Tip-vortex breakdown of wind turbines subject to shear

Sheared velocity profiles pervade all wind-turbine applications, thus making it important to understand their effect on the wake. In this study, a single wind turbine is modeled using the actuator-line method in the incompressible Navier-Stokes equations. The tip vortices are perturbed harmonically, and the growth rate of the response is evaluated under uniform inflow and a linear velocity profile. Whereas previous investigations of this kind were conducted in the rotating frame of reference, this study evaluates the excitation response in the fixed frame of reference, thus necessitating a frequency transformation. It is shown that increasing the shear decreases the spatial growth rate in the upper half of the wake while increasing it in the lower half. When scaled with the local tip vortex parameters, the growth rate along the entire azimuth collapses to a single value for the investigated wavenumbers. We conclude that even though the tip-vortex breakdown is asymmetric in sheared flow, the scaled growth rates follow the behavior of axisymmetric helical vortices. An excitation amplitude reduction by an order of magnitude extends the linear growth region of the wake by one radius for uniform inflow. In the sheared setup, the linear growth region is extended further in the top half than in the bottom half because of the progressive distortion of the helical tip vortices. An existing model to determine the stable wake length was shown to be in close agreement with the observed numerical results when adjusted for shear.