Multidisciplinary robust optimization approach of fan rotors under structural constraints with blade curvature

The robust optimization approach is an important method to solve the problem of fans/compressors performance disparities caused by geometric tolerances. Nonetheless, since the optimum design of turbomachinery blades is multidisciplinary in nature, traditional robust optimization approaches that only consider aerodynamic performance may result in the blade strength exceeding their material limit. Therefore, it is necessary to investigate the multidisciplinary robust optimization approach (MROA) considering both aerodynamic and structural performance. For MROA, there is a big challenge of huge computation cost and runtime for the time-consuming high-fidelity CFD and FEM. In this paper, a new method to reduce the computation cost and runtime of MROA is proposed by using the blade curvature to approximate the evaluation of blade stress. Firstly, data mining by self-organizing mapping method is used to analyze and extract the constraint value of the blade curvature. And the blade curvature constraint value is used as a penalty function instead of the time-consuming high-fidelity FEM, which greatly reduces the computational cost and runtime of the multidisciplinary optimization. Then, Polynomial chaos Kriging (PCK) is then used as a surrogate model for uncertainty quantification (UQ) of aerodynamic performances, and one MROA based on the PCK model-based UQ method and the curvature constraints is developed. The proposed method is verified using a fan rotor as a case study. The results show that the maximum stress of the traditional optimization method was 453 MPa, which exceeded the yield limit of aluminum alloy (420 MPa). In contrast, the maximum stress of the method proposed in this paper was 343 MPa. In terms of aerodynamic performance, compared with the baseline, the mean efficiency of the traditional and the proposed method increased by 2.6% and 2.1%, with a variance reduced by 45.5% and 48.5%, respectively. Therefore, compared with the traditional robust optimization method, the proposed method reduces the maximum stress of the blade by 24.3% with almost the same improvement for aerodynamic performance means and disparities.