Liquid sloshing dynamics in a barge carrying container subjected to random wave excitation
Keywords:Random wave, barge response, sloshing oscillation, natural mode frequency, secondary resonance, parametric resonance,
The sloshing phenomenon of liquid in a partially filled tank mounted rigidly on a barge exposed to random beam waves has been investigated through a well controlled experimental program. Four relative liquid depths, (liquid depth, hs/ length of tank, l) of 0.163, 0.325, 0.488 and 0.585 were considered for the tests. The sloshing oscillation was measured along the length of the tank at predefined locations. The effect of variation of the peak wave excitation frequency on the sloshing oscillation in the frequency domain is studied. The dominant energy is found to be concentrated around lowest nth sloshing mode frequency and, secondary peaks are observed at higher order sloshing frequencies. Odd modes contributions are dominating even modes irrespective of the excitation peak frequency. The sacrifice of second mode is observed while the excitation peak frequency is closer to its primary resonance.
Journal of Naval Architecture and Marine Engineering 9(2012) 43-65
Benjamin, T.B. and Ursell, H.W. (1954): The Stability of the Plane Free Surface of a Liquid in a Vertical Periodic Motion, Proceedings of Royal Society of London, Series A225, pp.505 515. http://dx.doi.org/10.1098/rspa.1954.0218
Chen, B.F. and Chiang, H.W. (2000): Complete Two Dimensional Analysis of Sea Wave Induced fully Nonlinear Sloshing Fluid in a Rigid Floating Tank, Ocean Engineering, Vol.27, pp.953 977. http://dx.doi.org/10.1016/S0029-8018(99)00036-0
Faraday, M. (1831): On the Forms and States assumed by Fluids in Contact with Vibrating Elastic Surfaces, Transactions of Royal Society of London, Vol.121, pp.309 - 346.
Faltinsen, O.M. (1974): Nonlinear Theory of Sloshing in Rectangular Tanks, Journal of Ship Research, Vol.18, No.4, pp.224 241.
Faltinsen, O.M. (1978): A Numerical Nonlinear Method of Sloshing in Tanks with Two Dimensional Flow, Journal of Ship Research, Vol.22, No.3, pp.193 202.
Faltinsen, O.M., Rognebakke, O.F., Lukovksky, I.A. and Timokha, A.N. (2000): Multimodal Analysis of Nonlinear Sloshing in a Rectangular Tank with Finite Water depth, Journal of Fluid Mechanics, Vol.407, pp.201 234. http://dx.doi.org/10.1017/S0022112099007569
Faltinsen, O.M. and Timokha, A.N. (2001): Adaptive Multimodal approach to Nonlinear Sloshing in a Rectangular Tank., Journal of Fluid Mechanics, Vol.432, pp.167 200.
Faltinsen, O.M. and Timokha, A.N. (2002): Asymptotic Modal approximation of Nonlinear Resonant Sloshing in a Rectangular Tank with small Fuid depth, Journal of Fluid Mechanics, Vol.470, pp.319 357. http://dx.doi.org/10.1017/S0022112002002112
Francescutto, A. and Contento, G. (1994): An Experimental Study of the Coupling between Roll motion and Sloshing in a Compartment, Proceedings of the 4th International Offshore and Polar Engineering Conference, Osaka, Japan.
Frandsen, J.B. (2003): Simulation of Sloshing motions in Fixed and Vertically Excited Containers using a 2-D Inviscid sigma-transformed Finite Difference Solver, Journal of Fluids and Structures, Vol.18, pp.197 214. http://dx.doi.org/10.1016/j.jfluidstructs.2003.07.004
Frandsen, J.B. (2004): Sloshing in Excited Tanks, Journal of Computational Physics, Vol.196, pp.53 87. http://dx.doi.org/10.1016/j.jcp.2003.10.031
Ibrahim, R.A. (2005): Liquid Sloshing Dynamics Theory and Applications, Cambridge University press, Newyork.
Kim, M.S., Park J.S. and Lee, W. (2003): A new VOF based Numerical scheme for the Simulation of Fluid flow with Free Surface Part II: Application to the Cavity Filling and Sloshing problems, International Journal of Numerical Methods in Fluids, Vol.42, pp.791 - 812. http://dx.doi.org/10.1002/fld.554
Kim, Y., Shin, Y., Kim, W. and Yue, D. (2003): Study on Sloshing problem Coupled with Ship Motion in Waves, Proceedings of the 8th International Conference on Numerical Ship Hydrodynamics, Busan, Korea.
Lui, A.P. and Lou, Y.K. (1990): Dynamic Coupling of a Liquid Tank system under Transient Excitations, Ocean Engineering, Vol.17, No.3, pp.263 277. http://dx.doi.org/10.1016/0029-8018(90)90005-Q
Lee, D.H., Kim, M.H., Kwon, S.H., Kim, J.W. and Lee, Y.B. (2005): A Parametric and Numerical study on LNG-tank Sloshing loads, Proceedings of the 15th International Offshore and Polar engineering Conference, Seoul, Korea
Lee, S.J., Kim, M.H., Lee, D.H., Kim, J.W. and Kim, Y.H. (2007): The Effects of LNG tank Sloshing on the Global motions of LNG carriers, Ocean Engineering, Vol.34, pp.10 20. http://dx.doi.org/10.1016/j.oceaneng.2006.02.007
Mitra, S., Wang, C.J., Reddy, J.N. and Khoo, B.C. (2012): A 3D fully Coupled analysis of Nonlinear Sloshing and Ship motion, Ocean Engineering, Vol.39, pp.1 13. http://dx.doi.org/10.1016/j.oceaneng.2011.09.015
Moiseyev, N.N. (1958): On the Theory of Nonlinear Vibrations of a Liquid of Finite volume. Applied Mathematics and Mechanics, Vol. 22, No.5, pp.612 621.
Molin, B., Remy, F., Rigaud, S., and de Jouette, Ch. (2002): LNG-FPSOs: Frequency Domain Coupled Analysis of Support and Liquid Cargo motion, Proceedings of the International Maritime Association of Mediterannean Conference, Rethymnon, Greece.
Malenica, S., Zalar, M. and Chen, X.B. (2003): Dynamic Coupling of Sea keeping and Sloshing, Proceedings of the 13th International Offshore and Polar Engineering Conference, Honolulu, USA.
Nayfeh, A.H. and Mook, D.T. (1979): Nonlinear Oscillations, John Wiley sons, Newyork.
Nakayama, T. and Washizu, K. (1980): Nonlinear Analysis of Liquid motion in a Container subjected to Forced Pitching Oscillation. International Journal of Numerical Methods in Engineering, Vol.15, pp.1207 - 1220. http://dx.doi.org/10.1002/nme.1620150808
Nam, B.W. and Kim, Y. (2007): Effect of Sloshing on the motion Response of LNG FPSO in Waves, Proceedings of the 22nd Workshop on Water Waves and Floating Bodies, Plitviz, Croatia.
Nasar T., Sannasiraj S.A. and Sundar V. (2008a): Experimental Study of Liquid Sloshing Dynamics in a Barge carrying Tank. Fluid Dynamics Research, Vol.40, pp.427 - 458. http://dx.doi.org/10.1016/j.fluiddyn.2008.02.001
Nasar, T., Sannasiraj, S.A. and Sundar, V. (2008b): Sloshing Pressure Variation in a Barge carrying Tank, Ships and Offshore Structures, Vol.3, No.3, pp.185 - 203. http://dx.doi.org/10.1080/17445300802204363
Nasar, T., Sannasiraj, S.A. and Sundar, V. (2008c): Wave Induced Sloshing pressure in a Liquid Tank under Irregular Waves, Part M: Journal of Engineering for Maritime Environment, Vol.223, No.2, pp.145 - 161. doi: 10.1243/14750902JEME135
Nasar, T., Sannasiraj, S.A. and Sundar, V. (2010): Motion Responses of Barge carrying Liquid Tank, Ocean Engineering, Vol.37, pp.935 - 946. http://dx.doi.org/10.1016/j.oceaneng.2010.03.006
Newman J.N. (2005): Wave effects on Vessels with Internal Tanks, Proceedings of the 20th Workshop on Water Waves and Floating Bodies, Spitsbergen, Norway.
Ockendon, H., Ockendon, J.R. and Waterhouse, D.D. (1996): Multimode Resonances in Fluids, Journal of Fluid Mechanics, Vol.315, pp.317 344. http://dx.doi.org/10.1017/S0022112096002443
Rognebakke, O.R. and Faltinsen O.M. (2001): Effects of Sloshing on Ship Motions, Proceedings of the 16th Workshop on Water Waves and Floating Bodies, Hiroshima, Japan.
Sannasiraj, S.A., Sundar, V. and Sundaravadivelu, R. (1995): The Hydrodynamic behaviour of Long Floating Structures in Directional Seas, Applied Ocean Research, Vol.17, pp.233 - 243. http://dx.doi.org/10.1016/0141-1187(95)00011-9
Sriram V., Sannasiraj S.A. and Sundar V. (2006): Numerical Simulation of 2D Sloshing Waves due to Horizontal and Vertical Random Excitations, Applied Ocean Research, Vol.28, pp.19 32. http://dx.doi.org/10.1016/j.apor.2006.01.002
Waterhouse, D.D. (1994): Resonant Sloshing near Critical depth, Journal of Fluid Mechanics, Vol.281, pp.313 318. http://dx.doi.org/10.1017/S0022112094003125
Wu, G.X., Ma, Q.W. and Eatock Taylor, R. (1998): Numerical Simulation of Sloshing Waves in a 3D Tank based on a Finite Element Method, Applied Ocean Research, Vol.20, pp.337 355. http://dx.doi.org/10.1016/S0141-1187(98)00030-3
Wang C Z. and Khoo B.C. (2005): Finite Element Analysis of Two-Dimensional Nonlinear Sloshing problems in Random Excitations, Ocean Engineering, Vol.32, pp.107 133. http://dx.doi.org/10.1016/j.oceaneng.2004.08.001
Watanabe, M., Kobayashi, N. and Wada, Y. (2004): Dynamic Stability of Flexible Bellows subjected to Periodic Internal Fluid Pressure Excitation, Journal of Pressure Vessel Technology, Vol.126, No.2, pp.188 - 193. http://dx.doi.org/10.1115/1.1687380
Zhao, W., Yang, J., Hu, Z. and Xiao, L. (2012): Experimental investigation of Effects of inner- tank Sloshing on Hydrodynamics of an flng system, Journal of Hydrodynamics Ser.B, Vol.24, No.1, pp.107 115. http://dx.doi.org/10.1016/S1001-6058(11)60224-2