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Long-wave instability of a helical vortex

Published online by Cambridge University Press:  09 September 2015

Hugo Umberto Quaranta ,
Hadrien Bolnot  and
Thomas Leweke
Hugo Umberto Quaranta
Affiliation:
IRPHE UMR 7342, Aix-Marseille Université, CNRS, Centrale Marseille, 13384 Marseille, France Aerodynamics Department, Airbus Helicopters, 13725 Marignane, France
Hadrien Bolnot
Affiliation:
IRPHE UMR 7342, Aix-Marseille Université, CNRS, Centrale Marseille, 13384 Marseille, France Aerodynamics Department, Airbus Helicopters, 13725 Marignane, France
Thomas Leweke*
Affiliation:
IRPHE UMR 7342, Aix-Marseille Université, CNRS, Centrale Marseille, 13384 Marseille, France
*
†Email address for correspondence: leweke@irphe.univ-mrs.fr
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Abstract

We investigate the instability of a single helical vortex filament of small pitch with respect to displacement perturbations whose wavelength is large compared to the vortex core size. We first revisit previous theoretical analyses concerning infinite Rankine vortices, and consider in addition the more realistic case of vortices with Gausssian vorticity distributions and axial core flow. We show that the various instability modes are related to the local pairing of successive helix turns through mutual induction, and that the growth rate curve can be qualitatively and quantitatively predicted from the classical pairing of an array of point vortices. We then present results from an experimental study of a helical vortex filament generated in a water channel by a single-bladed rotor under carefully controlled conditions. Various modes of displacement perturbations could be triggered by suitable modulation of the blade rotation. Dye visualisations and particle image velocimetry allowed a detailed characterisation of the vortex geometry and the determination of the growth rate of the long-wave instability modes, showing good agreement with theoretical predictions for the experimental base flow. The long-term (downstream) development of the pairing instability leads to a grouping and swapping of helix loops. Despite the resulting complicated three-dimensional structure, the vortex filaments surprisingly remain mostly intact in our observation interval. The characteristic distance of evolution of the helical wake behind the rotor decreases with increasing initial amplitude of the perturbations; this can be predicted from the linear stability theory.

JFM classification

Vortex Flows: Vortex Flows Vortex Flows: Vortex instability Vortex Flows: Vortex interactions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 780 , 10 October 2015 , pp. 687 - 716
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© 2015 Cambridge University Press 

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