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

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Abstract
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 atSt*= 0·178 over the range of wake Reynolds numbersRe*= 700-5 × 104. This value is in good agreement with the results obtained by Roshko (1954a) 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 ε of the shed vorticity in the individual vortices is found to be dependent upon the base-pressure parameter K = (1 −Cpb)½. Consequently, ε is also a function of the amplitude and frequency of the vibrations in the locking-on regime.

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