# The Investigation of a New End Wall Contouring Method for Axial Compressors
## 3 Application in a High-Load Compressor Cascade
### Results and Discussion  
To apply the new method to the cascade, a software named _PEWs_ was developed based on the newly proposed method and was used in this study. This software has a graphical interface for the design variables and enables up to 10 independent units for the end wall contouring. Three different groups of end wall contouring were designed using _PEWs_. Table 3 shows their main parameters. Figure 8 provides an overview of their geometry. The contours show the ratio between the end wall contouring height and the blade height (\(\overline{H}\)). Figure 7: The experimental and CFD results of the pitch-averaged performance at 40% \(C_{\text{a}}\) downstream of the TE at \(i=-1^{\circ}\). (**a**) Total pressure loss coefficient; (**b**) Outflow angle. The first case simply uses a full-area unit. The geometry of end wall contouring forms an upslope from the SS to the PS. The aim is to reduce the transverse pressure gradient of the end wall region and decelerate the cross-passage secondary flow over the end wall range. This case is named c1. The geometry of case c1 is similar to the previously mentioned DPS in Ref. [7]. Thus, it represents the end wall contouring generated using a conventional empirical method. The second and third cases both adopt a full-area unit and a localized unit to form the end wall contouring, named c2 and c3, respectively, to show their difference. Their design ideas come from previous research [4], which suggests that the end wall contouring should suppress the secondary flow over the end wall surface while accelerating the secondary flow near the SS corner. The difference between the two cases lies in the weight factors. The localized unit of case c3 has a greater weight than case c2, meaning that the latter tends to enhance the secondary flow locally in the SS corner more than the former. Figure 9 gives the variation of the overall total pressure loss (\(c_{p}\)) with incidence (\(i\)) for the three end wall contouring cases. The working condition with \(i=-1^{\circ}\) is the design point. Compared to case c1, case c2 and case c3 improve the performance of the cascade at the design point. Case c2 improves very little, and case c3 reduces the overall loss by about 0.13%; case c1, on the contrary, slightly increases the loss at the design point. As the incidence increases, the benefit of end wall contouring is gradually lost, but the ranking of the three cases is almost unchanged. When \(i\) exceeds \(+3^{\circ}\), all three end wall contouring cases, including case c3, result in a higher loss than the baseline cascade. Corresponding to the overall performance, Figure 10 provides the spanwise distribution of total pressure loss and flow angle at 0.4\(C_{\text{a}}\) downstream of the TE. At the design point (Figure 10a), all three cases reduce _Loss_ at 0.05_span_, indicating that the three cases have a comparable effect in suppressing the accumulation of low energy fluid at 0.05_span_. The difference is mainly between 0.08_span_ and 0.15_span_, where case c1 and case c2 show larger _Loss_ than the baseline case, and _Loss_ in case c3 is roughly the same as the baseline case. The plots of \(\beta\) show stronger overturning for the baseline case than the end wall contouring cases, indicating that all three end wall contouring cases weaken the end wall secondary flow. Note the phenomenon here: case c3, which reduces the spanwise _Loss_ most, does not correspondingly minimize the overturning, while case c1, which increases the spanwise _Loss_, shows the best control of the overturning in the end wall region. Figure 8: The geometry of the end wall contouring cases: (**a**) case c1; (**b**) case c2; (**c**) case c3.