Simplified model for helical vortex dynamics in the wake of an asymmetric rotor

Helical vortex systems, such as those found in the wakes of wind turbines, helicopter rotors and propellers, are subject to instabilities that lead to pairing between adjacent vortex loops. 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. The current study presents 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 highly simplified model is shown to accurately reproduce the helical vortex dynamics predicted by a more sophisticated filament model and observed in water channel experiments on model rotors. The model is then used to investigate different types of vortex perturbations. Perturbation direction is found to have an important effect on the evolution of the instability, and displacements are observed to induce vortex pairing more quickly than circulation changes. These findings can be used to design asymmetric rotors that induce vortex breakdown more effectively, mitigating detrimental wake effects such as increased fatigue loading on downstream structures.