The Use of Helical Vortex Solutions in Wind Turbine Performance Analysis

Abstract eng:
The exact solutions for the velocities induced by helical line vortices are applied to two related aspects of wind turbine performance analysis. First it is shown that they allow the determination of the “tip loss factor” which relates the velocities at the blades to the average velocity at the same radius. The new calculation of tip loss is shown to be suitable for the computational modeling of wind turbine performance and is more accurate than the simple approximation due to Prandtl that is commonly used. Second, the conservation equations for momentum and angular momentum are nonlinear so the azimuthal variation of the induced velocities can be important. The exact solutions are used to determine the nonlinear terms in the torque and thrust equations. Approximate forms for the nonlinear terms are developed.

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