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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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