## 3 Results and Discussion
### Simulation of Contact Brush Seal with Porosity Correction  
For brush seals in a contact state without clearance, the geometries used by [PERSON] et al. (2015) and [PERSON] et al. (2016) were analyzed via 2D CFD simulation. The geometrical parameters and flow conditions are listed in Table 2. Figure 6 compares the CFD results with the experimental data. The main differences between the two brush seal geometries lie in their bristle diameter, bristle pack thickness, and bristle density. These differences significantly affect the porosity of each brush seal, leading to variations in flow characteristics and performance. Additionally, as the fence height differs by more than two-fold between these geometries, analyzing the associated difference in flow behavior is crucial. As shown in Figure 6a, the leakage flow rates were accurately predicted for the two geometries. However, as seen in Figure 6b, the predictions were less accurate for pressure ratios above 6; this is attributed to the increasing influence of the non-linear effects arising from the combination of high pressure and friction in the brush seals ([PERSON] et al., 2015). For both the [PERSON] et al. (2015) and [PERSON] et al. (2016) geometries, the pressure (Figure 7a) was the highest upstream and gradually decreased as the fluid passed through the bristle pack toward the downstream region. For the [PERSON] et al. (2015) geometry, the pressure drop occurred gradually through the bristle pack, enabling a more stable state to be maintained downstream. However, for the [PERSON] et al. (2016) geometry, the pressure decreased more rapidly and stabilized relatively quickly in the downstream region. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **[PERSON] et al. (2015)** & **[PERSON] et al. (2016)** \\ \hline Bristle diameter (\(d\)) & 0.0762 mm & 0.051 mm \\ Bristle pack thickness (\(t\)) & 0.7 mm & 0.8 mm \\ Bristle lay angle (\(\phi\)) & 45\({}^{\circ}\) & 40\({}^{\circ}\) \\ \multicolumn{2}{c}{Fence height (\(H\))} & 1.5 mm & 0.655 mm \\ \multicolumn{2}{c}{Clearance (\(CL\))} & 0 mm & 0 mm \\ Bristle density (\(N\)) & 94.5 per mm & 180 per mm \\ Upstream temperature & 293.15 K & 290 K \\ Downstream pressure & 100 kPa & 100 kPa \\ Pressure ratio \(\left(\frac{p_{u}}{\mu_{d}}\right)\) & 1.07–3.8 & 2–8 \\ \multicolumn{2}{c}{Porosity (\(\epsilon\))} & 0.129 & 0.285 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Flow conditions and geometrical parameters of brush seals without clearance ([PERSON] et al., 2015; [PERSON] et al., 2016). Figure 5: Leakage flow rate predicted based on 2D CFD simulation with porosity obtained from the initial geometry used by [PERSON] et al. (2015). Figure 6: Leakage flow rates of contact brush seals predicted by 2D CFD with porosity correction: (a) [PERSON] et al. [25]; (b) [PERSON] et al. [26]. Figure 7: \(Cont\). In both studies, the axial velocity (Figure 7b) increased downstream as the flow passed through the bristle pack, highlighting a common trend of high-velocity regions being formed near the backing plate [51]. For the [PERSON] et al. [25] geometry, a distinct high-velocity region was observed immediately downstream of the bristle pack, with a more localized distribution relative to the [PERSON] et al. [26] geometry. Conversely, for the [PERSON] et al. [26] geometry, the high-velocity region was more broadly spread, but its intensity was less pronounced than in the [PERSON] et al. [25] geometry. The changes in radial velocity (Figure 7c) also show a common trend between the two geometries, with fluctuations observed as the flow passed through the bristle pack and moved downstream. These changes in radial velocity are associated with pressure drops. For the [PERSON] et al. [25] geometry, the variation in radial velocity was more distinct and followed a more consistent pattern compared with that for the [PERSON] et al. [26] geometry.