Numerical investigation into the effect of spacing on the flow-induced vibrations of two tandem circular cylinders at subcritical Reynolds numbers

Abstract

Abstract Two-degree-of-freedom (2DOF) flow-induced vibrations (FIV) for a pair of elastically mounted circular cylinders in tandem arrangement with varying centre-to-centre spacings ( S x ) are numerically studied. The Reynolds number range R e = 1470 –10320 belongs to the subcritical flow regime. Two identical cylinders with a mass ratio of m ∗ = 2 . 6 and a mass-damping parameter of m ∗ + C a ζ = 0 . 013 are considered in the simulation. Four spacing ratios ( S x ∕ D , where D is the identical diameter) ranging from 3.0 to 8.0 are employed to investigate the effect of S x ∕ D on the FIV responses, hydrodynamic characteristics and wake patterns of the two cylinders. It is found that the effect of the downstream cylinder on the FIV of the upstream one becomes insignificant when S x ∕ D ≥ 4 . 0 . Due to the unsteady wake-cylinder interactions, multi-peak responses are observed for the downstream cylinder. Dual resonance with the 2:1 in-line to cross-flow oscillation frequency ratio and figure-eight orbital trajectories is found to occur for the upstream cylinder. In contrast, the trajectories of the downstream cylinder are rather irregular because of the low frequency components in the in-line response at high reduced velocity ( V r ). Both shear flow and vortex shedding may appear in the gap region depending on S x ∕ D and the relative motion of the two cylinders. In general, the vortex shedding modes of the upstream cylinder are similar to those of a single cylinder. Whereas, the analyses on the wake patterns suggest that the interactions of the upstream wake with the downstream cylinder and its own wake contribute to the unsteady fluid dynamics, which is crucial to maintaining the large-amplitude vibrations of the downstream cylinder at high V r .