Abstract

The vortex–induced motions (VIM) of bluff bodies and multi–column structures has been studied extensively through experiments and numerical simulations. Nevertheless, most numerical simulations ignore the existence of free surface and treat it as a rigid plane using boundary conditions. The objective of this paper is to investigate the effect of free surface on VIM for the Reynolds number covering 1.0×105<Re<1.6×105. The two degree–of–freedoms (DOF) vortex–induced motions of a circular cylinder with and without free surface are investigated with our in–house solver naoe–FOAM-SJTU. The Delay Detached–Eddy Simulation (DDES) approach is used to simulate the turbulent flow. To capture the free surface, the Piecewise Linear Interface Calculation (PLIC) which is a geometric Volume of Fluid (VOF) method is adopted. The results show that the free surface has major effects on the in–line motion amplitude, transverse oscillation frequency and motion trajectory, which cannot be ignored.

INTRODUCTION

As the typical structures, cylindrical columns are widely applied in many offshore platforms. When these bluff bodies are subjected to currents, the motion amplitude will increase significantly especially in the crossflow direction induced by the alternative vortex shedding. Distinct from traditional vortex–induced vibration (VIV) of flexible cylinders with large aspect ratio, the monocolumn platforms often undergoes the motion with a long period and all degrees of freedom. This particular phenomenon is termed the vortex–induced motion (VIM). It will impact the fatigue of mooring and riser systems and the structure itself. Hence, it is essential to study the hydrodynamic characteristics of this complex problem.

To better understand the basic mechanism behind it, cylinders are often chosen as the research object. There are extensive experiments and numerical simulations in this regard. Jauvtis and Williamson (2004) firstly extended the vortex–induced vibration of cylinders to two degrees of freedom. In their experiments, they found that a new amplitude response branch will appear when the mass ratio is less than 6. Gonçalves et al. (2013) conducted a series of experiments about the vortex–induced vibration of low aspect ratio cylinders with two degrees of freedom in a recirculating water channel. By measuring response amplitudes and frequencies of cylinders, they found that motion characteristics were related to the mass ratio and aspect ratio. On this basis, Gonçalves et al. (2018) set the mass ratio to 1 and released all degrees of freedom to analyze the effect of aspect ratio at different Reynolds numbers. The results showed that motion amplitudes in the in–line and transverse directions decreased as the aspect ratio decreased. And the free–end effect became predominant when the aspect ratio was less than 0.5. Based on this experiment, He et al. (2019) used in–house solver naoe–FOAM–SJTU to simulate the conditions when the aspect ratio is equal 2. The results were in good agreement with the experimental data in term of hydrodynamic forces and response frequencies.

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