## 4 Conclusions  
Results from numerical simulations indicate that seal cavity leakage flow though the cavity and the labyrinth seal under a shrouded stator of moderate hub/tip ratio can have a significant and detrimental impact on the performance of a compressor. Compared with no leakage, the pressure ratio can be reduced by 2% and the efficiency can be reduced by 1.9% for a 0.74% increase of seal-tooth clearance-to-span ratio. The major findings of this study can be summarized as follows:  
1. With the increase in leakage flow rate, both the total to total pressure ratio and the efficiency of the compressor decrease significantly.
2. With the leakage flow rate increasing, the incidence at the stator root increases dramatically, which reflects the hub blockage caused by seal cavity leakage, and the incidence above 20% spanwise decreases overall, which reflects the spanwise migration induced by hub blockage.
3. The axial momentum of the fluid decreases gradually with the increase in leakage flow at the stator root near the hub, which reflects the hub blockage caused by seal cavity leakage. The reduction in axial momentum at the hub with leakage addition causes an increase in axial momentum higher up the span, which reflects the spanwise migration induced by the hub blockage.
4. The increase in hub incidence and hub blockage as well as spanwise migration induced by seal cavity leakage in turn reduces the effective flow area, thus reducing the diffusion within the stator passage. The result is a reduction in pressure ratio as well as efficiency.
5. Compared with the traditional design, which only considers the mainstream in compressors, the design incidence at the root of the shrouded stator should be increased and the design incidence at middle span should be reduced in order to make the stator blade more suitable for the changed flow field under the impact of seal cavity leakage flow.  
Overall, the circumferentially averaged throughflow model can reasonably reflect the influence of leakage flow on the performance and flow field of a single-stage axial compressor. This study provides a diagnostic tool to quickly analyze the effect of seal cavity leakage flow during compressor design and performance degradation, which lays a solid foundation for further research on the influence of leakage flow in multistage compressors.  
Conceptualization, D.L. and X.G.; methodology, D.L.; software, D.L.; validation, D.L.; formal analysis, D.L.; investigation, D.L.; resources, D.L.; data curation, D.L.; writing--original draft preparation, D.L.; writing--review and editing, D.L., D.J. and X.G.; project administration, D.J. All authors have read and agreed to the published version of the manuscript.  
Figure 11: The radial distribution of the Stator’s static pressure ratio.  
**Funding:** This research was funded by the National Science and Technology Major Project (2017-I-0005-0006).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data sharing is not applicable to this article.  
**Acknowledgments:** The authors would like to thank [PERSON] for the guidance and kind advice, and the fellow apprentices in the research group for their help.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
**Abbreviations**  
**Nomenclature**  
c **labyrinth clearance**  
p **static pressure**  
_p\({}^{*}\) **total pressure**  
m **massflow rate**  
LF **leakage flow rate**  
h **blade height of S1**  
**Subscripts**  
IN **the inlet of compressor**  
LF **seal cavity leakage flow**