On the vortex-induced oscillations of a freely vibrating cylinder in the vicinity of a stationary plane wall

A partitioned iterative scheme based on Petrov–Galerkin formulation by Jaiman et al. (2016) has been employed for simulating flow past a freely vibrating circular cylinder placed in proximity to a stationary plane wall. In the first part of this work, wall proximity effects on the vortex-induced vibrations (VIV) of an elastically mounted circular cylinder with two degree-of-freedom (2-DoF) are systematically studied in two-dimension (2D) laminar flow at Reynolds number, Re=200Re=200 based on the diameter of cylinder. We investigate the hydrodynamic forces, vibration characteristics, phase relations, response frequencies, motion trajectories as well as vortex shedding patterns. For that purpose, a careful comparison has been established between the isolated and near-wall cylinders. Our 2D simulations reveal that (i) the vibrating near-wall cylinder exhibits larger streamwise oscillation and smaller streamwise vibration frequency as compared to its isolated counterpart owing to the energy transfer from fluid to cylinder and streamwise frequency lock-in caused by the suppression of shear layer roll-up from the bottom cylinder surface; (ii) the mechanism of this vortex shedding suppression for the near-wall configuration can be described by a cyclic process where counter-clockwise vortices shed from the bottom surface of the cylinder force the wall boundary layer to separate and induce secondary clockwise vortices which merge with clockwise vortices shed from the upper surface of the cylinder, eventually suppressing the counter-clockwise vortices from the bottom cylinder surface; (iii) beating oscillations during VIV are found at the critical reduced velocities entering and leaving the lock-in region; and (iv) VIV response becomes much more sensitive to the wall proximity in the energy-in phase than in the energy-out phase. In the second part, we perform three-dimensional (3D) simulations for VIV of a circular cylinder for both isolated and near-wall cases at subcritical Re=1000Re=1000. We compare the hydrodynamic forces and vibration characteristics in 3D with the results corresponding to the 2D study at Re=200Re=200. We show that the wall proximity effects on VIV are also pronounced in 3D with the following observations: (i) the wall proximity increases the mean lift force to a lesser extent as compared to 2D at Re=200Re=200; (ii) the wall proximity also enhances the streamwise oscillation to a lesser extent as compared to 2D at Re=200Re=200; and (iii) the wall proximity increases the wavelength of streamwise vorticity blob.