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Effects of Free Heave Motion on Wave Forces on Two Side-by-Side Boxes in Close Proximity Under Wave Actions

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Abstract

Wave forces on two side-by-side boxes in close proximity under wave actions were analyzed using the OpenFOAM package. The upstream box heaved freely under wave actions, whereas the downstream box remained fixed. For comparison, a configuration in which both boxes were fixed was also considered. The effects of the heave motion of the upstream box on the wave loads, including the horizontal wave forces, vertical wave forces, and moments on the boxes, were the focus of this study. Numerical analyses showed that all frequencies at which the maximum horizontal wave forces, maximum vertical wave forces, and maximum moment appeared are dependent on the heave motion of the upstream box and that the effects of the heave motion on these frequencies are different. Furthermore, these frequencies were observed to deviate from the corresponding fluid resonant frequency. Moreover, the heave motion of the upstream box reduced the wave forces acting on both boxes and altered the variation trends of the wave forces with the incident wave frequency.

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References

  • Faltinsen, O.M., Rognebakke, O.F. and Timokha, A.N., 2007. Two-dimensional resonant piston-like sloshing in a moonpool, Journal of Fluid Mechanics, 575, 359–397.

    Article  MathSciNet  Google Scholar 

  • Feng, X. and Bai, W., 2015. Wave resonances in a narrow gap between two barges using fully nonlinear numerical simulation, Applied Ocean Research, 50, 119–129.

    Article  Google Scholar 

  • Feng, X. and Bai, W., 2017. Hydrodynamic analysis of marine multibody systems by a nonlinear coupled model, Journal of Fluids and Structures, 70, 72–101.

    Article  Google Scholar 

  • Feng, X., Bai, W., Chen, X.B., Qian, L. and Ma, Z.H., 2017. Numerical investigation of viscous effects on the gap resonance between side-by-side barges, Ocean Engineering, 145, 44–58.

    Article  Google Scholar 

  • Gao, J.L., Chen, H.Z., Zang, J., Chen, L.F., Wang, G. and Zhu, Y.Z., 2020a. Numerical investigations of gap resonance excited by focused transient wave groups, Ocean Engineering, 212, 107628.

    Article  Google Scholar 

  • Gao, J.L., He, Z.W., Huang, X.H., Liu, Q., Zang, J. and Wang, G., 2021. Effects of free heave motion on wave resonance inside a narrow gap between two boxes under wave actions, Ocean Engineering, 224, 108753.

    Article  Google Scholar 

  • Gao, J.L., He, Z.W., Zang, J., Chen, Q., Ding, H.Y. and Wang, G., 2019a. Topographic effects on wave resonance in the narrow gap between fixed box and vertical wall, Ocean Engineering, 180, 97–107.

    Article  Google Scholar 

  • Gao, J.L., He, Z.W., Zang, J., Chen, Q., Ding, H.Y. and Wang, G., 2020b. Numerical investigations of wave loads on fixed box in front of vertical wall with a narrow gap under wave actions, Ocean Engineering, 206, 107323.

    Article  Google Scholar 

  • Gao, J.L., Zang, J., Chen, L.F., Chen, Q., Ding, H.Y. and Liu, Y.Y., 2019b. On hydrodynamic characteristics of gap resonance between two fixed bodies in close proximity, Ocean Engineering, 173, 28–44.

    Article  Google Scholar 

  • Huang, X.H., Xiao, W., Yao, X.L., Gu, J.Y. and Jiang, Z.Y., 2020a. An experimental investigation on reduction effect of damping devices for the recessing type moonpool with a large aspect ratio, Journal of Ship Research, doi: https://doi.org/10.5957/JOSR.08190045.

  • Huang, X.H., Xiao, W., Yao, X.L., Gu, J.Y. and Jiang, Z.Y., 2020b. An experimental investigation of reduction effect of damping devices in the rectangular moonpool, Ocean Engineering, 196, 106767.

    Article  Google Scholar 

  • Iwata, H., Saitoh, T. and Miao, G.P., 2007. Fluid resonance in narrow gaps of very large floating structure composed of rectangular modules, Proceedings of the 4th International Conference on Asian and Pacific Coasts, China Ocean Press, Beijing, China, pp. 815–826.

    Google Scholar 

  • Jacobsen, N.G., Fuhrman, D.R. and Fredsoe, J., 2012. A wave generation toolbox for the open-source CFD library: OpenFoam®, International Journal for Numerical Methods in Fluids, 70(9), 1073–1088.

    Article  MathSciNet  Google Scholar 

  • Jiang, S.C., Bai, W., Cong, P.W. and Yan, B., 2019a. Numerical investigation of wave forces on two side-by-side non-identical boxes in close proximity under wave actions, Marine Structures, 63, 16–44.

    Article  Google Scholar 

  • Jiang, S.C., Bai, W. and Tang, G.Q., 2018. Numerical simulation of wave resonance in the narrow gap between two non-identical boxes, Ocean Engineering, 156, 38–60.

    Article  Google Scholar 

  • Jiang, S.C., Bai, W. and Tang, G.Q., 2019b. Numerical investigation of piston-modal wave resonance in the narrow gap formed by a box in front of a wall, Physics of Fluids, 31, 052105.

    Article  Google Scholar 

  • Jiang, S.C., Cong, P.W., Sun, L. and Liu, C.F., 2019c. Numerical investigation of edge configurations on piston-modal resonance in a moonpool induced by heaving excitations, Journal of Hydrodynamics, 31(4), 682–699.

    Article  Google Scholar 

  • Koftis, T.H., Prinos, P. and Koutandos, E., 2006. 2D-V hydrodynamics of wave-floating breakwater interaction, Journal of Hydraulic Research, 44(4), 451–469.

    Article  Google Scholar 

  • Kristiansen, T. and Faltinsen, O.M., 2009. Studies on resonant water motion between a ship and a fixed terminal in shallow water, Journal of Offshore Mechanics and Arctic Engineering, 131(2), 021102.

    Article  Google Scholar 

  • Li, S. and Teng, B., 2015. Numerical examination of wave-induced coupling roll motion and fluid resonance between twin floating barges in proximity, Procedia Engineering, 126, 242–246.

    Article  Google Scholar 

  • Lu, L., Tan, L., Zhou, Z.B., Zhao, M. and Ikoma, T., 2020. Two-dimensional numerical study of gap resonance coupling with motions of floating body moored close to a bottom-mounted wall, Physics of Fluids, 32(9), 092101.

    Article  Google Scholar 

  • Lu, L., Teng, B., Cheng, L., Sun, L. and Chen, X.B., 2011a. Modelling of multi-bodies in close proximity under water waves—Fluid resonance in narrow gaps, Science China Physics, Mechanics and Astronomy, 54(1), 16–25.

    Article  Google Scholar 

  • Lu, L., Teng, B., Sun, L. and Chen, B., 2011b. Modelling of multi-bodies in close proximity under water waves—Fluid forces on floating bodies, Ocean Engineering, 38(13), 1403–1416.

    Article  Google Scholar 

  • Miao, G.P., Saitoh, T. and Ishida, H., 2001. Water wave interaction of twin large scale caissons with a small gap between, Coastal Engineering Journal, 43(1), 39–58.

    Article  Google Scholar 

  • Molin, B., 2001. On the piston and sloshing modes in moonpools, Journal of Fluid Mechanics, 430, 27–50.

    Article  MathSciNet  Google Scholar 

  • Moradi, N., Zhou, T.M. and Cheng, L., 2015. Effect of inlet configuration on wave resonance in the narrow gap of two fixed bodies in close proximity, Ocean Engineering, 103, 88–102.

    Article  Google Scholar 

  • Ning, D.Z., Su, X.J., Zhao, M. and Teng, B., 2015. Numerical study of resonance induced by wave action on multiple rectangular boxes with narrow gaps, Acta Oceanologica Sinica, 34(5), 92–102.

    Article  Google Scholar 

  • Ning, D.Z., Zhu, Y., Zhang, C.W. and Zhao, M., 2018. Experimental and numerical study on wave response at the gap between two barges of different draughts, Applied Ocean Research, 77, 14–25.

    Article  Google Scholar 

  • Pauw, W.H., Huijsmans, R.H.M. and Voogt, A., 2007. Advances in the hydrodynamics of side-by-side moored vessels, Proceedings of the 26th International Conference on Offshore Mechanics and Arctic Engineering, ASME, San Diego, California, USA.

    Google Scholar 

  • Saitoh, T., Miao, G.P. and Ishida, H., 2006. Theoretical analysis on appearance condition of fluid resonance in a narrow gap between two modules of very large floating structure, Proceedings of the 3rd Asia-Pacific Workshop on Marine Hydrodynamics, Shanghai, China, pp. 170–175.

  • Sun, L., Taylor, R.E. and Choo, Y.S., 2011. Responses of interconnected floating bodies, The IES Journal Part A: Civil & Structural Engineering, 4(3), 143–156.

    Google Scholar 

  • Sun, L., Taylor, R.E. and Taylor, P.H., 2015. Wave driven free surface motion in the gap between a tanker and an FLNG barge, Applied Ocean Research, 51, 331–349.

    Article  Google Scholar 

  • Tan, L., Lu, L., Liu, Y., Sabodas, O.A. and Teng, B., 2014. Dissipat-ive effects of resonant waves in confined space formed by floating box in front of vertical wall, Proceedings of the 11th ISOPE Pacific/Asia Offshore Mechanics Symposium, ISOPE, Shanghai, China.

    Google Scholar 

  • Tan, L., Lu, L., Tang, G.Q., Cheng, L. and Chen, X.B., 2019. A viscous damping model for piston mode resonance, Journal of Fluid Mechanics, 871, 510–533.

    Article  Google Scholar 

  • Tan, L., Tang, G.Q., Zhou, Z.B., Cheng, L., Chen, X.B. and Lu, L., 2017. Theoretical and numerical investigations of wave resonance between two floating bodies in close proximity, Journal of Hydrodynamics, 29(5), 805–816.

    Article  Google Scholar 

  • Wang, H., Wolgamot, H.A., Draper, S., Zhao, W., Taylor, P.H. and Cheng, L., 2019. Resolving wave and laminar boundary layer scales for gap resonance problems, Journal of Fluid Mechanics, 866, 759–775.

    Article  Google Scholar 

  • Zhao, W., Wolgamot, H.A., Taylor, P.H. and Taylor, R.E., 2017. Gap resonance and higher harmonics driven by focused transient wave groups, Journal of Fluid Mechanics, 812, 905–939.

    Article  Google Scholar 

  • Zhao, W.H., Pan, Z.Y., Lin, F., Li, B.B., Taylor, P.H. and Efthymiou, M., 2018. Estimation of gap resonance relevant to side-by-side offloading, Ocean Engineering, 153, 1–9.

    Article  Google Scholar 

  • Zhu, R.C., Miao, G.P. and You, Y.X., 2005. Influence of gaps between 3-D multiple floating structures on wave forces, Journal of Hydrodynamics, 17B(2), 141–147.

    MATH  Google Scholar 

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Correspondence to Jun-liang Gao.

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This research is financially supported by the National Key Research and Development Program (Grant No. 2017YFC1404200), the National Natural Science Foundation of China (Grant Nos. 51911530205 and 51809039), the Natural Science Foundation of Jiangsu Province (Grant No. BK20201455), the Natural Science Foundation of the Jiangsu Higher Education Institutions (Grant No. 20KJD170005) and the Qing Lan Project of Jiangsu Universities. This work is also partially supported by UK EPSRC (Grant No. EP/T026782/1), the Royal Academy of Engineering (Grant No. UK-CIAPP/73) and the Royal Society (Grant No. IEC\NSFC\181321).

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He, Zw., Gao, Jl., Zang, J. et al. Effects of Free Heave Motion on Wave Forces on Two Side-by-Side Boxes in Close Proximity Under Wave Actions. China Ocean Eng 35, 490–503 (2021). https://doi.org/10.1007/s13344-021-0045-9

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  • DOI: https://doi.org/10.1007/s13344-021-0045-9

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