Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-19T13:11:04.758Z Has data issue: false hasContentIssue false
  • English
  • Français

The motion of constant-volume air cavities in long horizontal tubes

Published online by Cambridge University Press:  21 April 2006

W. D. Baines ,
James W. Rottman  and
John E. Simpson
W. D. Baines
Affiliation:
Department of Mechanical Engineering, University of Toronto, Toronto, Canada M5S 1A4
James W. Rottman
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge CB3 9EW
John E. Simpson
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge CB3 9EW
Get access Rights & Permissions [Opens in a new window]

Abstract

Experimental results are presented for the instantaneous release of a constant volume of air into water in a long horizontal tube of square cross-section. The tube is closed at both ends and the volume of air is confined at one of the ends before it is released. The resulting motion, after the rapid formation of an air-cavity front, may be divided into three phases: initially the front of the air cavity moves at constant speed, later its speed decreases monotonically, and finally its speed executes a long series of erratic stops and starts before coming entirely to rest. The transition from the first to the second phase is observed to occur when a disturbance due to the tube end overtakes the cavity front. The final phase is dominated by surface-tension effects, complicated by surface contaminants. A simple model of the flow, based on Benjamin's (1968) theory of steady cavity flow and the classical theory of hydraulic jumps, is developed. With correction for surface tension, the model results compare well with the experimental results for the first two phases.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 161 , December 1985 , pp. 313 - 327
Copyright
© 1985 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

Batchelor, G. K. 1967 Introduction to Fluid Dynamics. Cambridge University Press.
Benjamin, T. B. 1968 Gravity currents and related phenomena. J. Fluid Mech. 31, 209–248.Google Scholar
Fuentes, R. 1969 Contribution à l'étude d'une bulle d'air en mouvement dans l'eau sous une paroi. Thèse de docteur d'Université, Grenoble.
Gardner, C. G. & Crow, I. G. 1970 The motion of large air bubbles in horizontal channels. J. Fluid Mech. 43, 247–255.Google Scholar
Meric, R. A., Tubarrok, B. & Baines, W. D. 1982 Finite element analysis of finite gravity surges. Proc. 4th Intl Symp. on Finite Elements in Flow Problems, pp. 487–494. University of Tokyo Press.
Rottman, J. W. & Simpson, J. E. 1983 Gravity currents produced by instantaneous release of a heavy fluid in a rectangular channel. J. Fluid Mech. 135, 95–110.Google Scholar
Wilkinson, D. L. 1982 Motion of air cavities in long horizontal ducts. J. Fluid Mech. 118, 109–122.Google Scholar
Zukoski, E. E. 1966 Influence of viscosity, surface tension and inclination angle on motion of long bubbles in closed tubes. J. Fluid Mech. 25, 821–840.Google Scholar