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Slosh dynamics of inviscid fluids in two-dimensional tanks of various geometry using finite element method. (English) Zbl 1171.76030

Summary: This paper brings into focus some interesting effects arising from the motion of the liquid free surface due to sloshing in partially filled containers of several geometrical shapes in two dimensions. We examine slosh characteristics that include frequencies, free surface profiles and the hydrodynamic pressure over the container walls. The equations of motion of the fluid, considered inviscid, are expressed in terms of the pressure variable alone. It is assumed that the frequency of the exciting oscillation is not in the immediate neighborhood of the natural slosh frequency, so that the slope of the free surface is small. Simple harmonic oscillation and earthquake excitations are used as prescribed boundary conditions. A finite difference-based iterative time-stepping technique is employed to advance the solution in the time domain. The paper presents numerical solutions for rectangular, vertically mounted annular cylindrical, trapezoidal and horizontal circular cylindrical containers. Numerical results are compared with existing solutions to validate the code. The parametric study of slosh dynamic systems shows the importance of the excitation, fluid height and the geometry of the container.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
76M20 Finite difference methods applied to problems in fluid mechanics
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