# A Theoretical Comparative Study of CO\({}_{2}\) Cascade Refrigeration Systems
## 1 Introduction
[PERSON] et al. [26] developed correlations for the performance of a cascade NH\({}_{3}\)/CO\({}_{2}\) system for a great range of operating conditions. Moreover, [PERSON] et al. [27] performed an advanced exergy analysis in a cascade NH\({}_{3}\)/CO\({}_{2}\) system and they optimized the system performance about 42.13%. In another study, [PERSON] et al. [28] found that the incorporation of an ejector in both circuits of a cascade NH\({}_{3}\)/CO\({}_{2}\) system leads to 8% lower exergy destruction. The use of R290 in the high-temperature circuit has been examined by [PERSON] et al. [29]. They designed a system for refrigeration and heating production. Their system includes internal heat exchangers and it is able to produce refrigeration at \(-40\)\({}^{\circ}\)C and heating at 120\({}^{\circ}\)C. Also, they examined their system exergetically and they tried to maximize the exergy performance of this system. The use of another natural refrigerant (R1270) has been examined by [PERSON] et al. [30]. They applied the R1270 in the low circuit, while the CO\({}_{2}\) in the upper-temperature circuit and they proved that \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Working Fluids** & **Classification** & **GWP (100 Years)** & **ASHRAE Safety Group** & **Limitations** \\ \hline R744 (CO\({}_{2}\)) & Natural refrigerant & 1 & A1 & Low COP \\ R717 (NH\({}_{3}\)) & Natural refrigerant & 0 & B2L & High Toxicity \\ R290 (propane) & HC (Natural refrigerant) & 3.3 & A3 & High flammability \\ R600a (iso-butane) & HC (Natural refrigerant) & 3 & A3 & High flammability \\ R600 (butane) & HC (Natural refrigerant) & 4 & A3 & High flammability \\ R1270 (propylene) & HO (Natural refrigerant) & 1.8 & A3 & High flammability \\ R1234 yf & HFO & 4 & A2L & Stability issues \\ R1234 ze(E) & HFO & 6 & A2L & Low flammability, \\  & & & & Stability issues \\ R152a & HFC & 124 & A2 & Intermediate \\  & & & & Flammability, Low GWP \\ R450A & HFO & 601 & A1 & High GWP \(>\) 150 \\  & & & & High GWP \(>\) 150 \\  & & & & Low flammability, \\  & & & & Medium GWP \\ R448A & HFO & 1273 & A1 & High GWP \\ R134a & HFC & 1430 & A1 & High GWP \\ R407C & HFC & 1774 & A1 & High GWP \\ R227 ea & HFC & 3200 & A1 & High GWP \\ R404A & HFC & 3922 & A1 & High GWP \\ R507A & HFC & 3985 & A1 & High GWP \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Refrigerants and their characteristics [20; 21; 22]. this configuration is better than the revere and better than the combination N\({}_{2}\)O/CO\({}_{2}\). The N\({}_{2}\)O is a refrigerant with relatively low critical points (\(\sim\)36 \({}^{\circ}\)C) and it has also studied by some researchers. More specifically, [PERSON] et al. [31] studied it in a system with ejectors, while [PERSON] et al. [32] in a conventional system. It is found that the N\({}_{2}\)O has similar performance compared to CO\({}_{2}\) because of the similar critical point temperatures [32]. R134a is another examined working fluid in the upper circuit. [PERSON] et al. [33] examined an R134a/CO\({}_{2}\) cascade refrigeration system and they found that the direct cascade system is more efficient than the indirect system with a difference up to 11%. Moreover, [PERSON] et al. [34] found that the R134a can be replaced by R152a without any efficiency cost in a CO\({}_{2}\)-based cascade refrigeration system. [PERSON] et al. [1] performed a detailed experimental investigation of an R134a/CO\({}_{2}\) cascade refrigeration system for evaporating temperatures between \(-40\) up to \(-30\)\({}^{\circ}\)C and condensing temperatures from 30 up to 50 \({}^{\circ}\)C. [PERSON] et al. [3] studied various refrigeration systems for supermarkets. They compared all the configurations with the cascade system. According to their results, the cascade configuration is one of the most effective systems energetically with the conventional booster system to have 20% higher energy consumption.