A universal Strouhal number for the ‘locking-on’ of vortex shedding to the vibrations of bluff cylinders

It is well known that the vortices shed from a circular cylinder lock on in frequency to the vibrations when the cylinder is forced to vibrate or is naturally excited to sufficient amplitudes by flow-induced forces. This paper presents a model for a universal wake Strouhal number, valid in the subcritical range of Reynolds numbers, for both forced and vortex-excited oscillations in the locking-on regime. The Strouhal numbers thus obtained are constant at St * = 0·178 over the range of wake Reynolds numbers Re * = 700-5 × 10 4 . This value is in good agreement with the results obtained by Roshko (1954 a ) and Bearman (1967) for stationary circular cylinders and other bluff bodies in the same range of Reynolds numbers. A correspondence between the amplification of the cylinder base pressure, drag and vortex circulation is demonstrated over a wide range of frequencies and for vibration amplitudes up to a full cylinder diameter (peak to peak). The fraction e of the shed vorticity in the individual vortices is found to be dependent upon the base-pressure parameter K = (1 − C pb ) ½ . Consequently, e is also a function of the amplitude and frequency of the vibrations in the locking-on regime.

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