A constrained vortex model with relevance to helicopter vortex ring state

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Description/Abstract

A planar model of a lifting surface descending into its own wake is constructed with the aim of demonstrating some underlying mechanisms of the ‘vortex ring’ state that may be entered
by a rotary wing aircraft during a vertical descent. The model uses line vortices that are periodically released from a point in space and then allowed to evolve in a constrained manner. For low descent velocities the model reproduces a hover state, where the wake vortices move downwards relative to the lifting plane. A critical descent speed is reached after which the model produces a quasi-periodic shedding of vortex agglomerations. This state is reached via a Hopf bifurcation of the steady state and persists until another critical descent velocity after which a steady windmill brake state is possible, in which vortices travel upwards in a regular manner. Unconstrained simulations reveal a more chaotic vortex pattern, but frequency analysis reveals an underlying structure similar to that shown for the constrained model. Besides offering a qualitative understanding of possible mechanisms of vortex ring state, the analysis suggests some dimensionless parameters that collapse the
model data.