Airfoil Optimization Design Based on the Pivot Element Weighting Iterative Method

Class function/shape function transformation (CST) is an advanced geometry representation method employed to generate airfoil coordinates. Aiming at the morbidity of the CST coefficient matrix, the pivot element weighting iterative (PEWI) method is proposed to improve the condition number of the ill-conditioned matrix in the CST. The feasibility of the PEWI method is evaluated by using the RAE2822 and S1223 airfoil. The aerodynamic optimization of the S1223 airfoil is conducted based on the Isight software platform. First, the S1223 airfoil is parameterized by the CST with the PEWI method. It is very significant to confirm the range of variables for the airfoil optimization design. So the normalization method of design variables is put forward in the paper. Optimal Latin Hypercube sampling is applied to generate the samples, whose aerodynamic performances are calculated by the numerical simulation. Then the Radial Basis Functions (RBF) neural network model is trained by these aerodynamic performance data. Finally, the multi-island genetic algorithm is performed to achieve the maximum lift-drag ratio of S1223. The results show that the robustness of the CST can be improved. Moreover, the lift-drag ratio of S1223 increases by 2.27% and the drag coefficient decreases by 1.4%.