The turbomachinery cascades design is a typical high dimensional computationally expensive and black box (HEB) problem, for which a meta-model based design optimization and data mining method is proposed and programmed in this work. The method combines an EI-based global algorithm with two data mining techniques of self-organizing map (SOM) and analysis of variance (ANOVA); 3D blade parameterization method and RANS Solver technique. NASA Rotor 37, a typical axial transonic rotor blade, is selected for the research. Firstly, the SOM is employed to explore the interactions between critical performance indicators. Based on SOM analysis, a design optimization with 19 design variables is carried out to maximize the isentropic efficiency of Rotor 37 configuration with constraints prescribed on the total pressure ratio and mass flow rate. An EI-based global algorithm is programmed for above optimization process and the number of CFD evaluations needed amount to only 1/5 of that required when employing a modified differential evolution algorithm as the optimizer. Throughout the optimization the isentropic efficiency is increased by 1.74% and a subsequent analysis of the redesign reveals that the performance of the rotor blade is significantly improved. And then, the ANOVA is employed to explore the correlations among design variables and objective function as well as the constraints. It is confirmed that the shock wave has the most significant influence on the aerodynamic performance of transonic rotor blades, the combination of proper 2D section profiles and 3D radial stacking is effective for improving the performance of rotor blade. Meanwhile, isentropic efficiency and total pressure ratio of transonic compressor blade is found to be in slight trade-off relation due to the effect of 3D sweep in tip sections. Furthermore, an ANOVA-based optimization strategy is tried, which can obtain remarkable optimal designs with much less computational resource. On a whole, it’s demonstrated that the meta-model based design optimization strategy by coupling data mining techniques is promising for solving HEB problems like the design of turbomachinery cascades.

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