Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-30T01:14:25.867Z Has data issue: false hasContentIssue false
  • English
  • Français

Large-amplitude motions of a liquid—vapour interface in an accelerating container

Published online by Cambridge University Press:  28 March 2006

L. M. Perko
L. M. Perko
Affiliation:
Lockheed Palo Alto Research Laboratory, Palo Alto, California
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers the large-amplitude symmetric and asymmetric irrota-tional motion of an inviscid incompressible fluid with a liquid—vapour interface in an accelerating container of revolution. A combined analytical—numerical method which involves no linearizations in the hydrodynamical equations and applies to all but surface-tension dominated motions is used to compute a variety of such motions. One important aspect of this non-linear method is that it accurately determines the initial development of surface instabilities such as breakers near the wall of the container.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 35 , Issue 1 , 16 January 1969 , pp. 77 - 96
Copyright
© 1969 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramson, H. N., Chu, W. H. & Kana, D. D. 1966 Some studies of nonlinear lateral sloshing in rigid containers J. Appl. Mech. 33, 774–84.Google Scholar
Bellman, R. & Pennington, R. H. 1954 Effects of surface tension and viscosity on Taylor instability Q. Appl. Math. 12, 151–62.Google Scholar
Bowman, T. E. 1966 Dynamics of an axi-symmetric liquid free surface following a stepwise acceleration change. Inst. Environmental Sci. Annual Meeting Proc.
Bussinger, P. & Golub, G. 1965 Linear least squares solutions by Householder transformations Numerische Math. 7, 269.Google Scholar
Concus, P., Crane, G. E. & Perko, L. M. 1965 Inviscid fluid flow in an accelerating axisymmetric container. Fluid Mech., and Heat Transfer Under Low-G Symp. Proc., Palo Alto, California.
Davis, P. J. & Rabinowitz, P. 1961 Advances in orthonormalizing computation. I. Advances in Computers, volume 2. New York: Academic Press.
Fung, F. C. W. 1965 Dynamic response of liquids in partially filled containers suddenly experiencing weightlessness. Fluid Mech. and Heat Transfer Under Low-G Symp. Proc., Palo Alto, California.
Harlow, F. H. & Welch, J. E. 1965 Numerical calculation of time dependent viscous incompressible flow of a fluid with a free surface Phys. Fluids, 8, 2182–9.Google Scholar
Harlow, F. H. & Welch, J. E. 1966 Numerical study of large amplitude free surface motions Phys. Fluids, 9, 842–51.Google Scholar
Householder, A. S. 1958 Unitary triangularization of a nonsymmetric matrix J. Assoc. Comp. Mach. 5, 339–42.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. London: Permagon Press.
Lewis, D. J. 1950 The instability of liquid surfaces in a direction perpendicular to their planes. II. Proc. Roy. Soc. A 202, 81.Google Scholar
Moore, R. E. & Perko, L. M. 1965 Inviscid fluid flow in an accelerating cylindrical containers J. Fluid Mech. 22, 305–20.Google Scholar
Penny, W. G. & Price, A. T. 1952 Some gravity wave problems in the motion of perfect liquids. II. Finite periodic stationary gravity waves in a perfect liquid. Phil. Trans A 244, 254–68.Google Scholar
Satterlee, H. M. & Reynolds, W. C. 1964 The dynamics of the free liquid surface in cylindrical containers under strong capillary and weak gravity conditions. Technical Report LG-2, Stanford University.
Satterlee, H. M., Hollister, M. P., Perko, L. M. et al. 1967 A study of liquid propellant behaviour during periods of varying acceleration. NASA MSFC Contract NAS-9-5174, LMSC Report A 874728.
Taylor, G. I. 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. Proc. Roy. Soc A 201, 192–6.Google Scholar