Modeling the mean flow through a rotor in axial flight including vortex ring conditions

Abstract

The distinction between the unsteady flow through a rotor in axial flight and its mean or time-averaged component is identified. Fully unsteady rotor wake calculations and experimental data show that the mean wake tube is truncated by the migration of vorticity from the mean to the transient part of the flow. The mean wake is thus modeled as a truncated vortex tube, in a fashion similar to the model proposed by Wang. The truncated tube model is equivalent to simple momentum theory for axial flight, but can provide a continuous solution through the vortex ring regime if correction terms are introduced. The model is simple to implement and its equivalence with momentum theory suggests that it can easily be extended to forward flight. A specific model for the transient component of the flow will be required, though, before the transient response of an aircraft operating deep within the vortex ring state can be predicted.