## 3 Results and Discussions
### Effect of Groove on Cavity Surface  
The energy dissipation and sealing performance are achieved by throttling and expansion effect at the seal gap and vortex formed in the seal cavity. The change of the seal cavity wall shape affects the secondary flow and further the energy dissipation in the seal cavity. Therefore, three types of grooves, namely rectangle, circle and V-shaped, are set on the cavity wall near the seal gap outlet. The influence of the groove on the flow characteristics and aerodynamic performance is investigated. Figure 9: Variations of performance parameters under different seal clearance with pressure ratio (left: relative leakage; right: power and efficiency). The non-dimensional groove depth is given by  
\[\overline{D}=\frac{D}{C}, \tag{8}\]  
The non-dimensional groove width is given by  
\[\overline{H}=\frac{H}{P}, \tag{9}\]  
where \(D\) denotes groove depth and \(H\) denotes groove width. The profiles of the three types of structures are illustrated in Figure 10. Where, according to the geometric structure, the values of \(\overline{C}\), \(\overline{D}\) and \(\overline{H}\) are set as 0.008, 3.5 and 0.3 respectively. The Mach number contours of the meridional plane of leakage passage on stator1 and rotor of different structures are presented in Figures 11 and 12 respectively. The flow field distribution of the two leakage passages is similar. After the working fluid flows through the seal gap, a large vortex is formed in the seal cavity and a small one with reverse direction is produced in both rectangle and circle groove. This further strengthens the disturbance of the working fluid and enhances the energy dissipation. However, for the V-shaped groove, only a tiny vortex is generated at the bottom of the groove, and most streamlines are only slightly deflected. Figure 11: The Mach number contours of meridional plane of leakage passage on stator1. Figure 12: The Mach number contours of meridional plane of leakage passage on rotor. Figure 10: Profiles of seals under different cavity surface shape. The pressure distributions in Line1 and Line2 are selected to characterize the pressure distributions in leakage passages along an axial direction, just as shown in Figure 13. Where Line1 is the intersection line of the X-Z plane and the outer surface of leakage passage on stator1. Line2 is the intersection line of the X-Z plane and the outer surface of leakage passage on rotor1. The pressure drop along the flow direction can be observed clearly. Due to the throttling effect at the inlet of the seal gap, the flow acceleration occurs and the pressure decreases significantly. Moreover, a local expansion exists at the outlet of the seal gap and the local pressure increased. The pressure in the seal cavity with groove is much higher than that in the seal cavity without groove, which is the conversion of more kinetic energy to potential energy owing to the enhanced flow disturbance. The variations of relative leakage, power and efficiency under different groove on the cavity surface with pressure ratio are presented in Figure 14. Configurations with groove have lower leakage, higher power and efficiency compared with the non-grooved configuration under any working condition. It can conclude that arranging groove on the seal cavity wall near the outlet of the seal gap can enhance the sealing effect and improve the aerodynamic performance. Further comparison shows that the configuration with circle groove achieves the lowest leakage, the highest power and efficiency. This can be explained by the following fact. From the streamline distributions in Figures 11 and 12, it can be seen that no vortex is formed in the V-shaped groove and most streamlines are only slightly deflected. Thus, the energy dissipation in the leakage channel is the lowest and the performance is relatively the worst. As for the rectangle and circle groove, there are local small vortices which are opposite to the large vortices in the seal cavity.