On the calculation of the free surface temperature of gas-tungsten-arc weld pools from first principles: Part II. modeli
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I.
INTRODUCTION
IN Part I tn we presented computed results describing the velocity and the temperature fields in welding arcs, together with the heat and current flux that fails on the weld pool surface. Indeed, the calculation of this heat and current flux was the principal objective of this work. In Part II, we shall examine the behavior of the weld pool, which receives the energy and current flux from the welding arc, which has been described in Part I. III This treatment is thought to be more satisfactory than that described in earlier publications by the authors t21 and others, t3-71 because in the present case, we can represent the interaction between the welding arc and the weld pool, rather than specifying the boundary conditions for the energy and the current flux independently, as has been done in the past. As a result of previous weld pool modeling efforts, t2-7] it has been established that weld pool circulation, and hence, heat transfer in weld pools, is governed by electromagnetic forces, by buoyancy forces, by arc drag, and also by thermocapillary forces--the latter being dominant in most cases. Since thermocapillary motion is essentially driven by the temperature gradients at the free surface of the weld pool, the precise knowledge of this temperature profile is critical. In the calculations to be presented in the following, we shall be able to address this problem meaningfully, by carefully calculating both the heat flux falling on the free surface (through the solution of the previously developed arc equations) and the heat loss by vaporization. Furthermore, in computing the thermocapillary forces, use will be made of the most recently developed relationships. R.T.C. CHOO, Research Associate, is with the Department of Metallurgy and Materials Science, University of Toronto, Toronto, ON M5S 1A4, Canada. J. SZEKELY, Professor, is with the Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139. S.A. DAVID, Group Leader, is with the Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37381. Manuscript submitted June 10, 1991. METALLURGICAL TRANSACTIONS B
In Section II, we shall present the mathematical formulation, while the computed results will be presented in Section III; these latter will include a critical comparison with measurements. The discussion is contained in Section IV.
II. M A T H E M A T I C A L FORMULATION OF THE WELD POOL The gas tungsten arc welding (GTAW) process is shown schematically in Figure 1. The arc is struck between the electrode (cathode) and the workpiece (anode); thus, thermal energy is transferred to the anode, which will raise the temperature of the surface, and a molten pool develops. This pool will grow until the heat input equals the heat loss by radiation, convection, conduction, and vaporization. The recirculating flow field in the pool is driven by a combination of buoyancy, Lorentz (J • B), and surface tension forces. The complex transport phenomena that occur in the system are summar
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