Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-13T01:26:31.910Z Has data issue: false hasContentIssue false
  • English
  • Français

Equilibrium shape and stability of a liquid cylinder in cross flow at low Weber numbers

Published online by Cambridge University Press:  20 April 2006

D. Weihs  and
I. Frankel
D. Weihs
Affiliation:
Department of Aeronautical Engineering, Technion-Israel Institute of Technology, Haifa, Israel
I. Frankel
Affiliation:
Department of Aeronautical Engineering, Technion-Israel Institute of Technology, Haifa, Israel
Get access Rights & Permissions [Opens in a new window]

Abstract

The cross-section shape and stability of a liquid cylinder moving perpendicularly to its axis in a gaseous medium is studied. Such liquid cylinders are formed during the break-up process of thin, rapidly moving liquid sheets, appearing in spray and atomization processes. The equilibrium shape is affected mainly by two factors: the dynamic-pressure distribution in the gas flow and the surface tension on the liquid boundary. The former tends to distort the liquid cross-section into an oval shape while the latter tends to restore the circular cross-section.

A series expansion for the shape of the cylinder cross-section was determined by assuming incompressible potential flow, neglecting the effects of body forces and internal circulation in the liquid.

The stability analysis shows that in the range of low Weber numbers the cylinder break-up is due to the divergence of varicose perturbations. The wavenumber of the most rapidly growing perturbation, its rate of growth and the maximal wavenumber for which varicose instability occurs, are all found to decrease as the Weber number grows, owing to a pressure distribution caused by the varicose distortion, which tends to reduce these perturbations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 116 , March 1982 , pp. 393 - 409
Copyright
© 1982 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

Anno, J. N. 1977 The Mechanics of Liquid Jets. Lexington.
Bogy, D. B. 1979 Ann. Rev. Fluid Mech. 11, 207.
Brodkey, R. S. 1967 The Phenomena of Fluid Motions. Addison-Wesley.
Clark, E. J. & Dombrowski, N. 1972 Proc. R. Soc. Lond. A 329, 467.
Crapper, G. D., Dombrowski, N., Jepson, W. P. & Pyott, G. A. D. 1975 J. Fluid Mech. 57, 671.
Crapper, G. D., Dombrowski, N. & Pyott, G. A. D. 1975 Proc. R. Soc. Lond. A 342, 209.
Dombrowski, N., Hasson, D. & Ward, D. E. 1960 Chem. Engng Sci. 12, 35.
Dombrowski, N. & Hooper, P. C. 1962 Chem. Engng Sci. 17, 291.
Dombrowski, N. & Johns, W. R. 1963 Chem. Engng Sci. 18, 203.
Frankel, I. 1980 Investigation of aerodynamic instabilities leading to atomization of jets. M.Sc. thesis, Technion.
Fraser, R. P., Eisenklam, P., Dombrowski, N. & Hasson, D. 1962 A.I.Ch.E. J. 8, 672.
Hagerty, W. W. & Shea, J. F. 1955 J. Appl. Mech. 22, 509.
Leclair, B. P., Hamielec, A. E., Pruppacher, H. R. & Hall, W. D. 1972 J. Atmos. Sci. 29, 728.
Levich, V. G. 1962 Physicochemical Hydrodynamics. Prentice-Hall.
Pruppacher, H. R. & Pitter, R. L. 1971 J. Atmos. Sci. 28, 86.
Rayleigh, Lord 1894 The Theory of Sound, 2nd edn. Reprinted 1945 by Dover.
Squire, H. B. 1953 Brit. J. Appl. Phys. 4, 167.
Sterling, A. M. & Sleicher, C. A. 1975 J. Fluid Mech. 68, 477.
Tanasawa, Y., Sasaki, S. & Nagai, N. 1957 Techn. Rep. Tohoku Univ. 22, 73.
Weber, C. 1931 Z. Angew. Math. Mech. 11, 136.
Weihs, D. 1978 J. Fluid Mech. 87, 289.