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Wind Energy Science The interactive open-access journal of the European Academy of Wind Energy
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https://doi.org/10.5194/wes-2020-51
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/wes-2020-51
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: research article 28 Feb 2020

Submitted as: research article | 28 Feb 2020

Review status
This preprint is currently under review for the journal WES.

On the velocity at wind turbine and propeller actuator discs

Gijs A. M. van Kuik Gijs A. M. van Kuik
  • Duwind, Delft University of Technology, Kluyverweg 1, 2629HS Delft, the Netherlands

Abstract. The first version of the actuator disc momentum theory is more than 100 years old. The extension towards very low rotational speeds with high torque for discs with a constant circulation, became available only recently. This theory gives the performance data like the power coefficient and average velocity at the disc. Potential flow calculations have added flow properties like the distribution of this velocity. The present paper addresses the comparison of actuator discs representing propellers and wind turbines, with emphasis on the velocity at the disc. At a low rotational speed, propeller discs have an expanding wake while still energy is put into the wake. The high angular momentum of the wake, due to the high torque, creates a pressure deficit which is supplemented by the pressure added by the disc thrust. This results in a positive energy balance while the wake axial velocity has lowered. In the propeller and wind turbine flow regime the velocity at the disc is 0 for a certain minimum but non-zero rotational speed.

At the disc, the distribution of the axial velocity component is non-uniform in all flow states. However, the distribution of the velocity in the plane containing the axis, the meridian plane, is practically uniform (deviation approximately 0.2 %) for wind turbine disc flows with tip speed ratio λ > 5, almost uniform (deviation 2 %) for wind turbine disc flows with λ = 1 and propeller flows with advance ratio J = Π, and non-uniform (deviation 5 %) for the propeller disc flow with wake expansion at J = 2 Π. These differences in uniformity are caused by the different strengths of the singularity in the wake boundary vorticity strength at its leading edge.

Gijs A. M. van Kuik

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Gijs A. M. van Kuik

Gijs A. M. van Kuik

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Latest update: 29 Mar 2020
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Short summary
Actuator discs are the most simple models for a wind turbine rotor or propeller, and still used in design codes. The velocity at the disc itself is important for performance prediction. The length of the velocity vector composed of the axial and radial component appears to be constant for fast running wind turbine discs, so does not depend on the radial position. For fast running propeller discs this is practically constant with a few % deviation. An explanation for this is presented.
Actuator discs are the most simple models for a wind turbine rotor or propeller, and still used ...
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