A Mathematical Representation of Transport Phenomena Inside a Plasma Torch
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A MATHEMATICAL REPRESENTATION OF TRANSPORT PHENOMENA INSIDE A PLASMA TORCH R. Westhoff, A. H. Dilawari, and J. Szekely Department of Materials Science and Engineering Massachusetts Institute of Technology, Cambridge, MA. 02139 ABSTRACT A mathematical representation is developed to describe heat and fluid flow phenomena inside the plasma torch for a non-transferred arc system. In the model a joule heating pattern is postulated for the arc column and then the heat flow and fluid flow equations are solved rigorously. The resultant solutions give information on the temperature and the velocity fields in the plasma gas inside and outside the torch. By postulating "reasonable" values for the heat generation pattern, very good agreement has been obtained between measurements and predictions for a laminar system, used by the INEL researchers. The agreement was less satisfactory with measurements obtained using a Metco torch, where the flow was turbulent. These findings indicate that this is a promising avenue for research, but a great deal more needs to be done before a model of general validity can be developed. INTRODUCTION In recent years a great deal of work has been done on the modelling of plasma systems. However, most of these efforts focussed on the plume(1- 14 ), which in turn required that assumptions be made about the velocity and temperature profiles of the gas exiting the torch. Work by the present authors(15) has shown that the computed results for the plume may be very markedly affected by these assumptions. It follows that it would be highly desirable to predict, on a fundamental basis, the parameters that characterize the gas exiting the torch. This is the ultimate purpose of the work to be described in the following. DESCRIPTION OF THE PHENOMENA AND THE MODEL Fig. 1 shows a schematic sketch of the non-transferred arc plasma torch. The arc which is struck between the cathode and anode heats, ionizes and accelerates the gas which is introduced upstream (often with a swirl component for arc stabilization). The ionized gas or plasma exits the torch, forming the plasma plume. A complete description of the phenomena inside the torch would require the solution of a complex set of coupled partial differential equations which govern fluid and heat flow, turbulence, electromagnetic phenomena, and species conservation. The approach taken here was to simplify the problem by neglecting the electromagnetic effects namely: current flow, magnetic field and the JXB or Lorentz forces. The remaining equations are the continuity equation, the axial and radial momentum equations, the equations for turbulent kinetic energy and turbulent energy dissipation, the heat equation and the species balance. To approximate the effects of the arc, the joule heating was estimated from the total power level, discounting the electrical energy carried by the arc, which was estimated from the total electronic heat flux at the anode. This heat was included in the energy equation as a constant heat density source term within the region of an id
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