Journal cover Journal topic
Wind Energy Science The interactive open-access journal of the European Academy of Wind Energy
Wind Energ. Sci., 2, 307-316, 2017
https://doi.org/10.5194/wes-2-307-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
Research articles
15 Jun 2017
Joukowsky actuator disc momentum theory
Gijs A. M. van Kuik Duwind, Delft University of Technology, Kluyverweg 1, 2629HS Delft, the Netherlands
Abstract. Actuator disc theory is the basis for most rotor design methods, albeit with many extensions and engineering rules added to make it a well-established method. However, the off-design condition of a very low rotational speed Ω of the disc is still a topic for scientific discussions. Several authors have presented solutions of the associated momentum theory for actuator discs with a constant circulation, the so-called Joukowsky discs, showing the efficiency Cp → ∞ for the tip speed ratio λ → 0. The momentum theory is very sensitive to the choice of the radius δ of the core of the centreline vortex as the pressure and velocity gradients become infinite for δ → 0. Usually the vortex core area is not included in the momentum balance, as it vanishes for δ → 0. However, the pressure in the vortex core behaves as a Delta function and so contributes to the balance, thereby cancelling the singular behaviour. Applying this in the momentum balance results in Cp → 0 for λ → 0, instead of Cp → ∞. The Joukowsky actuator disc theory is confirmed by a very good match with numerically obtained results. At the disc the velocity in the meridian plane is shown to be constant. The Joukowsky calculations give higher Cp values than corresponding solutions for discs with a Goldstein-based wake circulation published in literature.

Citation: van Kuik, G. A. M.: Joukowsky actuator disc momentum theory, Wind Energ. Sci., 2, 307-316, https://doi.org/10.5194/wes-2-307-2017, 2017.
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Short summary
Actuator disc theory is the basis of most rotor design methods. However, the off-design condition of a very low rotational speed Ω is still a topic for scientific discussions. A small modification in the momentum theory for Joukowsky discs with uniform circulation results in the efficiency going to 0 instead of ∞ when Ω goes to 0. For high values of Ω, the classical momentum theory is reproduced. The new theory is confirmed by a very good match with numerically obtained results.
Actuator disc theory is the basis of most rotor design methods. However, the off-design...
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