# 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 Sweep
#### 3.1.1 Effects of the Sweep Height  
The influence of sweep height is first compared using the control variate method. As shown in Figure 4, the design schemes are A1B2, A2B2, and A3B2. A slight forward sweep is also adopted at the tip region to balance the pressure gradient in the radial direction (135\({}^{\circ}\), 70% span). Results are compared to the orthogonal/straight blade (Orth.). Note that no dihedral is utilized in this section. The pressure rise and loss characteristics of the cantilevered stators are demonstrated in Figure 5. Results show that, except for the near-stall condition of A1B2, the utilization of the forward sweep could always improve the stator aerodynamic performance in comparison to the baseline case. Moreover, the comparison of different schemes indicates that the 60% sweep height (A2B2) outperforms the other designs. At the near-stall condition, the static pressure rise coefficient and the total pressure loss coefficient in A2B2 are increased and decreased by 14.3% and 5.4%, respectively. \begin{table}
\begin{tabular}{c c c c} \hline
**Parameter Type** & **1** & **2** & **3** \\ \hline A: Sweep height & 30\% span & 60\% span & 70\% span \\ B: Sweep angle & 120\({}^{\circ}\) & 135\({}^{\circ}\) & 150\({}^{\circ}\) \\ \hline \end{tabular}
\end{table} 
Table 1: Modeling scheme for blade sweep. Figure 4: Radial distribution of blade sweep for the cases with different sweep heights. Figure 6 illustrates the flow field distribution for the cases with different sweep heights. Both the leakage streamlines and the surface streamlines are depicted. Results show that the forward sweep moves the hub leakage flow upstream, thus enhancing the hindrance to the secondary flow and attenuating the accumulation of the low-energy fluid toward the corner region. Consequently, the blockage at the corner region of the suction surface witnesses a remarkable shrink. However, the forward sweep will incur the radial expansion of the suction surface flow separation; hence, the wake is broadened in the upper span areas. Moreover, under the same mass flow ratio, the sweep height exhibits little effect on the leakage flow but will influence the trailing edge separation significantly. At the sweep height of 60% blade span (A2B2), the trailing edge separation tends to be uniform along the radial direction, thus bringing optimum aerodynamic performance. To evaluate the aerodynamic performance of the cantilevered stator quantitatively, the radial distribution of the aerodynamic parameters is given in Figure 7. The variation of the mass flow coefficient suggests that the forward sweep is able to improve the flow capacity in the hub region, whereas the alleviation of corner separation flow brings a reduction in the deviation angle. The effect of the forward sweep is more pronounced at small mass flow ratios (i.e., the conditions with higher loading). By comparing different blading schemes, it can be seen that the larger sweep height adds to the beneficial effect. Nevertheless, when the sweep height is greater than 60% (A3B2), the performance improvement at the  
Figure 5: Pressure rise and loss characteristics for the stator with different sweep heights. (**a**) Pressure rise and (**b**) loss. Figure 6: Flow field distribution for the cases with different sweep heights. corner region by further increasing the sweep height becomes less significant, yet the upper span performance starts to deteriorate; hence, the 60% sweep height is suitable for the present case. To reveal the effect of sweep height on the leakage flow, the variation of the mass flow rate of the leakage flow is presented in Figure 8. Results indicate that the leakage flow rate first decreases in the areas between 0-20% blade chord and then continues to increase toward the trailing edge. The increase in the mass flow rate of the leakage flow will enhance the removal of low-energy fluid in the corner region of the blade suction surface, thus confirming the former analysis.