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The wandering motion of tip vortices trailed from a hovering helicopter rotor is described. This aperiodicity is known to cause errors in the determination of vortex properties that are crucial inputs for refined aerodynamic analyses of helicopter rotors. Measurements of blade tip vortices up to 260 deg vortex age using stereo particle-image velocimetry (PIV) indicate that this aperiodicity is anisotropic. We describe an analytical model that captures this anisotropic behavior. The analysis approximates the helical wake as a series of vortex rings that are allowed to interact with each other. The vorticity in the rings is a function of the blade loading. Vortex core growth is modeled by accounting for vortex filament strain and by using an empirical model for viscous diffusion. The sensitivity of the analysis to the choice of initial vortex core radius, viscosity parameter, time step, and number of rings shed is explored. Analytical predictions of the orientation of anisotropy correlated with experimental measurements within 10%. The analysis can be used as a computationally inexpensive method to generate probability distribution functions for vortex core positions that can then be used to correct for aperiodicity in measurements.

The stability and turbulence characteristics of a vortex filament emanating from a single-bladed rotor in hover are investigated using proper orthogonal decomposition (POD). The rotor is operated at a tip chord Reynolds number and tip Mach number of 218 000 and 0.23, respectively, and with a blade loading of C T /σ = 0.066. Inplane components of the velocity field (normal to the axis of the vortex filament) are captured by way of two-dimensional particle image velocimetry with corrections for vortex wander being performed using the Γ 1 method. The first POD mode alone is found to encompass nearly 75 % of the energy for all vortex ages studied and is determined using a grid of sufficient resolution to avoid numerical integration errors in the decomposition. The findings reveal an equal balance between the axisymmetric and helical modes during vortex roll-up, which immediately transitions to helical mode dominance at all other vortex ages. This helical mode is one of the modes of the elliptic instability. The spatial eigenfunctions of the first few Fourier-azimuthal modes associated with the most energetic POD mode is shown to be sensitive to the choice of the wander correction technique used. Higher Fourier-azimuthal modes are observed in the outer portions of the vortex and appeared not to be affected by the choice of the wander correction technique used.

Low-dimensional characteristics of a helical vortex filament from a reduced-scale rotor are investigated using proper orthogonal decomposition (POD). Measurements are captured by way of particle image velocimetry. Experiments are performed on a 1.0 m diameter, single-bladed rotor in hover. The rotor is operated at 1500 RPM, which corresponds to a blade tip chord Reynolds number of 218,000 and a tip Mach number of 0.23. The blade is set to a collective pitch angle of 7.3 • , which resulted in a blade loading (C T /σ) of 0.066. Classical and snapshot techniques of POD are applied to a helical vortex filament, both of which revealed similar characteristics of the dominant modes. Two different techniques (Γ 1 and geometric center methods) of wander correction are applied to test the sensitivity of the low-dimensional characteristics using POD. Using the Γ 1 method, POD revealed that an elliptic instability dominated the energy spectrum of the velocity fluctuations within the tip vortex. However, at early vortex ages an axisymmetric mode, which is found to perform vortex roll-up, is found to be equally dominant. Further, the spatial structures of the most energetic modes derived from POD are found to be sensitive to the choice of the centering technique used.

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