## 4 Results and Discussion
### The Optimal Design  
Figure 13 shows the velocity vector distribution of the 50% blade height section for the compressor optimal design, and the partial enlargement of the LE and TE of rotor and diffuser blades. It can be seen from the diagram that there was no serious flow separation phenomenon and backflow phenomenon in the impeller and diffuser. The flow field was uniform. The local acceleration phenomenon was inevitable only in the LE of the impeller blade and diffuser blade. In addition, there was a small vortex produced by the impeller blade blunt TE. Figure 14 shows the secondary flow velocity vector with different axial chord lengths on the S3 cross section. The vortex structure and development process of the compressor impeller can be analyzed by secondary flow velocity. For the horseshoe vortex, its intensity and influence range were obviously weaker than that of the radial inflow turbine. Only horseshoe vortex bifurcation on the PS (HVp) was found near the LE of the rotor blade, while horseshoe vortex bifurcation on the SS (HVs) was not found. Under the pressure gradient, the boundary layer was rolled up and the horseshoe vortex bifurcation was formed on the PS. As the fluid flows downstream, the influence range increased continuously. It finally merged with the passage vortex under the dissipation of the adverse pressure gradient. Additionally, the difference between the passage vortex and other vortex structures was not obvious. Figure 14a shows that there was an up passage vortex (PVu) and down passage vortex (PVd)  
Figure 13: The velocity vector distribution of the 50% blade height section for the optimal design of the compressor. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Performance Parameter** & \begin{tabular}{c} **The Initial Design** \\ **(12 Main Blades +** \\ **12 Splitter Blades)** \\ \end{tabular} & \
\begin{tabular}{c} **Case A** \\ **(9 Main Blades +** \\ **9 Splitter Blades)** \\ \end{tabular} &
\begin{tabular}{c} **Case B** \\ **(12 Main Blades)** \\ \end{tabular} \\ \hline Input power/kW & 147.72 & 137.55 & 131.98 \\ Total pressure ratio & 1.67 & 1.67 & 1.65 \\ Total static efficiency/\% & 50.30 & 63.36 & 64.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Performance analysis of the initial design compressor. with the same rotational direction at the tip and root of the blade on the PS, respectively. However, the intensity was small and the influence range was narrow. The up passage vortexes were generated mainly by the interaction of three parts. The first part was the scraping flow produced by the relative motion of the upper end wall due to the high-speed rotation of the impeller. The second part was the leakage flow from the PS to the SS in the tip clearance. Another part was the effect of transverse pressure gradient. As the fluid flowed along the radial direction, the scraping effect caused by the high-speed flow of the impeller became stronger, and the vortices on the PS expanded gradually. The influence range of vortex in the down passage gradually decreased. Its position was gradually squeezed into the SS and eventually dissipated and disappeared, as shown in Figure 14b. Near the TE of the rotor blade, the pressure on the SS was basically the same as that on the PS. The leakage flow and the transverse pressure gradient disappear, and the vortex system was dissipated and disappeared, as shown in Figure 14c. Figure 15 shows the pressure and temperature distribution of the 50% blade height section for the compressor optimal design. Generally speaking, the pressure and temperature of the PS were greater than that of the SS. Under the action of centrifugal force, the CO\({}_{2}\) pressure and temperature from the LE to the TE of the rotor gradually increased, and there was a larger gradient at the TE. The diffusing action of diffuser maximized the outlet pressure and outlet temperature. The outlet static pressure reached 14.25 MPa.