Freely vibrating circular cylinder in the vicinity of fully developed scour holes at low Reynolds numbers

In this work, a numerical study is conducted on the flow past an elastically mounted circular cylinder with two degrees of freedom (2-DoF) placed in the vicinity of a fully developed scour hole in both two-dimension (2D) and three-dimension (3D). This paper focuses to study how different fully developed scour profiles affect the hydrodynamic quantities of vortex-induced vibrations (VIV) of an elastically mounted circular cylinder in proximity and the flow fields. To begin with, we systematically conduct the 2D simulations at Reynolds number of Re=200 in the laminar flow regime and characterize the cylinder amplitudes, the hydrodynamic force coefficients and phase differences. For the 2D study, two representative fully developed scour hole profiles with Shields parameters of θ*=0.098 and 0.048 are considered and the case of a plane wall (i.e. θ*=∞) is taken into account as a reference for comparison. In the 3D simulations at Re=300, which is at the beginning of the subcritical flow regime, with θ*=0.098, the cylinder response characteristics and the 3D flow fields are investigated. It is shown that the upper boundary of the lock-in regime at θ*=0.048 is much smaller than those of θ*=0.098 and ∞, and the vortex shedding is ceased for Ur ≥ 5.3 at θ*=0.048. It is also found that the equilibrium scour profile affects the mean force coefficients to a large extent: the mean lift coefficient CL¯ for θ*=∞ is larger than those of θ*=0.098 and 0.048 in the pre-lock-in and post-lock-in regimes; and the mean drag coefficient CD¯ for θ*=∞ is larger than those of θ*=0.098 and 0.048 in all regimes.