Freely vibrating circular cylinder in the vicinity of a stationary wall

• Mechanism of enhanced streamwise oscillation of freely vibrating near-wall cylinder. Phase relation between drag force and streamwise displacement <180° for near-wall cylinder.
• Third response branch found between initial and lower branch at gap ratio ≤0.6 for near-wall cylinder.
• At a sufficient distance above the stationary wall (between gap ratio of 5 and 7.5), the effect of wall proximity on the frequency response tends to disappear.
• Investigations on effects of mass-ratio and new correlations for peak amplitudes and forces as a function of gap ratio.
• Vortex dynamics and wake topology of near-wall VIV for varying gap ratios. Suppression of alternate vortex shedding related to the change in vibration response for freely vibrating near-wall cylinder.

We present a numerical study on vortex-induced vibration (VIV) of a freely vibrating two degree-of-freedom circular cylinder in close proximity to a stationary plane wall. Fully implicit combined field scheme based on Petrov–Galerkin formulation has been employed to analyze the nonlinear effects of wall proximity on the vibrational amplitudes and hydrodynamic forces. Two-dimensional simulations are performed as a function of decreasing gap to cylinder diameter ratio e/D∈[0.5,10]e/D∈[0.5,10] for reduced velocities U⁎∈[2,10]U⁎∈[2,10] at ReD=100 and ReL=2900, where ReD and ReL denote the Reynolds numbers based on the cylinder diameter and the upstream distance, respectively. We investigate the origin of enhanced streamwise oscillation of freely vibrating near-wall cylinder as compared to the isolated cylinder counterpart. For that purpose, detailed analysis of the amplitudes, frequency characteristics and the phase relations has been performed for the isolated and near-wall configurations. Initial and lower branches in the amplitude response are found from the gap ratios of 0.75 to 10, similar in nature to the isolated cylinder laminar VIV. A third response branch has been found between the initial and the lower branch at the gap ratio of e/D≤0.60e/D≤0.60. For near-wall cases, phase relation between drag force and streamwise displacement varies from close to 0° to 180°. Between e/D∈[5,7.5]e/D∈[5,7.5], the effect of wall proximity on the frequency response tends to disappear. The effect of mass-ratio is further investigated. Finally, we introduce new correlations for characterizing peak amplitudes and forces as a function of the gap ratio for a cylinder vibrating in the vicinity of a stationary plane wall.