Vortex-induced vibrations of two rigidly coupled circular cylinders of unequal diameters at low Reynolds number

Two-dimensional numerical computations are carried out for two rigidly connected cylinders of unequal sizes undergoing vortex-induced vibrations (VIV) perpendicular to the free stream. Results are examined for Re = 250 and a fixed diameter ratio of d/D=0.2. The VIV response of the system is investigated for various positions of the small cylinder, covering a fine grid of wide radial (r) and azimuthal (θ) ranges, relative to the origin of the main cylinder. It is shown that the structural dynamics and hydrodynamic forces are strongly dependent on the arrangements. Regions of VIV reduction and amplification are distinguished, and the highest and lowest oscillation amplitudes are, respectively, acquired at configurations of (r,θ)=(0.7D,90°) and (r,θ)=(0.88D,130°). A deeper analysis in terms of the wake topology and surface pressure is then provided for these two extreme cases, to figure out the underlying mechanisms that lead to such markedly distinct responses. For the former case, the shear layers from two cylinders intensely interact and amalgamate during the oscillation, setting off subsequent processes of shear layer reattachment and downflow that are responsible for the observed high-amplitude response, while for the latter case, the shear layers from the small cylinder are highly stretched and absent from direct interaction with that from the large cylinder, which is favorable for stabilizing the wake and maintaining the low-amplitude response. Proper orthogonal decomposition (POD) is further utilized to correlate the key features of the wake with the dominant coherent structures in the flow.