## 2 Numerical Calculation Model of Four-Tooth Three-Stage Brush Seal
### The Verification of the Accuracy of the Numerical Method
#### 3.1.2 Uneven Pressure Drop Characteristics  
The axial pressure distribution of the extracted four-tooth three-stage brush combination seal is shown in Figure 12. Like other multi-stage brush seals, the combination seal has a marked characteristic of uneven pressure drop between stages. From the upstream high pressure along the axial direction (X-negative direction) to the downstream low pressure, the pressure value in the area of the first grate tooth shows a significant decrease, and the grate teeth behind are also slightly decreased, with a total decrease of about 8.4%. Continuing along the X-negative direction to the area of the first-stage brush bundle, the pressure drop increases significantly, and the ratio of pressure drop for the first, second, and third-stage brush bundles is about 18.3%, 30.0%, and 43.3%, respectively. This shows a tendency for the pressure drop ratio to expand by stages, and there is an uneven characteristic of the pressure drop of the three-stage brush bundle.  
In the process of high-pressure gas flowing through the three-stage brush seal, the pressure energy of the fluid is continuously converted into kinetic energy, and the gas flow rate increases quickly. As the gas flows through the brush beam, into the gap of the brush wire in the high-speed winding flow, the brush wire surface layer will produce viscous dissipation, and the back of the brush wire separation produces a large number of small-scale vortexes, which will produce an inertial dissipation of resistance. The two types of dissipation increase by stages, the entropy value of the gas also increases by stages, and the pressure drop increases rapidly with the increase in entropy value.  
Figure 11: Flow traces of four-tooth three-stage brush seal combination (differential pressure 0.6 MPa, gauge pressure).  
Figure 10: Vector cloud diagram of the flow velocity of four-tooth three-stage brush combination seal (differential pressure 0.6 MPa, gauge pressure).  
Figure 9: Pressure distribution of four-tooth three-stage brush combination seal (differential pressure 0.6 MPa, gauge pressure).  
_Seal Leakage Rate and Pressure Drop Distribution Change Rule Under Different Structural Parameters of Four-Tooth Three-Stage Brush-Type Combination Seal_  
To analyze the pressure drop unevenness and sealing characteristics of the four-tooth three-stage brush combination seal, different values of key parameters such as axial distance, thickness of brush bundle, radial clearance of brush bundle, height of backstop, as well as the inclination angle of grate teeth, the number of grate teeth, and the clearance at the top of the teeth were set up, the geometric model of the combination seal with different structural parameters was designed, and the changes in leakage rate and pressure drop distribution were calculated for the different models.  
To simplify the graphical labeling, the models with different structural parameters are numbered in the following Figures in the form of 'X-YYY-ZZ' and 'X-Z1-ZZ-Z3', where 'X' represents the structural parameter, specifically: '1-' represents the 'Axial distance', '2-' represents the brush bundle thickness, '7-' represents the radial clearance of the brush bundle, and '9-' represents the height of the baffle; where 'YYY-ZZ' means that the first, second, and third stages of the brush bundles are set with the same value of ZZ; and 'Z1-Z2-Z3' means that the first, second, and third stages of the brush bundles are set with different values of Z1, Z2, and Z3. For example, '1-123-15' means that the axial distance of the first-, second-, and third-stage brush bundles are set to 1.5 mm, and '1-24-22-20' means that the axial distance of the first-, second-, and third-stage brush bundles are set to 2.4 mm, 2.2 mm, 2.0 mm, respectively. Other structural parameters take similar markings.