The Simulation And Analysis Of Ship Tank Sloshing In Time Domain

The problem of sloshing in liquid tanks is a classic one in hydrodynamics, which is also a concern in both academic and engineering circles. With the development of the special liquid carriers, such as LNG and LPG, the research of sloshing in liquid tank has become a hot hydrodynamic topic. For this kind of problem, many researchers had carried out a lot of researches, for example, Umemoto and Yoshikawa[1] had conducted a series of experiments for various liquid tanks. Due to the strong nonlinear phenomenon in free surface, the progress in theoretical solutions is very limited. Theoretically, there are many methods, such as Boundary Element Method (BEM), Finite Element Method (FEM), Finite Difference Method (FDM), computational fluid approach, mesh free method and so forth. For FEM, FDM and computational fluid approach, huge amount of computational resources and time is consumed. Generally, BEM reduces the dimension of the model and saves the resources of the computer and the computational time. And this method is always used to simulate the hydrodynamic phenomenon with free surface. For example, Faltinsen [2] has adopted this method to investigate sloshing in liquid tank without girder, Zhu[3] has adopted MBEM to simulate sloshing in liquid tank with girder. In fact, the girder in tank is always permeable. Miao[4, 5] studied the sloshing in liquid tank with permeable girder in frequency domain by using analytical method, but it can only deal with the linear problem, it can't be applied for nonlinear phenomenon.Usually, the girder in the liquid tank is quite thin and the thickness almost can be neglected. When the Green function is applied, it will brings some trouble because of the singularity the thin girder brings about. Nishino[6] introduced the thin plate boundary element method by modifying the BEM, but this method has certain difficulties in simulating the sloshing with permeable girder.In this paper, MBEM is outlined and applied in simulating the nonlinear phenomenon of both two-dimensional and three-dimensional sloshing in liquid tanks with permeable girders of various porosities. And comparison of the present results and references is conducted and they agree well with each other. Generally, the two-dimensional model ignores the effect of the width and it is equivalent to the three-dimensional model with the width tending to be infinite. The three dimensional effect of the model is discussed in this paper and it can be a reference when the results based on two-dimensional model are compared with the ones on three-dimensional model. In addition, the simulations of sloshing in liquid tanks of different width and with girders of different height and porosities are carried out and these factors influencing on the natural frequency of the tank are discussed. The MBEM also can be extended to analyze and simulate fluid motions in roll-damping tanks.The coupling of the ship motion and sloshing in liquid tank has also been simply discussed. The sloshing in liquid tank is excited by the ship motion and in turn, it influences the ship motion and the coupling effect is sometimes critical in ship design or motion control. In this paper, the STF method is applied to simulate the exterior flow domain of the ship in frequency domain. Then, the results in frequency domain from STF are transformed to time domain by using inverse Fourier transformation. And the Boundary Element Method is used to simulate the sloshing in the liquid tank in time domain. The ship motion is first gotten by the STF and Fourier transformation and then it is used for the motion of the liquid tank. The force of the flow to the liquid tank is calculated by BEM and transferred to the equation of the ship motion.