Flow-induced vibrations of two circular cylinders in tandem with shear flow at low Reynolds number

Abstract

The flow-induced vibrations of two elastically mounted circular cylinders subjected to the planar shear flow in tandem arrangement are studied numerically at Re=160. A four-step semi-implicit Characteristic-based split (4-SICBS) finite element method is developed under the framework of the fractional step method to cope with the vortex-induced vibration (VIV) problem. For the computational code verification, two benchmark problems are examined in the laminar region: flow-induced vibration of an elastically mounted cylinder having two degrees of freedom and past two stationary ones in tandem arrangement. Regarding the two-cylinder VIVs in shear flow, the computation is conducted with the cylinder reduced mass Mr=2.5π and the structural damping ratio ξ=0.0. The effects of some key parameters, such as shear rate (k=0.0, 0.05, 0.1), reduced velocity (Ur=3.0–18.0) and spacing ratio (Lx/D=2.5, 3.5, 4.5, 8.0), are demonstrated. It is observed that the shear rate and reduced velocity play an important role in the VIVs of both cylinders at various center-to-center distances. Additionally, in comparison with the single cylinder case, a further study indicated that the gap flow has a significant impact on such a dynamic system, leading it to be more complex. The results show that, the performances of ‘dual-resonant’ are discovered in the shear flow. A valley is formed in transverse oscillation amplitude of DC for each spacing ratio when Ur is about 6.0. For the X–Y trajectories of the circular cylinders, figure-eight, figure-O and oval shape are obtained. Finally, the interactions between cylinders are revealed, together with the wake-induced vibration (WIV) mechanism underlying the oscillation characteristics of both cylinders exposed to shear flow. Besides, the “T+P” wake pattern is discovered herein.