Supercritical airfoil parameterization method feasible to optimum design

To reduce the number of design variables in the supercritical airfoil optimization, eliminate the unfairness phenomenon, ensure C₂ condition, control the geometric characteristics of the airfoil in the optimization process, a parameterization method for supercritical airfoil based on four rational Bézier curve was presented. In the parametric process to the airfoil data, the Bézier curve approximation algorithm and SPSA(simultaneous perturbation stochastic approximation) algorithm were used and in the Bézier curve approximation algorithm the way to choose the parameter to the data points is different from the common method. Supercritical airfoil shape optimization can be achieved by combining this method with optimization algorithms. It contents 21 design variables, the optimization result is fair and satisfies the C₂ condition, the geometric characteristics of the airfoil such as leading edge radius, upper and lower crest location including curvature there, the boattail angle can be controlled in the optimization process by setting the range of the design variables.