How does the blade element momentum method see swept or prebent blades?

Abstract

The blade element momentum (BEM) method is among the mostly used engineering aerodynamic models for wind turbine rotors. Even though the BEM method is strictly only applicable to straight blades forming a planar rotor, it is in practice used for load calculation and design optimization of blades with relatively large sweep, prebend or coning. The present work aims to answer the question: How does the BEM method see swept or prebent blades? The blade element part of the method can be adapted for swept or prebent blades by projecting the velocity and loads between the 2-D airfoil section and the 3-D blade geometry under the cross-flow principle. However, momentum theory considers the 3-D wake and the induction of a planar actuator disc with straight blades. There could be significant differences between the results calculated from different implementations of the BEM method, while the details of the implementations are often omitted in the literature. In the present work, a consistent implementation including the definition of airfoil section alignments and the coordinate systems is provided. It is shown that for a given circulation distribution, the BEM method will predict approximately the same local aerodynamic loads for non-straight blades as if the blades were straight and the rotor was planar. This means using the BEM method to perform aerodynamic optimization of modern rotors with curved blades and/or rotors that are not planar can only have little meaningful result. In order to model the impact of the wake geometry on the induction, more advanced models that take into account the wake geometry on the induction are necessary.