## 3 Effects of Incidence Angle and Circumferential Location of Splitter Vane
### Blade Performance with Different Incidence Angles and Circumferential Locations  
Figure 6 plots the total pressure loss and pressure rise on the design condition for both the original designs and the \"impact-free entry\" designs. It can be seen that the two incidence rules have consistent effects on total pressure loss for the cascades with different blade loading level. For Cases 1 and 2 with comparably lower loading, it is showed that the \"impact-free entry\" designs have benefits somewhat compared to the original designs. In addition, significant gains can be attained for Case 3 with comparably higher blade loading, especially at a large range of PP. The overall static pressure rise is essentially insensitive to the incidence rules. On the other hand, PP itself has a significant influence on blade pressure rise and loss. It is indicated that the responses of the \"impact-free entry\" designs to PP remain similar as those of the original designs. For Cases 1 and 2 with comparably lower loading, it is illustrated that they have the smallest loss at PP = 0.5. For Case 3, larger PP is, surprisingly, associated with lower loss. As for the static pressure rise, all the three cases show consistently a peak pressure rise at about PP = 0.5.  
Figure 7 presents the blade surface pressure distributions at different PP for Case 2. For the typical case, it shows that all \"impact-free entry\" designs eliminate the strong leading-edge acceleration on SS or PS due to the improper selection of incidence angles for SVs. This explains why the \"impact-free entry\" designs show lower loss in Figure 6.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Case\_1** & **Case\_2** & **Case\_3** \\ \hline camber angle, \(\phi_{\text{pb}}\) (\({}^{\circ}\)) & 46.7 & 46.7 & 53.8 \\ equivalent solidity (ES), \(\sigma_{\text{eq}}\) & 2.04 & 2.04 & 1.59 \\ principal blade solidity, \(\sigma_{\text{pb}}\) & 1.39 & 1.21 & 1.08 \\ chord ratio (CR) & 0.47 & 0.68 & 0.47 \\ diffusion factor (DF), PP = 0.5 & 0.51 & 0.55 & 0.62 \\ percent pitch (PP) & & 0.22–0.83 & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Geometry parameters of three splittered cascades for performance sensitivity analyses.  
Figure 6: Total pressure loss and static pressure rise of three cases with “#” denoting “impact-free entry” designs, without “#” denoting original designs.  
On the other hand, it is indicated that the pressure distribution is considerably influenced by PP. At PP = 0.5 in Figure 7b, the principal blade and splitter vane have similar blade surface pressure distribution, resulting in a suitable balance in loading between the two blades. This favorable pressure distribution contributes to the highest static pressure rise in Figure 6. As SVs are located near PBs, the interaction of SVs and PBs tends to be stronger. At PP = 0.83 in Figure 7a, the acceleration of the SS of SVs significantly decreases the pressure of the PS of PBs so that the rear part of PBs is completely unloaded. Therefore, the overall static pressure rise apparently decreases, as shown in Figure 6. At PP = 0.22 in Figure 7c, the peak on PS of the SVs is higher because of the acceleration at the front part of PS of SVs so that the load of SVs is decreased. That is why lower PP decreases the overall static pressure rise.