# Toward the Utilization of 3D Blading in the Cantilevered Stator from Highly Loaded Compressors
## 1 Introduction  
The cantilevered stator is signified by its simple structure and low weight and hence is a promising configuration in the high-performance compressor. However, the leakage flow created by the radial gap at the stator root substantially complicates the endwall flow, necessitating a thorough understanding and advanced design techniques. [PERSON] stated in the 1950s that the cantilevered stator could obtain better aerodynamic performance than the shrouded stator [1]. His conclusion was then verified experimentally by [PERSON] and [PERSON], who also pointed out the existence of an optimum clearance size [2; 3; 4]. Although the leakage flow could, in a way, benefit endwall flow, it will at the same time introduce flow blockage and mixing loss; thus, studies have been conducted to reveal the flow mechanisms in the corner region. For example, [PERSON] and [PERSON], [PERSON] et al., and [PERSON] et al. believe the leakage flow weakens the corner separation by suppressing the endwall flow [5; 6; 7], whereas [PERSON] et al. argue that it is the suppression of the horseshoe vortex in the leading edge that causes removal of the corner separation [8]. [PERSON] et al. state that the suppression of corner separation is mainly caused by the mixing of the high-energy leakage flow with the low-energy corner flow [9]. In terms of the clearance size, [PERSON] et al. proposed that the optimum choice is when the strengths of the leakage flow and the secondary flow are identical [2; 4], whereas [PERSON] et al. revealed that the clearance flow tends to strengthen the corner separation when theclearance size is very small [8]. While [PERSON] et al. proposed an optimum hub clearance of 1% blade height [5], the optimum stator clearance remains in question [9; 10; 11; 12; 13]. [PERSON] et al. investigated the hub clearance height and found that the interaction of hub leakage and passage vortex leads to mitigation of overall secondary flow adverse effects [14]. Three-dimensional blading can improve the compressor aerodynamic performance through reorganization of the flow field and hence is widely used in axial compressors. In general, 3D blading can be classified as sweep and dihedral. It is well known that the forward sweep of the rotor blade tip can reduce the local inlet Mach number, thereby weakening the shock wave and reducing the loss [7; 13; 15; 16; 17; 18; 19; 20]. The sweep of the blade can also be used to control the corner flow in the subsonic compressor. As for the dihedral, it is recognized that the positive dihedral can construct a radial pressure gradient in the blade passage, thereby weakening the accumulation of the boundary layer at the corner region and inhibiting the occurrence of flow separation. According to the research of [PERSON] et al. and [PERSON] et al., the positive dihedral at both ends of the blade can reduce the endwall loss but will increase the loss in the midspan areas [21; 22]. [PERSON] further notes that the beneficial effect of positive dihedral on the near-wall region is mainly related to the dihedral angle, whereas the negative effect at the midspan is determined by the dihedral height [23]. More information on 3D blading can be found in references [24; 25]. Although the application of 3D blading is quite common in conventional rotors/stators, there are few reports about its utilization in the cantilevered stator. [PERSON] et al. attributed the beneficial effect of dihedral to the improvement of the rotor flow according to their experimental measurements [26]. [PERSON] et al. found that the forward sweep can draw the high-momentum flow to the corner region of the suction surface, thereby suppressing the thickening of the viscous flow [20]. [PERSON] et al. performed a numerical investigation of the effect of the forward sweep in the cantilevered stator, indicating that a reasonable sweep can not only reduce the shock wave at the stator hub but also reduce the loading near the blade leading edge [27].