Magnetohydrodynamic flow in a weldpool

Weatherill, Nigel Peter (1980) Magnetohydrodynamic flow in a weldpool. University of Southampton, Doctoral Thesis.

Abstract

In arc welding electromagnetic forces are thought to be the major cause of fluid motion in the weldpool and in this thesis we are concerned with some examples of such flows. There has been recent experimental evidence to suggest that the application of a uniform magnetic field normal to the weldpool free surface stabilises the welding process. In view of this we investigate motion in a hemispherical pool due to a stationary current source with a superimposed uniform magnetic field applied parallel to the axis of symmetry. When inertial effects are ignored and a simple point source or source-sink model of the current source is introduced we obtain analytic solutions for the fluid flow valid for low currents and low applied fields. Using the analytic solutions for the source-sink current model we derive an approximate expression for the curvature of the free surface. A numerical scheme using finite-differences and the vorticity-streamfunction approach is then developed to solve the full non-linear flow problem and results are derived for the source-sink current model of the current source and for a more realistic numerically constructed distributed current source. Results obtained for typical welding currents and applied magnetic fields indicate radially outward flow on the plane free surface of the hemisphere, this direction being opposite to that predicted when there is no applied field. We go on to investigate asymmetric flows arising in a hemisphere induced by an applied current source and a uniform magnetic field acting parallel to the plane face of the pool. A three-dimensional analytic solution to this flow problem is obtained when the inertial terms in the Navier-Stokes equations are neglected and the source-sink current model is adopted. A three-dimensional numerical scheme using finite-differences and the vorticity-vector potential method is developed to solve the non-linear flow problem when the source-sink and the realistic current models are used. The three-dimensional numerical scheme is extended to consider flows induced in a moving hemisphere when a current source is applied to the fluid.

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