Eigenvalue analysis of ideal fluids' sloshing movement in containers using virtual mass method

Abstract

The sloshing motion of fluids in rectangular and cylindrical containers which have different sizes and materials are investigated. 2 different analytical methods, the methods of Abramson [1] and Housner [2] are utilized. With Abramson’s method the sloshing motion of ideal fluid which has the properties of being inviscid, irrotational and incompressible with its governing Laplace equation in rigid rectangular and cylin drical tanks is examined. The boundary conditions are defined through tank bottom and tank wall whereas its kinematic boundary condition comes from its free surface. With Housner’s analytical method, first natural frequencies of the sloshing motion in rectangular and cylindrical tanks assumed in 2D are found. In addition to analytical methods, a numerical method, virtual mass method of Nastran is used to obtain nat ural frequencies and modeshapes of the sloshing motion by eigenvalue analysis. The parameters of tank thickness, tank material, tank mesh resolution, phantom surface mesh resolution and phantom surface mesh topology are investigated with the aim of finding an optimum model in analyses that uses virtual mass method. The success of numerical model is tested by comparing frequencies with analytical ones. In terms of sizes of numerical models, small scale, and large scale models that can be seen in real life applications are analyzed. This study is enriched with laboratory experiment results of Erginbas [3]. In order to make the modelling easier for eigenvalue analyses over rectangular and cylindrical tanks, 2 Matlab scripts are developed. With these scripts, the time to create tanks and implement eigenvalue analyses are reduced.