artigo 2018 Simulation and analysis of heat transfer and fluid flow characteristics of arc plasma in longitudinal magnetic field-tungsten inert gas hybrid welding

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ORIGINAL ARTICLE
Simulation and analysis of heat transfer and fluid flow characteristics
of arc plasma in longitudinal magnetic field-tungsten inert gas
hybrid welding
Zhengjun Liu1 & Yuhang Li1 & Yunhai Su1
Received: 2 August 2017 /Accepted: 5 June 2018
# Springer-Verlag London Ltd., part of Springer Nature 2018
Abstract
In the present work, an axisymmetrical model based on the magnetohydrodynamics (MHD) is established to investigate the effect
of external longitudinal magnetic field (LMF) on arc characteristics during the gas tungsten arc welding (GTAW) process. The
profiles of temperature and voltage drop, distributions of axial velocity, shear stress, and arc pressure, etc., in the cases of different
applied LMF strengths ranging from 0 to 0.06 T are simulated by utilizing the fluid dynamic theory coupled with Maxwell
equations. In order to achieve more accurate values of heat transfer and fluid flow of arc plasma, we take the boundary layer of
electrodes into consideration. The results show that the applied LMF could drive particles to rotate and expand the arc, and a
negative pressure area appears at the center and induces an upward streaming of gas (i.e., anti-gravity flow) through the arc core
with the effects of centrifugal force, concentrating the anodic energy to the cathode. When the magnetic induction strength is
0.06 T, vortexes are dramatically formed around the arc axis by the interaction between the anti-gravity flow from the arc center
and outside downward flow from the arc fringes. Thus, the distribution of current density, anodic heat flux, and arc pressure shifts
from the arc center to the periphery and forms a bimodal pattern. The various thermal fluxes and subsequent thermal efficiency
are also quantitatively investigated for a better understanding of the effects of LMF on arc behaviors and the theoretical
predictions show good agreement with the experimental results.
Keywords Longitudinal magnetic field . Arc behavior . Anti-gravity flow . Negative pressure . Heat transfer . Fluid flow
Nomenclature
A Vector magnetic potential
ADu Dushman constant
Az, Ar Axial, radial electrical vector potential
B Magnetic induction vector
Bext External magnetic flux density
Bθ Tangential magnetic field
CP Specific heat of argon
Cp, a Specific heat of specimen
e Electronic charge
h Total enthalpy
hc Heat transfer coefficient
Hanode Additional energy source for the anode
Hcathode Additional energy source for the cathode
j Current density
je Electron current density
ji Ion current density
jDu Dushman current density
kb Stefan-Boltzman constant
n Normal vector
P Pressure
Qtotal Total anode heat flux
Qe Electron contribution to the anode heat flux
Qc Conduction contribution to the anode heat flux
Qr Radiation contribution to the anode heat flux
r, z Radial, axial coordinate
SR Surface radiation loss
t Time
T Temperature
T0 Ambient temperature
* Zhengjun Liu
liuzhengjun1962@163.com
1 Department of Materials Science and Engineering, Shenyang
University of Technology, Shenyang 110870, Liaoning, People’s
Republic of China
The International Journal of Advanced Manufacturing Technology
https://doi.org/10.1007/s00170-018-2320-3
Ta Temperature at the anode surface
Te, a Temperature at 0.15 mm from the anode
ugas Flow rate of shielding gas
vr, vz Velocity in radial and axial directions
Va Anode fall
Vi Ionization potential of argon
Greek symbols
α Stefan-Boltzmann constant
δ Thickness of boundary layer
ε Radiation emissivity
κ Thermal conductivity
κa Thermal conductivity of specimen
μ0 Permeability of vacuum
ρ Mass density
σ Conductivity
τp Plasma drag force
Φ Voltage drop
ϕ Electric potential
ϕa Work function of the anode
ϕc Work function of the cathode
Subscripts
a Anode
c Cathode
1 Introduction
Magnetic control technique has been extensively applied
in material manufacturing process and is favored in many
fields, e.g., surface alloying [1], casting [2], and welding
[3–10]. Among them, electromagnetic welding technolo-
gy is of tremendous practical backgrounds given its abil-
ity to achieve good weld forming and better mechanical
properties by appending magnetic control on the conven-
tional welding process [3–10]. According to research re-
ported by many scholars [11–16], external magnetic field
(EMF) can be classified as transversal and longitudinal
according to its direction of action on the welding arc
and molten pool. The longitudinal magnetic field (LMF),
also known as the coaxial magnetic field can not only
change the flow of the arc so as to affect the heat trans-
fer on the anode surface, but affect the weld morphology
via electromagnetic stirring in the molten metal, which
plays an important role in refining the primary solidifi-
cation structure, reducing the chemical inhomogeneity,
and ultimately improving the quality of resultant welds
[8–10].
Even though great progress has been made [12–14],
note that only by experiment, it is difficult to thorough-
ly clarify the physical phenomenon for the complexity
of thermos-fluid fields in arc-electrode system. With the
rapid development of computer technology, numerical
simulation has become an effective and reliable method
on dealing with complex problems in the welding pro-
cess. Therefore, many numerical models have been de-
veloped with the aim to reproduce details and discover
its physical essence [16–25]. A unified model was de-
veloped by Tanaka et al. [17, 18] for clarifying the
formative mechanism of weld penetration by making
quantitative analysis on the interfaces of the whole
arc-electrode system, which was successfully achieved
and proven validated. Based on the model proposed
by Tanaka [17, 18], Traidia et al. [19] took into account
eddy current in their unified formalism to deal with the
arc plasma and weld pool time evolution under a dis-
continuous current welding process. Pan et al. [20] also
established a tungsten-arc-pool coupled model but con-
sidering two treatments of boundary layers for two
phases, i.e. DCEN and DCEP, respectively, to study
the heat transfer and fluid flow characteristics in vari-
able polarity gas tungsten arc welding (GTAW) for al-
loys with thin oxide films, i.e., aluminum and magne-
sium. Based on the numerical approaches raised by
Tanaka [17], Gonzalez et al. [21] first attempted to thor-
oughly study the effect of EMF on arc plasma. In con-
trast to the free-burning arc, the arc column deflects
with the help of cross flows from transversal magnetic
field, and slightly increases the total anodic flux.
Similar results were also obtained from a coupled model
developed by Chen et al. [22] to study the arc behavior
under the LMF in which arc plasma was considered as
turbulent flow. Luo et al. [12–14] studied the effect of
LMF on arc plasma by means of both experimental and
numerical approaches, and believed that the current den-
sity and heat flux agree with the Gaussian relations in
the circumstances of low welding current (less than
200 A) and low magnetic field strength (less than
0.1 T). However, Yin et al. [23] argued that the distri-
butions of current density, anodic heat flux, and plasma
shear stress agree with double-peaked instead of normal
Gaussian in a relatively low magnetic induction by es-
tablishing a three-dimensional unified model and also
claimed that the temperature on the interface of arc
plasma and weld pool decreases with stronger LMF
due to a reverse flow along the axis of the arc, resulting
in a wide and shallow weld. Followed by research of
Yin et al. [19], Luo et al. [24] established an axisym-
metrical model performed by the finite volume method
(FVM) to study the threshold conditions from free-
burning arc to constraint arc in magnetic controlled
TIG welding, and believed that the reverse flow inside
the arc from Yin et al. [23] could form a vortex grow-
ing up with magnetic flux intensity and resulting from a
negative pressure by the high-speed rotation of charged
particles. To thoroughly study the flow motion from
LMF, Xiao et al. [16] established a three-dimensionalInt J Adv Manuf Technol
unified model and took metal vapor into consideration
to study arc behavior and flow characteristic on the
interface of arc and weld pool with the effect of both
longitudinal and transverse magnetic fields. However,
the mechanisms of vortex formation and heat transfer
on LMF-TIG hybrid welding, especially for the energy
balance between the electrodes, were still unclear and
lacking quantitative analysis.
This paper is focused on the arc behavior and energy
transfer for the LMF-TIG hybrid welding process. The
fluid dynamic theory and Maxwell equations were applied
to predict the distributions of arc temperature, arc voltage,
current density, and arc pressure of both axial and radial
directions. In addition, boundary layers of electrode were
taken into account to achieve the various forms of heat
flux between arc plasma and weld pool. Based on the
numerical procedure, the effects and movement mecha-
nism of LMF on the arc behavior were systematically
analyzed and discussed. The theoretical results from the
study was verified by experimental data and may provide
guidance for possible industrial applications and further
investigations.
2 Experimental work
Figure 1(a) shows a schematic of the experimental process of
GTAW with an LMF device. The directing LMF can be in-
duced via encircling copper coils coaxially to the weld torch
after charging by the power source. Thus, the magnetic field
parallels to the welding current, perpendicular to the speci-
men. The welding tractor and torch were set to be immovable
to provide a stationary arc, and a high-speed camera device
(FASTCAM ultima 512 series, manufactured by Photron,
Japan) was used in the present study to capture the changing
process of the arc plasma under different magnetic fields.
Thus, a comparison between the photographed arc profile
and simulated temperature contours will be used to validate
our model. The specific sectional views of magnetic device
and welding arc are shown in Fig. 1(b, c), respectively. The
diameter of the exciting coil we used is about 90 mm, which is
significantly larger than the cross-sectional radius of the arc
plasma, and the distance of the fixtures was set to a length
greater than 30 mm so that the effect of the fixture and spec-
imen on the LMF distribution can be ignored. Thus, the addi-
tional magnetic field for our experiments and simulations can
Fig. 1 Schematic illustration of
experimental equipment: a
overall view of experimental
setup with an applied LMF; b
specific sectional view of the
magnetic device; and c welding
arc
Int J Adv Manuf Technol
be considered as fully longitudinally distributed without any
lateral components. The intensity of the LMF can be con-
trolled by adjusting the rotary knobs on the power source
directly to alter the excitation current in the coil. A stainless
steel was chosen as the specimen on top of the cooling copper
plate fixed by a fixture, and the gap between the tungsten tip
and the specimen sheet is 5 mm.
In the present article, we assumed that the anode is a 5-mm
thick stainless steel under a welding current of 150 A, so the
diameter of the tungsten cathode is 3.2 mm with about a 60°
conical tip. Pure argon was adopted as shielding gas with a
flow rate of 15 L/min to ensure the optimum degree of pro-
tection for welds.
3 Numerical simulation
3.1 Basic assumptions
In this study, a two-dimensional axisymmetrical model for
LMF-TIG hybrid welding process was established, and some
basic assumptions that could simplify the calculations were as
follows:
& The arc is optically thin and supposed to be in the local
thermodynamic equilibrium (LTE) state, which means the
temperatures of heavy particles and electrons are approx-
imately the same [18].
& The plasma flow is assumed to be laminar [23–25]; the
gravity and thermal viscous dissipation are neglected.
& The calculation domain is filled with incompressible pure
argon, whose properties are only temperature dependent
[26, 27].
& Heat loss due to vaporization in the anode boundary and
its effect to arc behavior are neglected.
3.2 Governing equations
(a) Mass continuity equation:
∂ρ
∂t
þ 1
r
∂
∂r
rρvrð Þ þ ∂∂z ρvzð Þ ¼ 0 ð1Þ
(b) Axial conservation momentum equation:
1
r
∂ρvz
∂t
þ 1
r
∂
∂r
rρvrvzð Þ þ ∂∂z ρv
2
z
� � ¼ − ∂P
∂z
þ ∂
∂z
2η
∂vz
∂r
� �
þ 1r ∂∂r ð rη ∂vr∂z þrη ∂vz∂r Þ þ jrBθ
(c) Radial conservation momentum equation:
1
r
∂ρvr
∂t
þ 1
r
∂
∂r
rρv2r
� �þ ∂
∂z
ρvzvrð Þ ¼ − ∂P∂r þ
1
r
∂
∂r
2η
∂vr
∂r
� �
þ ∂
∂z
η
∂vr
∂z
þ η ∂vz
∂r
� �
−2η
∂vr
r2
− jzBθ þ Sext
ð3Þ
Where jr and jz are obtained by solving the Maxwell equa-
tions based on the electromagnetic induction vector method.
The additional source Sext is the radial external magnetic force
generated by interaction of longitudinal magnetic field and
helical current due to stirring effect, which may therefore be
expressed as ∂∂r jj jBext.
(d) Energy conservation equation:
∂ρh
∂t
þ 1
r
∂
∂r
ρrvrhð Þ þ ∂∂z ρvzhð Þ
¼ ∂
∂z
κ
Cp
∂h
∂z
� �
þ 1
r
∂
∂r
r
κ
Cp
∂h
∂r
� �
þ j
2
z þ j2r
σ
þ 5
2
κb
e
jz
Cp
∂h
∂z
þ jr
Cp
∂h
∂r
� �
−SR
ð4Þ
The last three terms of Eq. (4) represent the joule heating,
the diffusive transport of enthalpy due to the electron drift, and
the radiation loss, respectively.
(e) Current continuity equation:
∂
∂z
jz
� �þ 1
r
∂
∂r
∇ ⋅ r jrð Þ ¼ 0 ð5Þ
(f) Axial and radial currents can be obtained from Ohm’s
law:
jr ¼ −σ
∂ϕ
∂r
; jz ¼ −σ
∂ϕ
∂z
ð6Þ
(g) The inducedmagnetic field can be derived from the mag-
netic vector potential equation:
∇ 2⋅A ¼ −μ0 j ð7Þ
So, we can deduce the azimuthal magnetic induction:
B ¼ ∇ � A ð8Þ
Therefore,
Bθ ¼ ∂Ar∂z −
∂Az
∂r
ð9Þ
Int J Adv Manuf Technol
According to Ramírez-Argáez et al. [28], there are
two approaches representing the same physics when
dealing with welding arcs and giving very close results
in terms of arc properties but involving different math-
ematical formulations, namely, the “potential” and
“magnetic” approaches. The electric potential approach
shows to be more superior than the magnetic approach
due to not appearing singularity in the axis of symmetry
(r = 0) and no need to be modified when calculating
magnetic induction and Lorentz force. Thus, it will be
used in our model.
3.3 Treatment of boundary layers
There are boundary layers possessing the thickness of a few
mean free path lengths on the surface of the cathode and the
anode, namely electrode sheath, which are not in the local
thermodynamic equilibrium (LTE) state due to the existence
of collisions of electron-ion or electron-neutral atom, resulting
in low-temperature layers. Recently, many scholars have tak-
en boundary layers into consideration in their numerical
models [17, 18, 29–32], because of its significant effect on
heat and mass transfer from welding arc to molten pool.
Hence, the calculation of energy flux through the electrode
is of great importance.
3.3.1 Cathode boundary layer
Thermionic emission and a small amount of field emis-
sion from electrons occurred in the arc-tungsten bound-
ary layer, from the cathode (tungsten) to the anode
(specimen), leading to the cathode cooling and a small
amount of radiation loss; meanwhile, ion heating from
the ionization of argon is also part of the thermal flux
on the cathode surface. Hence, the additional energy
flux for the cathode, Hcathode is
Hcathode ¼ − jej jϕc−εαT4 þ jij jVi ð10Þ
According to the maximum electron density due to thermal
emission from the cathode surface assumed by Pan [20] and
Traidia et al. [33], je cannot exceed Dushman current density
jDu [34], given by
jDuj j ¼ ADuT2exp −
eϕe
kbT
� �
ð11Þ
Therefore, both electron and ion current density can be
obtained from the following expressions [17–19, 33]:
je ¼ jDu if j⋅nj j− jDu > 0j⋅nj j if j⋅nj j− jDu≤0
�
ji ¼ j⋅nj j− je ð12Þ
where |j ⋅ n| is the total current density on the cathode surface
which can be obtained from Eq. (5).
3.3.2 Anode boundary layer
Thermionic heating from electron emission would trans-
fer to the anodicboundary layer, as well as the conduc-
tion heat from plasma, which may accelerate the melt-
ing of anode and form a deeper penetration. In addition,
there is also a small amount of energy loss by radiation
from the anode to the ambient. On this point, Tanaka et
al. [17] reported an energy flux term which could de-
scribe the energy exchange on the anode surface more
accurately. Two additional terms of which have been
considered in most cases [21, 35, 36], i.e., the anode
fall heating, j ⋅ Va, and electron enthalpy entering the
anode, j(5/2(kbTe/e)). The j ⋅ Va term is more than the
actual heat input to the anode and already included in
Eq. (4), so it may be redundant to be a part of energy
flux for the anode. The j(5/2(kbTe/e)) term only becomes
effective when the arc is in low current and non-
equilibrium state instead of high current of 150 A we
used in the present article. Therefore, the additional en-
ergy flux for the anode, Hanode, is
Hanode ¼ jj jϕa þ κ Te;a−Ta
� �
=δ−εαT4a ð13Þ
According to the assumptions proposed by Lago et
al. [35] and Pan et al. [30], the thickness of the anode
boundary layer is about 0.15 mm, which is necessary in
the calculation of conduction heat. Wu [37] and Lu et
al. [36] proposed that radiation also occurred from arc
plasma to the anode, less than 5% of the total heat flux,
which is assumed to be negligible in the present work.
Fig. 2 Schematic illustration of the computational domain
Int J Adv Manuf Technol
3.4 Computational domain and boundary conditions
In order to solve all the differential equations for the compu-
tational domain, initial values for calculation of boundaries
need to be specified. Figure 2 shows the computational do-
main for the present simulation work; boundaries are lines
linked by points expressed by capital letters. The computa-
tional domain contains a tungsten region (ABJI), arc zone
(BCDEHIJ), and specimen region (HEFG). AB is electrode
area on which is imposed a uniform current density normal to
the surface. BC is gas inflow where the velocity distribution
should be given to yield argon flow rate of 15 L/min, DE is the
outflow, and GHIA is an axisymmetric boundary. The whole
computational domain is meshed using structure quadrilateral
elements with variable mesh sizes when considering the ther-
mal and electric gradients occurring in the electrode sheath
regions. So, the mesh size densities are as follows: a cell
thickness of 2.5 × 10−4 m in the plasma domain (BCDEHIJ),
1 × 10−4 m in the cathode domain (ABJI) for resolving the
effects of the applied electric field due to the shape of the
Table 1 Boundary conditions for
the welding arc model AB BC CD DE EF FG GHIA
P – – 1 1 – – –
vz – ugas ∂vz/∂z = 0 vz = 0 vz = 0 vz = 0 ∂vz/∂r = 0
vr – vr = 0 vr = 0 ∂vz/∂z = 0 vr = 0 vr = 0 ∂vr/∂r = 0
T T = T0 T = T0 T = T0 T = T0 T = T0 T = T0 ∂T/∂r = 0
ϕ j ⋅ n ∂ϕ/∂z = 0 ∂ϕ/∂z = 0 ∂ϕ/∂r = 0 ∂ϕ/∂r = 0 ϕ = 0 ∂ϕ/∂r = 0
Fig. 3 Physical properties of argon as a function of temperature: a viscosity and thermal conductivity; b density and conductivity; c specific heat; d
radiation loss
Int J Adv Manuf Technol
conical tip of the cathode, and a finer size of 7.5 × 10−5 m at
the interface of the arc and weld pool (HE), where high ther-
mal and electric gradients occur. The whole calculations are
performed on a Lenovo PC with 0.01 s of time step. Boundary
conditions adopted for the present model are listed in Table 1
in detail.
3.5 Material properties for the gas and electrodes
Physical properties of the tungsten electrode are assumed to be
constant in this work due to its insensitivity to high tempera-
ture [38] and taken from the data of Perović [39] and Righini
et al. [40]. Radiation loss term for argon in the conservation
equation and its physical properties are assumed to be
piecewise-linearly temperature dependent according to data
taken from published literature [26, 27, 41] shown in Fig. 3.
The thermal conductivity and specific heat of anode are also
functions of temperature and were taken from Wu [37] which
can be represented as:
κa ¼
10:717þ 0:014955T if T ≤780K
12:076þ 0:01321T if 780K < T ≤1672K
217:12−0:109T if 1672K < T ≤1727K
8:278þ 0:0115T if T ≥1727K
8>><
>>:
ð14Þ
Cp;a ¼
438:95þ 0:198T if T ≤773K
137:93þ 0:59T if 773K < T ≤873K
871:25−0:25T if 873K < T ≤973K
555:2þ 0:0775T if T ≥973K
8>><
>>:
ð15Þ
All of these data and other major physical properties for the
argon and electrodes used in this model are shown in Table 2.
3.6 Numerical method
The whole mathematical models are solved by CFD software
FLUENT. Partial differential Eqs. (1) to (9) of which are
discretized by the FVM and solved iteratively by using the
numerical procedure. The additional sources of energy, mo-
mentum, thermophysical properties, and boundary conditions
were compiled into the form of user-defined functions
(UDFs), some special properties of which, e.g., voltage, cur-
rent density, and each single compound of heat flux, are de-
fined as scalar equations. The conservation equations are
solved by the SIMPLE algorithm with second-order upwind
scheme due to greater precision and more adaptive for cou-
pling calculations of pressure and velocity [36]. The conver-
gence criterion for energy equation is 10−6, and that for other
equations (e.g., momentum, scalar, etc.) is 10−3.
Since this study specializes in the behavior and mechanism
of arc plasma with or without the EMF applied, the mecha-
nism and property which might be relevant to the molten pool
are not discussed.
4 Results and discussion
4.1 Temperature and flow fields
Figure 4(a–f) represents the temperature profile and flow
fields for the arc plasma with the applied LMF in the level
of 0 to 0.06 T, respectively. The maximum temperature of arc
calculated in this study is 17,057 K at the location nearly
0.5 mm below the tungsten tip, just slightly higher than that
of 17,000 K calculated by Tanaka [17]. The maximum tem-
perature of the tungsten tip is 3769 K, which is in good
Table 2 Major physical
properties used in this numerical
model [17, 26, 27, 36, 37, 41]
Physical interpretation Value Unit
Cathode Work function 4.52 V
Effective work function
for thermal emission
2.63 V
Thermal conductivity 95 W/(m ⋅K)
Electrical conductivity 1.37 × 106 S/m
Specific heat 130 J/(Kg ⋅K)
Density 1.89 × 104 Kg/m3
Arc plasma Ionization potential of argon 15.68 V
Thermal conductivity Fig. 3(a) W/(m ⋅K)
Electrical conductivity Fig. 3(b) A/(V ⋅m)
Specific heat Fig. 3(c) J/(Kg ⋅K)
Density Fig. 3(b) Kg/m3
Anode Work function 4.65 V
Melting point 1750 K
Thermal conductivity Eq. (14) W/(m ⋅K)
Specific heat Eq. (15) J/(Kg ⋅K)
Int J Adv Manuf Technol
agreement with experimental data measured by Zhou and
Heberlein [42]. As can be seen, the arc profile close to the
tungsten tip constricts and near the anode becomes more dis-
persedwith the application of stronger magnetic field strength,
resulting in a more exceptional form of “bell shape” different
from that of free-burning arc. The temperature of location
about 2.5 mm below the tungsten tip along the symmetry axis
is more than 15,000 K as shown in Fig. 4(a), decreasing to
14,000 K in Fig. 4(b), and then keeps dropping until it reaches
to approximately 11,000 K as shown in Fig. 4(f). That means
the energy transferred to the anode trends to converge on a
small area of about 0.6 mm length below the tungsten tip and
then transfers part of the heat to the arc fringes bymeans of hot
plasma flow (Fig. 4(f)), consequently, leading to a higher peak
arc temperature and lower anodic energy density. The same
phenomenon was also predicted and proved by the spectro-
scopic measurement from Yin et al. [23] who claimed that the
low-temperature region indeed exists in the arc center close to
the anode surface when applying the LMF.
From the flow fields of arc plasma shown in Fig. 4(a), it can
be seen that the plasma jet flows from the cathode to the anode
along the symmetry axis with a maximum velocity of 218 m/s
at the central of arc column without any magneticfield ap-
plied, which is close to the results predicted by some re-
searchers [17, 18]. According to the results shown in Fig.
4(b–e), the velocity of plasma flow has the tendency to reduce
slightly with the stronger LMF applied. When the magnetic
field strength reaches 0.06 T, an abnormal arc behavior occurs
as can be seen in Fig. 4(f). Two counterclockwise vortexes
with lengths of respectively 0.4 and 2 mm are generated
around the arc axis by the interaction of downward plasma
flow on the periphery of the arc and a streaming of upward gas
flow (i.e., anti-gravity flow) along the arc axis. The smaller
one is located just below the cathode tip with a flow rate of
Fig. 4 Temperature distribution and flow fields of welding arc in GTAWwith different magnetic induction strengths applied: a Bext=0 T; b Bext=0.01 T; c
Bext=0.02 T; d Bext=0.04 T; e Bext=0.05 T; f Bext=0.06 T
Int J Adv Manuf Technol
59m/s while the bigger one is 37m/s above the anode surface.
The peak velocity, however, decreases to 125m/s, is located in
the intersection area of vortex and downward plasma flow,
and is consistent with the location of maximum velocity pre-
dicted by Xiao [16], Yin [23], and Luo et al. [24]. The de-
crease in velocity of plasma may be due to changes of charged
particle movement caused by a stirring effect from the LMF.
4.2 Electric potential field and current density
Figure 5(a–f) shows the electric potential field and maximum
axial current density for welding arc with the application of
LMF in the level of 0 to 0.06 T, respectively. In free-burning
arc, the voltage drop between the tungsten tip and anode sur-
face is 9.5 Vas shown in Fig. 5(a), which is close to the value
of 10.4 V calculated by Tanaka et al. [17]. The electric poten-
tial distribution near the cathode sheath is more intense be-
cause of the difference in speed between electrons and ions
[34]. In the presence of the LMF (Fig. 5(b–f)), the voltage
drop increases slightly with the higher EMF strength due to
the elongation of arc length caused by rotating particles and
eventually reaches 11.9 V, where exactly the plasma flow
pattern starts to transition (cf. Fig. 4(f)). The axial current
Fig. 5 Electric potential field and maximum axial current density of welding arc in GTAWwith different magnetic induction strengths applied: a Bext =
0 T; b Bext=0.01 T; c Bext=0.02 T; d Bext=0.04 T; e Bext=0.05 T; f Bext=0.06 T
Fig. 6 Effect of magnetic induction strength on the anodic current density
for GTAW arc
Int J Adv Manuf Technol
density and streamlines of current in different levels of
magnetic-field strength are also shown in Fig. 5(a–f). As the
LMF strength increases, the maximum axial current density
increases from 2.3 × 107A/m2 at 0 T to 3.1 × 107A/m2 at
0.06 T due to the thermal pinch effect caused by rotating
charged particles. The streamlines represent the macrotrends
of current flow travels from the anode to the cathode. Its pro-
file also acts like a shape of bell, constricting slightly on the
top and expanding distinctly on the bottom.
4.3 Physical properties
In order to investigate the effect of LMF on arc characteristic
and explain the abnormal behavior “anti-gravity flow” and
“flow vortex” from the simulation (cf. Fig. 4f), arc properties
in different magnetic induction strengths are needed to reveal
the mechanics behind the phenomenon. Therefore, in this
study, the arc properties, namely, arc pressure, plasma shear
stress, current density, plasma velocity, and anodic heat flux,
under the LMF in a range of 0~0.06 T were studied; the mu-
tual relation between them was also systematically analyzed.
Figure 6 shows the anodic current density distribution in
different cases of LMF strength ranges from 0 to 0.06 T. In the
conventional arc, the anodic current density shows a typical
Gaussian distribution; as the LMF strength increases, the max-
imum of current density on the anode decreases, and the peak
of current density trends to deviate from the arc center to the
edges, causing a lower value on the symmetry axis, i.e., bi-
modal distribution. Because the orbit of charged particle
seems to expand to a larger size, more particles turn to distrib-
uting in the location away from the center and increases its
distribution radius slightly with the help of LMF. The maxi-
mum axial current density for free-burning arc in the present
Fig. 7 Effect of magnetic induction strength on the anodic heat flux for
GTAW arc
Fig. 8 Effect of magnetic induction strength on the anodic arc pressure
for GTAW arc
Fig. 9 Distribution of axial arc pressure with and without the LMF
applied
Fig. 10 Effect of magnetic induction strength on the plasma shear stress
for GTAW arc
Int J Adv Manuf Technol
work is consistent with value calculated by Lowke et al. [43]
and Tanaka et al. [17].
Figure 7 shows the radial variation of anodic heat flux with
different LMF strengths (0~0.06 T) applied, and similar to
distribution of current density, the location of maximum of
heat flux also has the tendency to move from center to edges,
decreasing with the increasing LMF strength, causing a wider
heat distribution radius; as a result, a shallow and wide weld
formed. Hence, the increase of the LMF can lead to the exten-
sion of energy distribution on the anode surface; meanwhile, a
large amount of energy is lost to the ambient by convection.
The heat flux intensity without the applied LMF fairly agrees
well with the experimental data obtained by Lowke et al. [43],
which proves the validity of the anodic heat transfer for the
conventional arc.
The effects on different levels of LMF (0~0.06 T) on the
distribution of arc pressure at the anode surface are shown
in Fig. 8. The maximum of arc pressure decreases with the
increasing LMF at lower intensity, when the magnetic field
strength increases to 0.05 T, the arc pressure increases at
first and then decreases with increasing radial distance, that
means the location of peak arc pressure moves from the arc
center to edges, similar to current density (Fig. 6) and heat
flux distribution (Fig. 7). When the magnetic field strength
is 0.06 T, a negative pressure occurs at the arc center, in-
creases with increasing radial distance, and achieves posi-
tive at nearly 1.1 mm, then reaches to peak value at nearly
2.2 mm. The emergence of negative pressure may be the
reason why the anti-gravity flow occurs in the arc center
and also leads to vortexes. Hence, it is of great significance
to study the distribution of arc pressure inside the arc col-
umn with the effect of LMF.
Figure 9 shows the axial distribution of arc pressure at the
arc center for free-burning arc and the LMF-TIG hybrid arc.
The areas near the cathode and the anode along the symmetry
axis were marked as points A and B, respectively. In free-
burning arc, the plasma gas flows from the cathode to the
anode along the symmetry axis (cf. Fig. 4(a)), which means
the average pressure gradient along the axis should be nega-
tive. The axial pressure is always positive from the tungsten
tip (600 Pa) to A (351 Pa) and reaches the anode surface
(400 Pa), causing a negative average pressure gradient (∂P/
∂z < 0); the whole axial distribution characteristic of arc pres-
sure agrees with the results approximately obtained by Tanaka
et al. [18]. However, in the presence of LMF (Bext = 0.06 T),
the arc pressure distribution has a dramatic change, from pos-
itive to negative along the symmetry axis, and the anti-gravity
flow starts from B (− 50 Pa) to A (− 366 Pa) (cf. Fig. 4(f)),
giving rise to a positive average pressure gradient (∂P/∂z < 0).
The distribution pattern of arc pressure analyzed above for the
LMF-TIG hybrid arc is consistent with calculation results
achieved by Xiao [16] and Luo et al. [28].
Figure 10 shows the radial variations of shear stress in
different cases of LMF ranges from 0 to 0.06 T; combined
Fig. 11 Effect of magnetic induction strength on the axial velocity for
GTAW arc
Fig. 12 Comparison of heat flux distribution at the surface of specimenunder the LMF strengths of a 0 and b 0.06 T
Int J Adv Manuf Technol
with analysis of arc temperature, the distribution of shear
stress can be better understood. Without the applied LMF,
the plasma drag force increases firstly, reaching the maximum
of 73 N/m2 and then decreasing with the increasing radial
distance. When the LMF is applied, the plasma shear stress
decreases slowly at a lower intensity of the magnetic flux.
However, it decreases sharply when the LMF reaches
0.04 T, and the location of maximum shear stress starts to
deviate from initial position to the edge because of the expan-
sion of arc. Bimodal distribution for shear stress appears with
the application of strong EMF (Bext ≥ 0.05T). When the LMF
increases to 0.06 T, the distributions of twin peaks become
significant, and the emergence of the smaller peak is attributed
to the vortex on the anode surface (cf. Fig. 4(f)). The trough
between the twin peaks happens to be the location of intersec-
tion between the vortex and downward plasma flow (cf. Fig.
4(f)). However, the normal stress (i.e., arc pressure) of which
is approaching the maximum (cf. Fig. 8). Plasma shear stress
is already proved to be one of the main driving forces affecting
the fluid flow and heat transfer of weld pool in conventional
GTAW. Thus, a study focused on weld pool behavior taking
the plasma shear stress into consideration under the effect of
LMF is urgently needed in the future works.
For a better understanding of anti-gravity flow in the arc
plasma with the LMF applied, the distributions of axial veloc-
ity along the symmetry axis of the plasma flow in different
levels of magnetic field are necessary and shown in Fig. 11.
For conventional arc, the axial velocity of plasma flow along
the symmetry axis increases sharply at first and then declines
slowly. With the applied LMF, similar with the shear stress
and anode heat flux, the axial velocity decreases with the
increasing LMF; when the LMF reaches 0.05 T, the distribu-
tion pattern of axial velocity for plasma flow becomes a little
cluttered and happens to reverse near the anode. However,
when the LMF reaches 0.06 T, reverse flow distributes along
the whole symmetry axis and reaches the maximum (a little
over 150 m/s) near the cathode, resulting in a vortex by
interacting with downward flow on the periphery of the arc
(cf. Fig. 4(f)). The results in Fig. 11 agree well with other
properties of the arc demonstrated in Figs. 4 and 9.
4.4 Heat transfer analysis
As mentioned above in this paper, with the application of the
LMF, energy transfer seems to congregate to the location near
the cathode and makes the arc temperature rise. However,
Table 3 Comparison of heat transfer balance with and without the LMF in the GTAW process (with study of Tanaka [17] as reference)
Energy balance (W)
Manabu Tanaka (for comparison) This study
Magnetic induction strength (T) 0 0 0.06
Total heat input 1215 1425 1785
Voltage drop (V) 8.1 9.5 11.9
At anode Input Ohmic heating 1 – –
Conduction from arc Qc 373 387.7 512.7
Electron absorption Qe 697 679.6 664.6
Output Conduction to bottom 1009 – –
Radiation Qr 30 26 28.7
Total heat flux Qtotal 1041 1041.3 1148.6
Thermal efficiency (%) 85.7 73.1 64.3
Fig. 13 Schematic diagram of arc mechanism: a without the LMF applied; b with the LMF applied
Int J Adv Manuf Technol
unfortunately, the details of heat and mass transfer for the
LMF-TIG hybrid arc have rarely been studied. In this paper,
every single heat flux transferred to the anode, i.e., qe, qc, and
qr with and without the applied LMF, was analyzed quantita-
tively. The comparisons of various heat flux distributions for
arc plasma with and without the presence of LMF are shown
in Fig. 12(a and b). In free-burning arc, all various heat fluxes
decline with the increases in radius; however, in LMF-TIG
hybrid arc, heat fluxes just increase at the arc column and then
decrease at the periphery of the anode. The energy transfer to
the anode is obtained by integrating the various heat fluxes qe,
qc, and qr over the whole anode surface, respectively, and is
compared with that from the study of Tanaka [17] for its va-
lidity, listed in Table 3.
The energy transfer to the anode for free-burning arc is:
Qtotal ¼ Qe þ Qc þ Qr ¼ ∫Ωqedsþ ∫Ωqcdsþ ∫Ωqrds
¼ 679:6W þ 387:7W−26W ¼ 1041:3W ð16Þ
From the above equation,Qe,Qc, andQr accounts for 65.3,
37.2, and 2.5% of Qtotal, respectively; the heat from electrons
contributes to the main part of the total heat flux, which can
explain the similarity of the distribution between heat flux and
current density (Figs. 6 and 7). The heat from conduction is
relatively small, and a radiation loss of 26Waccounts for only
2.5% of total heat flux to reach the neglect degree. The thermal
efficiency for conventional welding process can be obtained
from Eq. (17) and is 73.1%, which is lower than the efficiency
of 85.7% from Tanaka [17].
η ¼ Qtotal
Φ⋅I
ð17Þ
The energy transfer to the anode for LMF-hybrid arc is:
Qtotal ¼ Qe þ Qc þ Qr ¼ ∫Ωqedsþ ∫Ωqcdsþ ∫Ωqrds
¼ 664:4W þ 512:7W−28:7W ¼ 1148:6W ð18Þ
The various heat fluxes Qe, Qc, and Qr for the LMF-hybrid
welding process account for 57.8, 44.6, and 2.5% of total heat
flux, respectively, and the thermal efficiency is 64.3%.
Compared with the conventional arc, we can see the total heat
flux and the heat from conduction are higher, which is mainly
because the arc rotation in high speed expands its radial and
increases the anode surface area for heat conduction, as well as
the heat loss from convection. According to the principle of
minimum voltage, the arc withstands the loss of heat which
will maintain its origin state by increasing the input power;
thus, a higher voltage occurs (cf. Fig. 5). However, although
the total heat flux to the anode increases, the thermal efficien-
cy is still lower due to a large amount of heat loss.
Fig. 14 Comparison of
temperature distribution for
conventional arc. The
experimental results (200 A at
5 mm arc length) are from Farmer
et al. [44]
Fig. 15 Comparison between experimental photographs and calculated temperature profiles for arc plasma in different cases: a conventional GTAW; b
with LMF (Bext = 0.06 T)
Int J Adv Manuf Technol
4.5 Movement mechanism
According to the above description, the arc temperature, ve-
locity field, voltage drop, current density, and other properties
which might be relevant to arc behaviors with and without the
LMF applied were predicted and validated; nevertheless, the
movement mechanism of the charged particles with the stir-
ring effects from the LMF still remains uncertain and needs
more exploration.
In the conventional arc (Fig. 13(a)), the plasma flow accel-
erated by self-induced electromagnetic force to a high speed
of over 200 m/s to the anode (cf. Fig. 4(a)), meanwhile, elec-
trons emitted from the cathode to the anode become dispersed
on the anode. Accordingly, welding current flows from the
anode to the cathode and makes a slight contraction on the
arc column due to the pinch effect. However, in the LMF-TIG
hybrid arc (Fig. 13(b)), charged particles are driven to the
periphery of the arc and take a high-speed rotation in the
bell-helical way by means of Lorenz force from the LMF,
giving rise to a dispersed arc. However, the cathodic arc at-
tachment is significantly constricted with the help of pinch
effect due to extremely high current density (cf. Fig. 5(b–f)).
The gas flow direction on the periphery of arc remains un-
changed, in the arc core, however, it is completely reversed.
That is because the high-speed rotation of plasma on the pe-
riphery of arc may generate a centrifugal force, thus inducing a
negative pressure along the arc axis (cf. Fig. 9) for balancing
the pressure of both internal and external. Under the circum-
stances, a reverse gas flow, namely, the anti-gravity flow, is
generated in the arc core from the anode to the cathode (B→
A) along the arc axis. As a result, a suction force on the anode
surface is generated. Meanwhile, the anodic arcattachment
may get more dispersed due to the radial Lorenz force gener-
ated by tangential rotating particles and LMF.
According to previous studies [12, 13, 22–24], under the
effect of the LMF, a thin shell consisting of welding current is
located on the periphery of the arc, leaving a completely hol-
low area in the arc core. However, as demonstrated above,
vortexes can be generated around the arc axis by the interac-
tion of anti-gravity flow and typical downward flow. The anti-
gravity flow would strengthen with the increase of magnetic
induction strength, and also the size of vortexes. Essentially,
the arc center is not completely hollow.
5 Experimental validation
As was stated in the aforementioned experimental work, some
experimental welding arc studies in the literature combined
with the photographed arc profile obtained from our experi-
ment can be used to validate the predictions of our model.
The comparison between experimental from Farmer et al.
[45] (right side) and calculated temperature contours (left side)
for argon arc is shown in Fig. 14. The same welding parame-
ters (200 A of welding current and 5 mm arc length) as Farmer
are used for validating our model. The maximum temperature
obtained from our model is over 21,500 K, slightly lower than
that of the experimental result (22,000 K); the upper part of the
arc plasma from our model shows a good agreement with
experimental data. However, discrepancies between the two
approaches appear at the periphery of the arc near the anode
where the LTE state does not dominate. Thus, the arc fringes
expressed by isotherm of 10,000 K from our model seem
more dispersed.
Figure 15 shows the comparison between experimental
photographs and calculated temperature profiles in the cases
of conventional arc and LMF-TIG hybrid arc. The photo-
graphs were taken from the high-speed camera shown in our
experiment (Fig. 1), and magnetic flux densities of 0 and
0.06 T were selected for validation. As can be clearly seen in
Fig. 15(a), the typical bell shape of the arc periphery expressed
by the isotherm of 8000 K shows a fairly agreement with its
photographed profile from the experiment for conventional
arc. And also, with the effect of LMF (Bext = 0.06T), the
photographed arc profile close to the cathode tip constricts
and expands near the anode, shown as the exceptional form
of “bell shape” and can be clearly seen in Fig. 15(b), which is
consistent with our numerical results.
The simulation results of arc shape changing with the effect
of LMF were verified in our experiment, which can indirectly
prove that our analysis is reasonable. However, the verifica-
tion of other arc characteristics, e.g., velocity distribution, an-
odic current density with the effect of LMF, etc., to further
prove theoretical findings about the LMF-TIG hybrid arc is
currently unable to implement due to the difficulties of exper-
iment and lack of relevant literature data. Further in-depth
validations and investigations of weld pool with the effect of
LMF need to be accomplished in the future works.
6 Summary and conclusion
The behavior and movement mechanisms for both conven-
tional and LMF-TIG hybrid arcs are investigated; the quanti-
tative analyses are obtained as well based on a two-
dimensional axisymmetrical model. The conclusions can be
summarized as follows:
(1) Particles in the arc plasma are driven to rotate under the
influence of LMF and make the arc column more dis-
persed with the help of centrifugal force and radial
Lorenz’s force. Thus, a negative pressure arises at the
arc core and concentrates the anodic energy to the cath-
ode; consequently, the peak temperature increases while
the anodic temperature decreases.
Int J Adv Manuf Technol
(2) The anti-gravity flow generated by negative pressure at
the arc core interacts with the downward flow on the
periphery of arc and gives rise to vortexes around the
arc axis. The distributions of arc properties (e.g., anodic
heat flux, arc pressure, and anodic current density) are
converted from normal to bimodal.
(3) Although with the application of LMF, the anodic ther-
mal efficiency is lower than that without the LMF ap-
plied, the total heat flux is higher due to a larger heating
area and is dominated by the conductive heat.
(4) A thin shell of current is generated by centrifugal force
on the periphery of arc. However, the arc core is not
entirely hollow.
Acknowledgements Our deepest gratitude goes to the editors and anon-
ymous reviewers for their careful work and thoughtful suggestions that
have helped improve this paper substantially.
Funding information This work was founded by Dr. Foundation Start-up
Project of Liaoning Province (grant number 20131079).
Compliance with ethical standards
Conflict of interest The authors declare that they have no conflict of
interest.
Publisher’s Note Springer Nature remains neutral with regard to jurisdic-
tional claims in published maps and institutional affiliations.
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