［溶接学会論文集　第 33 巻　第 2 号　p. 116s-119s （2015）］
[溶接学会論文集 第 33 巻 第 ○ 号 p. 000s-000s（2015)]
Effects of surface tension on predictions of weld pool formation in
TIG welding
by Masayoshi Miyake**, Masaya Shigeta*** and Manabu Tanaka***
TIG welding process consists of close energy balance between arc plasma and weld pool which plays an important role of anode electrode.
Although arc is a heat source of welding and then energy produced by the arc is transferred into the anode, energy transfer inside the weld
pool as the anode is more important for welding due to formation of weld geometry. In particular, the difference of convective direction of
fluid flow in the weld pool dramatically leads to different weld geometry. In this paper, mechanisms of weld pool formation in TIG welding
process is discussed on the basis of numerical simulation which takes account of close interaction between the arc plasma and the anode
electrode. We also discuss the influence of the data of surface tensions from literatures. It is shown that surface tension gradient with
temperature strongly dominates the direction of convective flow in the weld pool due to Marangoni effect and then greatly affects the
formation of weld pool due to change in energy transfer inside the weld pool.
Key Words:
TIG, Weld pool, Convective flow, Marangoni effect, Surface tension
upper boundary at the flow rate of 10L/min. The arc current is
1. Introduction
fixed at 150 A.
In arc welding, the depth of the weld pool is one of the most
important factors for welding quality. It is indispensable to
understand not only arc phenomena but also weld pool formation.
The formation and shape of a weld pool are determined by the
direction of convection inside the weld pool. The convective flow
is driven by four driving forces: the surface drag force, the
buoyancy, the electromagnetic force, and the Marangoni effect
due to temperature-dependency of surface tension.
This paper discusses especially the effect of surface tensions
whose data are obtained from two literatures on the flow direction
and the weld pool geometry.
For the purpose, numerical simulation is performed for process
which includes melting of the anode and a convective flow in the
molten anode. The time-dependent fields of temperature and flow
velocity in the whole region are clarified. The whole region of a
welding process, namely, a tungsten cathode, arc plasma and an
anode is treated by a unified two-dimensional model. 1)
2. Model description
Fig. 1 Schematic illustration of computational domain.
2.2 Governing equations
The governing equations are represented as follows:
2.1 Computational conditions
Figure
1
shows
the
two-dimensional
the mass continuity equation
axisymmetric
computational domain. It is assumed that the flow is laminar and
the arc plasma is in a local thermodynamic equilibrium (LTE)
state. Furthermore, the anode surface is assumed to be flat and
unperturbed by the arc pressure. The diameter of the tungsten
cathode is 1.6mm with a 60-degrees conical tip. Pure helium gas
is used as an atmospheric shielding gas in this model. The helium
shielding gas is supplied from the outside of the cathode on the
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
+
1 𝜕𝜕
𝑟𝑟 𝜕𝜕𝜕𝜕
(𝑟𝑟𝑟𝑟𝜈𝜈𝑟𝑟 ) +
𝜕𝜕
𝜕𝜕𝜕𝜕
(𝜌𝜌𝜈𝜈𝑧𝑧 ) = 0
(1)
the radial momentum conservation equation
𝜕𝜕𝜕𝜕𝑣𝑣𝑟𝑟
𝜕𝜕𝜕𝜕
1 𝜕𝜕
𝑟𝑟 𝜕𝜕𝜕𝜕
+
1 𝜕𝜕
𝑟𝑟 𝜕𝜕𝜕𝜕
(2𝑟𝑟𝑟𝑟
(𝑟𝑟𝑟𝑟𝑣𝑣𝑟𝑟2 ) +
𝜕𝜕𝑣𝑣𝑟𝑟
𝜕𝜕𝜕𝜕
)+
𝜕𝜕
𝜕𝜕𝜕𝜕
𝜕𝜕
𝜕𝜕𝜕𝜕
(𝜂𝜂
(𝜌𝜌𝜈𝜈𝑧𝑧 𝑣𝑣𝑟𝑟 ) = −
𝜕𝜕𝑣𝑣𝑟𝑟
𝜕𝜕𝜕𝜕
+ 𝜂𝜂
the axial momentum conservation equation
𝜕𝜕𝑣𝑣𝑧𝑧
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
) − 2𝜂𝜂
− 𝑗𝑗𝑧𝑧 𝐵𝐵𝜃𝜃 +
𝜕𝜕𝑣𝑣𝑟𝑟
𝑟𝑟 2
,
(2)
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𝜕𝜕𝜕𝜕𝑣𝑣𝑧𝑧
𝜕𝜕𝜕𝜕
1 𝜕𝜕
𝑧𝑧 𝜕𝜕𝜕𝜕
+
1 𝜕𝜕
𝑟𝑟 𝜕𝜕𝜕𝜕
(2𝜂𝜂
(𝑟𝑟𝑟𝑟𝑣𝑣𝑟𝑟 𝑣𝑣𝑧𝑧 ) +
𝜕𝜕𝑣𝑣𝑧𝑧
𝜕𝜕𝜕𝜕
)+
1 𝜕𝜕
𝑟𝑟 𝜕𝜕𝜕𝜕
𝜕𝜕
𝜕𝜕𝜕𝜕
(𝑟𝑟𝑟𝑟
𝜕𝜕𝑣𝑣𝑟𝑟
the energy conservation equation
𝜕𝜕𝜕𝜕ℎ
𝜕𝜕𝜕𝜕
𝜕𝜕
1 𝜕𝜕
+
𝑟𝑟 𝜕𝜕𝜕𝜕
𝑟𝑟𝑟𝑟 𝜕𝜕ℎ
(
𝜕𝜕𝜕𝜕 𝐶𝐶𝑝𝑝 𝜕𝜕𝜕𝜕
(𝑟𝑟𝑟𝑟𝑣𝑣𝑟𝑟 ℎ ) +
(𝜌𝜌𝑣𝑣𝑧𝑧2) = −
𝜕𝜕
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
+ 𝑟𝑟𝑟𝑟
𝜕𝜕𝑣𝑣𝑟𝑟
𝜕𝜕𝜕𝜕
(𝜌𝜌𝑣𝑣𝑧𝑧 ℎ ) =
) + 𝑗𝑗𝑟𝑟 𝐸𝐸𝑟𝑟 + 𝑗𝑗𝑧𝑧 𝐸𝐸𝑧𝑧 − 𝑈𝑈,
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
+ 𝑗𝑗𝑟𝑟 𝐵𝐵𝜃𝜃 +
) + 𝜌𝜌𝜌𝜌,
1 𝜕𝜕
𝑟𝑟𝑟𝑟 𝜕𝜕ℎ
(
𝑟𝑟 𝜕𝜕𝜕𝜕 𝐶𝐶𝑝𝑝 𝜕𝜕𝜕𝜕
(3)
2.4 Boundary conditions and numerical method
The equations (1) to (7) are discretized on the computational
domain divided into 95 and 70 control volumes axially and
radially, respectively, using a non-uniform grid system. The
discretized equations are then solved iteratively by the SIMPLEC
) +
(4)
numerical procedure.4) The other approximations and boundary
conditions and major physical properties used in this model are
the same as Ref. 1).
the current continuity equation
1 𝜕𝜕
𝑟𝑟 𝜕𝜕𝜕𝜕
(𝑟𝑟𝑗𝑗𝑟𝑟 ) +
the Ohm's low
𝜕𝜕
𝜕𝜕𝜕𝜕
3. Result and discussion
(𝑗𝑗𝑧𝑧 ) = 0,
(5)
Figure
𝑗𝑗𝑟𝑟 = 𝜎𝜎𝐸𝐸𝑟𝑟 , 𝑗𝑗𝑧𝑧 = 𝜎𝜎𝐸𝐸𝑧𝑧 ,
(6)
and Maxwell's equation
1 𝜕𝜕
𝑟𝑟 𝜕𝜕𝜕𝜕
117s
3
shows
the
time
dependent
two-dimensional
distributions of temperature and flow velocity for a low sulfur
stainless steel at t = 20 s after arc ignition. Note that no
modification was made to the material functions in vicinity of the
(𝑟𝑟𝐵𝐵𝜃𝜃 ) = 𝜇𝜇0 𝑗𝑗𝑧𝑧 ,
(7)
where 𝑡𝑡 is time, 𝜌𝜌 is the density, 𝑣𝑣𝑟𝑟 and 𝑣𝑣𝑧𝑧 are the axial and
radial velocities, 𝜂𝜂 is the viscosity, P is pressure, 𝑗𝑗𝑟𝑟 and 𝑗𝑗𝑧𝑧 are
the radial and axial components of the current density, 𝑔𝑔 is
acceleration due to gravity, ℎ is enthalpy, 𝜅𝜅 is the thermal
conductivity, 𝑐𝑐𝑝𝑝 is specific heat, 𝑈𝑈 is the radiation loss, and 𝜎𝜎
is the electrical conductivity. 𝐸𝐸𝑟𝑟 and 𝐸𝐸𝑟𝑟 are respectively the
radial and axial components of the electric field defined by
𝐸𝐸𝑟𝑟 = −𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 and 𝐸𝐸𝑧𝑧 = −𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 , where 𝑉𝑉 is the electric
potential.
2.3 Surface tension data
electrodes due to the effects of metal vapor or non-equilibrium
electrons.
The weld pools mainly grow in the radial direction, which is
caused by an outward flow by the drag force and the Marangoni
effect with the negative temperature gradients of surface tension.
Only the center of the weld pools flow in the axial direction,
which is caused by the inward electromagnetic force.
Contrary to the low sulfur cases, the weld pool mainly
penetrates in the axial direction because of the inward flow by the
Marangoni effect with high sulfur and the electromagnetic force.
Figs. 2 (a) and (b) high sulfur stainless steel exhibits the change
of temperature gradients of surface tension from positive to
Figure 2 shows the temperature-dependent data of surface
negative around 2350K. Because the maximum temperature of
tensions which are used in this study. Figure 2(a) shows the data
the anode becomes over 2500K at the center of the molten anode
obtained by the theoretical work of McNallan
2)
, and Fig. 2(b)
shows the data obtained by the experiment by Matsumoto et al.3)
Both figures present low and high sulfur characteristics.
surface at t = 20 s after arc ignition, an inward flow is generated
with a positive temperature gradient of surface tension.
Figures 3 and 4 show that the penetration depth obtained with
McNallan’s data is shallower and wider than that with
3)
2)
(a)
(b)
Fig. 2 Surface tension data of molten SUS304 containing low sulfur and high sulfur from (a) McNallan’s calculation 2) and
(b) Matsumoto’s experiment. 3)
118s
研究論文　MIYAKE et al.: Effects of surface tension on predictions of weld pool formation in TIG welding
溶 接 学 会 論 文 集 第巻（）第○号 with Matsumoto’s data shows better agreement with the
Matsumoto’s data.
Figures 5 and 6 show the comparisons between the present
experiment.
calculations and the experimental results. The test materials were
For the low sulfur cases, the temperature gradient of surface
SUS304 disks, with 50 mm in diameter and 10 mm in thickness,
tension with McNallan’s data is larger than that with Matsumoto’s
mounted on a water-cooled copper plate. The sulfur contents of
data in most of the weld pool area. The Marangoni effect is
SUS304 anodes were 10 ppm and 250 ppm. The welding
caused by the difference of the surface tension depending on
conditions such as the arc length, electrode diameter and flow rate
temperature. When the temperature gradient of surface tension is
of shielding gas were the same as the conditions of the
larger, the Marangoni force is larger as well.
Therefore, the Marangoni effect calculated with McNallan’s
calculation.
For the low sulfur cases in Fig. 5, the calculation with
McNallan’s data show better agreement with the experiment. On
data becomes larger and the outward flow, which results in the
shallower penetration depth.
the other hand, for the high sulfur cases in Fig.6, the calculation
(a)
(b)
Fig. 3 2D distributions of temperature and flow velocity at 20 s after arc ignition in helium arc welding process of SUS304 containing low sulfur
using the data of (a) Ref. 2) and (b) Ref. 3).
(a)
(b)
Fig. 4 2D distributions of temperature and flow velocity at 20 s after arc ignition in helium arc welding process of SUS304 containi ng high sulfur
using the data of (a) Ref. 2) and (b) Ref. 3).
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For the high sulfur case, the temperature gradient of surface
tension with Masumoto’s data remains constant at 0.49 from 1800
119s
that from the center to the edge of the weld pool at higher than
2350 K.
K to 2350 K. However, it has a negative value of -0.12 over the
For the high sulfur case of McNallan’s data, the absolute values
2350 K. The absolute values of that positive temperature gradient
of the negative and positive temperature gradient of surface
of surface tension are larger than that of that negative temperature
tension are almost equal. Consequently, the force caused by the
gradient. This means that the Marangoni effect from the edge to
negative temperature gradient of surface tension and the force
the center of the weld pool at lower than 2350 K is larger than
caused by the positive temperature gradient of that are balanced.
Therefore, for the high sulfur case, the penetration depth obtained
with McNallan’s data is predicted to be shallower than that with
Matsumoto’s data.
These results have revealed the importance of the data of surface
tension. However, there are still lack of data. Theoretical data are
usually obtained with simplifications. Experimental data cover
only a low temperature range.
Therefore, more accurate and reliable data which cover the
(a)
whole range of welding temperature are necessary for more
precise prediction of weld pool formation.
4. Conclusions
The mechanisms of weld pool formation in TIG welding process
was discussed on the basis of numerical simulation which took
account of close interaction between the arc plasma and the anode
electrode. The main conclusions are as follows:
(b)
Fig. 5 Comparison of penetrations after 20 s for low sulfur using the
data of (a) Ref. 2) and (b) Ref. 3).
(1) The weld penetration geometry strongly depends on the data
of surface tension.
(2) For the low sulfur cases, the penetration depth obtained with
McNallan’s data shows better agreement with the experimental
results.
(3) For the high sulfur cases, the penetration depth obtained with
Matsumoto’s data shows better agreement with the experimental
results.
(4) For more precise predictions of weld pool formation, more
accurate and more and reliable data which cover the whole range
of welding temperature are required.
References
(a)
1)
(b)
Fig. 6 Comparison of penetrations after 20 s for high sulfur using
the data of (a) Ref. 2) and (b) Ref. 3).
M. Tanaka et al: "Numerical Study of a Free-Burning Argon Arc
with Anode Melting.", Plasma Chemistry and Plasma Processing
23.3 (2003), 585-606.
2) M. J. McNallan and T. DebRoy: "Effect of temperature and
composition on surface tension in Fe-Ni-Cr alloys containing
sulfur.", Metallurgical and Materials Transactions B 22.4 (1991),
557-560.
3) T. Matsumoto et al: "Surface tension of molten stainless steels
under plasma conditions.", Journal of materials science 40.9-10
(2005), 2197-2200.
4) J. P. Van Doormaal and G. D. Raithby: "Enhancements of the
SIMPLE method for predicting incompressible fluid flows.",
Numerical heat transfer 7.2 (1984), 147-163.