22nd International Symposium on Plasma Chemistry
July 5-10, 2015; Antwerp, Belgium
Effects of electrode sheath/boundary layer on the characteristics of an
atmospheric free-burning argon arc
H. Guo1, W. Zhou2, Z.-Y. Li2 and H.-P. Li1
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2
Department of Engineering Physics, Tsinghua University, 100084 Beijing, P. R. China
Key Laboratory of Thermal Fluid Science and Engineering, Ministry of Education, Xi’an Jiaotong University, 710049
Xi’an, P. R. China
Abstract: Interaction between plasmas and electrodes play a significant role for producing
and sustaining arc discharges. In this paper, a self-consistent five-region
physical-mathematical model, including the cathode and anode solid bodies, the cathode
sheath, the arc column and the anode boundary layer, is proposed to investigate the
plasma-electrode interaction processes. This newly developed model is used to study the
characteristics of a free-burning argon arc with a cylindrical tungsten cathode and copper
anode at an arc current of 50 A. The modeling results show that the plasma-electrode
interactions have a significant influence on the features of the arc plasmas.
Keywords: Thermal plasma, arc-electrode interaction, modelling
1. Introduction
Large-scale industrial applications of thermal plasma
technologies have promoted both theoretical and
experimental research on the complicated physical and
chemical processes in a plasma system with a wide arc
current range (e.g., from 10 A to 1000 A) and using
different types of plasma generators (e.g., the free-burning
arc, non-transferred arc, water-cooled wall constricted
transferred arc, multi-cathode arc, etc.) in the past few
decades. These efforts enhance our understanding, as well
as our controllability, to the thermal plasma sources.
Previous results indicated that the arc-electrode
interactions play a significant role for producing and
sustaining the arc discharges. The sheath/boundary layer
regions between the electrode solid body and the arc
column always have an extremely small spatial scale in
which large parameter gradients of the plasmas exist and
the plasma usually deviates from local thermodynamic
equilibrium (LTE) and/or local chemical equilibrium
(LCE) states and charge neutrality condition.
Up to now, many papers have been published to study
the electrode-plasma interactions. For example, there are
three kinds of models to describe the plasma-cathode
interactions as summarized in Ref. [1]; while for the
anode boundary layer, numerous experimental and
numerical studies were also conducted to reveal the
influences of the arc attachment on the current and heat
flux distributions along the anode surface [2]. One of the
key problems, in our opinion, for developing the
plasma-electrode interaction models is to properly
describe the flux conservations, including the number,
heat, and current fluxes, at the electrode-plasma interface.
And up to now, a complete numerical model for an arc
plasma system is still seldom. So, the goal of this paper is
to develop a self-consistent physical-mathematical model
to describe both the cathode- and anode-plasma
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interactions in an atmospheric free-burning argon arc
plasma system, and to investigate the influences of the
electrode sheath/boundary layer on the characteristics of
the arc plasmas.
2. Model Descriptions
Based on previous studies, a five-region self-consistent
model is proposed, as shown in Fig. 1, which includes: a
two-dimensional (2-D) heat and electric conduction model
for the cathode and anode solid bodies, a one-dimensional
(1-D) collisionless cathode sheath with pre-sheath model, a
2-D local thermodynamic equilibrium (LTE) arc column
model, and a 1-D anode boundary layer model. The anode
sheath is not considered in the present model since it was
reported that the very thin anode sheath had a negligible
influence on the arc behavior [3]. The thickness of the
anode boundary layer is on the order of 0.1 mm which is
much larger than the particle mean free path length, and
thus, a fluid model is used to characterize the steep
gradients of plasma parameters [4]. The cathode sheath
model is mainly contributed by Benilov et al. [5] to
describe four kinds of charged particle fluxes, i.e., the
thermionic electron emission flux, back diffusion electron
flux, ion flux and secondary emission electron flux, and to
define the current and heat flux density in the cathode
sheath region. Details on the governing equations and
boundary conditions can be referred to Refs. [1, 3, 5].
3. Modeling Results and Discussions
The calculation domain used in this study is OABCO as
indicated in Fig. 2. The diameter and length of the
tungsten cathode are 2.0 mm and 10.0 mm, while the
thickness and radius of the copper anode are 5.0 mm and
30.0 mm, respectively. Distance from the cathode tip to
the anode inner surface is 10.0 mm. The atmospheric
free-burning argon arc operates at 50 A.
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plasma-electrode interaction process has a significant
influence on the features of the arc plasmas.
5. Acknowledgment.
This work has been supported by the National Natural
Science Foundation of China (11035005).
Fig. 1.
Schematic of the self-consistent model.
Fig. 2.
6. References:
[1] J.J. Gonzalez, F. Cayla and P. Freton. J. Phys. D:
Appl. Phys., 42, 145204 (2009)
[2] J. Heberlein, J. Mentel and E. Pfender. J. Phys. D:
Appl. Phys., 43, 023001 (2010)
[3] M. Cao, P. Proulx, M.I. Boulos and J. Mostaghimi,
J. Appl. Phys., 76, 7757 (1994)
[4] H.A. Dinulescu and E. Pfender, J. Appl. Phys., 51,
3149 (1980)
[5] M.S. Benilov and A. Marotta.
J. Phys. D: Appl.
Phys., 28, 1869(1995)
[6] M.S. Benilov, L.G. Benilova, H.-P. Li and G.-Q.Wu.
J. Phys. D: Appl. Phys., 45, 355201 (2012)
Schematic of the calculation domain.
The potential drops near the electrode surfaces are very
important to determine the current-voltage characteristics
of the arc plasmas. The calculated cathode sheath voltage
drops vary along the cathode surface from 10 V to 15 V;
while the voltage drop across the anode boundary layer is
about -2.0 V because of the ambipolar diffusion effect
resulting from a much larger electron mobility compared
with that of ions. The calculated electric potential profile
along the arc axis is presented in Fig. 3 with a total arc
voltage of 18.3 V, which is larger than that (14.0 V)
predicted in Ref. [6]. The reason leading to this
discrepancy needs to be studied in future work.
Fig. 3.
Potential profiles along the axis.
4. Concluding Remarks
In this paper, a self-consistent five-region
physical-mathematical model is proposed, and is also
employed to predict the heat transfer and flow patterns of
an atmospheric free-burning argon arc. The modeling
results on the temperature, velocity, current density
distributions and arc voltages are also compared with the
previously published data. It is indicated that the
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