Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-27T14:20:13.611Z Has data issue: false hasContentIssue false
  • English
  • Français

Spherical cap bubbles with laminar wakes

Published online by Cambridge University Press:  29 March 2006

Jean-Yves Parlange
Jean-Yves Parlange
Affiliation:
Department of Engineering and Applied Science, Yale University, New Haven, Connecticut
Get access Rights & Permissions [Opens in a new window]

Abstract

The steady rise of a given amount of gas in an infinite liquid under the action of buoyancy forces is examined. The shape of the bubble is that of a spherical cap. Behind the bubble there is a region of closed streamlines where the flow is assumed to be steady and rotational. The predicted velocity and geometry of the cap agree well with observation for a limited range of values of the Reynolds number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 37 , Issue 2 , 23 June 1969 , pp. 257 - 263
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

Adams, V. W., Guile, A. E., Lord, W. T. & Naylor, K. A. 1967 Correlation of experimental data for electric arcs in transverse magnetic fields. Contributions to Eighth Intl. Conf. on Ionisation Phen. in Gases, Vienna and Proc. I.E.E. 114, no. 10, p. 1556.Google Scholar
Broadbent, E. G. 1965a A theoretical exploration of the flow about an electric arc transverse to an air stream using potential flow methods. R.A.E. T.R. 65056.Google Scholar
Broadbent, E. G. 1965b Electric arcs in cross-flow. Proc. Seventh Intl. Conf. on Ionisation Phenomena in Gases, Belgrade and R.A.E. T.M. Aero. 897.
Cole, J. D. & Roshko, A. 1954 Proc. 1954. Heat Transfer and Fluid Mechanics Institute, Univ. of California, Berkeley.
Dautov, G. Yu. & Zhukov, M. F. 1965 Co-ordinated results of research on electric arcs. Prikl. Mekh. i Tekh. Fiz. no. 2, pp. 97–105.Google Scholar
Dennis, S. C. R. & Shimshoni, M. 1964 The steady flow of a viscous fluid past a circular cylinder. A.R.C. Rep. 26104.Google Scholar
Dennis, S. C. R. & Smith, N. 1964 Forced convection in the steady flow of a viscous fluid past a heated circular cylinder. A.R.C. Rep. 26106.Google Scholar
Hodnett, P. F. 1967 An electric arc held stationary by a magnetic field in a uniform flow: theory for low Reynolds number flow. Chap. II of Ph.D. Thesis, Leeds University and Aerospace Research Laboratories Report ARL 68–0025 (to appear in Phys. Fluids).
Illingworth, C. R. 1963 Flow at small Reynolds number. Chap. IV. Laminar Boundary Layers, ed. L. Rosenhead. Oxford: Clarendon.
Kaplun, S. 1957 Low Reynolds number flow past a circular cylinder J. Math. Mech. 6, 595–603.Google Scholar
King, L. A. 1961 The voltage gradient of the free-burning arc in air or nitrogen. Proc. Fifth Intl. Conf. on Ionisation Phenomena in Gases, Munich.
Kuethe, A. M., Harvey, R. L. & Nicolai, L. M. 1967 Model of an electric arc balanced magnetically in a gas flow. AIAA Paper no. 67–96.Google Scholar
Lagerstrom, P. A. 1964 Laminar flow theory. Chap. B. Theory of Laminar Flows, ed. F. K. Moore. Oxford University Press.
Lamb, H. 1932 Hydrodynamics. Sixth Edition. Cambridge University Press.
Lord, W. T. 1964 Effects of a radiative heat-sink on arc voltage-current characteristics. AGAR Dograph 84 pp. 673–708 and R.A.E. T.M. Aero. 871.
Lord, W. T. 1967 Theory for electric arcs of low power gradient. Contributions to Eighth Intl. Conf. on Ionisation Phenomena in Gases, Vienna.
Lord, W. T. & Broadbent, E. G. 1965 An electric arc across an air stream. R.A.E. T.R. 65055.Google Scholar
Maecker, H. 1959 The properties of nitrogen up to 15,000°K. AGARD Rep. 324.Google Scholar
Myers, T. W. & Roman, W. C. 1966 Survey of investigations of electric arc interactions with magnetic and aerodynamic fields. Aerospace Research Laboratories Report ARL 66–0184.
Otis, D. R. 1967 A source model for predicting the drag force on a moving arc column AIAA J. 5, 582–4.Google Scholar
Proudman, I. & Pearson, J. R. A. 1957 Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder J. Fluid Mech. 2, 237–62.Google Scholar
Roman, W. C. & Myers, T. W. 1966 Investigation of electric arc interaction with aerodynamic and magnetic fields. Aerospace Research Laboratories Report ARL 66–0191.
Schrade, H. O. 1965 On arc pumping and the motion of electric arcs in a transverse magnetic field. Proc. Seventh Intl. Conf. on Ionisation Phenomena in Gases, Belgrade, an Aerospace Research Laboratories Report ARL 65–178.
Shercliff, J. A. 1965 A Textbook of Magnetohydrodynamics. London: Pergamon.
Stine, H. A. & Watson, V. R. 1962 The theoretical enthalpy distribution of air in steady flow along the axis of a direct current arc. N.A.S.A. T.N. D-1331.Google Scholar
Thiene, P. G., Chambers, J. E. & Jaskowsky, W. V. 1961 An experimental investigation of the behaviour of an arc positive column in the presence of forced convection. Plasmadyne Report T-4TNO 31–334.
Yas'Ko, O. I. 1964 General characteristics of electric arcs. Inzh. fiz. Zh. 7, 12, 112–16.Google Scholar