Abstract
A simple analytical vortex model is presented and used to study an idealized wind turbine rotor in uniform and sheared inflow, respectively. The work reveals that locally 1D momentum theory is valid for a non-uniformly loaded rotor in a sheared inflow. Hence the maximum local power coefficient (expressed with respect to the local, upstream velocity) of an ideal rotor is not affected by the presence of shear. We study the interaction between the wake vorticity generated by the rotor and the wind shear vorticity, and find that their mutual interaction results in no net generation of axial vorticity: the wake effects and the shear effects exactly cancel each other out. This means that there is no resulting cross-shear induced velocities and therefore also no cross-shear deflection of the wake in this model.
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