Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-20T09:02:14.473Z Has data issue: false hasContentIssue false
  • English
  • Français

Fluid flow in a hemisphere induced by a distributed source of current

Published online by Cambridge University Press:  12 April 2006

J. G. Andrews  and
R. E. Craine
J. G. Andrews
Affiliation:
Central Electricity Generating Board, Marchwood Engineering Laboratories, Southampton, England
R. E. Craine
Affiliation:
Department of Mathematics, University of Southampton, England
Get access Rights & Permissions [Opens in a new window]

Abstract

One of the main problems in welding is to produce consistent weld profiles. Simple heat-flow models of the weldpool, which are currently used to predict the shape of the solid-liquid boundary, do not take account of fluid motion which is observed in practice and the effect of such motion could be significant. Electromagnetic j × B forces due to the welding arc have been proposed as a major cause of the motion and we attempt here to develop existing flow models towards more practical welding situations. We consider the steady-state flow of an incompressible viscous conducting fluid in a hemispherical container due to various axisymmetric representations of the distributed current sources which can arise in arc welding. A solution is found for sufficiently small currents that inertial effects may be ignored and no singularities appear in the velocity field. We discover that varying the current distribution can lead to qualitatively different flow patterns, i.e. poloidal flows in opposite directions and breakup into two distinct counter-rotating loops.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 84 , Issue 2 , 30 January 1978 , pp. 281 - 290
Copyright
© 1978 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

Andrews, J. G. & Graine, R. E. 1977 C.E.G.B. Lab. Note R/M/N919.Google Scholar
Carslaw, H. S. & Jaeger, J. C. 1959 Conduction of Heat in Solids, 2nd edn. Oxford: Clarendon Press.Google Scholar
Christensen, N., Davies, V. DE L. & Gjermundsen, K. 1965 Br. Weld. J. 12, 54.Google Scholar
Jeans, J. 1925 The Mathematical Theory of Electricity and Magnetism, 5th edn, p. 226. Cambridge University Press.Google Scholar
Kublanov, V. & Erokhin, A. 1974 Int. Inst. Weld. Doc. no. 212-318-74.Google Scholar
Narain, J. P. & Uberoi, M. S. 1971 Phys. Fluids 14, 2687.Google Scholar
Narain, J. P. & Uberoi, M. S. 1973 Phys. Fluids 16, 940.Google Scholar
Rosenthal, D. 1941 Weld. J. Easton 20, 220S.Google Scholar
Shercliff, J. A. 1970 J. Fluid Mech. 40, 241.Google Scholar
Smithells, C. J. 1967 Metals Reference Book, vol. 3. Butterworths.Google Scholar
Sozou, C. 1971 J. Fluid Mech. 46, 25.Google Scholar
Sozou, C. 1972 Phys. Fluids 15, 272.Google Scholar
Sozou, C. 1974 J. Fluid Mech. 63, 665.Google Scholar
Sozou, C. & English, H. 1972 Proc. Roy. Soc. A 329, 71.Google Scholar
Sozou, C. & Pickering, W. M. 1975 J. Fluid Mech. 70, 509.Google Scholar
Sozou, C. & Pickering, W. M. 1976 J. Fluid Mech. 73, 641.Google Scholar
Woods, R. A. & Milner, D. R. 1971 Weld. J. Res. Suppl. 50, 163S.Google Scholar