Some numerical simulation results of the dynamic temperature distribution in dc plasma torch «Thermoplasma 50-01»

A DC plasma torch “Thermoplasma 50-01” has been modeled and simulated by developing a 2D axisymmetric model of laminar flow and heat transfer coupled to electromagnetic fields. As a result of the numerical solution, the dynamics of the formation of the temperature field and the velocity field in the plasma torch channel and at its exit is presented. The numerical results of the gas temperature and axial velocity result to be quite satisfactory.


Introduction
DC arc plasma torches have been known, studied and used for many decades. They used to generate thermal plasma jets in different industrial applications, such as thermal plasma waste treatment, atmospheric or low-pressure plasma spraying, plasma-assisted chemical vapor disposition, plasma preparation of ultra finepowder, etc [1][2][3][4][5].
At present, new plasma torches are being developed and created all over the world. In particular, modern developments is the «Thermoplasma 50-01» plasma torch, developed in Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the RAS [7][8][9][10].
One of the important tools for understanding physical processes in plasma torches is numerical modeling. In the last 10-20 years, much research has been undertaken to improve modeling of electric arcs, with the ambitious goal to be able to simulate numerically a working device, like a plasma torch [11,12].
More recently, in [13] and [14] the complete arc and jet dynamics are simulated with a thermodynamic-equilibrium-based model.
The purpose of this work is numerical simulation of the plasma jet dynamics of the «Thermoplasma 50-01» plasma torch.

Description of the Mathematical Model
The continuum assumption is valid and the plasma is considered as a compressible, perfect gas in Local Thermodynamic Equilibrium (LTE), hence characterized by a single temperature T for all its species (atoms, ions, electrons, molecules); the quasi-neutrality condition holds; the plasma is optically thin; Hall currents, gravitational effects, and viscous dissipation are considered negligible.
As the plasma is a conducting fluid, its description requires the solution of the fluid conservation and electromagnetic equations; which, according to the assumptions stated above, are given by:  The computational domain consisted of two parts: a plasma channel inside the plasma torch and a plasma jet at the output of the plasma torch.

Numerical simulation and results
In Fig. 1 shows the dynamics of the formation of the temperature field both the plasma torch channel and its output. It is seen that the temperature in the near-cathode region reaches 30000K, and in the near-anode region and at the exit of the plasma torch it is 10000-15000 K. The velocity in the near-cathode region reaches 2500 m/s and in the near-anode region and at the exit of the plasma torch it is 1000 m/s. The plasma jet is set in a time equal to 1.3-1.5 ms. Figure 1. Dynamics of the temperature field in the plasma torch "Thermoplasma 50-01" channel and its output.

Conclusions
A DC plasma torch "Thermoplasma 50-01" has been modeled and simulated by developing a 2D axisymmetric model of laminar flow and heat transfer coupled to electromagnetic fields. In order to solve the partial differential equations of electric currents and magnetic fields, both in the gas than in the anode region, we have contemplated appropriate boundary conditions in the modeling work. Lorentz forces and Joule heating effects have been modeled, coupled to the physical model of the plasma torch and finally computed. The dynamics of the formation of the temperature field and the velocity field in the plasma torch channel and at its outlet is presented. The numerical results of the gas temperature and axial velocity result to be quite satisfactory. We foresee to develop a more complete reproduction of the thermal and fluid phenomena in a future three dimensional model, which might include the modeling of other issues. In particular, in the future work, it is necessary to consider the effect of gas supply for the anode curtain.