metal vapour behaviour in gas tungsten arc thermal ... - Springer Link

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METAL VAPOUR BEHAVIOUR IN GAS TUNGSTEN ARC THERMAL PLASMA DURING WELDING


M. Tanaka a

K. Yamamoto a

S. Tashiro a

K. Nakata a

M. Ushio a

K. Yamazaki b

E. Yamamoto b

K. Suzuki b

A.B. Murphy c

J.J Lowke c

a

Joining and Welding Research Institute, Osaka University (Japan) b Welding Company, Kobe Steel Ltd (Japan) c CSIRO, Industrial Physics (Australia)

ABSTRACT The present modelling of a gas tungsten arc in helium or argon accounts for metal vapour contamination from the weld pool as an anode. The whole region of gas tungsten arc welding, namely, tungsten cathode, arc plasma and weld pool is treated in a unified numerical model. A viscosity approximation is used to express the diffusion coefficient in terms of the viscosities of shielding gas and iron vapour. The time dependent two-dimensional distributions of temperature, velocity and iron vapour concentration are predicted, together with the weld penetration as function of time for a 150 A arc at atmospheric pressure. It is shown that the thermal plasma in a gas tungsten arc is markedly influenced by iron vapour from the weld pool surface and the concentration of iron vapour in the plasma is dependent on the temperature of the weld pool surface. IIW-Thesaurus keywords: Arc welding; Diffusion; Gas shielded arc welding; GTA welding; Molten pool; Reference lists; Simulating; Temperature; Vapours; Weld zone.

1 INTRODUCTION During the arc welding process, four states of matter, namely, as solid, liquid, gas and plasma, exist simultaneously in a space only 1 cm3 and these states Doc. IIW-1879-07 (ex-doc. SG-212-1107r1-07) recommended for publication by SG-212 “The physics of welding”. Welding in the World, Vol. 52, n° 11/12, 2008 – Research Supplement

mutually interact. Temperature range is very wide, including the arc plasma about 20 000 K, tungsten cathode about 3 000 K, molten steel about 2 000 K and also a room temperature environment [1]. Due to the remarkable progress in computer simulation and observation techniques recently, it has been possible to understand the phenomena in arc welding processes quantitatively [2, 3]. For example, the authors have investigated the numerical simulation which calculates “the tungsten


cathode, the arc plasma and the weld pool”, and then this simulation enables visualization of the relationship between energy and momentum in each region and the formation of a weld pool [4]. However, it has not been possible to accurately predict the welding results, such as the arc voltage and the weld geometry. In order to generate an accurate understanding and prediction, it is necessary to understand the behaviour of metal vapour. Figure 1 shows appearances of “He arc between a solid tungsten electrode and a solid water-cooled copper anode” and “a He arc between a molten steel wire electrode and a molten pool on steel plate” [5]. The former is a pure He arc discharge and the latter is an arc welding process in a He gas and metal vapour mixture. It is easily supposed that plasma conditions are obviously different although both arc currents are quiet similar. This difference is mainly caused by metal vapour from the both molten electrodes. In gas tungsten arc (GTA) welding, it is empirically known that amounts of the smut around a weld bead are much different between Ar gas shielding and He gas shielding, furthermore, the arc voltage in GTA on a water-cooled copper anode is also different from that in GTA welding. These phenomena are also caused by the metal vapour from the weld pool. Metal atoms generally have more states of low-energy excitation and more likely to be ionized than atoms of shielding gases such as Ar and He. These characteristics contribute to an increase in the radiative emission coefficient and electric conductivity of plasma. It is estimated that the former affect the thermal pinch effect and the energy efficiency of arc plasma and the latter affect the current path. Tashiro [5] conducted a virtual experiment by a numerical simulation of the arc assuming a pure He arc and a He arc uniformly mixed with 30 mol% Fe atom, and showed that an obvious arc constriction appeared due to the Fe vapour mixing. Furthermore, they reported that the energy efficiency greatly decreased from about 80 % to about 35 %. These results suggest that the existence of metal vapour changes the heat source property in the arc welding process, and consequently changes the size and the shape of the molten pool. As noted above, the simulation technology for arc welding has greatly advanced. For example, a numerical

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simulation of gas metal arc weld, including the formation of droplets from a steel wire electrode, has been reported [6]. However, the welding gas was pure Ar, and the effect of metal vapour was not considered. On the other hand, calculations of the behaviour of metal vapour in an atmospheric pressure plasma have also been reported [7]. However, conditions were far from those of welding because a solid electrode with constant temperature was assumed. It is important for accurate understanding of arc welding processes to consider the mixing of metal vapour in a model that takes into account the tungsten cathode, the arc plasma and the weld pool. In the present paper, we use a numerical model of a stationary GTA weld taking into account the Fe vapour produced from the weld pool surface and simulate the distribution of metal vapour, plasma temperature and formation of the weld pool.

2 SIMULATION MODEL The tungsten cathode, arc plasma and anode are described relative to cylindrical coordinates, assuming rotational symmetry around the arc axis. The calculation domain is shown in Figure 2. The diameter of the tungsten cathode is 3.2 mm with a 60 degrees conical tip. The anode is of water-cooled copper or stainless steel. As the shielding gas, He gas is introduced at the flow rate of 30 l/min from the outside of the cathode on the upper boundary or Ar gas at the flow rate of 10 l/min. The area where the shielding gas is supplied is illustrated in Figure 2. The governing equations used in this model are shown. The mass continuity equation is wU 1 w w r Uvr Uv z wt r wr wz

0

(1)

The radial momentum conservation equation is wU v r 1 w w r U v r2 Uv zvr wt r wr wz

1w § wv 2rK r r wr ¨© wr

w § wv r wv z · ¸ wz ¨K wz K wr ¹ ©

wp j z BT wr vr · ¸ 2K r 2 ¹

Figure 1 – Effect of metal vapour from molten electrodes on helium arc plasma Welding in the World, Vol. 52, n° 11/12, 2008 – Research Supplement

(2)

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The v × B term is neglected in Eq. (6). Er and Ez are respectively the radial and axial components of the electric field defined by Er

wV , Ez wr

wV wz

(7)

where V is electric potential, and Bθ, the azimuthal magnetic field induced by the arc current is evaluated by Maxwell’s equation, 1w rBT r wr where

P0 j z

(8)

μ0is the permeability of free space. Special account needs to be taken at the electrode surfaces for effects of energy transfer that only occur at the surface. The additional energy flux for cathode and anode are respectively Cathode : FK= − εαT4 − jeφK + jiVi Anode : FA= − εαT4 − jφA

(9) (10)

where

ε is surface emissivity, α is Stefan-Boltzmann constant, φK is the work function of the tungsten cathode, Vi is the ionization potential of plasma gas, je is the electron current density, ji is the ion current density, φA is the work function of the anode, and T is the temperature.

Figure 2 — Schematic illustration of simulation domain

The axial momentum conservation equation is wp wU v z 1 w w r U v r v z U v z2 wz jr BT wt r wr wz w § wv z · 1 w § wv r wv · ¨ 2K rK rK z ¸ U g ¸ ¨ wz © wr ¹ r wr © wz wr ¹

(3)

The energy conservation equation is wU h 1 w w r U v r h U v z h wt r wr wz 1 w § rN wh · w § N wh · j E j E U z z ¨ ¸ ¨ ¸ r r r wr ¨© cp wr ¸¹ wz ¨© cp wr ¸¹

(4)

0

jr= − σEr , jz= − σEz

(5)

(11)

kB is Boltzmann’s constant, and (6)

where t is time, h is enthalpy, p is pressure, ρ is the density, η is the viscosity, vr and vz are the radial and axial velocities, g is the acceleration due to gravity, jr and jz are the radial and axial components of the current density, cp is the specific heat, κ is the thermal conductivity, U is the radiative emission coefficient, σ is the electrical conductivity. Welding in the World, Vol. 52, n° 11/12, 2008 – Research Supplement

§ eI · AT 2 exp ¨ K ¸ © kBT ¹ where jR

The current continuity equation is w 1w rjr jz r wr wz

For the cathode surface, FK needs to be included in Eq. (4) to take into account thermionic cooling by emission of electrons, radiative cooling and ion heating. Similarly, for the anode surface, FA is required in Eq. (4) to take into account radiative cooling and thermionic heating. For the cathode surface, the electron current and the ion current are considered separately and defined based on the Richardson-Dushman equation for thermionic emission as follows.

A is Richardson’s constant, which depends on cathode material. The ion current density ji is then assumed to be ji = j − jR, where the total current density j is j = je + ji. The convection in the weld pool is influenced by the shear stress due to the convective flow of the cathode jet, the Marangoni force due to the gradient in the surface tension of the weld pool, buoyancy due to gravity and electromagnetic pinch force due to the arc current. Only the driving forces of the weld pool convection at the boundary between weld pool and arc plasma are explained here. First, the shear stress is already included in Eq. (2) for radial momentum conservation through the viscosity at the anode surface. Second, the Marangoni force is given by [4]


w § wJ wT · wz ©¨ wT wr ¹¸

MA

(12)

where γ is the surface tension of the weld pool. In this paper, stainless steel is assumed as low sulfur (about 10 ppm) content and the variation of the surface tension at the weld pool surface is assumed to decrease linearly with increasing temperature (γ /T= − 0.46 mN / mK) [4]. A species conservation equation expressed by Eq. (13) is also applied to take into account the metal vapour behaviour [7]. In practice, metal vapour species in an arc plasma with a stainless steel anode plasma include Fe, Cr, Ni, Mn and so on [8]. However, to simplify the model and facilitate calculation, only Fe vapour is considered in this model. w 1w w U C1 r U v r C1 U v z C1 wt wz r wr

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such as Ar, He, H2, N2, O2, CO2 and so on. It is assumed that β1= β2=1.385, which is based on the mean value of experimental data [9]. The viscosity approximation is not strictly justified since it does not take into account ionized species and is at best reasonably accurate [10]; however it is considered to be a useful first approximation for the arc welding model. C1 is set to be 0 in the cathode area and the solid area of the anode. However, at the anode surface where the temperature is above the melting point, C1 is set to be the value of the boundary condition expressed by Eq. (15) [7].

C1

pv ,1M1

pv ,1M1 patm pv ,1 M2 where

(15)

patm is atmospheric pressure (1 atm), and pv,1 is the Fe vapour partial pressure as function of the weld pool temperature [11].

(13)

Due to Eq. (15), C1 is set to be 0 ~1.0. For other boundary conditions, C1 = 0 at AF and FE shown in Figure 2, and (C1/r) = 0 at the arc axis (AB).

C1 is the mass fraction of Fe vapour, and D is the binary diffusion coefficient, which is expressed by the viscosity approximation equation:

In the present model, plasma properties are dependent on not only the temperature but also mole fraction concentration of Fe vapour. Plasma properties at optional concentration of Fe vapour are calculated due to linear approximation based on the properties at 0 mol%, 1 mol%, 10 mol%, 20 mol% and 30mol% [12]. The properties were calculated using the Chapman-Enskog approximation [12] under the assumption that the arc plasma is in a local thermodynamic equilibrium (LTE) condition. Accuracy of the model is not lost so much due to the assumption of a LTE condition because the significant differences between temperatures of heavy particles and of electrons occur only in the region around the cathode tip and outer plasma region at low temperatures [13]. For example, the electrical conductivities and the radiative emission coefficients which are significantly affected are shown in Figures 3 and 4 respectively. Figure 3 shows change of the electrical conductivities for an Ar plasma. The electrical conductivities greatly increase by mixing the Fe vapour in the range lower than 8 000 K, and the values for mixing ratio at 1 mol%, 10 mol%, 20 mol% and 30 mol% are almost the same. On the other hand, Figure 4 shows change of the radiative emission coefficients. The radiative emission coefficient increases with increasing the mixing ratio of Fe vapour and the radiative emission coefficient for pure Ar plasma is very small.

1w § wC · w § wC · rUD 1 ¸ ¨ UD 1 ¸ ¨ r wr © wr ¹ wz © wz ¹

where

D

Û

2 1

2 2 1 / M1 1 / M2 / E12K12 M1

0.25

0.5

U 22 / E 22K 22 M2

`

0.25 2

(14)

where M1 and M2 are molecular weight of Fe and the shielding gas respectively. Similarly, ρ1, ρ2, η1, η2 are respectively density and viscosity of Fe and the shielding gas. β1, β2 are dimensionless constants defined as β1=(Dii ρi )/ ηi, and theoretically become 1.2~1.543 for various species of gas,

The governing and auxiliary equations are solved iteratively by the SIMPLEC numerical procedure. The other approximations and boundary conditions are given in detail in our previous papers [5, 14].

3 CALCULATED RESULTS

Figure 3 – Dependence of electrical conductivities of argon gas on temperature for each mixing ratio

The present model is applied to the calculation for stationary He GTA welding of stainless steel. Figure 5 shows a two-dimensional distribution of temperature, Welding in the World, Vol. 52, n° 11/12, 2008 – Research Supplement

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Figure 4 – Dependence of radiant power density of argon gas on temperature for each mixing ratio fluid flow velocity and mole fraction concentration of Fe vapour at 20 s after arc ignition. Distribution of Fe vapour consists of the diffusion term and the convection term, as described in Eq. (13). Due to the cathode jet, which leads to flow velocities of over 300 m/s in the welding arc, the convection term has a strong influence. Therefore, it is found that distribution of Fe vapour expands in the radial direction and concentrates around the weld pool surface. The mole fraction concentration of Fe vapour in the arc plasma is up to 7 mol%, which is in good agreement with experimental data by Terasaki [8].

Figure 6 shows calculated results of arc voltage for 50 A, 100 A, 150 A and 200 A arc current. Similarly, experimental results are shown, where calculated results are described as lines and experimental results are described as points. Arc voltages for water-cooled copper anode and stainless steel anode are shown and in the case of stainless steel, arc voltages are shown at 20 s after arc ignition; namely, after the weld pool grows sufficiently. The experiment is consistent with the calculation. The work piece is SUS304 stainless plate (50 mm × 100 m × 10 mmt) mounted on a watercooled copper plate in close thermal contact and the

Figure 5 – Calculated results for helium GTA welding for 150 A at 20 s after arc ignition

Figure 6 – Comparison of calculated arc voltage with experimental results

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sulfur content of SUS304 plate is 10 ppm. Welding conditions, such as arc length, electrode diameter and flow rate of shielding gas, are the same as the conditions of the calculation. Figure 6 shows that the arc voltages for the stainless steel anode obviously decrease compared with those for the water-cooled copper anode for all arc current conditions examined. This is due to the effect of Fe vapour from the weld pool, and, as shown in Figure 3, even a small amount of Fe vapour increases the electrical conductivity. Therefore, the arc voltage comprehensively decreases by about 5 V because of the decrease of the voltage gradient mainly in the arc just above the weld pool. He GTA welding shows load resistance characteristics in the low current range, and both calculation and experimental results agree with the characteristics. In the case of water-cooled copper anode, difference for 2~3 V between calculation and

Figure 7 – Comparison of calculated current densities at the anode surface

Figure 8 – Calculated results for argon GTA welding for 150 A at 20 s after arc ignition

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experiment at 100 and 200 A arc current is observed. A dominant reason for this difference is expected that, in the experiment, a small amount of Cu vapour from anode surface decreases the arc voltage in the high current range where the heat input density is large. Figure 7 shows the current density distributions at the anode surface. For the stainless steel anode, the calculation result which neglects the addition of Fe vapour into arc plasma is also shown to highlight the effect of Fe vapour addition. The current density distribution for the water-cooled copper anode is the highest, over 5 000 A/cm2. The distribution for the stainless steel anode considering the Fe vapour is obviously different from that for neglecting the Fe vapour. The distribution neglecting the Fe vapour is over 3 500 A/cm2, whereas the distribution considering the Fe vapour decreases to about 1 100 A/cm2, and the current path is obviously

Figure 9 — Relation between maximum weld pool temperature and maximum concentration of iron vapour in helium GTA welding

Figure 10 — Relation between maximum weld pool temperature and maximum concentration of iron vapour in argon GTA welding Welding in the World, Vol. 52, n° 11/12, 2008 – Research Supplement

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expanded by the increase of the electric conductivity in lower temperature area away from arc axis. Figure 8 shows two-dimensional distribution of temperature, fluid flow velocity and mole fraction concentration of Fe vapour at 20 s after arc ignition for the argon gas shielding. The Fe vapour concentration is significantly smaller than for the case of He gas shielding shown in Figure 5. The distribution of Fe vapour is strongly influenced by plasma jet, even more so than in the case of He gas shielding, because of the higher flow velocities near the anode in the Ar arc. Figure 9 and Figure 10 show time dependent maximum concentration of Fe vapour in the arc plasma for He gas shielding and Ar gas shielding, respectively. Simultaneously, time dependent maximum temperature of weld pool is also shown. These figures show Fe vapour concentrations increase with increasing the temperature of weld pool, both for He gas and Ar gas. However, for Ar gas, weld pool temperature is 500 K lower than that for He gas. Thus, maximum concentration of Fe vapour is about 0.25 mol% and 1/30 smaller than that for He gas. It is found that because total heat input and heat intensity for He gas are greater than those for Ar gas, the surface temperature of the weld pool increases, thus, addition of Fe vapour into the arc plasma increases. From the above results, the present model suggests that the amount of metal vapour in GTA welding for He gas shielding is significantly larger than that for Ar gas shielding. This tendency qualitatively agrees with the amount of the smut around the weld bead which is empirically known.

4 CONCLUSION We used a numerical model of a stationary GTA welding arc considering the Fe vapour from weld pool surface and simulated the effect of the Fe vapour in GTA welding. The main conclusions are summarized as follows: (1) Due to the cathode jet velocity of over 300 m/s in the welding arc, the convection term has a strong influence. Therefore, it was found that distribution of Fe vapour expanded in the radial direction and concentrated around the weld pool surface. (2) Calculated values of arc voltage were in good agreement with experimental results, and the arc voltage for a stainless steel anode was clearly lower than that for a water-cooled copper anode. (3) The arc current distribution for a stainless steel anode considering the Fe vapour was obviously different from that neglecting the Fe vapour. The distribution neglecting the Fe vapour was over 3 500 A/cm2, whilst the distribution considering the Fe vapour decreased to about 1 100 A/cm2 and the current path was expanded by the increase of the electric conductivity in the lower temperature area away from arc axis.

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(4) For Ar gas shielding, the weld pool temperature was 500 K lower than that for He gas. Consequently, the maximum concentration of Fe vapour was 1/30 smaller than that for He gas shielding.

ACKNOWLEDGEMENTS This work was supported by grant-in-aid for Scientific Reseach (B) (2007) from the Japan Society for Promotion of Science (JSPS).

REFERENCES [1] Tanaka M., et al.: New development of welding and thermal spraying, J. Plasma & Fusion Res., 2006, 82-8, pp. 492-496 (in Japanese). [2] Fan H.G., Kovacevic R.: The front line of modeling heat and mass transfer in arc welding processes, J. Japan Welding Soc., 2007, 76-2, pp. 82-89. [3] Nishiyama H., et al.: Computational simulation of arc melting process with complex interactions, ISIJ Int., 2006, 46-5, pp. 705-711. [4] Tanaka M., Lowke J.J.: Predictions of weld pool profiles using plasma physics, J. Phys. D: Appl. Phys., 2007, 40, R1-R23. [5] Tashiro S., et al.: Plasma properties of helium gas tungsten arc with metal vapour, Quarterly J. Japan Welding Soc., 2006, 24-2, pp. 143-148 (in Japanese). [6] Fan H.G., Kovacevic R.: A unified model of transport phenomena in gas metal arc welding including electrode, arc plasma and molten pool, J. Phys. D: Appl. Phys., 2004, 37, pp. 2531-2544. [7] Menart J., Lin L.: Numerical study of a free-burning argon arc with copper contamination from the anode, Plasma Chem. & Plasma Process., 1999, 19-2, pp. 153170. [8] Terasaki H., et al.: Effects of metal vapour on plasma state in helium gas tungsten arcs, Quarterly J. Japan Welding Soc., 2002, 20-2, pp. 201-206. [9] Wilke C.R.: A viscosity equation for gas mixtures, J. Chem. Phys., 1950, 18-4, pp. 517-519. [10] Murphy A.B.: A comparison of treatments of diffusion in thermal plasmas, J. Phys. D: Appl. Phys., 1996, 29, pp. 1922-1932. [11] The Japan Institute of Metals: Edition No. 3 Data Book of Metals, MARUZEN CO., LTD, 1993 (in Japanese). [12] Murphy A.B.: Transport Coefficients of Air, Argon-Air, Nitrogen-Air, and Oxygen-Air Plasmas, Plasma Chem. & Plasma Process., 1995, 15-2, pp. 279-307. [13] Haider J.: Non-equilibrium modeling of transferred arcs, J. Phys. D: Appl. Phys., 1999, 32, pp. 263-272. [14] Tashiro S., et al.: Properties of mass and heat transfer for tube cathode arcs, Quarterly J. Japan Welding Soc., 2007, 25-1, pp. 3-9 (in Japanese).