## 3 Results
### Effect of Stator Hub Clearances on the Stator Performance
When the stator hub clearance increases to 0.50\(\uptau\), the induced leakage flow successfully eliminates the hub corner stall, so the value of _Cvz_ below 60% span increases significantly and the main flow region expands from 30% span (70%-100% span) to 60% span (40%-100% span). In this case, though the hub corner stall is eliminated, the hub corner separation still exists. Hence, when the stator hub clearance continually increases (at 1.00\(\uptau\)), the value of _Cvz_ below 20% span will continually decrease, and the value between 20%-50% span will increase. On the one hand, the decrease of the axial velocity in the corner means the increase of the flow blockage. Figure 16a shows the flow blockage coefficient at the stator outlet, where the blockage  
Figure 15: Circumferentially averaged flow parameters at the stator outlet. coefficient is defined in the way given by [PERSON], et al. (2019). At arbitrary radial position, the blockage is defined as follow:  
\[\text{Blockage}=\left\{\int_{0}^{S}\!\!\!\left[1-\frac{V_{z}(r,s)}{V_{z,fs}(r)} \right]ds\right\}/t(r), \tag{1}\]  
where \(t\) is the blade pitch, \(r\) is the radial position, \(s\) is normalized circumferential position, \(V_{z,fs}\) is the axial velocity at the edge of the wake, and \(\delta\) is the wake width in pitchwise. It can be seen that the tendency of variation of the flow blockage along with the stator hub clearance is just contrary to that of _Cvz_. On the other hand, the increase of the flow blockage means the decrease of the flow area, and the decrease of the flow area means the acceleration of the flow velocity and the decrease of the static pressure. Hence, when the flow in the hub corner is improved, the flow blockage decreases and the stator static pressure rise increases, as shown in Figure 16b, which can explain the variation of the stator static pressure rise coefficient shown in Figure 12.  
Besides, the flow blockage inside the stator passage can also influence the flow inside the rotor. Taking the situation at the NS condition as an example, when the stator hub clearance increases, the flow blockage in the hub corner decreases, at the stator inlet (i.e., the rotor outlet) the axial flow velocity near the hub increases and the axial flow velocity near the tip decreases (as shown in Figure 17). As the rotor outlet relative flow angle almost does not change, at the rotor outlet the relative flow velocity near the hub increases and the relative flow velocity near the tip decreases. Near the hub, the increased relative flow velocity at the rotor outlet results in a decrease in the static pressure rise. Near the tip, the decreased relative flow velocity at the rotor outlet should bring about an increase of the static pressure rise, but the very strong rotor tip leakage flow at the NS condition makes it hard to increase the static pressure rise anymore. As a result, the total static pressure rise decreases with the decrease of the flow blockage in the stator hub corner. That is why the general tendency of the variation of the rotor static pressure rise coefficient along with the stator hub clearance is opposite to that of the variation of the stator static pressure rise coefficient at the NS condition. Figure 16: Circumferentially averaged flow parameters of the stator. Figure 17: Circumferentially averaged flow parameters at the stator inlet at the NS condition. Except for the flow blockage, corner separation/stall can also induce much flow loss. The circumferential averaged distribution of the stator total pressure loss is shown in Figure 18. It can be seen that the variation of the loss with the stator hub clearances is similar to that of the _Cvz_. At the DE condition, the loss above 40% span almost does not change with the variation of the stator hub clearance. Compared with the results at zero clearance, when a small stator hub clearance (0.25\(\uptau\)) is introduced, the hub corner separation is enhanced, so the loss below 40% span increases to some extent.