Joukowski’s wake model for tip-splitting rotors

A Castillo-Castellanos,S Le Dizés,E Durán Venegas

doi:10.1088/1742-6596/1934/1/012005

Abstract

The interaction between a tip vortex and a solid surface is responsible for premature structural component fatigue in wind turbines and undesirable noise in helicopter rotors during low speed and descending flight. One noise reduction strategy uses a modified airfoil to split and spread the vorticity in two tip vortices. The present paper aims to provide the wake structure produced by such a rotor for wind turbine and helicopter regimes. We use a filamentary approach, such that vortices are assumed to roll-up quickly to form thin vortex filaments of finite but small size and compute the induced velocity using a cut-off method. The structure of the wake is analyzed in the near- and far-fields separately. It is found to have a dual nature and to be well-described by a twisted vortex pair locally aligned along with a larger helical structure. The linear stability of the far-wake with respect to long-wave displacements is also analyzed. Two kinds of instability modes are obtained associated with a pairing between successive turns of the large helical structure and a pairing between successive turns of the vortex pair.

Highlights

Rotating blades, such as those of a helicopter rotor or a horizontal-axis wind turbine, generate concentrated vortices at their tips, transported downstream, creating a helical pattern
We study the long-wavelength stability for the wake produced by a tip-splitting rotor blade
Base solutions are characterized by a rotation of the vortex pair as it moves along a large-scale helical motif

Summary

Introduction

Rotating blades, such as those of a helicopter rotor or a horizontal-axis wind turbine, generate concentrated vortices at their tips, transported downstream, creating a helical pattern. Long-wavelength instabilities are characterized by a local displacement of the vortex, without changing the internal core structure. Perturbations were found to be quickly advected away from the rotor, such that stability properties are consistent with theoretical predictions for the far-wake (uniform helices in the case of [11]). Base solutions are characterized by a rotation of the vortex pair as it moves along a large-scale helical motif.

Results

Conclusion