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Experimental Investigation and Prediction Model of the Loads Exerted by Oblique Internal Solitary Waves on FPSO

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Abstract

By using a 30-meter-long wave flume equipped with a double-plate wave maker, a series of depression ISWs were generated in a density stratified two-layer fluid and the forces exerted by oblique internal solitary waves (ISWs) on fixed FPSO model had been measured. According to the laboratory experiments, a numerical flume taken the applicability of KdV, eKdV and MCC ISWs theories in consideration was adopted to study the force components. Based on the experimental data and the force composition, the simplified prediction model was established. It was shown that the horizontal and transversal loads consisted of two parts: the Froude—Krylov force that could be calculated by integrating the dynamic pressure induced by ISW along the FPSO wetted surface, as well as the viscous force that could be obtained by multiplying the friction coefficient Cfx (Cfy), correction factor Kx (Ky) and the integration of particle tangential velocity along the FPSO wetted surface. The vertical load was mainly the vertical Froude—Krylov force. Based on the experimental results, a conclusion can be drawn that the friction coefficient Cf and correction factor K were regressed as a relationship of Reynolds number Re, Keulegan—Carpenter number KC, upper layer depth h1/h and ISW accident angle α. Moreover, the horizontal friction coefficient Cfx yielded the logarithmic function with Re, and transversal friction coefficient Cfy obeyed the exponent function with Re, while the correction factors Kx and Ky followed power function with KC. The force prediction was also performed based on the regression formulae and pressure integral. The predicted results agreed well with the experimental results. The maximum forces increase linearly with the ISWs amplitude. Besides, the upper layer thickness had an obvious influence on the extreme value of the horizontal and transversal forces.

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References

  • Alford, M.H., Peacock, T., MacKinnon, J.A., Nash, J.D., Buijsman, M.C., Centurioni, L.R., Chao, S.Y., Chang, M.H., Farmer, D.M., Fringer, O.B., Fu, K.H., Gallacher, P.C., Graber, H.C., Helfrich, K.R., Jachec, S.M., Jackson, C.R., Klymak, J.M., Ko, D.S., Jan, S., Johnston, T.M.S., Legg, S., Lee, I.H., Lien, R.C., Mercier, M.J., Moum, J.N., Musgrave, R., Park, J.H., Pickering, A.I., Pinkel, R., Rainville, L., Ramp, S.R., Rudnick, D.L., Sarkar, S., Scotti, A., Simmons, H.L., St Laurent, L.C., Venayagamoorthy, S.K., Wang, Y.H., Wang, J., Yang, Y.J., Paluszkiewicz, T. and Tang, T.Y., 2015. The formation and fate of internal waves in the South China Sea, Nature, 521(7550), 65–69.

    Article  Google Scholar 

  • Bole, J.B., Ebbesmeyer, C.C. and Romea, R.D., 1994. Soliton currents in the south China sea: measurements and theoretical modeling, Offshore Technology Conference, Houston, 304–307.

  • Cai, S.Q., Long, X.M. and Gan, Z.J., 2003. A method to estimate the forces exerted by internal solitons on cylindrical piles, Ocean Engineering, 30(5), 673–689.

    Article  Google Scholar 

  • Cai, S.Q., Long, X.M. and Wang, S.G., 2008. Forces and torques exerted by internal solitons in shear flows on cylindrical piles, Applied Ocean Research, 30(1), 72–77.

    Article  Google Scholar 

  • Cai, S.Q., Wang, S.G. and Long, X.M., 2006. A simple estimation of the force exerted by internal solitons on cylindrical piles, Ocean Engineering, 33(7), 974–980.

    Article  Google Scholar 

  • Cai, S.Q., Xie, J.S. and He, J.L., 2012. An overview of internal solitary waves in the South China Sea, Surveys in Geophysics, 33(5), 927–943.

    Article  Google Scholar 

  • Cai, S.Q., Xu, J.X., Chen, Z.W., Xie, J.S., Deng, X.D. and Lv, H.B., 2014. The effect of a seasonal stratification variation on the load exerted by internal solitary waves on a cylindrical pile, Acta Oceanologica Sinica, 33(7), 21–26.

    Article  Google Scholar 

  • Chen, J.H., 1996. The development of Liuhua 11–1 oilfield in South China Sea, China Offshore Platform, 11(1), 43–45(1), 43–45. (in Chinese)

    Google Scholar 

  • Chen, M., Chen, K. and You, Y.X., 2017. Experimental investigation of internal solitary wave forces on a semi-submersible, Ocean Engineering, 141, 205–214.

    Article  Google Scholar 

  • Cheng, M.H., Hsu, J.R.C. and Chen, C.Y., 2011. Laboratory experiments on waveform inversion of an internal solitary wave over a slope-shelf, Environmental Fluid Mechanics, 11(4), 353–384.

    Article  Google Scholar 

  • Choi, W. and Camassa, R., 1996. Weakly nonlinear internal waves in a two-fluid system, Journal of Fluid Mechanics, 313, 83–103.

    Article  MathSciNet  Google Scholar 

  • Du, H., Wei, G., Gu, M.M., Wang, X.L. and Xu, J.X., 2016. Experimental investigation of the load exerted by nonstationary internal solitary waves on a submerged slender body over a slope, Applied Ocean Research, 59, 216–223.

    Article  Google Scholar 

  • Guo, C. and Chen, X., 2014. A review of internal solitary wave dynamics in the northern South China Sea, Progress in Oceanography, 121, 7–23.

    Article  Google Scholar 

  • Haddara, M.R., 1980. On the parametric excitation of nonlinear rolling motion in random seas, International Shipbuilding Progress, 27(315), 290–293.

    Article  Google Scholar 

  • Helfrich, K.R., 1992. Internal solitary wave breaking and run-up on a uniform slope, Journal of Fluid Mechanics, 243, 133–154.

    Article  Google Scholar 

  • Helfrich, K.R. and Melville, W.K., 2006. Long nonlinear internal waves, Annual Review of Fluid Mechanics, 38, 395–425.

    Article  MathSciNet  Google Scholar 

  • Hirt, C.W. and Nichols, B.D., 1981. Volume of fluid (VOF) method for the dynamics of free boundaries, Journal of Computational Physics, 39(1), 201–225.

    Article  Google Scholar 

  • Huang, W.H., You, Y.X., Shi, Q., Wang, J.Y. and Hu, T.Q., 2013. The experiments of internal solitary wave loads and their theoretical model for a semi-submersible platform, Chinese Journal of Hydrodynamics, 28(6), 644–657. (in Chinese)

    Google Scholar 

  • Huang, X.D., Chen, Z.H., Zhao, W., Zhang, Z.W., Zhou, C., Yang, Q.X. and Tian, J.W., 2016. An extreme internal solitary wave event observed in the northern South China Sea, Scientific Reports, 6(1), 30041.

    Article  Google Scholar 

  • Michallet, H. and Barthélemy, E., 1997. Ultrasonic probes and data processing to study interfacial solitary waves, Experiments in Fluids, 22(5), 380–386.

    Article  Google Scholar 

  • Morison, J.R., Johnson, J.W. and Schaaf, S.A., 1950. The force exerted by surface waves on piles, Journal of Petroleum Technology, 2(5), 149–154.

    Article  Google Scholar 

  • Roberts, J.B., 1982. Effect of parametric excitation on ship rolling motion in random waves, Journal of Ship Research, 26(4), 246–253.

    Article  Google Scholar 

  • Wang, S.D., Wei, G., Du, H., Wu, J.L. and Wang, X.L., 2020. Experimental investigation of the wave-flow structure of an oblique internal solitary wave and its force exerted on a slender body, Ocean Engineering, 201, 107057.

    Article  Google Scholar 

  • Wang, X., Zhou, J.F., Wang, Z. and You, Y.X., 2018. A numerical and experimental study of internal solitary wave loads on semi-submersible platforms, Ocean Engineering, 150, 298–308.

    Article  Google Scholar 

  • Xie, J.S., He, Y.H. and Cai, S.Q., 2019. Bumpy topographic effects on the transbasin evolution of large-amplitude internal solitary wave in the northern South China Sea, Journal of Geophysical Research: Oceans, 124(7), 4677–4695.

    Article  Google Scholar 

  • Xie, J.S., He, Y.H., Lü, H.B., Chen, Z.W., Xu, J.X. and Cai, S.Q., 2016. Distortion and broadening of internal solitary wavefront in the northeastern South China Sea deep basin, Geophysical Research Letters, 43(13), 7617–7624.

    Article  Google Scholar 

  • Xie, J.S., Jian, Y.J. and Yang, L.G., 2010. Strongly nonlinear internal soliton load on a small vertical circular cylinder in two-layer fluids, Applied Mathematical Modelling, 34(8), 2089–2101.

    Article  MathSciNet  Google Scholar 

  • Xie, J.S., Xu, J.X. and Cai, S.Q., 2011. A numerical study of the load on cylindrical piles exerted by internal solitary waves, Journal of Fluids and Structures, 27(8), 1252–1261.

    Article  Google Scholar 

  • Zhang, R.R., Chen, K. and You, Y.X., 2019. Experimental, numerical and simplified theoretical model study for internal solitary wave load on FPSO with emphasis on scale effect, China Ocean Engineering, 33(1), 26–33.

    Article  Google Scholar 

  • Zhang, R.R., Chen, K., You, Y.X. and Ji, M., 2021. Experimental investigation and simplified prediction model study of internal solitary wave forces on FPSO, Journal of Ship Mechanics, 25(6), 704–715.

    Google Scholar 

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Funding

The present work was financially supported by the National Natural Science Foundation of China (Grant No. 11802301) and the Sci-tech Project of Sanya Yazhou Bay Science and Technology City Administration (Grant No. SKJC-KJ-2019KY08).

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Correspondence to Ke Chen.

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Zhang, Rr., Wang, Hw., Chen, K. et al. Experimental Investigation and Prediction Model of the Loads Exerted by Oblique Internal Solitary Waves on FPSO. China Ocean Eng 36, 179–190 (2022). https://doi.org/10.1007/s13344-022-0017-8

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  • DOI: https://doi.org/10.1007/s13344-022-0017-8

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