Thermodynamic Analysis of an NH 3 /CO 2 Cascade Refrigeration System with Subcooling in the Low-Temperature Circuit Utilizing the Expansion Work

NH 3 /CO 2 cascade refrigeration system is recognized one of the most promising technologies in low-temperature application. In this paper, a NH 3 /CO 2 cascade refrigeration system with subcooling in low-temperature circuit driven by recovery expansion work has been proposed. The aim of this study is to investigate the proposed cascade refrigeration system compared with conventional cascade refrigeration system. Mathematical models based on energy conservation and exergy balance are established. The selection of di ﬀ erent refrigerants in auxiliary subcooling system is discussed. The e ﬀ ects of operating parameters such as the condensation temperature of the low-temperature circuit, evaporation temperature, and expander e ﬃ ciency on system performance are evaluated. The results show that the coe ﬃ cient of performance and exergy e ﬃ ciency of the proposed system are about 7.56% and 7.98% higher than that of conventional cascade refrigeration system. The discharge temperature of NH 3 compressor can be signi ﬁ cantly reduced by 18.33%. The isentropic e ﬃ ciency of the expander has a large impact on the system performance.


Introduction
Cascade refrigeration system (CRS) is generally used in commercial and industrial refrigeration applications due to its ability to meet two different cooling requirements at medium and low temperatures and high coefficient of performance (COP) values [1,2].As the requirements of rather low freezing temperature (ranging from -30 to 50 °C) are constantly needed, these temperatures cannot be reached with a single-stage steam compression refrigeration system [3].Carbon dioxide (CO 2 ) is an environmentally friendly refrigerant which has low global warming potential (GWP) and no ozone depletion potential (ODP).The use of CO 2 as a refrigerating fluid in low-temperature circuit of CRS has increased especially in recent years due to its good thermal properties and heat transfer characteristics under lowtemperature conditions.The NH 3 /CO 2 cascade refrigeration system is a well-known system in for food storage in lowtemperature refrigeration fields such as rapid freezing system and the storage of frozen food [4].Two natural refrigerants, NH 3 and CO 2 , are used in high-temperature circuit (HTC) and low-temperature circuit (LTC), respectively [5].Meanwhile, the amount of NH 3 charge in CRS is reduced significantly, and the safety of the cascade refrigeration system is improved.
Improving the performance of the refrigeration system has always been one of the hot issues for energy saving.A variety of methods were adopted to improve refrigeration system performance.Among them, increasing subcooling degree at the outlet of the condenser or gas cooler is an effective way to save energy and further COP of all refrigeration circuit, especially for the CO 2 transcritical refrigeration or heat pump systems.This can be done with thermoelectric (TE) subcooling, mechanical subcooling, and absorption subcooling [6].Pottker et al. [7] made a theoretical analysis about the effect of condenser subcooling on the work efficiency of vapor compression systems.The study found that the latent heat of vaporization was inversely proportional to the amplitude of COP improvement.The performance of CO 2 transcritical refrigeration system can be improved by adding a thermoelectric cooler which can cool the CO 2 discharged from the gas cooler to the temperature below the environmental temperature.From theoretical points of view, Dai et al. [8] proposed new system of transcritical CO2 refrigeration system combined with a thermoelectric (TE) subcooler and an expander.The new system achieved the highest COP while statistically comparing the discharge pressure was also found to be very low.Besides, the new configuration of transcritical carbon dioxide refrigeration system combined with a thermoelectric subcooler and an ejector was proposed by Lu et al. [9].Sánchez et al. [1] conceived and experimented a thermoelectric subcooling system in a CO 2 transcritical refrigerating plant.The experimental results show that under the optimal operating conditions, the coefficient of performance and cooling capacity of the refrigeration unit are increased by 9.9% and 16.0%, respectively.
The addition of a mechanical subcooling system to improve the performance of the vapor compression system is also a known and mature method of energy saving and high efficiency.Experiments showed that the efficiency and cooling capacity could be improved by adding dedicated subcooling.Qureshi et al. [10] conducted an experimental study on the energy implications by using a dedicated mechanical subcooling circuit in a residential 1.5-ton conventional compression refrigeration cycle.It was also noticed that the exergetic efficiency of the system rose by an average of 21%.On this basis, in order to improve the performance of carbon dioxide transcritical refrigeration system, a dedicated mechanical subcooling circuit was used, and the theoretical and experimental analyses were carried out [11,12].Going a step further, Miran et al. [13] studied the performance of transcritical refrigeration system with dedicated MS from the perspective of energy, exergy, and exergy economics.Wang et al. [14] conducted a simulation analysis of a transcritical, single-stage CO 2 refrigeration system with different subcooling method, including dry coolers, cooling towers, dedicated MS, and heat exchangers.Yu et al. [15] combined mechanical subcooling and ejector refrigeration and improved the performance coefficient of ejector refrigeration to a certain extent.
Specific to the effect of subcooling on subcritical circuit or CRS, comparative energy, exergy, and economic analysis of natural refrigerant couples working in a cascade refrigeration system incorporated with a flash tank in its higher temperature circuit and a flash intercooler in its lowertemperature circuit had been investigated [16].For the subcooling in the LTC side for specific operating conditions and the same isentropic efficiency of compressors in both circuits, Getu et al. [17] found that before entering the evaporator, the necessary expansion of the working medium was carried out; the subcooling of the working medium would increase the COP of the system, while the increase of the superheat and condensation temperature would reduce the COP.Chen et al. [18] proposed a new method of subcooling for CRS based on mechanical subcooling, and the results showed that the maximum COP was increased by 4.58% and the exergy efficiency was increased by 4.40%.
Since the conventional CO 2 expansion process using the expansion valve in the vapor refrigeration system is highly irreversible, replacement of the throttling valve by an expander or an ejector is also an effective method to improve the performance of the CO 2 refrigeration system [19], especially for transcritical system.When the throttling valve is replaced by the expander, the enthalpy of refrigerant flowing into the evaporator can be reduced, the cooling capacity can be improved, and then the exergy loss can be reduced.In addition, the expansion work can be used by the motor to input energy to the compressor that needs to consume power.
For CO 2 transcritical refrigeration cycle, the throttling valve could be replaced by an ejector to enhance the performance.Deng et al. [20] presented a theoretical study on the transcritical CO 2 ejector expansion refrigeration system that used the ejector as the main expansion device instead of an expansion valve.The COP can be improved by 22% as compared to the conventional system.Besides, the multiejector expansion pack can be used to replace the standard highpressure expansion valve [21].
For CO 2 subcritical refrigeration system, the CO 2 throttling valve also can be replaced by ejector to improve the performance.In 2012, exergy analysis conducted by Ejemni et al. [22] showed that exergy efficiency was increased by 27.3% at T eva = −30 °C when ejectors were added to the R744/R152a cascade system.Dokandari et al. [23] thermodynamically evaluated the ejector utilization's impact on the performance of the CO 2 /NH 3 cascade circuit based on the first and the second laws of thermodynamics.The research also illustrated the facts that the maximum COP and exergy efficiency are 7% and 5% higher than that of CCRS.This new type of eject-expansion cascade system was a valuable refrigeration system from the theory and engineering point of view.They further investigated the novel ejector expansion transcritical cascade refrigeration system using proposed natural refrigerants CO 2 /N 2 O [24].Mofrad et al. investigated the CO 2 /CO 2 cascade refrigeration system with heat recovery and the expansion valve in HTC and LTC are all replaced by ejector to enhance the system performance [25].Chi et al. [26] added an injector to achieve subcooling based on subcooling idea to improve the COP of the CRS, and the discharge temperature of the NH 3 compressor was also significantly reduced.Chi et al. [27] conducted the advanced exergy analysis on the ejectorexpansion NH3/CO2 cascade refrigeration system proposed by Dokandari et al. [23]; they reported that the main irreversibility of conventional NH 3 /CO 2 cascade cycle occurs in the compressor, condenser, and throttling valve.Exergy losses through CO 2 expansion valves can be reduced by ejector utilization and 8% exergy destruction decreased for the system.Gholamian et al. [28] conducted an advanced exergy analysis on NH 3 /CO 2 cascade refrigeration system, and the results identify that CO 2 throttling valve, CO 2 compressor, and cascade heat exchanger are the components where improvements are necessary to enhance since they have potential for efficiency improvement.Rostamzadeh et al. [29] performed a multiobjective optimization and comparison of the basic system and the ejector expander CRS system.It was found that when the conventional throttling valve of NH 3 /CO 2 CRS system was replaced by two ejectors, 2 International Journal of Energy Research the overall plant risk was reduced by 37.08%, and the optimal COP, exergy efficiency, and total cost were increased by 4.16%, 4.16%, and 2.5%, respectively.In addition to the ejector, expander is another device which was used to replace the throttling valve in CO 2 refrigeration or heat pump system to reduce the throttling loss.Tian et al. [30] established an expander model to replace the expansion valve in the CO 2 water-water heat pump system.The isentropic efficiency and recovery rate obtained through experiments were 58.7% and 14.5%, respectively.From the same research point of view, Jia et al. [31] proposed an improved expander to replace the throttling valve in the transcritical CO 2 refrigeration system, and experimental results showed that the maximum COP was increased by up to 27.2%.Murthy et al. [19] reviewed and summarized the research progress of expander recovery expansion power and system efficiency and found that most engineering application scenarios were transcritical carbon dioxide refrigeration systems, and some studies showed that the COP of related systems increased by 30%.
From the above summary, most of the research was aimed at transcritical CO 2 refrigeration or heat pump.It can be found that relatively little research has been done on expanders or ejectors in subcritical CO 2 vapor refrigeration systems.Wenzel et al. [32] investigated a free piston expansion-compression device applied to subcritical and transcritical CO 2 circuits.Their study showed a 9.9% increase in the coefficient of performance, a decrease of 6 K and 4.7 bar in the discharge temperature and heat discharge pressure, respectively.She et al. [33] proposed a novel way of subcooling on the idea of expansion work recovery and investigated the performance of the system.Results showed that in terms of COP, the system has a better performance than the conventional refrigeration system.However, their research on subcritical refrigeration system is limited.
Since in the LTC side of CRS, CO 2 is used as the refrigerant and rather large expansion loss exists due to high-pressure difference between the cascade heat exchanger and evaporator.On the other hand, the COP of CRS increases more when subcooling is utilized on the LTC side for specific operation conditions rather than that in the HTC.Therefore, for the present studied system, both subcooling in LTC and expansion work recovery are considered at the same time, the subcooling method based on expansion power recovery is proposed to be used in the low-temperature cycle of CRS.Therefore, in the proposed system, the expansion valve in the LTC is replaced by an expander and recovery expansion power is used to drive a compressor in an auxiliary subcooling system, and the working fluid CO 2 in the LTC at the outlet of the cascade heat exchanger is subcooled by a subcooler, which is the evaporator of the auxiliary subcooling circuit.The aim of this paper is to evaluate the performance of the proposed system.Thermodynamic energy and exergy analysis are performed to investigate the performance of the proposed system and the effect of main operation parameters, such as evaporation temperature, intermediate temperature (condensation temperature of LTC), and expander efficiency on system performance is researched.A comprehensive comparison is also performed with conventional cascade refrigeration systems.

System Description and Modeling
2.1.Description of the Current System.A schematic diagram of the NH 3 /CO 2 conventional cascade refrigeration system (CCRS) is illustrated in Figure 1(a), and the temperatureentropy diagram of CCRS is shown in Figure 1(b).The CCRS is constituted by two single-stage refrigeration circuits, HTC and LTC.These two circuits are connected by a cascade heat exchanger, which serves as the condenser of LTC and evaporator of HTC.Schematics and temperatureentropy diagrams of expansion work driven subcooling cascade refrigeration system (SECRS) are shown in Figures 2(a) and 2(b), respectively.The proposed SECRS concludes three circuits, namely the high-temperature circuit (HTC), lowtemperature circuit (LTC), and the auxiliary subcooling circuit (ASC).The LTC adopts refrigerant CO 2 and includes an evaporator, a LTC compressor, a cascade heat exchanger, a subcooler, and an expander, while the HTC adopts NH 3 as the refrigerant and consists of a HTC compressor, a cascade heat exchanger, a condenser, and an expansion valve.HTC and LTC are combined by a cascade heat exchanger (CHE), which serves as the condenser of the LTC and the evaporator of the HTC.ASC is used to provide the energy to subcool the CO 2 refrigerant fluid flow out of the CHE by using the expansion work of LTC.
The proposed SECRS system operates as follows: For the LTC, the working fluids exiting the compressor circulates through the cascade heat exchanger; firstly, the CO 2 liquid leaving the cascade heat exchanger is subcooled by the subcooler, where the cooling capacity is supplied by the subcooling refrigeration circuit.The expansion valve in LTC is replaced by an expander, and recovery expansion power is used to drive the coaxial auxiliary compressor in the subcooling circuit, which provides the cooling capacity for further subcooling of CO 2 fluid at cascade heat exchanger outlet in LTC.Then the cooling capacity per unit mass is increasing due to the subcooling.The auxiliary subcooling circuit consists of a subcooler, which is an evaporator of the circuit, a compressor, a condenser, and an expansion valve.As shown in the temperature-entropy diagram of Figure 2(b), the LTC working medium at the outlet of the condensing side is subcooled to the subcooled liquid through the subcooler, and then through the expansion process in the expander, the pressure is reduced to the state point 5.The proposed system can improve circuit performance compared to the basic CRS because expansion work is recovered and used to drive the auxiliary compressor.Although the expansion work recovered in this system is not as much as that in a transcritical CO 2 refrigeration circuit, the subcooling degree is achieved simultaneously in LTC of CRS, which is beneficial to the system performance improvement.

Thermodynamic Modeling and Analysis.
The performance of the proposed system is evaluated from energetic and exergetic aspects.According to the first and second laws International Journal of Energy Research of thermodynamics, a mathematical model of the proposed system is established.To simplify the analysis and calculations of the proposed refrigeration system, the following assumptions are considered: (1) All equipment are assumed to be steady-state and steady-flow processes [3,34] (2) The gravitational potential energy and kinetic energy are not considered in the refrigeration system [3] (3) All the circuit components and pipelines are well isolated so that heat loss and pressure drop in connecting pipes and heat exchangers are ignored [35] (4) Refrigerants at the CHE outlets, evaporator outlet, and condenser outlet are in the saturated state [36] (5) The ambient temperature and pressure are fixed at 25 °C and 0.1 MPa (6) The difference between the refrigerated space temperature and the evaporation temperature is constant and is 5 °C [37] Based on the above assumptions, the following equations for each component can be obtained.For given working conditions, the evaporation temperature T e and condensation temperature T c are known and the cooling capacity is assumed to be 9 kW.The mass flow rate of refrigerant in LTC can be expressed according to the equation The compression process and expansion process are irreversible.The isentropic efficiency of compressors η s is used to evaluate the work consumption of the compressor and related to the pressure ratio.The work consumption of LTC and HTC compressor can be calculated as follows: where h 2s is the refrigerant enthalpy at state 2 for the isentropic process.η mec and η ele are mechanical efficiency and electrical efficiency which are assumed to be 0.95 and 0.9 for the HTC and ASC compressors in this paper and 0.9 for both efficiencies for the LTC compressor [37].The isentropic efficiency of LTC and HTC compressor is estimated according to the followed equations [27] [38]: For auxiliary subcooling circuit, the compressor work consumption is calculated as follows: The isentropic efficiency of auxiliary compressor is as follows [37]: The temperature difference in the CHE is shown by the equation and is assumed to be 5 °C in the analysis [39]: The heat load for the CHE is solved as From the energy balance of the CHE, the NH 3 fluid mass flow rate in the HTC can be obtained as The heat load for condenser is The expansion processes in HTC and ACS are assumed isenthalpic.For the subcooling process and expansion process in the proposed system, the cooling capacity in the subcooler is decided by the compression work consumed by the auxiliary compressor and the operation conditions of the subcooling circuit.When the condensation temperature of LTC changes, the recovery expansion power also changes at the same time.Therefore, iterative calculations are required to determine the subcooled degree and the operating conditions of the subcooling circuit.The evaporation temperature of the subcooling circuit is set to be 3 °C lower than the CO 2 temperature at the outlet of the subcooler in LTC.Once the subcooled degree of the LTC refrigerant is known, the subcooling capacity can be calculated as follows: The recovery expansion work can be obtained according to an ideal isentropic expansion process and the expander efficiency.The ideal expansion process is isentropic, and the state at the outlet of the expander can be determined by the expander isentropic efficiency and the evaporation temperature [40].
The value of expander efficiency has an important effect on the recovery expansion work and the system performance.Du et al. [41] present a critical overview of microscale (<200 kW) expanders for carbon dioxide cycles.Reported experimental data for volumetric expanders used in CO 2 refrigeration were summarized, and the expander isentropic efficiency ranges from 32 to 83%.Li et al. [30,42] researched the performance of rolling-piston-type expanders and pointed that the isentropic efficiency of the expander varies depending upon operating conditions.Maximum isentropic efficiency of 58.7% was obtained.Zhang et al. [43] developed a double-acting free piston expander, and the experimental studies by means of p-V diagrams showed that the isentropic efficiency could reach 62%.Hiwata et al. [44] investigated a scroll-type expander through control the axial force, and the test results demonstrated a maximum isentropic efficiency of 62%.Matsui et al. developed a two-stage rolling-piston expander, and its isentropic efficiency of 60% was obtained by optimizing clearances between the parts [45].Yang et al. investigated the CO 2 transcritical two-stage compression refrigeration system with two-phase expander, and the value of expander isentropic efficiency is 65% in their analysis [46].Therefore, it is reasonable to take the isentropic efficiency of the expander as 0.6 for this analysis [47].Then the expander output power can be acquired using Equation (12).The auxiliary compressor and the expander are coaxial.Taking the mechanical efficiency η mec into account for the coaxial compressor-expander, the power that can be used to drive the auxiliary compressor is calculated by the following equation: The cooling capacity of the subcooling circuit is obtained by Equation (11) and is used to subcool the refrigerant in LTC from states 3 to 4. It should be equal to the cooling capacity needed in the subcooler.
The overall COP of SECRS can be calculated by the following equation: To assess the exergy destruction in the SECRS, the exergy analysis is further conducted.The specific exergy of the refrigerant at each state point can be expressed as [48] where s 0 and h 0 are the entropy value and enthalpy value of the working medium determined by Hypothesis 5, respectively.
Exergy destruction of each equipment can be expressed by The detailed exergy destruction calculation formula is shown in Table 1.
Exergy destruction of all devices in the system is summed up to obtain the total exergy destruction, expressed as X des,total = X des,comp + X des,cond + X des,SC + X des,eva + X des,expv + X des,expa + X des,CHE : ð18Þ The overall exergy efficiency η II of SECRS is calculated by the following equation: where W Rev and W Act are the SECRS reversible power input and actual power input, respectively.

Model of the System
According to the above assumptions and the mathematical model of the proposed system, the simulation program has been developed using MATLAB to investigate the influence of operating parameters on system performance.The needed refrigerants thermophysical parameters were obtained by using REFPROP 9.0.The simulation algorithm flow chart of the whole system is shown in Figure 3.During the 6 International Journal of Energy Research simulation, the condensation temperature is assumed to be 35, 40, and 45 °C, and the evaporation temperature of the system ranges from -55 to -30 °C.The temperature difference in the subcooler and CHE is set at 3 °C and 5 °C, respectively.And the environmental temperature T 0 is assumed to be 25 °C.The expander isentropic efficiency is an important   7 International Journal of Energy Research factor in determining the performance of this system, and the influence of expander isentropic efficiency on system performance is also investigated.The refrigerants adopted in the subcooling circuit also affect the system performance.Therefore, the effects of different refrigerants such as R152a [49] and R290 [50] that were used in the auxiliary subcooling system on system performance are researched.

Cycle Analysis Code Validation
The conventional NH 3 /CO 2 cascade refrigeration system analysis code was validated with the results reported by Dokandari et al. [27].The working conditions were set to the same values as were given in the reference.Figure 4 shows the comparison between the simulated results with those in the literature.It can be seen that the simulation results have a good agreement with the reported data by Dokandari et al.The relative error was in the order of mag-nitude of 5.5%.The mathematical model in this analysis and the program code is reliable.

Results and Discussion
A parametric study is conducted to investigate the performance of the proposed SECRS performance compared to CCRS.The intermediate temperature T m (condensation temperature of LTC) has a significant effect on the performance of CRS.In general, there is an optimal intermediate temperature to maximize the cascade refrigeration system performance [51].Since an auxiliary subcooling circuit is added in the proposed SECRS, the selection of refrigerants in this ASC and the effect of expander isentropic efficiency on the performance improvement are discussed.In addition, with the change of evaporation temperature and condensation temperature, the COP, exergy destruction and exergy efficiency of the SECRS, discharge temperature, input power

Selection of Refrigerants in the Subcooling
Circuit.In order to evaluate the effect of the working fluid used in the auxiliary subcooling circuit on the operation of the SECRS and determine the suitable refrigerants, the system performance is evaluated when using different refrigerants as shown in Table 2.In the analysis, T c and T e of the system are 40 °C and -45 °C, respectively.The isentropic efficiency of the expander adopted in the subcooling circuit is assumed to be 0.6, which is acceptable for the CO 2 two-phase expander.It is notable that the performance is obtained at the T m,opt , which maximizes the COP and exergy efficiency.
It can be seen that both COP and η II of the proposed SECRS are higher than that of CCRS.The COP Max of SECRS is 1.357, and the COP Max improvement is 7.78% when R152a, R12, and R717 are chosen.Maximum η II is 0.3798, and the maximum η II improvement is 8.24% when these same three refrigerants are chosen.However, R12 has high OWP (ozone depletion potential) and GWP (global warming potential) and is not considered in this analysis.This is in agreement with the conclusion of this paper [27].Taking into account the wide range of R134a used and the better percentage of improvement (it is only slightly a few tenths of a percent lower than the refrigerant with the greatest improvement), R134a is chosen as the refrigerants used in the subcooling circuit in the following analysis.

Influence of Condensation Temperature of LTC.
The condensation temperature of LTC T cond,LTC has a significant effect on the operation of this system.Figure 5 shows the variation of COP L , COP H , and COP sub with T cond,LTC for CCRS and SECRS systems.It can be seen that COP H raises while COP L falls with the increasing of T cond,LTC .HTC have the same increasing trend according to the working principle of CCRS and SECRS.COP L in SECRS is higher than that of CCRS, especially for a higher T cond,LTC .This is due to the subcooling of the CO 2 outlet from the cascade heat exchanger in LTC.The COP SubC of the auxiliary circuit is increasing as the increasing of T cond,LTC .For the auxiliary subcooling circuit, the T cond,LTC is kept constant, the pressure difference is decreased with the increase in T cond,LTC .This can be easily understood for a standard single-stage vapor compression refrigeration circuit.The COP of the SECRS is determined by the combined effect of these three systems' performance, namely, COP L , COP H , and COP SubC .Figure 6 illustrates the influence of the condensation temperature of LTC on the overall COP of CCRS and SECRS under different working conditions.In both systems, there exists an T opt,m to enable the over COP maximum.It also can be observed that the overall COP of SECRS is always higher than that of CCRS.When the T e is -50 °C, the maximum COP of CCRS is about 1.140, and the corresponding optimal T cond,LTC is about -8.28 °C, while the SECRS has the maximum COP of 1.228 and the optimum T cond,LTC is 0.75 °C.When T e rises to -45 °C, the maximum COP of CCRS and SECRS is 1.259 and 1.354, respectively, and the optimal T cond,LTC which maximizes the COP is -6.37 °C in CCRS and 2.94 °C in SECRS.From the data mentioned above, it is further observed that the optimum T cond,LTC is different for different T e .At the same working condition, the optimum T cond,LTC in SECRS is higher than that in CCRS, especially for a higher intermediate temperature.The main factors leading to this phenomenon are that the COP L is increasing with the increase of T cond,LTC as shown in Figure 5. 9 International Journal of Energy Research Figure 7 shows the input power of LTC compressor and HTC compressor for both systems and recovery expansion power in SECRS at different T cond,LTC .It can be learned that the power consumption of NH 3 compressor in HTC is decreasing and the power consumption of LTC compressor is increasing with the increases of T cond,LTC .Both the input power of the HTC compressor and LTC compressor in SECRS is lower than those of CCRS.There exists minimum total power consumption during the variation of condensation temperature of LTC.The minimum compressor input power in CCRS is about 7.15 kW, and the corresponding optimal T cond,LTC is -6.37 °C.In the SECRS, the optimum T cond,LTC is 3.27 °C, and the minimum input power is 6.63 kW.This is in agreement with the results discussed in Figure 6.For the SECRS, the subcooling in LTC causes an increase in refrigeration quality per unit mass flow according to the principle of vapor compression refrigeration system, so the m in LTC decreases, and the LTC compressor input power is then decreasing.In addition, since the optimum T cond,LTC in the SECRS is higher than that in CCRS, the pressure ratio of the HTC compressor has a decreasing trend.The compressor input work of both LTC and HTC in the SECRS is lower than that of CCRS due to the recovery expansion work and subcooling in LTC.

Influence of Evaporation
Temperature.The cascade refrigeration system obtained its best performance when selecting an optimum T cond,LTC as discussed above.Therefore, all the following results were obtained at the optimum T cond,LTC in these two systems.Figure 8 displays the optimum value of T cond,LTC at different T e .It can be seen that the optimum T cond,LTC increases as evaporation increases in both systems.And the T cond,LTC in SECRS is higher by about 8.49-9.70°C when T e changes from -55 °C to -30 °C.For example, when the T e is -45 °C and the T c of the system is 40 °C, the optimum T cond,LTC in SECRS and CCRS is about 2.94 °C and -6.37 °C, respectively.The main reason is COP L of SECRS is higher than that of CCRS while the COP H in these two systems has the same variation trend as shown in Figure 5.The optimum T cond,LTC will increase to maximize the overall performance.
Figure 9 presents the effect of T e on the T dis,comp of LTC compressor and HTC compressor in these two systems.It is obvious that the discharge temperature of the LTC and HTC compressor in both systems decrease with the increasing evaporation temperature.The T dis,HTC,comp in SECRS is lower than that in CCRS, while T dis,LTC,comp in SECRS is higher than that in CCRS.This is due to the optimum intermediate temperature in SECRS is higher than that in CCRS.Therefore, the pressure ratio in the HTC compressor is decreasing, and the pressure ratio in the LTC compressor is increasing, although the suction temperature of the HTC compressor in SECRS is increasing compared with that of the HTC compressor in CCRS.The reduction in HTC compressor discharge temperature due to the decreasing pressure ratio is larger than that caused by the rising suction temperature.The main benefit is that the T dis,comp of the HTC NH 3 compressor is decreasing.Under the working conditions of T e = −55 °C and T c = 40 °C, T dis,HTC,comp decreased from 155.01 °C in CCRS to 126.60 °C in SECRS, and 28.41 °C is reduced.With the increase of T e , the T dis,HTC,comp decreased slightly.When T e is -30 °C, the T dis,HTC,comp decreased from 123.82 °C in CCRS to 98.80 °C in SECRS, and 25.02 °C is reduced.On the other hand, the T dis,LTC,comp in SECRS is higher than that of CCRS.It can be observed that T dis,LTC,comp increased about 21.26 °C to 22.56 °C.The maximum T dis,LTC,comp is about 84.44 °C as the Figure 10 shows the compression work and total exergy destruction versus T e .The total exergy destruction of both systems decreases as evaporation temperature increases.
When T e ranges from -55 °C to -30 °C and the T c is kept constant at 40 °C, the total exergy destruction of CCRS and SECRS decreases from 5.705 kW and 5.057 kW to 3.469 kW and 3.125 kW, respectively.The exergy destruction of SECRS decreased by about 11.35% to 9.93%.The total exergy destruction in SECRS is always lower than that of CCRS.For the total compressor power consumption, it has the same trend.
Figure 11 illustrates the variation of optimal COP and η II in both systems with T e .It is obvious that COP opt increases with the increases of T e .The maximum values of COP of SECRS are higher by about 6.76-7.88%than that of CCRS under the same working condition when T e is changing.Their difference is changed slightly with the variation of T e .As shown in Figure 11, the optimum η II in two systems first increases and then decreases as T e increases.Under the same temperature, the η II of SECRS is always higher than that of CCRS, about 7.33-8.23%.There are maximum η II values for both systems.The optimum η II in SECRS and CCRS reaches a maximum value of 0.379 and 0.351 at the T e value 98 °C, respectively.This can be explained by the change rate of compressor power consumption and total exergy destruction with the variation of T e as shown in Figure 10.For SECRS, the decline of exergy destruction is larger than that of the input work when evaporation temperature is below -45.53 °C and results in a higher η II .When evaporation temperature is higher than -45.53 °C, the decline of exergy destruction is smaller than that of input work, leading to a lower η II .
Figure 12 shows the effect of T e on the maximum recovery expansion work and the subcooling degree that can be obtained in LTC.It can be observed that the recovery work is decreasing linearly with the rising of T e .The subcooling degree that can be obtained is decreasing slowly at first and then decreasing rapidly.The value of the subcooling degree is reduced from 7.54 °C to 6.58 °C when the T e ranges from -55 °C to -30 °C.It should be noted the state point of the CO 2 at the outlet of this LTC condenser is assumed saturated.The actual value of the subcooling degree that considering the cooling effect of the condenser should be larger than the value shown in this figure.
Figure 13 shows the variation of the proportion of exergy destruction in each equipment of two systems versus the T e .It indicates that at the same T e , the exergy destruction in both systems mainly exists in the HTC compressor, LTC compressor, and condenser.When T e is 55 °C, the HTC compressor accounts for the highest proportion in CCRS, about 0.28, followed by the condenser with a proportion of  about 0.22.The LTC compressor's proportion is about 0.18 and lower than HTC compressor's proportion.But for the SECRS, the highest proportion of exergy destruction is the LTC compressor, which is about 0.25.It is followed by the HTC compressor, at about 0.23, and the condenser ranks third, accounting for about 0.20.In SECRS, the proportion of LTC compressor increases significantly, because the LTC condenser outlet is subcooled, resulting in a larger optimum condensation temperature of LTC, lower LTC compressor efficiency, and significantly increased power consumption.Therefore, the method of replacing the expansion valve with an expander reduces the overall exergy destruction, the changes in both aspects eventually lead to this phenomenon.As the evaporation temperature is raised from -55 °C to -35 °C, it can be seen that the trend of changes in the components of the two systems is similar.Among them, the proportion of the condenser and the evaporator increased, and the proportion of CHE and LTC compressor declined.The proportion of subcooling compressor in SECRS is on the rise.

Influence of Expander Isentropic Efficiency.
The expander efficiency has a large effect on system performance and determined the recovery work than can be used to drive subcooling system.The effect of expander isentropic efficiency on optimum T cond,LTC is shown in Figure 14.It can be seen that the optimum T cond,LTC rises slowly with the increasing of expander efficiency at a given evaporation temperature.When expander efficiency increased from 0.2 to 0.95 and T e is -45 °C, the T cond,LTC increased from -2.93 °C to 6.48 °C.The higher the expander isentropic efficiency, the more recovery expansion could be obtained, and then the subcooling degree that can be obtained increases as shown in Figure 15.This figure indicates the effect of expander efficiency on the subcooling degree of LTC in the proposed SECRS.Subcooling degree increases with the increase of expander efficiency.When the T e is -45   13 International Journal of Energy Research is 0.95, and it is reduced to 2.05 as the expander efficiency is 0.2.The data show that the higher the expander efficiency, the greater the recovery power of the expander, so the subcooling capacity of the subcooler is improved, and the subcooling degree becomes larger.The value of subcooling degree at different evaporation temperatures T e has a little different, and it is decreasing with the increasing T e .
Figures 16 and 17 show the influence of expander efficiency on COP and η II improvement in SECRS.With the increasing of expander efficiency, both COP improvement and η II improvement increase.When T e is -55 °C, COP improvement increases significantly from 2.64% to 11.71%, and exergy efficiency improvement increases considerably from 2.98% to 12.07% as expander efficiency ranges from 0.2 to 0.95.When T c is kept constant at 40 °C, the improvement of COP and η II is increased slightly when the T e decreases.The lower the T e , the larger of COP and η II improvement.

Conclusions
The paper proposes a novel method to enhance the performance of NH 3 /CO 2 cascade refrigeration system by using the expansion work in low-temperature circuit to drive an auxiliary subcooling system.Thermodynamic performance comparison analysis on this proposed system is conducted to evaluate the performance based on conventional cascade refrigeration system.The effects of key operation parameters such as evaporation temperature, condensation temperature, and expander isentropic efficiency on the system performance are investigated.The main conclusions we obtained are as follows: (1) The proposed SECRS system shows better performance than CCRS.The COP and exergy efficiency of SECRS can be increased 7.15-7.78%and 7.55-8.24%when using different refrigerants in auxiliary subcooling circuit.The selection of refrigerants in auxiliary subcooling circuit has little effect on the COP improvement for SECRS this system (2) The SECRS system has an optimum condensation temperature of low-temperature circuit T cond,LTC which makes the COP maximum.The optimum of T cond,LTC in SECRS is 8-10 °C higher than that of CCRS (3) The COP max of SECRS is higher by about 6.76-7.88%than that of CCRS under the same working condition when evaporation temperature changes.The exergy efficiency of SECRS is always higher about 7.33-8.23%than that of CCRS (4) The discharge temperature of the compressor in high-temperature circuit in SECRS is lower by about 18.33% than that in CCRS, and the discharge temperature of the compressor in low-temperature circuit is increased.The discharge temperature of NH 3 compressor can be reduced effectively (5) The isentropic efficiency of the expander has a large impact on this system performance.When the expansion efficiency increased from 0.2 to 0.95, the COP and exergy efficiency increased from 2.64% to 11.71% and 2.98% to 12.07%, respectively.Improving the isentropic efficiency of the expander is crucial for the actuarial application of this proposed system The proposed system adds an auxiliary refrigeration system and increases the complexity of the system.Thermoeconomic analysis and experimental studies on SECRS should be conducted in further studies.

Figure 2 :
Figure 2: Proposed cascade refrigeration system with subcooling driven by expansion work.(a) Schematic diagram of SECRS.(b) Temperature-entropy diagram of SECRS.

Figure 3 :
Figure 3: The simulation algorithm flow chart of system.

Figure 4 :
Figure 4: Comparison of COP curve of present model with reference [23].

Figure 5 :Figure 6 :
Figure 5: Effect of condensation temperature of LTC on COP H , COP L , and COP SubC .

Figure 11 :
Figure 11: Effect of T e on overall COP and η II .

Figure 12 :
Figure 12: Variation of recovery work and subcooling degree with evaporation temperature.

Figure 13 :
Figure 13: Effect of T e on the proportion of exergy destruction in each equipment.(a) CCRS.(b) SECRS.

Figure 14 :
Figure 14: Variation of condensation temperature of LTC with expander efficiency.
a) assumed Input operating conditions Q, T cond , T eva , T CHE ,  Mec ,  Elec ,  Expa

Table 2 :
Performance comparison between CCRS and SECRS using different refrigerants in auxiliary subcooling circuit.
°C, the subcooling degree is about 11.53 °C as the expander efficiency