## 2 Numerical Calculation Model of Four-Tooth Three-Stage Brush Seal
### Calculation Conclusions and Parameter Improvements
#### 3.3.2 Parameter Improvements  
The aim is to achieve the goal of combining seals, with a lower incremental cost of leakage rate, for significant improvement of pressure drop evenness between brush bundles. According to the law of the influence of different structural parameters on the interstage pressure drop of multistage brush seals in Section 3.2, the structural parameters are improved for the four-tooth three-stage brush combination seal, which has the same values of thickness of brush bundle, axial distance, radial clearance, and height of backplate in each stage. The adjustment and improvement of the seal structure parameters use the method of 'axial dimensions' to compensate for 'radial dimensions', and 'non-gradient setting of brush bundle parameter'. It is necessary to increase the thickness of the first-stage brush bundle, in order to enhance the viscous damping dissipation of the first-stage brush bundle and to compensate for the increase in leakage rate, which is caused by the radial clearance setting of the brush bundle in the subsequent stages. At the same time, it is necessary to reduce the height of the first-stage backplane to enhance the fluid velocity in the first-stage brush bundle, which in turn increases the inertial damping dissipation of the first stage and compensates for the rising leakage rate caused by the increase in the height of the second- and third-stage backplanes. And the thicknesses, radial clearances, the heights of the backplanes of the second- and third-stage are adjusted according to the law of pressure drop unevenness in Section 3.2, instead of being enlarged or reduced stage-by-stage. For the complexity of the unevenness characteristics of the interstage pressure drop distribution, the flexible adjustment of the structural parameters is more reasonable and effective in improving the interstage pressure drop distribution. In the improved combined seal, the thickness of the first-, second-, and third-stage brush bundles are set to 2.3 mm, 2.2 mm, and 2.2 mm, and the height of the backplane of the brush bundle is set to 0.6 mm, 0.8 mm, and 0.9 mm, and the radial clearance of the brush bundle is set to 0.00 mm, 0.05 mm, and 0.07 mm, other structural parameters do not change. A comparison of the structural parameters of the improved and prototype combined seals is shown in Table 3.  
For the improved combined seal structure, its interstage pressure drop distribution and leakage rate are calculated using the numerical model in Section 2.2, and a comparison of the characteristics of the improved combined seal and the prototype combined seal is \begin{table}
\begin{tabular}{c c c} \hline
**Structural Parameters** & **Prototype (Basic Type)** & **Improved Type** \\ \hline Outside diameter/mm & \(158\) & \(158\) \\ Inside diameter/mm & \(138\) & \(138\) \\ Axial distance of first-stage brush bundle/mm & \(1.8\) & \(1.8\) \\ Axial distance of second-stage brush bundle/mm & \(1.8\) & \(1.8\) \\ Axial distance of third-stage brush bundle/mm & \(1.8\) & \(1.8\) \\ Thickness of first-stage brush bundle/mm & \(2.2\) & \(2.3\) \\ Thickness of second-stage brush bundle/mm & \(2.2\) & \(2.2\) \\ Thickness of the third-stage brush bundle/mm & \(2.2\) & \(2.2\) \\ Height of backplane for first-stage brush bundle/mm & \(1.0\) & \(0.6\) \\ Height of backplane for second-stage brush bundle/mm & \(1.0\) & \(0.8\) \\ Height of backplane for third-stage brush bundle/mm & \(1.0\) & \(0.9\) \\ Radial clearance of the first-stage brush bundle/mm & \(0.0\) & \(0.00\) \\ Radial clearance of second-stage brush bundle/mm & \(0.0\) & \(0.05\) \\ Radial clearance of third-stage brush bundle/mm & \(0.0\) & \(0.07\) \\ Number of grate teeth & \(4\) & \(4\) \\ Inclination of grate teeth/\({}^{\circ}\) & \(55\) & \(55\) \\ Radial clearance of grate teeth/mm & \(0.3\) & \(0.3\) \\ \hline \end{tabular}
\end{table} 
Table 3: Structural Parameters of Improved Combination Seal and Prototype Combination Seal.