## 3 Results
### Effect of Stator Hub Clearances on the Stator Performance  
To have a clear understanding of the flow mechanisms of the effect of stator hub clearances on the stator performance, the flow profiles before and after the stator passage obtained using the five-hole probe will be discussed in this section. The circumferential averaged distribution of the total pressure and the incidence at the stator inlet are shown in Figure 14, where results at all stator hub clearances are displayed. It can be seen that the difference of the circumferential averaged parameters between different stator hub clearance cases is very small, which validates the conclusion drawn above. In addition, at the NS condition, the stator incidence near the hub is about 7\({}^{\circ}\), which has already exceeded the critical incidence (about 5.2\({}^{\circ}\), as revealed in [34], hence, the hub corner stall occurs at zero clearance. The circumferential averaged distribution of the flow angle at the stator outlet is shown in Figure 15. It can be seen that at zero clearance the over-turning phenomenon near the hub is very  
Figure 14: Circumferentially averaged flow parameters at stator inlet. Figure 13: The stator total pressure loss coefficient obtained from the five-hole probe results. serious, while it is much weaker near the tip. When a small stator hub clearance is introduced, a weak leakage flow is induced, as a result, the migrant of the low energy flow near the end wall is suppressed to some extent, so the overturning phenomenon near the hub is decreased slightly. When the stator hub clearance increases to 0.50\(\uptau\), the leakage flow becomes stronger and the suppression of the migrant of the low energy flow near the end wall is enhanced, so the overturning phenomenon is obviously decreased. When the stator hub clearance continually increases to 1.00\(\uptau\), the leakage flow becomes further stronger, which is more than enough to suppress the migrant of the low energy flow near the end wall, so the flow near the hub becomes a little of lack of turning. This coincides well with the oil-flow visualization results discussed above. The circumferential averaged distribution of the normalized axial velocity at the stator outlet is also shown in Figure 15. At the DE condition, it can be seen that the value of _Cvz_ 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 value of _Cvz_ below 20% span decreases slightly while the value between 20%-40% span does not change, which is consistence with the strengthening of the hub corner separation mentioned in Section 3.3. When the stator hub clearance increases to 0.50\(\uptau\), the leakage flow increases, and the increased leakage flow is mostly offset by the migrant of the low energy flow near the end wall. As a result, the value of _Cvz_ below 20% span does not decrease obviously, however, as the hub corner separation is suppressed, the value between 20%-40% span increases distinctly. When the stator hub clearance continually increases to 1.00\(\uptau\), the leakage flow gets a further increment, as the leakage flow in the 0.50\(\uptau\) case is already enough to suppress the hub corner separation, the further increased leakage flow, in this case, will induce a further decrease of _Cvz_ below 20% span while the value between 20%-40% span almost does not change. At the PP condition, the situation is similar to that at the DE condition, while the deterioration of the flow near the hub is much more obvious at 0.25\(\uptau\) as the hub corner stall occurrs. At the NS condition, the hub corner stall occurs at zero clearance. In this situation, when a small stator hub (0.25\(\uptau\)) is introduced, the hub corner stall still exists, but the value of _Cvz_ below 50% span increases slightly, which means that when hub corner stall happens even a small stator hub clearance may be benefit for the flow.