# Numerical simulation of the sloshing of liquids in tanks

Sexton, Jeffrey B. (1996) Numerical simulation of the sloshing of liquids in tanks. Masters thesis, Memorial University of Newfoundland.

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•  [English] PDF - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. (Original Version)

## Abstract

This thesis presents the development and implementation of a Finite Volume Method (FVM) to simulate the sloshing behaviour of incompressible, constant density liquids in a two- dimensional, rigid rectangular tank. The phenomenon of sloshing is of importance to engineers involved in the design of all types of vehicles which transport confined liquids. This paper reports on the research conducted in the context of the transport of liquids on the ocean surface. The method presented has two immediate applications in this context: the transport of petroleum products, and roll stabilization systems for ocean-going vessels. -- The FVM is used to discretize the governing momentum and mass conservation equations using primitive variables in a fully Eulerian approach. The method is formulated by integrating the governing equations over appropriate control volumes, and assembling systems of linear equations. A fixed rectangular grid with variable spacing is utilized, and momentum control volumes (CVs) are staggered relative to the continuity CVs. The inertial accelerations caused by a specified tank motion are applied to the fluid by the inclusion of additional source terms in the momentum equations. The method can accommodate the simultaneous translation and rotation of the tank relative to an absolute reference frame, and rotation of the tank about a frame attached to it. -- The free surface boundary is handled using the Volume of Fluid (VOF) method, which permits arbitrary movement of the surface, including the possibility of overlapping and smaller regions breaking away. The VOF method is based on the assignment of a variable Ffor each continuity CV, where F represents the average fraction of the cell volume which is occupied by fluid. The VOF method, therefore, defines the shape of the fluid-occupied calculation domain, and the free surface. -- Results were obtained in the form of the free surface configuration, and velocity and pressure distributions throughout the fluid domain. Results are presented for various prescribed tank motions, chosen to verify the method's stability, reliability, and conformance to behaviour predicted by other established means. Prescribed tank motions were; (i) rotation to a constant angle of inclination; (ii) excitation with the predicted natural period; (iii) excitation near the natural period (producing a surface wave with a beating behaviour ); (iv) impulsive translation; (v) continuous rotation; and (vi) arbitrary simultaneous rotation and translation. All input tank motions are of a sinusoidal form. The method generated results in good agreement with expected physical behaviour. In particular, the wave period characteristics has been verified, and the ability of the method to accommodate a combined rotational and translational tank motion (representing ship roll and sway) lias been proven. -- To fully develop and define the capabilities of the proposed method, it is necessary to conduct further testing of the method to verify the surface heights calculated, and to optimize the use of various calculation parameters. In addition, testing with general tank motion (i.e. roll, sway, and heave), and with motions extreme in nature, is recommended. It is also recommended that a version of this method be developed to model a three-dimensional rectangular tank, thus ensuring its applicability to the widest possible range of practical design problems.

Item Type: Thesis (Masters) http://research.library.mun.ca/id/eprint/1644 1644 Bibliography: leaves 55-57 Engineering and Applied Science, Faculty of 1996 Submission Liquids--Transportation; Sloshing (Hydrodynamics)