# 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
#### 3.2.2 Effects of the Dihedral Angle  
To investigate the influence of the dihedral angle, under the optimum dihedral height, the stator performances with different dihedral angles are inspected. As illustrated in Figure 19, the cases to be investigated are C1D1, C1D2, and C1D3; note that the blade tip also adopts positive dihedrals (at 80% span with the same dihedral angle as the hub) to balance the pressure gradient in the radial direction.  
The pressure rise and loss characteristics for the design schemes with different dihedral heights are demonstrated in Figure 20. The influence of the dihedral is more pronounced in terms of pressure rise coefficient and at small mass flow ratios. In comparison to the orthogonal blade, the positive dihedral will always improve the blade static pressure coefficient, whereas the increment will first increase and then decrease with the increase of the dihedral angle. The optimum dihedral angle in the present study is 135\({}^{\circ}\), where the value of _Cps_ is improved by 23.5% at the near-stall condition.  
The flow field distributions at the mass flow coefficients of 0.52 and 0.46 are given in Figure 21. It is apparent that the leakage flow will deviate from the blade suction surface with the increase of the dihedral angle. As a result, the mixing of the leakage flow with the mainstream is more sufficient, and the blockage at the outlet alleviates. However, the increase of the dihedral angle will also enhance the radial migration of the blade corner flow, thus strengthening the flow separation on the suction surface. Of all the design schemes, C1D2 could not only suppress the secondary flow at the hub endwall but also avoid excessive flow separation on the blade suction surface, hence obtaining the optimum aerodynamic performance.  
Figure 19: Radial distribution of blade dihedral for the cases with different dihedral angles.  
Figure 20: Pressure rise and loss characteristics for the stator with different dihedral angles. (**a**) Pressure rise and (**b**) loss.  
As shown in Figure 22, the influence of the dihedral angle on the performance of the cantilevered stator is illustrated clearly. Results show that the current dihedral angles barely influence the distribution of the mass flow coefficient at the stator inlet; however, the mass flow distribution at the stator outlet is altered. To be specific, at the \(\varphi=0.52\) condition, the mass flow coefficient in the lower and upper regions of the 20% blade height is increased and decreased, respectively, which echoes the flow field characteristics in Figure 21. The comparison of different design schemes indicates that with the increase of the dihedral angle, the enhancement of flow capacity at the stator hub will become inconspicuous, yet the worsening of aerodynamic performance at the upper span becomes more significant, which consequently weakens the total beneficial effect. The above phenomenon is more significant at small mass flow ratios.  
Figure 23 presents the variation of the leakage mass flow rate. Results demonstrate that although the mass flow rate of the leakage flow is increased slightly in comparison with the orthogonal blade, the current range of the dihedral angle barely influences the axial distribution of the leakage flow, and the absolute mass flow rates for different blading schemes are approximately identical.  
Figure 21: Flow field distribution for the cases with different dihedral angles.  
Figure 22: Radial distribution of aerodynamic performances for the cases with different dihedral angles. (**a**) \(\varphi=0.52\); (**b**) \(\varphi=0.46\).  
Hence, 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 at the hub corner. A large dihedral height will elongate the blade wake and induce the radial transportation of the leakage flow.