## 5 Results and Discussions
### Discussion on Stall Margin Extending  
To determine where the stall occurred, we compared the flow fields at different flow coefficients and separately calculated the 1.5-stage and 2-stage compressor flow fields of the original compressor. We found that the compressor can operate at a lower flow coefficient without the second-stage stator, so we infer that the stall of the original compressor occurs in the second-stage stator. From the peak efficiency condition to the near stall condition, when the mass flow decreases the blade loading on the compressor increases. It can be seen in Figure 17 that the flow field near the tip region of the second-stage stator deteriorates and the low-speed region near the trailing edge increases. From Figure 18, we can also find that the fluid separation moves forward on the suction side. Large-scale low-speed areas eventually evolve from small corner separation into corner stall with three-dimensional space spatial backflow. Figure 16: Isentropic Mach number on 70% of the span height of second-stage rotor of the original and optimized compressor. Figure 15: Relative Mach number in 70% of the span height of second-stage rotor of the original and optimized compressor. (**a**) Relative Mach number of the original compressor; (**b**) relative Mach number of the optimized compressor. After optimization, the stall margin of the compressor is increased by 2.69%. To reveal the mechanism of the stall margin improvement, Figure 19 shows absolute Mach number in 95% of the span height of second-stage stator. The near-stall point is chosen for the original compressor, and the same dimensionless flow condition is chosen for the optimized compressor. As shown in Figure 19, compared with the original stator the flow field near the trailing edge region of the optimized second-stage stator in 95% span is improved and the separation region is reduced. As shown in Figure 20, the separation region of the optimized stator moves upstream significantly above the 50% span height. This prevents the occurrence of the corner stall of the second-stage stator and increases the stall margin of the compressor. Figure 17: Absolute Mach number in 95% of the span height of second-stage stator from the peak efficiency condition to near stall condition. (**a**) Absolute Mach number at peak efficiency condition; (**b**) absolute Mach number at near stall condition. Figure 18: Limiting streamline on the suction surface of the second-stage stator from the peak efficiency condition to the near stall condition. (**a**) Limiting streamline on the suction surface at peak efficiency condition; (**b**) limiting streamline on the suction surface at near stall condition. However, the study found that at the same normalized mass flow, the inlet swirl angle of the second-stage stator is almost similar, which illustrates the same direction of upcoming flow. The difference of stall margin is in the flow detail of the second-stage stator. Figure 21 shows the isentropic Mach number at the 95% span. It can be seen that the acceleration ability of the fluid near the leading edge on the suction surface of the optimized stator slows down and the peak value of isentropic Mach number slightly decreases. The blade loading is decreased from the leading edge to about 20% of the chord length. The reduced blade loading results in the growth rate of the boundary layer decreases. Finally, the separation region and the three-dimensional spiral backflow decreases. This is mainly as shown in Figure 11, because compared with the original stator the optimized stator has a larger turning angle above the 50% span height. At the same direction of upcoming flow, this means that the incidence is smaller, so the blade loading near the leading edge is smaller and stalls later. Further flow mechanisms, including secondary flows, are worthy of further discussion. Figure 19: Absolute Mach number in 95% of the span height of the second-stage stator for original and optimized compressor.