## 3 Results of Vortical Flow Structure Analysis
### Comparison of the Optimization Result with Conventional Centrifugal Compressor  
The conventional and enhanced centrifugal compressor impellers are shown in Figure 12. The conventional impeller is colored grey, and the enhanced impeller is colored red. The enhanced impeller was analyzed in 4 cases and the highest adiabatic efficiency improved case was selected as the enhanced centrifugal compressor impeller as shown in Table 3.  
Figure 10: Pressure surface view of vortical flow structure distribution of conventional centrifugal compressor at (**a**) OP1 and (**b**) OP5. The pressure difference and adiabatic efficiency between conventional and enhanced centrifugal compressor impellers were compared (Figure 13). The enhanced impeller had an average improvement of pressure difference and adiabatic efficiency of 1.47% and 0.47%, respectively. This showed that the enhanced impeller supplied the combustion gases more efficiently, thereby improving the efficiency of hydrogen fuel cell electric vehicles. Figure 11: Streamwise cross-sectional view of vortical flow structure and entropy function distribution at (**a**) OP1 and (**b**) OP5. \begin{table}
\begin{tabular}{c c c} \hline
**Case** & **Normalized Efficiency Difference at Design Flow Rate** & **Normalized Efficiency Difference at Low Flow Rate** \\ \hline Opt. 1 & \(-\)0.34\% & \(-\)0.36\% \\ Opt. 2 & \(-\)0.05\% & 0.21\% \\ Opt. 3 & 0.00\% & 0.00\% \\ Opt. 4 & 0.07\% & 0.00\% \\ \hline \end{tabular}
\end{table} 
Table 3: Comparison of normalized efficiency difference for 4 enhanced impeller cases. Additionally, the relative velocity distribution in the meridional view between conventional and enhanced centrifugal compressor impellers at OP5 was compared in Figure 14. The relative velocity in the passage is represented by colored contours. The blue region indicates the occurrence of reverse flow, where the velocity in the passage was 0 m/s. The enhanced impeller had a thinner reverse flow region as compared to the conventional one. This showed that the enhanced impeller had a higher performance than the conventional impeller. Figure 15 shows the vortical flow structure distribution of enhanced centrifugal compressor impeller at OP1 and OP5 in perspective view, respectively. In Figure 15b, it was found that the region of reverse flow (blue color) was larger than the conventional impeller  
Figure 14: Relative velocity distribution in meridional view at OP5 for the (**a**) conventional and (**b**) enhanced centrifugal compressor impellers. Figure 13: Comparison of (**a**) pressure ratio and (**b**) adiabatic efficiency, between conventional centrifugal compressor impeller and enhanced centrifugal compressor impeller. that is shown in Figure 8b, but as seen in Figure 14b, the reverse flow region was thinner than in the conventional impeller, which meant that the performance of centrifugal compressor had improved. In Figure 16, the vortical flow structure distribution of the enhanced impeller at OP1 and OP5 in the suction surface view is shown. In both flow rates, low-energy air near the pressure surface leaked between the shroud and blade tip due to the pressure difference at the suction surface and the pressure surface. This led to the generation of a tip leakage vortex at the main blade's leading edge, which was crushed with the leading edge of the splitter blade leading to the generation of a small reverse flow region. However, because of a smaller vortex core of the enhanced impeller as compared to the conventional impeller, the effect of the small reverse flow was compensated for, and a passage vortex occurred at the pressure surface of the splitter blade.