Abstract: Based on the Joukowski conformal transformation theory and Theodorsen method, a novel parametric representation function (shape function) for wind turbine airfoils is developed. The airfoil design space and shape control equations are studied. Results of the analyses of FX66-S196-V1 airfoil are shown to illustrate the evaluation processes and to demonstrate the rate of convergence of the geometric and aerodynamic characteristics. The geometric coordinates and aerodynamic performance of approximate airfoils gradually approach the baseline airfoil along with the increase of polynomial orders. The surface pressure distribution of 11-order airfoil is in good agreement with the original airfoil. The differences of lift and drag performance between 11-order airfoil and experimental data of actual airfoil are very small. 11-order airfoil can be used to substitute for the actual airfoil in wind turbine design. The lowest orders of different airfoils parametric representation are presented.

Key words: Airfoil profile, Convergence property, Parametric representation, Pressure distribution, Wind turbine