Stability of helical vortices

Background
Helical vortices are essential features of wind turbine wakes and are often seen to extend a long distance behind the rotor before eventually breaking down to turbulence. In a modern wind farm where turbines are densely positioned, a majority of turbines will be partly or entirely located in the wake of other turbines. In such situations the fatigue loading of the downstream turbines will be much higher if the wake consists of stable helical vortices, compared to if the vortices have broken down to turbulence, thus making the study of instability and transition in this type of flows an important research topic. Previous studies have identified three types of instabilities in this system, namely (i) short-wave instabilities, (ii) long-wave instabilities, and (iii) mutual inductance instabilities. The focus of the present project lies in the latter two. Over the years, theoretical work has been performed in order to unfold the characteristics of these instabilities and in particular, to predict their growth rates. However, there is no experimental study employing well-defined perturbations that provides a quantitative comparison between the theoretical predictions provided by vortex theory and the modes observed in experiments

Aims
The aim of the project is to improve the understanding of long-wave instabilities of helical vortices, and to experimentally verify theoretical growth rate estimates for these instabilities.

Approaches
Classical vortex theory is reviewed and theoretical estimates regarding the growth rates of the instabilities are computed. These theoretical results are subsequently compared with the results obtained from an experimental study involving a two bladed rotor, where quantitative measurements are obtained using particle image velocimetry (PIV) and dye visualization

Keywords
Transition, helical vortices, vortex instability, vortex interactions

Research Group

Project leader
Prof. Dan S. Henningson

Dept. of Mechanics, KTH Royal Institute of Technology

Other project members

Mr. Mattias Brynjell-Rahkola, Ph.D. student

Dept. of Mechanics, KTH Royal Institute of Technology

Links and references

H. U. Quaranta, M. Brynjell-Rahkola, T. Leweke, D. S. Henningson, ”Long-wave instabilities of two interlaced helical vortices”, J. Phys.: Conf. Ser. 753 (2016) 032022

H. U. Quaranta, M. Brynjell-Rahkola, T. Leweke, D. S. Henningson, ”Long-wave instabilities of two interlaced helical vortices”, To be submitted to J. Fluid Mech.