Flow-induced vibration of a cylinder-plate assembly in laminar flow: Branching behavior

Abstract

The transverse flow-induced vibration of an elastically supported cylinder-plate assembly (viz., a rigid splitter-plate attached to the downstream side of a circular cylinder) with a low mass ratio of 10 and a zero structural damping coefficient at a Reynolds number of 100 is investigated in the present work. A careful identification of all the branches in the amplitude response of an assembly with various plate lengths is undertaken, in conjunction with the associated flow dynamics responsible for these branches involving various aspects of the flow, such as the vortex-shedding in the far wake and the evolution of the shear layers generated on the upper and lower surfaces of the cylinder in the near wake. This knowledge offers crucial new perspectives on the nature and physical mechanisms behind the complex dynamics of a cylinder-plate system. These investigations involve a wide range of plate lengths LSP/D=0–4 (where D is the diameter of the circular cylinder) over an extensive span of reduced velocities Ur = 2–30. For LSP/D≤0.5, a self-limiting oscillation is induced in the structure—this can be either a vortex-induced vibration (VIV) or an integrated VIV-galloping response. For LSP/D≥0.75, the amplitude response is non-limited in the sense that the amplitude increases linearly with increasing Ur. More precisely, the amplitude response consists of either a strongly correlated VIV-galloping regime (at LSP/D=0.75) or two clearly separated regimes of VIV and galloping (for LSP/D>0.75). In the galloping regime, both odd- and even-multiple synchronizations between the system oscillation and the vortex shedding are supported. “Kinks” in the amplitude response signal the onset of synchronization branches in the galloping regime. Two new branches have been identified for a cylinder-plate assembly with longer plate lengths, namely, an initial galloping branch and a still (quiescent) branch. The initial galloping branch is associated with wake meandering. For the still branch, the assembly is stationary (no vibratory motion), and flow over the assembly is steady (no vortex shedding or shear-layer meandering).