## 5 Conclusions  
This paper experimentally investigates the 3D separating flows inside the stator with varied hub clearances of a highly loaded low-speed axial compressor. Measurements including oil-flow visualization, five-hole probe are conducted to reveal the effect of stator hub clearance size on the corner separation and on the compressor performance. Conclusions can be drawn as follows:  
1. At zero clearance, hub corner separation turns into a corner stall as long as the stator incidence is larger than the critical incidence, which makes the compressor performance drop rapidly.
2. At large mass flow rate conditions (before the occurrence of the hub corner stall), the introduction of a very small stator hub clearance (0.25% blade height here) will not improve the hub corner flow, on the contrary, it makes the corner separation more severe and prompts the occurrence of corner stall, which is mainly caused by the fact that the leakage flow has relatively low energy due to the viscosity effect in the clearance and large flow loss generation as the clearance flow comes across and mixes with the transverse secondary flow; when the stator hub clearance increases, the enhanced leakage flow can suppress the transverse migration of the low energy flow near the hub, but excessive leakage flow could induce new mixing loss.
3. At small mass flow rate conditions (when the corner stall occurs), the hub clearance flow can also suppress the low energy flow to roll into the recirculation region around focus point at the downstream of leading edge on the hub, hence, the strength of the corner stall is diminished even at the very small clearance, and the hub corner stall is eliminated when the hub clearance increases to 0.5% blade height or bigger.  
Figure 18: Circumferentially averaged distribution of the stator total pressure loss.  
As the stator hub clearance varies, there are five typical flow structures in the stator hub corner, namely, Type A, Type B, Type C, Type D and Type E. Type A and Type B correspond to the traditional hub corner separation and corner stall, Type C corresponds to the traditional hub clearance flow, Type D corresponds to the coexistence of the hub leakage flow and the corner separation, and Type E corresponds to the coexistence of the hub leakage flow and the corner stall.
* The evolution of the flow topologies inside the stator passage along with the variation of stator hub clearance has an obvious influence on the performance of the compressor, and the flow mechanisms of the effect of the stator hub clearance on the compressor performance is discussed in detail. It is found that there exists an optimum stator hub clearance makes the flow inside the stator to be the most rational and the compressor performance to be the best.  
Conceptualization, B.L.; methodology, Y.Q.; investigation, Y.Q. and G.A.; Writing--Original Draft preparation, Y.Q. and G.A.; Writing--Review and Editing, G.A., Y.Q. and X.Y.; supervision, B.L., X.Y. and G.A.  
This work was supported by the National Natural Science Foundation of China (Grant Nos. 51806004, 51790511) and National Science and Technology Major Project (Grant No. 2017-II-0001-0013).  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} \(Cps\) & Static pressure rise coefficient \\ \(Cpt\) & Total pressure coefficient \\ \(Cvz\) & Normalized axial velocity, \(V_{z}/U_{m}\) \\ \(Loss\) & Total pressure loss coefficient \\ \(Re\) & Reynolds number \\ \(r\) & Radial position \\ \(s\) & Circumferential position \\ \(t\) & Blade pitch \\ \(U_{m}\) & Rotor speed at middle span \\ \(V_{z}\) & Axial velocity \\ \(\varphi\) & Mass flow coefficient \\ \(\lambda\) & Ratio of the clearance size to the maximum thickness of the blade airfoil \\ \(\epsilon\) & Ratio of blade maximum thickness to the blade chord \\ \(\rho\) & Flow density \\ \(\delta\) & Blade wake width in pitchwise \\ \end{tabular}