Vortex-induced vibrations of two rigidly coupled circular cylinders in tandem arrangement

In this paper, we study the transverse vortex-induced vibrations (VIV) of two rigidly connected circular cylinders of equal size, arranged in a tandem configuration, by means of two-dimensional numerical computations. Results are examined for Re= 250 and a fixed center-to-center separation of 2D. The dynamic response of the two-cylinder system is investigated in detail over a domain of reduced velocities ranging from U-r= 2 to 8. The diverse types of branches are identified, on the basis of their distinct characteristics in the amplitude and frequency responses. Among them, the lower branch is of particular interest as it is quasi-periodic in nature, instead of the periodic regime that is well documented for the isolated cylinder case. By scrutinizing the vorticity dynamics, it reveals that this quasi-periodicity arises from the switching between two flow states, which are essentially distinguished by whether an active gap flow is present. The dynamically rich response leads to a rich variety of phase dynamics, involving phase locking, trapping, slipping and drifting; in particular, phase drifting is indicative of a forthcoming phase jump of 180 between the lift force and the displacement. It is also found that in the initial branch, the excitation of the system is driven by the pressure lift force on the rear cylinder; by contrast, in the lower branch, it is the pressure lift force on the front cylinder that acts as a source of excitation.