**TRANSACTION PAPER**

**Mathematical and computational modelling of the dynamic behaviour of direct current plasma arcs**

**Q.G. Reynolds ^{I}; R.T. Jones^{I}; B.D. Reddy^{II}**

^{I}Mintek, Randburg, South Africa ^{II}CERECAM, University of Cape Town, Rondebosch, South Africa

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**SYNOPSIS**

The problem of direct-current plasma arc behaviour, interaction, and dynamics is considered in the context of metallurgical DC arc furnace applications. Particular attention is paid to the transient flow behaviour of arc systems. A mathematical formulation of the physics used to describe the arc system is presented, and includes the spatial and temporal evolution of fluid flow, heat transfer, and electromagnetism. Based on this formulation, a numerical model is developed using a finite difference approach on a regular cartesian grid in both two and three dimensions, with a special focus on robust stability, high resolution modelling, and high performance. A collection of results produced using the numerical model to study pilot plant-scale furnaces is then presented. These address a range of process and design variables and their effect on the numerical model's results. Where possible, the qualitative behaviour of the model is compared to available experimental data. A number of novel effects and phenomena are seen in the dynamic behaviour of the DC plasma arc model for both single and multiple arc systems, which may lead to improved understanding, control, and manipulation of such systems where they occur in industrial applications.

**Keywords:** Pyrometallurgy, direct-current furnace, plasma arc, modelling

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