Two-Dimensional Numerical Simulations of Wall Proximity Effect on Cylinders

In the oil and offshore industry, it is a common phenomenon that subsea pipelines placed on or in the proximity of the seabed are exposed to underwater waves and currents. Free spanning in sections along the length of pipeline frequently results from the erosion of sediments or the irregular terrain. This scenario can be modelled by a much more simplified set-up, where a circular cylinder situated near a plane wall is subjected to the oncoming flows. In this case, unlike the well-studied isolated cylinder, the hydrodynamic forces exerting on the near-wall cylinder will depend largely upon on the gap between the wall and the cylinder itself. In this work, flows around a stationary and a freely vibrating two-dimensional circular cylinder near a plane boundary are numerically simulated using the Immersed Interface Method (IIM) and Finite Element Method (FEM) with Arbitrary Lagrangian-Eulerian (ALE) approach, respectively. In the case of a stationary cylinder, instead of a fixed wall, a moving wall with no-slip boundary is considered in order to avoid the complex involvement of the boundary layer and to focus only on the shear-free wall proximity effects in evaluating the lift and drag forces in the low Reynolds number regime (Re ≤ 200), with the aim of validating our IIM solver since it is the first time to apply IIM in solving flows past a near-wall cylinder. The gap ratio e/D is typically taken from 0.1 to 2.0 in this part of studies, where e denotes the gap between the cylinder and the wall and D denotes the diameter of the cylinder. The key findings are that the mean drag coefficient increases and peaks at e/D = 0.5 with the increase of e/D and keeps decreasing from e/D = 0.5 to e/D = 2.0, while the mean lift coefficient decreases monotonically with the increase of e/D. In the case of the freely vibrating cylinder in both transverse and in-line directions, the fixed wall is used to include the shear-layer effect from the bottom wall in considering the near-wall vortex-induced vibration (VIV) by using FEM with ALE approach. It can be concluded from our observations that when the cylinder is brought closer to the wall from e/D = 10.0 to e/D = 0.75, the peak transverse displacement amplitude decreases, while the peak in-line displacement amplitude increases, by greater than 20 times that of an isolated cylinder.