Missing critical mass ratio in VIV of rigidly connected cylinders

Abstract

Two-dimensional numerical study is carried out for two rigidly coupled cylinders in tandem arrangement undergoing the transverse vortex-induced vibration (VIV) at low Reynolds numbers of $Re=60$, 100, 150 and 200. A fixed center-to-center spacing ratio of $s/D=2$ is selected. Results are examined over the reduced velocity range of $U_r=0.25-100$ and low mass ratios ($0.02⩽m^{\ast }⩽1$) are considered. This study reveals several distinct features that differ significantly from single cylinder VIV. First, contrary to single cylinder cases where a critical mass ratio exists, no critical mass ratio is observed in the tandem system at $s/D=2$ and the amplitude response increases smoothly with decreasing mass ratio. Second, decreasing mass ratio leads to enhanced soft lock-in behavior with frequency ratios progressively decreasing below unity while triggering earlier and more rapid amplitude growth. The lock-in bandwidth also shows an unexpected trend by narrowing with decreasing mass ratio in the extremely low mass ratio regime ($m^{\ast }⩽1$), which is opposite to the widening trend observed in systems with $m^{\ast }>1$. Third, a distinctive quasi-periodic response characterized by beating phenomena appears in the lower branch ($U_r=2.5-4.25$). Detailed force decomposition reveals pressure forces dominate over viscous forces with pressure lift coefficients of the upstream and downstream cylinders. It is the phase differences between two cylinders that leads to the quasi-periodic behavior. Moreover, Dynamic mode decomposition analysis shows this quasi-periodicity results from vortex impingement on the downstream cylinder. These findings offer new insights into the complex fluid–structure interactions in tandem cylinder arrangements at extremely low mass ratios, with practical implications for engineering applications such as the design of twin-tube submerged floating tunnels.