Vortex-induced vibration of a flexible splitter plate attached to a square cylinder in laminar flow

Vortex-induced vibration (VIV) of a flexible splitter plate attached to a square cylinder in laminar flow is investigated using fluid–structure interaction (FSI) simulation. The Reynolds number based on the edge length of the square cylinder ( L ) is fixed at Re = 100, while the structural parameters of the plate are set as ρ p (density ratio) = 84.75, H/L (non-dimensional thickness) = 0.06, E (non-dimensional elastic modulus) = 5 × 1 0 3 ∼ 5 × 1 0 6 and l/L (non-dimensional length) = 0.5, 1 and 2, respectively. It is found that the bending rigidity and plate length have significant influences on the dynamic response of the plate, fluid loads on the cylinder–plate body and the vortex pattern in the flow field. At l/L = 0.5, the natural frequency of the plate does not intersect with the vortex shedding frequency in the parameter range considered; VIV of the flexible plate is negligible, and the fluid loads and flow pattern are similar to those in the case of a rigid plate. At l/L = 1, lock-in occurs when the first natural frequency approaches the vortex shedding frequency. In the lock-in regime, the vibrating frequency of the plate shifts to be commensurate with the first natural frequency, and the first-mode bending motion of large amplitude is observed, resulting in higher vortex shedding frequency and narrower vortex street in the wake. At l/L = 2, besides the first-natural-frequency lock-in, the off-centerline phenomenon and second-natural-frequency lock-in are also observed at low elastic modulus. In the off-centerline regime, the mean deflection of the splitter plate shifts to one side and a second-mode-like bending motion appears, which breaks the symmetry of the flow pattern and generates a non-zero mean lift. In the second-natural-frequency lock-in region, the plate vibration and fluid loads are also amplified. The model proposed could be taken as a benchmark for VIV of the flexible plate in laminar flow, and the results obtained are insightful to the design of FSI-based piezoelectric energy harvesters using flexible plates.