## 3 Results and Discussions  
### Effect of Seal Clearance  
Seal clearance is a critical variable that affects the performance of LS. In this chapter, straight LS teeth are arranged on the top of stator1 and rotor. The no-dimensional seal clearance is defined by  
\[\overline{C}=\frac{C}{H_{\text{in}}}, \tag{4}\]  
where, \(H_{\text{in}}\) represents the blade height at inlet of rotor. The no-dimensional seal clearances (\(\overline{C}\)) are 0.004, 0.008, 0.012 and 0.016 respectively. The flow characteristics and aerodynamic performance of four configurations under different speed and pressure ratio are discussed in detail. The static pressure contours of meridional planes of four configurations under the design condition are demonstrated in Figure 5. In the cascade passage, the pressure decreases gradually along the flow direction. The rotor passage bears the maximum pressure drop due to the fact that the working fluid pushes the rotor blade to generate power. In the top leakage passage of stator1 and rotor, the pressure \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Grid Number** & **Mass Flow Rate/(kg/s)** & **Deviation/\%** & **Power/kW** & **Deviation/\%** \\ \hline \(5\times 10^{5}\) & 135.82 & - & 3.373 & \\ \(1.2\times 10^{6}\) & 136.18 & 0.264 & 3.384 & 0.325 \\ \(1.8\times 10^{6}\) & 138.14 & 1.419 & 3.435 & 1.485 \\ \(2.5\times 10^{6}\) & 138.25 & 0.079 & 3.442 & 0.203 \\ \(3.2\times 10^{6}\) & 138.26 & 0.007 & 3.443 & 0.029 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Grid independence study. Figure 4: The geometric structure and analysis results for validation. also gets reduced along the flow direction. Vortex is formed in the cavity between each LS tooth, which is caused by the throttling and expansion effect at the seal gap. The existence of secondary flow further leads to energy dissipation and pressure drop. Furthermore, the mixing effect generated by the main flow and leakage flow at the outlet of leakage passage is raised gradually with an increase in seal clearance, which is represented by the deflection of nearby main flow streamline and even the local vortex. This has a notable effect on turbine performance. The static entropy contours of meridional planes of four configurations under the design condition are depicted in Figure 6. It concludes that the static entropy in the main flow passage is always at a low level. High static entropy is observed in the central area of the seal cavity, indicating chaotic flow and high energy loss. The static entropy at the outlet of leakage passage increases gradually with an increase in seal clearance, indicating a gradual increase in energy loss. This is because when the leakage flow enters the cascade, it has a certain radial velocity. This is quite different from the main flow along the axial direction, resulting in a high mixing loss. Figure 5: The static pressure contours of the meridional planes. Figure 6: The static entropy contours of the meridional planes. When the leakage flow of stator1 enters the rotor cascade, it affects the flow field distribution of the rotor near the hub side. Similarly, the flow field distribution of stator2 near the shroud side is affected by the leakage flow of the rotor. Therefore, the flow characteristics of 1% blade height of the rotor and 99% blade height of stator2 are obtained, indicated in Figure 7. It is observed that there is a strong mismatch between the angle at the inlet side and the geometry installation angle because of the mixing of the main flow and leakage flow. Moreover, the stronger mismatch and disordered streamlines are achieved as the seal clearance increases, causing the reduction of the working ability of the rotor blade.