Introduction

With the development of industry and society, the attainment of low temperatures below − 50 °C has drawn more and more attentions in many fields [1]. In recent years, in response to the current COVID-19 pandemic, the ultra-low temperature (UTL) around − 80 °C is increasingly demanded in biomedical areas such as the cryopreservation of new vaccines and cryosurgery. Economical refrigeration in the ULT range cannot be achieved with standard single-stage systems because of the required high compression ratio, which leads to a low efficiency and high discharge temperature [2]. Principally, temperatures below − 40 °C can be obtained by multi-stage compression refrigeration cycles, cascade refrigeration cycles and auto-cascade refrigeration cycles (ARC) [3]. Among these applications, the ARC systems have been extensively used because of their simple structure, high reliability, low cost and high thermodynamic efficiency [4]. In recent decades, energy shortage and environmental pollution have become progressively severe, calling for more utilizations of the ARC system which is higher in refrigeration efficiency and more environmentally friendly [5]. Thus, much effort has been made on improving the ARC systems, which mainly includes two aspects: to improve the structure of the existing ARC systems, and to look for mixed refrigerants that can meet the needs of environmental protection and exhibit high thermodynamic efficiency as well [6].

In terms of structural optimization of refrigeration systems, the ejector was found to be able to convert the pressure energy of the refrigerant into kinetic energy and then return to pressure energy, thereby recovering the throttling loss and improving the system efficiency [7,8,9,10,11]. Hao et al. [12] proposed a novel hybrid auto-cascade refrigeration system coupled with an ejector cycle. This hybrid cycle effectively saves high-grade electric energy or mechanical energy by the ejector driven by low-grade thermal energy such as waste heat and solar energy. It was found that the ejector can reduce the compressor input power by 50%. Yu et al. [13] studied the performance of an ejector-enhanced two-stage ARC and found that the modified system can effectively improve the coefficient of performance (COP). When using R23/R134a as the working fluid, the pressure ratio of compressor was reduced by 25.8% and the COP was improved by 19.1% over the conventional ARC. Similarly, Bai et al. [14, 15] also studied a two-stage ARC, and results show that by adding an ejector to the system can boost the exergy efficiency and COP by 25.1% and 9.6%, respectively. Rodríguez-Jara et al. [2] used an ejector as the expansion valve in ARC and found that the COP was increased by 12%. This study also indicates that the mixture of R1150/R600a is a suitable combination for ARC.

As for other aspects of system structure optimization, a double internal ARC system was introduced by Cheng et al. [16], and the authors concluded that the modified system can effectively increase the mass flow of the low boiling point component entering the evaporator, and further improve the system performance. Compared with the flash tank system, the proposed system shows a 9.6% higher heating capacity and a 6.1% higher COP. Chen et al. [17] used two separators in a modified ARC to achieve partial-condensation separation, and used the corresponding capillary tubes to get flash separation for a composition shift effect. Under the given operation conditions, the cycle performance improvement of the modified system in terms of COP, volumetric cooling capacity and exergy efficiency can reach up to 12.7%, 32.6% and 20%, respectively. Similar optimizations also concluded that the modified cycle can improve the cycle performance due to the composition shift effect of the zeotropic mixture during the flash separation process [18, 19]. The results show that the maximum COP of the modified system with R290/R600a and R134a/R236fa can be improved by 26.7% and 18.6%, respectively [19]. A modified ARC with a fractionation heat exchanger was experimentally studied by Zhang et al. [20]. It was found that the corresponding refrigeration capacity, power input and COP were reduced by 37.1–61.7%, 24.7–36.8% and 16.4–42.7%, respectively. Chen et al. [21] concluded that the addition of the subcooler in the ARC could improve both the energy and exergy performances, and the COP, volumetric cooling capacity and exergy efficiency of the modified cycle can be improved by up to an average of 37.5%, 42.3% and 34.3% compared to those of the basic cycle, respectively. Liu et al. [22] introduced an auxiliary separator into a conventional ARC, and found that the overall performance of the modified system was higher. Under a typical operating condition, the improvements of COP and exergy efficiency were increased by 16.1% and 10.23% respectively, and the overall cost rate was decreased by 2.51%. Research on the structural optimization and efficiency improvement of the energy systems was also carried out by Toghraie and co-workers [23,24,25,26,27,28,29]. Asgari et al. [30] used R600 as the refrigerant in an internal ARC, and all heat exchangers were modeled by taking pressure drops into consideration. The multi-objective optimization indicated that the improvements of total avoidable exergy destruction rate, total avoidable investment and total avoidable exergy destruction cost rates were 76.78%, 38.66% and 103.38%, respectively. Yan et al. [31] used R290/R600a as refrigerants in an internal ARC. The simulation results show that the internal ARC has 7.8–13.3% improvement in COP, 10.2–17.1% improvement in volumetric refrigeration capacity and 7.4–12.3% reduction in pressure ratio of compressor.

On the other hand, the environmentally benign refrigerants with low GWP values are used for the sustainability of ARC equipment [32]. Mota-Babiloni et al. [1] summarized the recent developments in ultra-low temperature refrigeration systems and working fluids, and concluded that the HC refrigerants of R170 and R1150 are the best solutions. Aprea and Maiorino [33] achieved  − 150 °C in a space of 0.25 m3 for a medical application by using a mixture of R507, R245fa, R116, R23, R14, R740 and R290. Wang et al. [4] theoretically investigated the system performance of a two-stage ARC using six binary mixtures and concluded that the R170/R600 (0.55/0.45) was an ideal substitute at − 60 °C. Sivakumar and Somasundaram [34, 35] experimentally investigated a three-stage ARC using R290/R170/R14, R290/R23/R14 and R1270/R170/R14 and found that the system operating with R290/R23/R14 showed a better performance. Qin et al. [36] theoretically analyzed the thermodynamic characteristics of a three-stage ARC using four ternary mixtures composed of R1234yf, R1132a, R23, R41, R170 and R14. The results show that all the three medium-temperature alternatives of R1132a, R41 and R170 could be good drop-in replacements for R23. The COP and exergy efficiency of the ARC operating with R1234yf/R41/R14 with the mass fraction of 0.64/0.17/0.19 were 0.2713 and 13.91% at − 100 °C, respectively. Kilicarslan and Hosoz [37] studied the thermodynamic performance of a two-stage ARC using R404a/R23, R234a/R23, R152a/R23, R717/R23, R507/R23 and R290/R23. It was found that the R717/R23 system and R507/R23 system showed the highest and the lowest COP, respectively. Lizarte et al. [38] used R152a to replace R134a in the ARC system. The highest COP and exergy efficiency were 0.79 and 31.6% corresponding to organic Rankine cycle evaporation temperatures of 315 °C and 255 °C, respectively. Liu et al. [39] proposed a modified two-stage ARC with a self-recuperator. The energy and exergy analysis indicated that the COP of the modified ARC was increased by 6.24% and 24.17% when using R290/R170 and R600a/R1150, respectively. It was also found for the modified ARC that COP and refrigeration capacity were positively correlated with intermediate pressure. A zeotropic mixture of R600a/R744 was employed as a working fluid in an ARC system by Sobieraj [40]. It was found that the working mass concentration of R744 was higher, since it was closer to the nominal concentration and the discharge pressure was lower by 19% to even 39% when a recuperative heat exchanger was employed in the system. An increase of up to 20% in the COP was observed. Rui et al. [41] proposed a novel ternary mixture, R600a/R23/R14, for ARC systems for 190 K applications. The results demonstrated the feasibility of the proposed R600a/R23/R14 ternary mixture as an environmental benign alternative for ARC systems, and a mass ratio of 35/30/35 mixture was recommended. He et al. [42] studied the theoretical performance of a two-stage ARC system using R170/R600a, R170/R600, R1150/R600a, R1150/R600, and R23/R134a. The results showed that R170/R600 showed the best performance, and the exergy loss ratios of the heat exchanger in the R170/R600 and R23/R134a systems were the highest at 52.3% and 56.7%, respectively. A comparison study was conducted by Hamad et al. [43] to investigate the performance of an ARC using R290 and R600a. R290/R600a with four mass ratios (70/30, 60/40, 50/50 and 40/60) was used to investigate the performance of the system and compared with R134a. Results show that the mixed refrigerant with the mass fraction of 60/40 displayed a higher performance comparing with other mass fractions and R134a. Also, a 29% increase in COP and a 26% increase in refrigeration effect were achieved, respectively.

Generally, the low separation efficiency is an important reason for the poor performance of the ARC systems. It is seen from the literature review outlined above that the studies related to the energy and exergy analysis of the ARC have been based on the perspective of cycle structure modification to improve separation efficiency, in which the decrease of refrigerant flow to evaporator was not taken into account [18, 20]. On the other hand, some studies mentioned these effects without performing a detailed cycle analysis, especially for the three-stage ARC. To solve this problem, this paper proposed a modified three-stage ARC (MTARC) with an additional expansion valve installed between the condenser and the vapor–liquid separator for refrigeration applications at ultra-low temperatures around − 80 °C. The pressure regulator can effectively increase the refrigerant flow to the evaporator but has little effect on its composition (maintain a high separation efficiency), thereby the system performances can be further improved. Under consideration of the environmental issues and the process of sustainable development, the experimentally benign ternary mixture of R1234yf/R170/R14 with low GWP value was selected as the working fluid. This study is different from the ones in the literature because it presents a detailed first and second law analysis of the MTARC in comparison with the conventional three-stage ARC (CTARC) under various operating characteristics. The proposed MTARC offers new pathways for designing energy-efficient cryogenic refrigeration systems and applications that operate below − 80 °C for sustainable development.

Mathematical model of the modified three-stage ARC

Cycle description

Figure 1a and b are the schematic diagram and the lgp-h diagram for the MTARC operating with R1234yf/R170/R14, respectively. Compared with the MTARC, the structure of the CTARC doesn’t have the expansion valve between the condenser and the vapor–liquid separator, so the schematic diagram of the CTARC is not given again. For the MTARC, the zeotropic mixture from the compressor is partially condensed in the condenser. After that, the two-phase refrigerant is expanded in the first expansion valve EV1, and then enters the first vapor–liquid separator VLS1. The R1234yf-enriched liquid flows out from the bottom of VLS1, and the R170/R14-enriched vapor flows out from the top of VLS1. The saturated vapor at state point 7 is partially condensed in the first condensing evaporator CE1 and then enters the second vapor–liquid separator VLS2. At state point 5, the saturated liquid expands to vapor–liquid fluid by the second expansion valve EV2.

Fig. 1
figure 1

a The schematic diagram of the MTARC; b The schematic lgp-h diagram of the MTARC

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The R14-enriched vapor coming out from the top of VLS2 is condensed efficiently in the second condensing evaporator CE2. After the pressure decreases in the fourth expansion valve EV4, the R14-enriched refrigerant becomes vapor–liquid state and then fully evaporates in the evaporator. The R170-enriched liquid out from the bottom of VLS2 is expanded to vapor–liquid fluid by the third expansion valve EV3. Afterwards, it mixes with the refrigerant exiting from the evaporator, and then the mixture cools the saturated vapor in CE2. After leaving CE2, the mixture at state point 16 mixes with the two-phase refrigerant out from EV2. The mixture at state point 17 cools the saturated vapor in CE1 and then is sucked into the compressor.

Thermodynamic model

To facilitate the calculations, some assumptions are adopted as follows [44]:

  1. (a)

    The system operates in steady state;

  2. (b)

    The throttling processes are considered to be isenthalpic;

  3. (c)

    The compression process is isentropic and irreversible;

  4. (d)

    The heat losses in pipelines and equipment are neglected, and the pressure drop in the pipelines and heat exchangers is negligible.

  5. (e)

    Fluid exiting the phase separator is considered to be saturated. The mixture at state point 12 is saturated liquid.

  6. (f)

    The kinetic exergy and potential exergy of the refrigerant are ignored.

Energy and exergy balance

The governing equations of the system components satisfy the mass and energy conservation equations. The general expressions are as follows:

Mass conservation:

$$\sum {\dot{m}}_{\mathrm{in}}=\sum {\dot{m}}_{\mathrm{out}}$$
(1)

Energy conservation:

$$\sum \dot{Q}=\sum {\dot{m}}_{\mathrm{out}}{h}_{\mathrm{out}}-\sum {\dot{m}}_{\mathrm{in}}{h}_{\mathrm{in}}+\sum \dot{W}$$
(2)

The COP of the ARC can be determined by:

$$\mathrm{COP}=\frac{{\dot{Q}}_{\mathrm{eva}.}}{{\dot{W}}_{\mathrm{com}.}}$$
(3)

Incorporating the second law of thermodynamics, the general expression of the exergy conservation equation of each system component can be expressed as:

$${\dot{\upchi }}_{\mathrm{D}}=\sum {\dot{m}}_{\mathrm{in}}{\dot{\upchi }}_{\mathrm{in}}-\sum {\dot{m}}_{\mathrm{out}}{\dot{\upchi }}_{\mathrm{out}}\pm \dot{Q}(1-{T}_{0}/T)\pm \dot{W}$$
(4)

The exergy carried by the stream can be expressed as:

$$\dot{\upchi }=\dot{m[}{h-h}_{0}-{T}_{0}(s-{s}_{0})]$$
(5)

where \({h}_{0}\) and \({s}_{0}\) stand for the enthalpy and entropy at the reference temperature and pressure, respectively. \(\dot{Q}\) is the heat exchanged between the component and a heat source, \(T\) is the temperature of heat source (K), and the \(\dot{W}\) is the input power or output power of the system components.

The total exergy destruction can be obtained by:

$$ \dot{\chi }_{{{\text{D,total}}}} = \dot{\chi }_{{{\text{D,~~com.}}}} + \dot{\chi }_{{{\text{D,con.}}}} + \dot{\chi }_{{{\text{D, CE1}}}} + \dot{\chi }_{{{\text{D, CE2}}}} + \dot{\chi }_{{{\text{D, EV1}}}} + \dot{\chi }_{{{\text{D, EV2}}}} + \dot{\chi }_{{{\text{D, EV3}}}} + \dot{\chi }_{{{\text{D, EV4}}}} + \dot{\chi }_{{{\text{D,eva}}.}}$$
(6)

The percentage of contribution of the total exergy destruction in each component:

$${\beta }_{\mathrm{D},i}={\dot{\upchi }}_{\mathrm{D},i}/{\dot{\upchi }}_{\mathrm{D},\mathrm{total}}$$
(7)

The exergy efficiency of the ARC is calculated as:

$$\psi =1-{\dot{\upchi }}_{\mathrm{D},\mathrm{total}}/{\dot{W}}_{\mathrm{com}.}$$
(8)

The exergy and exergy conservation equations of the system components are shown as Table 1.

Table 1 Equations for exergy and exergy analysis [45]
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Basic conditions

Based on the above assumptions and models, the commercial software Aspen Plus 11.0 [46] is used to calculate the thermodynamic performance of the two cycles under the given operating conditions. The thermal properties of each state point in the system are calculated using the Redlich–Kwong–Aspen equation of state [47]. The environmentally benign ternary zeotropic mixture R1234yf/R170/R14 is used as the working fluid. The influence of the operating parameters on system performance will be evaluated. Table 2 lists the basic operating parameters for all the simulations below.

Table 2 Input parameter values assumed in the simulation models
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Simulation results and discussion

The initial composition

Usually, ternary mixtures are used in the three-stage ARC system to obtain refrigeration temperatures below − 80 °C. Calm [51] pointed out that refrigerants with low GWP value, such as R41, R170, R1132a and R1150, could be good replacements for R23 (GWP:12,000) with the standard boiling point around, ternary mixtures are used 80 °C. R1234yf is one of the most suitable replacements for R134a (GWP: 1430) [35, 36]. The standard boiling point of R14 is − 128.05 °C and can be used to obtain an evaporating temperature around − 100 °C. Thus, the ternary mixture of R1234yf/R170/R14 was chosen as the working fluid in the MTARC [50]. Table 3 lists the thermodynamic properties of the three pure refrigerants concerned [52].

Table 3 Physical properties of the alternative refrigerants
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In the operation process of the MTARC, the saturated liquid at state point 5 and state point 12 are R1234yf/R170-enriched mixture and R170/R14-enriched mixture, respectively. Thus, the initial composition of R1234yf/R170/R14 can be determined by combining the compositions of R1234yf/R170 and R170/R14. Figure 2a and b are the isobaric three-dimensional equilibrium diagram and isothermal-isobaric ternary equilibrium diagram of R1234yf/R170/R14, respectively. As shown in Fig. 2b, the bubble-surface and the dew-surface intersect with S1 at Line-1 and Line-2, respectively, since the condensation temperature is about 30 °C. Thus, the mass ratio of R1234yf/R170 can be obtained, which is about z1 = 0.815/0.185 [18]. Similarly, the mass ratio of z2 = 0.425/0.575 for R170/R14 can be obtained according to the intersection line between the S2 and the bubble-surface. Consequently, the initial composition of 0.65/0.15/0.20 for R1234yf/R170/R14 can be calculated.

Fig. 2
figure 2

a Isobaric three-dimensional phase equilibrium diagram at 2 MPa; b Isothermal-isobaric ternary phase equilibrium diagram of R1234yf/R170/R14

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The performance comparison under a typical operating condition

Apart from the assumptions mentioned above and the input parameters listed in Table 1, the condenser outlet quality q3 and the intermediate pressure \({p}_{4}\) are set as 0.65 and 1.5 MPa, respectively. In order to better compare the refrigeration performance, the mixture at the evaporator outlet is assumed to be saturated vapor (q14 = 1). Under this typical operating condition, thermodynamic characteristics of the MTARC and CTARC are calculated using the ternary mixture of R1234yf/R170/R14 (0.65/0.15/0.20) and are listed in Table 4.

Table 4 The performance comparisons between two cycles under the typical operating condition
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From Table 4, we can see that the compressor input power of the MTARC is moderately greater than that of the CTARC, while the MTARC has a much larger cooling capacity. There are two factors that affect the input power, namely the refrigerant enthalpy at the compressor inlet and the compression ratio. As shown in Table 4, the quality in the separator will increase under the effect of intermediate pressure, and then the refrigerant enthalpy at the compressor inlet and the mass flow rate in the evaporator both increase, resulting in the increase of input power and cooling capacity of the MTARC. Consequently, the COP of MTARC reaches 0.4989, which is 11.69% higher than that of the CTARC. In addition, both the evaporator inlet and outlet temperatures of the MTARC are lower than those of the CTARC. This is because the mass fraction of the volatile component R14 is increased due to the increase of quality, thus the evaporating temperatures decrease when the evaporating pressure is fixed. However, the suction and exhaust temperatures of the MTARC are about 10 °C higher than that of the CTARC. It indicates that the MTARC can effectively prevent the compressor from liquid hammering under special circumstances. Compared with the CTARC, the MTARC has a smaller total exergy destruction and a greater input power. Consequently, the exergy efficiency of the MTARC is increased by 7.65%.

According to the operation process of the MTARC, it was found that the specific enthalpies of the refrigerant at the condenser outlet and VLS1 inlet are equal, but the temperature and pressure at the VLS1 inlet are greatly decreased. This is due to the effect of the isenthalpic throttling process of EV1. Therefore, when the suction and discharge pressures are fixed, the mass flow rate of the refrigerant in the low temperature circuit is increased due to the increase of quality at the VLS1 inlet. Besides, the mass fraction of the low boiling point component in the evaporator will not be decreased. That is, the cooling capacity and COP of the MTARC are increased without increasing the evaporating temperature. Thus, under the premise of ensuring no liquid in the compressor suction, the cycle performance can be improved when the suction and discharge pressures are fixed.

Effect of quality q3 on the system performance

In order to acquire an appropriate mass flow of the R170/R14-enriched refrigerant, the mixture should be partially condensed in the condenser. Thus, the refrigerant quality q3 at the condenser outlet is limited. By ensuring no liquid existence in the compressor suction and a proper exhaust temperature, the system performance was investigated under the q3 range of 0.58–0.75, and the refrigerant at the evaporator outlet is also assumed to be saturated vapor (q14 = 1). The results show that the evaporating temperatures of the MTARC are always lower than those of the CTARC within the entire q3 range. On the other hand, the compressor outlet temperature of the MTARC is higher than that of the CTARC. This means that the refrigerant temperature at the compressor inlet also increases, which can effectively prevent liquid hammer of the compressor.

Figure 3 shows the effect of quality q3 on the cooling capacity, COP, total exergy destruction and exergy efficiency. From Fig. 3a we can see that the cooling capacities of both the MTARC and CTARC increase with increasing q3. This is due to the increase of the mass flow of the refrigerant mixture in the evaporator. When q3 is 0.75, the cooling capacity and compressor input power of the MTARC are 65.51 kW and 126.87 kW, respectively, which are 31.04% and 24.67% greater than those of 49.99 kW and 101.76 kW when q3 is 0.58, respectively. That is, the growth rate of the cooling capacity is significantly higher than that of the input power. As a result, the COP gradually increases with increasing q3 as shown in Fig. 3a. On the other hand, the cooling capacity and COP of the MTARC are always greater than those of the CTARC within the entire q3 range as shown in Fig. 3b. Similar to the variation trend of the cooling capacity and COP, the total exergy destruction and exergy efficiency of the two cycles monotonically increase with increasing q3. Besides, the total exergy destruction of the MTARC is always slightly less than that of the CTARC, while the exergy efficiency of the MTARC is much higher than that of the CTARC under the same q3. This is because the input power of the MTARC is higher than that of the CTARC, resulting in the higher exergy efficiency according to Eq. (8). When q3 is 0.58 and 0.75, the exergy efficiency of the MTARC is 40.58% and 42.27% respectively, while those of the CTARC are 37.47% and 39.57%, respectively.

Fig. 3
figure 3

a Effect of quality q3 on the cooling capacity and COP; b Effect of quality q3 on the total exergy destruction and exergy efficiency

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Effect of initial composition on the system performance

Since the strong zeotropic mixture has a large temperature glide when evaporating at a constant pressure, it is necessary to study the system performance of the two cycles with different initial compositions. In this section, the mixture at the evaporator outlet is assumed to be saturated vapor (q14 = 1). The calculated results show that the discharge temperatures of the two cycles monotonically increase with increasing initial mass fraction of R1234yf (ZR1234yf), but decrease with increasing initial mass fraction of R14 (ZR14). In addition, the compressor discharge temperature of the MTARC is higher than that of the CTARC at each initial composition. However, the evaporating temperatures of the two cycles decrease with increasing ZR1234yf and ZR14. The reason is that the increase of ZR1234yf will reduce the mass fraction of R170 (ZR170), which leads to the increase of the R14 mass fraction in the R170/R14-enriched mixture at state point 7. Then, the R14 mass fraction in the refrigerant mixture entering the evaporator is further increased when the quality at state point 8 (q8) is fixed as 0.5. On the other hand, the evaporator inlet temperatures of the MTARC is about 4 °C lower than that of the CTARC at each initial composition.

Figure 4 illustrates the variations of the cooling capacity and COP of the two cycles with different initial compositions. As shown in Fig. 4a, the cooling capacities of the two cycles decrease gradually with increasing ZR1234yf and ZR14. In addition, the cooling capacities of the MTARC are always greater than those of the CTARC within the entire composition range. When the initial composition of R1234yf/R170/R14 is 0.61/0.21/0.18, the MTARC has a cooling capacity of 60.01 kW, which is 16.41% greater than that of 51.55 kW for the CTARC. Contrary to the variation trend of the cooling capacity, the COP of the two cycles increase with increasing ZR1234yf and ZR14. According to Eq. (3), it indicates that the decrease rate of input power is higher than that of cooling capacity. When the initial composition of R1234yf/R170/R14 is 0.69/0.09/0.22, the MTARC has a COP of 0.5148, which is 11.62% higher than that of 0.4612 for the CTARC as shown Fig. 4b. When ZR14 is 0.20, the cooling capacity of the MTARC increases by 4.84% from 0.4893 to 0.5130 as ZR1234yf increases from 0.61 to 0.69.

Fig. 4
figure 4

a Effect of composition on cooling capacity; b Effect of composition on COP of the MTARC and CTARC

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Figure 5 shows the effects of initial composition on the total destruction and exergy efficiency of the two cycles. We can see from Fig. 5a that the total exergy destruction of both the MTARC and CTARC decrease gradually with increasing ZR1234yf and ZR14. Although the input power also decreases with increasing ZR1234yf and ZR14, the growth rate is smaller than that of the total exergy destruction. As a result, the exergy efficiency increases with increasing ZR1234yf and ZR14 as shown in Fig. 5b. Within the entire composition range, the exergy efficiencies of the MTARC are always higher than those of the CTARC, which indicates that the additional pressure regulator can significantly reduce the exergy loss of the system. When the initial composition of R1234yf/R170/R14 is 0.69/0.09/0.22, the MTARC has an exergy efficiency of 44.35%, which is 7.33% higher than that of 41.32% for the CTARC.

Fig. 5
figure 5

a Effect of composition on total exergy destruction; b Effect of composition on exergy efficiency of the MTARC and CTARC

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Effect of evaporating temperature on the system performance

The evaporating temperature is of great significance in influencing the performance of refrigeration systems. Figure 6a and b show the effects of evaporator outlet temperature T14 on the compressor temperature, cooling capacity, COP and exergy efficiency under the given operating conditions. As shown in Fig. 6a, all the temperatures increase gradually with increasing T14, and both the compressor inlet and outlet temperatures of the MTARC are higher than those of the CTARC. It should be noted that the liquid refrigerant exists at the compressor inlet of the MTARC when T14 is below − 75 °C, while the compressor of the CTARC will suck liquid when T14 is below − 70 °C. This demonstrates that the MTARC can acquire lower evaporating temperaure without liquid hammering of the compressor. In addition, the quality q14 at the evaporator outlet decreases with decreasing T14, which indicates that there is less liquid mixture evaporating in the evaporator. As a result, the cooling capacities of the two cycles decrease with decreasing T14 as shown in Fig. 6b. When T14 drops from − 55 to − 75 °C, the cooling capacity of the MTARC deceases by 42.66% from 52.74 kW to 30.24 kW. Meanwhile, the input power decreases by 11.20% from 110.95 to 98.52 kW. Consequently, the COP is decreased by 35.44% from 0.4754 to 0.3069. On the other hand, the performances of the MTARC are better than those of the CTARC in all given T14 ranges. When T14 is − 65 °C, the cooling capacity and COP of the MTARC are 41.41 kW and 0.3949 respectively, which show 28.20% and 17.98% improvements over the CTARC, respectively.

Fig. 6
figure 6

a Effect of evaporator outlet temperature on T1, T2, and q14; b Effect of evaporator outlet temperature on cooling capacity and COP; c Effect of evaporator outlet temperature on total exergy destruction and exergy efficiency

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Figure 6c displays the variation trend of exergy performance with respect to T14. Both the total exergy destruction and exergy efficiency of the two cycles gradually increase with increasing T14. This indicates that the decrease rate of the total exergy destruction is greater than that of the total input power. Besides, the total exergy destructions of the MTARC are less, while the exergy efficiencies are higher than those of the CTARC within the entire T14 range. According to Eq. (8), the exergy efficiency is inversely proportional to the total exergy destruction, while is proportional to the input power. Therefore, it can be concluded that the MTARC can significantly reduce the input power of the compressor. This is because the pressure ratio is fixed as a constant, and the specific enthalpy difference of refrigerant at the compressor inlet and outlet of the MTARC is less than that of the CTARC. When T14 is − 65 °C, the exergy efficiency of the MTARC is improved by 9.89%, while that is improved by 9.03% when T14 is − 55 °C.

Effect of intermediate pressure on the MTARC performance

Under the action of the additional EV1, an intermediate pressure is obtained, and the relative independence between the refrigerant at VLS1 inlet and the refrigerant at condenser outlet is further realized. Therefore, it is possible for the MTARC to improve the system performance. Figure 7 shows the effect of intermediate pressure p4 on the thermodynamic performance of the MTARC under the premise of no liquid existence at the compressor inlet. In this section, the mixture at evaporator outlet is also assumed to be saturated vapor (q14 = 1). From Fig. 7a we can see that when p4 drops from 2 to 1 MPa, the refrigerant temperature T4 at VLS1 inlet decreases by 20.38 °C, while the quality q4 at the VLS1 inlet increases gradually. Thus, the mass flow of the refrigerant entering the low-temperature circuit (Streams 7 and 11) is further increased as shown in Fig. 7b. As a result, the cooling capacity of the MTARC increases with decreasing p4 as shown in Fig. 7c. As q4 increases, the increase of the specific enthalpy of the refrigerant at compressor inlet increases, accounting for the increase of input power. Finally, the MTARC shows an improvement of 35.43% in cooling capacity when p4 drops from 2 to 1 MPa. In addition, the evaporating temperatures also decrease with decreasing p4. When p4 drops from 2 to 1 MPa, the evaporator inlet temperature decreases by 7.23 °C from − 89.67 to − 96.90 °C, and the evaporator outlet temperature decreases by 3.43 °C from − 50.76 to − 54.19 °C.

Fig. 7
figure 7

a Effect of intermediate pressure on temperature (T4) and quality (q4) at VLS1 inlet; b Effect of intermediate pressure on mass flow rate; c Effect of intermediate pressure on evaporating temperature, input power and cooling capacity

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Figure 8 illustrates the effect of intermediate pressure on the compressor outlet temperature, COP and exergy efficiency of the MTARC. Clearly, the decreasing p4 results in an increase of COP and exergy efficiency. This is because the growth rate of the cooling capacity is larger than that of the input power, which leads to an increase of COP. When the pressure is 1.2 MPa, the COP reaches 0.5340, and the compressor outlet temperature is 107.54 °C, which is an appropriate operating temperature. When p4 drops from 2 to 1 MPa, the COP and exergy efficiency are improved by 25.25% and 16.74%, respectively. However, the compressor outlet temperature increases by 19.93 °C from 92.27 to 112.20 °C. The reason is that the quality in the separator increases as p4 decreases, which leads to the increase of vapor refrigerant mass flowing to the low-temperature circuit (Steam 7 and 11) and the decrease of liquid refrigerant mass flow at state point 5. Because the quality at the evaporator outlet is fixed as 1, the mixed refrigerant at state points 17 and 15 cannot provide sufficient cooling capacity to condense the vapor refrigerant. As a result of the comprehensive effect, the temperature of the refrigerant at the compressor inlet increases, further increasing the discharge temperature. Therefore, the selection of the intermediate pressure should be comprehensively considered to ensure a desirable thermodynamic performance and a proper working temperature of the compressor in actual applications.

Fig. 8
figure 8

Effect of intermediate pressure on compressor outlet temperature, COP and exergy efficiency of the MTARC

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In order to determine the main locations of irreversibility in the MTARC, the effect of p4 on the exergy destruction and exergy destruction percentage of each system component are depicted in Fig. 9. It can be seen from Fig. 9a that when p4 drops to 1 MPa, the compressor, condenser and EV1 contribute the most to the exergy destruction. With decreasing p4, the exergy destruction percentages of the condenser and EV1 increase gradually as show in Fig. 9b. This is attributed to the increase of heat transfer temperature difference in the condenser and the pressure drop in the EV1. On the contrary, the exergy destruction percentages of the CE1 and EV2 decrease with decreasing p4, while those of the compressor remain almost constant. This indicates that the exergy efficiency of the MTARC can be further improved mainly by enhancing the heat transfer performance of condenser and the structural optimization of EV1.

Fig. 9
figure 9

a Effect of intermediate pressure on exergy destruction; b Effect of intermediate pressure on exergy destruction percentage

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Conclusions

At present, the studies related to the performance analysis of the ARC mainly focus on the improvement of separation efficiency, in which the decrease of the refrigerant flow to the evaporator was not considered. In order to solve this problem and propose an efficient refrigeration cycle to obtain the refrigeration temperatures around − 80 °C, this paper introduces a pressure regulator into a modified three-stage ARC, which can effectively decrease the refrigerant pressure and temperature in the separator to obtain a high separation efficiency, and can increase the vapor quality and the refrigerant flow to the evaporator. The environmentally benign ternary mixture of R1234yf/R170/R14 was used as the working fluid for sustainability concerns. Energy and exergy analyses of the CTARC and MTARC are conducted theoretically considering the key operating parameters of the composition, quality and intermediate pressure. The foregoing analysis results indicate that the MTARC is meaningful and manifest significant performance improvements. Major conclusions drawn from this research are summarized as follows:

  1. (1)

    The MTARC can effectively increase the refrigerant flow rate to the evaporator, which rendering the MTARC always shows significantly better performance than the CTARC. Under a typical working condition, the cooling capacity, COP and exergy efficiency of the MTARC are improved by 15.85%, 11.69% and 7.65% comparing with those of the CTARC, respectively.

  2. (2)

    As the mass fraction of the less volatile component increases, the cooling capacity of two cycles are deteriorated, while the COP and exergy efficiency are increased due to the decline of the compressor input power. When the initial composition of R1234yf/R170/R14 is 0.69/0.09/0.22, the COP and exergy efficiency of the MTARC are 11.62% and 7.33% higher than those of the CTARC, respectively.

  3. (3)

    As the quality at condenser outlet increases, the COP, cooling capacity and exergy efficiency of the two cycles are improved gradually. When the quality is 0.75, the COP and exergy efficiency of MTARC are 10.25% and 6.82% higher than those of the CTARC.

  4. (4)

    The performance of the MTARC is improved with decreasing intermediate pressure. When the intermediate pressure drops from 2 to 1 MPa, the cooling capacity, COP and exergy efficiency of the MTARC are improved by 35.43%, 25.25% and 16.74%, respectively, while the compressor outlet temperature increases by 19.93 °C from 92.27 to 112.20 °C. Therefore, the selection of the intermediate pressure should be comprehensively considered to ensure a desirable thermodynamic performance and a proper working temperature for the compressor in actual applications.

In general, the MTARC can offer many advantages for its applications in low-temperature equipment down to − 80 °C, such as freezers, cryopreservation chamber, and the pre-cooling system for cryoablation devices. Because many assumptions were adopted in the modeling process, the analytical results still show some deviation from the actual operating conditions and the MTARC only verifies its improvements in theory. Thus, further experimental work will be necessary in the next step before practical application. Besides, the exergy analysis suggests that the heat transfer enhancement of the air-cooled condenser and the structure optimization of the throttle valves are the key improvements of the ARC systems.