A partitioned iterative scheme based on Petrov-Galerkin formulation  has been employed for simulating flow past a freely vibrating circular cylinder placed in proximity to a stationary plane wall in both two-dimension (2D) and three-dimension (3D). In the first part of this work, effects of wall proximity on the vortex-induced vibration (VIV) of an elastically mounted circular cylinder with two degree-of-freedom (2-DoF) are systematically studied in 2D by investigating the hydrodynamic forces acting on the cylinder, the vibration amplitudes, the phase differences between the forces and displacements, the response frequencies as well as the vortex shedding dynamics. For that purpose, a careful comparison has been established for the isolated and near-wall cylinders, in which the gap ratio, e/D (where e denotes the gap between the cylinder and the wall and D denotes the diameter of the cylinder), is set to be 0.9, at Re = 200. Our 2D simulations have revealed that larger streamwise vibration amplitude and smaller streamwise vibration frequency can be observed in VIV of the near-wall cylinder compared to its isolated counterpart. We then focus on the explanation of the enhanced streamwise vibration amplitude when the cylinder is placed in the vicinity of the plane wall. It is found that the wall proximity largely amplifies the streamwise vibration amplitude due to net energy transfer from the fluid to the cylinder in the pre-lock-in region as well as the initial branch of the lock-in region, while reduces the streamwise vibration frequency to the level of the transverse vibration frequency. In the second part, the main focus of this article, following Tham et al. (2015)  where 2D results were systematically reported, we perform 3D simulations of VIV of a circular cylinder for both isolated and near-wall cases (e/D = 0.9) at Re = 1000 to compare the hydrodynamic forces and vibration characteristics in 3D with the results corresponding to the 2D study. We show that wall proximity effects on VIV are also pronounced in 3D with the following observations: (1) the wall proximity increases the mean lift to a lesser extent compared to 2D, while also enhances the mean drag unlike in 2D; (2) the wall proximity enhances the streamwise oscillation as well owing to a combined effect of increased drag force together with energy transfer from fluid to structure as in 2D; (3) in terms of the flow field, the wall proximity increases the wavelength of streamwise vorticity blob; and (4) similarly with the mechanism of vortex suppression in 2D, wall boundary layer vorticity strongly strengthens the negative vorticity shed from upper surface of cylinder, stretching and suppressing the positive vorticity shed from the bottom surface of cylinder.
On the Streamwise Oscillations of Freely Vibrating Cylinder Near a Stationary Plane Wall in Steady Flow
Li, Z, Yao, W, Jaiman, RK, & Khoo, BC. "On the Streamwise Oscillations of Freely Vibrating Cylinder Near a Stationary Plane Wall in Steady Flow." Proceedings of the ASME 2016 35th International Conference on Ocean, Offshore and Arctic Engineering. Volume 2: CFD and VIV. Busan, South Korea. June 19–24, 2016. V002T08A008. ASME. https://doi.org/10.1115/OMAE2016-54442
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