B. Bauer et al- Magnetized High Energy Density Laboratory Plasmas
Numerical Modelling of a Free -Burning Arc in Argon A Tool ......thermal plasmas. with: • High...
Transcript of Numerical Modelling of a Free -Burning Arc in Argon A Tool ......thermal plasmas. with: • High...
COMSOL Conference 2009, october 14-16, Milan
Numerical Modelling of a Free-Burning Arc in Argon
A Tool for Understanding the Optical Mirage Effectin a TIG Welding Device
J.M. Bauchire, E. Langlois-Bertrand, C. de Izarra
GREMI, UMR 6606 CNRS/Université d’Orléans, France
Presented at the COMSOL Conference 2009 Milan
COMSOL Conference 2009, october 14-16, Milan
INTRODUCTION – Electric Arc & TIG Welding Device
Electric arcs at atmospheric pressure are thermal plasmas with:
• High energy density
• High temperature
• High light emissivity
• High electric current intensity
Point-to-plane discharge configuration, “free-
burning arc”, nearly TIG welding device
configuration
Standard diagnostic of electric arcs: emission spectroscopy
INTRODUCTION – Experimental Observation
Rays of light, emitted from the cathode tip, are bent when passing through the plasma. Optical mirage effect...?
Numerical modelling of the electric arc + ray-tracing...
As lens is shifted upward, cathode tip is still visible, whereas the lens optical axis is above the nozzle exit...!
COMSOL Conference 2009, october 14-16, Milan
FREE-BURNING ARC SIMULATION – General Assumptions
COMSOL Conference 2009, october 14-16, Milan
Axisymmetry 2D (r,z) simulation
Flow Laminar and steady-state
Inlet and surrounding gases Argon at atmospheric pressure
Temperature Local thermodynamic equilibrium
Radiative losses Net emission coefficient method
Gravity effect Not taken into account
Electrode erosion, electrode sheath Not taken into account
Electric current DC
FREE-BURNING ARC SIMULATION –Model & COMSOL Application Modes
COMSOL Conference 2009, october 14-16, Milan
JA
0V
0
µ∆
σ
=
=∇⋅∇
BJ
×
Laminar Non-Isothermal Flow
Weakly Compressible Navier-Stokes
Meridional Induction and Electric Currents, Potentials
General Heat Transfer radUEJ −⋅
AB
VJ
VE
×∇=
∇=
∇−=
σ
Explicit coupling
Temperature (K)
Mas
s de
nsity
(kg.
m-3
)
Visc
osity
(kg.
m-1
. s-1
)Temperature (K)
FREE-BURNING ARC SIMULATION – Input data
COMSOL Conference 2009, october 14-16, Milan
Thermodynamic properties & transport coefficients depend on temperature
COMSOL Conference 2009, october 14-16, Milan
Temperature (K)Temperature (K)
Ther
mal
con
duct
ivity
(W.m
-1.K
-1)
Elec
tric
con
duct
ivity
(A.V
-1. m
-1)
FREE-BURNING ARC SIMULATION – Input data
Implicit coupling
FREE-BURNING ARC SIMULATION – Calculation Domain & Boundary Conditions
COMSOL Conference 2009, october 14-16, Milan
Flat electrode (20 mm)Grounded electrodeInsulation or T profile
Computation domain
Flow inlet (0.5 m/s, 300 K)
Noz
zle
Poin
ted
elec
trod
eAx
is(6
mm
)
Open Boundary
(300 K)
2.5 mm
(15
mm
)T pr
ofile
T pr
ofile10
00 K
Cathode tipCurrent density
I = 100 A
Mesh points = 67 937
Triangular elements= 134 655
Degrees of freedom= 2 096 423
Solver = PARDISO
stationary
COMSOL Conference 2009, october 14-16, Milan
FREE-BURNING ARC SIMULATION – Results
Electric potential (V) Velocity (m/s)
Good agreement with:• Experimental results• Previous simulations based on finite volume method
FREE-BURNING ARC SIMULATION – Results
COMSOL Conference 2009, october 14-16, Milan
Temperature (K) Temperature (K)
Anode boundary condition: Insulation Anode boundary condition: T profile
Only weak influence on temperature field in cathode and nozzle exit regions
COMSOL Conference 2009, october 14-16, Milan
FREE-BURNING ARC SIMULATION – Results
Refractive index & index gradients (streamlines)
Anode boundary condition: Insulation
Anode boundary condition: T profile
λ = 632.8 nm
• Validation of refractive index gradients• Mainly for “low” temperatures• Nozzle region
Ray-tracing
COMSOL Conference 2009, october 14-16, Milan
RAY-TRACING – Theory
( ) ( )nundsd
∇=
=
=
θ
θ
cosndl
dz
sinndldr
00
00
The ray path in a non homogeneous zone can be calculated with vectorial formulation of Snell-Descartes laws:
• ds is the curvilinear abscissa
• the unit vector tangent at any point in the trajectory of the light
• n the refractive index
u
This equation system is solved with Euler method
If the ray of light comes from a point M0(r0,z0) with a θ angle between the cathode axisand the ray propagation direction at M0 point, we obtained:
COMSOL Conference 2009, october 14-16, Milan
RAY-TRACING – Results
COMSOL Conference 2009, october 14-16, Milan
CONCLUSION
Demonstration of COMSOL Multiphysics capability to simulate arc discharges
Still remain difficulties to reach convergence according to boundary condition type (Dirichlet’s)
Success in exporting and post-processing results (for ray-tracing)
Further works on this subject to improve model and to take into account the electrodes