22nd International Symposium on Plasma Chemistry
July 5-10, 2015; Antwerp, Belgium
Arc fluctuation modeling in non-transferred direct current argon plasma torch
E. Safaei Ardakani and J. Mostaghimi
Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Canada
Abstract: A comprehensive three dimensional unsteady of DC argon plasma torch and
plasma jet model was solved. The arc root attachment point was calculated based on
matching experimental voltage fluctuations with arc length estimation from steady models.
Unsteady results show velocity at the torch outlet fluctuate up to 30% of maximum values
of maximum velocity. Then, to study the plasma jet and the particle heating, steady model
of plasma jet cannot predict the particle heating and we should use unsteady model to capture more accurate results.
Keywords: argon plasma torch, plasma jet, CFD simulation, arc fluctuations
1. Introduction
Plasma spray technology is widely employed by industry to apply coatings on different component to protect them from corrosion, wear and high temperature
environments. Powders are injected into a plasma jet
which is issued from a DC plasma torch. The powder is
then accelerated, heated, and subsequently melted before
impacting the substrate. Consistency of heating and acceleration of the powder primarily depends on the state
of the plasma jet, which is in turn dictated by the arc
movement within the torch. Plasma arc exhibits strong
voltage fluctuations which correspond to the movement
of the anode arc root attachment. Understanding the arc
movement within the torch and how it affects the flow
and temperature fields of the plasma jet exiting the torch
is of great importance. Prediction of the flow, temperature and electromagnetic fields within the DC plasma
torch is challenging and there is only a limited number of
investigations in the literature [1]. Figure 1 illustrates the
structure of a DC plasma torch, locations of anode and
cathode and the gas flow direction.
Fig. 1. Schematic of a SG-100 DC plasma torch
High quality coatings are crucial in good performance
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and cost saving, particularly in applications like combustors or turbine blades. In order to create a high quality
coating, appropriate combination of powder and base
materials must be produced. Then, powder particles
should be uniformly heated, and deposited onto the substrate. Consistent heating and powder acceleration primarily depends on the state of the plasma jet, which in
turn is governed by the movement of DC arc within the
torch. The movement of the anode arc root attachment
results in strong voltage fluctuations in DC arc plasma.
Understanding the arc movement within the torch and its
effects on the flow and temperature fields of the plasma
jet exiting the torch is of great importance.
The study that covers aforementioned topics is extremely challenging and there are only a limited number
of investigations reported in the literature (e.g. [2]).
Trelles et al. create a 3D unsteady model of the arc, and
studied the arc attachment dynamics. They reported that
there is a balance between drag force and Lorentz force.
Drag force and Lorentz force are two of the most important parameters in arc stability. There are three modes
in DC arc plasma that form arc attachment dynamics: (i)
steady mode, (ii) retaken mode and (iii) random model
[3,4].
Producing a good estimation of arc root attachment
point is very important because: (i) The main erosion
occurs at the attachment point, making this point of torch
susceptible to early thermal fatigue, failure, or meltdown,
therefore, this point should be reinforced when being
manufactured. (ii) The consistency of the location of root
attachment point helps keeping the flow uniform and
hence producing consistent and high quality coating [7].
In this study, we investigated the fluctuations of arc
root attachment point in a 3D numerical model of
SG-100 non-transferred DC argon plasma torch and also
the effects of arc instability on plasma jet instability. The
arc root attachment moving inside the torch generate
instability in temperature, velocity, and turbulent param-
1
eters of plasma jet which can affect heating of particles.
We find the result that best matches the experiment results.
current density and magnetic field. Finally, we can calculate the source terms in the momentum and energy
equations, i.e., Lorentz force and Joule heating.
2. Governing equations
In the present study, we solved the continuity, momentum and energy equations, as described below:
Continuity:
3. Modeling
In this model, plasma is considered continuum and optically thin. To model turbulence, we use k − ϵ turbulence model. Plasma is considered to be in local thermodynamics equilibrium (LTE).
A 3D model of SG-100 [6] non-transferred DC argon
plasma torch was created in ICEM [8] with 800,000 cells
and also an extended domain (for plasma jet) was created
with 600,000 cells. Implementing a few User Defined
Functions (UDF) in ANSYS FLUENT [9] commercial
software, we solved electric potential and magnetic vector potential equations besides of mass, momentums and
energy equations. Boundary conditions were set as mentioned in Table 1.
(1)
∂ρ
�⃗) = 0
+ ∇. (ρV
∂t
Momentum:
�⃗
∂V
2
�⃗� = −∇ �P + µ∇. �V⃗�
ρ � + �V⃗. ∇V
∂t
3
Energy:
(2)
⃡� + ⃗ȷ × B
�⃗
+ 2∇. �µS
∂T
DP
j2
ρcp � + �V⃗. ∇T� = ∇. (κ∇T) +
−R+
∂t
Dt
σ
Table 1. Boundary conditions.
Inlet
(3)
�⃗,c p , T, κ, R, P, ⃡
where ρ, �V⃗, µ, ⃗ȷ, B
S are density, velocity,
viscosity, current density, magnetic field, specific heat,
temperature, heat transfer conductivity, radiation source,
pressure, and shear stress tensor, respectively.
To predict magnetic and electric fields, we need to
solve electric potential and magnetic vector field in three
dimensions. The electromagnetic equations of the flow
under study are described below:
∇. (σ∇ϕ) = 0
�⃗ = −µ0⃗ȷ
∇2 A
�⃗
∂A
𝐸�⃗ = −∇ϕ −
∂t
�⃗
�⃗ = ∇ × A
B
⃗ȷ = σ𝐸�⃗
(4)
(5)
(6)
(7)
(8)
�⃗, µ0 , E
�⃗ and B
�⃗ are electric potential, elecwhere ϕ, σ, A
trical conductivity, magnetic vector potential, permeability of free space, electric field and magnetic field, respectively. ⃗ȷ × �B⃗ is the Lorentz force and J2/σ is the Joule
heating term.
In this study, we solve electric potential and magnetic
vector potential equations (equations 4 and 5) in addition
to the energy and momentum equations. Then, using
Equations 6, 7 and 8, we can calculate electrical field,
2
P
Outlet
Pin
𝜕P/𝜕n=0
𝜕T/𝜕n=0
T(r)
j(r)
𝑄 = ℎ(T − 𝑇𝑤 )
0
�⃗/𝜕n=0
𝜕A
�⃗/𝜕n=0
𝜕A
T
ṁ in
300
�⃗/𝜕n=0
𝜕V
ϕ
𝜕ϕ/𝜕n=0
𝜕ϕ/𝜕n=0
0
Anode
𝜕P/𝜕n=0
101325
�V⃗
�A⃗
Cathode
0
0
0, 𝜕ϕ/𝜕n=0
For the electric current and temperature boundary conditions on the cathode, equations 9 and 10 are used, respectively [4].
r 4
j(r) = j0 exp(− � � )
rc
r 4
T(r) = 300 + 3200exp[− � � ]
2rc
(9)
( 10 )
For the thermal boundary conditions at the anode, the
cooling water is modeled as convective heat transfer with
h=100000 W/Km2 , Tw = 300K (similar to former research [3, 6, 7]). r c in equations 9 and 10 is assumed to
be 0.913 mm (similar to former research [4]).
4. Results and discussion
Unsteady case with moving arc root attachment point
was solved to find the effects of arc fluctuations on temperature and velocity of plasma jet. The electric current is
500 A and the inlet flow rate is 70 Standard Liter per
Minute (slpm) Argon. Table 2 shows results from experiment where η is torch efficiency.
Table 2. Values of measured parameters in steady
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state model
Voltage
Power
Water Flow
Water
Cooling
η
(V)
(kW)
(slpm)
ΔT(℃)
Power(kW)
(%)
42
21.4
29.1
6
12.2
42.9
Several steady cases with different arc radii and
lengths were solved. Results compared with experimental
voltage fluctuations and also torch efficiency to find the
matched arc root attachment radius and the range of arc
length. Later, by using voltage drop fluctuations extracted from the experiment, arc root attachment position in
time is estimated and the numerical model was solved to
investigate the effects of arc fluctuation on the plasma
leaving the torch.
Figure 2 shows temperature at the
outlet on the centerline of the torch versus time. Results
show the temperature fluctuates at torch outlet where
particles release. The temperature fluctuation can decrease uniformity of particle heating.
Fig. 2. Temperature at the outlet on the centreline of torch.
As expected, due to arc moving inside the torch velocity at the torch outlet also fluctuates. The temperature
fluctuate between 870 to 1220 m/s which causes particles
experience different gas velocity at different position and
time. Velocity is more sensitive compare to temperature
when arc fluctuates.
Figures 4 and 5 show temperature and velocity contours for different distances from cathode respectively.
Results show temperature and velocity dramatically increase close to the arc root. Also, as shown in Figures 4
and 5, when the distance from cathode increases, the velocity and temperature profiles show a tendency to remain uniform. The outlet velocity profile is observed to
be more uniform than the temperature profile.
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Fig. 3. Velocity at the outlet on the centreline of torch.
Due to mixing of hot and cold jet streams and radiation
maximum temperature decreases by increasing distance
from cathode. Since velocity depends on density, the
change in velocity profile is slower and smoother.
Therefore, we expect to have maximum velocity close to
the torch outlet.
Figure 4 shows contours of velocity along the torch.
The higher velocity region (where V > 800 m/s) is
slightly shifted towards the downstream of the torch. The
outlet velocity profile is observed to be more uniform
than the temperature profile. Due to diffusion, maximum
temperature decreases by increasing distance from cathode. Since velocity depends on density, the change in
velocity profile is slower and smoother. Therefore, we
expect to have maximum velocity close to the torch outlet.
Contours of temperature inside the torch are plotted in
Figure 5. Maximum temperature for these operating conditions is 32000 K and it occurs close to where density
current is maximum. This region is where heat generation is maximum. Due to Lorentz force effects, the
maximum temperature occurs close to cathode and not
exactly in the center. This can be explained considering
the fact that the maximum temperature occurs where
thermal energy due to Joule heating is maximum. Joule
heating is influenced by two parameters: i) electrical
conductivity, and ii) the magnitude of electric field. The
electrical conductivity of the fluid is small on the wall,
while the magnitude of electric field is stronger. Therefore, the maximum of Joule heating occurs at the point
where the product of electrical conductivity times the
square of electric field intensity is a maximum, close to
cathode.
3
Fig. 4. Velocity contours on at various distances from
torch inlet at t=1500 µs.
5. References
[1] Fauchais P, Vardelle A and Dussoubs B, J. Thermal
Spray Technol. 10(2001).
[2] P. Fauchais, J.F. Coudert and M. Vardelle, J. High
Temp.Mater. Process. 6(2002).
[3] J.P. Trelles and J.V.R. Heberlein, J. Thermal Spray
Technology, 15(4) ( 2006).
[4] J.P. Trelles, E. Pfender and J.V.R. Heberlein, J. Phys.
D: Appl. Phys. 40 (2007).
[5] J.P. Trelles, E. Pfender and J.V.R. Heberlein, J. IEEE
Transactions on Plasma Science 36 (2008).
[6] R. Huang, H. Fukanuma, Y. Uesugi, and Y. Tanaka, J.
IEEE Transactions on Plasma Science, 39(2011).
[7] B. Selvan, K. Ramachandran, K.P. Sreekumar, T.K.
Thiyagarajan, P.V. Ananthapadmanabhan, Vacuum
84 (2010).
[8] ANSYS Inc., ANSYS ICEM CFD meshing software,
http://www.ansys.com/Products/Other+Products/AN
SYS+ICEM+CFD
[9] ANSYS
Inc.,
ANSYS
Fluent
software,
http://www.ansys.com/Products/Simulation+Technol
ogy/Fluid+Dynamics/Fluid+Dynamics+Products/AN
SYS+Fluent
Fig. 5. Temperature contour at various distances from
torch inlet at t=1500 µs.
Due to the radiation losses, and heat losses to the wall
plasma temperature decreases downstream of the arc root
region. Heat transfer between wall and flow and mixing
in flow result in a more uniform temperature profile as
we move downstream.
In summary, these results are in good agreement with
experiment. The arc root attachment point fluctuations
can affect plasma jet and particle heating.
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