Helical self-similarity of tip vortex cores

Abstract

The present work investigates local flow structures and the downstream evolution of the core of helical tip vortices generated by a three-bladed rotor. Earlier experimental studies have shown that the core of a helical tip vortex exhibits a local helical symmetry with a simple relation between the axial and azimuthal velocities. In the present study, a self-similarity scaling argument further describes the downstream development of the vortex core. Self-similarity has up to now only been investigated for longitudinal vortices and it is the first time that helical vortices have become the subject of such an analysis. Combining symmetry arguments from previous studies on helical vortices with novel experiments and knowledge regarding the self-similarity evolution of the core of longitudinal vortices, a new model describing what is referred to as ‘helical self-similarity’ is proposed. The generality of the model is verified and supported by experimental data. The proposed model is important for fundamental understanding of the behaviour of helical vortices, with a range of applications in both industry and nature. Examples of this are tip vortices behind aerodynamic devices, such as vortex generators, and fixed and rotary aircraft, and in combustion chambers and cyclone separators.