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An electric arc in a transverse magnetic field: a theory for low power gradient

Published online by Cambridge University Press:  28 March 2006

W. T. Lord
W. T. Lord
Affiliation:
Royal Aircraft Establishment, Farnborough, Hampshire
Now at Rocket Propulsion Establishment, Westcott, Aylesbury, Buckinghamshire.
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Abstract

A uniform electric arc column is held at rest against an imposed low-speed flow perpendicular to its length by an applied magnetic field transverse to both the arc and the flow. The situation is represented mathematically by two regions separated by an isothermal boundary, the arc periphery, across which certain gas properties change discontinuously. It is assumed that the arc has low power gradient so that the Nusselt number is small compared with unity. The Reynolds number is then small also and the methods of the theory of flow at low Reynolds number are used to obtain solutions for the temperature, magnetic field, velocity and pressure inside and outside the arc. It is found that the periphery of the arc is a circle and its radius is determined by heat transfer. The flow near the periphery, and the drag of the arc, are found to depend on a final boundary condition at the periphery, the form of which is not yet clear. Several examples of possible flow patterns are given, and it is shown that the arc may be likened to a slippery porous body for which the slipperiness and porousness are governed by the final boundary condition. The electric and magnetic characteristics of the arc are derived and shown to be amenable to examination by experiment and to empirical extension for arcs of higher power gradient.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 35 , Issue 4 , 10 March 1969 , pp. 689 - 709
Copyright
© 1969 Cambridge University Press

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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 o. 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 o. 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'’o, O. I. 1964 General characteristics of electric arcs. Inzh. fiz. Zh. 7, 12, 112–16.Google Scholar