Optimization analyses on the performance of an auto-cascade absorption refrigeration system operating with mixed refrigerants

Optimization analyses on the performance of an auto-cascade absorption refrigeration system... Abstract Waste heat can be well utilized in absorption refrigeration systems. The auto-cascade absorption refrigeration system could obtain a lower temperature than that of the traditional absorption refrigeration system since the non-azeotropic mixed refrigerants with large temperature glides were used. In this article, the performance of an auto-cascade absorption refrigeration system using R23/R134a/DMF (dimethylformamide) solutions as the working substance was analyzed. Optimization analysis results showed that, to some extent, the coefficient of performance (COP) could be increased when the low pressure of the system decreased or the high pressure increased. The reasonable upper limit of the high pressure was the high pressure at the turning point of COP, and the reasonable lower limit of the low pressure was the low pressure at the turning point of COP. The COP of the system monotonously increased with the increase of the mole fraction of R23 in solutions. The low R23 mole fraction solutions were more appropriate. 1 INTRODUCTION The absorption refrigerator was a kind of refrigerating devices driven by heat, which obtained low temperature based on the variations of solution properties under different pressures and temperatures. Because the industrial waste heat, solar heat and geothermal heat can be used to drive absorption refrigerators, absorption refrigerators were attracted more and more attentions nowadays. Traditional LiBr/H2O or NH3/H2O absorption refrigerators had been widely applied in industries and daily life, but they were limited by the relatively high refrigeration temperature of H2O or the flammability and toxicity of NH3. For example, huge quantities of waste heat were released in oil refining industries and the refrigeration temperature below −50°C was demanded during the process of recovery of LPG. Under the circumstances, traditional NH3/H2O absorption refrigerators had to add additional devices and complex pipe arrangement to reach that low temperature by the multi-stage absorption systems. Chen et al. [1] proposed non-azeotropic mixed refrigerant R22/R142b in the traditional absorption refrigeration system to replace R22, and DMF (N, N-dimethylformamide) was selected as the absorbent. Furthermore, Chen et al. [2, 3] proposed R32/R134a as the mixed refrigerant and found similar system performances can be obtained from test results. Gao et al. [4] analyzed the feasibility of replacing R22 with R32/R227ea in the traditional absorption system. The results also showed that similar system performances can be obtained when DMF was used as the absorbent. Chen [5] introduced the auto-cascade module into the traditional absorption refrigeration system to obtain a lower refrigerating temperature with the non-azeotropic mixed refrigerant. The auto-cascade module was commonly used in the auto-cascade compression refrigeration system (ACCRS) to obtain refrigerating temperature lower than −60°C [6–9]. Therefore, the new absorption refrigeration system was named as the auto-cascade absorption refrigeration system (ACARS). The experiments conducted by He et al. [10, 11] showed promising system performances: the lowest refrigerating temperature of −47.2°C was both obtained when R23/R134a and R23/R32/R134a were selected as the mixed refrigerants at the generation temperatures of 157 and 163°C, respectively, in which DMF was selected as the absorbent. Xu et al. [12–14] coupled the ACARS with the ACCRS to reduce the power consumption at low-temperature refrigeration (−60 to −170°C). Theoretical and experimental results showed that the performance of ACCRS was obviously improved. As the operation mechanism of the new system was far more complicated than that of the traditional one, theoretical analyses on the performance of the new system has not been investigated systematically so far. Therefore, this article proposed a new approach to analyze and optimize the performance of the new system. The results can lay a solid basis for the future experiments. 2 THEORETICAL MODEL The key characteristic of the auto-cascade absorption refrigeration system was that the non-azeotropic mixed refrigerants with large temperature glides in condensation and evaporation were used as working substances, which was different from the isothermal phase change processes of the pure refrigerants. Thus, at the exits of the evaporator and condenser, the mixed refrigerants still remained in the two-phase states, which demanded a recuperator with a large area to liquefy the mixed refrigerants in the high pressure side before entering the expansion valve to obtain a low refrigerating temperature. The flow chart of the auto-cascade absorption refrigeration system was shown in Figure 1. Figure 1. View largeDownload slide Flow chart of the auto-cascade absorption refrigeration system Figure 1. View largeDownload slide Flow chart of the auto-cascade absorption refrigeration system 2.1 Assumption The generating temperature TG, surroundings temperature TH and refrigerating temperature TL were specified. The mole fraction of the rich solution was specified as well as the mole fraction of DMF at the exit of the rectification column point 3. The high pressure and low pressure of the system were specified. The pressure losses in the heat exchangers and rectifier were neglected. The pinch point temperature differences of the condenser ΔTC,min and evaporator ΔTE,min occurred at the cold end of the condenser and hot end of the evaporator, respectively. The pinch point temperature differences of the refrigerant recuporator R1, R2 and solution recuperator R3 were ΔTR1,min, ΔTR2,min and ΔTR3,min, respectively. All of the pinch points occurred at the cold or hot end of the recuperators. The pinch point temperature difference of the absorber ΔTA,min occurred at the exit of absorber. Refrigerant recuperators, solution recuperator and throttle valves were adiabatic. 2.1.1 Thermodynamic model The mass conservation and energy conservation equations of all parts in the auto-cascade absorption refrigeration system were listed as follows. (1) Generator QG=m22h22+m21h21–m1h1 (1) m1=m22+m21 (2) m1z1,i=m22z22,i+m21z21,i (3) where m is the mole flow rate of the working substance [mol s−1], h is the specific enthalpy [J mol−1], QG is the heat input in the generator [W], z is the mole fraction of the component, the first subscript denotes the state point in the cycle, the second subscript i denotes the ith component of the mixture R23/R134a/DMF. (2) Rectifier m22=m3+mL (4) m22z22,i=m3z3,i+mLz21,i (5) m22h22=m3h3+mLhL+QD (6) where QD is the rectifying heat capacity [W], subscript L denotes the backflow to the generator. (3) Absorber QA=m20h20+m17h17–m18h18 (7) m18=m20+m17 (8) m18z18,i=m20z20,i+m17z17,i (9) where QA denotes the absorbing heat released to the surroundings [W]. (4) Condenser QC=m4(h4–h3) (10) where QC denotes the condensing heat released to the surroundings. (5) Gas–liquid separator The compositions of R23/R134a/DMF vapor and weak solution in the separator could be determined by the vapor–liquid equilibrium. m4=m42+m41 (11) m4z4,i=m42z42,i+m41z41,i (12) m4h4=m42h42+m41h41 (13) (6) Recuperators Two refrigerant recuperators were treated as a whole one. m42(h5–h42)=m7(h8–h7) (14) Solution recuperator was defined as follows: m21(h21–h10)=m9(h9–h1) (15) (7) Throttle valves The throttle valve at the bottom of the separator: m41h41=m11h11 (16) The refrigerant throttle valve: m5h5=m6h6 (17) The solution throttle valve: m10h10=m20h20 (18) (8) Evaporator m7(h7–h5)=QE (19) where QE denotes the refrigerating capacity [W]. (9) Solution pump Compared to the amount of heat input into the system, the work consumed by the solution pump was small which was neglected. (10) Coefficient of performance (COP) COP=QE/QG (20) COP could also be expressed as the following form: COP=(h7–h5)/(f(h21–h1)+(h22–h21)) (21) COP=(h8–h42)/(f(h21–h1)+(h22–h21)) (22) where circulating ratio: f=m1/m22 (23) 2.2 Calculation on properties of the mixture Modified Patel–Teja equation was applied in this article to calculate the enthalpy, entropy and phase equilibrium of the mixed refrigerants. The interaction parameters of each pair among R23, R134a and DMF were fitted from literatures [15, 16]. 3 PERFORMANCE ANALYSIS AND OPTIMIZATION In calculations, the generation temperature TG = 140°C, surroundings temperature TH = 20°C, refrigerating temperature TL = −50°C, the mole fraction of DMF at point 3 z3,3 = 0.03. The pinch point temperature difference ΔTR1,min = ΔTR2,min = ΔTC,min = ΔTE,min = 5°C, ΔTA,min = 10°C. The flow rate at point 2 was set to be 1 mol/s. 3.1 Optimization of pressures The high and low pressures of the auto-cascade absorption refrigeration system were not only related with condensation temperature and evaporation temperature respectively, but also associated with the generation temperature, absorption temperature and the temperature distribution of mixed refrigerants in recuperators, because the condensation and evaporation of the non-azeotropic mixed refrigerants were no longer at constant temperatures but at large temperature glides. Hence, the high pressure and low pressure were treated as two important design parameters in simulations, which was different from the constant high and low pressures in isothermal phase change processes of the pure refrigerants. The variations of COP with the high pressure PH under different low pressures were shown in Figure 2. Figure 2. View largeDownload slide The variations of COP with the high pressure PH (z1,1 = 0.2, z1,3 = 0.6). Figure 2. View largeDownload slide The variations of COP with the high pressure PH (z1,1 = 0.2, z1,3 = 0.6). From Figure 2, it can be seen that a peak COP occurred with the increase of the high pressure at each low pressure. Hence, the corresponding high pressure can be selected as the reasonable upper limit of the high pressure at certain low pressure. It can also be noted from Figure 2 that COP monotonically increased with the decrease of the low pressure at certain high pressure. In order to see clearly the variations of COP with the low pressure, the abscissa was reset as the low pressure PL as shown in Figure 3. Figure 3. View largeDownload slide The variations of COP with the low pressure PL (z1,1 = 0.2, z1,3 = 0.6). Figure 3. View largeDownload slide The variations of COP with the low pressure PL (z1,1 = 0.2, z1,3 = 0.6). From Figure 3, it can be seen that COP increased with the decrease of the low pressure at the specified high pressure and there existed a turning point along the line. When the low pressure was larger than the turning point low pressure COP increased obviously, but when the low pressure was smaller than the turning point low pressure, COP increased very slightly. Hence, the turning point low pressure can be selected as the reasonable lower limit of the low pressure at certain high pressure, because the extreme low pressure deteriorated the performance of the absorber and increased the power consumption of the solution pump. The variations of COP with the high pressure and low pressure discussed above have been found when the system operated with other mole fractions of R23/R134a/DMF solutions. It can also be found that the temperature differences at the hot end of the refrigerant recuperator R1 and at the cold end of the refrigerant recuperator R2 varied regularly with the pressures. Figures 4 and 5 gave out relationships between the COP, ΔThot, ΔTcold and PH, PL, respectively. Figure 4. View largeDownload slide The variations of COP, ΔThot, ΔTcold with the high pressure (z1,1 = 0.2, z1,3 = 0.6, PL=130kPa) Figure 4. View largeDownload slide The variations of COP, ΔThot, ΔTcold with the high pressure (z1,1 = 0.2, z1,3 = 0.6, PL=130kPa) Figure 5. View largeDownload slide The variations of COP, ΔThot, ΔTcold with the low pressure (z1,1 = 0.2, z1,3 = 0.6, PH=1000kPa). Figure 5. View largeDownload slide The variations of COP, ΔThot, ΔTcold with the low pressure (z1,1 = 0.2, z1,3 = 0.6, PH=1000kPa). From Figure 4, it can be found that the temperature differences at the hot end of R1 and the cold end of R2 were both approximately equal to the pinch point temperature differences of R1 and R2, respectively, namely, ΔTcold = ΔThot = ΔTmin, when COP reached a peak value with the increase of high pressure. In other words, at a specified low pressure the pinch point temperature difference transferred from the hot end of R1 to the cold end of R2 when the high pressure increased. Because the heat demanded for the generator varied slightly, hence, the variations of COP were mainly determined by the change of the cooling capacity with the increase of the high pressure. After the transfer of the pinch point to the cold end of R2, the specific enthalpy difference between state points 5 and 7 increased slightly, but the refrigerant flow rate decreased from the top outlet of the gas–liquid separator when the high pressure increased. These factors can account for the occurrence of the peak value of COP in Figure 4. Figure 5 also shows that the temperature differences at the cold end of R2 and the hot end of R1 were both approximately equal to the pinch point temperature differences of R1 and R2, respectively, namely, ΔTcold = ΔThot = ΔTmin, COP occurred a turning point with the decrease of the low pressure. From the above analyses, we knew that the low and high pressures at the turning points should be the reasonable lower limit of the low pressure and upper limit of the high pressure for the specified mole fractions of the solution. In this article, the reasonable low pressure was specified as 100kPa. The peak value of COP at the reasonable lower limit low pressure and upper limit high pressure for the specified mole fractions was defined as the COPopt. 3.2 Optimization of mole fractions According to the pressure optimizing method in previous section, COPopt of the system operated with different mole fractions could be obtained. Figure 6 shows the variations of COPopt and refrigerating capacity QE with the mole fraction of R23 when the mole fractions of DMF z1,3 were set to be 50, 60 and 70%. Figure 6. View largeDownload slide The variations of COPopt and QE with the fraction of R23 (TG = 140°C, TH = 20°C, TL= −50°C, z3,3 = 0.03). Figure 6. View largeDownload slide The variations of COPopt and QE with the fraction of R23 (TG = 140°C, TH = 20°C, TL= −50°C, z3,3 = 0.03). From Figure 6, it can be seen that QE and COPopt both increase monotonically with the increase of R23 for the specified mole fraction of DMF z1,3. The maximum COPopt for different mole fractions of DMF were almost same, but the corresponding high pressures to COPopt were different. The larger mole fraction of DMF was, the higher the corresponding high pressure was. 4 CONCLUSIONS The performance of an auto-cascade absorption refrigeration cycle operated with non-azeotropic mixed refrigerant R23/R134a/DMF was investigated in this article by a new approach. The analysis results showed that: At a specified low pressure, COP increased at first and then decreased with the increase of the high pressure. The high pressure corresponding to the peak COP should be the reasonable upper limit of the high pressure. At a specified high pressure, COP was obviously increased with the decrease of low pressure within a certain range. The turning point low pressure should be the reasonable lower limit of the low pressure. When the temperature differences at the cold end of R2 and at the hot end of R1 were both approximately equal to the pinch point temperature differences of R1 and R2, respectively, the peak value or the turning point reached. When the mole fraction of DMF was specified, refrigerating capacity QE and COPopt both increased monotonically with the increase of the mole fraction of R23. But the maximum COPopt were almost the same for different mole fractions of DMF. As the high pressure corresponding to the maximum COPopt for the low mole fraction of DMF solution was lower than that of high mole fraction of DMF solutions, the low mole fraction DMF solutions should be the better. ACKNOWLEDGEMENT This work is supported by Industrial project of public welfare technology research in Zhejiang Province (Foundation No. 2016C31125). REFERENCES 1 Chen G , Yin Z , Wang J , et al. . The characteristics of an absorption system with azeotropic refrigerant mixture refrigerant . J Refrigeration 1998 ; 1 : 1 – 5 . 2 Chen S , Chen G , Zheng F , et al. . Operation characteristics of absorption refrigeration using alternative working fluids . Cryogenics 1999 ; 112 : 22 – 30 . 3 Chen S , Zheng F , Wang J , et al. . Replacement refrigerant HCFC22 for absorption refrigeration features . J Eng Thermophys 1999 ; 20 : 410 – 2 . 4 Gao W , Zhao X , Liu Z . Calculation of HFC32+HFC227ea/DMF absorption refrigeration cycle . J Eng Thermophys 2010 ; 31 : 545 – 8 . 5 Chen G . Absorption refrigeration device used for deep freezing. Chinese Patent, 02110940.0 ( 2002 ) 6 Wang Q , Chen F , Xia P , et al. . Influence of mixture composition on cooling rate of a freeze-dryer with an auto-cascade refrigerating system . J Xi’anJiaotong Univ 2009 ; 43 : 37 – 42 . 7 Wang Q , Cui K , Sun T , et al. . Performance of a single-stage auto-cascade refrigerator operating with a rectifying column at the temperature level of −60°C . J Zhejiang Univ Sci A (Appl Physics & Eng) 2011 ; 12 : 139 – 45 . Google Scholar CrossRef Search ADS 8 Wang Q , Liu R , Wang J , et al. . An investigation of the mixing position in the recuperators on the performance of an auto-cascade refrigerator operating with a rectifying column . Cryogenics 2012 ; 52 : 581 – 9 . Google Scholar CrossRef Search ADS 9 Wang Q , Li D , Wang J , et al. . Numerical investigations on the performance of a single-stage auto-cascade refrigerator operating with two vapor-liquid separators and environmentally benign binary refrigerants . Appl Energy 2013 ; 112 : 949 – 55 . Google Scholar CrossRef Search ADS 10 He Y , Hong R , Chen G . Heat driven refrigeration cycle at low temperatures . Chinese Sci Bull 2005 ; 50 : 485 – 9 . Google Scholar CrossRef Search ADS 11 He Y , Chen G . Experimental study on an absorption refrigeration system at low temperatures . Int J Therm Sci 2007 ; 46 : 294 – 9 . Google Scholar CrossRef Search ADS 12 Xu Y , Chen F , Wang Q , et al. . A novel low-temperature absorption-compression cascade refrigeration system . Appl Therm Eng 2015 ; 75 : 504 – 12 . Google Scholar CrossRef Search ADS 13 Xu Y , Jiang N , Wang Q , et al. . Comparative study on the energy performance of two different absorption-compression refrigeration cycles driven by low-grade heat . Appl Therm Eng 2016 ; 106 : 33 – 41 . Google Scholar CrossRef Search ADS 14 Xu Y , Jiang N , Pan F , et al. . Comparative study on two low-grade heat driven absorption-compression refrigeration cycles based on energy, exergy, economic and environmental (4E) analyses . Energy Convers Manage 2017 ; 133 : 535 – 47 . Google Scholar CrossRef Search ADS 15 Han X , Gao Z , Xu Y , et al. . Solubility of refrigerant 1,1,1,2-tetrafluoroethane in the N,N-dimethyl formamide in the temperature range from 263.15K to 363.15K . Chem Eng Data 2011 ; 56 : 1821 – 6 . Google Scholar CrossRef Search ADS 16 Gao Z , Xu Y , Li P , et al. . Solubility of refrigerant trifluoromethane in n,n-dimethyl formamide in the temperature range from 283.15K to 363.15K . Int J Refrig 2012 ; 35 : 1372 – 6 . Google Scholar CrossRef Search ADS © The Author(s) 2018. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Low-Carbon Technologies Oxford University Press

Optimization analyses on the performance of an auto-cascade absorption refrigeration system operating with mixed refrigerants

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Abstract

Abstract Waste heat can be well utilized in absorption refrigeration systems. The auto-cascade absorption refrigeration system could obtain a lower temperature than that of the traditional absorption refrigeration system since the non-azeotropic mixed refrigerants with large temperature glides were used. In this article, the performance of an auto-cascade absorption refrigeration system using R23/R134a/DMF (dimethylformamide) solutions as the working substance was analyzed. Optimization analysis results showed that, to some extent, the coefficient of performance (COP) could be increased when the low pressure of the system decreased or the high pressure increased. The reasonable upper limit of the high pressure was the high pressure at the turning point of COP, and the reasonable lower limit of the low pressure was the low pressure at the turning point of COP. The COP of the system monotonously increased with the increase of the mole fraction of R23 in solutions. The low R23 mole fraction solutions were more appropriate. 1 INTRODUCTION The absorption refrigerator was a kind of refrigerating devices driven by heat, which obtained low temperature based on the variations of solution properties under different pressures and temperatures. Because the industrial waste heat, solar heat and geothermal heat can be used to drive absorption refrigerators, absorption refrigerators were attracted more and more attentions nowadays. Traditional LiBr/H2O or NH3/H2O absorption refrigerators had been widely applied in industries and daily life, but they were limited by the relatively high refrigeration temperature of H2O or the flammability and toxicity of NH3. For example, huge quantities of waste heat were released in oil refining industries and the refrigeration temperature below −50°C was demanded during the process of recovery of LPG. Under the circumstances, traditional NH3/H2O absorption refrigerators had to add additional devices and complex pipe arrangement to reach that low temperature by the multi-stage absorption systems. Chen et al. [1] proposed non-azeotropic mixed refrigerant R22/R142b in the traditional absorption refrigeration system to replace R22, and DMF (N, N-dimethylformamide) was selected as the absorbent. Furthermore, Chen et al. [2, 3] proposed R32/R134a as the mixed refrigerant and found similar system performances can be obtained from test results. Gao et al. [4] analyzed the feasibility of replacing R22 with R32/R227ea in the traditional absorption system. The results also showed that similar system performances can be obtained when DMF was used as the absorbent. Chen [5] introduced the auto-cascade module into the traditional absorption refrigeration system to obtain a lower refrigerating temperature with the non-azeotropic mixed refrigerant. The auto-cascade module was commonly used in the auto-cascade compression refrigeration system (ACCRS) to obtain refrigerating temperature lower than −60°C [6–9]. Therefore, the new absorption refrigeration system was named as the auto-cascade absorption refrigeration system (ACARS). The experiments conducted by He et al. [10, 11] showed promising system performances: the lowest refrigerating temperature of −47.2°C was both obtained when R23/R134a and R23/R32/R134a were selected as the mixed refrigerants at the generation temperatures of 157 and 163°C, respectively, in which DMF was selected as the absorbent. Xu et al. [12–14] coupled the ACARS with the ACCRS to reduce the power consumption at low-temperature refrigeration (−60 to −170°C). Theoretical and experimental results showed that the performance of ACCRS was obviously improved. As the operation mechanism of the new system was far more complicated than that of the traditional one, theoretical analyses on the performance of the new system has not been investigated systematically so far. Therefore, this article proposed a new approach to analyze and optimize the performance of the new system. The results can lay a solid basis for the future experiments. 2 THEORETICAL MODEL The key characteristic of the auto-cascade absorption refrigeration system was that the non-azeotropic mixed refrigerants with large temperature glides in condensation and evaporation were used as working substances, which was different from the isothermal phase change processes of the pure refrigerants. Thus, at the exits of the evaporator and condenser, the mixed refrigerants still remained in the two-phase states, which demanded a recuperator with a large area to liquefy the mixed refrigerants in the high pressure side before entering the expansion valve to obtain a low refrigerating temperature. The flow chart of the auto-cascade absorption refrigeration system was shown in Figure 1. Figure 1. View largeDownload slide Flow chart of the auto-cascade absorption refrigeration system Figure 1. View largeDownload slide Flow chart of the auto-cascade absorption refrigeration system 2.1 Assumption The generating temperature TG, surroundings temperature TH and refrigerating temperature TL were specified. The mole fraction of the rich solution was specified as well as the mole fraction of DMF at the exit of the rectification column point 3. The high pressure and low pressure of the system were specified. The pressure losses in the heat exchangers and rectifier were neglected. The pinch point temperature differences of the condenser ΔTC,min and evaporator ΔTE,min occurred at the cold end of the condenser and hot end of the evaporator, respectively. The pinch point temperature differences of the refrigerant recuporator R1, R2 and solution recuperator R3 were ΔTR1,min, ΔTR2,min and ΔTR3,min, respectively. All of the pinch points occurred at the cold or hot end of the recuperators. The pinch point temperature difference of the absorber ΔTA,min occurred at the exit of absorber. Refrigerant recuperators, solution recuperator and throttle valves were adiabatic. 2.1.1 Thermodynamic model The mass conservation and energy conservation equations of all parts in the auto-cascade absorption refrigeration system were listed as follows. (1) Generator QG=m22h22+m21h21–m1h1 (1) m1=m22+m21 (2) m1z1,i=m22z22,i+m21z21,i (3) where m is the mole flow rate of the working substance [mol s−1], h is the specific enthalpy [J mol−1], QG is the heat input in the generator [W], z is the mole fraction of the component, the first subscript denotes the state point in the cycle, the second subscript i denotes the ith component of the mixture R23/R134a/DMF. (2) Rectifier m22=m3+mL (4) m22z22,i=m3z3,i+mLz21,i (5) m22h22=m3h3+mLhL+QD (6) where QD is the rectifying heat capacity [W], subscript L denotes the backflow to the generator. (3) Absorber QA=m20h20+m17h17–m18h18 (7) m18=m20+m17 (8) m18z18,i=m20z20,i+m17z17,i (9) where QA denotes the absorbing heat released to the surroundings [W]. (4) Condenser QC=m4(h4–h3) (10) where QC denotes the condensing heat released to the surroundings. (5) Gas–liquid separator The compositions of R23/R134a/DMF vapor and weak solution in the separator could be determined by the vapor–liquid equilibrium. m4=m42+m41 (11) m4z4,i=m42z42,i+m41z41,i (12) m4h4=m42h42+m41h41 (13) (6) Recuperators Two refrigerant recuperators were treated as a whole one. m42(h5–h42)=m7(h8–h7) (14) Solution recuperator was defined as follows: m21(h21–h10)=m9(h9–h1) (15) (7) Throttle valves The throttle valve at the bottom of the separator: m41h41=m11h11 (16) The refrigerant throttle valve: m5h5=m6h6 (17) The solution throttle valve: m10h10=m20h20 (18) (8) Evaporator m7(h7–h5)=QE (19) where QE denotes the refrigerating capacity [W]. (9) Solution pump Compared to the amount of heat input into the system, the work consumed by the solution pump was small which was neglected. (10) Coefficient of performance (COP) COP=QE/QG (20) COP could also be expressed as the following form: COP=(h7–h5)/(f(h21–h1)+(h22–h21)) (21) COP=(h8–h42)/(f(h21–h1)+(h22–h21)) (22) where circulating ratio: f=m1/m22 (23) 2.2 Calculation on properties of the mixture Modified Patel–Teja equation was applied in this article to calculate the enthalpy, entropy and phase equilibrium of the mixed refrigerants. The interaction parameters of each pair among R23, R134a and DMF were fitted from literatures [15, 16]. 3 PERFORMANCE ANALYSIS AND OPTIMIZATION In calculations, the generation temperature TG = 140°C, surroundings temperature TH = 20°C, refrigerating temperature TL = −50°C, the mole fraction of DMF at point 3 z3,3 = 0.03. The pinch point temperature difference ΔTR1,min = ΔTR2,min = ΔTC,min = ΔTE,min = 5°C, ΔTA,min = 10°C. The flow rate at point 2 was set to be 1 mol/s. 3.1 Optimization of pressures The high and low pressures of the auto-cascade absorption refrigeration system were not only related with condensation temperature and evaporation temperature respectively, but also associated with the generation temperature, absorption temperature and the temperature distribution of mixed refrigerants in recuperators, because the condensation and evaporation of the non-azeotropic mixed refrigerants were no longer at constant temperatures but at large temperature glides. Hence, the high pressure and low pressure were treated as two important design parameters in simulations, which was different from the constant high and low pressures in isothermal phase change processes of the pure refrigerants. The variations of COP with the high pressure PH under different low pressures were shown in Figure 2. Figure 2. View largeDownload slide The variations of COP with the high pressure PH (z1,1 = 0.2, z1,3 = 0.6). Figure 2. View largeDownload slide The variations of COP with the high pressure PH (z1,1 = 0.2, z1,3 = 0.6). From Figure 2, it can be seen that a peak COP occurred with the increase of the high pressure at each low pressure. Hence, the corresponding high pressure can be selected as the reasonable upper limit of the high pressure at certain low pressure. It can also be noted from Figure 2 that COP monotonically increased with the decrease of the low pressure at certain high pressure. In order to see clearly the variations of COP with the low pressure, the abscissa was reset as the low pressure PL as shown in Figure 3. Figure 3. View largeDownload slide The variations of COP with the low pressure PL (z1,1 = 0.2, z1,3 = 0.6). Figure 3. View largeDownload slide The variations of COP with the low pressure PL (z1,1 = 0.2, z1,3 = 0.6). From Figure 3, it can be seen that COP increased with the decrease of the low pressure at the specified high pressure and there existed a turning point along the line. When the low pressure was larger than the turning point low pressure COP increased obviously, but when the low pressure was smaller than the turning point low pressure, COP increased very slightly. Hence, the turning point low pressure can be selected as the reasonable lower limit of the low pressure at certain high pressure, because the extreme low pressure deteriorated the performance of the absorber and increased the power consumption of the solution pump. The variations of COP with the high pressure and low pressure discussed above have been found when the system operated with other mole fractions of R23/R134a/DMF solutions. It can also be found that the temperature differences at the hot end of the refrigerant recuperator R1 and at the cold end of the refrigerant recuperator R2 varied regularly with the pressures. Figures 4 and 5 gave out relationships between the COP, ΔThot, ΔTcold and PH, PL, respectively. Figure 4. View largeDownload slide The variations of COP, ΔThot, ΔTcold with the high pressure (z1,1 = 0.2, z1,3 = 0.6, PL=130kPa) Figure 4. View largeDownload slide The variations of COP, ΔThot, ΔTcold with the high pressure (z1,1 = 0.2, z1,3 = 0.6, PL=130kPa) Figure 5. View largeDownload slide The variations of COP, ΔThot, ΔTcold with the low pressure (z1,1 = 0.2, z1,3 = 0.6, PH=1000kPa). Figure 5. View largeDownload slide The variations of COP, ΔThot, ΔTcold with the low pressure (z1,1 = 0.2, z1,3 = 0.6, PH=1000kPa). From Figure 4, it can be found that the temperature differences at the hot end of R1 and the cold end of R2 were both approximately equal to the pinch point temperature differences of R1 and R2, respectively, namely, ΔTcold = ΔThot = ΔTmin, when COP reached a peak value with the increase of high pressure. In other words, at a specified low pressure the pinch point temperature difference transferred from the hot end of R1 to the cold end of R2 when the high pressure increased. Because the heat demanded for the generator varied slightly, hence, the variations of COP were mainly determined by the change of the cooling capacity with the increase of the high pressure. After the transfer of the pinch point to the cold end of R2, the specific enthalpy difference between state points 5 and 7 increased slightly, but the refrigerant flow rate decreased from the top outlet of the gas–liquid separator when the high pressure increased. These factors can account for the occurrence of the peak value of COP in Figure 4. Figure 5 also shows that the temperature differences at the cold end of R2 and the hot end of R1 were both approximately equal to the pinch point temperature differences of R1 and R2, respectively, namely, ΔTcold = ΔThot = ΔTmin, COP occurred a turning point with the decrease of the low pressure. From the above analyses, we knew that the low and high pressures at the turning points should be the reasonable lower limit of the low pressure and upper limit of the high pressure for the specified mole fractions of the solution. In this article, the reasonable low pressure was specified as 100kPa. The peak value of COP at the reasonable lower limit low pressure and upper limit high pressure for the specified mole fractions was defined as the COPopt. 3.2 Optimization of mole fractions According to the pressure optimizing method in previous section, COPopt of the system operated with different mole fractions could be obtained. Figure 6 shows the variations of COPopt and refrigerating capacity QE with the mole fraction of R23 when the mole fractions of DMF z1,3 were set to be 50, 60 and 70%. Figure 6. View largeDownload slide The variations of COPopt and QE with the fraction of R23 (TG = 140°C, TH = 20°C, TL= −50°C, z3,3 = 0.03). Figure 6. View largeDownload slide The variations of COPopt and QE with the fraction of R23 (TG = 140°C, TH = 20°C, TL= −50°C, z3,3 = 0.03). From Figure 6, it can be seen that QE and COPopt both increase monotonically with the increase of R23 for the specified mole fraction of DMF z1,3. The maximum COPopt for different mole fractions of DMF were almost same, but the corresponding high pressures to COPopt were different. The larger mole fraction of DMF was, the higher the corresponding high pressure was. 4 CONCLUSIONS The performance of an auto-cascade absorption refrigeration cycle operated with non-azeotropic mixed refrigerant R23/R134a/DMF was investigated in this article by a new approach. The analysis results showed that: At a specified low pressure, COP increased at first and then decreased with the increase of the high pressure. The high pressure corresponding to the peak COP should be the reasonable upper limit of the high pressure. At a specified high pressure, COP was obviously increased with the decrease of low pressure within a certain range. The turning point low pressure should be the reasonable lower limit of the low pressure. When the temperature differences at the cold end of R2 and at the hot end of R1 were both approximately equal to the pinch point temperature differences of R1 and R2, respectively, the peak value or the turning point reached. When the mole fraction of DMF was specified, refrigerating capacity QE and COPopt both increased monotonically with the increase of the mole fraction of R23. But the maximum COPopt were almost the same for different mole fractions of DMF. As the high pressure corresponding to the maximum COPopt for the low mole fraction of DMF solution was lower than that of high mole fraction of DMF solutions, the low mole fraction DMF solutions should be the better. ACKNOWLEDGEMENT This work is supported by Industrial project of public welfare technology research in Zhejiang Province (Foundation No. 2016C31125). REFERENCES 1 Chen G , Yin Z , Wang J , et al. . The characteristics of an absorption system with azeotropic refrigerant mixture refrigerant . J Refrigeration 1998 ; 1 : 1 – 5 . 2 Chen S , Chen G , Zheng F , et al. . Operation characteristics of absorption refrigeration using alternative working fluids . Cryogenics 1999 ; 112 : 22 – 30 . 3 Chen S , Zheng F , Wang J , et al. . Replacement refrigerant HCFC22 for absorption refrigeration features . J Eng Thermophys 1999 ; 20 : 410 – 2 . 4 Gao W , Zhao X , Liu Z . Calculation of HFC32+HFC227ea/DMF absorption refrigeration cycle . J Eng Thermophys 2010 ; 31 : 545 – 8 . 5 Chen G . Absorption refrigeration device used for deep freezing. Chinese Patent, 02110940.0 ( 2002 ) 6 Wang Q , Chen F , Xia P , et al. . Influence of mixture composition on cooling rate of a freeze-dryer with an auto-cascade refrigerating system . J Xi’anJiaotong Univ 2009 ; 43 : 37 – 42 . 7 Wang Q , Cui K , Sun T , et al. . Performance of a single-stage auto-cascade refrigerator operating with a rectifying column at the temperature level of −60°C . J Zhejiang Univ Sci A (Appl Physics & Eng) 2011 ; 12 : 139 – 45 . Google Scholar CrossRef Search ADS 8 Wang Q , Liu R , Wang J , et al. . An investigation of the mixing position in the recuperators on the performance of an auto-cascade refrigerator operating with a rectifying column . 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Comparative study on the energy performance of two different absorption-compression refrigeration cycles driven by low-grade heat . Appl Therm Eng 2016 ; 106 : 33 – 41 . Google Scholar CrossRef Search ADS 14 Xu Y , Jiang N , Pan F , et al. . Comparative study on two low-grade heat driven absorption-compression refrigeration cycles based on energy, exergy, economic and environmental (4E) analyses . Energy Convers Manage 2017 ; 133 : 535 – 47 . Google Scholar CrossRef Search ADS 15 Han X , Gao Z , Xu Y , et al. . Solubility of refrigerant 1,1,1,2-tetrafluoroethane in the N,N-dimethyl formamide in the temperature range from 263.15K to 363.15K . Chem Eng Data 2011 ; 56 : 1821 – 6 . Google Scholar CrossRef Search ADS 16 Gao Z , Xu Y , Li P , et al. . Solubility of refrigerant trifluoromethane in n,n-dimethyl formamide in the temperature range from 283.15K to 363.15K . Int J Refrig 2012 ; 35 : 1372 – 6 . Google Scholar CrossRef Search ADS © The Author(s) 2018. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com

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International Journal of Low-Carbon TechnologiesOxford University Press

Published: Sep 1, 2018

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