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Freely vibrating circular cylinder in the vicinity of fully developed scour holes at low Reynolds numbers. (English) Zbl 1390.76472
Summary: 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 \(\mathrm{Re} = 200\) 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 \(\theta^* = 0.098\) and 0.048 are considered and the case of a plane wall (i.e., \(\theta^* = \infty\)) is taken into account as a reference for comparison. In the 3D simulations at \(\mathrm{Re} = 300\), which is at the beginning of the subcritical flow regime, with \(\theta^* = 0.098,\) the cylinder response characteristics and the 3D flow fields are investigated. It is shown that the upper boundary of the lock-in regime at \(\theta^* = 0.048\) is much smaller than those of \(\theta^* = 0.098\) and, the vortex shedding is ceased for \(U_{r}\geq 5.3\) at \(\theta^* = 0.048\). It is also found that the equilibrium scour profile affects the mean force coefficients to a large extent: the mean lift coefficient \(\overline{C_L}\) for \(\theta^* = \infty\) is larger than those of \(\theta^* = 0.098\) and 0.048 in the pre-lock-in and post-lock-in regimes; and the mean drag coefficient \(\overline{C_D}\) for \(\theta^* = \infty\) is larger than those of \(\theta^* = 0.098\) and 0.048 in all regimes.
MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
74H45 Vibrations in dynamical problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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