A Two-Dimensional Liquid Sloshing Analysis in a Partially Filled Complicated-Shape Tank by the Schwarz–Christoffel Transformation

Abstract

The nonlinear sloshing of an incompressible fluid with irrotational flow in a complicated-shape tank due to horizontal excitation is studied with a semi-analytical method proposed in this study. In this method, the velocity potential function of a liquid in a complicated-shape tank is estimated by using an approximate analytical transformation function from a complicated-shape region to a rectangular region. This function is obtained through Schwarz–Christoffel mapping and polynomial fitting. Nonlinear dynamic equations for the fluid–structure coupled system are developed based on the Hamilton–Ostrogradskiy principle. Nonlinear kinematic equations for the fluid–structure coupled system are derived based on the relationship between the liquid velocity and the free-surface equation. The Galerkin method is used to convert partial differential equations into ordinary differential equations. When tank movement is given, nonlinear models for the coupled system can be reduced to simple ones for liquid sloshing. Natural frequencies for the coupled system and liquid sloshing are analyzed, and the semi-analytical results agree with the numerical ones calculated with the software DampSlosh. Hydrodynamic forces and moments are also analyzed, and the semi-analytical results agree well with the numerical ones calculated with the Flow3D v10.1.1.

Keywords

• Schwarz–Christoffel transformation
• liquid sloshing
• complicated-shape tank
• natural frequency
• hydrodynamic force
• hydrodynamic moment