Smoothed-Particle Hydrodynamics Simulation of Ship Motion and Tank Sloshing under the Effect of Regular Waves

Predicting the response of liquefied natural gas(LNG)contained in vessels subjected to external waves is extremely important to ensure the safety of the transportation process.In this study,the coupled behavior due to ship motion and liquid tank sloshing has been simulated by the Smoothed-Particle Hydrodynamics(SPH)method.Firstly,the sloshing flow in a rectangular tank was simulated and the related loads were analyzed to verify and validate the accuracy of the present SPH solver.Then,a three-dimensional simplified LNG carrier model,including two prismatic liquid tanks and a wave tank,was introduced.Different conditions were examined corresponding to different wave lengths,wave heights,wave heading angles,and tank loading rates.Finally,the effects of liquid tank loading rate on LNG ship motions and sloshing loading were analyzed,thereby showing that the SPH method can effectively provide useful indications for the design of liquid cargo ships.

Review on the Progress and Issues in Liquid Tank Sloshing of Ships

With the development of large liquid cargo ships,liquid tank sloshing has gradually become a hot research topic in the area of shipping and ocean Engineering.Liquid tank sloshing,characterized by strong nonlinearity and randomness,not only affects the stability of the ship but also generates a huge impact force on the wall of the tank.To further investigate liquid tank sloshing,a comprehensive review is given on the research process of the most focused subjects of liquid sloshing.Summarizing the existing research will help to identify issues in the current field and provide useful references.The methods for investigating sloshing,the research progress and the situations worldwide are discussed.The advantages and defects of experiments and numerical simulations are also explored.The problems which need to be explored in the future are subsequently proposed.

SIMULATION OF TANK SLOSHING BASED ON OPENFOAM AND COUPLING WITH SHIP MOTIONS IN TIME DOMAIN

Tank sloshing in ship cargo is excited by ship motions, which induces impact load on tank wall and then affects the ship motion. Wave forces acting on ship hull and the retardation function are solved by using three-dimensional frequency domain theory and an impulse response function method based on the potential flow theory, and global ship motion is examined coupling with nonlinear tank sloshing which is simulated by viscous flow theory. Based on the open source Computational Fluid Dynamics （CFD） development platform Open Field Operation and Manipulation （OpenFOAM）, numerical calculation of ship motion coupled with tank sloshing is achieved and the corresponding numerical simulation and validation are carried out. With this method, the interactions of wave, ship body and tank sloshing are completely taken into consideration. This method has quite high efficiency for it takes advantage of potential flow theory for outer flow field and viscous flow theory for inside tank sloshing respectively. The numerical and experimental results of the ship motion agree well with each other.

CALCULATION OF FUEL SLOSHING AND ITS COUPLING VIBRATION WITH A TANK

The response of fuel-tank-sloshing to aircraft maneuver is a difficult mathematical problem to be solved. Beginning with setting up the mechanical model and the respective mathematical model, this paper uses both F.E. and B.E.M. to imitate the sloshing process. The paper has developed some special techniques to deal with strong nonlinear characteristics, and provided satisfactory numerical results of displacements and stress for low frequency, resonance, high frequency and fuel tank dynamic response characteristics. The program not only assures convergence and stability of the solution, but also has the function of graphic display. It is a valuable technique to deal with the strong nonlinear oscillation of fuel tank with large amplitude and moving boundary condition on free surface.

An Approximation to Energy Dissipation in Time Domain Simulation of Sloshing Waves Based on Linear Potential Theory

This paper proposes a new approximation to energy dissipation in time domain simulation of sloshing waves by use of a linear potential theory. The boundary value problem is solved by the NURBS （non-uniform rational B-spline） higher-order panel method, in which a time-domain Green function is employed. The energy dissipation is modeled by changing the boundary condition on solid boundaries. Model experiments are carried out in a partially filled rectangular tank with forced horizontal motion. Sloshing-induced internal pressures and horizontal force obtained numerically and experimentally are compared with each other. It is observed that the present energy dissipation approximation can help produce a fair agreement between experimental forces and those of numerical simulations.

The Equal-Norm Multiple-Scale Trefftz Method for Solving the Nonlinear Sloshing Problem with Baffles

In this paper,the equal-norm multiple-scale Trefftz method combined with the implicit Lie-group scheme is applied to solve the two-dimensional nonlinear sloshing problem with baffles.When considering solving sloshing problems with baffles by using boundary integral methods,degenerate geometry and problems of numerical instability are inevitable.To avoid numerical instability,the multiple-scale characteristic lengths are introduced into T-complete basis functions to efficiently govern the high-order oscillation disturbance.Again,the numerical noise propagation at each time step is eliminated by the vector regularization method and the group-preserving scheme.A weighting factor of the group-preserving scheme is introduced into a linear system and then used in the initial and boundary value problems(IBVPs)at each time step.More importantly,the parameters of the algorithm,namely,the T-complete function,dissipation factor,and time step,can obtain a linear relationship.The boundary noise interference and energy conservation are successfully overcome,and the accuracy of the boundary value problem is also improved.Finally,benchmark cases are used to verify the correctness of the numerical algorithm.The numerical results show that this algorithm is efficient and stable for nonlinear two-dimensional sloshing problems with baffles.

FREE BENDING VIBRATION OF ANNULAR CYLINDRICAL TANK PARTIALLY FILLED WITH LIQUID IN THE CONSIDERATION OF SURFACE WAVE

This paper studies the problem of free bending vibration of annular cylindricaltank partially filled with liquid in the consideration of surface wave.The exactformulae of the mode shape functions and frequencies are deduced.Results can beobtained by means of computer.The analysis shows that the effect of liquid on vibration of annular cylindrical tank is equivalent to different generalized distributivemasses attached to inner and outer cylinders respectively.

Optimization of the roll motion of box-shaped hull section with anti-rolling sloshing tanks and fins in beam waves

With the development of ocean engineering and demand for safety of the ship and offshore structures, the transportation and storage of liquid have become an important issue nowadays. Furthermore, in order to improve the hydrodynamic performances of the ship and offshore structures, the anti-rolling liquid tanks are often taken into consideration. The internal-external coupling flow effect is vital for the ship and liquid tank designs, especially when the external wave frequency is close to the natural frequency of liquid tanks with a certain filling ratio, large amplitude motions may occur, which is dangerous to some extent. In this paper, the simulation-based-design method is introduced at first, and the verification of the numerical calculation of internal-external coupling flow with liquid tanks is done then. Finally, the filling ratio of the anti-rolling liquid tank and the installation angle of the anti-rolling fins are optimized to reduce the roll motion amplitude of the hull section to the greatest extent under the combined action of the two anti-rolling devices. Optimization results show that the roll motion amplitude of box-shaped hull section can be successfully reduced by reasonably designing the two anti-rolling devices, which can be a reference to the future design of the fishing ship and other ships with anti-rolling devices.

Numerical simulations of FPSO with sloshing tanks in a random freak waves

This paper presents a potential-viscous coupled method to simulate a floating production storage and offloading(FPSO)with two liquefied natural gas(LNG)sloshing tanks in a random freak wave.The potential theory uses high-order-spectral(HOS)method.The random wave is generated by HOS for 2000 s,and a freak wave is observed around 1830 s.The FPSO LNG model was firstly verified in regular waves using HOS-computational fluid dynamics(CFD)coupled method and validated the HOS-CFD coupled method can solve the ship motion coupled with sloshing tanks accurately.The FPSO with LNG tanks are then simulated in the freak wave,showed the coupling effects when the freak wave passes.With the existence of the sloshing tanks,the amplitude of the roll motion decreases and the period of roll motion changed.Wave breaking phenomenon can be observed when the wave crest of the freak wave encounters with the ship.