A simple method for studying low-gravity sloshing frequencies

Shankar, PN (2003) A simple method for studying low-gravity sloshing frequencies. Proceedings of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences, 459 (2040). pp. 3109-3130. ISSN 1364-5021

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A general method is presented to compute low-gravity sloshing frequencies of liquids in spherical and cylindrical tanks. The key idea is to use two independent coordinate systems for the interface displacement amp;eta; and liquid velocity potential amp;Phi;, respectively, which permit the contact-angle condition and the normal-velocity condition on the tank wall to be satisfied exactly. The functions amp;eta; and amp;Phi; are then expanded in terms of independent complete sets of spatial functions. When these are substituted into the liquid free-surface conditions and the latter are projected onto the basis used for amp;eta;, we obtain a standard matrix eigenvalue problem Az=amp;lambda;Bz, where the eigenvalue amp;lambda;G is either the natural frequency of oscillation or its square. It is shown that the method easily applies for all the cases of interest. In particular, it is shown that, for the flat-meniscus case at infinite Bond number, the present results generally agree with the accurate results of McIver. A useful by-product of the method is that estimates of the lowest frequencies, requiring quadratures alone, can be obtained in simple closed form. Finally, it is shown that the method can be extended to the arbitrary Bond number case, the only extra complication being the need to determine the distorted static meniscus

Item Type: Article
Uncontrolled Keywords: Capillarity;Contact angle;Eigenvalues and eigenfunctions;Fluid oscillations;Functional analysis;Gravity;Interface phenomena;Sloshing
Subjects: ENGINEERING > Fluid Mechanics and Thermodynamics
Depositing User: MS Jayashree S
Date Deposited: 10 May 2007
Last Modified: 24 May 2010 04:25
URI: http://nal-ir.nal.res.in/id/eprint/4183

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