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Linear stability of a cylindrical falling film

Published online by Cambridge University Press:  21 April 2006

Francisco J. Solorio  and
Mihir Sen
Francisco J. Solorio
Affiliation:
Facultad de Ingeniería, Universidad Nacional Autónoma de México, 04510 México, DF, México
Mihir Sen
Affiliation:
Facultad de Ingeniería, Universidad Nacional Autónoma de México, 04510 México, DF, México Present address: Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA.
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Abstract

The problem of a cylindrical falling film, descending vertically outside an infinitely long cylinder is considered. The linear stability of the fully developed flow is studied, first with a perturbation technique for small wavenumbers, and then by direct numerical computation. The numerical results are in agreement with other published values for the cylindrical jet and flat plate limits. The study shows that the cylindrical falling film is unstable for all Reynolds numbers, Weber numbers and radius ratios. Stability and amplification curves are calculated for different values of the parameters. With increasing curvature of the film the range of unstable wavenumbers and the wavenumber of the most amplified wave increase. For low curvature the wavenumber of the most amplified wave decreases with Reynolds number or Weber number, while for high curvatures it increases.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 183 , October 1987 , pp. 365 - 377
Copyright
© 1987 Cambridge University Press

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