## 4 Discussion
### Flow Field Details
A tip leakage vortex (TLV) was generated by the pressure difference between the pressure surface and suction surface and interacted with the shock waves, which influenced the performance of the rotors. The geometric modifications changed the pressure distribution and affected the TLV. The strength of the TLV depends on the chordwise integration of the pressure difference between the pressure surface and the suction surface, as illustrated by [PERSON] [44]. Therefore, even though the TLV was stronger when it was just initiated because of the  
Figure 19: Relative Mach number distribution of the different rotors. (**a**) Distribution of the reference rotor. (**b**) Distribution of the GA case. (**c**) Distribution after modification by the agent. higher pressure difference near the leading edge, it was weakened after development because of the lower pressure of difference at the rear spanwise. Figure 21 showed the static pressure distribution around the blade, at the near tip spanwise at 90% and around the tip clearance spanwise at 99.8%. The tip of the rotor was swept back, so the load was larger after the GA step, but \(\chi_{in}\) near the tip decreased, so the peak static pressure at the pressure surface in Figure 21 did not increase much, and the location moved. Then, when the agent introduced more back sweeps and rose \(\chi_{in}\), the peak static pressure increased and moved farther toward the leading edge. The minimum static pressure near the tip and around the tip clearance was increased, and the modification of the agent further improved the static pressure downstream after the minimum location. Figure 21: Static pressure distribution through the chord line near and around the tip span: (**a**) 90% span; (**b**) 99.8% span. Figure 20: Radial velocity at the axial surface (80% length). Figure 22 showed the tip clearance flow feature of the rotors, together with the static pressure distribution at a 98% span. It was observed that the TLV did not expand after modification, even when the pressure difference between the pressure surface and suction surface increased near the leading edge. The passage shock wave caused a severe rise in pressure, which can interact with the TLV and distort it, as analyzed by [PERSON] [45]. The inverse pressure gradient declined in the GA case and the RL results, as plotted in Figure 22. As a result, the distortion of the TLV was diminished compared with the reference rotor case, which helped raise the overall efficiency. The modifications added by GA and RL also enhanced the flow field by influencing the end wall secondary flow. As emphasized in Figure 22, the leakage flow in the reference rotor moved across the whole passage and passed the next tip clearance, which generated considerable loss. In the flow field of the GA case, a larger portion of the leakage flow was directed downstream rather than toward the next tip clearance. This flow feature remained after the RL agents modified the rotor and benefited the overall efficiency. The static pressure downstream in Figure 22 indicated the change in the pressure ratio, which also agreed with the local pressure ratio change in Figure 17. The flow with relatively high static pressure mixed with the flow at lower spanwise, and the static pressure decreased. The static pressure downstream was lower than the reference; then, upon modification by the RL agent, the static pressure improved and became higher than the reference. Figure 23 showed the entropy distribution at the outlet of the rotors in the axial surface, which also indicated the improvement after the modifications. As marked by arrows, the thickness of the flow area with relatively high entropy decreased in the GA case, then slightly increased in the RL result and remained better than the reference. A similar reduction in entropy appeared in the wake flow area, as marked in the dashed circle, where the high entropy area was reduced. Figure 22: Tip leakage flow of the rotors and static pressure distribution at 99.8% spanwise.