## 4 Component Design  
### Turbomachinery Design  
The turbomachinery was designed to arrange components optimally and to conduct the off-design analysis by predicting the performance for the modified partial heating cycle with SA heat. It is generally known that in case of small scale power conversion systems under a few tens of MW level, radial turbomachinery is suitable since the volumetric flow rate of working fluid is relatively low enough to use axial turbomachinery. Argonne National Laboratory (ANL) has suggested suitable design choices for designing S-CO\({}_{2}\) turbomachinery. The ANL also presented that small scale turbomachinery of S-CO\({}_{2}\) system is better to design with radial type [25]. Therefore, the radial type turbomachinery was selected for component design of the modified partial heating cycle with SA heat. In this turbomachinery design study, the [PERSON]'s diagram known as the most useful turbomachinery preliminary design method was utilized for the design prediction [26]. The base parameters of turbomachinery design can be easily obtained with the specific speed (n\({}_{s}\)) and diameter (d\({}_{s}\)) since [PERSON]'s diagram suggests optimal values. Additionally, it represents the efficiency of turbomachinery depends on specific speed as shown in Figure 21. Table 10 shows the turbomachinery design results such as stages, impeller diameter and rotational speed for the designed operating condition by using the [PERSON]'s diagram with the non-dimensional numbers. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Cycle Layout**} & **Optimal CO\({}_{2}\) Mass Flow Rate (kg/s)** & **Number of** & **Total** & **Waste** & **Cycle Net** & **Net** & **Protocol** & **WHRI** \\  & **Mass Flow** & **HX/Turb./** & **Heat** & **Recovery** & **(\%)** & **(\%)** & **(\%)** \\ \hline (1-1) Simple recuperated cycle & 12 & 3/1/1 & 6.23 & 2.55 & 20.20 & 515 & 11.6 \\ \hline (1-2) Simple recuperation cycle & & & & & & & \\ with SA heat & 16 & 4/1/1 & 7.58 & 3.21 & 17.67 & 568 & 12.8 \\ \hline (2-1) Recompression cycle with SA heat & 18 & 5/1/2 & 8.29 & 3.45 & 17.65 & 613 & 13.8 \\ \hline (3-1) Partial heating cycle & 16 & 4/1/1 & 8.17 & 3.63 & 16.73 & 607 & 13.7 \\ \hline (3-2) Partial heating cycle with SA heat & 18 & 4/1/1 & 8.46 & 3.70 & 16.67 & 616 & 13.9 \\ \hline (3-3) **Modified partial heating cycle with SA heat** & 20 & 4/1/1 & 8.99 & 3.91 & 16.47 & **645** & **14.5** \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Main characteristics comparison with S-CO\({}_{2}\) cycles for a bottoming cycle. The specific speed and diameter:  
\[n_{\mathrm{s}}=\frac{\omega\sqrt{V_{1}}}{\left(gH_{ad}\right)^{3/4}},\quad d_{ \mathrm{s}}=\frac{D(gH_{ad})^{1/4}}{\sqrt{V_{1}}} \tag{5}\]  
The performance maps prediction was obtained with the in-house code KAIST-Turbomachinery Design (KAIST-TMD [27]. The turbomachinery design method of the KAIST-TMD code is a one dimensional mean-line analysis including a real gas approach for overcoming the limitation of conventional turbomachinery design tools near the S-CO\({}_{2}\) critical point. The reliability of the 1D turbomachinery code depends on choice of loss models. The loss model combination for radial compressor was validated with S-CO\({}_{2}\) compressor test data [28]. However, due to the lack of S-CO\({}_{2}\) turbine test data, the loss model combination for radial turbine was validated with test data of air radial turbine. Although S-CO\({}_{2}\) has a higher Reynolds number than air, it is acceptable to utilize air turbine data as an alternative, because the effect on turbine performance can be ignored over half a million in Reynolds number and S-CO\({}_{2}\) behaves like ideal gas in turbine operation range [29]. The performance map results such as pressure ratio and efficiency of the turbomachinery for the modified partial heating cycle with SA heat was calculated using the KAIST-TMD code and are shown in Figures 22-25.