Download Liquid metal flow behavior during vacuum consumable arc remelting

International Journal of Engineering & Technology IJET-IJENS Vol: 12 No: 01
50
Liquid metal flow behavior during vacuum
consumable arc remelting process for titanium
Hongchao Kou, Yingjuan Zhang, Zhijun Yang, Pengfei Li, Jinshan Li, Lian Zhou
Abstract—To better understand the vacuum arc remelting
(VAR) process, a 3D finite element model is established to
analyzing the electromagnetic, temperature and flow fields of
titanium alloy ingot during steady state melting process using
ANSYS software. The research results show that the current flows
from the crucible to consumable electrode. The magnetic field
induced by current is rotary on axial line, which increases firstly
and then decreases from the center to edge of crucible. The
buoyancy, self-induced and stirring Lorentz forces are three main
motion forces in molten pool. The molten pool is strongly
influenced by fluid flows which in turn are driven by buoyancy
and Lorentz force created by the melting current without stirring
magnetic field. The flow velocity vectors resulted from buoyancy
and self-induced Lorentz forces are opposite. The buoyancy
dominates the liquid metal flow at lower current, but the
self-induced Lorentz force becomes dominant with the increasing
current. A transition from the buoyancy to self-induced Lorentz
force dominant fluid flow occurs in the molten pool atop the ingot
between 1.6 and 2.6 kA for size ingots. The stirring Lorentz force
leads to a rotary flow of the molten pool in horizontal direction
with stirring magnetic field.
Index Terms—VAR, FEM, electromagnetic field, fluid field
I. INTRODUCTION
created by an external induction coil. This field is also used to
create electromagnetic stirring of the liquid metal flow [4]. And
the electrode is translated downward toward the molten pool to
keep a constant mean distance between the electrode tip and the
pool surface; this mean distance is called the arc gap. After a
sufficient time elapses, a quasi-steady state is established in
which relatively steady, molten pool and mushy zone sizes and
shapes are maintained on the top of a solid ingot base [5].
Though VAR process is researched and developed for many
years, there are still many challenges in making high quality
ingots without LDI, HDI defects and macrosegregation which
badly affect the quality of ingots [6-9]. Recently, Xu et al. [10]
researched the formation of casting microstructure and
estimated the casting defects, such as segregation and shrinkage
by simulating. Hyun et al. [11] investigated the effect of VAR
process parameters on the solidification behavior of titanium
alloys and predicted the optimum VAR process by using the
PROCAST software. In addition, P. Chapelle [12] studied the
effect of electromagnetic stirring on melt pool free surface
dynamics during VAR process. Although there were some
researches for electromagnetic field and temperature field in the
past, the investigation on coupling of electromagnetic,
temperature and flow fields fluid field is not comprehensive in
VAR process.
V
acuum arc remelting (VAR) is an important secondary
melting process that is widely used for the industrial
production of refractory metal ingots, such as titanium alloy and
nickel alloy, which melt at high temperatures and are highly
reactive in the liquid state [1-3]. The schematic of VAR process
is shown in figure 1. A cylindrical electrode is loaded into the
top of the water-cooled copper crucible. During remelting
process, an electric arc is maintained between the tip of the
electrode and the top of the secondary ingot, in order to heat the
electrode sufficiently for melting. The liquid metal drops, which
fall from the electrode, undergo solidification into the
water-cooled crucible. The secondary ingot formed in this way
is composed of three distinct zones, namely the liquid pool,
fully solidified metal and intermediate mushy zone. The arc can
be stabilized and confined with the aid of an axial magnetic field
Fig. 1 Schematic of the vacuum arc remelting process
Manuscript received January 10, 2011. This work was supported by
National Basic Research Program of China (973 Project) (No. 2011CB605502)
and Program of introducing Talents of Discipline in the project of Advanced
Materials and their Forming Technology.
Hongchao Kou is with the State Key Laboratory of Solidification
Processing, Northwestern Polytechnical University, Xi’an 710072, China. Tel.:
+86-29-88460568, E-mail address: [email protected]
The performance of titanium alloy ingots depends largely on
structure and chemical uniformity which is strongly influenced
by the liquid metal flow behavior [13]. The Lorentz force
resulted by electromagnetic fields influence macro fluid flow
patterns in molten pool, which is typically as important as
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International Journal of Engineering & Technology IJET-IJENS Vol: 12 No: 01
buoyancy in creating the pool profile. In VAR ingots
solidification, the molten metal through their part of the macro
flow realize heat transfer process. At the same time, there is a
much smaller interdendritic fluid flow in the mushy zone
responsible for the transport of solute, which can cause the
formation of macrosegregation and structure defects [14].
Therefore, to obtain a sound ingot, it is required to studying the
electromagnetic, temperature and flow fields during VAR
process. Actually, the direct measurement is extremely difficult
due to the aggressive environment in VAR vacuum chamber. So
it’s very effective to understand and optimize the VAR process
by computational model.
The present study describes a comprehensive computational
3D-FE model of the VAR process that considers the
electromagnetic field, temperature field and flow field within
the ingots for axisymmetric conditions. The model performs the
analysis of ingot in the steady state melting process. And the
movement of molten metals under multi-field coupling and its
effect on solidification behavior of ingot during VAR process
are discussed in this paper.
→
→ →
F = J× B =
1
µ
→
→
( B⋅ ∇ ) B −
1 →
∇B
2µ
51
2
(5)
The analysis of electromagnetic field is made by means of
indirect coupling method. The followings are the procedure:
First, based on electric field analysis, the current distribution of
VAR process is obtained. Then, the magnetic field resulting
from melting and stirring current is computed by electric field.
In the end, on the basis of electromagnetic field, the
electromagnetic force in ingot is analyzed.
B. Fluid field
The macro-scale fluid motion that occurs in the molten pool
and the outer mushy region during VAR process is governed by
mass and momentum conservation equations. Since the motion
is turbulent in the molten pool, time-averaged forms of the
Navier-Stokes equations are used to describe the mean flow
velocity field [18]. Governing equation is derived from
Navier–Stokes equation:
(1) Continuity Equation:
∂ρ ∂ ( ρv x ) ∂ ( ρv y ) ∂ ( ρv z )
+
+
+
=0
∂t
∂x
∂y
∂z
(6)
II. PHYSICS MATHEMATICS MODEL
A. Electromagnetic field
All practical ingot remitting processes constitute magnetic
field systems induced by the imposed current. Therefore,
Maxwell’s equations accurately describe the behavior of the
electromagnetic phenomena that occur in these processes. The
→
electromagnetic field is described by vector potential A and
scalar potential φ [15-17]. The relationship is as follows
→
→
B = ∇× A
(1)
→
E = −dA / dt − ∇ϕ
(2)
→
→
Where, B is the magnetic induction intensity, E is the electric
field intensity. The partial differential equation of magnetic
field and electric field is deduced by Maxwell’s equations. It
follows that
→
→
∂2 A
= −µ J
2
∂t
→
∇ 2 A − µε
∇2ϕ − µε
(3)
∂ 2ϕ
= −ρ / ε
∂t 2
(4)
Where, ρ denotes the fluid density; vx, vy and vz represent the
velocity vector in the x, y and z directions, respectively; t
stands for time.
(2) Incompressible energy equation:
∂
∂
∂
∂
( ρC pT ) + ( ρv xC pT ) + ( ρv y C pT ) + ( ρv yC pT ) =
∂t
∂x
∂y
∂y
∂
∂T
∂
∂T
∂
∂T
(K
) + (K
) + (K
) + Qv
∂x
∂x
∂y
∂y
∂y
∂z
(7)
Where, K is thermal conductivity, T is temperature, Cp is the
specific heat and Qv is the volumetric heat source.
(3) Momentum equation:
∂ρu ∂ ( ρuu ) ∂ ( ρvu) ∂ ( ρwu )
∂P
+
+
+
= Fx −
+ µe∇ 2u
∂t
∂x
∂y
∂z
∂x
∂ρv ∂( ρuv) ∂( ρvv) ∂( ρwv)
∂P
+
+
+
= Fy −
+ µ e∇ 2 v
∂t
∂x
∂y
∂z
∂y
∂ρw ∂ ( ρuw) ∂ ( ρvw) ∂ ( ρww)
∂P
+
+
+
= ρg + Fz −
+ µe∇ 2 w
∂t
∂x
∂y
∂z
∂z
(8)
(9)
(10)
→
Where, J is the current density, t is the time, ρ is the charging
density, µ represents the magnetic permeability and ε represents
the dielectric constant.
→
The distributing value of magnetic vector A and electric
potential φ are solved by finite-element method through
Equations (3) and (4). Then, the various physical quantity of
electromagnetic field is obtained.
→
The Lorentz force F is computed from electrical current
→
→
density J and the magnetic induction vector B as follow
where x,y and z are coordinate of a point in a solving regional
heat, m; u,v and w are the flow velocity in x,y and z direction,
respectively; µe represents the effective viscosity; ρ denotes
the density; QV denotes the volumetric heat source; T is
temperature; t is time; P represents the pressure. Fx, Fy and Fz are
the body force in x,y and z direction, respectively; g is
gravitational acceleration, equal to 9.8m2·s here; µe represents
effective viscosity.
C. Establishment of FE model
(1) Geometric model
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The 3D finite element model of VAR is showed as figure
2. It consists of a cylindrical copper crucible containing
liquid metal pool, though which a DC electric current is
flowing. The crucible is surrounded by an electromagnetic
coil, which produces an external magnetic field across the
liquid metal. In order to simplify calculation, the model is
based on the following assumptions.
1) Molten metal is incompressible Newtonian fluid and
turbulent flow.
)
)
K
·
g
k
(
/
J
(
/
t
a
e
H
c
i
f
i
c
e
p
S
0.004
Crucible outer diameter
(mm)
2400
48
)
2000
m
40
(
1600
1200
800
400
8
300
4) Heat radiation is neglected at the surface of the VAR
molten pool.
)
3
m
/
g
k
(
/
y
t
i
s
n
e
D
128
)
K
·
/
W
(
/
n
32
o
i
t
c
u
d
24
n
o
c
l
a
16
m
r
e
h
T
600
K
/
e
r
u
t
a
r
e
p
m
e
T
2) Surface arc pressure and metal steam pressure are
neglected.
3) The chemical reactions in the molten pool are
neglected.
Stirring magnetic field
(T)
52
900
1200
1500
1800
4900
700
3920
s
560
)
)
·
m
(
/
g
k
420
(
/
y
t
i
s
o
280
c
s
i
V
2940
1960
980
140
0
0
600
900
K
/
e
r
u
t
a
r
e
p
m
e
T
300
1200
1500
1800
2100
Fig. 3 Thermal physical properties of the Ti-6Al-4V alloy
(3)Boundary conditions
In VAR, the only source of heat is electric arc from VAR
power. The temperature on molten pool surface located under
the tip of the consumable is determined by the overheat value
above the alloy liquidus temperature [19]:
Fig. 2 The 3D FE model of VAR process
The fluid142 is selected for finite mesh elements of flow field
in the model. First, the electromagnetic fields and temperature
field are computed by the VAR model, respectively. And the
applied load in flow field simulation comes from the result of
electromagnetic field and temperature field.
(2)Physical parameters
Thermal conduction and specific heat of Cu are 390 W/m·K
and 383 J/kg·K, respectively. Electrical resistivity of Ti-6Al-4V
and Cu are 1.9×10-6 and 2.0×10-8 Ω ⋅ m , respectively. The arc
zone is considered to be a high resistance conductor. Due to the
electric current varies directly as voltage, the electrical
resistivity of the arc zone is calculated by the current and
voltage of the arc zone in the experiment and it is
3.5×10-3 Ω ⋅ m . The relative permeability of all materials is set
to be 1. The settings of VAR and geometry parameters in the
model are listed in Table 1. The thermophysical parameters of
Ti-6Al-4V alloy are showed in figure. 3 [21-23].
TABLE 1
TECHNOLOGY OF VAR AND GEOMETRY PARAMETERS
Parameters
Value
Geometry
Steady state Volt.(v)
28
Ingot diameter (mm)
Arc current (kA)
1.6-2.6
Ingot height (mm)
Ingot growth rate (mm/s)
0.5
Electrode diameter(mm)
Value
100
180
60
T = TL + ∆T ( J , Di )
(11)
Where, TL is the alloy liquidus temperature, K; ∆T is the
overheat of the metal above the liquidus temperature, K. The
melt overheat ∆T (J, Dc) is described by Belyanchikov’s
formula [20]:
∆T ( J , Di ) = 400e
−12
Di
J
(12)
Where, J is the current, kA; and Di is the diameter of the ingot,
m. According to calculating, the overheat ∆T is about 232K and
the alloy liquidus temperature is 1933K. So the temperature on
molten pool surface is about 2165K in simulation.
The heat transfer coefficient between copper crucible and
cooling water is defined as 5000 W/m2·K in this simulation.
And the heat transfer between the ingot and the copper crucible
is modelled as follows: there is a contact boundary condition at
the top, where the ingot touches the mould. In the case of
contact the crucible and the ingot are ideal heat conductions.
After gap formation, the heat transfer coefficient is set to 280
W/m2·K.
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International Journal of Engineering & Technology IJET-IJENS Vol: 12 No: 01
The crucible wall and crucible bottom are no slip wall
boundary. The flow velocity of crucible wall is zero in X and Y
direction and the flow velocity of crucible bottom is zero in Z
direction. So we assume boundary conditions for the momentum
equations as follows:
u
r =0.05
u
z =0
= 0 , v r =0.05 = 0 , w r =0.05 = 0
= 0,v
z =0
= 0,w
z =0
(13)
=0
(14)
where u,v and w are velocities in X, Y and Z directions,
respectively.
(4)Initial conditions
The initial temperature of VAR chamber is set to be 300K.
III. RESULTS AND DISCUSSION
53
simulation result agrees with the previous conclusion obtained
by Ward et al [24]. The current density at the molten pool
surface in different directions is shown in figure 5. It can be seen
that the current density becomes strong gradually from the
crucible wall to the electrode edge in X direction, and the
change is very small in Y direction.
The vector distribution of magnetic field induced by
remelting current in the mold is seen in figure 6. It can be seen
that the self-induced magnetic field is revolving on axial line.
Figure 7 shows the magnetic flux of the molten pool surface
from the symmetry axis to the crucible edge. The magnetic
density increases firstly and then decreases from the symmetry
axis to the crucible edge and gets a maximum value at the
electrode edge. The current flow out through the crucible and its
return the electrode are axisymmetric, so it is shown that the
resultant magnetic field external to the crucible will be zero
according to Ampere’s law.
A. Distribution of the electromagnetic field during VAR process
Fig. 6 The vector distribution of the magnetic field during VAR
Fig. 4 The distribution of the remelting current during VAR
Fig. 7 The magnetic flux of the molten pool sueface
Fig. 5 The current density at the surface of the molten pool
The distribution of the remelting current and the corresponding
magnetic fields during VAR can affect the temperature and flow
velocity distributions in molten pool [24]. Figure 4 shows the
distribution of the current among the electrode, ingot and
crucible at steady state melting. The current flows from the
crucible to consumable electrode. It is radial distribution at the
ingot top and axial direction in both the arc zone and electrode,
and tiny current flows out from the crucible bottom. This
Figure 8 shows the vector distribution of self-induced
Lorentz force of molten pool in different directions. The
Lorentz forces come from the vertical remelting current and the
revolving electromagnetic field in a horizontal direction. When
the current passes through the melting ingot, it produces a
significant revolving electromagnetic field, which induces
self-induced Lorentz force that has important effects on the
molten liquid fluid flow. The self-induced Lorentz force field is
radial inwards (figure 8a) and axial downwards which give rise
to an axisymmetric recirculation in the molten pool (figure 8b).
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54
Further study shows that the remelting current is very small at
the bottom of the molten pool, while it is larger at the top of the
molten pool. As a result, the azimuthal distribution of the
Lorentz forces is not uniform, the Lorentz forces is bigger at the
top of the molten pool than that at the bottom of the molten pool.
With magnetic stirring in VAR process, there will be a vertical
magnetic field which is introduced to stabilize the arc and it
about 0.004T.
Fig. 8 Vector distribution of the self-induced Lorentz force in molten pool: (a)
cross section and (b) Longitudinal section
B. The liquid metal flow behavior during VAR process
Fig. 10 Flow field in molten pool during stead state melting process without
magnetic stirring: (a) velocity resulting from buoyancy, (b) velocity Lorentz
force and (c) velocity resulting from buoyancy coupled Lorentz force
Fig. 9 The molten pool profile of titanium alloy ingots: (a) simulation results
and (b) experimental results
Liquid metal flow comes from buoyancy and Lorentz force
that affects the melting in VAR process and the current in the
stirring coils [14]. Figure 8a shows the temperature field and
flow field in titanium alloy ingots during VAR steady state
melting process, which are calculated by the 3D FEM. The
boundary between the isotherm of 1877K and 1933K is
regarded as the mushy region [25]. In order to validate VAR
model, a tungsten block was dropped into the molten pool
during a melt. And the macrostructure of φ100×180mm ingots
was observed after melting. The calculated molten pool profile
is in good agreement with its measured value in the same
process, as shown in Figure 9a and 9b.
Figure 10 shows the flow field in molten pool during VAR
steady state melting process without magnetic stirring. Flow
velocity of molten metal resulting from buoyancy is shown in
figure 10a. The buoyancy tends to drive hot metal up along the
axis of the ingot and down along the side wall. As a result, they
bring cool molten metal to the bottom of the pool, resulting in
clockwise flow in the right half of the molten pool. The
maximum velocity distribute along the ingot vertical axis. On
the other hand, it can be seen that the self-induced Lorentz force
drives the molten metal down along the axis and up along the
side wall from figure 10b. Thus, they drive hot molten metal to
the bottom, leading to an anticlockwise flow in the right half of
the molten pool. Figure 10c shows that the fluid flow pattern of
molten metal is the result of interaction between the buoyancy
and self-induced Lorentz force. At the top of the molten pool,
where the current density is very big, the flow velocity of molten
metal resulting from self-induced Lorentz force is much
stronger than that buoyancy, which causes an anticlockwise
recirculation, while it is reverse at the bottom of the molten
pool. In other words, considering the mushy zone is far away the
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55
electrode tip, the effects of self-induced Lorentz force on the
interdendritic fluid flow are considered to be much weaker than
buoyancy in the molten pool. This conclusion agrees well with
the simulation results obtained by Reiter et al [3].
Fig. 12 The comparing the simulations with the experiments: (a) flow velocity
resulting from string coil and (b) macrostructure of ingot in cross section
Fig. 11 The variation of flow velocity resulting from the buoyancy and
self-induced Lorentz force with the increasing remelting current
The flow pattern resulting from buoyancy and self-induced
Lorentz force effects on the interdendritic fluid flow, which has
strong influences on the structure of the ingots [26, 27]. The
variation of maximum flow velocity resulting from buoyancy
and self-induced Lorentz force with increasing remelting
current is illustrated in figure 11. It manifests that the flow
velocity resulting from buoyancy dominates at low current
operation. As the current increased, the self-induced Lorentz
force increases rapidly and overpower the buoyancy, so that it
becomes dominant in the molten pool. The value of flow
velocity resulting from the buoyancy and self-induced Lorentz
force is very close at 2.2 kA melting current for φ100 mm
diameter titanium alloy ingots, which is considered to be the
optimal remelting current. Under the circumstances, since the
effects of buoyancy and self-induced Lorentz forces are close
and opposite, their impact on the flow velocity in molten pool
are both decreasing. For example, take Ti-10V-2Fe-3Al alloy,
this case makes the Fe element macrosegregation degree
decrease, which improves the quality of ingot. Furthermore,
Zanner [29] finds that when the melting current changes from
6.6KA to 7.6KA for remelting 508mm diameter INCOEL718
alloy, the flow pattern between the thermal buoyancy forces and
the electromagnetic Lorentz force has transformed in VAR.
Davidson [30] studies that the flow pattern has transformed for
remelting 250mm diameter nickel alloy by numerical
experiments. At melting current is 3.6KA, the buoyancy
dominates flow pattern, but melting current reaches 10KA, the
buoyancy driven motion has completely disappeared and the
electromagnetic Lorentz force dominates flow pattern.
When a stirring magnetic field is applied for VAR process, it
will generate a stirring Lorentz force in the molten pool. The
current in the stirring coils creates a magnetic field parallel to
the axis. The interaction of the radial remelting current and the
vertical magnetic field gives rise to a rotating Lorentz force
which leads to a rotary flow in the molten pool horizontal
direction, as shown in Figure 12a, which are in good agreement
with the experimental results (Figure 12b).
IV. CONCLUSIONS
The computational model predicts the electromagnetic,
temperature and flow fields of the titanium ingot during VAR
process. To better understand the physical phenomena that
govern the flow fields, the distribution of electromagnetic field
is analyzed and the temperature field is obtained. Further, the
liquid metal flow behavior is studied in this paper. In
longitudinal section direction, the flow velocity vectors
resulting from buoyancy and self-induced Lorentz force are
opposite. The buoyancy dominates the liquid metal flow at
lower current, but the self-induced Lorentz force becomes
dominant with increasing current. A transition from the
buoyancy to self-induced Lorentz force dominant fluid flow
occurs in the molten pool atop the ingot about 2.2 kA for 100
mm diameter titanium alloy ingots. When bring to bear on a
stirring magnetic field, the stirring Lorentz force leads to a
rotary flow in the molten pool horizontal direction. Liquid
metal flow behavior obtained from the model is of significant
to optimize the operation process so as to produce sound ingots
with the desired composition and microstructure. In the future
work, we will study the solidification structure of the ingot,
investigate the effect the fluid flow on the macrosegregation of
the ingot and establish the relationship between the process
parameters and solidification structure finally.
ACKNOWLEDGMENT
This work was supported by National Basic Research
Program of China (973 Project) (No. 2011CB605502) and
Program of introducing Talents of Discipline in the project of
Advanced Materials and their Forming Technology.
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