Dynamics of helical vortices in the wake of asymmetric rotors

Abstract

The wakes behind rotors such as wind turbines, propellers, and helicopters are characterized by helical vortices shed from the blade tips, which can have detrimental effects on downstream structures. Helical vortices are subject to displacement instabilities that lead to pairing between adjacent vortex loops and eventually cause the vortices to break down. Certain modes of these instabilities can be triggered by an asymmetry in the rotor generating the vortices. In three-vortex systems, like those formed by many industrial rotors, the nonlinear vortex interactions are highly complex, introducing the need for a simple model to predict their dynamics. We here present a model for helical vortex systems based on an infinite strip of periodically repeating point vortices, whose motion can be computed using a single equation. This greatly simplified model is shown to accurately reproduce the helical vortex dynamics predicted by a more sophisticated filament model and observed in previous experiments on model rotors. The model is then used to investigate different types of vortex perturbations representing rotor asymmetries, such as a displacement of a vortex (achievable by varying the blade tip geometry in an experiment), or a change of circulation (by varying the pitch). The effectiveness of the different types of rotor asymmetries for triggering the pairing instability was also investigated experimentally, by testing various rotor configurations in a water channel. The findings of the current study can be used to design rotors that passively accelerate wake recovery and mitigate negative effects on downstream structures. Preliminary numerical results concerning the influence of rotor asymmetry on wind turbine wake interactions will be shown.