Study On Liquid Sloshing In A Tank With Porous Structures Based On Finite Element Method

The movement of the liquid in partial filled storage tanks under the external excitation is called liquid sloshing.Liquid sloshing is an important branch of fluid dynamics,involving physics,mathematics,mechanics and many other engineering fields,and has a complete theoretical system.Under the external excitation,the impact load generated by liquid sloshing in the storage tank will seriously threaten the stability and safety of the structures.Moreover,it is more and more important to carry out research on the sloshing reduction with the increasingly complex environment of the storage tank in practical engineering.The porous structure,as a damping structure,has received considerable attention of many scholars due to its good characteristics for dissipation of energy.Finite Element Method(FEM),which can solve the problems of partial differential equations with specific boundary conditions in mathematics and mechanics,has been widely used with the rapid development of computer technology.By means of the FEM,the complex structure can be decomposed into many elements connected by nodes,and the physical quantities can also be interpolated in terms of the nodal values through certain assumptions.Therefore,the FEM has strong adaptability and flexibly for the simulation of the structures with complex geometry and boundary conditions.In this paper,the research of liquid sloshing in the storage tank with porous structures,which has important scientific research value and engineering guiding significance,is carried out based on the finite element method.Firstly,the sloshing of an incompressible fluid in partially liquid-filled tanks is mathematically established.The governing equations involving the Euler equation,continuity equation of fluid motion,boundary conditions as well as the wave height,dynamic water pressure and sloshing force are described in detailed.Based on the linear potential flow theory,the two-dimensional(2D)and three-dimensional(3D)finite element governing equations of liquid sloshing in storage tank with porous structures are established and solved in detail by introducing the boundary conditions,respectively.Secondly,the finite element model is established to numerically simulate the two dimensional rectangular and concave storage tanks.The sloshing characteristics of liquid in the grid container under external displacement excitation are calculated and compared with the analytical solutions in the available literature.Numerical results of proposed method are in good agreement with those in the literature,which verifies the accuracy of the theoretical derivation and the calculation program.Reasonable and accurate numerical research method provides a foundation for the investigation of liquid sloshing mechanism in storage tank.According to the considered working conditions of two-dimensional model,the resonant frequency,free liquid surface height and sloshing force of the liquid are calculated under different lengths,heights,quantities and porous coefficients of porous structures,and the influence of porous structures on sloshing behaviors and the mechanism of sloshing reduction were discussed.Finally,3D cuboid container,cylinder container and PCS gravity water tank(which is the focus of practical nuclear power engineering)model are further established,and the porous structures with different sizes,shapes,positions and opening coefficients are reasonably set to suppress the shaking of PCS water tank.For the problem of liquid sloshing in a rectangular container,the free surface heights under low and high frequency excitation are calculated,and the results are in good agreement with the analytical solutions,which proves the reliability of the three dimensional formulations and the calculation program.The influences of porous structures on liquid sloshing characteristics in the container are discussed by calculating the physical quantities concerned with liquid sloshing under different working conditions.The results provide certain reference significance for the design of slosh reduction structure and practical engineering.