## 2 The Design of Single-Stage Centrifugal Compressor
### Throughflow Design of Compressor  
The main design parameters of the single-stage centrifugal compressor for the 1 MWe sCO\({}_{2}\) power cycle are shown in Table 2. The pseudo-critical temperature corresponding to the total inlet pressure of 8 MPa is 34.6 \({}^{\circ}\)C, while the total inlet temperature of the compressor is 35 \({}^{\circ}\)C, which is slightly higher than the pseudo-critical temperature and belongs to the supercritical gas-like phase. The estimated isentropic efficiency of the single-stage compressor is not less than 80%, under which the compressor input power is about 500 kW.  
Under the design parameters given in Table 2, the optimal working speed corresponding to the single-stage centrifugal compressor is about 49000 RPM (Ns = 0.6) [11]. However, in the actual design process, it is necessary to comprehensively consider factors such as bearings, compressor rotor dynamics design and assembly process. Referring to the operation experience of sandia, IST and TIT compressors, the compressor speed should not be too high, and the tip clearance should not be too large. The working speed of the compressor is set at 40,000 RPM and tip clearance is 0.25 mm.  
The small volume flow rate and the high-pressure ratio of the single-stage compressor lead to a small impeller blade height of 3.5 mm; the tip clearance is close to 10%. The main structural parameters of the semi-open impeller are shown in Table 3.  
Considering that the single-stage centrifugal compressor is mainly for experimental testing and variable inlet conditions, a vaneless diffuser is used and the radius ratio of the diffuser section is set at 1.7, which is constrained by the surge boundary and diffuser efficiency.  
Figure 2 further gives the beta and thickness distribution of the semi-open impeller, in which the blue line represents the hub and the red line represent the shroud, which is designed using an authorized commercial software (@ Concepts NREC). It is convenient to rebuild the impeller using the curve in Figure 2.  
Figure 3 shows the numerical simulation performance curve of the single compressor. The yellow point in the figure represents the compressor design point. As this numerical simulation calculation only includes the impeller and vaneless diffuser, and does not include the solute; the numerical simulation calculation results may be higher than the experimental performance.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Inlet** & **Inlet** & **Mass Flow** & **Pressure** & **Power** & **Isentropic** \\
**Pressure** & **Temperature** & **Rate** & **Ratio** & **Efficiency** \\ \hline
8 MPa & 35 \({}^{\circ}\)C & 16.3 kg/s & 2.5 & \(\sim\)500 kW & \(>\)80\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Main design parameters of the single-stage centrifugal compressor.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Hub radius/mm & 10 mm & Blade angle (leading-edge) & 60\({}^{\circ}\)/54\({}^{\circ}\)/48\({}^{\circ}\) \\ Impler radius/mm & 48 mm & Blade angle (training-edge) & 55\({}^{\circ}\) \\ Blade number & 15 & Blade height (leading-edge) & 7.5 mm \\ Tip clearance & 0.25 mm & Blade height (training-edge) & 3.5 mm \\ Blade inclination angle & 60\({}^{\circ}\) & Thickness (leading-edge) & 0.3–0.6 mm \\ \hline \hline \end{tabular}
\end{table}
Table 3: Main structural parameters of the semi-open impeller.  
Figure 3: Performance curve of the single-stage compressor (@ 40,000 RPM).  
Figure 2: Distribution of the semi-open impeller. (**a**) Beta distribution, (**b**) Thickness distribution.