Flow-mediated interaction between a vibrating cylinder and an elastically-mounted cylinder

Abstract This study investigates the interaction between two cylinders of an identical diameter immersed in still fluid: the master cylinder is subject to forced vibration, while the adjacent slave cylinder is elastically-mounted and has only one-degree-of-freedom along the centreline of the two cylinders. The hydrodynamic interaction is simulated with an extensively-validated 2D Navier-Stokes solver that is based on the finite element method and the Arbitrary Lagrangian-Eulerian method. Extensive simulations are conducted, with a fixed Reynolds number of 100. The initial clearance distance, normalised by the cylinder diameter, ranges from 0.2 to 1.0. The mass ratio of the cylinder over the displaced fluid ranges from 1.5 to 2.5. The vibrating amplitude of the master cylinder, normalised by the cylinder diameter, varies from 0.025 to 0.1. Frequencies of the master's vibration, normalised by the slave's structural natural frequency, ranges from 0.05 to 2.4. When the frequency of the master cylinder reaches the immersed natural frequency of the slave cylinder, the slave cylinder’s vibration observes resonance, and the phase difference between the two cylinders’ movement experiences a 180 ∘ shift. In resonance, the slave-master phase difference is about 90 ∘ . The frequency of the vibration is found to significantly affect the flow features.