Manuscript received 30 October 2007; revised XX-XXXX-XXXX. J. P. Trelles, E. Pfender, and J. V. R. Heberlein are with the University of Minnesota, Department of Mechanical Engineering, 111 Church St. SE, Minneapolis, MN 55455 (email: jptrelles@me.umn.edu). Publisher Identifier S XXXX-XXXXXXX-X

The Reattachment Process in Non-Equilibrium Arc Simulations

J. P. Trelles, J. V. R. Heberlein, and E. Pfender Abstract - The reattachment process is an essential part of the dynamics of thermal plasma flows. Simulations of the flow inside a direct-current arc plasma torch performed with a two-temperature model produce a reattachment process triggered by local flow instabilities and driven by local high electric fields and electron temperatures. These results indicate that an arc reattachment can occur not only due to a breakdown of the gas surrounding the plasma, but also due to the macroscopic characteristics of the flow, and emphasize the importance of non-local thermodynamic equilibrium-based models to properly describe arc dynamics. The reattachment process, the process by which a new electrical connection between an arc and an electrode forms, is an essential part of the dynamics of thermal plasma flows. To simulate the reattachment process as part of a thermodynamic equilibrium plasma model, “reattachment models” are typically employed [1, 2]. These models try to mimic the physical reattachment process and consist of artificially modifying the electrical configuration of the plasma (e.g. by artificially imposing an electrically conducting channel between the arc and the anode). Recent simulations of the arc dynamics inside a plasma torch performed with a two-temperature model [3] produce a reattachment process - without the use of any “reattachment model” - not observed in local thermodynamic equilibrium simulations. This reattachment is driven by local high electric fields and electron temperatures, and is triggered by local flow instabilities. This finding is significant because it points towards the possibility of a fluid-dynamically-driven reattachment process, i.e. a reattachment driven by the macroscopic characteristics of the flow and not only by microscopic charge build-up. Therefore, a reattachment could be produced by fluid dynamic instabilities, including turbulent fluctuations. This paper presents simulation results of the flow inside the same torch studied in [3], but for a lower total current (300 A) in order to observe in greater detail the characteristics of the reattachment process. The mathematical and numerical models used here are the same used in [3] and consist of a two-temperature chemical equilibrium model of argon plasma solved by a variational multi-scale finite element method. Figure 1 shows time sequences of the

distributions of heavy-particle and electron temperatures (Th and Te), and effective electric field (Ep), as well as the time evolution of the total voltage drop across the torch. The initial attachment (indicated by the arrows) cannot be observed clearly in frames 2 in the Th and Te distributions due to the smallness of the attachment root and the color scales used, but the distribution of Ep shows a significant change due to the newly formed attachment (i.e. see region surrounding the arrow tip in frame 2 of the log10(Ep) plots). Moreover, Th over the anode increases only slightly at the beginning of the attachment (i.e. from 500 K to ~ 550 K), whereas Te increases significantly (i.e. from ~ 5 kK to over 10 kK). Furthermore, the location of the new attachment can be predicted by the local growth of Te at the anode surface, as observed in frame 1 of the Te distributions. These results also show that once the new attachment is established (i.e. frame 2), the newly formed attachment moves slightly upstream (i.e. frame 3) due to a sudden growth of the electromagnetic forces due to the local curvature of the new configuration of the arc. Figure 1 has been created using Matlab® [4]. Matlab has very attractive features for plasma flow visualization, e.g. as demonstrated in [5]. Particularly, the unstructured finite element data was plotted using the patch function. Acknowledgements: A grant from the Minnesota Supercomputing Institute is gratefully acknowledged.

REFERENCES

[1] E. Moreau, C. Chazelas, G. Mariaux and A. Vardelle, “Modeling of the restrike mode operation of a dc plasma spray torch”, J. Thermal Spray Tech., vol. 15, No. 4, pp. 524-530, 2006

[2] J. P. Trelles, E. Pfender, and J. V. R. Heberlein, “Modeling of the arc reattachment process in plasma torches”, J. Phys. D: Appl. Phys., vol. 40, pp. 5937-5952, Sept. 2007

[3] J. P. Trelles, J. V. R. Heberlein and E. Pfender, “Non-equilibrium modelling of arc plasma torches”, J. Phys. D: Appl. Phys., vol. 40, pp. 5937-5952, Sept. 2007

[4] The Mathworks Inc., Natick, MA. [Online]. Available: http://www.mathworks.com

[5] X. Franceries, F. Lago, J.-J. Gonzalez, P. Freton, and M. Masquère, “3-D visualization of a 3-D free-burning arc model deflected by external magnetic or convective forces”, IEEE Trans. Plasma Sci., vol. 33, no. 2, pp. 432-433, April 2005

Fig. 1. Arc reattachment process inside an arc plasma torch; distribution of: (top row, from left to right) heavy particle temperature (Th), electron temperature (Te), and effective electric field in the radial direction (Ep, in logarithmic scale) in a 45° plane across the torch; (bottom row, from left to right) heavy particle temperature (Th) and electron temperature (Te) over the anode surface, and temporal evolution of the total voltage drop (Δφ; mean value: 26.3 V, frequency 6.2 kHz). The arrows indicate the location where a new arc attachment starts forming. Conditions: gas: Ar; flow rate: 60 slpm with 45° swirl injection; current: 300 A. The diameter of the nozzle at the outlet is 8 mm.