Parametric exploration on the airfoil design space by numerical design of experiment methodology and multiple regression model

Robust airfoil design is crucial to efficient, stable, and safe operation for modern wind turbines. However, even for deterministic wind turbine airfoil design, the problem is complex regarding to aerodynamic, acoustic, and structural requirements of wind turbine blades. Therefore, this study aims to assess the design variable impact, identify significant variables, and obtain the correlation with the airfoil responses, to reduce the cost of the airfoil robust optimization. In this paper, the optimal hypercube design method was applied to an airfoil designed by the National Advisory Committee for Aeronautics, NACA 63-421, which is commonly employed in the outboard modern wind turbine blade, to perform the numerical design of experiments. Then, a parametric exploration on the characteristics of airfoil design space by the multiple regression model and statistical analysis method were conducted. It was identified that in regular design space, the variations of aerodynamic and structural parameters are dominated by the airfoil camber and radius of leading edge. Meanwhile, the chord-wise position of the maximum thickness also has strong impacts on the airfoil performance. In further, the overall design spaces are explored to be highly nonlinear in aerodynamic and acoustic responses because of the nonlinear effects of the airfoil chord-wise position of the maximum camber and radius of leading edge. Strong but undesirable correlations were demonstrated between the maximum lift-to-drag ratio and the total sound pressure level. These findings could serve as a valuable guidance for wind turbine airfoil robust design to screen the stochastic design variables, simplify the design space, and reduce the cost.