The Role of Filament Stretching in the Free-Vortex Modeling of Rotor Wakes

The problem of filament strain or flow field "stretching" effects are discussed within the context of time-marching, free-vortex filament modeling of rotor wakes. It is shown that for most practical rotor flight conditions, wake distortions create velocity fields that impose three-dimensional strain on the vortex filaments, stretching these filaments, and changing their vorticity and induced velocity field. Such strain or stretching effects are not easly neglected without proper justification. The basic approach used here to model these effects, applies a Prandtl-type decomposition of the inviscid and viscous contributions into successive sub-processes, with a recombinant solution to give a consistent level of approximation to the rotor wake problem. A parsimonious model based on an equivalent diffusion time is developed to account for and couple the effects of filament straining into the viscous part of the solution. Examples of wake predictions are shown for rotors operating in hover, forward flight, flight near the ground, and during descending flight. It is shown that even for benign flight conditions, strain effects on vortex filaments can be significant, and including the effects of strain on the viscous characterization of the vortices is important for predictions of the rotor wake development.