Numerical simulation of sloshing motion inside a two dimensional rectangular tank by level set method

Abstract

Purpose

The purpose of this paper is to develop the numerical simulated methodology for sloshing motion of fluid inside a two dimension rectangular tank, and parametric studies were performed for three parameters – excitation frequency, excitation amplitude, and liquid depth.

Design/methodology/approach

A numerically simulated methodology by using the cell‐centered pressure‐based SIMPLE scheme and level set method for the sloshing motion of fluid in a rectangular tank has been developed. The convection term in the Navier‐Stokes equations and the equations used in the level set method were treated by the second‐order upwind scheme. The temporal derivative terms were solved by the three‐level second order scheme. The diffusion term in the Navier‐Stokes equations alone was solved by the central‐difference scheme. All algebraic equations were solved by the point Gauss‐Seidel method. A fully implicit scheme to treat the level set distancing equation, written as the advection equation, was developed. In addition, the level set distancing equation was solved by the iterative procedure to determine the variation of free surface.

Findings

For given excitation amplitude together with a liquid depth, the free surface displacement increases when the excitation frequency is less than the resonance frequency of tank. However, the free surface displacement decreases when the excitation is greater than the resonant frequency of the tank. It is noted that the maximum free surface displacement is generated under the circumstance for which the excitation frequency approaches the resonant frequency. The excitation amplitude and the excitation frequency have a substantial effect on the impact pressure on the wall of the tank being investigated.

Originality/value

The sloshing motion of fluid in a rectangular tank has been studied by researchers and scholars using many numerical methods; however, literature employing the level set method to study the sloshing motion of fluid is limited. In this study, the cell‐centered pressure‐based SIMPLE scheme and level set method can be employed to predict the sloshing motion. The numerical methodology can help the engineer to predict sloshing motion of fluid.

Citation

Wang, C., Teng, J. and Huang, G.P.G. (2011), "Numerical simulation of sloshing motion inside a two dimensional rectangular tank by level set method", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 21 No. 1, pp. 5-31. https://doi.org/10.1108/09615531111095049