A Visual Study of Vortex Instabilities in the Wake of a Rotor in Hover

Abstract

A visual study of the instability characteristics of the helical vortex filaments trailing from the tips of a three-bladed lifting rotor in a water tank is presented. The rotor diameter was 25.4 cm, and its rotation rate ranged from 4 to 12 revolutions per second. Soon after their formation, the vortex filaments developed long- and short-wave instabilities. In the long-wave instability mode, two of the three vortices coming off the rotor orbited around each other and merged in about 0.4 of the theoretical orbit time of equistrength two-dimensional vortices, after which the third vortex joined the merger to form a single, apparently turbulent helical vortex filament. The wavelengths of the short-wave instabilities were about 0.4 of the wake radius, about 17 cycles over the circumference. The short waves exhibited a linear growth rate during the first half of their orbital motion and an exponential growth prior to merging. The linear growth rate was about 0.0034 D/rad. The e-folding time for the exponential growth rate was about 0.52 rad.