## 3 Results and Discussion  
### Compressor Performance  
Figure 8 shows the flow field at near-stall operation point of configuration 4 of the compressor with seal cavity leakage flow. Figure 8 shows that, forced by pressure difference, the leakage flows into the seal cavity from the stator trailing edge gap, and then flows into the mainstream from the stator leading edge gap after dissipated in vortex form for many times. It can be seen from Figure 8c,d that the labyrinth (the part marked with black box in Figure 8c) is the main sealing part in the cavity flow. When the leakage flows through the labyrinth tip clearance, the flow path contracts, the velocity increases and the static pressure decreases. After passing through the tip clearance, the flow path expands rapidly. The kinetic energy of the fluid dissipates in the cavity between the teeth, during which the velocity decreases, and the pressure change is not obvious. After that, the fluid enters into the next labyrinth tip clearance, and the above process is repeated. After the leakage flow through the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Configuration** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline c1/mm & 0 & 0.4 & 0.5 & 0.5 & 0.5 & 0.5 \\ c2/mm & 0 & 0 & 0 & 0.5 & 0.75 & 1 \\ c1/h1 \(\times\) 100 & 0 & 0.30 & 0.37 & 0.37 & 0.37 & 0.37 \\ c2/h2 \(\times\) 100 & 0 & 0 & 0 & 0.54 & 0.81 & 1.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Clearance values for the different configurations. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Position** & **S0 with Inlet** & **R1** & **S1** & **R2** & **S2** & **R3** & **S3 with Outlet** & **Cavity 1** & **Cavity 2** & **Sum** \\ \hline No. of grid points & 67 \(\times\) 49 & 29 \(\times\) 49 & 29 \(\times\) 49 & 36 \(\times\) 49 & 39 \(\times\) 49 & 32 \(\times\) 49 & 51 \(\times\) 49 & 6975 & 8753 & 29,595 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Number of grid points of configuration 4. Figure 7: Silhouettes for different configurations. multi-stage labyrinth structure, the pressure is significantly reduced, and the sealing process is completed. Such a low-energy leakage flow converges into the main stream at the leading edge of the stator, causing losses by mixing with the main stream. As a result, the flow field at the root of the stator is affected and a low Mach number region is formed. With the increase of labyrinth tip clearance, the overall performance of the compressor decreases. The compressor characteristics of each configuration are shown in Figure 9. It can be seen that, on the one hand, the change in labyrinth tip clearance causes flow rate change near the stall point of the compressor. This is due to the different leakage flow rate in the sealing cavity under different configurations, which makes the stall position of the compressor change. Figure 10 shows the streamlines at near-stall point for 3 different configurations. The minimum compressor inlet flow rate of the configuration 2 is close to that of the configuration 1. It is found in Figure 10 that in both configurations 1 and 2, compressor stall occurs at the root of the third stage stator (S3). When c1 increases to 0.5 mm (configurations 3 and 4), the flow rate near the stall point increases significantly, which means the stall margin decreases. At this time, in contrast to what happens in the first two configurations, the location where stall occurs first moves to the S1 root. It can be seen that when the seal cavity leakage flow increases to a certain extent, the flow field structure of S1 root is destroyed, and the compressor stall occurs ahead of time. With the increase of c2, the minimum flow rate increases further, and the stall starting point becomes S2 root (configurations 5 and 6). Figure 8: Flow field at near-stall point of configuration 4. Figure 10: Streamlines at near-stall point for 3 different configurations. Figure 9: Overall performance of the compressor.