# The Investigation of a New End Wall Contouring Method for Axial Compressors
## 3 Application in a High-Load Compressor Cascade
### Results and Discussion
\(\overline{p}\) is defined as  
\[\overline{p}=\frac{p-p_{\rm in}}{(pt_{\rm in}-p_{\rm in})} \tag{10}\]  
Figure 11c shows that case c1 significantly weakens the cross-passage secondary flow. The significant changes are mainly reflected in three areas:  
1. First, the corner region near \(0.2C_{\rm a}\) to \(0.4C_{\rm a}\) from the LE (in the rightmost black box in Figure 11c), which, according to the streamlines, shows that this is precisely where the corner separation starts. The iso-curves of \(\overline{p}\) show that the sinking end wall near the SS corner increases the pressure gradient significantly. Thus, the reverse flow is intensified, and more low-energy fluids accumulate in the corner region. This ultimately increases the local shear loss and exacerbates corner separation. 2. Second, from the mid-chord to the rear region of the SS corner (located in the red box in the middle), the secondary climbing flow weakens, and the same is true for the cross trend of the end wall flow in the outer region (as shown by the red arrows). This is caused by the sinking surface of the end wall on the suction side. The weakened cross trend of end wall secondary flow will inhibit the accumulation of the low-energy fluid and thus help to reduce loss. 3. Third, near the TE of the SS (in the blue box on the left), the end wall iso-curves of \(\overline{p}\) show a high-density region, indicating that the streamwise pressure gradient is significantly reduced compared to the baseline case. This should be induced by the local streamwise upslope in the SS corner. This effect enhances the flow momentum of both the end wall flow (shown by the solid blue arrow) and its climbing motion after colliding with the SS (indicated by the dashed blue arrow). The acceleration of the climbing flow mixes with the low-energy fluid on the SS and increases its streamwise momentum. According to the contour of \(\mu_{t}/\mu\) at the TE plane, this \"pre-mixing\" effect reduces the shear effect between the separation flow and the main flow and thus brings benefits. The correlation between the low-energy flow near the TE and upstream streamline is worth noting. According to the streamlines in the baseline cascade, the low-energy flow of the lower span at the TE plane (labeled with a solid white circle in Figure 11a) is associated with the secondary flow in the rear part of the corner region. In contrast, the low-energyflow of the higher span (labeled with a dashed white circle in Figure 11a) comes from the climbing flow along with the SS at the onset of separation in the upstream corner region. Because case c1 exacerbates the corner separation in the upstream SS corner, this indicates that the reduction of the _Loss_ within 0.05_span_ in Figure 10 comes from the second and third effects mentioned above, while the increase of _Loss_ between 0.08_span_ and 0.15_span_ is mainly due to the first effect. Compared to case c1, both case c2 and case c3 have less sinking end wall near the SS due to the localized unit. In the SS corner region from 0.2\(C_{\text{a}}\) to 0.4\(C_{\text{a}}\), the iso-curves of \(\overline{p}\) suggest that the inverse pressure gradient is lower than that of case c1, which makes the local inverse flow induced by case c2 and c3 less severe than that of case c1 (as shown by the black arrows in Figure 11e,g). As a result, the low-energy separation flow at the high span region near TE is also significantly reduced. Another region affected by the localized unit is the corner region from the 0.5\(C_{\text{a}}\) to the TE. The rise of the end wall near the corner region makes the climbing flow near the TE accelerate significantly and sweep downstream (as shown by the blue arrows in Figure 11e,g). This is consistent with the research in [4]. On the one hand, the energized secondary flow eliminates the low-energy flow in the corner vortex. More importantly, it enhances the \"pre-mixing\" effect of the secondary flow with the low-energy flow in the corner region mentioned in case c1.