Vortex-induced vibrations (VIV) of two flexible cylinders arranged in tandem are studied using a two-way fluidstructure interaction (FSI) method with different spacing ratios (Sx/D) at Reynolds number Re = 500 using a twoway fluid-structure interaction (FSI) method. The main objective of this study is to investigate the effect of spacing on the hydrodynamic interactions and the VIV responses of these cylinders. The responses of the two flexible cylinders are found to be similar to the classical VIV responses at small Sx/D. Once Sx/D is large enough for the vortices to become detached from the upstream cylinder, the response of the upstream cylinder is similar to the typical VIV response whereas the downstream cylinder undergoes wake-induced vibration (WIV). The characteristics of the response of the downstream cylinder in the present study are similar to those of the first two response regimes classified by previous researchers. The third regime is not observed for the flexible downstream cylinder with both ends fixed. The two changes in the phase relation between the cross-flow displacements of the two tandem flexible cylinders are discovered to be linked with the initial-upper branch transition and the upperlower branch transition, respectively. The correlation lengths of the two flexible cylinders decrease significantly in the transition range between the upper and lower branches. Three modes of vortex shedding (2S, P + S and 2P) have been identified in the present study. The upper-branch 2P mode is found to be associated with largeamplitude vibration of the upstream cylinder and the P + S mode is observed to be related to large-amplitude vibration of the downstream cylinder for Sx/D = 3.5 and 5. On the other hand, the lower-branch 2P mode leads to small-amplitude vibration of the downstream cylinder in the post-lock-in range at Sx/D = 2.5. The relative phase shifts of the sectional lift coefficients on different spanwise cross sections can be attributed to the variation of the vortex shedding flow along the flexible cylinders, and these phase shifts result in poor phasing between the forces and the displacements which is related to the decrease of the correlation lengths.
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