## 3 Results
### Influence of the Size of Stator Hub Clearance on the Evolution of Flow Topologies
#### 3.3.1 Results at the DE Condition  
The oil-flow visualization results in the DE condition are shown in Figure 6. Similarly, only results on the suction side and the hub are shown here. Compared with the results at zero clearance, the scale of the tip corner separation almost did not change with the introduction of the stator hub clearances. For the hub corner separation, the situation is different as the stator hub clearance varies. Firstly, when the clearance was small (0.25\(\pi\)), the spanwise scale of the hub corner separation expanded to some extent and the hub corner separation originated earlier than that at zero clearance, which was also visualized by [PERSON], et al. [22]. In addition, the separation line on the hub, SL3, was replaced by three separation lines, i.e., SL3, SL4, and SL5. It should be noted that SL4 points to the upstream, which is contrary to the direction of SL4 and SL5, and between SL3 and SL4 there exists a focus point, F, while between SL4 and SL5 there exists a saddle point, S. Then, when the stator hub clearance grows to 0.50\(\tau\), the separation line SL1 on the blade suction surface disappears and is replaced by an attachment line AL2, besides, the separation lines on the hub becomes one separation again (the SL3 in Figure 6c) and it was significantly far away from the blade suction side. Finally, when the stator hub clearance increases to 1.00\(\tau\), the flow structure was similar to that at 0.50\(\tau\), but the separation line SL3 on the hub is further away from the blade suction surface. The flow structures on the hub corner of a cantilevered stator depends on the interaction of the secondary flow and the clearance leakage flow. When the stator hub clearance changed, the secondary flow was effected slightly, but clearance leakage flow was effected obviously, for example, [PERSON] [33] pointed out that when the flow leaks from the blade pressure side to the blade suction side, the flow property inside the clearance mainly depends on the nondimensional clearance size, \(\lambda^{2}Ree\) (where \(\lambda\) is the ratio of the clearance size to the maximum thickness of the blade airfoil, \(Re\) is the Reynolds number based on the blade chord and the mainflow velocity near the hub, \(e\) is the ratio of blade maximum thickness to the blade chord), i.e., when \(\lambda^{2}Ree<21\), the flow inside the clearance was dominated by the flow viscosity, while when \(\lambda^{2}Ree>125\), the flow viscosity could be ignored. When the stator hub clearance equals to 0.25\(\tau\), \(\lambda^{2}Ree=25\), the flow inside the clearance was mainly dominated by the  
Figure 6: The evolution of flow topologies on the suction surface and hub with the variation of hub clearance at the design condition (DE) condition. flow viscosity, hence, large flow loss were generated when the flow leaks from the blade pressure side to the blade suction side, and the velocity of the clearance flow at the clearance outlet (the blade suction side) became very small. On the one hand, the very small transversal velocity component could not push away the secondary flow near the hub, so the separation line SL3 was very close to the blade suction side; on the other hand, when the streamwise adverse pressure along the blade suction side was very large, the very small streamwise velocity component separated and flowed backward, so the separation line SL4 pointed to the upstream, but when the streamwise adverse pressure along the blade suction side became small (at the rear part near the blade trailing edge) the clearance flow pointed to the downstream again, as shown as the separation line SL5. In this case, as there exists some backflow (between the focus point, F, and the saddle point, S), the corner separation becomes even larger than that at 0.0\(\uptau\).