Beating of a circular cylinder mounted as an inverted pendulum

Abstract

This paper contains temporally and spatially resolved flow visualization and DPIV measurements characterizing the frequency–amplitude response and three-dimensional vortex structure of a circular cylinder mounted like an inverted pendulum. Two circular cylinders were examined in this investigation. Both were 2.54 cm in diameter and ~140 cm long with low mass ratios, m* = 0.65 and 1.90, and mass–damping ratios, m*ζ = 0.038 and 0.103, respectively. Frequency–amplitude response analysis was done with the lighter cylinder while detailed wake structure visualization and measurements were done using the slightly higher-mass-ratio cylinder. Experiments were conducted over the Reynolds number range 1900≤Re≤6800 corresponding to a reduced velocity range of 3.7 ≤ U* ≤ 9.6. Detailed examination of the upper branch of the synchronization regime permitted, for the first time, the identification of short-time deviations in cylinder oscillation and vortex-shedding frequencies that give rise to beating behaviour. That is, while long-time averages of cylinder oscillation and vortex-shedding frequencies are identical, i.e. synchronized, it is shown that there is a slight mismatch between these frequencies over much shorter periods when the cylinder exhibits quasi-periodic beating. Data are also presented which show that vortex strength is also modulated from one cylinder oscillation to the next. Physical arguments are presented to explain both the origins of beating as well as why the quasi-periodicity of the beating envelopes becomes irregular; it is believed that this result may be generalized to a broader class of fluid–structure interactions. In addition, observations of strong vertical flows associated with the Kármán vortices developing 2–3 diameters downstream of the cylinder are presented. It is hypothesized that these three-dimensionalities result from both the inverted pendulum motion as well as free-surface effects.