Heat transfer and fluid flow in the welding arc
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I.
INTRODUCTION
THE purpose
of the work described in this paper is to develop a quantitative representation of heat and fluid flow phenomena in welding arcs, with particular reference to the interface between the arc and the bounding surfaces. The main motivation for this work is provided by recent research into weldpool behavior. In modeling the electromagnetic, heat and fluid flow phenomena in weldpools, the interaction between the welding arc and the weldpool appears as boundary conditions. Up to the present these boundary conditions were introduced on an empirical basis. Ultimately it would be highly desirable to represent arc welding systems in terms of a formulation where the transport phenomena in the arc and in the pool are fully and interactively coupled. The present work represents a useful intermediate step in this direction by allowing an explicit definition of the interaction of an impinging plasma jet with a solid surface. In recent years there has been considerable interest in representing the electromagnetic heat and fluid flow phenomena in DC plasma arcs. Work in this laboratory has involved the study of high current arcs, with emphasis on turbulence phenomena and on the overall behavior of the system. 2'3'4 The interesting and useful work carried out by Pfender and his associates 5'6 involved the direct incorporation of experimental measurements in their models. More specifically, in modeling heat flow phenomena the boundary conditions for temperature at the anode surface were deduced from experimental measurements. The work to be described in this paper differs from previous research because it seeks to develop a general, internally self-consistent engineering representation of the system, without recourse to empiricism.
J. McKELLIGET is Assistant Professor, Department of Mechanical Engineering, University of Lowell, Lowell, MA 01854. J. SZEKELY is Professor of Materials Engineering, Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139. Manuscript submitted January 31, 1985.
METALLURGICALTRANSACTIONS A
II.
MODEL FORMULATION
The presence of an electric field between the cathode and the weldpool (anode), sketched in Figure 1, causes the passage of an electric current through the ionized plasma region which, in turn, gives rise to a self-induced magnetic field. The magnetic field interacts with the current transferring momentum to the gas, which is accelerated toward the anode in the form of the characteristic cathode jet. Due to the electrical resistance of the plasma, the energy produced by the current maintains the plasma in the ionized state and provides the heating mechanism for the welding process. In modeling the system the following simplifying assumptions have been made: 1. The arc is radially symmetric and the governing equations take a two dimensional form when expressed in terms of cylindrical polar coordinates.
CATHODE
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I J_E_~\
GAS FLOW /
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~'~_B
WELD POOL
Fig. 1 - - Schematic representation of the arc and weldpool
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