## 4 Results and Discussion
### The Optimal Design
Figure 14: Second flow velocity on S3 sections of the optimal compressor impeller: (**a**) 30% axial chord length; (**b**) 40% axial chord length and (**c**) 90% axial chord length. Figure 16 shows the surface pressure distributions of the impeller blades and diffuser blades of the compressor optimal design. The blade surface pressure curves with different blade height sections are shown in Figure 17. In general, the pressure increased gradually from the inlet to the outlet, the pressure gradient distribution was uniform. The maximum pressure was at the diffuser outlet. Due to the decrease of the CO\({}_{2}\) leakage caused by the tip clearance, the surface pressure of rotor was basically the same along the blade height direction from the position of the 50% chord length to the TE. The cross critical region of the blade surface is shown in Figure 18. Similarly, the fluid in the blade tip clearance at the impeller blade LE was 'ejected'. Meanwhile, the fluid at the LE of the impeller blade would be affected by the phenomenon of an 'off vortex at the LE on the top of blade'. The simultaneous action of the two phenomena led to obviously low-pressure-temperature regions at the impeller blade LE, and the carbon dioxide entered the two-phase region. The fluid state at the corner position of the LE on the top of the blade was far below the critical state. This might cause 'condensation'. The flow in the transcritical region was very complex and the physical properties changed dramatically. This would cause great loss and affect the flow condition in the impeller. By optimizing the geometry of the flow passage, the influence range of the transcritical phenomenon in the optimal design was obviously weakened. It was mainly concentrated on the SS of the LE. Figure 16: The pressure distribution of the blade surface. Figure 15: The pressure and temperature distribution of the 50% blade height section for the optimal design of the compressor: (**a**) pressure distribution and (**b**) temperature distribution. In order to study the loss of flow in the compressor more intuitively, the entropy distribution of different blade height sections, the impeller outlet and diffuser outlet are given in Figure 19. It can be found that the flow loss inside the compressor was more and more serious from the hub to the shroud. It is consistent with the gradual deterioration of the flow situation mentioned above. The entropy of the 10% blade height section had little change. The working medium was pressurized in the impeller, which is similar to the isentropic process. In the diffuser, due to the influence of the viscous boundary layer and the wake, an increase in entropy appeared on the blade surface and the extension of the outlet. At the 50% blade height section, the entropy of blade TE increased greatly under the influence of the wake. The flow loss in this region was increased. A large range of higher entropy increases occurred at the 90% blade height section near the blade top. This area is close to the wall, and the working fluid was strongly sheared by the impeller at high speed. Therefore, there was a large viscous dissipation loss. At the same time, this area was affected by the tip clearance layer. Various vortex structures were blended here, and the flow was very complicated. The entropy at the impeller outlet was evenly distributed in the circumferential direction and gradually increased along the blade height. This is because the area near the shroud was greatly affected by the tip clearance layer and the cutting of the wall surface. The entropy at the diffuser outlet was basically unchanged. There was only a slight  
Figure 17: The pressure curves of the blade surface with different blade high cross sections. Figure 18: The cross critical region of the blade surface. increase in entropy on the suction side. This means that there were no backflow and secondary flow in this area. In summary, the optimal design had small flow loss and good aerodynamic performance.