A 2D model of a DC Plasma torch in comsol

October 12 – 14, 2016
A 2D Model of a DC Plasma Torch
B. Chinè
School of Materials Science and Engineering
Costa Rica Institute of Technology, Cartago, Costa Rica
bchine@itcr.ac.cr

2
COMSOL CONFERENCE 2016 MUNICH
Presentation overview
• DC plasma torch and modeling
• Simplifying assumptions and physical model
• Equations
• Boundary conditions
• Numerical results
• Conclusions

3
DC plasma torch and modeling
inflow
outflow
 Direct currents (DC) arc plasma torches represent the primary
components of thermal plasma processes (plasma spraying, metal
welding and cutting, waste treatment, biogas production, etc.).
 In a non-transferred arc plasma torch, an electric arc can be
glowed by applying a direct current (DC) between the cathode and
anode, both placed inside the torch.
 Then, the plasma is obtained by heating, ionizing and expanding a
working gas, flowing into the torch upstream of the cathode.
 Due to the cooling of the anode, the gas close to the anode surface
is cold, electrically no conductive, constricting the plasma.
gas temperature:
gas velocity:
K
10
4

s
m
10
2


rounded
cathode
tip
cathode
(-)
gas
anode
(+)
arc

4
DC plasma torch and modeling
inflow
outflow
The modeling of the DC arc plasma torches is extremely challenging:
 plasma constituted by different species (molecules, atoms, ions
and electrons)
 several coupled phenomena due to the interaction between
electric, magnetic, thermal and fluid flow fields
 highly nonlinear plasma flow, presence of strong gradients and
chemical and thermodynamic nonequilibrium effects
rounded
cathode
tip
cathode
(-)
gas
anode
(+)
arc
B
J
F x
L 
)
x
(
J B
u
E
J 


Q
Lorentz force
Joule heating

5
Simplifying assumptions and physical model
 The DC plasma torch region is 2D, the plasma flow is assumed axisymmetric and in a steady
state.
 We doesn’t consider either the formation of the electric spot on the anode surface and
the arc reattachment process on the same anode (in 2D the electric spot is annular, while the
arc reattachment is strictly a transient phenomenon).
 We assume conditions of local thermodynamic equilibrium (LTE), then the electrons and
heavy particles temperatures are equal.

6
Simplifying assumptions and physical model (cont.)
 The plasma is modeled by using the magnetohydrodynamics equations.
 The plasma is considered optically thin and a net emission coefficient is used for the heat
transferred by radiation mechanisms.
 The plasma is considered as a weak compresible gas (Mach number < 0.3).
 Free vortex flow is set at the inlet.
 The working gas is argon, copper is the material both of the anode and the cathode.

7
Equations: electric currents, magnetic fields, heat transfer and laminar flow
The modeling of the DC arc plasma torch is implemented in
Comsol® by using the physics of the following modules:
- Plasma module (Equilibrium Discharges Interface)
- AC/DC module (Electric currents, Magnetic fields)
rounded cathode tip, argon and anode
using the vector magnetic potential A :
and the electric potential V
- Heat Transfer module (Heat transfer in fluids/solids)
cathode, argon and anode
- CFD module (Laminar flow)
argon
B
A 


anode
(+)
cathode
(-)
gas
inlet
outlet
cathode
tip
68
9 4
10
28
6
34.5
4
5
r (mm)
z (mm)
z (mm)
V


E

8
Equations: multiphysics couplings
Moreover, the coupling phenomena of the plasma flow in the DC torch
are represented by setting in Comsol ® :
- plasma heat source (electric  heat)
- static current density component (electric  magnetic)
- induction current density (magnetic  electric)
- Lorentz forces (magnetic  fluid flow)
- boundary plasma heat source (rounded cathode tip) (electric  heat)
- boundary plasma heat source (anode) (electric  heat)
- temperature couplings
(heat  electric, heat  magnetic, heat  fluid flow)
anode
(+)
cathode
(-)
gas
inlet
outlet
cathode
tip
68
9 4
10
28
6
34.5
4
5
r (mm)
z (mm)
z (mm)

9
Boundary conditions
Electric currents
• constant current density of -107 A/m2 used on the rounded
cathode tip, where the temperature is set to a value
of 3500 K (thermionic emission)
• the external anode wall is grounded (electric potential = 0 V)
• axial symmetry on the z axis, the other surfaces are
electrically insulated
Magnetic fields
• magnetic potential A fulfills the condition
on the boundaries (magnetic insulation) and the axial
symmetry on the z axis;
• a gauge fixing 0 = 1 A/m field is used for a A
anode
(+)
cathode
(-)
gas
inlet
outlet
cathode
tip
68
9 4
10
28
6
34.5
4
5
r (mm)
z (mm)
z (mm)
0

 A
n
0

 J
n

10
Boundary conditions (cont.)
Heat transfer
• the anode is externally cooled: h= 104 W/(m2 K),
Text= 500 K
• axial symmetry on the z axis
• the cathode tip has a temperature of 3500 K and
the temperature of argon at the inlet is 300 K
• the other surfaces are insulated
• prescribed radiosity (gray body) on the internal surfaces
Fluid flow
• free vortex flow at the inlet v =k1 /r
k1 is varied : 81x10(-3) m2/s, 67.5x10(-3) m2/s, 54x10(-3) m2/s
vz = 4m/s, vr = 0 ( 0.175x10(-2) kg/s of argon)
• no slip on the walls
• pressure is set to 0 at the outlet
anode
(+)
cathode
(-)
gas
inlet
outlet
cathode
tip
68
9 4
10
28
6
34.5
4
5
r (mm)
z (mm)
z (mm)
0

  q
n

11
Solution with Comsol Multiphysics ®
.
z (mm)
partial view of the mesh
• meshing with nearly 7x104 triangle elements, mesh
refinement in the plasma region and close to the walls
DoFs are 9.2x105
• using a fully coupled approach, the MUMPS direct solver
is selected
• parametric sweep study of the heat source term is set in
order to improve the convergence of the computations
• computational model was run in a workstation with Intel
Xenon CPU E5-2687W v2 16 cores, 3.40 GHz (2
processors), 216 GB RAM, 64bit and Windows 7
Operative System
• solution time was approximately of 34600 s

12
Numerical results: temperature and velocity magnitude
arc column of argon gas, heated, ionized and
expanded by the Joule heating
velocity distribution resulting from both the gas expansion
and acceleration, the latter one due to the Lorentz force
)
x
(
J B
u
E
J 


Q
)
x
(
J B
u
E
J 


Q B
J
F x
L 

13
Numerical results: Lorentz forces in the plasma torch
B
J
F x
L 

14
Numerical results: radial profiles of axial velocity and temperature
- z= 65.0 mm
- z= 52.5 mm
- z= 40.0 mm
- z= 65.0 mm
- z= 52.5 mm
- z= 40.0 mm
magnitude of the axial velocity increases with
increasing distance from the cathode tip
magnitude of the temperature decreases with
increasing distance from the cathode tip

15
Numerical results: variation of the temperature in the plasma torch
Dilawari et al. [12]
- z= 65.0 mm
- z= 52.5 mm
- z= 40.0 mm

16
Numerical results: variation of the axial velocity in the plasma torch
- z= 65.0 mm
- z= 52.5 mm
- z= 40.0 mm
Felipini and Pimenta [13]
with variation of the inlet swirl

17
Variation of the current density with Q, at the inner anode wall
- 10(-5)Q
- 10(-4)Q
- 10(-3)Q
- 10(-2)Q
Evolution of the current density normal to the anode wall
computed with the parametric study for the heat source
term Q;
by proportionally reducing the heat source term, which
accounts also for the Joule heating effect in the energy
conservation equation.
The maximum current density would correspond to the arc
root attachment at the inner anode walls (Deng et al., [5]).
With increasing Q the electric current moves forward.

18
Variation of the electric potential and electric displacement field with Q
10(-5)Q 10(-2)Q
Electric potential and electric displacement field for the reduced heat terms 10(-5) Q and 10(-2) Q.
Dependence of fluid-electric phenomena on the parametrized heat source term is evident.

19
Conclusions
• A DC plasma torch has been modeled and simulated by developing a 2D model of laminar
flow, heat transfer and electromagnetic fields.
• To solve the partial differential equations of electric currents and magnetic fields, both in
the gas than in the anode region, specific boundary conditions have been used.
• Lorentz forces and Joule heating effects have been modeled, coupled to the physical
model and computed.
• The numerical results of the gas temperature and axial velocity result to be quite
satisfactory.
• We foresee to develop a more complete reproduction of thermal and fluid phenomena in
a 3D model, but computational requirements and computing times should be also taken
into account.

20
References
[1] M. I . Boulos, P. Fauchais, and E. Pfender, Thermal Plasmas: Fundamentals and Applications, Plenum Press,
New York, (1994).
[2] J.P. Trelles, C. Chazelas, A. Vardelle, and J.V.R. Heberlein, Arc plasm torch modeling, Journal of Thermal Spray
Technology, 18, No. 5/6, 728-752, (2009).
[3] He-Ping Li, E. Pfender and Xi Chen, Application of Steenbeck’s minimum principle for three dimensional
modelling of DC arc plasma torches, Journal of Physics D: Applied Physics, 36, 1084-1096, (2003).
[4] B. Selvan, K. Ramachandran, K.P. Sreekumar, T.K. Thiyagarajan and P.V. Ananthapadmanabhan, Numerical and
experimental studies on DC plasma spray torch, Vacuum, 84, 442-452, (2010).
[5] Deng Jing, Li Yahojian, Xu Yongxiang and Sheng Hongzhi, Numerical simulation of fluid flow and heat transfer in
a DC non-transferred arc plasm torch operating under laminar and turbulent conditions, Plasma Science and
Technology, 13, vol. 2, 201-207, (2011).
[6] N.Y. Mendoza Gonzalez, L. Rao, P. Carabin, A. Kaldas and J.L. Meunier, A three-dimensional model of a DC
thermal plasma torch for waste treatment applications, International Symposium on Plasma Chemistry ISPC-19,
July 27-31, 2009, Bochum, Germany.
[7] B. Chiné, M. Mata, I. Vargas, Modeling a DC plasma with Comsol Multiphysics, Comsol Conference 2015,
October 14-16 2015, Grenoble, France.
[8] Comsol AB, Comsol Multiphysics-CFD Module, User’s Guide, Version 5.1, (2015).
[9] Comsol AB, Comsol Multiphysics-Heat Transfer Module, User’s Guide, Version 5.1, (2015).
[10] Comsol AB, Comsol Multiphysics-AC/DC Module, User’s Guide, Version 5.1, (2015).
[11] Comsol AB, Comsol Multiphysics-Plasma Module, User’s Guide, Version 5.1, (2015).
[12] A. H. Dilawari, J. Szekely and R. Westhoff, An assessment of the heat and fluid flow phenomena inside plasma
torches in non-transferred arc systems, ISIJ International, 30, 381-389, (1990).
[13] C.L. Felipini and M.M. Pimenta, Some numerical simulation results of swirling flow in d.c. plasma torch, 15th
Latin American Workshop on Plasma Physics, Journal of Physics: Conferences Series, 591, 01238, (2015).

21
Acknowledgements
Many thanks for your attention !
We would like to also acknowledge:
Vicerrectoría de Investigación y Extensión

A 2D model of a DC Plasma torch in comsol

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