The effects of blade 3D designs in different orthogonal coordinates on the performance of compressor cascades

The chordwise based Sweep-Dihedral Coordinates (SDC) and axial-tangential based Axial Sweep-Lean Coordinates (ASLC) are the two widely used coordinates systems for blade 3D design. In order to clarify the relationships between them, some numerical simulations were conducted in a simplified planar cascade model. The cascade model has a large aspect ratio of 3.0 and free-slip endwalls, which are used to minimize the endwall flow effects. The simulation results of totally 9 cases with different blade 3D design schemes, including sweep, dihedral, axial sweep and lean, were analyzed. Firstly, the effects of each type of blade 3D designs were summarized. And then, based on the rule of vector decomposition in an orthogonal coordinates, the effects of blade axial sweep and lean in ASLC were deduced from the effects of blade sweep and dihedral in SDC. It was found that forward/backward axial sweep is combined by positive/negative dihedral and forward/backward sweep, which have opposite trends of effects, resulting in a counterbalance phenomenon. Moreover, positive/negative lean is combined by positive/negative dihedral and forward/backward sweep, which have the same trends of effects, resulting in a superposition effect.