Two-stage cascade configurations based on ejectors for ultra-low temperature refrigeration with natural refrigerants

Research in ultra-low temperature refrigeration applications has intensified in recent years after the appearance of vaccines in response to the COVID-19 pandemic. There are few current technologies for this low-temperature range, with reduced energy performance and high global warming potential refrigerants. This work analyses the introduction of the ejector in two-stage cascade cycles for ultra-low temperature refrigeration. The proposal includes the assessment of the behaviour of the ejector while implementing it in a single stage or simultaneously in both stages. The study is carried out with refrigerants R-290 in the high-temperature stage and R-170 in the low-temperature stage since these are natural refrigerants with very low global warming potential. The results show that the ejector is a component that causes improvements in the cycle when placed in the high-temperature and low-temperature stages. On the other hand, changing evaporation and condensation temperatures, the evaporation temperature is more critical regarding cycle energy performance. With the results obtained, a cascade cycle with an ejector in both stages is proposed, obtaining a 21% higher coefficient of performance than the standard cascade cycle. Also, the cycle with the ejector in both stages causes an improvement of 13.6% compared to the previous generation's refrigerants (R-23 and R-507A) in the same cycle. The carbon footprint analysis shows that this cycle emits less than half of the equivalent CO2 than actual cycles for ultra-low temperatures, also with a new refrigerant like R-472A.


Introduction
Around − 80 • C, RNase (destruction of RNA), proteases (destruction of proteins), or phosphatases (dephosphorylation) happen slowly. Therefore, the number of ultra-low temperature freezers of different capacities has increased worldwide due to their application for preserving unstable RNA solutions, liquid nitrogen (LN 2 ) snap-frozen tissues, and protein extracts [1]. However, several sustainable development goals are fostered by cold chains, including supplying vaccines and reducing greenhouse gas emissions [2]. Materials and methods are being designed to improve cooling technologies, meet the temperature needs of facilities, and reduce harmful emissions [3]. Sun et al. [4] highlighted the need for a quick, effective, secure, and safe ultra-low temperature refrigeration solution to mitigate the challenges faced by the distribution logistics of vaccines based on mRNA and lipid nanoparticles.
Systems working at these temperatures are called ultra-low temperature (ULT) refrigeration applications [5]. Because of the low temperature of the heat source and considering the ambient as the heat sink, the efficiency of these systems is reduced if compared with other cooling applications. The increase of the energy efficiency of refrigeration applications is achieved by reducing the electricity consumption [6]. Mota-Babiloni et al. [7] observed that two-stage cascade and auto-cascade configurations are the most common option for freezers down to − 86 • C. Besides ULT refrigeration, two-stage cascades are considered in high-temperature heat pumps for industrial purposes [8].
Wang et al. [9] experimentally researched the two-stage ULT cascade system pull-down performance with a liquid-to-suction heat exchanger in the low-temperature cycle, highlighting the superheating degree in the rapid cooling phase and the evaporation and condensation pressures in the stable one. Song et al. [10] analysed a system with a heat collector in the same cycle but focusing on the refrigerant mass, zeotropic component fraction, and heat collector opening on the discharge temperature.
Several attempts have been made to replace the traditional two-stage ULT cascades composed of greenhouse gases R-404A/R-23 (Global Warming Potential, GWP, of 14,000). To mention a few examples, Xu et al. [11] compared CO 2 sublimation and conventional R-23 cycles and achieved 600 W cooling capacity at the sublimation temperature of − 79 • C. Still, the CO 2 sublimation cycle COP was lower (despite the future potential for system optimisation). Bai et al. [12] proposed an R-170/R-290 Joule-Thomson cycle for − 60 • C refrigeration and recommended reducing the operating pressure and compression ratio to improve the possibilities of this arrangement.
Regarding new working fluids for two-stage ULT cascade refrigeration cycles, Rodriguez-Criado et al. [13] retrofitted a standard low-temperature R-290 packaged unit to use R-170. For a cold room temperature of − 80 • C and − 65 • C, the COP ranged from 0.6 to 1.6. Winkler et al. [14] tested the new mixture R-473A in an environmental test chamber with a compressor and expansion valve retrofit. High-temperature stability but a lower performance was measured regarding the pull-down speed and the minimum achieved chamber temperature. Sun et al. [15] theoretically studied 28 refrigerant cascade pairs, recommending R-41/R-161 and R-170/R-161 attending to COP and thermodynamic performance results. Gong et al. [16] compared mixtures for − 80 • C refrigeration and recommended the R-170/R-116 binary mixture considering COP, cooling capacity, compression ratio and discharge temperature. Similarly, Sun and Wang [17] compared two and three-stage cascade refrigeration cycles in five different climate zones of China. Above − 80 • C, two-stage cycles presented an annual total power consumption around 10% lower than three-stage cycles. Faruque et al. [18] considered trans-2-butane combined with toluene, cyclopentane, and cis-2-butane in a parametric analysis. The trans-2-butane/toluene pair resulted in the best overall performance and was recommended to replace refrigerant pairs R-717/R-23, R-152a/R-23, R-41/R-404A, R-23/R-404A, R-744/R-717, R-13/R-717, R-13/R-134a, R-41/RE-170 and R-41/R-601.
In a previous article, several configurations have been considered for ULT refrigeration, including liquid-to-suction heat exchanger, vapour injection, liquid injection, and parallel compression with and without an economiser. The conclusions were that the configuration selected for the high stage does not influence the two-stage cascade COP and that the liquid and vapour injection cascade configurations in the lowtemperature stage result in the highest COP, all using the R-290/R-170 pair [19]. Similarly, Bani Issa et al. [20] also recommended the R-290/R-170 pair in an economiser to a single-stage cascade configuration in which an MT evaporator is connected to an eight-way valve that can achieve a 92% average improvement compared to the reference configuration.
Ejectors have been considered in other refrigeration applications with promising results [21]. However, the influence of the ejector in two-stage cascades for ULT refrigeration has yet to be considered. Cao and Brake [22] observed that, unlike most refrigeration applications, ejectors at low temperatures are scarce, with a few works focusing on concept design, experimental investigation, and thermodynamic analysis. After reviewing different types of cascade refrigeration systems for ULT application, Kasi and Cheralathan [23] recommended configurations including an ejector. Moreover, studies for increasing the energy efficiency of these systems can be found in literature, such as Bai et al. [24]. They successfully added a liquid-to-suction heat exchanger with increased COP and exergy efficiency.
Mota-Babiloni et al. [7] concluded that using ejectors has recently been considered in research papers in auto-cascade architectures. Rodríguez-Jara et al. [25] thermodynamically evaluated natural refrigerants R-600a and R-1150 in auto-cascade ultra-low temperature applications, ranging from − 50 • C to − 100 • C. The ejector as an expansion device improved the COP up to 12%, with an optimal R-1150 mass fraction of 0.45. Contrarily, the ejector as a pre-compression stage did not show any improvement. Bai et al. [26] experimentally considered HFCs R-134a/R-23. They concluded that the ejector-enhanced auto-cascade refrigeration cycle had more advantages in terms of lower refrigeration temperature and higher coefficient of performance and exergy efficiency over conventional cycles.
In two-stage ULT refrigeration cycles, Li et al. [ capacity system to include an ejector applied in the first stage cycle. The energy consumption for the whole prototype is 4.8% lower than that of the baseline freezer at the ambient temperature of 25 • C. Liu and Yu [28] designed an ejector subcooling refrigeration cycle with promising theoretical results down to − 65 • C regarding COP, volumetric refrigeration capacity and exergy efficiency due to less throttling loss and improved lifted suction pressure. The ejector is a component that allows improvements in some thermodynamic cycles under particular operating conditions but can also have drawbacks. The literature review reveals previous works on autocascade and Joule-Thomson configurations that include ejectors for ultra-low temperature refrigeration. However, research is limited concerning two-stage cascades. Two-stage cascades, auto-cascade and Joule-Thomson cycles are architectures not comparable regarding operation principles, design, or analysis. Therefore, this article studies the impact of including an ejector for two-stage cascades used in ultralow temperature refrigeration. Different positions of the ejector are compared in terms of thermodynamics, environmental and economic aspects. The main parameters analysed are the coefficient of performance, volumetric cooling capacity, optimal cascade temperature, economic analysis and TEWI. Different refrigerants' influence on the two-stage cascade's low-temperature cycle is also analysed.

Methods
This section will explain the configurations on which this article is based, and the strategy used from the assumptions to the final model.

Configurations
This article studies the applicability of ejectors in a cascade cycle. Therefore, said ejector has been placed separately in the hightemperature stage and the low-temperature stage and also in both stages. Four cycles have been studied in Table 1.

Strategy
The simulation of the configuration with the ejector in LT and HT is based on the methods presented in Fig. 1. The input parameters are the stages, refrigerants, boundary conditions and assumptions for the configurations. The model is developed using Python with the REFPROP database.

Boundary conditions and assumptions
The cycle will refrigerate a cooling capacity of 10 kW to simulate medium-capacity refrigeration conditions present in ultralowtemperature rooms, more concretely at an evaporation temperature of -80 • C. The condensation temperature is set to 30 • C, a simulated controlled room condition temperature. 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.

Modelling common details
The common equations used in the modelling process are presented in this section.
The proposed cooling capacity is used as an input of the methodology. It calculates the mass flow rate of the low-temperature stage, Eq.
(1). Moreover, the mass flow rate of the high-temperature stage uses a heat balance in the cascade heat exchanger, in which all the heat in the LT condenser is transferred to the HT evaporator.
The isentropic efficiency Eq. (2) is expressed in terms of compression ratio Eq. (3). The proposal of Udroiu et al. [19] has been used. This proposal analysed the behaviour of commercial compressors using information available in their software. This model is also valid for R-170 [13] To calculate the thermodynamic stage at the compressor's discharge, the isentropic efficiency has been used, Eq. (4).
The power consumption has been calculated as the sum of each power compressor consumption, Eq. (5).
Compressor power consumption is the product of mass flow rate and the enthalpy difference, Eq. (6).
The coefficient of performance (COP) of the two-stage cascade is the relation between the low-temperature cooling capacity and total power consumption, Eq. (7).
The intermediate cascade temperature is optimised to maximise COP.

Ejector model
The ejector is a component that is still under study and development. Due to this, based on the existing proposals [29][30][31][32], a computational model has been developed to calculate the ejector operation that is as reliable as possible. A constant-pressure mixing model is adopted. Ejector efficiencies are considered constant at 0.8.
In the ejector model, the principal value to determine is the entrainment ratio, which is the ratio of the secondary and primary fluid mass flow rates. The initial value is assumed to be adjusted in subsequent calculations, Eq. (8).
The ejector model is based on the enthalpy and velocity of the different parts of the component. First, the outlet velocity of each nozzle can be calculated with the inlet enthalpy and the outlet isentropic enthalpy with the nozzle efficiency, Eq. (9).
In the mixing chamber, operational conditions and thermodynamic stages can be calculated with the energy and momentum conservation equations, Eq. (10) and Eq. (11).
For the ejector outlet conditions, the diffuser enthalpy can be calculated with the enthalpy and the velocity of the mixing chamber, Eq. (12).
The outlet pressure of the diffuser can be determined with the ideal specific enthalpy and the ideal entropy at the diffuser outlet, Eqs. (13), (14) and (15). The mixing process pressure is assumed to be constant.
With the outlet conditions, the initial value can be modified using a condition based on the vapour quality in the ejector outlet, Eq. (16).

Model validation
The proposed model has been validated with data shown in the literature. Specifically, Sarkar's [33] work has been used by validation with COP [34,35]. Fig. 2 shows the agreement between the proposed and Sarkar models. The maximum deviation is 0.169 with a mean of 0.106, which is 2.12%, an acceptable deviation for an ejector model.

Economic model
The cascade heat exchanger model is shown in Eq. (19) [36].
Eq. (20) shows the flash tank cost based on the total volume. The thermostatic expansion valve cost depends on the mass flow rate through this element, Eq. (21). The ejector has set a fixed cost because it is a recently developed element and cost based on capacity is not still available.

TEWI
The COP of a refrigeration application is an important parameter to compare the performance between configurations, but insufficient for the equivalent carbon footprint. Because of that, a TEWI (Total Equivalent Warming Impact) analysis is necessary for a more comprehensive evaluation. The TEWI analysis considers direct emissions from refrigerant leaks or recycling and indirect emissions from the generation of electricity that feeds the cycle, Eq. (22).
Being a cascade cycle, the total TEWI has been taken as the sum of the TEWI of each stage (23). (23) The different parameters of the TEWI calculation are based on the data from the installation. The leakage percentage has been taken at 5% with a 15 years lifetime period. After the end of the useful life, a recycling rate of 85% has been proposed. These data are those offered by the International Institute of Refrigeration [37]. The emission factor in European Union has been considered the emission factor 0.229 kgCO 2 e kWh − 1 [38].

TEWI = TEWI HT + TEWI LT
The TEWI analysis has been included to compare the case where the ejector is included in both stages with R-170 and R-290 and the singlestage cascade cycle with R-23 and R-507A representing a commercially available ultra-low temperature refrigeration solution. Also, new refrigerant blend R-472A is included in the simulation.

Refrigerants
This work focused on two natural refrigerants due to the saturation pressure-temperature values and operational characteristics: R-170 (ethane) for the LT stage and R-290 (propane) for the HT stage. The working fluids' main properties (physical, chemical, toxicological, and environmental) are included in Table 2.
An important aspect is that both refrigerants have a very low GWP [39], so they are future-proof natural refrigerants that environmental regulations will not restrict. The 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 vaporisation enables them to be refrigerants with a considerable expected refrigerating effect. Moreover, they can be used with different commercially available lubricating oils. A significant restriction is flammability, for both refrigerants could be taken additional measures depending on the final refrigerant charge and the installation location because they are highly flammable (A3).

Results
This section presents the main results of the cycles, focusing on the main parameters of interest: entrainment ratio, mass flow rate, specific compressor work, COP, volumetric cooling capacity, temperature, and equivalent carbon dioxide.

Impact of ejector
This subsection shows the results when the ejector is used in both stages (E + E). In this configuration, the resulting coefficient of performance (COP) is 0.75. Therefore, this is an increase of 21% compared to a two-stage cascade based on basic cycles and considering the same refrigerants (0.62 COP).
Another interesting parameter to analyse is the entrainment ratio, as discussed in the Methods section. This parameter initially assumes a value and then is recalculated. This adjustment for the LT stage is shown in Fig. 3, where the final value of the entrainment ratio is located at the intersection of both lines.
In terms of COP, the ejector allows an improvement in whatever stage it is placed in. Fig. 4 shows the COP in the three possibilities analysed and the cycle with the single stages. In both cycles, with an ejector in the LT stage and basic cycle HT stage and a cycle with an ejector in the HT stage and single LT stage, the COP is 0.68. In the cycle with ejector in both stages, the increase is even higher, 0.75.
These results indicate that the highest increase in energy performance is observed with the ejector in each stage, besides the circuit selected. Consequently, the cycle can be improved using the ejector in which the stage is preferred in terms of economy, components availability or compatibility, or control, amongst other design considerations. Then, an additional increase is obtained with the ejector in both stages.
The ejector presents a particular characteristic, combining two lines with different mass flow rates, as seen with the entrainment ratio formula. There, the condenser line has a higher mass flow rate than the line from the evaporator. This is not a challenge in single-stage cycles, but in cascade cycles, a higher condensation LT stage mass flow rate influences the HT stage mass flow and, therefore, the resulting compressor consumption.
Because of that, the evaluation of the mass flow rate is essential. Fig. 5 and Fig. 6 show the mass flow rate values in evaporators and compressors or condensers, respectively. The mass flow rate through the evaporator in the HT cycle decreases with the addition of ejectors (33%).
In the case of stages with ejectors in LT, this component allows a decrease of 28% in the evaporator mass flow rate, which is necessary to compensate for the cooling capacity. This increase is fundamental  Fig. 3. Entrainment ratio adjustment process.
because of the flash tank before the evaporator. On the other hand, the mass flow rate in the compressor is increased with the ejector because of the entrainment ratio. But this increment in the LT stage is negligible (0.6%). The HT compressor mass flow rate is lower when the LT stage is composed of an ejector cycle, the decrease is 5.5%, but for the ejector in the HT stage, the increment is also negligible.
A significant benefit can be seen in the specific compression work as it is reduced when the ejector is placed in the same stage (Fig. 7), which allows a compressor consumption reduction. This decrease is comparable in both stages, 15.7% in the HT stage and 15% in the LT stage.

Optimal intermediate cascade temperature
The intermediate temperature of cascade cycles is an essential parameter to analyse for optimisation of the cycle. Because of that, the influence of intermediate (or cascade) temperature variation in COP of the cycle with ejector in both stages has been analysed at − 80 • C evaporation temperature and 30 • C condensation temperature while keeping the same assumptions mentioned in the Methods section, Fig. 8.
As can be seen, the COP is maximised at the midpoint between the evaporating and condensing temperatures. If the intermediate temperature is not placed at the optimum point, the COP can be reduced by around 12.7% (15 • C difference regarding the optimum intermediate temperature). If the intermediate temperature presents a difference of 5 • C from the optimum temperature, the reduction is only 0.6%. Therefore, the difference between the design and optimum intermediate temperatures significantly influences the COP. The sign of the deviation in the intermediate temperature designed (higher or lower than the optimum temperature) has not influenced the magnitude of the COP decrease.
This analysis has been carried out also considering different evaporation and condensation temperatures, resulting in a similar conclusion in all conditions. Consequently, this study avoids additional calculations or analysis in designing and optimising for future two-stage cascades based on ejectors. It highlights the relevance of a proper intermediate

Volumetric cooling capacity
The VCC is a parameter that can be used to compare the compressor size required for each configuration or refrigerant combination. It is expressed in terms of energy per cubic metre; the higher the VCC, the lower the mass flow rate at the same energy or the higher the energy at the same mass flow rate. The VCC values for the set conditions and the proposed configurations are shown in Fig. 9.
The number of ejectors impacts the VCC values. Achieving a more substantial increase in the case of being placed in both stages, precisely an increment of 21.9%. If only one ejector is placed, the result is similar independently to the stage considered, and the VCC is 10.5% higher than the two-stage cascade.

COP according to operational temperatures
ULT conditions for refrigeration applications are considered from − 50 • C, and most ultra-low temperature freezers can operate between that temperature and approximately − 90 • C. Additionally, the condensation temperature depends on the location and conditions of the installation. Because of that, the study of energy performance has been extended to consider different evaporation and condensation temperatures. The COP in ULT is usually below 1, and it causes a significant impact on the operational costs of a freezer. Fig. 10 shows the COP variation at different LT cycle evaporation and HT cycle condensation temperatures of the cycle with the ejectors.
The COP decreases for higher temperature lifts, following the Carnot statement. When the condensation temperature changes from 10 • C to 40 • C at − 80 • C evaporation temperature, a 39% COP decrease is observed (0.65 COP). The evaporation temperature affects COP values more than the condensation temperature. For example, this can be observed at a 90 • C temperature lift, at an evaporation temperature of − 80 • C and at a condensation temperature of 10 • C; the COP is around 1. On the other hand, at an evaporation temperature of − 50 • C and a condensation temperature of 40 • C, the COP is around 1.4 (40% higher), both at a 90 • C temperature lift. Besides, increasing evaporation temperature from − 80 • C to − 50 • C at 10 • C condensation temperature causes a 94% COP increment (2.06 COP). The significant COP variation emphasises the relevance of a proper operational temperature selection and heat exchanger design. The minimum COP observed can be considered low, but still, it is higher than values typically registered for conventional two-stage cascade ULT applications.

Economic comparison
The cost of different configurations has been compared in Fig. 11, specifying the cost for each component and comparing the cost of each configuration to a conventional two-stage cascade cycle.
The prices have been estimated with manufacturers' costs particularising the necessary parameters of each component. Compressors represent more than half of the total cost but decrease the influence on the cost for advanced configurations (from 59% to 54%). As can be seen,  the cost differences are slight when considering advanced configurations. This is because the compressor cost savings offset the cost increase because of the volumetric cooling capacity explained before. Moreover, the ejector is a component whose cost is relatively low compared to other components of the cycle for this range of cooling capacity; therefore, its inclusion does not mean a significant increase in the total cost of the application.

Comparison with third generation refrigerants
The refrigeration industry is currently transiting from the third to the fourth generation of refrigerants. Therefore, hydrofluorocarbons are being phased down in favour of natural refrigerants and hydrofluoroolefines (and mixtures). European legislation exempts ultra-low temperature cycles (refrigeration below − 50 • C) but investigating environmentally friendly alternatives is also urgent. In this work, the cascade cycle with an ejector in both stages has been calculated with R-290 and R-170.
COP was calculated considering third-generation synthetic refrigerants, R-507A in the HT stage and R-23 in the LT stage at − 80 • C evaporation temperature and 30 • C condensation temperature while keeping the same assumptions mentioned in the Methods section. The E + E configuration based on third-generation refrigerants results in a COP of 0.66, 12% lower than the value of 0.75 obtained with the same configuration and natural refrigerants R-170 and R-290. Therefore, this statement highlights low GWP refrigerants as highly efficient alternatives besides the climate protection characteristic of natural refrigerants and low impact. As a higher COP is obtained, there are no objections  regarding energy efficiency for transiting to the fourth-generation refrigerants when considering configurations that include ejectors. Table 3 shows the different results of the carbon footprint analysis based on the TEWI. In this section, the new refrigerant blend for ULT applications R-472A is also included in the simulation. Besides natural refrigerants, there is a possibility to use synthetic fluids with low GWP in thermodynamic systems for high energy efficiency and low carbon footprint [40].

Carbon footprint assessment
The TEWI analysis for − 80 • C evaporation temperature and 30 • C condensation temperature shows that the cycle with ejector in both stages with R-290 and R-170 refrigerants (E + E) emits less than half (-57.5%) of the equivalent CO 2 than actual cycles for ultra-low temperatures (S + S), and also 17.1% less than R-290/R-472A ejector twostage cascade (E + E).
Even though the refrigerant mass charge is similar or even higher in the proposed configuration, the GWP of natural refrigerants is ultra-low. Moreover, the GWP of the synthetic refrigerants traditionally used in ultra-low temperature refrigeration is relatively high (around 14,000 for R-23 and around 4000 for R-507A). This causes direct emissions for the proposed configuration to be almost negligible. Considering refrigerants R-507A and R-23, the direct emissions represent 15% of total emissions. Given the low COP compared to other refrigeration applications, indirect emissions are remarkable in all configurations even though the carbon emission factor considered was the average of the EU, so it can be considered intermediate. If countries with higher carbon emission factors were considered, the impact of indirect emissions would be even more critical. The high reduction in emissions urges the transition to higher efficiency and low global warming potential refrigerants in the analysed application, as it is being done in other refrigeration units.

Conclusion
Studies show that refrigeration at such low temperatures requires cascade systems, and new cascade configurations can enhance energy performance. Currently, ultra-low temperature refrigeration systems based on cascades are already used, but with limited performance and use high global warming potential refrigerants. Therefore, this paper proposes implementing ejector technology with natural refrigerants R-170 and R-290 to achieve superior performance in two-stage cascade ultra-low temperature refrigeration. Ultra-low temperature refrigeration is considered from − 50 • C using different temperatures depending on the needs. Due to this, the behaviour of the proposed cycle in the evaporation temperature ranges from − 50 • C to − 80 • C has been studied. On the other hand, the condensation temperature will depend on where the cycle is located. This also leads to analysing the condensation temperature variation from 10 • C to 40 • C.
The ejector is a component that increases the cascade cycle performance in all cases by placing it in the low-temperature and hightemperature stages. Moreover, the energy performance is further augmented by being placed in both stages simultaneously. It is observed to offer a 21% improvement over the simple cascade cycle using the same refrigerants (0.75 and 0.62 of COP, respectively). By placing the ejector in a single stage, the improvement is 9.6% over the same cascade cycle (0.68 and 0.62 of COP, respectively). In addition to higher performance, the cascade cycle with ejectors allows a smaller compressor, resulting in a higher volumetric cooling capacity, precisely, a 21.9% VCC increase.
The cycle energy performance will be higher at a lower temperature lift, as observed in the results. However, for the two-stage cascade based on ejectors, the evaporation temperature affects performance to a greater extent than the condensation temperature. It can be concluded that the evaporator should prioritise investment and advanced design over the condenser. The intermediate temperature of the cascade is also a fundamental value to optimise. Studying the variation of performance according to the said intermediate temperature, it is observed that the COP is maximised by setting the intermediate temperature at the midpoint between evaporation and condensation. Also, a variation of 5 • C, the optimum temperature, has only 0.6% influence on COP. This facilitates the optimisation by avoiding extra calculations as in other cascade cycles.
The proposed cycle with refrigerants also has a higher performance than using greenhouse gas refrigerants of the previous generation (R-23 and R-507A), as the COP is 13.6% higher when considering natural refrigerants (0.66 and 0.75, respectively). Also, the ejector does not increase the total investment cost significantly. Finally, the TEWI analysis shows that the cascade cycle with ejector in both stages emits less than half (-57.52%) of the equivalent CO 2 than actual cycles for ultra-low temperatures, and also 17.14% less than R-290/R-472A ejector twostage cascade.

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.

Data availability
Data will be made available on request.