# The Investigation of a New End Wall Contouring Method for Axial Compressors
## 3 Application in a High-Load Compressor Cascade
### Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Cases**} & \multicolumn{3}{c}{**Parameters of the**} & \multicolumn{6}{c}{**Parameters of the Localized Units**} \\ \cline{2-9}  & **Full-Area Units** & & & & & & \\ \cline{2-9}  & **Number** & \(w\) & **Number** & \(\epsilon_{1}\) & \(\epsilon_{2}\) & \(\xi_{1}\) & \(\xi_{2}\) & \(w\) \\ \hline c1 & 1 & 1 & 0 & \(\backslash\) & \(\backslash\) & \(\backslash\) & \(\backslash\) & \(\backslash\) \\ c2 & 1 & 0.5 & 1 & 0.4 & 0.9 & 0.9 & 0.1 & 0.5 \\ c3 & 1 & 0.33 & 1 & 0.4 & 0.9 & 0 Figure 10: _Cont_. Figure 9: The overall total pressure loss (\(c_{p}\)) for the three end wall contouring cases. As incidence gradually increases, the benefits of end wall contouring at 0.05_span_ decrease, but the increment of _Loss_ from the 0.08_span_ to 0.15_span_ of the end wall contouring cases becomes more significant than the baseline cascade. When the incidence is larger than 3\({}^{\circ}\), the end wall contouring no longer significantly affects the distribution of _Loss_ at 0.05_span_, and the phenomenon continues till the NS point (\(i=7^{\circ}\)); between 0.08_span_ and 0.05_span_, and the phenomenon continues till the NS point (\(i=7^{\circ}\)); between 0.08_span_ and 0.05_span_, and the phenomenon continues till the NS point (\(i=7^{\circ}\)); between 0.08_span_ and 0.05_span_, and the phenomenon continues till the NS point (\(i=7^{\circ}\)); between 0.08_span_ and 0.05_span_, and the phenomenon continues till the NS point (\(i=7^{\circ}\)); between 0.08_span_ and 0.05_span_, and the phenomenon continues till the NS point (\(i=7^{\circ}\)); between 0.08_span_ and 0.05_span_, and the phenomenon continues till the NS point (\(i=7^{\circ}\)); between 0.08_span_ and 0.05_span_, and the phenomenon continues till the NS point (\(i=7^{\circ}\)); between 0.08_span_ and 0.05_span_, and the phenomenon continues till the NS point (\(i=7^{\circ}\)); between 0.08_span_ and 0.05_span_, respectively. Figure 10: The spanwise distribution of total pressure loss and flow angle at 0.4\(C_{\text{a}}\) downstream of the TE. (**a**) \(i=-1^{\circ}\), i.e., the design point; (**b**) \(i=1^{\circ}\); (**c**) \(i=3^{\circ}\); (**d**) \(i=5^{\circ}\); (**e**) \(i=7^{\circ}\), i.e., the near-stall point. 0.15_span_, the increase of _Loss_ due to the end wall contouring grows significantly with the incidence. During the incidence increase, all end wall contouring cases show no significant increase of \(\beta\). The above results show that the influence of end wall contouring on the cascade mainly works in two areas:  
Within 0.05_span_, the relief of the low-energy region due to the end wall contouring is the key to reducing the overall loss. The difference between cases c1, c2, and c3 is not significant, and this benefit gradually disappears with the increase of the incidence. Between 0.08_span_ and 0.15_span_, the different value of total pressure loss results in the difference among cases c1, c2, and c3. With the increase of the incidence, _Loss_ of the end wall contouring cases gradually grows to be much higher than the baseline case, leading to a significant drop in their overall performance at large incidence. In particular, Figure 11 shows the design point and the near stall point, giving the three-dimensional flow field of the baseline cascade and the end wall contouring cases near the end wall region. Figure 11: _Cont._  
At the design point (Figure 11a,c,e,g), the transparent grey area in the figures is the iso-surface of \(V_{\rm Z}=0.1V_{\rm max}\), which indicates the development of separation in the corner region. The contours show the normalized turbulent viscosity (\(\mu_{t}/\mu\)) within the TE plane, representing the local shear loss caused by separation. The colored curves in the figure are the three-dimensional streamlines in the end wall region, and the color indicates its velocity magnitude. The iso-curve of the static pressure coefficient (\(\overline{p}\)) is plotted on the end wall and blade surface.