Plasma arc welding: a mathematical model of the arc

A number of models of plasma arc welding have been constructed, including some that describe the arc itself. Relatively few rely solely on the physics of a plasma arc and the associated fluid dynamics for construction of mathematical models; for the most part they use a mixture of empirical results and basic physical principles. Models that depend on physical principles only have the advantage that they produce the kind of insight that makes them flexible enough to be applicable to situations for which they were not originally envisaged. Such an approach reduces the development time for revised models and increases confidence in modelling procedures. An example of this approach is considered here in more detail, with particular attention to the plasma arc. Information is obtained about the relative importance of radiation in the determination of plasma temperatures, and the transport of energy in the plasma jet itself. The mean temperature distribution along the length of the arc is considered using the ideas of classical thermodynamics. The fluid dynamical momentum balance of the arc is considered in some detail and it is found that these considerations play a substantial role in the determination of its shape. Two different kinds of solution are found, corresponding to the transferred arc and the non-transferred arc; the first type tend to broaden overall towards the work piece whereas the latter more closely resemble conventional flames.