Advanced two-stage cascade configurations for energy-efficient –80 °C refrigeration

In response to the COVID-19 pandemic, some vaccines have been developed requiring ultralow-temperature refrigeration, and the number of these freezers has been increased worldwide. Ultralow-temperature refrigeration operates with a significant temperature lift and, hence, a massive decrease in energy performance. Therefore, cascade cycles based on two vapor compression single-stage cycles are traditionally used for these temperatures. This paper proposes the combination of six different cycles (single-stage with and without internal heat exchanger, vapor injection, liquid injection, and parallel compression with and without economizer) in two-stage cascades to analyze the operational and energy performance in ultralow-temperature freezers. All this leads to 42 different configurations in which the intermediate cascade temperature is optimized to maximize the coefficient of performance. Ultra-low global warming potential natural refrigerants such as R-290 (propane) and R-170 (ethane) for the cascade high- and low-temperature stage have been considered. From the thermodynamic analysis, it can be concluded that liquid and vapor injection cascade configurations are the most energy-efficient. More specifically, those containing a vapor injection in the low-temperature stage (0.89 coefficient of performance, 40 % higher than traditional configurations). Then, using an internal heat exchanger for such low temperatures is unnecessary in terms of energy performance. The optimum intermediate cascade temperature varies significantly among cycles, from −37 °C to 2 °C, substantially impacting energy performance. Parallel compression configuration improves energy performance over single-stage cycles, but not as much as multi-stage (between 20 % and 30 % lower coefficient of performance). For most of low-temperature cycles, the high-temperature stage can be based on a single-stage cycle while keeping the maximum coefficient of performance.


Introduction
Ultralow-temperature refrigeration consists of cooling a particular product or room below a specific temperature, generally below -50 • C [1]. The recent appearance of the Sars-CoV-2 vaccines has put the light on a problem that has been present in society for a long time, deep freezing. Pfizer-BioNTech announced that its vaccines must be stored between -60 • C and -80 • C [2]. Consequently, news reports have echoed, alleging a huge logistical problem to keep vaccines in such conditions.
Refrigeration at this temperature range is usually based on vapor compression systems. There is a lack of studies and regulations in the ultralow-temperature range to motivate advanced environmentallyfriendly solutions [3]. The impact of energy efficiency on equivalent carbon dioxide emissions requires studying the broadest combination of configurations in detail. Cascade and auto-cascade systems are configurations typically found in commercial low or ultralowtemperature freezers [4], working between 20 • C and 30 • C ambient temperature and -50 • C to -80 • C freezing conditions [5].
The cascade configuration thermally connects single-stage cycles through a cascade heat exchanger, choosing the most suitable refrigerant for each temperature level. Most of the available studies for this application consider only two stages [6]. Compared to a two-stage configuration, Mumanachit et al., [7] observed that a two-stage cascade is more efficient below the coefficient of performance (COP) optimal point and cost-effective below -46.2 • C. Mateu-Royo et al., [8] observed that a two-stage cascade becomes the most appropriate configuration for high temperature lifts (60 • C and above).
Furthermore, the control of operational parameters of two-stage cascades is essential for proper energy performance. Chung et al., [9] observed that a higher low-temperature (LT) compressor discharge pressure allows a lower evaporator temperature. In addition, an inadequate pressure adjustment can cause fluctuations in the compressor operation and the intermediate cascade temperature distribution. Lee et al., [10] concluded that the COP increases with increasing LT evaporation temperature but decreases with increasing high-temperature (HT) condensation temperature and temperature variation. Chae and Choi [11] showed that the COP is lower when the system is undercharged because the heat transfer capacity decreases. Deymi-Dashtebayaz et al., [12] proposed the Pareto front curve to obtain the optimal operational conditions and refrigerants considering maximum COP, maximum exergy efficiency and minimum total cost rate. R-41/R-161 and R-41/R-1234ze(E) present the highest COP and exergy efficiency and lowest total cost rate.
Cascade configurations based on single stages can be modified by adding elements such as the internal heat exchanger (IHX, also known as liquid-to-suction heat exchanger). Di Nicola et al., [13] proposed an IHX in the LT stage, concluding that it could be helpful. Bhattacharyya et al., [14] optimized a cascade system with IHX in HT and LT stages and observed that the system performance does not depend on the IHX effectiveness. Liu et al., [15] concluded that the COP is lower if only the LT IHX operates, but the cycle with IHX in both stages has the potential to be energy efficient. Also, Dubey et al., [16] observed that the HT IHX impact on system performance is higher than that of the LT stage.
Due to the greenhouse effect caused by traditional refrigerants, the European Union approved the (F-Gas) Regulation 517/2014 [21], which aims to reduce refrigerants' equivalent carbon dioxide emissions by twothirds in 2030 compared to 2014 levels. Scientific articles published about refrigerants show that studying environmentally friendly fluids in cascades is essential.
Many previous studies considered ammonia (R-717) and carbon dioxide (R-744) for low temperature refrigeration (down to -40 • C evaporation temperature). Dopazo et al., [22] quantified with R-744 and R-717 that an increase in the evaporator temperature from -55 • C to -30 • C leads to a 70 % higher COP. In the same way, an increase in the condenser temperature from 25 • C to 50 • C causes a 45 % lower COP. Additionally, if the intermediate cascade temperature increases from 3 • C to 6 • C, it causes a 9 % COP reduction. Di Nicola et al., [13] compared different hydrofluorocarbons (HFCs) with R-717 at -70 • C, concluding that the latest is 5 % superior in COP. Getu and Bansal [23] found with R-744 and R-717 that a higher superheating degree and mass flow rate decreases the COP. Still, it can be counteracted with a higher subcooling degree in both stages. Eini et al., [24] compared R-744/R-717 and R-744/R-290 pairs, concluding that the one with R-717 is inherent safety. Ust and Karakurt [25] concluded that R-717 in the HT stage causes higher energy performance than R-290, R-404A, and R-507. Turgut and Turgut [26] tested the refrigerant pairs R-744/R-717, R-744/R-134a, and R-744/R-1234yf, observing that R-744/R-1234yf is superior as regards efficiency and annual costs. On the other hand, subcooling and superheating degrees have a negligible influence on the cost of the equipment.
According to Sun et al., [27], an optimal intermediate cascade temperature is essential, and R-41 is appropriate to replace R-23. Kilicarslan and Hosoz [28] expanded the selection of refrigerants by proposing R-152a/R-23, R-290/R-23, R-507/R-23, R-134a/R-23, R-717/R-23, and R-404A/R-23 to assess the influence of the operating temperature on the COP. Aktemur et al., [29] considered other novel refrigerants such as R-1243zf, R-423A, R-601, R-601a, R-1233zd(E) and RE-170, concluding that R-432A shows the lowest energy performance. Mota-Babiloni et al., [30]  [32] adapted a standard low-temperature R-290 packaged unit with R-170 between -80 • C and -65 • C evaporating temperature, and they measured COP between 0.6 and 1.6. The literature shows that cascade systems at ultralow-temperatures have hardly been studied. Only a few works propose IHXs, but there are more possibilities to modify single-stage cycles composing cascade configurations and increasing overall energy performance. Moreover, few works consider the refrigerant pair R-290/R-170, which can be the most promising in terms of energy performance and environment protection. Most papers dealing with cascade configurations hardly reach the extreme evaporation temperature of − 80 • C. Because of the recent interest in this application and the evident lack of studies, this work proposes the combination of different vapor compression cycles in twostage cascade configurations. Firstly, the cycles combined and are presented. Next, the methods and strategy of the simulation, including equations, input parameters and refrigerants, are exposed. Then, the computational simulation results are analyzed and discussed, focusing on COP, optimum intermediate cascade temperature, and mass flow rate. Finally, the main conclusions of the study are summarized.

Methods
The methods will explain the configurations used, from the standard vapor compression cycles to the cascade ones. A strategy has been used from the assumptions to the final modeling details.

Configurations
This article combines six standard vapor compression cycles in the high and low-temperature stages of a cascade configuration. As ultralow-temperature applications must cover a remarkable temperature lift (difference between condensation and evaporation temperatures), cascade configurations could benefit from an improvement in stages. Therefore, all possible combinations are simulated in the same operating conditions, and the energy performance is assessed. These cycles that are combined in the paper are shown in Fig. 1.
A total of 42 configurations are defined, considering them in both possible cascade stages. Table 1 describes all configurations simulated in this paper and the abbreviature proposed for simplifying the analysis. Fig. 2 illustrates the configuration of a two-stage cascade based on two single-stage cycles (S+S). This configuration will be used as a baseline, and other configurations will replace single-stages to achieve the maximum number of possible combinations. The intermediate cascade temperature is decisive in the system energy performance, among other factors.
The configurations explained above have been calculated with the following strategy.

Strategy
The simulation of the configurations is based on the methods presented in Fig. 3, where the input parameters are configuration, refrigerants, and boundary conditions and assumptions. This model is developed using the software Engineering Equation Solver (EES) [33] version Academic Commercial V100.835-3D. The Golden Search Algorithm incorporated in this software is used to find the optimum intermediate cascade temperature that maximizes overall COP.
Other information required for the modeling is exposed in the following subsections.

Table 1
List of configurations studied in this paper.

HT LT Abbreviature
Single

Boundary conditions and assumptions
The input parameters used in calculating the configurations are shown in Table 2. Evaporating temperature is set at the typical minimum value of ultralow-temperature freezers, even though they can work from − 50 • C. Hence, this temperature was selected to cover the most critical condition. Then, the condensing temperature of 30 • C was chosen to simulate controlled room conditions. A cooling capacity of 10 kW is fixed to simulate medium capacity refrigeration conditions present in ultralow-temperature rooms. Superheating and subcooling degrees of 5 K and 2 K are selected to propose optimized systems with minimum influence of these parameters.
Isenthalpic expansion is assumed in expansion valves present in the circuit. Pressure drops and heat exchange with the ambient in components and lines are neglected.

Modeling common details
This section presents the common equations used in the modeling process of each cycle configuration.
The refrigerant mass flow rate is calculated using the cooling capacity of the evaporator, Eq. (1).
The isentropic efficiency is used to calculate the thermodynamic state at the discharge of the compression stage, Eq. (2), which is the ratio between the ideal specific compression work and the real one.
Regarding the isentropic efficiency of the compressors, Eq. (3) is proposed. It is expressed in terms of compression ratio, Eq. (4).
The compression model is based on manufactured data. Fig. 4 shows the validation of the proposed compressor model using manufacturer values and proves the excellent match between both data.
The compressor power consumption is expressed in Eq. (5) as the product of mass flow rate and the real specific compression work.
The total compressor power consumption has been calculated as the sum of all compressors (or compression stages), Eq. (6).
The coefficient of performance (COP) depends on the cooling capacity and the power consumption, defined as Eq. (7).

Cycles
Considering the common equations presented in the previous subsection, each cycle incorporated in the cascade stages has particular characteristics. Additional equations and remarks for the cycles are exposed in the following, considering the schematics seen in Fig. 1.

Single-stage cycle with internal heat exchanger
This cycle has a heat exchanger that receives the refrigerant from the liquid and suction lines, hot and cold sides. Then, the vapor suctioned by the compressor and the liquid before the expansion valve has extra superheating and subcooling degrees, respectively. This heat exchanger is calculated using energy balances considering the hot and cold fluid, Eq. (8). The effectiveness of all heat exchangers existing in the configurations is set at 40 % to control excessive discharge temperature [34], Eq. (9).

Vapor and liquid injection two-stage cycles
These cycles (vapor injection and liquid injection) have a mass flow rate at an intermediate pressure, which joins the liquid line with the high-pressure compressor suction line. The intermediate mass flow rate of the two-stage cycle with liquid injection has been established at 30 % of the evaporator's low-pressure refrigerant mass flow rate. The intermediate flow rate of two-stage cycles with vapor injection has been based on setting the total superheating degree of the high-pressure compressor at 5 K. Required equations come from the energy and mass balance in the pipe joints, Eq. (10) and Eq. (11).
The intermediate pressure of the compressors in two-stage cycles has been established using Baumann and Blass correlation shown in Eq. (12).

Parallel compression with and without economizer
This cycle is based on two compressors, but they work parallel and Table 2 General conditions for the cycle comparison.

Parameter Value
LT evaporating temperature − 80 • C HT condensing temperature 30 • C LT cooling capacity 10 kW LT and HT superheating degree 5 K LT and HT subcooling degree 2 K Fig. 4. Isentropic efficiency result of compressor modeling and manufacture data.
share the discharge point. Therefore, Eqs. (10) and (11) are applied before the condenser. A variation of the parallel compression cycle is the addition of a heat exchanger named economizer.
To calculate the necessary mass flow rate through the intermediate line, the economizer effectiveness is set at 80 %. Using the equation for the effectiveness of the heat exchanger, it is possible to determine the necessary mass flow rate and subsequently the enthalpy using an energy balance in the economizer itself. Eq. (13) shows the effectiveness, and Eq. (14) shows the energy balance.

Cascade cycle
The modeling of the cascade cycles consists of two different stages but joining them through a cascade heat exchanger. First, the LT condenser temperature is optimized considering the maximum COP. Then, the parameters of the HT evaporator are obtained considering a temperature difference of 5 K between the LT condensing and the HT evaporating temperatures, Eq. (15). It is supposed that the HT evaporator absorbs all heat provided by the LT condenser.

Refrigerants
Two natural refrigerants with appropriate operational and pressure-temperature characteristics are selected for direct cycle comparison: R-170 (ethane) in the LT stage and R-290 (propane) in the HT stage. The thermodynamic states of the refrigerants are incorporated in the simulation software, EES. The working fluids' main properties (physical, chemical, toxicological, and environmental) are included in Table 3.
As seen, both refrigerants are highly flammable (A3), and additional measures could be taken, depending on the placement of the system and the final refrigerant charge. Besides, they have a very low GWP, and therefore, they are future-proof natural refrigerants that environmental regulations would not restrict. The normal boiling temperature ensures that they can be used without entering a vacuum in each stage. The critical temperature allows subcritical operation. The relatively high heat of vaporization enable them to be refrigerants with a considerable expected refrigerating effect. Moreover, they can be used with different commercially available lubricating oils. Fig. 5 presents the T-s and P-h diagrams of these refrigerants used in each stage.

Results
This section presents and analyses the main results of the proposed cycles, focusing on the main parameters of interest from an operational and energy point of view: coefficient of performance (COP), intermediate cascade temperature, and mass flow rate.

Coefficient of performance
The COP analysis is divided into subsections according to the primary cycles in which the cascade configuration is based. Fig. 6 shows the COP of the cycles considered in this study without combining them in cascades. This can help illustrate the ability of these cycles to cover high-temperature lifts. In this case, a single refrigerant is considered, R-170.

Base cycles
The use of single-stage cycles for such a high-temperature lift is unfeasible. The compressor cannot compress the very high-compression ratio (caused by the temperature lift). Because of that, the compression ratio must be split into more stages. Also, in the case of having a capable compressor, it must absorb a very high amount of energy to compress the refrigerant from suction to discharge pressure for a pressure ratio of 20. This high compression ratio also causes excessive energy consumption. In addition, the discharge temperature is outside the operating range of any compressor (156.5 • C) because there is no intermediate cooling during the compression process. The same happens using an IHX, but the discharge temperature will worsen because of a higher suction temperature.
The two-stage cycle with liquid injection can control the issue of excessive discharge temperatures and compression ratio. The refrigerant is cooled down during the compression stage by introducing liquid from the condenser. Henceforth, this modification results in a COP of 0.32. This low COP is because this cycle forces the refrigerant for ultralow temperatures to work at the higher temperatures for which it is aimed. R-170 has a critical temperature of 32.17 • C, close to the condenser temperature of 30 • C. Therefore, it immediately reaches saturation; the isenthalpic valve places the evaporator inlet at a very high enthalpy, causing an increased mass flow rate that increases the compressor power consumption.
The two-stage cycle with vapor injection can be modeled on two premises: setting the mass flow rate or the superheating degree at the high-pressure compressor suction. For the latter case, the mass flow rate at the intermediate pressure is very high because the enthalpy at this point corresponds to saturated vapor. This causes the mass flow rate through the second compressor to be extremely high, increasing the power consumption (at a constant cooling capacity), so the COP is reduced. On the other hand, by setting the mass flow rate to pass through that intermediate line, the cooling effect of the vapor is lower but sufficient so that the discharge temperature is no longer out of range. At the same time, the increase in the refrigerating effect of the evaporator causes the necessary mass flow rate of the cycle to be considerably lower.
Consequently, the necessary compressor power consumption is significantly reduced. Consequently, the COP is 0.83 for the two-stage cycle with vapor injection. Using the other premise, setting the superheating degree causes a very low COP as it has a mass flow rate ten times higher. The problem is again the low critical temperature which makes this cycle unfeasible.
The parallel compression is the last configuration used as a base in the cycle. This way, it is not possible to calculate it because of the same issue as the single-stage cycles. In this case, a second compressor has an excessive compression ratio and cannot operate. In the case of using an economizer, the same occurs.
The single-stage cycle and its successive modifications show that an acceptable COP cannot be obtained. Compressors cannot compress such a high compression ratio, and also refrigerants capable of reaching such ultralow temperatures have a low critical temperature. Fig. 7 shows the COPs of the cascade systems in all possible combinations in which parallel compression is not considered. Therefore, sixteen configurations are analyzed in this subsection.

Cascade systems
Once the base cycles have been discussed, they can be combined in a cascade. The two-stage cascade cycle based on single-stages yields a COP of 0.62. The division of the compression process into two compressors explains this significant improvement, as exposed in the previous section. By dividing into two stages and placing a specific refrigerant to the temperature level, the maximum discharge pressure of each stage is approximately 10 bar. In addition, the effect of the isentropic performance of the compressors also has a substantial influence.
By introducing an IHX in each stage, the COP remains similar, 0.62. Two two-stage cascade configurations have been modeled, each with the IHX in a different stage (HT or LT), to explore the variation of the COP. In both cases, the COP remains similar. The IHX in the HT stage, the COP is 0.63, whereas when placed in the LT stage, it is 0.61.
By separating the compression process and introducing a two-stage cycle with liquid injection in both stages, the COP increase to 0.77. The refrigerant injection explains the increase in the intermediate stage, which allows a lower compression ratio and an increase in energy performance. To a lesser extent, the efficiency of the compressors also leads to an improvement in COP because the compression slope is less steep. As the cascade reduces the partial compression ratio, dividing each compression ratio again, the performance increase less noticeable. When the liquid injection is only used in one of the two stages, the COP is similar or even lower. A two-stage with liquid injection cycle in HT and a single-stage cycle in LT decreases the COP to 0.74, whereas the reverse configuration results in a COP of 0.76. If an IHX is used in the singlestage cycle, more considerable variations can be observed than in the two-stage cascade. The COP decreases when the IHX is placed in the LT single-stage cycle (0.73), whereas it rises in the HT stage, 0.77.
The vapor injection causes the same effect as in the single-stage cycle. It enhances the COP until 0.84 when introduced in both stages. Besides, it causes a greater COP placed only in the LT stage (0.89) than in HT (0.85). A similar COP is observed when an IHX is introduced in the  single-stage cycle. In the option with vapor injection in HT and singlestage with IHX in LT, the COP decreases to 0.84. In contrast, in the reverse cycle, the COP remains at 0.89.
At this point, it is necessary to analyze the cycles with vapor injection in HT and also those with liquid injection in HT because the results of the COP of 0.85, 0.84, 0.74, and 0.73 are not the maximum obtained at the optimum temperature point. The problem is that the optimal intermediate cascade temperature would appear below the point with this COP, resulting in 0.9 the ones with vapor injection. The problem is that R-290 stage minimum pressure is around 0.6 bar at those temperatures, which  is not convenient in operational terms. Consequently, the intermediate cascade temperature has been raised manually. In the same system described above, the single-stage cycle can be changed to a two-stage with liquid injection. One stage with vapor injection in HT and liquid injection in LT and another with vapor injection in LT and liquid injection in HT are considered. Both versions offer different COP, being 0.87 and 0.83 each. Fig. 8 shows the COP of the cascade systems with a parallel compression cycle in high or low stages. The remaining combinations (twenty) are covered by this subsection, reaching 42 configurations studied in this article.

Cascade systems with parallel compression
The resulting COP for a parallel compression cycle in both stages is 0.71. By incorporating an economizer, the COP does not vary significantly, 0.72. These results are because the consumption of the second compressor is relatively low due to the cascade cycle. In addition, the parallel compression makes the consumption of the first compressor also low because of the reduced mass flow rate.
This system in parallel compression can, in turn, be combined with the rest of the cycles in a stage. By combining a parallel compression system with a single-stage cycle, the COP is modified depending on cycle configuration. When combining parallel compression in HT and a singlestage cycle in LT, a COP of 0.69 is obtained. If an IHX is introduced, a COP of 0.68 is observed. In the case of placing the reverse, that is, the single-stage cycle in HT, an increase of COP to 0.75 is obtained and when introducing an IHX remains at 0.67.
When replacing the single-stage cycle with a more complex cycle such as the two-stage with liquid injection, a COP of 0.71 is obtained for the parallel compression cycle in HT and liquid injection in LT, while being the reverse, the COP stands at 0.66. On the other hand, adding a vapor injection improves each cycle. With a parallel compression cycle in HT and LT two-stage cycles with vapor injection, the COP increases concerning the liquid injection cycle, reaching 0.74. In contrast, a twostage cycle with vapor injection in HT improves COP to a lesser extent (0.72).
Similar results are observed when changing to an economizer in the parallel compression cycle. In this way, by having a single-stage cycle in LT, the result is 0.68, while in HT is 0.67. By introducing an IHX, COP keeps in 0.67 and 0.68, respectively.
When replacing the single-stage cycle with a two-stage with liquid injection cycle as in the previous case, a slight increase in the COP is observed, reaching 0.70 with liquid injection in LT. Instead, the liquid injection in HT causes lower COP (0.68), always maintaining the parallel compression with economizer in the other stage. Finally, when adding a two-stage cycle with vapor injection, in the case of LT, the COP is 0.74 and in HT 0.76.
The last two cycles analyzed are the combination of parallel compression with and without economizer. The parallel compression in HT and parallel compression with economizer in LT results in a COP of 0.73. In the other case, in parallel compression with economizer in HT and parallel compression in LT, the COP decreases to 0.70.

Intermediate cascade temperature
As previously mentioned, the COP of all cycles has been maximized by employing the optimum intermediate cascade temperature. Fig. 9 shows the values of the optimized LT condensation temperature for all possible combinations studied in this work.
As can be seen, most configurations have their optimum intermediate cascade temperature roughly midway between condensation and evaporation temperatures. However, some cycles have their optimum intermediate cascade temperature closer to the HT condensation or LT evaporation temperatures, as is the case of cycles with a vapor injection. A vapor injection causes a greater temperature lift in the component's stage. This effect occurs both when incorporating it only in HT and only in LT, and it can also be observed that this stage accounts for approximately 75% of the temperature lift. Most of the temperatures of these cycles tend towards the opposite side of the vapor injection. This effect is more evident in the case of LT, when cycles like S+V, I+V, or L+V have the optimal intermediate cascade temperature closer to 0 • C. A particularly striking case is the cycle with vapor injection in both HT and LT. In this case, the intermediate cascade temperature is placed approximately in the middle of the total temperature lift, -24 • C.

Mass flow rate
Mass flow rate is another essential parameter to analyze the operation of the cycles. In Fig. 10, a graph is shown with the mass flow rate results of 38 of the 42 cycles that can be calculated, considering that the LT cooling capacity required for all configurations is the same, 10 kW.
The stages that contain a vapor injection tend to a lower mass flow rate. Contrarily, the stages that include a single-stage tend to a higher mass flow rate. Also, the LT stages have a lower mass flow rate than HT. This is typical of the cascade cycles because the LT condenser heat exchange is higher than the evaporator, so the heat exchange of the HT evaporator must be higher as well as the mass flow rate.
On the other hand, the mass flow rates, including single-stage cycles, are worth mentioning. In the case of cycles with vapor injection, the mass flow rate is minimal because it only has a stage, but it is not viable due to high discharge temperature. The cycle with liquid injection has a very high mass flow rate. This is due to the properties of the refrigerant itself. To reach such low temperatures, it is necessary to use a refrigerant that does not work at high temperatures. Because of that, R-170 has a critical temperature close to the 30 • C of the condenser, at a reduced latent heat. When adding a vapor injection or a heat exchanger, the increase in the latent heat is considerable, causing the mass flow to decrease substantially.

Conclusions
The lack of studies in ultralow-temperature refrigeration makes this field yet to be optimized and analyzed. However, the sector has not been studied in-depth beyond basic two-stage cascade cycles or three-stage cascades. The operational and energy performance of many cycles have been simulated considering natural refrigerants R-170 and R-290 in the low-and high-temperature stages, respectively. The following conclusions can be summarized.
On the one hand, the need for a minimum two-stage system to obtain acceptable performance is clear, and that the ideal configuration is a cascade. This is because by adding more stages, the pressure lift of the compressors decreases. Consequently, the COP of the stages increases because of a lower compressor power consumption. If only a cascade based on single cycles is preferred, an IHX is not a viable option. Incorporating the two-stage cycle with liquid injection causes an increase in the COP that is even higher when incorporating a vapor injection. Also, the two-stage cycle with vapor injection has a remarkable energy performance. Still, the lack of refrigerant capable of working with such a large temperature lift causes very high discharge temperatures and is unacceptable.
Other conclusions related to these technologies are that the vapor injection works at higher energy performance in the LT stage than in the HT stage. The parallel compression cycle improves the results of a singlestage cycle, but is not enough to be considered. In addition, the use of a compressor for the entire stage, being LT or HT, makes it expected to have a shorter useful life as it has a higher workload than the rest. Another critical aspect is the impossibility of using a parallel compression cycle with an economizer if the temperature lift is very high and requires a refrigerant that cannot work at standard or high temperatures.
To sum up, the cycles with the highest energy performance are two-stage with vapor injection in LT. Single-stage, single-stage with IHX and two-stage with liquid injection in LT with two-stage with vapor injection in HT offers the highest COP (0.89 and 0.87 the last one), 43.5 % higher with the same refrigerants than a two-stage cascade cycle based on single-stages (COP of 0.62). Parallel compression cycles offer a COP between 20 % and 30 % worse than those mentioned above. Cycles with single-stage with IHX offer similar COP to the single-stage cycles, making the IHX unnecessary. Future research can study the influence of other refrigerants (pure and mixtures) on the energy and operational performance of the proposed cycles, particularly the most promising ones. Moreover, the energy performance must be validated through measurements in an experimental setup. A multi-parameter evaluation involving exergy, environmental, and economic (or its combination) analyses could enrich and complement the assessment provided in this paper.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.