Research on parameterization and optimization procedure of low-Reynolds-number airfoils based on genetic algorithm and Bezier curve

Abstract

A systematic procedure of high-precision parameterization and multi-objective optimization for airfoils was proposed in this paper in order to improve the aerodynamic performance under full working conditions. The Bezier curve was applied in the airfoil parameterization with the coordinates of the 8 Bezier control points chosen to be the design variables. The control points were initialized by self-programming software and then optimized by direct search method to guarantee the fitting precision. The multi-objective optimization of low-Reynolds-number airfoil E387 was executed through NSGA II based on the result from XFOIL calculation, with the increment and variance of lift-drag ratio chosen to be the objective functions. Two representative solutions were selected from the Pareto front, and the performances of the new airfoils were promoted in different ways. The lift-drag ratio of the optimized airfoil with smaller variance is increased uniformly under different attack angles and maintains the similar characteristics with the original one. For the optimized airfoil with larger variance, the distribution of lift-drag ratio relative to the attack angle is altered obviously, and the performance under small attack angles and stall conditions are significantly ameliorated. The introduction of variance control in the objective function enables the differentiation of the optimized solutions for different requirement in engineering application.