# Toward the Utilization of 3D Blading in the Cantilevered Stator from Highly Loaded Compressors
## 3 Effects of 3D Blading on the Cantilevered Stator
### Effects of the Blade Dihedral  
#### 3.2.1 Effects of the Dihedral Height  
Except for the forward sweep, the positive dihedral is also adopted in the present study to optimize the stator performance. Therefore, the effects of the dihedral height and dihedral angle need to be clarified. As shown in Table 2, the dihedral height is varied between 20% and 60% of the total blade height, whereas the dihedral angle is between 120\({}^{\circ}\) and 150\({}^{\circ}\). The modeling schemes are named following the same rule as that of the sweep (e.g., scheme \"C1D1\" corresponds to a dihedral starting from 30% blade span with a dihedral angle of 120\({}^{\circ}\)). Likewise, the influence of dihedral height is first compared using the control variate method. As shown in Figure 14, the design schemes are C1D3, C2D3, and C3D3. A slight positive sweep is also adopted at the tip region (150\({}^{\circ}\), 90% span). Simulation results are compared to the orthogonal/straight blade (Orth. ); note that no sweep is utilized in this section. Figure 15 presents the pressure rise and loss characteristics for the design schemes with different dihedral heights. Compared with the orthogonal blade, the scheme with a small dihedral height (C1D1) could improve the diffusing capacity of the cantilevered stator without increasing its total pressure loss, thus improving the aerodynamic performance of the cantilevered stator. However, with the increase of the dihedral height (C2D3 and \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter Type** & **1** & **2** & **3** \\ \hline C: Dihedral height & 20\% span & 40\% span & 60\% span \\ D: Dihedral angle & 120\({}^{\circ}\) & 135\({}^{\circ}\) & 150\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Modeling scheme for blade dihedral. Figure 14: Radial distribution of blade dihedral for the cases with different dihedral heights. Figure 13: The comparison of the streamwise leakage mass flow rate under different sweep angles (\(\varphi=0.46\)). C3D3), the blade loss will start to rise, and the pressure rise capacity is reduced remarkably, thus eliminating the advantages of the positive dihedral. To determine the reason why increasing the dihedral height will reduce the stator performance, the flow field distribution was established for the cases with different dihedral heights, as presented in Figure 16. Results at the mass flow coefficient of 0.52 demonstrate that the positive dihedral will not only push the trajectory of the leakage vortex away from the blade suction surface but also promote the radial migration of the low-energy fluid. In scheme C1D3, the dihedral height is relatively low, and the accumulation of low-energy fluid at the corner region of the blade suction surface is reduced by the circumferential migration of the leakage flow. Therefore, the blockage at the blade outlet is alleviated significantly. With the increase of the dihedral height (C2D3), although the corner separation at the stator hub is weakened effectively, the wake in the lower and middle parts of the blade is elongated and widened remarkably, which is detrimental to the comprehensive aerodynamic performance of the cantilevered stator. Moreover, if the dihedral height is further increased to 60% (C3D3), the leakage flow will undergo an obvious radial migration under the strong blade force. As a result, the separation at the blade trailing edge will be significantly enhanced, and the performance of the cantilever stator will further deteriorate. Note that with the decrease of the mass flow coefficient, the influence of the dihedral amplifies substantially. Figure 16: Flow field distribution for the cases with different dihedral heights. Figure 15: Pressure rise and loss characteristics for the stator with different dihedral heights. (**a**) Pressure rise and (**b**) loss. The radial distribution of the aerodynamic parameter for the cases with different dihedral heights is given in Figure 17 to evaluate the stator performance quantitively.