## 4 Results and Discussions  
The current study was conducted to analyze and optimize the recompression of the supercritical carbon dioxide cycle (sCO\({}_{2}\)-BC). A mathematical model was based on abrupt variations in the thermophysical properties of the sCO\({}_{2}\) The cycle was developed by coupling NIST's Refprop with the main cycle simulation code. Initially, the effects of the various cycle components such as the recuperator, compressor, and turbine performance were investigated on the overall performance of the sCO\({}_{2}\)-BC. Later, the effects of critical operating parameters on the cycle's performance were analyzed, i.e., \(T_{1}\), \(P_{1}\), \(Pr\), and \(x\). Lastly, these parameters were optimized using a genetic algorithm to maximize the overall performance of the sCO\({}_{2}\)-BC.  
For the validation of the code, current work was compared with the available data in the literature, as listed in the Table 4. This showed the computed results using the employed model are in close agreement with the published data.  
Figure 3: Schematic genetic algorithm.  
It can be seen from Figure 1 that the main flow stream after the high-temperature recuperator (HTR) divided into two creeks, i.e., 10a and 10b. The flow toward 10a with a split mass fraction \"\(\times\)\" was directed to the central compressor after passing through the cooler, while fraction \"\(1-x\)\" of the flow passed through the recompression compressor. This was done to avoid early pinching within the low-temperature recuperator. Split streams, which were 3 (after gaining heat from the LTR) and 5 (from the re-compressor) combined again, forming stream 4. There is an optimized value of \"\(x\)\" for any set of operating conditions for maximum cycle efficacy. Figure 4 shows how split mass fractions affect the cycle's performance and its components. It can be visualized that cycle efficiency increased at first with the rise in the value of split mass fraction \"\(x\)\", reaching a maximum value and then decreasing. Thus, only a single value of \"\(x\)\" exists for which the cycle's efficiency is maximum. The split mass fraction's optimized value corresponds to the minimum temperature difference between streams 3 and 5, as shown in Figure 5. Moreover, Figure 5 shows a variation in the values of \(T_{3}\), \(T_{5}\), and cycle efficiency with split mass fraction. Cycle efficiency was maximum for the split mass fraction value of 0.82, corresponding to a minimum difference, as shown by the dotted line. The effects of the split mass fraction on the component's power can also be seen in Figure 4. It can be seen here that the primary compressor's power increased with the surge in the value of split mass fraction, while that of the recompression compressor and turbine decreased.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Parameters** & **[PERSON] [4]** & **[PERSON] et al. [7]** \\ \hline \multirow{8}{*}{Employed conditions} & \(T_{1}\) & 305 K & 308 K \\  & \(P_{1}\) & 7692 kPa & 8190 kPa \\  & \(T_{7}\) & 823 K & 753 K \\  & \(P_{T}\) & 2.6 & 2.51 \\ \cline{1-1}  & Efficiency, main compressor & 89\% & 88.3\% \\ \cline{1-1}  & Efficiency, recompressor & 89\% & 88.3\% \\ \cline{1-1}  & Efficiency, turbine & 90\% & 93.4\% \\ \cline{1-1}  & Effectiveness, HTR & 96.3\% & 97.9\% \\ \cline{1-1}  & Effectiveness, LTR & 92.1\% & 96.1\% \\ \hline \multirow{4}{*}{Cycle Efficiency (literature)} & 45.27\% & 42.05\% \\ \cline{1-1}  & Cycle Efficiency & 46.37\% & 43.83\% \\ \cline{1-1}  & (current work) & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Model validation.  
Figure 4: Impacts of the split mass fraction on the cycle and its modules.