Hamiltonian Formulation of Surface and Interface Sloshing in a Tank Containing Two Immiscible Fluids

Abstract

This paper deals with surface and interface sloshing in a tank containing two fluids of different desities. Scientific interest in this ploblem includes the need to quantify allowance loads on oil water separators and chemical plants. In this study, we give a Hamiltonian formulation of a system of two incompressible irrotational fluids with a dynamic free surface and interface. This study aims to analyze the linearized time history response and the linear properties (vibration mode and effect of surface tension on the natural frequency). As a result, it was revealed that this system has two different vibration modes (surface and interfacial mode) with same wave number and the surface tension causes natural frequency increases. The validity of the theory is verified by experimental results. This procedure can be directly applied to the nonlinear problem of this system.

Hamiltonian Formulation of Free Surface and Interface Motions in a Tank(N-Wave Resonant Interaction Caused by Nonlinearity of System)

“…In the previous study, we reported that this system has two coupled resonance modes which have the same wave number (4) . The larger one is the dominant frequency of the surface…”

“…2, No.6, 2008 In the previous studies, we proposed the Hamiltonian formulation for this problem based on a variational principle (4) . Moreover, the experimental and the theoretical analyses are conducted to obtain the effect of surface tension on the natural frequencies (4) and the nonlinear time history responses (5) for this system. However, we couldn't discuss the nonlinear characteristics of surface and interfacial motions in detail.…”

“…By using the definition of functional derivative (4) and the generalized Fourier series (19), the canonical equations (9) can be rewritten as…”

Hamiltonian Formulation for Nonlinear Sloshing in Layered Two Immiscible Fluids

“…(1) - (4). Handa and Tajima (1) studied dispersion relations and amplitude-frequency responses of a two-dimensional model.…”

“…In the previous study, we gave canonical conjugate variables and Hamiltonian equations for this problem by a variational formulation (4) . Then, the experimental and theoretical analyses are conducted to investigate the effect of surface tension on the natural frequencies and the linearized problems for this system (vibration modes and time histories).…”