Complete 2D and Fully Nonlinear Analysis of Ideal Fluid in Tanks

Abstract

A two-dimensional rectangular tank with rigid walls is used as the example for presenting the concepts of fully nonlinear and complete dimensional analysis. The container is subjected to simultaneous action of horizontal and vertical ground accelerations. The fluid is assumed to be inviscid and incompressible, and the flow is irrotational. The Euler equations as well as the nonlinear, kinematic free-surface boundary condition are used in the analysis. A time-independent finite difference method is used to evaluate the velocity fields and the surface profile of the sloshing fluid. The significance of the nonlinear effect on hydrodynamic force on tank face is studied. The comparison of numerical results evaluated by the complete two-dimensional analysis and the linear superposition (invalid when high nonlinearity is presented) of results evaluated by separated ground exciting is made. Details of the characteristics of nonlinear sloshing as well as of the beating phenomena are described. The occurrence of resonance is also studied.