Numerical study of helical vortices and their instabilities

Can Selçuk's thesis, monday May 9th, 14:00, at LIMSI

The work presented in this manuscript is a contribution to the numerical study of helical vortex systems and their instabilities, as encountered in the near wake of rotors (wind turbines, helicopters,...). In this work, such flows are locally modelled within the framework of helical symmetry. Using a dedicated DNS code, helical quasi-stationary basic state solutions are obtained for several configurations, and accurate tools for their characterisation are developed: angular velocity, core size and ellipticity, structure of the velocity and vorticity fields... An Arnoldi algorithm is then coupled to a linearised version of the code. The dominant instability modes with the same symmetry as the base flow are extracted as a function of the system parameters: number of vortices, helical pitch, core size, Reynolds number, presence of a central hub vortex. Under a critical helical pitch, the instability is dominated by a global displacement mode analogous to the pairing mode of an infinite array of point vortices or vortex rings. In the nonlinear regime, this mode gives rise to complex dynamics: overtaking events, leapfrogging and merging. Another linearised code is then used to extract modes characterised by a wavelength along the helix, which break the helical symmetry of the base flow. At low wavenumbers, these modes induce local displacements of the vortices and bring together portions of neighbouring coils. At large wavenumbers, another type of mode is found, which deforms the vortex cores through the elliptical instability mechanism.


Rapporteurs :

Thomas Leweke, Directeur de Recherche au CNRS, IRPHE, Marseille.
Jens Sørensen, Professeur de la Danmarks Tekniske Universitet (DTU), Lyngby, Danemark

Examinateurs :

Pierre Brancher, Professeur de l'Université Paul Sabatier, IMFT, Toulouse
Vincent Brion, Ingénieur de Recherche à l'ONERA-DAFE, Meudon
Stéphane Popinet, Directeur de Recherche au CNRS, d'Alembert, Paris.

Directeurs de thèse :

Ivan Delbende, Maître de Conférences à l'UPMC, LIMSI, Orsay
Maurice Rossi, Directeur de Recherche au CNRS, d'Alembert, Paris.


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