A numerical study: liquid sloshing dynamics in a tank due to uncoupled sway, heave and roll ship motions

Nasar Thuvanismail, Sannasiraj Sannasi, Sundar Vallam


In order to explore the physics implicated with the sloshing phenomenon subjected to independent regular sway, heave and roll excitations of the liquid tank system, theoretical studies are carried out. Four liquid fill levels with static liquid depth, hs, to the length, l of aspect ratio (hs/l) 0.163, 0.325, 0.488 and 0.585, are considered. The energy spectra of sloshing oscillation, their qualitative assessment and the harmonics present in the sloshing oscillation are studied. Frequency –Response amplitude has also been presented. The study reveals that sway excites a particular mode of sloshing (primary harmonic) by fulfilling the resonance conditions and also excites secondary modes. However, the roll motion excites the first mode of sloshing irrespective of the excitation frequencies. The heave motion excites the particular mode which is assumed as an initial perturbation.

DOI: http://dx.doi.org/10.3329/jname.v10i2.16215



Regular wave; perturbation; first mode; primary resonance; parametric resonance; barge; pitching

Full Text:



Armenio, V. and La Rocca, M. (1996): On the Analysis of Sloshing of water in Rectangular Containers: Numerical study and Experimental validation, Ocean Engineering, Vol.23, No.3, pp.705-739. http://dx.doi.org/10.1016/0029-8018(96)84409-X

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

British Maritime Corporate profile (2005): British Maritime Technology Limited, UK.

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

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.

Jermie, J.S., Sannasiraj S.A. and Sundar V. (2012): Numerical Simulation of Sloshing in a Rectangular Tank Subjected to Rotational Motion, Proceedings of the Twenty-second International Offshore and Polar Engineering Conference, Rhodes, Greece, June 17–22.

Jiang, L., Ting, C., Perlin, M. and Schultz, W.W. (1996): Moderate and steep Faraday waves: instabilities, modulation and temporal asymmetries, Journal of Fluid Mechanics, Vol.329, pp.275-307. http://dx.doi.org/10.1017/S0022112096008920

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

Miles, J. and Henderson, D. (1990): Parametrically forced surface waves, Annual review of Fluid Mechanics, Vol. 22, pp.143-165. http://dx.doi.org/10.1146/annurev.fl.22.010190.001043

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.

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. (2009): 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

Nasar, T., Sannasiraj, S.A. and Sundar, V. (2012): Liquid Sloshing Dynamics in a Barge subjected to Random Wave Excitations, Journal of Naval Architecture and Marine Engineering, Vol.9, No.1, pp.43-65. doi: 10.3329/jname.v9i1.7600

Ockendon, H., Ockendon, J.R and Johnson, A.D. (1989): Resonant Sloshing in Shallow water, Journal of Fluid Mechanics, Vol.167, pp.465-479. http://dx.doi.org/10.1017/S0022112086002926

Ockendon, H., Ockendon, J.R., Peake, M.R. and Chester, W.(1993): Geometrical effects in Resonance Gas Oscillations, Journal of Fluid Mechanics, Vol. 257, pp.201 – 217. http://dx.doi.org/10.1017/S0022112093003040

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

Pirker, S., Aigner, A. and Wimmer, G. (2012): Experimental and Numerical investigation of Sloshing Resonance phenomena in a spring - mounted Rectangular Tank, Chemical Engineering Science, Vol.68, pp.143 – 150. doi:10.1016/j.ces.2011.09.021

Solass, F. and Faltinsen, O.M.(1997): Combined Numerical and Analytical solution for Sloshing in Two-Dimensional Tanks of General Shape, Journal of Ship Research, Vol.41, No.2, pp.118-129.

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

The Naval Architect (September 2007): Simulating safe Shipping of LNG, The Royal Institution of Naval Architect, London, UK.

Warnitchai, P. and Pinkaew, T. (1998): Modeling of Liquid Sloshing in Rectangular Tanks with Flow-Dampening Devices, Engineering Structures, Vol.20, pp.593 – 600. http://dx.doi.org/10.1016/S0141-0296(97)00068-0

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

DOI: http://dx.doi.org/10.3329/jname.v10i2.16215