Numerical simulation of Ar-x%CO2 shielding gasand its effect on an electric welding arc

Isabelle Choquet1, Håkan Nilsson2, Alireza Javidi Shirvan1, Nils Stenbacka1

1University West, Department of Engineering Science, Trollhättan, Sweden,2Chalmers University of Technology, Department of Applied Mechanics, Gothenburg, Sweden

isabelle.choquet@hv.se

ABSTRACT

This study focuses on the simulation of a plasma arc heat source in the context of elec-tric arc welding. The simulation model was implemented in the open source CFD soft-ware OpenFOAM-1.6.x, in three space dimensions, coupling thermal fluid mechanicswith electromagnetism. Two approaches were considered for calculating the magneticfield: i) the three-dimensional approach, and ii) the so-called axisymmetric approach.The electromagnetic part of the solver was tested against analytic solution for an infiniteelectric rod. Perfect agreement was obtained. The complete solver was tested againstexperimental measurements for Gas Tungsten Arc Welding (GTAW) with an axisym-metric configuration. The shielding gas was argon, and the anode and cathode weretreated as boundary conditions. The numerical solutions then depend significantly onthe approach used for calculating the magnetic field. The so-called axisymmetric ap-proach indeed neglects the radial current density component, mainly resulting in a poorestimation of the arc velocity. Plasma arc simulations were done for various Ar-x %CO2shielding gas compositions: pure argon (x =0), pure carbon dioxide (x =100), and mix-tures of these two gases with x =1 and 10% in mole. The simulation results clearlyshow that the presence of carbon dioxide results in thermal arc constriction, and in-creased maximum arc temperature and velocity. Various boundary conditions were seton the anode and cathode (using argon as shielding gas) to evaluate their influenceon the plasma arc. These conditions, difficult to measure and to estimate a priori,significantly affect the heat source simulation results. Solution of the temperature andelectromagnetic fields in the anode and cathode will thus be included in the forthcomingdevelopments.

Keywords: electric arc welding, electric heat source, thermal plasma, magnetic poten-tial, inert gas, active gas, spatial distribution of thermal energy, GTAW, TIG, WIG.

1 INTRODUCTION

Man made electric arc was first produced in 1800 bySir Humphry Davy using carbon electrodes. Electricarc welding as a method of assembling metal partsthrough fusion was however initiated much later, at theend of the 19’s century, when C.L. Coffin introducedmetal electrode and metal transfer across an arc.Thanks to intense developments in the early 1900’s,

such as the first coated electrode developed by A.P.Strohmenger and O. Kjellberg, electric arc weldingstarted being utilized in production in the 1920’s, andthen in large scale production from the 1930’s.

This manufacturing process, althought used sincemany decades, is still under intensive development,in order to further improve different aspects such asprocess productivity, process control, and weld qual-

1

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ity. Such improvements are beneficial both from eco-nomical and environmental sustainability. Electric arcwelding is interdisciplinary in nature, and complex tomaster as it involves very large temperature gradients,and a number of parameters that do interact in a non-linear way. Its investigation was long based on experi-mental studies. Today, thanks to recent and significantprogress done in the field of welding simulation, ex-periments can be complemented with numerical mod-eling to reach a deeper process understanding. Asan illustration, the change in microstructure can besimulated for a given thermal history within the heataffected zone of the base metal, as in [1]. The numer-ical calculation of the residual stresses, to investigatefatigue and distortion, can now be coupled with theweld pool as in [2], calibrating functional approxima-tions of volume and surface heat flux transferred fromthe electric arc.

Electric arcs used in welding are generally formedcoupling an electric discharge between anode andcathode with a gas flow. A main goal is to forma shielding gas flow characterized by temperatureslarge enough to melt the materials to be welded, i.e.a thermal plasma flow. The numerical modeling of athermal plasma flow is thus a base element for char-acterising the thermal history of an electric arc weldingprocess, by calculating the thermal energy provided tothe parent metal, and its spatial distribution.A thermal plasma is basically modeled coupling ther-mal fluid mechanics (governing mass, momentum andenergy or enthalpy) with electromagnetism (govern-ing the electric field, the magnetic field, and the cur-rent density). Different thermal plasma models canbe found in the literature in the context of electricarc welding simulation. They were developed to ad-dress in more detail various aspects of electric arcwelding heat source. As an illustration, a simulationmodel for axisymmetric configuration, describing con-sistently the arc core, the arc sheath (or arc/anodeand arc/cathode boundary), and the solid electrodeswas developed in [3], and applied to Gas TungstenArc Welding (GTAW). Other models account for ther-mal non-equilibrium [4], or for the influence of metalvapour on the thermodynamic and transport prop-erties of a plasma arc [5]. Coupled arc and weldpool simulation tools were recently developed for ax-isymmetric configuration [6], without considering theplasma arc sheath. At least one of these coupled arc-

pool simulation tools also account for 3-dimensionaleffects and arc dynamic behavior [7].

The numerical modeling of the thermal plasma heatsource within the frame of electric arc welding startedonly recently in Sweden. The rigorous derivation of afluid arc model was done in [8], based on kinetic the-ory. This plasma arc model was derived from a systemof Boltzmann type transport equations. A viscous hy-drodynamic/diffusion limit was obtained in two stagesdoing an Hilbert expansion and using the Chapman-Enskog method. The resultant viscous fluid modelis characterized by two temperatures, and non equi-librium ionization. It applies to the arc plasma coreand the ionization zone of the arc plasma sheath.The development of a numerical tool for simulating athermal plasma arc was initiated in [9]. The presentstudy is in the continuation of [9]. The model im-plemented in this first stage is a simplified versionof the model derived in [8], as it assumes local ther-mal equilibrium, applies to the plasma core and doesnot consider the arc plasma sheath. The implemen-tation was done in the open source CFD softwareOpenFOAM-1.6.x (www.openfoam.com), consideringthree space dimensions. OpenFOAM was distributedas OpenSource in 2004. This simulation software isa C++ library of object-oriented classes that can beused for implementing solvers for continuum mechan-ics. It includes a number of solvers for different con-tinuum mechanical problems. Due to the availabilityof the source code, its libraries can be used to im-plement new solvers for other applications. The cur-rent implementation is based on the buoyantSimple-Foam solver, which is a steady-state solver for buoy-ant, turbulent flow of compressible fluids. The par-tial differential equations of this solver are discretizedusing the finite volume method. The thermal plasmasimulation model implemented in OpenFOAM-1.6.x isdescribed in section 2. It couples a simplified sys-tem of Maxwell equations (section 2.1) with a systemof thermal Navier-Stokes equations in three space-dimensions (section 2.2). Two approaches were con-sidered for calculating the magnetic field:

i) the three-dimensional approach, andii) a so-called axisymmetric approach,

as detailed in section 2.1.The electromagnetic part of the solver was testedagainst analytic solution for an infinite electric rod. Thetest case and the results are presented in section 3.1.

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The complete solver was tested against experimen-tal measurements for GTAW available in the litera-ture. The experimental configuration was axisymmet-ric, and the shielding gas was argon. The anode andcathode were treated as boundary conditions in thesimulations. This second test case, and the relatedsimulation results, are presented in section 3.2. Foreach test case both approaches for calculating themagnetic field were used, and the validity of the simpli-fied (or so-called axisymmetric) version are discussed.Plasma arc simulations with the three dimensional ap-proach for calculating the magnetic field, were alsodone for various Ar-x %CO2 shielding gas composi-tions. The simulation results of the following fourcases are reported and discussed in section 3.3: pureargon (x =0), pure carbon dioxide (x =100), and mix-tures of these two gases with x =1 and 10% in mole.The influence of the boundary conditions (set on theanode and cathode) on the arc temperature and veloc-ity were investigated using the three dimensional ap-proach for calculating the magnetic field, and retainingargon as shielding gas. The corresponding simulationresults are presented and discussed in section 3.4.The main results and conclusions are summarised insection 4.

2 MODEL

The model described below is a first step in the de-velopment of a simulation tool for thermal plasma arcapplied to electric arc welding. In this first stage,the model describes an arc plasma core, and thusassumes local thermal equilibrium. The arc plasmasheat is not included. The implementation was donein the open source CFD software OpenFOAM-1.6.x(www.openfoam.com), considering three space di-mensions, and coupling thermal fluid mechanics withelectromagnetism. The fluid and electromagneticmodels are tightly coupled. The Lorentz force, or mag-netic pinch force, resulting from the induced magneticfield indeed acts as the main cause of plasma flow ac-celeration. The Joule heating because of the electricfield is the largest heat source governing the plasmaenergy (and thus temperature). On the other handthe system of equations governing electromagnetismis temperature dependent, via the electric conductivity.The main specificities of the implemented electromag-netic and thermal fluid model are as follow.

2.1 Electromagnetic model

The electromagnetic component of the model is de-rived from the Maxwell equations (see [9] for furtherderivation details), assuming:- a Debye length λD much smaller than the charac-teristic length of the welding arc, thus local electro-neutrality in the plasma core,- characteristic time and length of the welding arc al-lowing neglecting the convection current compared tothe conduction current in Ampere’s law, resulting inquasi-steady electromagnetic phenomena,- a Larmor frequency much smaller than the averagecollision frequency of electrons, implying a negligibleHall current compared to the conduction current, and- a magnetic Reynolds number much smaller thanunity, leading to a negligible induction current com-pared to the conduction current.Then, the electric potential V is governed by theLaplace equation,

O· [σ(T ) OV] = 0 , (1)

where T is the temperature, O denotes the gradientoperator, and O· the divergence operator. The electricconductivity σ(T ) is temperature dependent, as illus-trated in Fig.1 for an argon plasma.

Figure 1: Argon plasma electric conductivity asfunction of temperature.

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The electric field ~E, is defined from the gradient of theelectric potential,

~E = −OV . (2)

The electric current density ~J is given by Ohm’s law,

~J = −σ(T ) OV . (3)

Two approaches are used in this paper for calculatingthe magnetic field, ~B. One of them computes the mag-netic potential field ~A in 3-space dimensions, Eq. (4),and from that the magnetic field, Eq. (5). While theother, called axisymmetric approach, computes onlyone component of the magnetic field, Eq. (6).The magnetic potential ~A is governed by the Poissonequation,

4~A = σ(T ) µo OV , (4)

where 4 denotes the Laplace operator, and µo the per-meability of free space. The magnetic field ~B is de-fined in 3-space dimensions as the rotational of themagnetic potential,

~B = O × ~A , (5)

where O× denotes the rotational operator.For axisymmetric configurations the calculation of themagnetic field, Eqs. (4)-(5), is often reduced to thesingle angular component

Bθ(r) =µo

r

∫ r

0Jaxial(l) l dl , (6)

where r is the radial distance to the symmetry axis,and Jaxial the axial component of the current density.Notice that this simplified expression is obtained doingan additional assumption sometimes omitted: the cur-rent density vector is axial, that is aligned with the di-rection of the symmetry axis. So axisymmetric config-urations should also be invariant by translation alongthe symmetry axis to satisfy this additional condition.Such a simplification can be used for investigatinglong arcs, as done by Hsu and co-authors in [10]. Tsaiand co-authors underlined in [11] that this simplifica-tion may need to be questioned for short arcs. Thearcs used in electric arc welding use to be short.

2.2 Fluid model

The thermal fluid component of the model applies to aNewtonian and thermally expansible fluid, assuming:- a one-fluid model,- in local thermal equilibrium, and- mechanically incompressible, because of the smallMach number.- the flow is steady-state and laminar, which is speci-fied using the option of laminar flow in the OpenFOAMturbulence model class.The model is thus suited to the plasma core. Thetreatment of the plasma sheath would require a two-fluid model with partial thermal equilibrium, to accountfor electron diffusion, and for the temperature differ-ence observed between electrons and heavy particlesin the plasma arc sheath.In the present framework, and with steady-state con-ditions, the continuity equation is written as

O·[ρ(T ) ~u

]= 0 , (7)

where ρ denotes the fluid density, and ~u the fluid veloc-ity. The density ρ(T ) is here temperature dependent,as illustrated for argon plasma in Fig. 2.

Figure 2: Argon plasma density as function oftemperature.

The momentum conservation equation is expressedas

O·[ρ(T ) ~u ⊗ ~u

]− ~u O·

[ρ(T ) ~u

]−O·

[µ(T )

(O~u + (O~u)T

)− 2

3 µ(T ) (O·~u)I]

= −OP + ~J × ~B ,

(8)

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where the operators ⊗ and × denote the tensorial andvectorial product, respectively. I is the identity tensor,µ the viscosity, and P the pressure. The last term onthe right hand side of Eq. (8) is the Lorentz force.The enthalpy conservation equation is

O·[ρ(T )~u h

]− h O ·

[ρ(T ) ~u

]− O·

[α(T ) Oh

]= O· (~u P) − P O·~u + ~J· ~E

−Qrad + O·[ 5 kB ~J2 e Cp(T )

h],

(9)

where h is the specific enthalpy, α is the thermal dif-fusivity, Qrad the radiation heat loss, kB the Boltzmannconstant, e the elementary charge, and Cp the specificheat at constant pressure. The third term on the righthand side of Eq. (9) is the Joule heating, and the lastterm the transport of electron enthalpy. The temper-ature, T , is derived from the specific enthalpy via thedefinition of the specific heat,

Cp(T ) =( dhdT

)P, (10)

which is plotted in Fig. 3 for Ar and CO2 plasma.

Figure 3: Specific heat as function of temperature forAr (solid line) and CO2 (dotted line).

The thermodynamic and transport properties arelinerarly interpolated from tabulated data implementedon a temperature range from 200 to 30 000 K, with atemperature increment of 100 K. These data tableswere derived for an argon plasma [12], and a carbondioxide plasma [13], using kinetic theory.

3 TEST CASES

Two test cases were considered. The first one, an infi-nite rod, was retained since it has an analytic solutionallowing testing the electromagnetic part of the simu-lation model, and the two calulation methods for themagnetic field. The second is the water cooled GTAWtest case described in [11]. It was investigated experi-mentally in [14], and used in the literature as referencecase for testing arc heat source simulation models.

3.1 Infinite rod

The magnetic field induced in and around an infiniterod of radius ro with constant electric conductivity, andconstant current density parallel to the rod axis, re-duces to an angular component Bθ with the followinganalytic expression (see [9] for further details):

Bθ(r) =µoJaxial r

2if r < ro ,

Bθ(r) =µoJaxial r2

o

2 rif r ≥ ro .

(11)

Jaxial = I/(π ro) denotes the current density along therod axis, and I the current intensity.

Figure 4: Schematic representation of thecomputational domain.

A long rod of radius ro = 1 mm with the largeand uniform electric conductivity σrod = 2700A/(Vm),

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surrounded by a poor conducting region of radiusrext = 16 mm, and uniform electric conductivity σsur =

10−5A/(Vm), was simulated. Notice that the conduc-tivity σrod and σsur correspond to an argon plasma at10600 and 300 K, respectively.The electric potential difference applied on the rodwas set to 707 V, as indicated in Fig. 4. It correspondshere to a current intensity of 600 A. The electric poten-tial gradient along the direction normal to the boundarywas set to zero on all the other boundaries.The magnetic field was calculated using both the i)three-dimensional approach, Eqs. (4)-(5), and theii) axisymmetric approach, Eq. (6). In the three-dimensional approach, the magnetic potential ~A wasset to zero at r = rext, and its gradient along the direc-tion normal to the boundary was set to zero on all theother boundaries.The calculation results, plotted in Fig. 5 for the angu-lar component of the magnetic field, are both in per-fect agreement with the analytic solution, as expectedwhen the current density is aligned with the symmetryaxis.

Figure 5: Angular component of the magnetic fieldalong the radial direction (ro = 1 × 10−3m).

3.2 Water cooled GTAW with Ar shielding gas

The 2 mm long and 200 A argon arc studied in [11],based on the experimental measurements of [14] re-

ported in Fig. 6, is now considered.

Figure 6: Temperature measurements of [14].

The configuration is sketched Fig. 7. The electrode, ofradius 1.6 mm, has a conical tip of angle 60◦ truncatedat a tip radius of 0.5 mm. The electrode is mounted in-side a ceramic nozzle of internal and external radius 5mm and 8.2 mm, respecively. The pure argon shield-ing gas enters the nozzle at room temperature and atan average mass flow rate of 1.66 . 10−4 m3/s.

Figure 7: Schematic representation of the GTAW testcase

The temperature and the current density set on thecathode boundary are explicitely given in [11]. Theanode surface temperature was also set as proposedin [11], extrapolating the experimental results of [14].Looking at the experimental results, Fig. 6, it can be

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noticed that the measured temperature is rather dif-ficult to extrapolate up to the anode. The boundaryconditions set on the cathode also suffer from a lackof accuracy, as experimental measurements could notbe done in the very close vicinity of the anode andcathode. These difficulties may explain the variety ofboundary conditions used in the literature for simulat-ing this test case.

Figure 8: Magnetic field magnitude calculated with theaxisymmetric (left) and the three-dimensional (right)

~B-approach.

Figure 9: Current density vector calculated with thethree-dimensional approach, Eqs (4)-(5) .

The simulation results presented here were calculatedusing 25 uniform cells along the 0.5 mm tip radius,100 uniform cells between the electrode and parentmetal along the symmetry axis, and a total number of136250 cells. A mesh sensitivity study can be foundin [15], concluding that the present mesh is sufficiently

fine. The magnetic field was calculated using both thei) three-dimensional approach, Eqs. (4)-(5), and theii) axisymmetric approach, Eq (6). The axisymmet-ric approach is simpler, and often used in the litera-ture to simulate GTAW problems. The numerical re-sults from the two approaches significantly differ, asshown in Fig. 8. Agreement is only observed be-low the cathode tip, where the non-axial component ofthe current density is negligible compared to the axialcomponent (see Fig. 9). The axisymmetric approachindeed neglects the radial current density component.The three-dimensional calculation, Fig. 9, shows thatthe non-axial component of the current density is noteverywhere negligible, in particular next to the elec-trode tip, where the largest induced magnetic field isobserved. Neglecting the non-axial component of thecurrent density would first of all result in a poor esti-mation of the magnetic pinch forces, and in turn of thearc velocity, as well as the pressure force the arc ex-erts on the base metal. Consequently, the so-calledaxisymmetric approach was not retained for simulat-ing this axisymmetric GTAW configuration.The next simulation results were all obtained with thethree-dimensional approach, Eqs (4)-(5).

Figure 10: Temperature along the radial direction,1 mm above the anode.

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The calculated temperature is plotted along the radialdirection 1 mm above the anode in Fig. 10, and alongthe symmetry axis in Fig. 11 (solid line). The experi-mental data available in [14] and shown in Fig. 6 areused for comparison with the numerical results alongthe radial direction, in Fig. 10. A good agreement isobtained. The comparison along the symmetry axisis difficult to perform, as the isotherms represented inFig. 6 are not plotted in this area. We can however ob-serve that the maximum temperature obtained numer-ically seems to underestimate the experimental one byabout 10%. This could be due to the boundary condi-tions set on the anode and cathode. Other boundaryconditions also used in the literature are investigatedin section 3.4.

3.3 Ar-x%CO2 shielding gas

Plasma arc simulations for the test case of section 3.2were also done changing the shielding gas composi-tion, and retaining the four following Ar-x %CO2 cases:pure argon (x= 0), pure carbon dioxide (x= 100), andmixtures of these two gases with x = 1% and 10% inmole. In each case the thermodynamic and transportproperties of the mixture (with 0≤ x≤ 1) are tabulatedas function of the temperature, and the tables are im-plemented in OpenFOAM-1.6.x as described in sec-tion 2.2. For both pure argon and pure carbon diox-ide the data tables result from derivations using kinetictheory, and done in [12] and [13], respectively. For theother mixtures (with 0 < x < 1) the data tables wereprepared doing an additional calulation step, basedon the related data for pure argon, pure carbon diox-ide, and standard mixing laws. These mixing laws usemass concentration as weigthing factor [16] for calcu-lating the mixture specific heat and the mixture entha-phy, while they use molar concentration as weigthingfactor [17] when applied to the calculation of the mix-ture viscosity, mixture thermal conductivity and mix-ture electric conductivity.The test cases of this section were investigated asa preliminary study for future extension of the GTAWmodel of section 2 to active gas welding. They shouldbe considered as academic, for various reasons nowdetailed.

Figure 11: Temperature along the symmetry axis.

Figure 12: Temperature along the radial direction,1 mm above the anode.

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Figure 13: Velocity along the symmetry axis.

Figure 14: Velocity along the radial direction, 1 mmabove the anode.

Because of lack of experimental data, the boundaryconditions set on the electrode and the base metalare the same as in section 3.2. These approximateboundary conditions are most probably oversimplifiedwhen the shielding gas contains a significant amountof CO2. Also, the difficulty met in setting appropriateboundary conditions on the anode and cathode raisesthe future need of extending the simulation model cou-pling cathode and anode simulation to the thermalplasma arc.The shielding gas containing x=1% in mole CO2should be close to the maximum amount of CO2 al-lowing producing a stable electric arc with a tungstenelectrode and water cooled base metal. Experimentsare being prepared for characterizing this case. For alarger amount of CO2 in the shielding gas, significantelectrode oxidation is expected, leading to arc insta-bility. A solution for making experiments feasible witha tungsten electrode could consist in shielding locallythe electrode tip with an inert gas such as argon. Butsuch a local shielding was not accounted for in thepresent simulations.The present aim was to evaluate qualitatively the in-fluence of the amount of active gas on the plasmaarc temperature and velocity for given boundary con-ditions.The calculated temperature is plotted along the sym-metry axis in Fig. 11, and along the radial direction 1mm above the anode in Fig. 12. In a similar way, thecalculated velocity is plotted along the symmetry axisin Fig. 13, and along the radial direction 1 mm abovethe anode in Fig. 14. The simulation results clearlyshow that the presence of carbon dioxide results in anincreased arc temperature (Figs. 11, 12), and a con-striction of the temperature field above the base metal(Fig. 12). It also results in a significant increase of theplasma arc velocity (Figs. 13, 14), which in turn in-creases the pressure force applied on the base metal,but no significant change concerning the extent of theplasma jet just above the base metal (Fig. 14).

3.4 Boundary conditions

As underlined above, the available experimental mea-surements need to be extrapolated for estimating apriori the boundary conditions. The extrapolation issomewhat uncertain, which may explain the variety ofboundary conditions used in the literature.

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Figure 15: Influence of the anode and cathodeboundary conditions on the temperature along the

symmetry axis.

Figure 16: Influence of the anode and cathodeboundary conditions on the velocity along the

symmetry axis.

Figure 17: Influence of the anode and cathodeboundary conditions on the pressure on the base

metal.

Three test cases (a, b, and c) that differ only by theboundary conditions set on the electrode and the an-ode were calculated to evaluate the influence of theseboundary conditions on the plasma arc. In case a(treated above using the boundary conditions definedin [11]), the current density is uniform on the 0.5 mmradius cathode tip, and it decreases linearly down tozero as the radius tip increases. In case b all the cur-rent density (also uniform) goes through the 0.5 mmradius cathode tip. The boundary conditions on theanode are the same in case a and b. In case c theboundary conditions on the cathode are the same asin case b. Case c is associated with an extreme ther-mal condition on the anode for testing the model: itsanode does not conduct heat. In all cases, argon isused as shielding gas.The temperature and the velocity calculated for eachcase are plotted along the symmetry axis in Fig. 15and Fig. 16, respectively; while the pressure on thebase metal is plotted in Fig. 17.

It can be observed in Fig. 15 that there is a large in-fluence of the current density distribution on the cath-ode on the maximum arc temperature. Also, com-pared to case a, the maximum temperature of case bis much closer to the maximum temperature observed

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experimentaly. The thermal boundary condition on theanode has almost no influence on the maximum arctemperature. However, it can significantly affect theheat transferred to the anode base metal, as it signifi-cantly changes the temperature close to the anode.Finally, Fig. 16 and 17 show that the velocity alongthe symmetry axis and the pressure force on thebase metal are significantly changed for each varia-tion tested on the anode and cathode boundary con-ditions.

4 CONCLUSION

This study focused on the modeling and simulationof an electric arc heat source in three space dimen-sions, coupling thermal fluid mechanics with electro-magnetism. The model was implemented in the opensource software OpenFOAM 1.6.x. Two approacheswere considered for calculating the magnetic field ~B :i) three-dimensional, and ii) axisymmetric.The electromagnetic part of the solver was testedagainst analytic solution for an infinite electric rod. Thesolutions are in perfect agreement.The complete solver was tested against experimen-tal measurements for GTAW with argon shielding gasand an axisymmetric configuration. The numerical so-lutions for the ~B-field then significantly differ. The ax-isymmetric approach indeed neglects the radial cur-rent density component. For axisymmetric configu-rations that are not invariant by translation along thesymmetry axis, such as GTAW, this simplification isnot everywhere justfified. Consequently, the axisym-metric approach, Eq. (6), was not retained for sim-ulating the GTAW heat source. The numerical re-sults obtained using the three-dimensional approach,Eqs. (4)-(5), show a good agreement with experimen-tal data when such comparisions can be made.Plasma arc simulations were done to evaluate quali-tatively the influence of the amount of active gas onthe plasma arc. The following Ar-x %CO2 shieldinggas compositions were used: pure argon (x =0), purecarbon dioxide (x =100), and mixtures of these twogases with x =1 and 10% in mole. The simulation re-sults clearly show that the presence of carbon diox-ide results in thermal arc constriction, and increasedmaximum arc temperature and velocity. The difficultymet in setting appropriate boundary conditions on theanode and cathode because of lack of experimental

data raises the future need of extending the simula-tion model coupling cathode and anode simulation tothe thermal plasma arc.Setting appropriate boundary conditions on the an-ode and cathode can also be a difficult issue evenwhen experimental data are available. The free-dom for extrapolating the boundary conditions canbe rather large. In addition different possible condi-tions significantly affect the simulation results, suchas the plasma arc temperature and velocity. Tem-perature and current density distribution on the elec-trode surface should thus be calculated rather thanset, to enhance the predictive capability of the simu-lation model. Solution of the temperature and elec-tromagnetic fields inside the anode and cathode, andthe modeling of the plasma arc sheath doing the cou-pling with the plasma core, will thus be included in theforthcoming development of the simulation model.

Acknowledgment: The authors thank Prof. JacquesAubreton and Prof. Marie-Françoise Elchinger forthe data tables of thermodynamic and transport prop-erties they did provide. This work was supportedby KK-foundation in collaboration with ESAB, VolvoConstruction Equipment and SSAB. Håkan Nilssonwas in this work financed by the Sustainable Produc-tion Initiative and the Production Area of Advance atChalmers. These supports are gratefully acknowl-edged.

5 References

[1] L. Lindgren, B. Babu, C. Charles, and D. Wed-berg (2010). Simulation of manufacturing chainsand use of coupled microtructure and constitu-tive models. Finite Plasticity and Visco-plasticityof Conventional and Emerging Materials, Khan,A. S. and B. Farrokh, (red.). NEAT PRESS, 4 s.

[2] A. Kumar, and T. DebRoy (2007). Heat transferand fluid flow during Gas-Metal-Arc fillet weldingfor various joint configurations and welding posi-tions. The minerals, metals and materials societyand ASM International.

[3] J. Wendelstorf (2000). Ab initio modelling of ther-mal plasma gas discharges (electric arcs). PhD.Thesis, Carolo-Wilhelmina University, Germany.

12 XII-2017-11

[4] Y. Tanaka, T. Michishita and Y. Uesugi (2005).Hydrodynamic chemical non-equilibrium modelof a pulsed arc discharge in dry air at atmo-spheric pressure. Plasma Sources Sci. Technol.14, pp. 134-151

[5] K. Yamamoto, M. Tanaka, S. Tashiro, K. Nakata,K. Yamazaki, E. Yamamoto, K. Suzuki, and A.B.Murphy (2008). Numerical simulation of metal va-por behavior in arc plasma. Surface and Coat-ings Technology, 202, pp. 5302-5305.

[6] J. Hu, and L.S. Tsai (2007). Heat and mass trans-fer in gas metal arc welding. Part I: The arc, PartII: The metal. International Journal of Heat andMass Transfer 50, pp. 808-820, 833-846.

[7] G. Xu, J. Hu and H.L. Tsai (2009). Three-dimensional modeling of arc plasma and metaltransfer in gas metal arc welding. InternationalJournal of Heat and Mass Transfer, 52, pp. 1709-1724.

[8] I. Choquet, and B. Lucquin-Desreux (2011),Non equilibrium ionization in magnetizedtwo-temperature thermal plasma, Kineticand Related Models, 4, to appear. (preprintwww.ljll.math.upmc.fr/publications/2010/R10043.pdf)

[9] M. Sass-Tisovskaya (2009). Plasma arc weldingsimulation with OpenFOAM, Licentiate Thesis,Chalmers University of Technology, Gothenburg,Sweden.

[10] K.C. Hsu, K. Etemadi and E. Pfender (1983).Study of the free-burning high intensity argon arc,J. Appl. Phys., 54, pp. 1293-1301.

[11] M.C.Tsai, and Sindo Kou (1990). Heat transferand fluid flow in welding arcs produced by sharp-ened and flat electrodes. Int J. Heat Mass Trans-fer, 33, 10, pp. 2089-2098.

[12] V. Rat, A. Pascal, J. Aubreton, M.F. Elchinger, P.Fauchais and A. Lefort (2001). Transport prop-erties in a two-temperature plasma: theory andapplication. Physical Review E, 64, 026409.

[13] P. André, J. Aubreton, S. Clain , M. Dudeck, E.Duffour, M. F. Elchinger, B. Izrar, D. Rochette, R.

Touzani, and D. Vacher (2010), Transport coef-ficients in thermal plasma. Applications to Marsand Titan atmospheres, European Physical Jour-nal D 57, 2, pp. 227-234.

[14] G.N. Haddad, and A.J.D. Farmer (1985) Temper-ature measurements in gas tungsten Arcs. Weld-ing Journal 24, pp. 339-342.

[15] I. Choquet, H, Nilsson, M. Sass-Tisovskaya(2011). Modeling and simulation of a heat sourcein electric welding, In Proc. Swedish ProductionSymposium, SPS11, May 3-5, 2011, Lund, Swe-den. to appear.

[16] R.E. Sonntag, C. Borgnakke, and G.J. VanWylen (2003). Fundamentals of thermodynam-ics, Wiley, 6th edition.

[17] R. J. Kee, M. E. Coltrin, P. Glaborg (2003).Chemically reacting flow. Theory and Practice,Wiley Interscience.