## 3 Results and Discussions
### Effect of Circle Groove Shape  
It concludes through the above analysis that the configuration with circle groove achieves the most outstanding performance. Configurations with circle groove under different width and depth are established to study the effect of circle groove shape on flow characteristics and aerodynamic performance in this chapter. Specifically, five types of configurations are established by changing \(W\) and \(D\). The structural parameters of five cases are shown in Table 5. Where case1 is the configuration with circle groove established in Section 3.2. The schematic diagram of the five cases is illustrated in Figure 15.  
The Mach number contours of the meridional plane of leakage passage on stator1 and rotor of five cases are depicted in Figures 16 and 17 respectively. By comparing case1, case2 and case3, with an increase in groove width, the vortex is formed in the front half of the circle groove in the opposite direction to that in the seal cavity. The streamlines in the back half deflect, and the working fluid flows into the seal cavity after impacting the groove bottom. By the comparison of case1, case4 and case5, the flow field distribution trends in the circle groove are almost the same. With an increase in groove depth, the size of the vortex is raised. Figure 14: Variations of performance parameters under different groove on cavity surface with pressure ratio (left: relative leakage; right: power and efficiency). Figure 15: Profiles of five cases. Similar to the above chapter, the pressure distributions in Line1 and Line2 are presented in Figure 18. The distribution trends are similar to that in Section 3.2. The pressure decreases gradually along the flow direction in general. There is a local pressure drop at the inlet of the seal gap and local pressure rises at the outlet of the seal gap respectively. The detailed comparison suggests that the variation of width changes the axial position of the pressure rise in the circle groove while the variation of depth affects the peak value of the pressure in the circle groove. The variations of relative leakage, power and efficiency of five cases with pressure ratio are presented in Figure 19. By comparing case1, case2 and case3, case3 holds the lowest leakage, the highest power and efficiency. The relative leakage of stator1 and rotor, power and efficiency under the design condition are \(6.04\times 10^{-3}\), \(8.09\times 10^{-3}\), \(3.467\) MW and \(86.86\%\) respectively. It proves that increasing groove width can improve aerodynamic performance. In addition, these performance parameters of case1, case4 and case5 are very close with a tiny difference. It concludes that the groove depth has little impact on aerodynamic performance. The variation trends of these performance parameters with pressure ratio are the same as those in Sections 3.1 and 3.2. The relative leakage gets increased as the pressure ratio is raised to the design value. The influence of the pressure ratio on the relative leakage is  
Figure 16: The Mach number contours of meridional plane of leakage passage on stator1 of case1–5. Figure 17: The Mach number contours of meridional plane of leakage passage on rotor of case1–5. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Case** & **W/mm** & **P/mm** & **D/mm** & **C/mm** & - & - & - \\ \hline
1 & 1.74 & 5.8 & 0.7 & 0.2 & 0.008 & 3.5 & 0.3 \\
2 & 2.32 & 5.8 & 0.7 & 0.2 & 0.008 & 3.5 & 0.4 \\
3 & 2.9 & 5.8 & 0.7 & 0.2 & 0.008 & 3.5 & 0.5 \\
4 & 1.74 & 5.8 & 0.5 & 0.2 & 0.008 & 2.5 & 0.3 \\
5 & 1.74 & 5.8 & 0.9 & 0.2 & 0.008 & 4.5 & 0.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Configurations of circle grooves. -seal clearance are investigated. Furthermore, the rectangle, circle and V-shaped grooves are arranged on the seal cavity surface. The investigations on the performance of these three configurations under various working conditions are studied. Finally, the effect of the circle groove shape is discussed in detail. Specifically, the following conclusions are drawn. 1. [label=(0)]
2.