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Oscillations of a vapour cavity in a rotating cylindrical tank

Published online by Cambridge University Press:  28 March 2006

Sui-Kwong P. Pao  and
J. Siekmann
Sui-Kwong P. Pao
Affiliation:
Department of Engineering Science and Mechanics, College of Engineering, University of Florida, Gainesville, Florida, U.S.A.
J. Siekmann
Affiliation:
Department of Engineering Science and Mechanics, College of Engineering, University of Florida, Gainesville, Florida, U.S.A.
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Abstract

The oscillations of a curved interface are considered, neglecting the effects of gravity. The system under consideration consists of a right, circular, cylindrical tank of finite length, partially filled with an inviscid, incompressible, wetting liquid. When the container spins about its axis of revolution, the large-scale vapour cavity takes an elongated spheroid-like shape, symmetric about the axis of rotation. The fluid—vapour interface will oscillate about the equilibrium configuration if disturbing forces are present. The case where the vapour cavity touches the walls of the tank is not included in this investigation.

The equations of motion are linearized. However, the resulting eigenvalue problem is non-linear. Surface tension and rotation are taken into account only to the extent allowed by a linearized stability theory.

The self-sustained oscillations are governed by a partial differential equation of elliptic type, the field equation of the perturbation pressure. According to the results obtained from theory, all eigenfrequencies for this case are greater than twice the angular speed of the tank. The first two eigenfrequencies can be computed with high accuracy. The relation between the bubble shape and the eigen-frequency is shown in a graph for a specific example.

The governing differential equation is hyperbolic for forced oscillations induced by a small force field of constant magnitude and direction in an inertial frame of reference. A solution for this problem exists only in case of a cylindrical tank of infinite length. Discontinuities in the velocity components occur in the flow field. A numerical example has been carried out.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 31 , Issue 2 , 29 January 1968 , pp. 249 - 271
Copyright
© 1968 Cambridge University Press

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References

Benjamin, T. B. & Barnard, B. J. S. 1964 A study of the motion of a cavity in a rotating liquid J. Fluid Mech. 19, 193.Google Scholar
Garabedian, P. R. 1964 Partial Differential Equations. New York: John Wiley.
Habip, L. M. 1965 On the mechanics of liquids in subgravity Astronautica Acta, 11, 401.Google Scholar
Morgan, G. W. 1951 A study of motions in a rotating liquid. Proc. Roy. Soc. A 206, 108.Google Scholar
Oser, H. 1957 Erzwungene Schwingungen in rotierenden Flüsigkeiten Archs. ration. Mech. Analysis, 1, 81.Google Scholar
Pao, SUI-KWONG P. 1967 Dynamic response of a wetting liquid enclosed in a rotating tank in a zero-g environment and subjected to various disturbing forces. dissertation, University of Florida.
Phillips, O. M. 1960 Centrifugal waves J. Fluid Mech. 7, 340.Google Scholar
Rosenthal, D. K. 1962 The shape and stability of a bubble at the axis of a rotating liquid J. Fluid Mech. 12, 358.Google Scholar
Struik, D. J. 1950 Lectures on Classical Differential Geometry. Cambridge, Mass.: Addison—Wesley.