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Three-dimensional simulations of offshore oil platform in square and diamond arrangements. (English) Zbl 1477.76025

Summary: The interaction of the solitary wave with an oil platform composed of four vertical circular cylinders is investigated for two attack angle of the solitary wave \(\beta= 0^\circ\) (square arrangement) and \(\beta= 45^\circ\) (diamond arrangement). The solitary wave is generated using an internal source line as proposed by the second author et al. [“Internal inlet for wave generation and absorption treatment”, Coastal Eng. 56, No. 9, 951–959 (2009; doi:10.1016/j.coastaleng.2009.05.001)]. This generation method is extended to three-dimensional wave flow and is integrated into the PHOENICS code. The volume of fluid approach is used to capture the free surface evolution. The present model is validated in the case of a solitary wave propagating on a flat bottom for \(H/h=0.25\) where \(H\) is the wave height and \(h\) is the water depth. Compared to the analytical solution, the pseudowavelength and the wave crest are well reproduced. For a solitary wave interacting with square and diamond cylinders, the simulated results show that the maximum run-ups are well reproduced. For the diamond arrangements, the diffraction process seems to not affect the maximum run-ups, which approached the isolated cylinder. For the square arrangement, the shielding effect leads to a maximum wave force more pronounced for the upstream cylinder array.

MSC:

76B25 Solitary waves for incompressible inviscid fluids
76M99 Basic methods in fluid mechanics
86A05 Hydrology, hydrography, oceanography

References:

[1] Hosseini, K.; Samavat, M.; Mirzazadeh, M.; Ma, W. X.; Hammouch, Z., A new (3+1)-dimensional Hirota bilinear equation: its Bäcklund transformation and rational-type solutions, Regular and Chaotic Dynamics, 25, 4, 383-391 (2020) · Zbl 1450.37065 · doi:10.1134/S156035472004005X
[2] Hosseini, K.; Seadawy, A.; Mirzazadeh, M.; Eslami, M.; Radmehr, S.; Baleanu, D., Multiwave, multicomplexiton, and positive multicomplexiton solutions to a (3 + 1)-dimensional generalized breaking soliton equation, Alexandria Engineering Journal, 59, 5, 3473-3479 (2020) · doi:10.1016/j.aej.2020.05.027
[3] Hosseini, K.; Ma, W. A.; Ansari, R.; Mirzazadeh, M.; Pouyanmehr, M.; Samadani, F., Evolutionary behavior of rational wave solutions to the (4 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation, Physica Scripta, 95, article 065208 (2020)
[4] Hafsia, H.; Nouri, S.; Boulaaras, S.; Allahem, A.; Alkhalaf, A.; Vazquez, A. M., Solitary wave diffraction with a single and two vertical circular cylinders, Mathematical Problems in Engineering, 2021 (2021) · doi:10.1155/2021/6634762
[5] Yates, G. T.; Wang, K. H., Solitary wave scattering by a vertical cylinder: experimental study, The Fourth International Offshore and Polar Engineering Conference
[6] Huang, Z., Wave interaction with one or two rows of closely spaced rectangular cylinders, Ocean Engineering, 34, 11-12, 1584-1591 (2007)
[7] Huang, Z.; Yuan, Z., Transmission of solitary waves through slotted barriers: a laboratory study with analysis by a long wave approximation, Journal of Hydro-environment Research, 3, 179-185 (2010)
[8] Wang, Q.; Fang, Y.; Liu, H., An experimental study of run-up and loads on a vertical truncated cylinder in a solitary wave, Ocean Engineering, 219, 1-10 (2021)
[9] Lin, P.; Man, C., A staggered-grid numerical algorithm for the extended Boussinesq equations, Applied Mathematical Modelling, 31, 2, 349-368 (2007) · Zbl 1169.76042
[10] Mohapatra, S. C.; Islam, H.; Guedes Soares, C., Boussinesq model and CFD simulations of non-linear wave diffraction by a floating vertical cylinder, Journal of Marine Science and Engineering, 8, 8, 1-27 (2020)
[11] Zhao, M.; Cheng, L.; Teng, B., Numerical simulation of solitary wave scattering by a circular cylinder array, Ocean Engineering, 34, 3-4, 489-499 (2007) · doi:10.1016/j.oceaneng.2006.03.005
[12] Wang, K.-H.; Ren, X., Interactions of cnoidal waves with cylinder arrays, Ocean Engineering, 26, 1-20 (1999)
[13] Liu, S.; Sun, Z.; Li, J., An unstructured FEM model based on Boussinesq equations and its application to the calculation of multidirectional wave run-up in a cylinder group, Applied Mathematical Modelling, 36, 9, 4146-4164 (2012) · Zbl 1252.76047
[14] Cao, H.; Wan, D., Benchmark computations of wave run-up on single cylinder and four cylinders by naoe-FOAM-SJTU solver, Applied Ocean Research, 65, 327-337 (2017)
[15] Frantzis, C.; Grigoriadis, D. G. E.; Dimas, A. A., Numerical study of solitary waves past slotted breakwaters with a single row of vertical piles: wave processes and flow behavior, Ocean Engineering, 211, 1, 1-21 (2020)
[16] Wang, X.; Zhou, J. F.; Wang, Z.; You, Y. X., A numerical and experimental study of internal solitary wave loads on semi-submersible platforms, Ocean Engineering, 150, 298-308 (2018)
[17] Yang, C.; Liu, Y.; Liu, C., Predicting wave loads on adjacent cylinder arrays with a 3D model, Journal of Hydraulic Research, 53, 6, 797-807 (2015)
[18] Kamath, A.; Alagan Chella, M.; Bihs, H.; Arntsen, Ø. A., Evaluating wave forces on groups of three and nine cylinders using a 3D numerical wave tank, Engineering Applications of Computational Fluid Mechanics, 9, 1 (2015)
[19] Xie, Z.; Stoesser, T.; Yan, S.; Ma, Q.; Lin, P., A Cartesian cut-cell based multiphase flow model for large-eddy simulation of three-dimensional wave-structure interaction, Computers & Fluids, 213, 15, 1-17 (2020) · Zbl 1521.76263
[20] Hirt, C. W.; Nichols, B. D., Volume of fluid (VOF) method for the dynamics of free boundaries, Journal of Computational Physics, 39, 1, 201-225 (1981) · Zbl 0462.76020 · doi:10.1016/0021-9991(81)90145-5
[21] Hafsia, Z.; Hadj, M. B.; Lamloumi, H.; Maalel, K., Internal inlet for wave generation and absorption treatment, Coastal Engineering, 56, 9, 951-959 (2009) · doi:10.1016/j.coastaleng.2009.05.001
[22] Domínguez, J. M.; Altomare, C.; Gonzalez-Caoa, J.; Lomonaco, P., Towards a more complete tool for coastal engineering: solitary wave generation, propagation and breaking in an SPH-based model, Coastal Engineering Journal, 61, 1-15 (2019)
[23] Artemov, V.; Beale, S. B.; de Vahl Davis, G.; Escudier, M. P.; Fueyo, N.; Launder, B. E.; Leonardi, E.; Malin, M. R.; Minkowycz, W. J.; Patankar, S. V.; Pollard, A., A tribute to DB Spalding and his contributions in science and engineering, International Journal of Heat and Mass Transfer, 52, 17-18, 3884-3905 (2009) · Zbl 1167.80300 · doi:10.1016/j.ijheatmasstransfer.2009.03.038
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