## 3 Results and Discussion
### Spanwise Parameters  
In order to further analyze the flow mechanism of the change of compressor stage characteristics caused by seal cavity leakage flow, the distribution of spanwise parameters reflecting the performance of blade row under different tip clearance conditions were analyzed and compared. Figure 14 shows the inlet axial momentum of the second stage stator S2 (normalized by the inlet axial momentum at the middle span of the second stage rotor when there is no gap leakage), incidence angle, diffusion factor and loss coefficient. The definition of diffusion factor D and loss coefficient \(\varpi\) and are as follows  
\[D=1-\frac{w_{2}}{w_{1}}+\frac{\Delta w_{u}}{2\tau w_{1}}\]  
Figure 12: Stage work coefficient penalty for varying seal-tooth clearance. Figure 13: Stage pressure coefficient penalty for varying seal-tooth clearance. \[\varpi=\frac{p_{1}^{*}-p_{2}^{*}}{p_{1}^{*}-p_{1}}\]  
where \(w_{1}\) is the average velocity at the blade inlet, \(w_{2}\) is the average velocity at the blade outlet, \(\Delta w_{u}=|w_{1u}-w_{2u}|\) is the torsional velocity, \(\tau\) is the blade solidity, \(p_{1}^{*}\) is the average total pressure at blade inlet, \(p_{2}^{*}\) is the average total pressure at blade outlet, and \(p_{1}\) is the average static pressure at blade inlet. In general, the change of cavity 1 clearance has little effect on S2, but with the increase of cavity 2 clearance c2, the inlet axial momentum of S2 blade below 15% span decreases, reflecting the increase of flow blockage; the incidence angle also increases obviously. The difference of incidence angle between c2 maximum clearance and non-clearance case reaches 6\({}^{\circ}\) at 0.25% span, which also confirms the increase of flow blockage and blade load. The flow blockage forces the fluid to migrate to the middle of the span, resulting in a decrease of the incidence angle of the blade above 15% of the span. The difference in the incidence angle between 20% and 40% relative span is the largest. The leakage flow of the seal cavity with an increase of c2 from 0 to 1 mm reduces the incidence angle by 1.6\({}^{\circ}\). The decrease of incidence angle leads to the decrease of blade load. In contrast to the other parameters, the change of loss mainly occurs at the root of the stator blade, which is shown as a pronounced bulge in the figure. With the increase of c2, the maximum loss coefficient of stator root increases from 0.2 to 0.55, and the spanwise range of bulge also expands from 5% to 18%. Figures 15 and 16 show the spanwise distribution of blade row parameters of rotors R2 and R3, respectively. The diffusion factor of R2 and the loss coefficient of both rotor blade rows are not shown since they change little. In addition, in order to make the contrast more obvious, Figure 15 only shows the distribution of R2 below 30% span. It should be pointed out that since the rotation direction of the rotor is defined as the positive direction of the circumferential angle in the calculation process, it can be seen from the velocity triangle of the elementary flow that when the axial momentum of the rotor inlet is small, the incidence angle is numerically negative, which is different from that of the stator. From Figure 15 it can be seen that the inlet axial momentum and incidence angle of R2 is basically unchanged with the change of c2, that is, the leakage flow from the seal cavity has little effect on the performance of upstream blade row. With the increase of c1, the inlet axial momentum of R2 root (below 8% span) decreases, and the incidence angle increases, which reflects that the flow is blocked. The blockage causes the flow to migrate to the middle of the span. In consequence, the inlet axial momentum above 10% span increases, and the incidence angle decreases. It can be seen that the change of leakage flow in the S1 root also affects the performance of downstream R2 blade row. Similar to Figure 15, Figure 16 shows that, with the increase of the tip clearance c2 of the seal cavity, the leakage flow also causes root blockage of R3.