Scaling and dynamics of vortex lock-in for circular cylinders in an oscillating flow

Abstract

The concept of vortex lock-in for a single circular cylinder in an oscillating flow, induced through acoustic forcing, is revisited. Multiple cylinder diameters are investigated over a Reynolds number range between 500 and 7200. The lock-in behaviour is investigated quantitatively through hot-wire anemometry and planar particle image velocimetry measurements. The results corroborate previous findings describing the frequency range over which vortex lock-in occurs. It is found that the cylinder location in a standing wave (pressure node or velocity node) had a significant influence on the lock-in behaviour. A novel scaling which captures the onset of vortex lock-in is proposed which demonstrates that the Strouhal number is important in predicting the amplitude of the velocity fluctuations required to induce lock-in. Velocity fields also reveal the existence of bimodal vortex shedding during lock-in. This is confirmed using snapshot proper orthogonal decomposition which demonstrates that symmetric and alternate shedding modes are simultaneously present during lock-in and that symmetric shedding is inherent to the near wake region only. Reduced-order reconstruction of the instantaneous velocity fields confirmed that features associated with the forcing frequency control the shear layer roll-up up to while the influence of the asymmetric mode is simply to skew the trajectory of the vortex pair. Since vortex roll-up and the cylinder wake ends at, the emergence of spectral content at is attributed to a wavelength doubling measured between the vortical structures in the flow field.