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The present study numerically explores the limiting two degrees of freedom (streamwise and transverse) free oscillation response of three circular cylinders, placed in an in-line configuration subjected to a uniform cross flow at low Reynolds numbers. Three identical cylinders with a low mass ratio (m⁎=4/πm⁎=4/π) and zero damping are considered. The spacing between the cylinders L/DL/D is equal to 4. The reduced velocity Ur is varied from 2 to 13 for two values of the Reynolds number (Re=100Re=100 and Re=150Re=150). For comparison purposes, the free oscillation responses of an isolated cylinder and a tandem cylinder pair under the same conditions are also evaluated. The results show that the dynamic behaviors of three in-line cylinders are significantly different from those of the tandem cylinder pair. While the maximum transverse oscillation amplitude increases by about 25%, there is now a very large streamwise oscillation amplitude (AX/D≈1.3AX/D≈1.3), comparable to those in the transverse direction. They appear at Ur>9Ur>9. The frequency responses of the triple cylinder case are much richer; in particular, at higher Ur. There is a clear low frequency component which is most evident in the streamwise direction. Many of the displacement trajectories of the triple cylinder case can almost be described as “bounded random movements”. The associated phase portraits and the Poincaré maps show that the dynamical characteristics of the triple cylinder configuration are considerably richer than those of the tandem cylinder pair. Even at such low Re, the free oscillations of three in-line cylinders already seem to approach a chaotic response. In particular, there is evidence that the fluid–structure system approaches to chaos via the quasi-periodic route. Due to such much more complex dynamical characteristics, it is therefore highly risky to predict the free oscillation behaviors of multiple in-line cylinders by extrapolating those of the tandem cylinder pair.
Journal: Journal of Fluids and Structures - Volume 60, January 2016, Pages 37–61