st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
Arc Length Estimation in Non-Transferred Direct Current Argon Plasma Torch
Using CFD Modeling and Experiment
E. Safaei Ardakani1, J. Mostaghimi2
1
PhD Student, Department of Mechanical and Industrial Engineering, University of Toronto, [email protected]
2
Professor, Department of Mechanical and Industrial Engineering, University of Toronto
Abstract: A three dimensional DC argon plasma torch model was solved for a range of arc
lengths and radii. To be able to compare the numerical results against experimental results, the
predicted voltage for each scenario was calculated from CFD results. The predicted voltages
were compared to the voltage measurements obtained from experiments, which were carried
out on a SG-100 DC torch operating at the same current and flow rate. Based on the comparison between the voltage fluctuations from experiments, and those predicted numerically, we
estimated the arc length with higher accuracy than previously employed methods.
Keywords: Arc Length, Argon Plasma Torch, CFD Simulation, Numerical Modeling
1. Introduction
Thermal plasma technology is widely employed in
thermal spray coating applications. 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. Figure 1 illustrates the structure of a DC plasma torch, locations of
anode and cathode and the gas flow direction [1].
Fig. 1. Schematic of a DC plasma torch
High quality coatings are crucial in good performance
and cost saving, particularly in applications like combus-
tors 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].
There are two approaches towards modeling the thermodynamic equilibrium in this system: (i) Local Thermodynamic Equilibrium (LTE) models, and (ii) Non Local Thermodynamic Equilibrium (Non-LTE) models.
Non-LTE models produce results with higher accuracy
close to the anode. However, setting up the model is complex and simulations are reported to be computationally
expensive [5]. Huang et al. worked on a LTE models and
suggested some improvements, their LTE model fails to
capture the arc attachment point [6]. 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
st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
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 arc root attachment
point in a 3D numerical model of SG-100 non-transferred
DC argon plasma torch. By solving electric potential and
magnetic vector potential equations for a range of arc
lengths and radii within the torch, we find the result that
best matches the experiment results.
ity of free space, electric field and magnetic field, respec�⃗ is the Lorentz force and J2/Ã is the Joule
tively. ⃗ȷ × B
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,
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:
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 is created in ICEM [8] with 800,000 cells.
Implementing a few User Defined Functions (UDF) in
ANSYS FLUENT [9] commercial software, we solved
electric potential and magnetic vector potential equations
for a range of arc lengths and radii within the torch.
Boundary conditions were set as mentioned in Table 1.
Continuity:
(1)
∂ρ
�⃗) = 0
+ ∇. (ρV
∂t
Momentum:
ρ�
�⃗
∂V
2
�⃗� = −∇ �P + µ∇. �V⃗�
+ �V⃗. ∇V
∂t
3
(2)
Table 1. Boundary conditions.
⃡� + ⃗ȷ × B
�⃗
+ 2∇. �µS
Energy:
Inlet
P
∂T
DP
j2
�⃗. ∇T� = ∇. (κ∇T) +
ρcp � + V
−R+
∂t
Dt
σ
(3)
�⃗, cp , 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
∇2�A⃗ = −µ0 ⃗ȷ
𝐸�⃗ = −∇ϕ −
�B⃗ = ∇ × �A⃗
⃗ȷ = σ𝐸�⃗
�⃗
∂A
∂t
(4)
(5)
(6)
(7)
(8)
�⃗, µ0 , E
�⃗ and B
�⃗ are electric potential, elecwhere ϕ, σ, A
trical conductivity, magnetic vector potential, permeabil-
Outlet
Pin
Cathode
𝜕P/𝜕n=0
𝜕P/𝜕n=0
𝜕T/𝜕n=0
T(r)
j(r)
𝑄 = ℎ(T − 𝑇𝑤 )
0
�⃗/𝜕n=0
𝜕A
�⃗/𝜕n=0
𝜕A
101325
�V⃗
T
ṁ in
300
�⃗/𝜕n=0
𝜕V
ϕ
𝜕ϕ/𝜕n=0
𝜕ϕ/𝜕n=0
�A⃗
0
Anode
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
T(r) = 300 + 3200exp [− �
(9)
r 4
� ]
2rc
( 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]). rc in equations 9 and 10 is assumed to be
0.913 mm (similar to former research [4]).
4. Results and discussion
Several cases with different arc lengths and radii are
solved to find the best matched case with experimental
results [7]. The electric current is 500 A and the inlet flow
st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
rate is 70 Standard Liter per Minute (slpm) Argon. Table 2
shows results from experiment where · is torch efficiency.
remain uniform. The outlet velocity profile is observed to
be more uniform than the temperature profile.
Table 2. Values of measured parameters
Voltage
Power
Water Flow
Water
Cooling
·
(V)
(kW)
(slpm)
” T(℃)
Power(kW)
(%)
42
21.4
29.1
6
12.2
42.9
Voltage Drop (V)
Voltage drop was calculated using the results from numerical simulations. Figure 2 shows voltage drop versus
arc length for different arc root radii. Voltage drop increases with respect to arc length and it decreases when
the arc radius increases. Then, the larger voltage drop is
the consequence of the larger arc length.
68
62
56
R=1.8 mm
50
R=2.0 mm
44
R=2.2 mm
38
3
6
9
12
Arc Length (mm)
Fig. 2. Effect of arc radius and length on voltage drop.
As expected, increasing the arc length increases the arc
power. Those changes in the arc length and radius can
show how power and voltage drop change by the movement of the arc root (Figure 3). Torch power increases by
increasing the arc length because of the increasing voltage.
Considering voltage drop to find the best matched numerical model, R=2.2 mm and an arc length of 5mm was
found to be in excellent agreement with measured values.
It should be mentioned that there is a fall in voltage near
electrodes due to existence of sheath layer. Due to the
complexity of modeling this layer, we did not consider the
sheath layer in our models. However, if this sheath layer
was to be modeled in similar CFD simulations, the model
will predict the results with more accuracy.
Using the results of the best matched case, we studied
different parameters such as velocity, temperature and
electrical potential fields and compared them with the
results of experiment. Figures 3 and 4 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 3 and 4, when the distance from cathode increases,
the velocity and temperature profiles show a tendency to
Power (kW)
36
32
28
R=1.8 mm
24
R=2.0 mm
R=2.2 mm
20
16
3
6
9
12
Arc Length (mm)
Fig. 3. Effect of arc radius and length on power.
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.
st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
Fig. 4. Velocity contours on at various distances from cathode
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 preliminary results are in good
agreement with experiment. The arc root attachment point
can be estimated with this method.
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).
Fig. 5. Temperature contour at various distances from cathode
[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+Prod
ucts/ANSYS+ICEM+CFD
[9] ANSYS
Inc.,
ANSYS
Fluent
software,
http://www.ansys.com/Products/Simulation+Technol
ogy/Fluid+Dynamics/Fluid+Dynamics+Products/AN
SYS+Fluent