Predicting the Onset of the Vortex Ring State Under Accelerated Flight Conditions

A general method for predicting the onset of the vortex ring state is developed in terms of a model for the propagation and growth of disturbances within the rotor flow. Newman et al.'s engineering model for the onset of the vortex ring state under quasi-steady conditions is shown to be a special case of this approach. A generalisation of Newman et al.'s model to the unsteady case is shown to reproduce earlier findings that the onset of the vortex ring state should be postponed to higher descent rates under accelerated flight conditions. Numerical simulations of the onset of the vortex ring state reveal though that the transition into the vortex ring state becomes increasingly gradual as the acceleration of the rotor is increased. Under a combination of high forward speed and vertical acceleration, the vortex ring state may even be replaced by a qualitatively different, highly transient state where the collapse of the wake into the toroidal form that is usually associated with the onset of this flow condition is suppressed. The absence of an abrupt and universal transition marking the onset of the vortex ring state under accelerated flight conditions complicates the application of simple analytical models and implies that the specific details of the time-dependent dynamics of the rotor wake and its interaction with the rotor cannot be ignored when modelling the onset of this flow regime.