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Helical self-similarity of tip vortex cores

Published online by Cambridge University Press:  28 November 2018

Valery L. Okulov Open the ORCID record for Valery L. Okulov [Opens in a new window] ,
Ivan K. Kabardin ,
Robert F. Mikkelsen ,
Igor V. Naumov Open the ORCID record for Igor V. Naumov [Opens in a new window]  and
Jens N. Sørensen Open the ORCID record for Jens N. Sørensen [Opens in a new window]
Valery L. Okulov*
Affiliation:
Department of Wind Energy, Technical University of Denmark, 2800 Lyngby, Denmark Kutateladze Institute of Thermophysics, SB RAS, 630090 Novosibirsk, Russia
Ivan K. Kabardin
Affiliation:
Kutateladze Institute of Thermophysics, SB RAS, 630090 Novosibirsk, Russia
Robert F. Mikkelsen
Affiliation:
Department of Wind Energy, Technical University of Denmark, 2800 Lyngby, Denmark
Igor V. Naumov
Affiliation:
Kutateladze Institute of Thermophysics, SB RAS, 630090 Novosibirsk, Russia
Jens N. Sørensen
Affiliation:
Department of Wind Energy, Technical University of Denmark, 2800 Lyngby, Denmark
*
†Email address for correspondence: [email protected]
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Abstract

The present work investigates local flow structures and the downstream evolution of the core of helical tip vortices generated by a three-bladed rotor. Earlier experimental studies have shown that the core of a helical tip vortex exhibits a local helical symmetry with a simple relation between the axial and azimuthal velocities. In the present study, a self-similarity scaling argument further describes the downstream development of the vortex core. Self-similarity has up to now only been investigated for longitudinal vortices and it is the first time that helical vortices have become the subject of such an analysis. Combining symmetry arguments from previous studies on helical vortices with novel experiments and knowledge regarding the self-similarity evolution of the core of longitudinal vortices, a new model describing what is referred to as ‘helical self-similarity’ is proposed. The generality of the model is verified and supported by experimental data. The proposed model is important for fundamental understanding of the behaviour of helical vortices, with a range of applications in both industry and nature. Examples of this are tip vortices behind aerodynamic devices, such as vortex generators, and fixed and rotary aircraft, and in combustion chambers and cyclone separators.

JFM classification

Vortex Flows: Vortex dynamics Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 859 , 25 January 2019 , pp. 1084 - 1097
Copyright
© 2018 Cambridge University Press 

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