High Performance Of Liquid Sloshing Problems In Cylindrical Container With Filling Structure

The problem of liquid sloshing is an important issue existed extensively in the field of engineering such as ocean and rail,aeronautics and astronautics,civil engineering,water conservancy,chemical industry and nuclear power and so on.It is significant to perform the research for the effects of liquid sloshing on the safety,stability and dynamic behavior of containers and relational structures.With the maximization and complication of engineering structure,the sloshing problem becomes more complicated and the research of sloshing mitigation or anti-sloshing techniques is of great significance.The scaled boundary finite element method(SBFEM)is a newly semi-analytic numerical method to solve systems of partial differential equations.Compared to the FEM,it discretises the computational domain boundaries only,so that the spatial dimensions are reduced by one.Besides,solutions can be obtained analytically in the radial direction of the scaled coordinate system,which improve the accuracy of the computation.Compared to the BEM,no fundamental solutions are required.It combines the main advantages of FEM and BEM,and overcomes their respective disadvantages to a large extent,so it has been employed successfully for many fields of study,and has very large application prospect in many fields.Based on the SBFEM,the problem of liquid sloshing is studied in this paper.The objectives of this study are as following:(1)The derivations of SBFEM governing equations in frequency domain for problems of liquid sloshing in cylindrical container with the filling structure are expressed in details.As for the uniform container with vertical direction,the 3D governing Laplace equations of liquid sloshing can be transformed to the 2D equations by using variables separation method so that the vertical variable can be isolated.Besides,based on the SBFEM features that discretes computational domain boundaries only and the modified scaled boundary finite element method with circular shape,the Bessel governing equation and inner and outer boundary conditions can be easily obtained for the problem of liquid sloshing in cylindrical container with the filling structure.(2)The filling structure in the cylindrical container is divided into three types: the circular shape structure,the ring shape structure attaching to the container wall and the ring shape structure.Then,based on the basic model of the filling structure and fluid action,the continuity equations of the interfacial surface between porous medium domain and fluid region can be obtained.The governing equations are solved by introducing the Bessel functions and modified Bessel functions of the first kind as base solutions and coupling with the corresponding boundary conditions.Comparison between the results solved by SBFEM and the analytical solutions in the literature is made.The results show that the proposed approach is effective to solve the sloshing problem.In addition,the influences of different parameters,such as radius and parameters of circular filling structure,standing wave number are examined.(3)Based on the basis of contents(2),the liquid sloshing in cylindrical container with inner column is studied.And the filling structure is divided into two types: the ring shape structure attaching to the inner column wall and the ring shape structure.Comparison between the results solved by SBFEM and the analytical solution in the literature show that the scaled boundary can easily make a great improvement for the computational efficiency and computational accuracy for the sloshing problems.In addition,the influences of different parameters,such as the position and range of filling structure are examined.