AN ASPECT OF THE PROPELLER-SINGING PHENOMENON AS A SELF-EXCITED OSCILLATION
1965
Shioiri, Jumpei
A model for the propeller-singing phenomenon considered as a self- excited oscillation is presented to interpret the finding of a recent experimental work; viz., that, although the singing frequency roughly obeys the well-known Strouhal relation, once the strong singing state has been established, the frequency is kept constant through a fairly wide range of flow velocity, and consequently the frequencyversus-velocity diagram exhibits step and jump characteristics. The model presented is a closed loop composed of a blade, as a mechanical-vibration system, and the Karman vortexshedding mechanism; the blade vibration controls the shedding mechanism, and the hydrodynamic reaction of shed vortices sustains the blade vibration. The control imposed by the blade vibration upon the vortex shedding actually implies the synchronization of the latter with the former. The model which simulates the vortex-shedding mechanism is essentially a simplified mathematical expression for the disintegration process of the vortex sheets shed from the separation points into the rows of discrete vortices. The stability criterion derived for the synchronized run of the shedding mechanism, together with the positive-work criterion imposed upon the phase relation between the blade vibration and the hydrodynamic reaction of the shed vortices, gives a reasonable interpretation for the step and jump characteristics.
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