Numerical simulation of nonlinear sloshing in a prismatic tank by a Cartesian grid based three-dimensional multiphase flow model

Abstract

This paper investigates large amplitude sloshing in a prismatic tank with or without a baffle by a Cartesian grid based three-dimensional (3D) multiphase flow model. In this model, an improved ghost cell method with a unified reconstruction scheme is developed to enforce boundary conditions on the slope walls of the tank. Arbitrary shape tanks and internal structures can be treated on the Cartesian grid, instead of the body-fitted grid. A 3D gradient-augmented level set (GALS) method is presented to capture highly nonlinear free surfaces. To validate the accuracy of the present ghost cell method, uniform flows around a sphere are simulated. An approximate second-order accuracy in space is achieved. Then, nonlinear sloshing induced by rolling excitations in the 3D prismatic tank is simulated. Satisfactory convergences of grid sizes and time steps are obtained. Also, good agreements are achieved between the present results and the experimental data for five filling water depths. In addition, highly nonlinear sloshing phenomena are captured such as plunging waves and wave beating. Furthermore, the variation of the excitation frequency with the pressure amplitude, and the effects of the baffle height on the impulsive pressure and the wave elevation are studied.