Numerical simulation of 2D and 3D sloshing waves in a regularly and randomly excited container

Abstract

In this paper, various aspects of the 2D and 3D nonlinear liquid sloshing problems in vertically excited containers have been studied numerically along with the help of a modified σ-transformation. Based on this new numerical algorithm, a numerical study on a regularly and randomly excited container in vertical direction was conducted utilizing four different cases: The first case was performed utilizing a 2D container with regular excitations. The next case examined a regularly excited 3D container with two different initial conditions for the liquid free surface, and finally, 3D container with random excitation in the vertical direction. A grid independence study was performed along with a series of validation tests. An iteration error estimation method was used to stop the iterative solver (used for solving the discretized governing equations in the computational domain) upon reaching steady state of results at each time step. In the present case, this method was found to produce quite accurate results and to be more time efficient as compared to other conventional stopping procedures for iterative solvers. The results were validated with benchmark results. The wave elevation time history, phase plane diagram and surface plots represent the wave nonlinearity during its motion.

Keywords

3D container / free surface / σ-transformation / sloshing wave / finite difference method / Numerical Simulation