Nonlinear dynamics of liquid-filled rectangular tank with elastic appendages are studied. Based on the assumption of ideal fluid, the coupling dynamic equations of rigid tank, elastic appendages and liquid fuel are derived using H-O principle. In the case of pitch excitation, the modified potential function and wave height function are introduced to describe the moving boundary of fluid, then Galerkin＇s method is used to discretize the dynamic equations into ordinary differential equations. The natural frequencics of the coupling system are formulated in liquid depth, the length of the tank, etc. The formulae are confirmed by numerical simulations, which also show that the effects of liquid and elastic appendages on the attitude angular of rigid.
Large amplitude sloshing in tanks is simulated by the least square particle finite element method （LSPFEM） in this paper. The least square finite element method （LSFEM） is employed to spatially discrete the Navier-Stokes equations, and to avoid the stabilization issues due to the incompressibility condition for equal-order interpolation of the velocity and the pressure, as usually used in Galerkin method to satisfy the well-known LBB condition. The LSPFEM also uses the Lagrangian description to model the motion of nodes （particles）. A mesh which connects these nodes is constructed by a triangulation algorithm to avoid the mesh distortion. A quasi a-shapes algorithm is used to identify the free surface boundary. The nodes are viewed as particles which can freely move and even separate from the main fluid domain. Finally this method is used to study the large amplitude sloshing evolution in two dimensional tanks. The results are compared with those obtained by Flow-3d with good agreement.
A method for simulation of free surface problems is presented. Based on the viscous incompressible Navier-Stokes equations, space discretization of the flow is obtained by the least square finite element method. The time evolution is obtained by the finite difference method. Lagrangian description is used to track the free surface. The results are compared with the experimental dam break results, including water collapse in a 2D rectangular section and in a 3D cylinder section. A good agreement is achieved for the distance of surge front as well as the height of the residual column.
