## 5 Results and Discussions
### Discussion on Peak Efficiency Improvement  
As shown in Figure 9, the improvement amplitude of the peak efficiency is 0.12%. It also can be seen from Figure 12 that the improvement of the peak efficiency of the highly loaded compressor is mainly due to the improvement in efficiency of rotors. However, the total pressure loss of the stators increases instead. Besides, if we only put the optimization variables on rotors of the original compressor without changing stators, the peak efficiency will be further increased by 0.17% compared with the original compressor, which further supports the trend of efficiency changes. The value of the peak efficiency improvement needs to be further confirmed through experiments. In order to guide the engineering redesign of high loaded compressors, it is worth further analyzing the flow mechanism. In the following, we will focus on analyzing the flow mechanism of the second-stage rotor to improve the peak efficiency of the compressor.  
Figure 13 shows the span-wise adiabatic efficiency of the second-stage rotor of the original and optimized compressor. As can be seen in Figure 13, compared with the original rotor the adiabatic efficiency of the optimized rotor above the 30% span height improves, and conversely, the adiabatic efficiency below the 30% span height slightly decreases. This is mainly due to the change of the second-stage rotor of the optimized compressor relative to the original compressor towards the pressure surface, which changes the flow field structure of the second stage rotor in the span-wise and chord-wise direction, as shown in Figure 9. It can be seen from Figure 14 that from the leading edge to 20% of the chord length of the second-stage rotor, the entropy rises rapidly, and then from 20% of the chord length to the trailing edge, the entropy rises gently. Compared with the original compressor, within the range of 10%-30% of the chord length the entropy rise rate of the optimized compressor decreases. Subsequently, the entropy value is always smaller than that of the original compressor. The reasons will be analyzed below.  
Figure 12: Rotor adiabatic efficiency and stator total pressure loss of the original and optimized compressor. (**a**) Rotor adiabatic efficiency at peak efficiency condition; (**b**) stator total pressure loss at peak efficiency condition.  
As shown in Figure 15, after rapid acceleration near the leading edge of the second-stage rotor, the fluid rapidly decelerates along the blade suction surface. Compared with the original rotor, the optimized rotor has a smaller high-speed area range as shown in orange. The fluid decelerates faster and the boundary layer grows more slowly, thus low-energy fluid decreases near the trailing edge. As shown in Figure 16, the isentropic Mach number of the suction surface located at 10% to 30% of the chord length is reduced, which means that the blade loading is reduced, and the change trend of the entropy value shown in Figure 14 is confirmed. Therefore, it indicates that the second-stage rotor of the optimized compressor generates less blade loading and boundary layer losses than that of the second-stage rotor of the original compressor.  
Figure 14: Chord-wise entropy rise of the second-stage rotor of the original and optimized compressors.  
Figure 13: Span-wise adiabatic efficiency of the second-stage rotor of the original and optimized compressor.