## 5 Summary  
The paper focuses on the problem of premature seal failure caused by the unevenness of the interstage pressure drop of a multistage brush seal; established a numerical calculation model of a four-tooth three-stage brush combination seal; calculated the pressure distribution, flow field distribution, flow traces, leakage rate, and interstage pressure drop distribution of the combination seal with different structural parameters and working condition parameters; analyzed the sealing mechanism of the combination seal and the unevenness characteristic of interstage pressure drop, and improved the combination seal with structural parameters; and elaborated the mechanism of the unevenness of the interstage pressure drop of a multi-stage brush bundle from the perspective of entropy increase. Specifically:  
1. In the four-tooth three-stage brush combined seal, the high-pressure fluid dissipation includes tooth cavity vortex dissipation, tooth-tip throttling dissipation, brush bundle viscous damping dissipation, and inertial damping dissipation, with the latter two being the primary dissipations. 2. For the prototype combined seal in different pressure ratio conditions, the first, second, and third stage of the brush bundle pressure drop percentage are about 18.3%, 33.0%, and 43.3%, the grate tooth are of the pressure drop percentage is 8.4%, and the pressure drop between the stages of the combination seal exhibits an obvious unevenness. 3. In combined seals, changes in the brush bundle axial distance and tooth inclination angle show no significant effect on leakage rate and inter-stage pressure drop distribution; the gradient setting of brush bundle thickness, as well as the number of teeth and the size of tooth tip clearance exhibit certain influences on pressure drop distribution; changes in the brush bundle radial clearance and backplane height exert the most visible effect on the adjustment of pressure drop imbalance; additionally, improvements in pressure drop equalization characteristics between brush bundles at different stages are often accompanied by an increase in seal leakage rate. 4. By cross-compensating the axial and radial dimensions of the brush bundle and setting the parameters of each stage in a non-gradient design, the goal of equalization the pressure drop between stages can be achieved at the cost of a small increase in leakage rate. The improved seal shows a 5.8% increase in leakage rate and a 23% reduction in maximum brush bundle pressure drop compared to the prototype. 5. In multi-stage brush seals, viscous damping dissipations and inertial damping dissipations of the brush bundle lead to an increase in the entropy value of the leakage gas, and the pressure drop increases nonlinearly by stages as the entropy value increases. 6. Compared to traditional methods, the leakage rate of the improved seal increased by only 5.8%, while the backplane height of the improved design (0.6 mm) remains greater than the typical radial clearance of labyrinth seals (0.3 mm), ensuring the practical feasibility of the modified design in engineering applications. This indicates that reducing the height of the first-stage backplane to enhance the inter-stage pressure drop characteristics of multistage brush seals holds significant engineering value. Conceptualization, C.G. and Y.M. ; methodology, C.G. and Y.M. ; software, C.G. ; validation, Y.M. ; formal analysis, W.Z. ; investigation, X.S. ; resources, Y.M. ; data curation, C.G. ; writing--original draft preparation, C.G; writing--review and editing, C.G and Y.M. ; visualization, B.H. ; supervision, Q.Z. ; project administration, Q.Z. ; funding acquisition, Q.Z. All authors have read and agreed to the published version of the manuscript. This study is supported by the National Natural Science Foundation of China (12402408) and the State Key Program of National Natural Science Foundation of China (No. 52236005). Not applicable.