One key element in the aerodynamic design of wind turbines is the use of specially tailored airfoils to increase the ratio of energy capture to the loading and thereby to reduce cost of energy. This work is focused on the design of a wind turbine airfoil by using numerical optimization. Firstly, the optimization approach is presented; a genetic algorithm is used, coupled with RFOIL solver and a composite Bezier geometrical parameterization. A particularly sensitive point is the choice and implementation of constraints; in order to formalize in the most complete and effective way the design requirements, the effects of activating specific constraints are discussed. A numerical example regarding the design of a high efficiency airfoil for the outer part of a blade by using genetic algorithms is illustrated and the results are compared with existing wind turbine airfoils. Finally a new hybrid design strategy is illustrated and discussed, in which the genetic algorithms are used at the beginning of the design process to explore a wide domain. Then, the gradient based algorithms are used in order to improve the first stage optimum. Nomenclature α = angle of attack [deg] α des = design angle of attack [deg] c = airfoil chord [m] C d = airfoil drag coefficient [-] C dmin = minimum airfoil drag coefficient [-] C f = skin friction coefficient [-] C l = airfoil lift coefficient [-] C ll = slope of the lift curve [deg-1 ] C lmax = maximum airfoil lift coefficient [-] C mc/4 = airfoil moment coefficient referred to the quarter of chord [-] F = objective function [-] g = inequality constraints [-] h = equality constraints [-] H = boundary layer shape factor [-] L/D = aerodynamic efficiency [-] X = design variables [-] X L = lower bounds for the design variables [-] X U = upper bounds for the design variables [-] w i = weight i th objective function p i = coefficient to make of the same order all the objective functions av ij = actual value of the j th constrained characteristic at the i th objective function evaluation cw j = weight of the j th constraint pc = coefficient to make of the same order the constraints and the objective functions
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