Momentum theory of Joukowsky actuator discs with swirl

The Science of Making Torque from Wind

Van Kuik, Gijs A. M.^1

Delft University of Technology, Kluyverweg 1, Delft

2629HS, Netherlands^1

关键词: Corresponding solutions;    Engineering rules;    Momentum balances;    Momentum theory;    Off design condition;    Rotational speed;    Velocity gradients;    Vortex core radius;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/753/2/022021/pdf
DOI  :  10.1088/1742-6596/753/2/022021

来源: IOP

【 摘 要 】

Actuator disc theory is the basis for most rotor design methods, be it 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 Ω → 0. The momentum balance is very sensitive to the choice of the vortex core radius δ as the pressure and velocity gradients become infinite for δ → 0. Viscous vortex cores do not show this singular behaviour so an inviscid core model is sought which removes the momentum balance sensitivity to singular flow. A vortex core with a constant δ does so. Applying this results in Cp→ 0 for Ω → 0, instead of Cp→ ∞. The Joukowsky actuator disc theory is confirmed by a very good match with the numerically obtained results. It gives higher Cpvalues than corresponding solutions for discs with a Goldstein-based wake circulation published in literature.