## 3 Results and Discussion  
### Reference System Performance  
The reference was a simple vapor compression transcritical cycle with CO\({}_{2}\) as the only working fluid. The system was examined for twenty different operating scenarios and the performance results are depicted in Figure 5. This figure illustrates the COP and the exergy efficiency of the examined cases and these results correspond to optimized operation. In this case, the optimization was conducted \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{4}{c}{**Initial Data**} & \multicolumn{3}{c}{**Results**} \\ \hline
**T\({}_{\text{c}}\)** (\({}^{\circ}\)C)** & **P\({}_{\text{high (bar)}}\)** & **T\({}_{\text{c}}\)** (\({}^{\circ}\)C)** & **\(\Delta\)T\({}_{\text{sc}}\)** (\({}^{\circ}\)C)** & **CO\({}_{\text{exp}}\)** & **CO\({}_{\text{sim}}\)** & **Deviation** \\ \hline
0.0 & 82.8 & 28.36 & 0.00 & 2.57 & 2.612 & 1.63\% \\
0.0 & 89.6 & 33.51 & 0.00 & 1.93 & 2.063 & 6.89\% \\
0.0 & 102.6 & 41.69 & 0.00 & 1.32 & 1.372 & 3.94\% \\ \(-\)10.0 & 77.6 & 27 & 0.00 & 1.91 & 1.897 & 0.68\% \\ \(-\)10.0 & 82.5 & 32.79 & 0.00 & 1.44 & 1.477 & 2.57\% \\ \(-\)10.0 & 101.9 & 41.09 & 0.00 & 0.98 & 0.933 & 4.80\% \\
0.0 & 78.6 & 29.71 & 13.28 & 2.85 & 3.090 & 8.42\% \\
0.0 & 81.6 & 34.78 & 12.07 & 2.35 & 2.581 & 9.83\% \\ \(-\)10.0 & 77.3 & 33.42 & 13.03 & 1.78 & 1.828 & 2.70\% \\ \(-\)10.0 & 107.1 & 40.48 & 15.62 & 1.27 & 1.211 & 4.65\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Checking the model validity using data from [25]. using only one optimization parameter, which was the pressure ratio parameter. Figure 5 shows that the COP increased with the increase of the evaporator temperature and with the decrease of the heat rejection temperature. On the other hand, the exergy efficiency was maximized for the evaporating temperature of \(-5\)\({}^{\circ}\)C, while it had a decreasing rate with the increase of the heat rejection temperature. The reason for the maximum exergy efficiency for T\({}_{\rm e}\) = \(-5\)\({}^{\circ}\)C is based on two factors; the different behavior of the COP and of the exergy factor (T\({}_{0}\)/T\({}_{\rm e}\) - 1) with the increase of the (T\({}_{\rm e}\)) (higher (T\({}_{\rm e}\)) leads to higher COP (see Figure 5)), but also to the lower exergy factor. The exergy efficiency is the product of these parameters, as it is given below using Equations (7) and (12):  
\[\eta_{\rm ex}=\rm COP\cdot\left(\frac{T_{0}}{T_{\rm e}}-1\right) \tag{16}\]  
So, the existence of an intermediate optimum temperature level at \(-5\)\({}^{\circ}\)C was a reasonable result because of the different behavior of the product factor with the (T\({}_{\rm e}\)) increase. The maximum exergy efficiency was 27.12% and it was obtained for (T\({}_{\rm e}\) = \(-5\)\({}^{\circ}\)C and T\({}_{\rm c}\) = \(35\)\({}^{\circ}\)C), whereas for this case the COP was 2.424. The previous results regard the optimum scenarios which have the optimum high pressure. Figures 6 and 7 show the exergy efficiency for different pressure ratio parameters and for various cases. Figure 6 gives results for the evaporating temperature of \(-15\)\({}^{\circ}\)C, while Figure 7 for the heat rejection temperature of 40 \({}^{\circ}\)C. It was obvious that, in all cases, there was an intermediate optimum pressure ratio parameter that leads to maximum exergy efficiency. It is remarkable to state that this optimum pressure ratio parameter leads also to maximum COP for the reference system because the exergy efficiency and the COP were proportional parameters for a constant (T\({}_{\rm e}\)) according to Equation (15). Figure 6 indicates that the optimum pressure ratio parameter changed for different heat rejection temperatures, and higher heat rejection temperatures needed higher pressure levels after the compressor for optimum operation. On the other hand, the optimum pressure ratio parameter is not so affected by the refrigeration temperature, as Figure 7 proves.