17 Oct 2022
17 Oct 2022
Status: this preprint is currently under review for the journal WES.

A simple vortex model applied to an idealized rotor in sheared inflow

Mac Gaunaa1, Niels Troldborg1, and Emmanuel Branlard2 Mac Gaunaa et al.
  • 1DTU Wind & Energy Systems, Frederiksborgvej 399, 4000, Roskilde, Denmark
  • 2National Renewable Energy Laboratory, 15013 Denver West Parkway, Golden, CO 80401, USA

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.

Mac Gaunaa et al.

Status: open (until 19 Dec 2022)

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  • RC1: 'Comment on wes-2022-94', Joseph Saverin, 05 Dec 2022 reply

Mac Gaunaa et al.

Mac Gaunaa et al.


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Short summary
We present an analytical vortex model. Despite its simplicity, the model is fully consistent with 1D momentum theory. It shows that the flow through a non-uniformly loaded rotor operating in non-uniform inflow behaves locally as predicted by 1D momentum theory. As a consequence, the local power coefficient (based on local inflow) of an ideal rotor is unaltered by the presence of shear. Finally, the model shows that there is no cross-shear deflection of the wake of a rotor in sheared inflow.