## 2 Numerical Calculation Model of Four-Tooth Three-Stage Brush Seal
### The Verification of the Accuracy of the Numerical Method
#### 3.2.5. Grate Tooth Radial Distance, Number of Teeth, and Angle of Inclined Teeth  
In the combined seal, the tooth-top throttling effect of the grate teeth and the vortex effect of the tooth cavity also contribute in part to the pressure drop and sealing performance. So, it is necessary to calculate their main structural parameters and analyze their influence on the pressure distribution and leakage of the combined seal.  
Calculations show that with the reduction in the radial distance between the grate teeth and the increase in the number of grate teeth, the leakage rate of the combined seal is effectively reduced, while the angle of tooth inclination is insensitive to the leakage, as shown in Figures 28-31. Calculations show that with the reduction in the radial distance between the grate teeth and the increase in the number of grate teeth, the leakage rate of the combined seal is effectively reduced, while the angle of tooth inclination is insensitive to the leakage, as shown in Figures 28-31. The reduction in the radial distance of the grate teeth will enhance the top-of-the-tooth throttling effect, and the increase in the number of teeth can enhance the vortex effect of the tooth cavity, both of which can increase the effect on the dissipation of high-energy fluids, and thus reduce the leakage.  
As shown in Figure 32, the change in the degree of inclination of the grate teeth has no obvious effect on the interstage pressure drop of the multistage brush bundle, because the change in the teeth's angle does not produce obvious changes in dissipation, so the leakage rate and the pressure drop percentage in the grate teeth region barely change with the teeth's angle. In turn, the uneven pressure drop characteristics of the three-stage brush bundle do not change obviously.  
Figure 28. Influence of grate tooth structure parameters on combined seal leakage rate.  
As shown in Figure 33, the distance between the teeth and rotos affects the pressure drop characteristics between the brush bundle stages. As the distance between the teeth increases, the pressure drop percentage in the grate teeth region gradually decreases, and the pressure drop percentage in the brush bundle region gradually improves, and the percentage of the first and second stages increases faster than that of the third stage. This is because, at an increased distance between the teeth, the top-of-the-teeth throttling effect is weakened and the conversion of the high-energy fluid pressure into kinetic energy through the grate teeth area is not effectively dissipated. High-speed fluid causes a downstream impact, the first and second brush bundle circulation area flow rate increases, and the brush bundle inertial damping-based dissipation with the flow rate increases, so the first and second pressure drop percentage increases. The weakening of the third stage is due to the fact that the first and second stages have absorbed the main fluid impacts in the front.  
Figure 30: Flow traces of combined seals with different numbers of teeth.  
Figure 29: Flow traces of combined seals with different radial tooth distances.  
Figure 31: Flow traces of combined seal for different tooth inclination angles.  
Figure 32: The effect of the degree of inclination of the grate teeth on the interstage pressure drop unevenness characteristics of the combined seals.  
Figure 33: Effect of radial teeth distance of grate teeth on unevenness characteristic of pressure drop between combined seal stages.  
As shown in Figure 34, a reduction in the number of grate teeth can also slightly adjust the unevenness characteristic of the pressure drop of the combined seal. This is due to the reduced number of teeth, the insufficient dissipation in the grate region, the higher kinetic energy of the fluid at the outlet of the grate region, and the higher velocity of the incoming flow to the first and second-stage brush bundles resulting in an increase in dissipation.