## 4 Conclusions  
In this paper, the circumferentially averaged method is used to calculate the coupling flow field between the seal cavity leakage flow and the main flow field at the root of the shrouded stator in a multistage axial-flow compressor. The influence of the leakage flow of the seal cavity on the compressor performance and flow field details is studied by changing the tip clearance of the labyrinth. In addition to the analysis of the effect of seal leakage flow on flow field and compressor performance, the effect of seal leakage flow on a particular blade row in multistage environment and its propagation in multistage axial flow compressor are also studied through the analysis of stage characteristics. The significant findings of this study can be summarized as follows:  
1. With the increase of leakage flow, the total pressure ratio and efficiency of the compressor decrease to some extent. The labyrinth clearance-to-span ratio of cavity 1 increases by 1%, and the compressor efficiency decreases by 0.4%. For cavity 2, the decrease in efficiency is 0.6% when labyrinth clearance-to-span ratio increases by 1%. Therefore, in order to predict the performance of the compressor correctly, the effect of leakage flow in the seal cavity should not be ignored.  
Figure 16: Spanwise distribution of blade element performance for Rotor 3.  
Figure 15: Spanwise distribution of blade element performance for Rotor 2.  
2. The leakage flow in the seal cavity has little effect on the performance of the upstream blade row, but will deteriorate the flow field and performance of the stator and the downstream rotor where the leakage occurs. Reflected in the stage characteristics, it has no effect on the front stage, but has a little influence on the work capacity of the current stage, while the work capacity of the later stage and the pressurizing capacity of the current stage and the rear stage reduces significantly. This is reflected in the performance of blade row that the total pressure loss at the root of stator increases obviously, and the load of stator and downstream rotor decreases in most of the span ranges.
3. The seal cavity leakage flow causes the blockage of the flow at the root of the blade, which leads to the spanwise migration of the flow. The blockage and spanwise migration further change the incidence angle characteristics of the blade row. As a consequence, the incidence angle increases at the hub, which induces an increase of total pressure loss. At midspan, on the other hand, the incidence angle decreases, resulting in a decrease of blade load.  
Generally, the circumferentially averaged throughflow program CAM used in this paper reasonably reflects the influence of seal cavity leakage flow on the performance and flow field details of a three-stage axial-flow compressor. The leakage flow from the sealed cavity will deteriorate the performance of the stator, and this effect will propagate downstream. This program can be used to quickly analyze the seal cavity leakage effect during compressor design as well as performance degradation caused by labyrinth wear in a multistage axial-flow compressor. The study lays a solid foundation for further considering the influence of seal cavity leakage flow in the calculation of aeroengine.  
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.  
This research was funded by National Science and Technology Major Project (2017-I-0005-0006).  
Not applicable.  
Data Availability Statement: Data sharing is not applicable to this article.  
The authors would like to thank [PERSON] for the guidance and kind advice, and the fellow apprentices in the research group for their help.  
The authors declare