Hamiltonian Formulation for Nonlinear Sloshing in Layered Two Immiscible Fluids
Hamiltonian Formulation for Nonlinear Sloshing in Layered Two Immiscible Fluids
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层状两种不混溶流体非线性晃动的哈密顿公式
DOI：
10.1299/jsdd.2.1183
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
H. Takahara
中科院分区：
文献类型：
--
作者：
K. Hara;H. Takahara
本文研究了层状两种不混溶流体中的非线性表面和界面的晃动问题。对表面和界面晃动的科学兴趣包括需要量化化工厂中分离器或搅拌器上的允许负荷等。利用哈密顿公式，我们给出了该问题中非线性晃动的分析方法。在理论分析中，应用哈密顿原理，给出了具有动态自由面和界面的两流体系统的控制方程和规范形式(哈密顿方程)。利用Dirichlet-Neumann算子和广义傅里叶级数展开，导出了控制液体表面和界面波动的非线性常微分方程组。求解这些常微分方程组，得到了矩形水池中表面和界面波运动的时程和跃迁。通过实验验证了理论分析的有效性。
This paper deals with a nonlinear surface and interface sloshing in layered two immiscible fluids of different desities. Scientific interest in surface and interface sloshing includes the need to quantify allowance loads on separators or agitators in chemical plants and so on. We propose the analytical method for nonlinear sloshing in this problem by using Hamiltonian formulation. In theoretical analysis, the governing equations and canonical form (Hamiltonian equations) of a system of two fluids with a dynamic free surface and interface are given by applying Hamilton's principle. Moreover, the nonlinear ordinary differential system which governs liquid surface and interfacial wave motions is derived by using Dirichlet-Neumann operators and the generalized Fourier series expansion. Solving these ordinary differential system yields the time histories and the transitions of surface and interfacial wave motions in a rectangular tank. The validly of the theoretical analysis is verified through the experiments.