Two-degree-of-freedom vortex-induced vibrations of two square cylinders in tandem arrangement at low Reynolds numbers

Abstract

Although flow past cylinders has a vast spectrum of applications in various fields of engineering, the existence of flow-induced vibrations (FIVs) add a need for a more precise and thorough approach when studying such flows. In this context, this work investigates the FIVs’ mechanism due to two square cylinders placed in tandem arrangement through a characteristics-based-split (CBS) finite element method. Both cylinders, with a low mass ratio (mr= 2), are free to oscillate in in-line and transverse directions. The center-to-center distance of 5D (D being the cylinder side width) is kept fixed between the cylinders. The Reynolds number (Re) is ranged from 40 to 200 with an increment of 40, and computations are carried out for the reduced velocity (Ur) ranging from 3 to 13 under each Re value. Results show that the effects of Re and Ur on the dynamic responses are qualitatively similar for both cylinders. However, effects on the downstream cylinder are stronger due to the upstream wake. For Re equal to or beyond 120, the in-line low-frequency characteristic becomes obvious at some higher values of Ur for the upstream cylinder, whereas it exists over a wide range of Ur for the downstream cylinder. For lower Re (up to 120), cylinders show steady behavior at Ur= 5. However, for higher Re, they vibrate with the maximum amplitudes (especially the in-line amplitude of the downstream cylinder), and show complex wake flow at the same Ur. Compared to higher Re, the maximum vibration amplitudes in the transverse direction of lower Re are relatively higher, while the opposite trend is observed for in-line vibration amplitudes. Several unstable trajectories are also identified other than the typical figure-eight trajectories. In context of vortex shedding, different permutation of steady state, 2S, P+S, and complex modes are observed for different values of Re. It is also noted that the vortex shedding pattern keeps changing in the far wake for higher Re.