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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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##### References:
 [1] Fredsøe, J., Pipeline-seabed interaction, J Waterw Port Coast Ocean Eng, 142, 6, 03116002, (2016) [2] Sumer, B. M.; Fredsøe, J., Hydrodynamics around cylindrical structures, (2006), World Scientific Pub Co Inc · Zbl 1153.76003 [3] Mao, Y., The interaction between a pipeline and an erodible bed, (1986), Technical University of Denmark, Lyngby, Denmark, PhD thesis [4] Brørs, B., Numerical modelling of flow and scour at pipelines, J Hydraul Eng, 125, 5, 511-523, (1999) [5] Li, F.; Cheng, L., Numerical model for local scour under offshore pipelines, J Hydrodyn Eng, 125, 400-406, (1999) [6] Li, F.; Cheng, L., Prediction of Lee-wake scouring of pipelines in currents, J Waterw Port Coast Ocean Eng, 127, 106-112, (2001) [7] Liang, D.; Cheng, L.; Yeow, K., Numerical study of the Reynolds-number dependence of two-dimensional scour beneath offshore pipelines in steady currents, Ocean Eng, 32, 1590-1607, (2005) [8] Liang, D.; Cheng, L.; Li, F., Numerical modeling of flow and scour below a pipeline in currents part II. scour simulation, Coast Eng, 34, 43-62, (2005) [9] Lu, L.; Li, Y.; Qin, J., Numerical simulation of the equilibrium profile of local scour around submarine pipelines based on renormalized group turbulence model, Ocean Eng, 32, 2007-2019, (2005) [10] Zhao, M.; Cheng, L., Numerical modeling of local scour below a piggyback pipeline in currents, J Hydraul Eng, 134, 10, 1452-1463, (2008) [11] Zanganeh, M.; Yeganeh-Bakhtiary, A.; Wahab, A. M.A., Lagrangian coupling two-phase flow model to simulate current-induced scour beneath marine pipelines, Appl Ocean Res, 38, 64-73, (2012) [12] Ong, M. C.; Utnes, T.; Holmedal, L. E.; Myrhaug, D.; Pettersen, B., Near-bed flow mechanisms around a circular marine pipeline close to a flat seabed in the subcritical regime using a $$k - \epsilon$$ model, J Offshore Mech Arct Eng, 134, 021803, (2012) [13] Fredsøe, J.; Sumer, B. M.; Anderson, J.; Hansen, E. A., Transverse vibrations of a cylinder very close to a plane wall, J Offshore Mech Arct Eng, 109, 52-60, (1987) [14] Fredsøe, J.; Sumer, B. M.; Andersen, J.; Hansen, E. A., Transverse vibration of a cylinder very close to a plane wall, Proceedings of the fourth international symposium on offshore mechanics and arctic engineering, 1, 601-609, (1985) [15] Zhao, M.; Cheng, L.; Teng, B., Numerical modelling of flow and hydrodynamic forces around a piggyback pipeline near the seabed, J Waterw Port Coast Ocean Eng, 133, 4, 286-295, (2007) [16] Zhao, M.; Cheng, L., Numerical investigation of local scour below a vibrating pipeline under steady currents, Coastal Eng, 57, 397-406, (2010) [17] Zhao, M.; Cheng, L., Numerical simulation of two-degree-of-freedom vortex-induced vibration of a circular cylinder close to a plane boundary, J Fluids Struct, 27, 1097-1110, (2011) [18] Wang, X. K.; Tan, S. K., Vortex-induced vibrations of a neutrally buoyant circular cylinder near a plane wall, J Fluids Struct, 39, 188-204, (2013) [19] Li, Z.; Yao, W.; Yang, K.; Jaiman, R. J.; Khoo, B. C., On the vortex-induced oscillations of a freely vibrating cylinder in the vicinity of a stationary plane wall, J Fluids Struct, 65, 495-526, (2016) [20] Issa, R. I., Solution of the implicitly discretized fluid flow equations by operator-splitting, J Comput Phys, 62, 40-65, (1986) · Zbl 0619.76024 [21] Patankar, S. V., Numerical heat transfer and fluid flow, (1981), Hemisphere Publishing Corporation [22] Holzmann, T., Mathematics, numerics, derivations and openfoam(R), (2017), Holzmann CFD, Leoben, fourth edition [23] Navrose, V.; Mittal, S., Free vibrations of a cylinder: 3d computations at re=1000, J Fluids Struct, 41, 109-118, (2013) [24] Tham, D. M.Y.; Gurugubelli, P. S.; Li, Z.; Jaiman, R. K., Freely vibrating circular cylinder in the vicinity of a stationary wall, J Fluids Struct, 59, 103-128, (2015) [25] Zhao, M.; Cheng, L.; An, H.; Lu, L., Three-dimensional numerical simulation of vortex-induced vibration of an elastically mounted rigid circular cylinder in steady current, J Fluids Struct, 50, 292-311, (2014) [26] Carmo, B. S.; Sherwin, S. J.; Bearman, P. W.; Willden, R. H.J., Flow-induced vibration of a circular cylinder subjected to wake interference at low Reynolds number, J Fluids Struct, 27, 503-522, (2011) [27] Lei, C.; Cheng, L.; Kavanagh, K., Re-examination of the effect of a plane boundary on force and vortex shedding of a circular cylinder, J Wind Eng, 80, 263-286, (1999) [28] Blackburn, H. M.; Henderson, R. D., A study of two-dimensional flow past an oscillating cylinder, J Fluid Mech, 385, 255-286, (1999) · Zbl 0938.76022 [29] Carberry, J.; Sheridan, J., Forces and wake modes of an oscillating cylinder, J Fluids Struct, 15, 523-532, (2001) [30] Bearman, P. W.; Zdravkovich, M. M., Flow around a circular cylinder near a plane boundary, J Fluid Mech, 89, 33-47, (1978) [31] Zdravkovich, M. M., Observation of vortex shedding behind a towed circular cylinder near a wall, Flow visualization: proceedings of the third international symposium on flow visualization, 3, 423-427, (1985) [32] Lin, C.; Lin, W. J.; Lin, S. S., Flow charateristics around a circular cylinder near a plane boundary, Proceedings of the sixteenth international symposium on transport phenomena (ISTP-16), (2005) [33] Li, Z.; Jaiman, R. K.; Khoo, B. C., An immersed interface method for flow past circular cylinder in the vicinity of a plane moving wall, Int J Numer Methods Fluids, 81, 611-639, (2016) [34] Kozakiewicz, A.; Sumer, B. M.; Fredsøe, J., Spanwise correlation on a vibrating cylinder near a wall in oscillatory flows, J Fluids Struct, 6, 371-392, (1992) [35] Tsahalis, D. T.; Jones, W. T., Vortex-induced vibration of a flexible cylinder near a plane boundary in steady flow, Proceeds of the thirteenth annual offshore technology conferences, Houston, 367-386, (1981) [36] Li, Z.; Jaiman, R. K.; Khoo, B. C., Coupled dynamics of vortex-induced vibration and stationary wall at low Reynolds number, Phys Fluids, 29, 093601, (2017)
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