# A Theoretical Comparative Study of CO\({}_{2}\) Cascade Refrigeration Systems
## 3 Results and Discussion
### Yearly Energetic and Environmental Analysis
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Refrigerants**} & \multicolumn{4}{c}{**Yearly Mean COP**} \\ \cline{2-5}  & \(T_{e}=-35\)\({}^{\circ}\)C & \(T_{e}=-25\)\({}^{\circ}\)C & \(T_{e}=-15\)\({}^{\circ}\)C & \(T_{e}=-5\)\({}^{\circ}\)C \\ \hline CO\({}_{2}\)/CO\({}_{2}\) & 1.901 & 2.436 & 3.183 & 4.315 \\ NH\({}_{3}\)/CO\({}_{2}\) & 2.362 & 3.075 & 4.097 & 5.712 \\ R290/CO\({}_{2}\) & 2.372 & 3.067 & 4.064 & 5.636 \\ R600a/CO\({}_{2}\) & 2.364 & 3.072 & 4.088 & 5.693 \\ R600/CO\({}_{2}\) & 2.362 & 3.075 & 4.097 & 5.712 \\ R1270/CO\({}_{2}\) & 2.377 & 3.070 & 4.064 & 5.631 \\ R1234 yf/CO\({}_{2}\) & 2.310 & 3.001 & 3.991 & 5.552 \\ R1234 ze(E)/CO\({}_{2}\) & 2.336 & 3.040 & 4.050 & 5.645 \\ R152a/CO\({}_{2}\) & 2.381 & 3.092 & 4.112 & 5.722 \\ R450A/CO\({}_{2}\) & 2.304 & 2.996 & 3.987 & 5.547 \\ R513a/CO\({}_{2}\) & 2.320 & 3.014 & 4.008 & 5.576 \\ R32/CO\({}_{2}\) & 2.346 & 3.036 & 4.023 & 5.578 \\ R448A/CO\({}_{2}\) & 2.293 & 2.973 & 3.947 & 5.477 \\ R134a/CO\({}_{2}\) & 2.341 & 3.043 & 4.049 & 5.637 \\ R407C/CO\({}_{2}\) & 2.265 & 2.937 & 3.895 & 5.399 \\ R227 ea/CO\({}_{2}\) & 2.255 & 2.944 & 3.929 & 5.483 \\ R404A/CO\({}_{2}\) & 2.273 & 2.946 & 3.909 & 5.421 \\ R507A/CO\({}_{2}\) & 2.278 & 2.953 & 3.918 & 5.434 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Yearly values of the mean COP for the examined cases. Figure 9: Mean yearly COP of four cases for different evaporator temperatures. harmful scenarios. This is an extremely important result which makes the use of another refrigerant in the high-temperature circuit, except the CO\({}_{2}\), to be an environmental need. Discussing some typical values, the TEWI for CO\({}_{2}\) is 1659.2, while the minimum value is 1326.8 for R1270 in the high-temperature circuit. The second choice is R290 with 1330.3, while R600a has 1334.6. NH\({}_{3}\), R600, R152a, R1234 yf and R1234 ze(E) present similar values and they are also acceptable choices. The highest TEWI is 2002.0 for R507C, while R404a has 1995.3. Other usual refrigerants are R134a and R32 which has TEWI equal to 15.68.9 and 1448.8 respectively. Figure 11 exhibits the TEWI for different evaporator temperatures. The values of the TEWI are lower for higher evaporator temperature because of the increase in the COP. The direct emissions are \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Refrigerants**} & \multicolumn{4}{c}{**TEWI (CO\({}_{2,\text{eq}}\) Tones)**} \\ \cline{2-5}  & \(T_{e}=-35\)\({}^{\circ}\)C & \(T_{e}=-25\)\({}^{\circ}\)C & \(T_{e}=-15\)\({}^{\circ}\)C & \(T_{e}=-5\)\({}^{\circ}\)C \\ \hline CO\({}_{2}\)/CO\({}_{2}\) & 1659.2 & 1294.6 & 990.9 & 731.1 \\ NH\({}_{3}\)/CO\({}_{2}\) & 1335.1 & 1025.7 & 769.8 & 552.1 \\ R290/CO\({}_{2}\) & 1330.3 & 1028.9 & 776.7 & 560.1 \\ R600a/CO\({}_{2}\) & 1334.6 & 1027.1 & 772.0 & 554.5 \\ R600/CO\({}_{2}\) & 1335.7 & 1026.3 & 770.5 & 552.8 \\ R1270/CO\({}_{2}\) & 1326.9 & 1027.4 & 776.3 & 560.4 \\ R1234 yf/CO\({}_{2}\) & 1366.2 & 1051.6 & 790.9 & 568.7 \\ R1234 ze(E)/CO\({}_{2}\) & 1351.0 & 1038.2 & 779.6 & 559.7 \\ R152a/CO\({}_{2}\) & 1343.9 & 1039.2 & 786.3 & 570.5 \\ R450A/CO\({}_{2}\) & 1461.8 & 1145.7 & 884.3 & 661.8 \\ R513a/CO\({}_{2}\) & 1457.0 & 1144.0 & 884.5 & 663.3 \\ R32/CO\({}_{2}\) & 1448.8 & 1143.6 & 888.6 & 670.0 \\ R448A/CO\({}_{2}\) & 1573.0 & 1258.0 & 996.5 & 773.2 \\ R134a/CO\({}_{2}\) & 1568.9 & 1258.0 & 1000.6 & 781.2 \\ R407C/CO\({}_{2}\) & 1667.6 & 1348.9 & 1084.6 & 859.1 \\ R227 ea/CO\({}_{2}\) & 1894.6 & 1567.4 & 1298.7 & 1071.3 \\ R404A/CO\({}_{2}\) & 1995.3 & 1678.3 & 1414.8 & 1189.7 \\ R507A/CO\({}_{2}\) & 2002.0 & 1685.7 & 1422.7 & 1198.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Total equivalent warming impact for the examined cases. Figure 10: TEWI of the examined systems for \(T_{e}=-35\)\({}^{\circ}\)C.  
the same for all the evaporator temperatures while the indirect TEWI has a decreasing rate with the evaporator temperature increase.