Self-similarity and helical symmetry of various vortex wakes

Abstract

The present work examines the local structure and downstream evolution of both longitudinal vortexes behind the vortex generators and the helical tip vortices generated by the rotating 3-bladed rotor. Both wakes flow with the strong longitudinal or helical vortices have been studied by stereo PIV measurements in a wind tunnel or a water flume accordingly. The vorticity field was calculated from the measured velocity fields. The downstream development of vortex local cores investigates by using self-similarity scaling arguments and local helical symmetry tests simultaneously. It was analyzed Batchelor’s vortex and 2-D vortex with a helical vortex to use a combined vortex model of the helical self-similarly for a comparison with the experimental data. The experimental study of the shape of both vortices was carried out to describe the downstream development of the expanding vortex core by the new combined vortex model based on the experimental observations triggered by previous studies of wakes behind vortex generators and rotors. It was established that the local helical symmetry with a simple correspondence between the axial and azimuthal velocity in the cores exists in all cross-sections along of both longitudinal and helical vortices. It is also found that the averaged vorticity profiles inside the core of both vortices are self-similar. This knowledge is important for the fundamental understanding of the vortex flows, as well as for the aspect of applications, for which parametric descriptions can be substantially reduced in terms of required time and cost by easing engineering models.