Institute of Mathematics for Industry


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Helical vortices: theory and applications

Hold Date 2018-01-25 16:00~2018-01-25 17:30

Place Lecture Room S W1-C-512, West Zone 1, Ito campus, Kyushu University

Object person  

Speaker Valery L. Okulov (Department of Wind Energy, Technical University of Denmark)

The main applications of 2D dynamics of helical vortices embedded in flows with helical symmetry are addressed. The fundamentals of the 2D helical vortex dynamics lie in
(i) 2D algebraical expression of Biot-Savart law for helical filament;
(ii) analytical solution for self-induced motion of the helical vortex cores;
(iii) Goldstein’s solution for circulation of equilibrium of helical vortex sheets;
(iv) Generalization of Kelvin’s problem on point vortex N-gon stability to helix etc.
The primary assumption of the 2D theory is the hypothesis of helical symmetry that has been carefully tested in swirling flows in different kinds of swirlers and vortex generators. Both right- and left-handed helical symmetries were found in these real flows and hypothesis of existence of possible transitions between the different types of the vortex structures have been put forward. The change in axial velocity distribution from a jet-like profile to a wake-like during vortex breakdown has been investigated from this point of view and the associated transition from right- to left-handed helical symmetry of the vorticity field has been confirmed from experimental data and numerical simulations. Various vortex models for far wakes behind rotors are analyzed.