Abstract:

What we call today “Vortex methods” appeared in various forms since 1930, when Rosenhead first introduced the notion of point vortices and formulated a numerical method for predicting the roll-up of the wake of an aircraft wing. Well known variants are the lifting-line and lifting surface methods for wings and rotors as well as the panel and boundary element methods used in aerodynamics. Although not always specifically said, all vortex methods are based on Helmholtz’s decomposition and Green’s theorem. The context is to solve the flow equations in Lagrangian (material) co-ordinates following the evolution of a set of markers. Depending on the choice one is making for the markers a variety of vortex methods can be defined. The older vortex methods used vortex segments or vortex panels as markers for the representation of vortex filaments and vortex sheets. In the late 70’s  point vortices were first  in 3D flows by Rehbach who also indicated the need for regularization. Also a few years earlier Chorin was the first to extend the point vortex method to viscous 2D flows. The elegance and simplicity of vortex methods attracted a lot of researchers from different fields. In the early 80’s Beale and Majda provided mathematical justification of the regularized point vortex methods in 2D and 3D which are today known as vortex particle or blob methods. Since then a long list of theoretical and applied contributions has been published covering a very wide range of topics, including wind energy.

This lecture aims at providing an overview on how vortex methods can be used in wind turbine aerodynamics and aeroelasticity. While the emphasis will be on the particle version of vortex methods, other particle methods will be briefly discussed. We will focus on cost reduction techniques (tree algorithms, Particle Mesh techniques), on viscous formulations though coupling to CFD and on aeroelastic simulations.

Representative results will be discussed in comparison to measurements and other (BEM & CFD) simulation methods addressing the range of applicability of vortex methods in connection to their accuracy/cost ratio. The talk will close with an outlook and a list of still open issues.