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**Numerical prediction of hydrodynamic loading on circular cylinder array in oscillatory flow using direct-forcing immersed boundary method.**
*(English)*
Zbl 1251.76029

Summary: Cylindrical structures are commonly used in offshore engineering, for example, a tension-leg platform (TLP). Prediction of hydrodynamic loadings on those cylindrical structures is one of important issues in design of those marine structures. This study aims to provide a numerical model to simulate fluid-structure interaction around the cylindrical structures and to estimate those loadings using the direct-forcing immersed boundary method. Oscillatory flows are considered to simulate the flow caused by progressive waves in shallow water. Virtual forces due to the existence of those cylindrical structures are distributed in the fluid domain in the established immersed boundary model. As a results, influence of the marine structure on the fluid flow is included in the model. Furthermore, hydrodynamic loadings exerted on the marine structure are determined by the integral of virtual forces according to Newton’s third law. A square array of four cylinders is considered as the marine structure in this study. Time histories of inline and lift coefficients are provided in the numerical study. The proposed approach can be useful for scientists and engineers who would like to understand the interaction of the oscillatory flow with the cylinder array or to estimate hydrodynamic loading on the array of cylinders.

### MSC:

76M15 | Boundary element methods applied to problems in fluid mechanics |

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\textit{M.-J. Chern} et al., J. Appl. Math. 2012, Article ID 505916, 16 p. (2012; Zbl 1251.76029)

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### References:

[1] | “Langlee Wave Power,” http://www.langlee.no/. |

[2] | B. M. Sumer and J. Fredsoe, Hydrodynamics Around Cylindrical Structures, chapter 3, World Scientific Publishing, Singapore, 1997. · Zbl 0964.76001 |

[3] | C. H. K. Williamson, “Sinusoidal flow relative to circular cylinders,” Journal of Fluid Mechanics, vol. 155, pp. 141-174, 1985. |

[4] | T. Sarpkaya, “Force on a circular cylinder in viscous oscillatory flow at low Keulegan-Carpenter numbers,” Journal of Fluid Mechanics, vol. 165, pp. 61-71, 1986. |

[5] | E. D. Obasaju, P. W. Bearman, and J. M. R. Graham, “A study of forces, circulation and vortex patterns around a circular cylinder in oscillating flow,” Journal of Fluid Mechanics, vol. 196, pp. 467-494, 1988. |

[6] | X. W. Lin, P. W. Bearman, and J. M. R. Graham, “A numerical study of oscillatory flow about a circular cylinder for low values of beta parameter,” Journal of Fluids and Structures, vol. 10, no. 5, pp. 501-526, 1996. |

[7] | G. Iliadis and P. Anagnostopoulos, “Viscous oscillatory flow around a circular cylinder at low Keulegan-Carpenter numbers and frequency parameters,” International Journal for Numerical Methods in Fluids, vol. 26, no. 4, pp. 403-442, 1998. · Zbl 0909.76049 |

[8] | W. Zheng and C. Dalton, “Numerical prediction of force on rectangular cylinders in oscillating viscous flow,” Journal of Fluids and Structures, vol. 13, no. 2, pp. 225-249, 1999. |

[9] | H. An, L. Cheng, and M. Zhao, “Direct numerical simulation of oscillatory flow around a circular cylinder at low Keulegan-Carpenter number,” Journal of Fluid Mechanics, vol. 666, pp. 77-103, 2011. · Zbl 1225.76141 |

[10] | M. J. Chern, P. Rajesh Kanna, Y. J. Lu, I. C. Cheng, and S. C. Chang, “A CFD study of the interaction of oscillatory flows with a pair of side-by-side cylinders,” Journal of Fluids and Structures, vol. 26, no. 4, pp. 626-643, 2010. |

[11] | P. Anagnostopoulos and C. Dikarou, “Numerical simulation of viscous oscillatory flow past four cylinders in square arrangement,” Journal of Fluids and Structures, vol. 27, no. 2, pp. 212-232, 2011. |

[12] | J. M. Yusof, Interaction of massive particles with turbulence [Ph.D. thesis], Department of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, USA, 1996. · Zbl 0870.93033 |

[13] | E. A. Fadlun, R. Verzicco, P. Orlandi, and J. M. Yusof, “Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations,” Journal of Computational Physics, vol. 161, no. 1, pp. 35-60, 2000. · Zbl 0972.76073 |

[14] | Y. H. Tseng and J. H. Ferziger, “A ghost-cell immersed boundary method for flow in complex geometry,” Journal of Computational Physics, vol. 192, no. 2, pp. 593-623, 2003. · Zbl 1047.76575 |

[15] | R. Verzicco, J. M. Yusof, P. Orlandi, and D. Haworth, “Large eddy simulation in complex geometric configurations using boundary body forces,” American Institute of Aeronautics and Astronautics Journal, vol. 38, no. 3, pp. 427-433, 2000. |

[16] | D. Z. Noor, M. J. Chern, and T. L. Horng, “An immersed boundary method to solve fluid-solid interaction problems,” Computational Mechanics, vol. 44, no. 4, pp. 447-453, 2009. · Zbl 1296.74142 |

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