Role of filament strain in the free-vortex modeling of rotor wakes

The problem of straining of vorticity is discussed within the context of time-marching, free-vortex filament modeling of rotor wakes. It is shown that for many practical rotor flight conditions, wake distortions create velocity fields that impose significant three-dimensional strain on the vortex filaments, stretching the filaments and so changing their vorticity and induced velocity field. The approach developed to model these effects applies a Prandtl-type decomposition of advection, strain, and viscous terms into successive sub-processes, with a recombinant solution to give a consistent level of approximation to the rotor wake problem. A model based on an equivalent diffusion time is developed to account for and couple the effects of filament strain into the diffusion model. Validation of the model is conducted. It is shown that strain terms in the rotor wake can be significant, and a proper representation of these effects can have important effects on the rotor wake developments and the spatial locations of blade/vortex interactions over the rotor disk. Examples documenting the significance of strain effects are shown for rotors in forward flight, during descending flight, and in ground effect.