## 3 Results and Discussion
### Simulation of Brush Seal with Clearance  
For the brush seal with clearance, 2D CFD simulations were performed using the [PERSON] et al. [27] geometry. The flow conditions and geometrical parameters are listed in Table 3. Moreover, the bristle density is known to be determined by the bristle diameter [20]. Therefore, since the bristle diameter of the [PERSON] et al. [27] geometry is very similar to that of the [PERSON] et al. [25] geometry, the same bristle density of 94.5 per mm was used to calculate the porosity for the [PERSON] et al. geometry [27]. In brush seals with clearances, the blow-down effect, whereby the bristle pack moves toward the rotor, must be considered as it significantly impacts the flow. Therefore, the calculations were performed after setting the blow-down clearance for each pressure ratio based on the findings of [PERSON] et al. [52], who analyzed the blow-down effect in the [PERSON] et al. [27] geometry using 2D axisymmetric CFD. The blow-down clearance is calculated by subtracting the extent of the blow-down from the initial clearance, as shown in Equation (5). The blow-down clearance for each clearance level is illustrated in Figure 8. As in the case without clearance, the flow resistance in the upper region was set 20% higher than that in the fence height region to match the experimental data [52]. \[Blow-down\ Clearance=Initial\ Clearance-(Blow-down). \tag{5}\]  
As shown in Figure 9, the leakage flow rates were accurately predicted for the two clearance levels in the brush seals. Leakage flow rates were calculated using Equation (1), regardless of the blow-down clearance levels. When disregarding the blow-down effect, the leakage flow rate tends to be overestimated relative to the experimental data under high  
Figure 8: Variation in blow-down clearance with pressure ratio for different initial clearances: (a) clearance = 0.27 mm; (b) clearance = 0.75 mm. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **[PERSON] et al. [27]** \\ \hline Bristle diameter (\(d\)) & 0.076 mm \\ Bristle pack thickness (\(t\)) & 0.75 mm \\ Bristle lay angle (\(\phi\)) & 45\({}^{\circ}\) \\ Fence height (\(H\)) & 1.4 mm \\ Clearance (\(CL\)) & 0.27 mm, 0.75 mm \\ Bristle density (\(N\)) & 94.5 per mm \\ Upstream temperature & 293.15 K \\ Downstream pressure & 100 kPa \\ Pressure ratio \(\left(\frac{p_{e}}{p_{d}}\right)\) & 1.07–3.8 \\ Porosity (\(\varepsilon\)) & 0.192 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Flow conditions and geometrical parameters of brush seals with clearance [27]. pressure conditions. Even a slight reduction in clearance results in a significant reduction in leakage [52]. The CFD predictions for the brush seal with clearances are presented in Figure 10, and the observations are compared with those for the brush seals without clearance (Figure 7). Specifically, a comparison between the pressure distributions in Figures 7 and 10 reveals that in the case without clearance, the pressure was more uniformly maintained as the flow passed through the bristle pack, and the pressure drop in the downstream region was less abrupt. Contrarily, in the brush seal with clearances, the pressure drop was distributed across the thickness of the bristle pack, including the clearance, and it became more abrupt from upstream to downstream. A comparison between the axial velocities in Figures 7 and 10 shows that in the case without clearance, the axial velocity remained relatively constant as the flow passed through the bristle pack, showing a more stable and consistent pattern. However, in the case with clearances, the axial velocity increased as the flow passed through the clearance, specifically at the clearance exit. The radial velocity is also compared between Figures 7 and 10. In the case without clearance, the radial velocity remained relatively constant as the fluid passed through the bristle pack, resulting in a less intense radial flow. By contrast, in the case with clearances, a strong radial flow was observed at the clearance inlet.