Numerical study of three-dimensional free surface dynamics  

作　　者：Baozeng Yue Zhaolin Wang 

机构地区：[1]Department of Mechanics,School of Science, Beijing Institute of Technology,Beijing 100081, China [2]Institute of Astronautics and Aeronautics,Tsinghua University, Beijing 100084, China

出　　处：《Acta Mechanica Sinica》2006年第2期120-126,共7页力学学报（英文版）

基　　金：The project supported by the National Natural Science Foundation of China （10272022, 10572022） and the Basic Research Foundation of Beijing Institute of Technology （000Y07）. The English text was polished by Yunming Chen.

摘　　要：The dynamic problem of three-dimensional free surface is numerically studied in this paper. The ALE （Arbitrary Lagrange-Euler） kinematic description is introduced into the control equation system. The ALE description method is used to track free surface. Accurate formulations for calculating the normal vector on the free surface are presented. The discrete numerical equations by finite element method are developed by Galerkin weighted residual method. The boundary condition about free-surface tension is represented in the form of weak integration that can be computed by a differential geometry method derived in the present paper. The effect of contact angle is incorporated in the numerical algorithm. Furthermore, the numerical computations are performed and the comparison between computational and analytical results validated the effectiveness of the method. The results of this paper provide a fundamental understandings of the dynamics of liquid free surfaces, in which the surface tension and contact angle boundary conditions are taken into account. Finally, numerical simulation of largescale amplitude sloshing of liquid in a cylindrical container is performed and a numerical analysis of the effect of an annular ring-shaped rigid damping baffle on liquid sloshing oscillations in a cylindrical tank is also carried out.The dynamic problem of three-dimensional free surface is numerically studied in this paper. The ALE （Arbitrary Lagrange-Euler） kinematic description is introduced into the control equation system. The ALE description method is used to track free surface. Accurate formulations for calculating the normal vector on the free surface are presented. The discrete numerical equations by finite element method are developed by Galerkin weighted residual method. The boundary condition about free-surface tension is represented in the form of weak integration that can be computed by a differential geometry method derived in the present paper. The effect of contact angle is incorporated in the numerical algorithm. Furthermore, the numerical computations are performed and the comparison between computational and analytical results validated the effectiveness of the method. The results of this paper provide a fundamental understandings of the dynamics of liquid free surfaces, in which the surface tension and contact angle boundary conditions are taken into account. Finally, numerical simulation of largescale amplitude sloshing of liquid in a cylindrical container is performed and a numerical analysis of the effect of an annular ring-shaped rigid damping baffle on liquid sloshing oscillations in a cylindrical tank is also carried out.

关 键 词：Free surface Surface tension Numerical simulation Finite element 

分 类 号：O35[理学—流体力学]