Vortex-induced vibrations of two inline circular cylinders in proximity to a stationary wall

Abstract Vortex-induced vibrations of two inline circular cylinders in proximity to a stationary wall are numerically studied using the immersed boundary method at a Reynolds number of 100. Two cylinders, having the same degree of freedom (DOF), can oscillate only in the transverse direction (1-DOF) or in both the transverse and streamwise directions (2-DOF). The center-to-center spacings (L) of the two cylinders are 1.5D, 3.0D and 5.0D, respectively, while the gaps (G) between the wall and the cylinders are 0.6D, 1.5D and ∞ , respectively. Here, D is the diameter of the cylinders. The mass ratio is 2.0 and the reduced velocity varies from 2.0 to 15.0, with the minimum interval of 0.1. We observe that the responses of the two cylinders are significantly influenced by the presence of a stationary wall, compared with those without near-wall effects. First, several hysteretic regions are observed at different gap ratios and spacing ratios. Second, the streamwise vibration amplitude is comparable to the transverse one in the 2-DOF cases. Third, the trajectories can be oval-shaped, figure-of-eight-shaped, quasi-periodic or chaotic depending on G and L. In the simulated parametric space, we divide the vibration response of the two cylinders into different branches, i.e., two stationary branches (SB-I and SB-II), two vibration branches (VB-I and VB-II), and one collision branch (CB). The features such as vibration amplitudes, vibration frequencies, wake patterns, fluid forces, mean position shifts, and vibration trajectories in each branch are explored in detail. Furthermore, the mechanisms of the excitation of the large-amplitude vibrations in both the streamwise and transverse directions are investigated.