Flow-Induced Vibrations of a Freely Vibrating Bidirectional Square Cylinder in the Presence of a Stationary Square Cylinder at a Low Reynolds Number

Undamped flow-induced bidirectional (In-line and transverse direction) vibrations of two square cylinders in tandem arrangement were explored numerically by a two-dimensional stabilized space-time solver. Two scenarios examined: (i) downstream cylinder oscillates while upstream remains stationary and (ii) upstream cylinder oscillates while downstream is stationary. The center-to-center distance of the two cylinders is 5D. The non-dimensional mass ratio, \(m^*\) is taken as 10 for the flexibly mounted cylinder. Computations were performed at a fixed Reynolds number of 100 across a reduced velocity ( \(U^*\) ) range of 1–10. The current exploration aims primarily at understanding the behaviour of oscillator response and fluid forcing in these contrasting cases. Strong interaction occurs between the wake of the upstream cylinder and the downstream cylinder. Vibration response, lock-in branch and wake structures are emphasized. The in-line and transverse direction trajectories of flexibly mounted cylinder greatly influence the response and formation of vortex shedding due to the impingement of the vortices from the upstream cylinder.