Application of the Vortex Theory to High-speed Horizontal-axis Wind Turbines

Abstract

The vortex theory of screw propellers is modified and applied to the high-speed horizontal-axis wind turbines. The turbine blade can be replaced by a bound vortex system, and when the energy loss per unit time is a minimum, the trailing vortices move backwards with a constant velocity and build a helical vortex sheet. A velocity potential function which represents the vortex system is obtained. The circulation distribution along the blade is calculated iteratively until the hydrodynamic pitch of helical vortices converges. This method is applied to two examples, one with a sectional shape of modified Clark-Y type and the other with a sectional shape of NACA 65-series type. Torque, power and resistance are computed for a turbine which has two to six blades, respectively. Numerical values agree well with the sectional shape of experimental ones and it is concluded that the vortex theory is applicable to high-speed horizontal-axis wind turbines.