:1 mixturemixture alsoalso increaseincrease withwith thethe heatheat0.100.10 sourcesource tempertemper2 atureature rise.rise. InIn addition,addition, thethe biggerbigger thethe numbernumber ofof He:N =2:1 He:N22=2:1 ） molemole fractionsfractions ofof helium,helium, thethe higherhigher） 0.09 thethe valuevalue He:N ofof=1:2 thermalthermal conductivityconductivity andand viscosity.viscosity. TheThe curvescurves forfor 0.09 He:N22=1:2 viscosityviscosity havehave thethe samesame variation,variation, butbut thethe differdifferenceence ofof viscosityviscosity valuesvalues forfor thethe threethree mixingmixing 0.080.08 W/m·K W/m·K （ proportionsproportions isis rerelativelylatively small.small. （ 0.070.07

0.060.06 0.110.11 Therm.cond. Therm.cond. 0.050.05 He:N He:N=1:1=1:1 0.100.10 22 He:N He:N=2:1=2:1 0.040.04 22 ） ） 0.09 400400 500 500He:N =1:2 600 600 700 700 800 800 900 900 1000 1000 0.09 He:N22=1:2 TemperatureTemperature（（KK）） 0.080.08 W/m·K W/m·K （ （ 0.070.07 FigureFigure 9. 9. ThermalThermal conductivity conductivity for for He-N He-N22 mixture.mixture. 0.060.06 5050 Therm.cond. Therm.cond. 0.050.05 He:N =1:1 He:N22=1:1 45 0.040.0445 He:NHe:N=2:1=2:1 400400 500 50022 600 600 700 700 800 800 900 900 1000 1000 ） ） He:NHe:N=1:2=1:2 4040 22 TemperatureTemperature（（KK）） Pa·s Pa·s μ μ

（ 35 （ 35 FigureFigure 9.9. ThermalThermal conductivityconductivity forfor He-NHe-N22 mixture.mixture. 3030 Viscosity Viscosity 5050 2525 He:N =1:1 He:N22=1:1 4545 He:N =2:1 2020 He:N22=2:1 400400 500 500 600 600 700 700 800 800 900 900 1000 1000 ） ） He:N He:N=1:2=1:2 4040 22 TemTempperatureerature（（KK）） Pa·s Pa·s μ μ （ （ 3535 Figure 10. Viscosity for He-N2 mixture. 3030 Viscosity Viscosity 2525

2020 400400 500 500 600 600 700 700 800 800 900 900 1000 1000 TemTempperatureerature（（KK））

Entropy 2017, 19, 46 9 of 14 Entropy 2017, 19, 46 9 of 14 Entropy 2017, 19, 44646 9 of 14 Figure 10. Viscosity for He-N2 mixture. Figure 10. Viscosity for He-N2 mixture. Figure 10. Viscosity for He-N2 mixture. ComparingComparing Figures Figures 11 11 and and 12 12 to to Figures Figures 99 andand 10,10 ,we we can can find find that that the the change change regulations regulations of of Comparing Figures 11 and 12 to Figures 9 and 10, we can find that the change regulations of He-NHe-N2Comparing 2andand H H2-N2-N2 Figuresare2 are similar. similar. 11 and The The 12 difference differenceto Figures is is 9the and the divergence divergence10, we can between betweenfind that each eachthe valuechange value of ofregulations each each mixing mixing of He-N2 and H2-N2 are similar. The difference is the divergence between each value of each mixing proportion.He-Nproportion.2 and For H For2 -Nthe the2 areH H2-N2 similar.-N2 mixture,2 mixture, The the difference the difference difference is ofthe of the thedivergence thermal thermal conductivity between conductivity each isis smaller.value smaller. of each mixing proportion. For the H2-N2 mixture, the difference of the thermal conductivity is smaller. proportion.ForFor the the helium, For helium, the hydrogenH hydrogen2-N2 mixture, and and nitrogen the nitrogen difference mixture, mixture, of the the thermal thermal conductivity conductivity andis and smaller. viscosity viscosity increase increase asas well wellForFor as as thethe the the helium,helium, heat heat source source hydrogenhydrogen temperature, temperature, andand nitrogennitrogen as as shown shownmixture,mixture, in in theFiguresthe Figures thermalthermal 13 13 and conductivityandconductivity 14. 14 .The The change and changeand viscosityviscosity of of viscosity viscosity increaseincrease is is obsoleted.asasobsoleted. wellwell asas Furthermore, thethe Furthermore, heatheat sourcesource for for temperature,thermaltemperature, thermal conductivity, conductivity, asas shownshown at at in inmi mixing FiguresFiguresxing ratio ratio 1313 ofandand of 1:2:1, 1:2:1, 14.14. 1:2:TheThe 1:2:2,2, change changeand and 2:1:2, 2:1:2, ofof viscositytheviscosity the values values isis areobsoleted.obsoleted.are relatively relatively Furthermore,Furthermore, small; small; at at ratio ratio forfor of ofthermalthermal 2:1:1, 2:1:1, it it conductivity, conductivity,has has the the smallest smallest atat mi mivalue. value.xingxing ratioratio ofof 1:2:1,1:2:1, 1:2:1:2:2,2, andand 2:1:2,2:1:2, thethe valuesvalues areare relativelyrelatively small;small; atat ratioratio ofof 2:1:1,2:1:1, itit hashas thethe smallestsmallest value.value. 0.11 0.11 H2:N2=1:1 0.100.11 H H:N2:N=2:12=1:1 ） 2H :N2 =1:1 0.10 2 2 0.10 H :N =2:1 ） H :N2 =1:22 0.09 2H :N2 =2:1

） 2 2 0.09 H2:N2=1:2 W/m·K 0.09 H2:N2=1:2

（ 0.08 W/m·K W/m·K

（ 0.08

（ 0.070.08 0.07 0.060.07 Therm.cond. 0.06

Therm.cond. 0.06

Therm.cond. 0.05 0.05 0.05 400 500 600 700 800 900 1000 400 500 600 700 800 900 1000 400 500Tem 600perature 700（K 800） 900 100 0 Temperature（K） Temperature（K） Figure 11. Thermal conductivity for H2-N2 mixture. Figure 11. Thermal conductivity for H -N mixture. Figure 11. Thermal conductivity for H2-N22 mixture. Figure 11. Thermal conductivity for H2-N2 mixture. 40 40 H :N =1:1 40 2 2 H H:N2:N=1:22=1:1 35 2H :N2 =1:1 H 2:N 2=1:2

） 35 H2:N2 2=2:12 35 H2:N2=1:2

） H :N =2:1

Pa·s 30 2 2 ） H :N =2:1

μ 2 2

Pa·s 30 （ μ Pa·s 30 μ （ 25 （ 25 25 Viscosity 20 Viscosity

Viscosity 20 20 15 15 400 500 600 700 800 900 1000 15 400 500 600 700 800 900 1000 400 500Temperature 600 700（K 800） 900 100 0 Temperature（K） Temperature（K） Figure 12. Viscosity for H2-N2 mixture. Figure 12. Viscosity for H2-N2 mixture. Figure 12. Viscosity for H22-N2 mixture.mixture. 0.45 1:1:1 0.45 0.45 1:1:2 1:1:1 0.40 1:1:1 ） 0.40 2:2:1 1:1:2 ） 0.40 1:1:2 ） 1:2:1 2:2:1 0.35 2:2:1

W/m·K 0.35 1:2:2 1:2:1 0.35 1:2:1 （ W/m·K 0.30 2:1:1 1:2:2

W/m·K 1:2:2 （ 0.30 2:1:2 2:1:1 （ 0.30 2:1:1 0.25 2:1:2 2:1:2 0.25 0.25 0.20 Therm.cond. 0.20 Therm.cond. 0.20 Therm.cond. 0.15 0.15 0.15 400 500 600 700 800 900 1000 400 500 600 700 800 900 1000 400 500Tem 600perature 700（K 800） 900 1000 Temperature（K） Temperature（K） Figure 13. Thermal conductivity for He-H2-N2 mixture. Figure 13. Thermal conductivity for He-H2-N2 mixture. Figure 13. Thermal conductivity for He-H22-N2 mixture.mixture.

Entropy 2017, 19, 46 10 of 14 Entropy 2017,, 19,, 44646 10 of 14 Entropy 2017, 19, 46 10 of 14

45 45 1:1:1 45 1:1:1 1:1:21:1:1 40 1:1:2 40 2:2:11:1:2 ） 40 1:2:12:2:1 ） 2:2:1

） 1:2:1 Pa·s 35 1:2:21:2:1 μ

Pa·s 35 1:2:2 μ

Pa·s 35 2:1:1 （ 1:2:2 μ 2:1:1 （ 30 2:1:22:1:1 （ 30 2:1:2 30 2:1:2

Viscosity 25

Viscosity 25

Viscosity 25 20 20 20 400 500 600 700 800 900 1000 400 500 600 700 800 900 1000 400 500Tem 600perature 700（ 800K） 900 1000 Temperature（K） Temperature（K） Figure 14. Viscosity for He-H2-N2 mixture. Figure 14. Viscosity for He-H2-N2 mixture. Figure 14.14. Viscosity forfor He-HHe-H22-N2 mixture.mixture. 4.2. Result Analysis 4.2. Result Analysis Figures 15 and 16 are the COP and exergy efficiency for VM cycle heat pump adopting He-H2 Figures 15 and 16 are the COP and exergy efficiency for VM cycle heat pump adopting He-H2 mixture.Figures There 15 isand a small 16 are difference thethe COPCOP of andand COP exergyexergy in diff efficiencyefficiencyerent proportions forfor VMVM cyclecycle of mixture. heatheat pumppump The COP adoptingadopting increases He-HHe-H at22 mixture. There is a small difference of COP in different proportions of mixture. The COP increases at elevatedmixture. temperature,There There is is a a small small reaches difference difference maximum of of COP COP value in in diff differentof erent3.5 at proportions calculating proportions range.of of mixture. mixture. Mixing TheThe ratio COP COP of increases 1:2 increases has the at elevated temperature, reaches maximum value of 3.5 at calculating range. Mixing ratio of 1:2 has the highestatelevated elevated values temperature, temperature, of exergy reaches reachesefficiency maximum maximum but when value value temp of 3.5 oferature 3.5at calculating at calculatingapproaches range. range.1000 Mixing K, Mixing the ratio values ratio of 1:2 of has 1:2exergy hasthe highest values of exergy efficiency but when temperature approaches 1000 K, the values of exergy efficiencythehighest highest values for values the of three exergy of exergy He-H efficiency efficiency2 mixtures but but arewhen when very temp close. temperatureerature approaches approaches 1000 1000 K, K, the the values values of of exergy efficiency for the three He-H2 mixtures are very close. efficiencyefficiency for the three He-HHe-H22 mixtures are very close.

3.5 3.5

3 3

COP He:H =1:1 COP He:H2=1:1 COP He:H2=1:1 2.5 He:H2=2:1 2.5 He:H2=2:1 2.5 He:H2=2:1 He:H2=1:2 He:H2=1:2 He:H2=1:2 2 2 4002 500 600 700 800 900 1000 4002 500Temperature600 of 700heat source800 （K900） 1000 400 500Temperature600 of700 heat source800 （K900） 1000 Temperature of heat source（K） Figure 15. The COP for He-H2 mixture. Figure 15. The COP for He-H2 mixture. Figure 15. The COP for He-H2 mixture. 0.21 0.21 He:H =1:1 0.21 He:H2=1:1 He:H2=1:1 He:H2=2:1 0.2 He:H2=2:1 0.2 He:H2=2:1 0.2 He:H2=1:2 He:H2=1:2 0.19 He:H2=1:2 0.19 2 0.19 0.18 Exergy efficiency Exergy 0.18 Exergy efficiency Exergy 0.18 Exergy efficiency Exergy

0.17 0.17400 500 600 700 800 900 1000 0.17400 500Temperature600 of 700heat source800 （K900） 1000 400 500Temperature600 of700 heat source800 （K900） 1000 Temperature of heat source（K） Figure 16. The exergy efficiency for He-H mixture. Figure 16. The exergy efficiency for He-H2 mixture. Figure 16. The exergy efficiency for He-H2 mixture. Figure 16. The exergy efficiency for He-H2 mixture.

Figures 17–2017–20 are the COP and exergy efficiencyefficiency for VMVM cyclecycle heatheat pumppump adoptingadopting He-NHe-N22 and Figures 17–20 are the COP and exergy efficiency for VM cycle heat pump adopting He-N2 and H2-N-NFigures22 mixture.mixture. 17–20 The The aretendency the COP of theand twotwo exergy kindskinds efficiency ofofbinary binary for mixtures mixtures VM cycle with with heat different different pump ratio adoptingratio is is similar. similar. He-N That 2That and is, H2-N2 mixture. The tendency of the two kinds of binary mixtures with different ratio is similar. That is,theH2 -Nthe higher2 mixture.higher the the heat The heat sourcetendency source temperature, oftemperature, the two kinds the biggerthe of bi binarygger the valuethe mixtures value of COP; ofwith COP; exergy different exergy efficiency ratio efficiency is goessimilar. goes up That then up is, the higher the heat source temperature, the bigger the value of COP; exergy efficiency goes up thendown;is, the down; thehigher 2:1 the proportionthe 2:1 heat proportion source of mixture oftemperature, mixture has the has largest the the bi lagger valuergest the value of COPvalue of and COP of exergyCOP; and exergy efficiency. efficiency.efficiency Overall, Overall,goes H -N up then down; the 2:1 proportion of mixture has the largest value of COP and exergy efficiency. Overall,2 2 Hmixturethen2-N down;2 mixture shows the shows better2:1 proportion performancebetter performance of mixture than that hasthanof the that the la rgestHe-Nof the value2 He-Nmixture. of2 mixture.COP and exergy efficiency. Overall, H2-N2 mixture shows better performance than that of the He-N2 mixture. H2-N2 mixture shows better performance than that of the He-N2 mixture.

Entropy 2017, 19, 446 11 of 14

Entropy 2017, 19, 46 11 of 14 The COPs of VM cycle heat pump using He-H2-N2 mixture as refrigerant are shown in Figure 21.

The COPThe increases COPs of asVM well cycle as heat the pump temperature using He-H of2-N heat2 mixture source. as refrigerant Among theare shown seven in mixture Figure 21. ratios, proportionThe COP 2:2:1 increases has the as largest well as COP, the ittemperature reaches about of heat 3.5 at source. 1000 K. Among The difference the seven of mixture COP is ratios, relatively smallproportion at lower 2:2:1 temperature, has the largest and becomesCOP, it reaches bigger about at higher 3.5 at 1000 temperature. K. The difference of COP is relatively smallFigure at 22lower is the temperature, exergy efficiency and beco ofmes VM bigger cycle at heat higher pump temperature. adopting the three refrigerant mixtures. At lowerFigure temperature, 22 is the exergy the tendency efficiency is of not VM clear. cycle Exergy heat pump efficiency adopting for the some three proportion refrigerant mixturemixtures. goes up, whileAt lower some temperature, goes down. the There tendency are is crossover not clear. points Exergy between efficiency mixing for some ratio proportion 1:2:1 to 2:1:1mixture and goes mixing up, while some goes down. There are crossover points between mixing ratio 1:2:1 to 2:1:1 and mixing ratioup, 1:2:2 while to 2:1:2.some goes At higher down. temperature,There are crossover the exergy points between efficiency mixing declines. ratio 1:2:1 Mixing to 2:1:1 ratio and 1:1:2 mixing has the ratio 1:2:2 to 2:1:2. At higher temperature, the exergy efficiency declines. Mixing ratio 1:1:2 has the worstratio curve 1:2:2 of to exergy 2:1:2. At efficiency. higher temperature, the exergy efficiency declines. Mixing ratio 1:1:2 has the worst curve of exergy efficiency. To sum up, there are 16 mixing ratios and four kinds of mixture refrigerants investigated in To sum up, there are 16 mixing ratios and four kinds of mixture refrigerants investigated in this this paper. For binary He-H2 mixture, the difference of COP is not significant; ratio 1:2 has higher paper. For binary He-H2 mixture, the difference of COP is not significant; ratio 1:2 has higher exergy exergy efficiency. For binary He-N or H -N , ratio 2:1 has both higher COP and exergy efficiency. efficiency. For binary He-N2 or H2-N2 2, ratio2 2:12 has both higher COP and exergy efficiency. Basically, Basically,the overall the overall systemsystem performances performances of mixture of H mixture2-N2 are Hbetter2-N2 thanare bettermixture than He-N mixture2. For trinary He-N 2He-H. For2-N trinary2 He-Hmixture,2-N2 mixture, at the proportion at the proportion of 2:2:1, the of sy 2:2:1,stem the has system the best has COP the and best exergy COP efficiency. and exergy efficiency.

3.5

3

2.5 COP COP COP He:N =1:1 2 2 He:N =2:1 2 He:N =1:2 1.5 2 1.5

400 500 600 700 800 900 1000 （ ） Temperature of heat source（K）

Figure 17. The COP for He-N2 mixture. FigureFigure 17. 17.The The COPCOP for He-N 22 mixture.mixture.

0.18

0.16

0.14 He:N =1:1 2 0.12 He:N =2:1 Exergy efficiency Exergy 0.12

Exergy efficiency Exergy 2 Exergy efficiency Exergy 2 He:N =1:2 2

0.1 400 500 600 700 800 900 1000 （ ） Temperature of heat source（K）

FigureFigure 18. 18.The The exergy exergy efficiencyefficiency for He-N He-N2 2mixture.mixture.

3.5

3

2.5

COP 2.5 COP COP H :N =1:1 2 2 H :N =2:1 2 2 2 H :N =1:2 2 2

1.5 400 500 600 700 800 900 1000 （ ） Temperature of heat source（K）

Figure 19. The COP for H2-N2 mixture.

EntropyEntropy 2017 2017, ,19 19, ,46 46 1212 of of 14 14 Entropy 2017, 19, 46 12 of 14

Entropy 2017, 19, 446 FigureFigure 19. 19. The The COP COP for for H H2-N2-N2 2mixture. mixture. 12 of 14 Figure 19. The COP for H2-N2 mixture.

0.18 0.18

0.16 0.16

0.140.14 0.14 HH:N:N =1:1=1:1 H22:N22=1:1 2 2 HH:N:N =2:1=2:1

Exergy efficiency Exergy 0.12 Exergy efficiency Exergy 0.12 H22:N22=2:1 Exergy efficiency Exergy 0.12 2 2 HH:N:N =1:2=1:2 H22:N22=1:2 2 2 0.10.1 0.1400 500 600 700 800 900 1000 400 500 600 700 800 900 1000 TemperatureTemperature of of heat heat source source（（KK）） Temperature of heat source（K）

FigureFigure 20. 20. The The exergy exergy efficiency efficiencyefficiency forfor HH2-N2-N-N22 2mixture. mixture. Figure 20. The exergy efficiency for H2-N2 mixture.

3.53.5 3.5 He:HHe:H:N:N=1:1:1=1:1:1 He:H22:N22=1:1:1 2 2 He:HHe:H:N:N=1:1:2=1:1:2 He:H22:N22=1:1:2 33 2 2 3 He:HHe:H:N:N=1:2:1=1:2:1 He:H22:N22=1:2:1 2 2 He:HHe:H:N:N=1:2:2=1:2:2 He:H22:N22=1:2:2 COP COP 2.52.5 2 2 COP 2.5 He:HHe:H:N:N=2:1:1=2:1:1 He:H22:N22=2:1:1 2 2 He:HHe:H:N:N=2:1:2=2:1:2 He:H22:N22=2:1:2 22 2 2 2 He:HHe:H:N:N=2:2:1=2:2:1 He:H22:N22=2:2:1 2 2 400400 500500 600600 700700 800800 900900 10001000 400 500Temperature600 of700 heat source800 （（K900）） 1000 Temperature of heat source（K）

FigureFigure 21.21. The The COP COP for for He-H He-H2-N2-N2 2mixture. mixture. Figure 21. The COP for He-H2-N-N22 mixture.mixture.

He:HHe:H:N:N=1:1:1=1:1:1 0.190.19 He:H22:N22=1:1:1 0.19 2 2 He:HHe:H:N:N=1:1:2=1:1:2 He:H22:N22=1:1:2 0.180.18 2 2 0.18 He:HHe:H:N:N=1:2:1=1:2:1 He:H22:N22=1:2:1 2 2 0.170.17 He:HHe:H:N:N=1:2:2=1:2:2 0.17 He:H22:N22=1:2:2 2 2 0.16 He:HHe:H:N:N=2:1:1=2:1:1 0.16 He:H22:N22=2:1:1 Exergy efficiency Exergy Exergy efficiency Exergy 2 2 Exergy efficiency Exergy He:HHe:H:N:N=2:1:2=2:1:2 He:H22:N22=2:1:2 0.150.15 2 2 0.15 He:HHe:H:N:N=2:2:1=2:2:1 He:H22:N22=2:2:1 2 2 400400 500500 600600 700700 800800 900900 10001000 400 500TemperatureTemperature600 of of 700heat heat source source800 （（KK900）） 1000 Temperature of heat source（K）

FigureFigure 22. 22. The The exergy exergy efficiency efficiencyefficiency for for He-HHe-H2-N2-N-N22 2mixture mixture Figure 22. The exergy efficiency for He-H2-N2 mixture

5.5.5. Conclusions ConclusionsConclusions MixtureMixtureMixture refrigerantsrefrigerantsrefrigerants may maymay have havehave effects effectseffects on the onon cycle thethe performances. cyclecycle performances.performances. In this paper, InIn thisthis at the paper,paper, temperature atat thethe temperatureoftemperature heat source ofof within heatheat sourcesource 400–1000 withinwithin K and 400–1000400–1000 at given KK system andand atat configuration givengiven systemsystem parameters, configurationconfiguration the COPparameters,parameters, and exergy thethe COPefficiencyCOP andand exergy ofexergy VM cycle efficiencyefficiency heat pump ofof VMVM adopting cyclecycle heatheat mixture pumppump as adoptingadopting refrigerants mixturemixture are calculated, asas refrigerantsrefrigerants and comparedareare calculated,calculated, with andeachand compared compared other or pure with with refrigerants. each each other other or or We pure pure can refrigerants. drawrefrigerants. conclusions We We can can as draw follows:draw conclusions conclusions as as follows: follows: (1)(1)(1) For For pure pure refrigerants, refrigerants, helium helium and and hydrogen hydrogen are are si si similarmilarmilar to to each each other, other, better better than than that that of of nitrogen. nitrogen. ConsideringConsidering thethethe liable liableliable explosion explosionexplosion problem problemproblem of hydrogen, ofof hydrogen,hydrogen, helium heliumhelium is the best isis thethe choice bestbest of choice purechoice refrigerant ofof purepure refrigerantrefrigerantfor VM cycle for for heat VM VM pump.cycle cycle heat heat pump. pump. (2)(2) ForFor binarybinary mixture,mixture, He-HHe-H22 mixturemixture hashas optimumoptimum thermothermodynamicdynamic performance,performance, thethe (2)(2) ForFor binarybinary mixture, mixture, He-H He-H2 mixture2 mixture has optimum has optimum thermodynamic thermo performance,dynamic performance, the recommended the recommendedrecommendedratio is 1:2. The ratio ratio other is is binary1:2. 1:2. The The mixture other other binary binary is also mixtur mixtur an optimumee is is also also proportion an an optimum optimum of mixture.proportion proportion of of mixture. mixture. (3)(3) For For trinary trinary mixture, mixture, at at the the proportion proportion of of He-H He-H22-N-N22 mixture mixture is is 2:2:1, 2:2:1, the the system system has has the the best best COP COP (3)(3) ForFor trinary trinary mixture, mixture, at at the the proportion proportion of He-H 2-N-N22 mixturemixture is is 2:2:1, 2:2:1, the the system system has has the the best best COP COP and exergy efficiency. Furthermore, all the system performances of recommended binary and andand exergy exergy efficiency. efficiency. Furthermore, Furthermore, all all the the sy systemstem performances of of recommended binary binary and trinarytrinary mixture mixture are are close close to to pure pure refrigerant refrigerant helium. helium. For For these these recommended recommended binary binary and and trinary trinary trinarytrinary mixture mixture are are close close to to pure pure refrigerant refrigerant helium. helium. For For these these recommended recommended binary binary and and trinary trinary

Entropy 2017, 19, 446 13 of 14

mixtures, system COPs are close to 3.3 and exergy efficiencies are about 0.2, which are close to pure refrigerant helium.

Acknowledgments: The Project is supported by the Natural Science Foundation of Hebei province. (No. E2014502085). Author Contributions: Yingbai Xie proposed and designed the research; Kai Zhong performed the calculation. Both authors jointly worked on deriving the results and wrote the paper. Both authors have read and approved the final manuscript. Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

Symbol Implication COP Coefficient of performance Dco Diameter of cold cylinder Ex,co Exergy of cold space Ex,h Exergy of heat space Ex,in Exergy of fluid inlet Ex,out Exergy of fluid outlet Pav Average pressure Pmax Maximum pressure Pmin Minimum pressure Qa Theoretical heating release of warm cylinder Qco Theoretical heat capacity absorbed by cold cylinder Qh Theoretical heating absorption of hot cylinder Ta Temperature of warm space Tco Temperature of cold space Th Temperature of hot space Tin Inlet temperature To Ambient temperature Tout Outlet temperature Vco Travel volume of the cold cylinder Z Distance of the stroke τ Temperature ratio τco Temperature ratio of the cold side τh Temperature ratio of the hot side φ Phase angle of volume θ Pressure phase angle δ Pressure parameter n Rotation rate ω Proportion of volume ηe Theoretical exergy efficiency

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