An ideal wind turbine with a finite number of blades

The effects of a finite number of blades on the efficiency of the ideal wind turbine is estimated on the basis of the vortex theory for an ideal propeller and turbine rotor of a small fineness ratio. The semi-infinite helicoidal vortex surfaces formed by free vortices behind the rotor blades are exchanged by infinite helical vortex sheets with the same geometry parameters and the same circulation distribution. The discretization of each vortex sheet performed on the basis of 100 discrete helical vortex lines estimate the optimum rotor with a finite number of blades for arbitrary exploitation regimes. The application of Goldstein function to the optimization of wind turbines is found to depend on adequate determination of the geometric and kinematic characteristics of infinite helical vortex sheets.