Liquid sloshing in half-full horizontal elliptical tanks

Abstract

A two dimensional hydrodynamic analysis based on the linear potential theory is introduced to study the natural sloshing frequencies of transverse modes in a half-filled non-deformable horizontal cylindrical container of elliptical cross section, without or with a pair of inflexible horizontal longitudinal side baffles of arbitrary extension positioned at the free liquid surface. Successive conformal coordinate transformations in conjunction with the method of separation of variables and the relevant boundary conditions are employed to obtain standard truncated matrix eigen-value problems which are then solved numerically for the resonance eigen-frequencies. The Gauss–Laguerre quadrature formula is used to approximate the integral eigen-problem obtained in the unbaffled case. Plots of the sloshing frequencies as functions of the container aspect ratio and baffle extension are presented and discussed for the three lowest antisymmetric and symmetric transverse oscillation modes. A convergence study is performed to demonstrate the fast convergence and remarkably small computational cost of the Fourier series approach used for the baffled container, and the effects of tank geometry and baffle length on the convergence are also examined. Limiting cases are considered and good agreements with available analytic and numerical solutions as well as experimental data are obtained, demonstrating the accuracy of proposed models.