A two-dimensional Boundary Element Method (BEM) based on potential flow theory is developed to study wave-body interaction problems with strongly nonlinear effects. In particular, the following pro ...

A Boundary Element Method Applied to Strongly Nonlinear Wave-Body Interaction Problems

An experimental study has been carried out to measure the pressures on the walls and on the top cover plate of a tank that is partially filled with liquid and rigidly mounted in a barge. Herein, the barge has been subjected to the combined degrees of excitation, namely, sway, heave and roll. Four liquid fill levels with aspect ratio (h s /l, where h s is the static liquid depth and l is the tank length) of 0.163, 0.325 (nearly critical depth), 0.488 and 0.585 are considered for the studies. The effects of wave excitation frequencies and amplitudes on the pressure variation have been studied in detail and, the salient results are herein reported.

Sloshing pressure variation in a barge carrying tank

Experimental Investigation on the Influence of Liquid Cargo in Floating Vessels Motions

The natural frequencies for sloshing without coupling with lateral tank motions differ from the natural sloshing frequencies with coupling. A consequence is that the nonlinear multimodal sloshing theory for prescribed tank motion should be revised when studying the liquid sloshing dynamics in connection with marine structures in ocean waves. The needed revisions are done for a rectangular rigid tank with finite liquid depth. Steady-state resonant solutions of the constructed nonlinear modal equations are derived to analytically describe the coupled resonant sloshing and sway of a floating rigid body in regular incident deep water waves with two-dimensional flow conditions at the lowest coupled sloshing–sway natural frequency. The steady-state theoretical results are validated by comparing them with the model tests by Rognebakke & Faltinsen (J. Ship Res., vol. 47, issue 3, 2003, pp. 208–221). The occurrence of an instability frequency range is theoretically justified.

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Coupling between resonant sloshing and lateral motions of a two-dimensional rectangular tank

The significant increase in demand for Liquefied Natural Gas (LNG) and the economic aspects of its transportation resulted in increases in the number and size of LNG carriers. One of the design issues for LNG carriers is the sloshing phenomenon because containment systems widely used nowadays have no internal structures. Furthermore, because the weights of ship and cargo are comparable and ship operators want more flexible operations allowing partial fillings in tanks, the coupling effect between ship motions and sloshing requires further investigation, including the effect of ship distortion. The previous study on coupling between rigid body and sloshing shows good agreement between methods of prediction and measurements [1,2]. Hence, in this paper the potential flow approach adopted for the coupling effect between rigid body ship motion and sloshing is extended to flexible ship-partially filled tank system, using the desingularised Rankine source method. In this case, the global deflection of the flexible ship is used for application of the body boundary condition on the partially filled tank. The aim of this paper is to investigate the influence of hull flexibility on the hydrodynamic forces and moments associated with liquid sloshing and vice versa, as well as the dynamic characteristics (e.g. resonance frequencies) of the whole system. As there are no experimental results available, the method is validated by comparing hydrodynamic forces from sloshing obtained using rigid and flexible body approaches. The coupling effect between flexible ship and sloshing in partially filled tanks is investigated for an idealized LNG Carrier in beam regular waves, considering different partial filling scenarios.Copyright © 2010 by ASME

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Coupling Between Flexible Ship and Liquid Sloshing Using Potential Flow Analysis

Sloshing is a violent resonent free surface flow in a container. The main objective of this thesis has been to study sloshing in rectangular and prismatic tanks. The tank may be excited by a harmonic motion or it may move with a ship in waves. In the latter case, the coupled ship motions and sloshing problem is investigated. A nonlinear analytically based sloshing model is used in the solshing calculations. Experiments have been conducedand collected data are utilized in the validation of the sloshing model and computations of interaction between sloshing and ship dynamics. Tank roof impacts are studied. Energy in the impact jet is dissipated and this leads to damping of the sloshing motion. An iterative procedure is applied to incorporate the effect of energy dissipation in the calculations. Damping of the soloshing motion is an important parameter around resonance for the coupled ship motion and sloshing system. The sloshing model is based on a nonlinear theory analysis of two-dimensional nonlinear sloshing of an imcompressible fluid with irrotational flow in a rectangular tank. Infinite tank roof height and no overtuning waves are assumed. The free surface is expressed as a Fourier series and the velocity potential is expanded in terms of the linear natural modes of the fluid motion. The infinite-dimensional modal system is approximated and the result is a finite set of ordinary differential equations in time for generalized coordinates (Fourier cofficients) of the free surface. This theory is not valid for small water depth or when water impacts heavily on the tank roof. The proposed method has a high computational efficiency, facilitates simulations of a coupled vehicle-fluid system and has been extensively validated for forced motions. Experiments with a smooth rectangular tank exited by forced harmonic horizontal oscillations have been performed and the results are used to validate the analytical sloshing model. Transients and associated nonlinear modulation of the waves, beating, are important due to the low level of damping of the fluid motion. The measured parameters are the motion of the tank and the free surface elevation at three positions. Pictures and video are used to study local flow details and the dynamics of the flow. At excitation periods in the vicinity of the first natural period for the fluid motion in the tank, even small motion amplitudes lead to violent sloshing and impacts between the rising water surface and the tank roof. Impacts cause high pressures and forces. The effect of slamming in the tank is included by a local anlysis interacting with the nonlinear sloshing model. A Wagner based mthod is used to find the flow induced by slamming. Hydroelastic effects are ignored. The hypothesis that the kinetic and potential energy in the jet flow coused by the impact is dissipated when the jet flow hits the free surface, enables a rational calculation of the damping effect of impacts on the slishing flow. The Wagner approach requires a small angle between the impacting free surface and the tank roof. A correction by a similarity solution, or alternatively, by a generalization of Wagner's theory valid for larger angles is applied when this is not the case. Since anslytically based methods are used, fluid impact load predictions are robust. A coupled ship motion and sloshing system is studied both experimentally and theoretically. Two-dimensional experiments on a box-shaped ship section excited by regular beam sea have been conducted. The section contains two tanks and can only move in sway. Fluid motion inside the tanks has a large effect on the sway motion response of the section. Simulatons of a corresponding system are performed by assuming a mainly linear external flow and applying the nonlinear sloshing model. The linear external hydrodynamic loads due to body motion are expressed in terms of a convoltion integral representing the history of the fluid motion. detailed numerical study of how to accuratly and numerical sway motion of the ship section is reported. The calculated cooupled motion is sensitive to the damping of the sloshing motion in a certain frequency range where the coupled sloshing and ship motions couse resonant ship motions. A quasi-linear frequency domain analysis is used to explain this by introducing the sloshing loads as a frequency dependent spring.

Oav Fredrik Rognebakke

Papers

Effect of sloshing on ship motions