### Abstract

When investigating limits of rotor aerodynamic models, the Betz limit serves as a solid marker of an upper limit which no model should be able to exceed. A century ago Joukowsky (1912) proposed a rotor aerodynamic model utilizing a rotating actuator disc with a constant circulation. This model has since then been the subject of much controversy as it predicts a power performance that for all tip speed ratios exceeds the Betz limit and which goes to infinity when the tip speed ratio goes to zero. Recently, it was demonstrated that the Joukowsky model is fully consistent with the inviscid Euler equations and that the apparent inconsistency partly can be explained by the lack of viscous effects (Sprensen and van Kuik [4]). However, even including a term to account for the effect of viscosity at small tip speed ratios, the model still predicts a power yield that exceeds the Betz limit. In the present work we study in detail, using a CFD actuator line model, the flow behavior for rotors at small tip speed ratios. It is shown that the excessive swirl appearing towards the rotor center at small tip speed ratios generates vortex breakdown, causing a recirculating zone in the wake that limits the power yield of the rotor. The appearance of vortex breakdown has a similar effect on the flow behavior as the vortex ring state that usually appears at higher tip speed ratios. Limits to where vortex breakdown might occur with tip speed ratio and rotor loading as parameter are investigated and presented in the paper. The limits found correspond to well-known criterion for vortex breakdown onset for swirling flows in general. By applying a criterion for vortex breakdown in combination with the general momentum theory, the power performance always stays below the Betz limit.

Original language | English |
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Article number | 012099 |

Book series | Journal of Physics: Conference Series (Online) |

Volume | 524 |

Issue number | 1 |

Number of pages | 1 |

ISSN | 1742-6596 |

DOIs | |

Publication status | Published - 2014 |

Event | 5th International Conference on The Science of Making Torque from Wind 2014 - Technical University of Denmark, Copenhagen, Denmark Duration: 10 Jun 2014 → 20 Jun 2014 Conference number: 5 http://indico.conferences.dtu.dk/conferenceDisplay.py?confId=138 |

### Conference

Conference | 5th International Conference on The Science of Making Torque from Wind 2014 |
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Number | 5 |

Location | Technical University of Denmark |

Country | Denmark |

City | Copenhagen |

Period | 10/06/2014 → 20/06/2014 |

Internet address |

### Bibliographical note

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd## Cite this

Mikkelsen, R. F., Sarmast, S., Henningson, D., & Sørensen, J. N. (2014). Rotor aerodynamic power limits at low tip speed ratio using CFD.

*Journal of Physics: Conference Series (Online)*,*524*(1), [012099]. https://doi.org/10.1088/1742-6596/524/1/012099