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Prediction of the hub vortex instability in a wind turbine wake: stability analysis with eddy-viscosity models calibrated on wind tunnel data

Published online by Cambridge University Press:  30 May 2014

F. Viola ,
G. V. Iungo ,
S. Camarri ,
F. Porté-Agel  and
F. Gallaire
F. Viola
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, Lausanne, CH-1015, Switzerland
G. V. Iungo
Affiliation:
Wind Engineering and Renewable Energy Laboratory, École Polytechnique Fédérale de Lausanne, Lausanne, CH-1015, Switzerland
S. Camarri*
Affiliation:
Department of Civil and Industrial Engineering, University of Pisa, Pisa 56122, Italy
F. Porté-Agel
Affiliation:
Wind Engineering and Renewable Energy Laboratory, École Polytechnique Fédérale de Lausanne, Lausanne, CH-1015, Switzerland
F. Gallaire
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, Lausanne, CH-1015, Switzerland
*
†Email address for correspondence: s.camarri@ing.unipi.it
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Abstract

The instability of the hub vortex observed in wind turbine wakes has recently been studied by Iungo et al. (J. Fluid Mech., vol. 737, 2013, pp. 499–526) via local stability analysis of the mean velocity field measured through wind tunnel experiments. This analysis was carried out by neglecting the effect of turbulent fluctuations on the development of the coherent perturbations. In the present paper, we perform a stability analysis taking into account the Reynolds stresses modelled by eddy-viscosity models, which are calibrated on the wind tunnel data. This new formulation for the stability analysis leads to the identification of one clear dominant mode associated with the hub vortex instability, which is the one with the largest overall downstream amplification. Moreover, this analysis also predicts accurately the frequency of the hub vortex instability observed experimentally. The proposed formulation is of general interest for the stability analysis of swirling turbulent flows.

JFM classification

Instability: Absolute/convective instability Turbulent Flows: Turbulent Flows Vortex Flows: Vortex instability
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 750 , 10 July 2014 , R1
Copyright
© 2014 Cambridge University Press 

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