22nd International Symposium on Plasma Chemistry
July 5-10, 2015; Antwerp, Belgium
Numerical study on the gliding behaviour of a DC argon arc root along the
electrode surface under gas blast and externally applied magnetic field
W. Wang1,2 and A. Bogaerts1
1
2
Research Group PLASMANT, Department of Chemistry, University of Antwerp, 2610 Antwerpen-Wilrijk, Belgium
Qian Xuesen Laboratory of Space Technology, China Academy of Space Technology, No.104 Youyi Road, CN-100094
Beijing, P.R. China
Abstract: This paper focuses on the numerical investigation of the gliding behaviour of a
DC argon arc under gas blast and externally applied magnetic field. A three-dimensional
simulation model of an argon arc generated between two diverging electrodes is built,
based on magneto-hydro-dynamic (MHD) theory. Besides the coupled electromagnetic and
gas dynamic interactions, the arc motion is described in detail by the temperature
distribution, and its gliding mechanism along the electrode surface, under the gas blast and
externally applied magnetic field, is discussed.
Keywords: numerical investigation, arc simulation, arc root, low voltage, applied
magnetic field
1. Introduction
A GlidArc is an auto-oscillating periodic discharge
between at least two diverging electrodes with gas blast.
A plasma column connecting the electrodes is formed by
self-initiation in the upstream narrowest gap.
Subsequently, this column is dragged by the gas flow
toward the diverging downstream section. Besides the
gas blast, an externally applied magnetic field can also
provide a driving force of arc root gliding phenomena
along the electrode surface [1]. The GlidArc, which can
produce a large density of highly reactive species, has
great potential in many industrial applications, such as the
conversion of greenhouse gases (mainly CO 2 , CH 4 ) to
value-added chemicals or renewable fuels [2, 3].
However, due to the complexity of the GlidArc, i.e.,
unsteady behaviour in time and space, detailed
investigations on gliding arc behaviour are rare in the
literature.
As the GlidArc is a kind of transitional plasma from
thermal to non-thermal state and can be assumed as
equilibrium plasma at the shortest electrode separation [4],
it is meaningful to first investigate the arc gliding
behaviour along the electrode surface under equilibrium
conditions where the discharge current is usually above
1 A. Besides the GlidArc applications, the arc root
gliding phenomenon is also quite common in thermal
plasma applications such as switching devices [5].
Therefore, we here preform a numerical modelling of the
gliding behaviour of an argon arc root along the electrode
surface based on the assumption of local thermodynamic
equilibrium and we intend to provide an insight in the
gliding mechanism along the electrode surface under the
gas blast and externally applied magnetic field,
respectively.
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2. Model geometry and numerical model
2.1. Model geometry
The model geometry of the argon arc reactor between
two diverging electrodes is shown in Fig. 1. Only half of
the geometry is presented, considering the symmetry.
The cathode and anode with a thickness of 5 mm in the
x direction which are found at the left and right side of the
geometry (see figure caption). The current is fed into the
plasma from the anode and flows out from the cathode.
Fig. 1. Structure of the arc reactor (units: mm), the
symmetry plane: A 1 B 1 C 1 D 1 E 1 F 1 G 1 H 1 , the anode surface:
the
cathode
surface:
B1C1D1E1E2D2C2B2,
A 1 H 1 G 1 F 1 F 2 G 2 H 2 A 2 , gas inlet: A 1 A 2 B 2 B 1 , gas exit,
E1E2F2F1.
2.2. Hypotheses
To reduce the complexity of the simulation, a few
assumptions and simplifications are adopted as follows: (a)
The plasma is assumed as a laminar flow in a state of
local thermodynamic equilibrium (LTE). (b) The arc
1
restrike process is not included in the simulation. (c) The
electrode erosion is not considered in the model. (d) The
Eddy current in the arc and metal part is not included in
this model.
2.3. Equations
The mathematical description of the arc plasma
includes nine coupled transport equations. The laws of
the compressible gas are described by Navier–Stokes
equations considering different sources of energy
generation and loss. The magnetic flux density is
determined through calculating the magnetic vector
potential. All the equations included in the arc model can
be written in a general formulation as follows:

∂ ( rΦ )
) div(Γ Φ grad Φ ) + SΦ (1)
+ div( rΦV=
∂t
where Φ is the field variable. For each equation, Γ Φ is the
corresponding property coefficient of the arc plasma and
S Φ is the source term. The variables and parameters for
the nine second-order partial differential equations are
given in Table 1.
Table 1. Equation variables and parameters.
Equations
Mass conservation equation
Momentum conservation
equation
Φ
ΓΦ
SΦ
1
0
0
u
h
Su
v
h
Sv
w
h
Sw
Energy conservation equation
h
λ/c p
Sh
Electrical field equation
φ
σ
0
Ax
1
S Ax
Magnetic field equation
Ay
1
S Ay
Az
1
S Az
For the source terms in the above equations
 

∂p
−
+ ρ g i + ( J × B )i
Si =
∂xi
(2)
where I = u, v, w,
Sh＝σ E 2－qrad + qh
(3)
where q rad is the radiative loss, which is calculated by
Lindmayer’s empirical model [7] considering the
complexity of the arc radiation mechanism, q h is the heat
lost due to viscous dissipation, and
S Ai = − µ0 ji
The electrical field is obtained using


E = − gradφ
2
(4)
(5)
The current density is defined by


J =σE
(6)
According to Maxwell’s equation, we can obtain the
magnetic flux density from


B = ∇× A
(7)
In the above equations, r is the density, σ is the electrical
conductivity, c p is the specific heat, h is the dynamic
viscosity, λ is the thermal conductivity, µ 0 is the argon
magnetic permeability, t is time, p is pressure, φ is the
electrical potential, S i is the momentum source term (S u ,
S v , S w ), S h is the enthalpy source term, S Ai is the magnetic

potential source term, h is the enthalpy, V is the velocity
vector, u, v, w are the velocity components in the x, y, z
directions, j i are the current density components (j x , j y , j z )

and A is the magnetic vector potential.
The argon plasma physical properties (σ, r, λ, h, c p )
described above, which depend on the temperature and
pressure, are taken from the literature [8].
2.4. Boundary conditions
According to the standard method to deal with the
velocity in the computational fluid dynamics method, a
non-slip boundary condition is imposed on the
wall-plasma interfaces.
At the interfaces between the electrodes and the plasma,
the heat is transferred from the plasma to the electrodes
according to the energy transfer conservation law [7].
Thus, the temperature of the elements on each side of the
electrode-arc interface is coupled during the calculation.
The electrode surface temperature is set below the melting
temperature of the electrode material, which was set to
2500 K for copper metal in the current calculation.
The magnetic vector potential, described in Table 1, is
used to calculate the self-magnetic field produced by the
currents in the electrodes and arc column. We set the
boundary condition of the magnetic vector potential to
zero at a large distance from the arc. A current density is
imposed on the interface between the cathode and the arc
plasma by Lindmayer’s methods [9] in which the arc root
commutation is described by the “thermally driven
model” based on the electrode temperatures deduced from
a heat flux balance. In this model, Richardson’s equation
is used to define the current density at the cathode-plasma
interface, i.e., the electron current from the cathode is
assumed to be produced by thermionic emission. Thus,
the current density at this boundary is mainly dependent
on the temperature of the interface elements and the total
arc current. We take the anode–arc interface as a collector
for negative particles. Thus, a Dirichlet condition is used
to define the potential boundary condition, i.e., a zero
electrical potential is imposed on the anode-arc interface
in our simulation work.
If not specially mentioned, the inlet and exit pressure is
set as 1atm in the computation. In the symmetry plane, the
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gradients of all the physical quantities are set zero. The
calculation begins with a stationary temperature
distribution between the two electrodes without gas blast
and externally applied magnetic field. In order to
investigate the influence of gas blast on the arc gliding
behavior, we give a mass flow rate of 0.005 kg/s during
the transient computation.
The equations mentioned above are solved by the
adapted commercial code Ansys FLUENT [10], which is
based on the finite volume method.
3. Results and Discussion
Fig. 2 shows the steady temperature distribution on the
symmetry plane of an argon arc with a current of 100 A.
As we can see, the relatively low temperature of the
electrode leads to an arc column constriction near the
electrodes. Besides, the self-induced magnetic field
generated by the arc current can also contribute to the arc
column constriction by the Lorenz force. Therefore, due
to the large current density and hence the joule heating
effects, the arc column temperature near the electrodes is
relatively high.
density, is influenced more intensely by the external
magnetic field and brings a more swift movement along
the surface. Because the magnetic field can only be
effectively applied to the high temperature gas by the
Lorenz force, in which the current density passes through,
the gas below 10000 K has a low electrical conductivity
and does not move apparently. This leads to an arc tailing
phenomenon behind the arc column with temperatures of
several thousand kelvins, as clearly indicated in Fig. 3.
Its length increases as the arc column moves along the
electrodes.
Similar results were also presented in
literature [11].
Fig. 3. Transient temperature distribution of an argon arc
with a current of 100 A under an external magnetic field
B y0 = 10 mT.
Fig. 2. Steady temperature distribution of an argon arc
with a current of 100 A.
We can separately investigate the influence of
externally applied magnetic field and gas blast on the arc
gliding behaviour along the electrode surface, which is
illustrated in Figs. 3 and 4, respectively. In Fig. 3, a
10 mT magnetic field is employed in the y direction at the
starting time of 0 ms. In the initial period of 0.071 ms,
the arc gliding velocity is low and the arc does not move
apparently. After that, the arc which is driven under the
applied magnetic field glides along the electrode surface
with continuously increasing velocity and a great change
in the arc column’s shape is observed. Compared to the
anode spot, the cathode spot, which has a larger current
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Similarly, after the gas blast is imposed at the inlet plane
at the time of 0 ms, the arc gliding velocity is not
increasing until 0.009 ms when the gas blow reaches the
arc column. Compared with the conditions under the
external magnetic field, the gas blast does not bring an arc
tailing phenomenon and can easily drag the column
toward the diverging downstream section in a quite thin
shape due to the strong cooling effects. The arc plasma
near both the anode and cathode moves slowly compared
with the arc column which can easily be influenced by the
coming gas blast, especially when the arc root moves into
the diverging section of the electrodes. We can also find
that although the arc root near the anode and cathode has
almost the same moving velocity, there exists a slight
deviation. For example, the arc gliding velocity near the
anode surface is slightly larger than that near the cathode
3
surface in the initial stage of constant electrode separation.
However, after the arc root comes into the diverging
section of the electrodes, the arc root near the cathode
surface glides faster. We believe this is mainly caused by
the different boundary conditions for the electric field.
Fig. 4. Transient temperature distribution of an argon arc
with a current of 100 A under a mass flow rate of
0.005 kg/s.
electrode surface should be quite dependent on the critical
parameter of the current value and this should be carefully
treated in future modelling of low current GlidArc
behaviour.
5. Acknowledgements
This research was supported by the Marie SkłodowskaCurie Individual Fellowship.
6. References
[1] A. Fridman, A. Gutsol, S. Gangoli, Y.G. Ju and
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[2] C.S. Kalra, A.F. Gutsol and A.A. Fridman. IEEE
Trans. Plasma Sci., 33, 32 (2008)
[3] A. Indarto, D.R. Yanga, J. Choib, H. Leeb and
H.K. Song. J. Hazard. Mater., 146, 309 (2007)
[4] I.V. Kuznetsova, N.Y. Kalashnikov, A.F. Gutsol,
A.A. Fridman and L.A. Kennedy. J. Appl. Phys., 92,
4231 (2002)
[5] Y. Wu, M.Z. Rong, A.B. Murphy, et al. IEEE
Trans. Plasma Sci., 36, 2831 (2008)
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[7] F. Karetta and M. Lindmayer. IEEE Trans. Comp.
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[8] W.Z. Wang, M.Z. Rong, A.B. Murphy, et al.
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4. Conclusions
The gliding behaviour of a DC argon arc under the gas
blast and externally applied magnetic field is studied in
this paper using a 3-D MHD model based on the
assumption of local thermodynamic equilibrium. It is
found that the current density can greatly influence the
magnetic force under the condition of externally applied
magnetic field and hence an arc tailing phenomenon
occurs behind the arc column with temperatures of several
thousand kelvins. Moreover, the gas blast can drag the
column toward the diverging downstream section in a
quite thin shape due to the strong cooling effects.
A thermal arc with a relatively high current, as
considered in our current work, can strongly heat the
electrode and influence the thermionic electron emission
processes of the cathode.
Therefore, the energy
interaction between the arc and electrode should have a
great influence on the arc root current density distribution
and hence on the gliding behaviour. For a low current
GlidArc, there is no significant heating of the cathode
surface and the discharge is sustained by field electron
emission from the cathode, accompanied by the formation
of a cathode spot. Therefore, the plasma and electrode
interaction and hence the gliding behaviour along the
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