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Modeling and Experimental Validation of Rapid Cooling and Solidification
during High-Speed Twin-Roll Strip Casting of Al-33 wt pct Cu
Article in Metallurgical and Materials Transactions B · August 2012
DOI: 10.1007/s11663-012-9659-x
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Modeling and Experimental Validation of Rapid Cooling
and Solidification during High-Speed Twin-Roll Strip Casting
of Al-33 wt pct Cu
SESHADEV SAHOO, AMITESH KUMAR, B.K. DHINDAW, and SUDIPTO GHOSH
The numerical modeling of heat transfer and solidification during twin-roll strip casting involves
incorporating fluid flow, heat transfer, and phase change in the liquid metals and knowledge of
heat flux distribution at the liquid metal–roll interface. Although efforts have been put in the
development of comprehensive modeling of the process simulation of the heat transfer, solidification during high-speed twin-roll casting and its experimental validation has not been
attempted. In the current paper, the results of simulation of twin-roll strip casting up to high
speeds has been reported for Al-33 wt pct Cu using FLUENT 6.3.16 (ANSYS, Inc., Canonsburg, PA). Further Jackson-Hunt plot for Al-33 wt pct Cu has been used to validate the
simulation. It has been shown by simulation as well as experiment that high speed twin-roll
casting can be a method for direct production of layered materials.
DOI: 10.1007/s11663-012-9659-x
Ó The Minerals, Metals & Materials Society and ASM International 2012
I.
INTRODUCTION
THE twin-roll strip casting process can eliminate the
requirement of hot rolling and produces thin strips with
thickness of 0.1 to 6 mm directly from the molten metal
by combining casting and rolling into a single step. The
process provides better control over the microstructure
and mechanical properties of the cast strip, and segregation is almost absent. The materials difficult to hot
roll are also manufactured by this technique.[1–3]
The process seems simple, but in practice, it is
necessary to control many strip casting parameters like
the feeding rate of liquid metal, melt level in the pool
region, pouring temperature of molten metal, roll
diameter, roll speed, roll gap, roll thickness, etc. in a
narrow range. It is important to understand the influence of these design and operational parameters on the
transport behavior within the liquid metal pool and the
structure of the cast strips. The study of these process
parameters experimentally is impossible because the
process of twin-roll strip casting is dynamic and quick,
and it occurs at a high temperature. Thus, comprehensive modeling of fluid flow, heat transfer, and solidification during the twin-roll casting is indispensable.
Mehrotra and coworkers[4,5] formulated a mathematical model for the fluid flow, heat transfer, and
SESHADEV SAHOO, Research Scholar, and SUDIPTO GHOSH,
Associate Professor, are with the Department of Metallurgical
and Materials Engineering, IIT, Kharagpur 721302, India. Contact
e-mail: sudipto@metal.iitkgp.ernet.in AMITESH KUMAR, Assistant
Professor, is with the NIFFT, Hatia, Ranchi 834003, India. B.K.
DHINDAW, Visiting Professor, is with the School of Materials and
Mineral Resources Engineering, Universiti Sains Malaysia, Pulau
Pinang 14300, Malaysia.
Manuscript submitted August 17, 2011.
Article published online April 10, 2012.
METALLURGICAL AND MATERIALS TRANSACTIONS B
solidification for the single roll strip casting process.
They studied the effect of different parameters, i.e.,
liquid steel head in the tundish, speed of rotation of the
caster drum, superheat of melt in the tundish, gap
between the caster drum and the tundish, drum geometry, and drum material on process performance using
the model. Saitoh et al.[6] developed a two-dimensional
numerical model of twin-roll continuous casting. They
studied the heat transfer and flow characteristics in both
the solid and liquid phases of metal and solved
governing equations separately using the finite-difference
method. However, they did not focus on the contact
phenomenon, contact heat transfer and heat conduction
to the roll and adopted constant temperature (290 K
[17 °C]) as a boundary condition at the roll surface. The
materials properties were also taken as constant in the
model.
Based on Saitoh et al.,[6] Santos et al.[7] developed a
model to simulate the solidification and heat transfer in
strip casting with a roll speed 14 rpm, the only main
difference being that Santos et al. introduced a heattransfer coefficient between liquid metal and roll instead
of constant temperature (290 K [17 °C]) boundary
condition. A computer model based on the finite-volume
method was developed by Lee[8] to predict the flow field
and solidification phenomena in the region of rotating
bank during twin-roll casting of molten steel (SUS304)
at 18 rpm roll speed. However, he did validate the model
and he used fixed values of thermophysical properties.
Chang and Weng[9] used the finite-element method
(FEM) to model the twin-roll casting. They coupled
fluid flow and heat transfer in this model, but they have
not validated the model experimentally, and the thermophysical properties of materials were not varied with
temperature. Gupta and Sahai[10] also formulated a twodimensional, finite-element method to simulate the
turbulent fluid flow, heat transfer, and solidification in
VOLUME 43B, AUGUST 2012—915
twin-roll strip casting with a 50 rpm roll speed. They
used the temperature-dependent viscosity of the liquid
metal, but the remaining properties of materials were
not varied. They identified some variables like roll
speed, melt roll heat-transfer coefficient, and melt
superheat that affect the thickness of the cast strip.
However, they did not validate their model.
An integral three-dimensional (3-D) model of fluid
flow and heat transfer during twin-roll strip casting was
developed by Miao et al.[11] using FEM. They studied
the effect of different parameters on the fluid flow and
temperature field. The theoretical results were compared
and validated with the experimental results by measuring the temperature of sampling site with different roll
speeds (13 to 26 rpm) and pouring temperatures. A
numerical investigation of the characteristics of the fluid
flow and heat transfer in a pool region with a roll speed
of 4 to 9 rpm was examined out by Bae et al.[12] The
main purpose of this study was to optimize the process
parameters to obtain good strip casting.
Zhang et al.[13] developed a 3-D FEM model to
simulate the twin-roll strip casting process at a 20 rpm
roll speed and studied the influence of the process
parameter to control the twin-roll strip casting process
and to improve the quality of the strip. They also
compared the variation of the calculated and measured
temperature of the strip surface with the pouring
temperature. The computational fluid dynamics (CFD)
model developed by Zeng et al.[14] focused on a better
understanding of the melt’s flow characteristics and
thermal exchanges during the rapid solidification of the
Mg during the twin-roll casting. They also highlighted
the effect of the casting speed and the gauge (twin-roll
gap opening) on the melt flow and solidification. They
used constant thermophysical properties like density,
specific heat, latent heat, thermal conductivity, and
viscosity to measure the temperature of the casting strip
both from the model and the experiment. They found
that the calculated results for varying casting speeds
match well with the experimental determination.
Fang et al.[15] simulated the temperature field of the
strip in the twin-roll casting method at 10 to 43 rpm roll
speed and the variation of temperature with different
process parameters. They did not vary all the thermophysical properties with temperature. Ren et al.[16]
developed a physical and numerical model of the molten
pool in twin-roll strip casting and studied the process
stability and quality of the product. Few articles/
research papers are available on experimental highspeed twin-roll casting.[17–22]
In the commercial production, casting is done at
speeds of less than 20 rpm. Therefore, most of the
research activities have been carried out for the range of
speed mentioned previously.[7,8,11–13] However, few
studies have been carried out recently at high casting
speeds.[17–22] The speed of 100 rpm is one order of
magnitude higher than the speed during the actual
practice and, therefore, has been referred to as highspeed casting.
However, most of the models mentioned have not
taken into account the variation of the thermophysical
properties with temperature, and no mathematical
916—VOLUME 43B, AUGUST 2012
model has been developed for high speed twin-roll
casting. Furthermore, few researchers have attempted
validation of the model. In the current study, a
comprehensive mathematical model for high-speed
twin-roll strip casting of the molten Al-33 wt pct Cu
alloy has been developed. The model takes into account
the coupled heat transfer and fluid flow in the liquid
pool. It takes into account the solidification characteristics. The model was validated experimentally using the
Jackson-Hunt plot for Al-33 wt pct Cu, and the effect of
process parameters on solidification front speed was
studied.
II.
MATHEMATICAL MODEL
The current study develops a mathematical model for
high speed twin-roll strip casting process in which liquid
metal is poured into the gap between two counter
rotating rolls, the liquid metal is solidified as the rollers
rotate and is deformed to strips at the exit.
Considering the practical process of casting, the
following assumptions were made in the development
of the mathematical model:
(a) The rolls are considered nondeformable and rotating with the same speed in opposite directions.
(b) The process is symmetric around the center line of
the roll gap.
(c) The process is assumed to be two dimensional,
neglecting the edge effect because of the high value
of the width-to-thickness ratio of the strip. The
nozzle diameter, for a given casting speed, will definitely influence the flow field. However the flow
field arrived from the nozzle will not significantly
influence the intense cooling occurring near the Cu
rolls. Also, the flow close to the solidified shell
(which is relevant for heat transfer in the shell) will
be dictated primarily by the rotation speed of the Cu
roll. Therefore, the problem has been simplified to a
two-dimensional one.
(d) The process is considered to have attained a steady
state.
(e) The top surface of the melt pool is considered flat
and maintained at a fixed level.
(f) The flow of molten metal is turbulent and incompressible.
(g) The molten metal is a Newtonian fluid.
(h) No slip condition exists between the liquid metal
and the roll/solidified strip.
(i) The thickness of solidified shell as well as the extent
of shrinkage at the roll nip will be low at a high
casting speed. Therefore, shrinkage has been
neglected.
(j) The heat transfer is dominated by convection and
conduction modes. In other words, radiation is
negligible.
(k) The value of average heat-transfer coefficient is
constant along the strip/roll interface. Taking the
average flux measurement is justified for following
reasons:
METALLURGICAL AND MATERIALS TRANSACTIONS B
(i) The shell formed at the exit of roll is thin. The
thickness of the shell is a cumulative effect that
can be predicted reasonably by the average flux.
(ii) The validation using J-H theory also needs to
be done over a substantial zone of the shell
using average interlamellar spacing over the
substantial zone. In other words, dividing the
solidified shell (in contact with the Cu roll) and
validation using J-H theory in each division is
not the correct approach. Therefore, the flux
distribution will not yield any better prediction
on the microstructural evolution.
A. Governing Equation
The turbulent form of the Navier-Stokes equation
was coupled fully with a differential energy balance
equation that took phase change (solidification) into
account. The conservation equations for each of the
dependent variables, i.e., u and v in the x and y
directions, respectively, k, e, and h (enthalpy) can be
written in the general form as follows:
@ @
@ @u
@
@u
quCu u þ
qvCu u ¼
Cu
Cu
þ
@x
@y
@x
@x
@y
@y
þ Su ðx; yÞ
½1
where q is the density, u represents the dependent
variable, and Cu and Su are its diffusion coefficient and
source term, respectively.
The continuity can be expressed by using u = 1,
Cu = 1, Cu = 0, and Su = 0
@ ðquÞ @ ðqvÞ
þ
¼0
@x
@y
½6
The dissipation rate of turbulence equation:
@e
@e
@ lt @e
@ lt @e
þv
q¼
þ
u
@x
@y
@x re @x
@y re @y
e
e2
þ C1 lt u C2 q
k
k
and that in the y direction is given by using u = v,
Cu = 1, and Cu =leff
@p @ðquvÞ
@
@v
þ
¼
leff
½4
þ Sy
@y
@y
@y
@y
The energy equation for the conservation of thermal
energy is given by using u = T, Cu = Cp, and Cu =Keff
@ @
@ @T
@
@T
quCp T þ
qvCp T ¼
Keff
Keff
þ
@x
@y
@x
@x
@y
@y
½7
where
leff ¼ l0 þ lt
½8
l0 is the laminar viscosity and lt is the turbulent
viscosity
½2
The momentum equation in the x direction is given by
using u = u, Cu = 1, and Cu ¼ leff
@p @ðquvÞ
@
@u
þ
¼
l
½3
þ Sx
@x
@x
@x eff @x
þ Su ðx;yÞ
effect of turbulence. For turbulence, the two-equation
k-e model of Launder and Spalding was used.[23]
Seyedein and Hasan[24] used a low Reynolds number
formulation of the k-e model to couple turbulent flow
with solidification in a vertical twin-roll strip casting
process. Of the various kinds of turbulence models
with a view of accuracy and computation cost, the k-e
turbulence model claimed better results compared with
other models. This model is examined by Patel et al.,[25]
and it was chosen for this study.
The governing transport equation for turbulent
kinetic energy k and its dissipation rate e can be written
as follows:
The turbulent kinetic energy equation:
@k
@k
@ lt @k
@ lt @k
q¼
þ
þ lt u qe
u þv
@x
@y
@x rk @x
@y rk @y
lt ¼ Cl qk2 =e
½9
Keff ¼ K0 þ Kt
½10
where K0 is the laminar contribution and Kt is the turbulent contribution of thermal conductivity.
Kt ¼ cp lt = Pr
½11
where Pr is the turbulent Prandtl number.
u in Eqs. [6] and [7] is given by the following
expression:
2 2 @u
@v
@v @u 2
þ
u¼2
þ2
þ
½12
@x
@y
@x @y
According to Launder and Spalding,[23] the constants
in the standard k-e equation takes the following values:
C1 = 1.44, C2 = 1.92, Cl = 0.09, rk = 1.0, and
re = 1.3.
½5
C. Solidification
B. Turbulent Model
In considering the complex flow pattern in twin-roll
strip casting, the transport equation should include the
METALLURGICAL AND MATERIALS TRANSACTIONS B
For solidification consideration, the enthalpy-porosity formulation[26] was incorporated in the solution
scheme. The enthalpy porosity technique treats the
solidifying system as a porous medium with varying
VOLUME 43B, AUGUST 2012—917
porosity. The porosity in each cell is set equal to the
liquid fraction in that cell. Thus, the porosity will be
zero in a solidified region, greater than zero and less
than one in a mushy region, and one in a liquid region.
Solidification also results in a phase change. It was
assumed that the mushy zone behaves like a porous
medium and obeys Darcy’s equation. So the effect of
porosity was incorporated in the momentum equation
through the momentum source term. The momentum
source term is given by
S¼
ð1 gl Þ2
Amush ðu up Þ
ðg3l þ bÞ
½13
where u is the x or y component of velocity, gl is the
liquid volume fraction, b is the small number (0.001 to
prevent division by zero when the liquid fraction goes to
zero), Amush is the mushy zone constant, and up is the
solid velocity resulting from the pulling of solidified
material out of the domain (pull velocity).
Amush is a constant that depends on the morphology.
As we move from a liquid to a solid region, a higher
value of Amush will lead to the rapid damping of
velocity near the solidification front. Another important issue in solidification modeling is the release of
latent heat and the evaluation of solid or liquid
fractions. Solidification results in latent heat generation
and a modified form of the energy equation; incorporating latent heat was used. The modified energy
equation is given by
r:ðquHÞ ¼ r:ðkrTÞ þ Sh
½14
The enthalpy of the material was computed as the
sum of the sensible enthalpy h and the latent heat DH. It
is expressed as
H ¼ h þ DH
where
h ¼ href þ
Z
½15
D. Steady-State and Boundary Conditions
The process is symmetric around the centerline of the
gap between two opposite rotating rolls. Therefore, a
computational model was adapted to only half of the
real domain as shown in the Figure 1. The velocity of
the melt at the top of the melt pool region was initialized
with zero velocity because the melt level was maintained
at a fixed height. The total domain was initialized at 300
K (27 °C), except the pouring temperature of the metal
was taken at 851 K (578 °C).
The boundary conditions are as follows (refer to
Figure 1):
(a) At the entrance of the liquid metal on the surface of
the melting pool (BC), Vx = Vin, Vy = 0,
k = 0.05(V2x+V2y), e = Clk1.5/0.03Din,Tin = 851 K
(578 °C), where Vx is the speed in the x direction, Vy
is the speed in the y direction, Vin is the speed of the
liquid metal at the entrance, k is the turbulence
kinetic energy, e is the dissipation rate of the turbulent kinetic energy, and Din is the size of the entrance.
@V
@k
@e
¼ @X
¼ 0,
(b) On the free surface (AB), @Xy ¼ @X
Vx = 0.
@k
@e
x
(c) At the symmetry interface (CD), @V
@Y ¼ @Y ¼ @Y ¼ 0;
Vy = 0.
(d) On the outer surface of the roll, the tangential
velocity of the roll is equal to the casting speed. So
the velocity components Vx and Vy on the roll
boundary have the following values, Vx= Vroll cosh,
Vy = Vroll sinh
where Vroll is the casting speed and h is the angular position
of the node on the roll surface. At the contact interface of
liquid Al-33 wt pct Cu and the roll, a constant value of the
heat-transfer coefficient was used in the model. The value
of the heat-transfer coefficient was calculated based on the
correlation given by Wang and Matthys.[27] The correlation is given by the following equation:
T
cp dT
½16
Tref
In Eq. [16], href is the sensible enthalpy at the reference
temperature and cp is the specific heat at constant
temperature.
The liquid fraction gl is defined as
gl = 0
gl = 1
gl ¼
if T < Tsolidus
if T > Tliquidus
T Tsolidus
Tliquidus Tsolidus
if Tsolidus <T<Tliquidus
½17
Equation [17] holds true for the equilibrium condition, and thus, for simplicity, the equilibrium condition
has been assumed.
The latent heat content can be written in terms of the
latent heat of freezing L
DH ¼ bL
918—VOLUME 43B, AUGUST 2012
½18
Fig. 1—Computational domain used for simulation.
METALLURGICAL AND MATERIALS TRANSACTIONS B
hs ¼ 17300 V0:65
roll
where hs is the average heat transfer coefficient
(W m2 K1) and Vroll is the casting speed (ms1).
This correlation was validated by Guthrie et al.[28]
experimentally and compared with the results of Chen
et al.[29]
The observed increase in the heat-transfer coefficient
with increasing casting speed can be explained in
different ways. According to Mizoguchi et al.,[30] an
entrapped gas film forms between the roll and the
solidifying metal and the heat transfer occurs by the
conduction through the gas film. The interfacial heattransfer coefficient can then be defined by
hs ¼
KG
dG
where KG is the thermal conductivity of the gas in the
gas film (W m1 K1) and dG is the thickness of the gas
film (m).
An increase in the casting speed decreases the gas film
thickness and would result in a higher heat-transfer
coefficient. Higher casting speeds usually lead to thinner
strips and, therefore, to less solidification shrinkage. The
air gap that forms between the roll and the strip, as a
consequence of this shrinkage, would then be thinner.
The thinner solidified shell is also weaker and tends to
remain close to the rolls because of the pressure exerted
by the liquid metal. This factor contributes to the
decrease of the thickness of the air gap and thus
increases the heat-transfer coefficient with an increase in
roll speed.
(e) At the exit or nip of the roll (ED), the fully developed boundary condition was used.
The outflow conditions at the exit or nip of the roll
are Vx = –Vroll, Vy = 0.
E. Solution Method
The conservation equations were discretized and
solved with the FLUENT 6.3.16 platform (ANSYS,
Inc., Canonsburg, PA). Fluent 6.3.16 solves the previously described equations using a control volume
approach. A segregated solution algorithm with a
control volume-based technique was used in the numerical method. The pressure and velocity were coupled
with a semi-implicit method for a pressure-linked
equation (SIMPLE) algorithm of Patankar,[31] which
used the guess-and-correct procedure to calculate
pressure on the staggered grid arrangement. The grid
for computation domain was finalized after a grid
independent test. The grid used in the computation was
composed of 1584 cells, 3258 faces, and 1675 nodes.
The algebraic equations were solved using an alternative line-by-line method. To guarantee convergence,
under-relaxation was applied to all variables and in the
enthalpy source term. The following convergence criterion is used in this study:
METALLURGICAL AND MATERIALS TRANSACTIONS B
mþ1
Ri
Rm
i econ
m
R
½19
½20
i
where the superscripts, m+1 and m represent the step of
iterative computation, and the subscript i represents the
nodal points at which the physical amount is calculated.
R is the residual and econ is a convergence criterion. The
value of econ in this study is taken to be 106 for energy
equation and 103 for all other quantities. The computation is terminated when Eq. [20] is satisfied for all the
computed values of the variables. The under-relaxation
parameters of 0.7, 0.8, 0.1, and 1 were used for updating
momentum, turbulence quantities, liquid fraction, and
energy, respectively.
F. Parameters of Casting and Thermophysical Properties
The casting parameters used in the simulation are
shown in Table I. Al-33 wt pct Cu alloy was selected as
the alloy system for two reasons. First, the thermophysical properties of the alloy are known, and second, the
Jackson-Hunt plot is available for the comparison. The
simulation was carried out for Al-33 wt pct Cu strip
casting with roll speed of 100 rpm. The thermophysical
properties used in the model for pure solid copper rolls
and Al-33 wt pct Cu alloys are given in Tables II and
III, respectively. The thermophysical properties of Al-33
wt pct Cu alloy at various temperatures are linearly
interpolated and placed in Table III.
III.
EXPERIMENTAL METHOD
The schematic sketch of a high-speed twin-roll casting
process is shown the Figure 2. The strip was prepared in
Table I.
Casting Parameters Used for Simulation
and Experiment
Parameters
Value
Roll diameter (m)
Roll width (m)
Casting speed (ms1)
Thickness of the strip (m)
Contact angle (deg)
Pour temperature [K (°C)]
Inlet diameter (m)
Heat transfer coefficient
(W m2 K1)
Table II.
0.1524
0.0254
0.7979 (100 rpm)
0.002
40
851 (578)
0.004
hs ¼ 17300V0:65
roll ¼
17300ð100 rpmÞ0:65
roll
Thermophysical Properties of Copper Roll[32]
Properties of Copper Roll Used in Model
Thermal conductivity (W m
Density (kg m3)
Specific heat (J kg1K1)
1
1
k )
Value
387.6
8978
381
VOLUME 43B, AUGUST 2012—919
Table III. Thermophysical Properties of Al-33
wt pct Cu Alloy[33]
Properties of Al-33 wt pct Cu
Used in Model
1
Thermal conductivity (W m
Density (kg m3)
Solidus temperature [K (°C)]
Liquidus temperature [K (°C)]
Melting heat (J kg1)
Specific heat (J kg1K1)
Viscosity (kg m1K1)
Value
1
K )
Ks = 155
Kl = 71
qs = 3410
ql = 3240
821 (548)
821 (548)
350,000
Cs = 1070
Cl = 895
At 943 K (670 °C) =
1.001 9 103
At 973 K (670 °C) =
8.624 9 104
At 1023 K (750 °C) =
5.65 9 104
Fig. 2—Schematic diagram of Vertical Twin roll caster.
a vertical twin-roll caster. The master alloy was
prepared from a 99.96 pct pure Al and a 99.99 pct pure
Cu by induction melting. The chemical analysis was
carried out to confirm the composition of the master
alloy by using optical emission spectroscopy (ARL3460;
Thermo Fisher Scientific, Waltham, MA). The alloy was
melted using an induction furnace at a temperature 851 K
(578 °C). After melting, the molten alloy was transferred
into a tundish and strip cast in air. The roll gap was 2
mm and the rotating speed of the roll was 100 rpm. The
solidified strips were prepared for metallographic examination using a standard metallographic procedure and
etched with Keller’s reagent. The microstructures were
studied using a JEOL JSM-6480LV scanning electron
microscope (JEOL Ltd, Tokyo, Japan).
IV.
RESULTS AND DISCUSSION
A. Steady-State Simulation of Strip Casting
In the current work, simulations were carried out for
casting of Al-33 wt pct Cu strips having thickness of
920—VOLUME 43B, AUGUST 2012
2 mm. Therefore, roll gap at the point of exit, i.e., a gap at
the point of roll nip, was set to 2 mm. The level of liquid
metal pool was kept fixed at 0.0489 m. The liquid metal
was fed through a nozzle measuring 4 mm diameter, and
the temperature decrease during feeding was assumed to
be negligible. Thus, the temperature at the inlet was taken
as the feeding temperature of the liquid metal. The
Reynolds number (Re = qk2/le) based on the k – e
turbulence model was approximately 381.
The simulation results show the velocity vector plot,
temperature, and solidification pattern of Al-33 wt pct
Cu in the pool region, respectively, for the case when the
roll speed was 100 rpm, the pouring temperature of
liquid metal was 851 K (578 °C), and the interfacial
heat-transfer coefficient between molten metal and roll
was 14,938 W m2 K1.[27–29]
In the vertical twin-roll casting process, the inlet flow
is driven by the pressure from an upstream tundish and
tends to go downward along the symmetry plane toward
the roll nip. The velocity vector plot in the melt pool is
shown in the Figure 3. The direction of arrow indicates
the flow direction, and the color gradient indicates
the quantitative value of the velocity. It shows that the
velocity of the metal in the vicinity of the rolls is the
same as the roll velocity due to no-slip condition.
The velocity direction of the melt is reverting back in the
middle region of the melt pool as shown in the velocity
profile in Figure 3.The region is marked by a circle and
the magnified views are shown in the side. A part of the
flow moves toward the free surface and gradually moves
toward the roll because of the influence of the shear flow
formed by the rotating roll.[24] Because the shear flow
rate generated by the roll motion is high compared with
the net outflow of the caster, it causes an upward flow
across the symmetry plane to develop in order to satisfy
the mass conservation law. As observed from the figure,
the forced flow of the melt through the nozzle and the
shear flow from the rotating rolls form strong counterrotating recirculating flows. The maximum liquid is
dragged and sheared by the counter-rotating roll by
their contacting surfaces toward the nip of the rolls. This
was also observed by several investigators; Kim et al.[34]
and Gupta and Sahai[10] also pointed out that the metal
that could not be solidified flows back with a relative
smaller velocity. They also found two circulation loops
in the flow of the liquid metal vector plot, which is found
in the current study as shown in Figure 3.
Figure 4 shows the temperature profile in the melt
pool obtained from the model. The temperature distribution in the melt pool region is shown by different
colors. The temperature contour of 821 K (548 °C)
defines the solid–liquid interface in the melt pool. The
temperature is higher around the symmetry line in the
pool region than in the region that is in contact with the
roll surface. The model was carried out for strip of 2 mm
thickness and roll speed of 100 rpm. The pouring
temperature of the melt was 851 K (578 °C). For these
conditions, the model predicts that the temperature of
Al-33 wt pct Cu liquid metal in contact with the surface
of the roll is below 821 K (548 °C), which is lower than
the central temperature of the metal at the nip of the
roll. As a result of the shear flow because of the roll,
METALLURGICAL AND MATERIALS TRANSACTIONS B
Fig. 3—Velocity profile of Al-33 wt pct Cu in the molten pool.
Fig. 5—Solidification profile of Al-33 wt pct Cu in the molten pool.
Fig. 4—Temperature profile of Al-33 wt pct Cu in the molten pool.
a relatively high temperature gradient appears near the
roll surface. Along the symmetry line temperature is
above the solidus temperature.
The simulated results of the solidification profile of
Al-33 wt pct Cu is shown in Figure 5. It is represented
by the variation of liquid fraction of Al-33 wt pct Cu,
which varies from 0 to 1. It can be observed that the
solidification of the Al-33 wt pct Cu alloy is not fully
complete at the point of the nip. So, the solidification
profile shows the liquid fraction 1 (means complete
liquid) in the central region of the nip of the rolls and the
liquid fraction 0 at the wall of the roll from approximately the middle (0.0243 m from free surface of melt
pool along the symmetry line) of the pool region. This is
because of the high roll speed. The casting speed is same
as the roll’s tangential speed. Therefore, a higher roll
speed does not provide sufficient time for heat transfer
from the liquid metal to the copper roll. So, liquid metal
in the center of the strip is dragged out with a solid shell
(outer surface of strip) as predicted by the model.
Solidification growth speed was estimated based on
the liquid fraction profile using seven different locations
(L1, L2, L3, L4, L5, L6, and L7), which are shown in
Figure 6. The growth velocity was measured by dividing
METALLURGICAL AND MATERIALS TRANSACTIONS B
Fig. 6—Profile of the liquid fraction for determination of front speed
at different locations.
the thickness of the solidified cell by the elapsed time.
The elapsed time was calculated based on the roll speed,
and it is time taken by an allocated position of any point
to its successive located position as shown in the
Figure 6. By this way, the growth velocities were
calculated from the model at six locations (L2, L3, L4,
L5, L6, and L7). The maximum growth speed was
obtained at location L2 and the minimum speed was
found at location L7 because of the temperature
difference between roll surface and the metal. The
temperature difference is higher at location L2 compared with the location L7.
B. Effect of Roll Speed on Solidification Front Speed
Simulations were done for different roll speeds (3 to
500 rpm) to know their effect on the solidification front
speed. Figure 7 shows the plot of the average solidification front speed with the variation of the roll speed. It
shows that the solidification front speed increases with
the roll speed. This is because of the rapid contact of
colder part of the roll with the cooling alloy. In other
VOLUME 43B, AUGUST 2012—921
Fig. 7—Effect of roll speed on solidification front speed.
words, this is caused by a higher heat transfer coefficient
leading to a higher heat flux.
Figure 8 shows the solidified shell thickness at the roll
nip as a function of the roll speed. It can be observed
that for a given superheat and roll diameter, complete
solidification occurs at the roll nip for roll speeds below
10 rpm. At higher speeds, the liquid metal is left over.
From the simulation, it is observed that, as the roll
speed is increased, the fraction of the liquid at the roll
nip increases. The cooling of the inner liquid, which
would require dissipation of heat through the solidified
shell, will be significantly slower than that of the outer
layer that was in direct contact with the roll surface.
The wide difference in the cooling rate/solidification
front speed is expected to give rise to a distinct
structure in the outer layer and the inner portion of the
cast Al-33 wt pct Cu. Based on the simulation, the
average solidification front speed in the outer layer was
found to be 6648.66 lm/s, which is high and corresponds to interlamellar spacing, k = 0.115 lm. However, the front speed of the inner region is expected to
be much lower.
C. Effect of Initial Melt Temperature on Solidification
Front Speed
Simulations were done for different initial pouring
temperatures [831 K to 971 K (558 °C to 698 °C)] of the
melt to know their effect on the solidification front
speed. Figure 9 shows the effect of the initial pouring
temperature of the melt on the solidification front speed.
The solidification front speed decreases with an increase
of the initial pouring temperature of the melt. This can
be understood in terms of the additional heat required
to cool liquid metal down to the melting point. The total
heat extracted is sum of (1) superheat and (2) heat
released from transformation of the liquid to solid. With
the increase in superheat, the second component of the
heat extracted, i.e., the one that is used for the formation
of a solid layer, decreases, which results in a decrease in
the shell thickness.
922—VOLUME 43B, AUGUST 2012
Fig. 8—Effect of roll speed on solidified shell thickness.
Fig. 9—Effect of initial melt temperature on solidification front
speed.
D. Validation of the Model with Experiment
The solidification front speed, which is computed
based on the comprehensive model, varied from few
thousand lm/s to close to 9000 lm/s for roll speed of
100 rpm. Such a rapid solidification cannot be validated
by direct measurement of temperature or other methods
of estimating the temperature. Because all the physical
properties of Al-33 wt pct Cu, an eutectic alloy, are
known and because it obeys Jackson-Hunt relationship,
even at a high speed,[35] the comprehensive mathematical model of the rapid solidification process was
validated using the Jackson-Hunt relationship. The
experimental validation was carried out for twin-roll
strip casting of Al-33 wt pct Cu. The microstructures in
the outer layer were taken at different locations of the
thickness direction, which is shown in the Figure 10.
For validation, the solidification front velocities of the
Al-33 wt pct Cu strip were calculated using the model
developed in the current work. The validation approach
is similar to the validation approach of droplet impingent
METALLURGICAL AND MATERIALS TRANSACTIONS B
Fig. 10—Microstructure of Al-33 wt pct Cu strip in the outer layer of the strip at different locations (Magnification 5.0 KX).
Fig. 11—Interlamellar spacing vs growth velocity.
Fig. 12—Microstructure of Al-33 wt pct Cu strip in the thickness
direction (Magnification 5.0 KX).
simulation by Kumar et al.[33] The experimental validation was carried out for a roll speed of 100 rpm and a
roll gap of 2 mm at the point of the nip, and the initial
temperature of melt was 851 K (578 °C). The solidified
strip was sectioned at seven different locations, and the
section pieces were prepared metallographically to
characterize the microstructure.
For validation, solidification growth velocities in a
strip of thickness 2 mm of Al-33 wt pct Cu alloy were
calculated using the model developed in the present
work. These values were plugged in the Jackson-Hunt
relationship k2V= 88 lm3s1[36] for calculation of k
from those velocities. Figure 11 shows the experimental
values obtained for various sections as shown in
Figure 6 superimposed on those calculated from this
model. A good correlation is found in the plot between
the experimental and simulated values within the standard errors of experimental measurements.
As predicted by simulation studies, the microstructure
of the solidified Al-33 wt pct Cu strip was not uniform,
and two distinct zones were observed. This is the effect
of the difference in the speeds of solidification front. In
the outer layer, the structure was lamellar with
k = 0.123 lm, which is closest to the predicted value,
and in the inner region, it was wavy as shown in
Figure 12. Thus, the current work shows that the
layered materials can be produced directly by highspeed twin-roll casting if the microstructure of the
solidified material is sensitive to the cooling rate.
METALLURGICAL AND MATERIALS TRANSACTIONS B
V.
CONCLUSIONS
1. A comprehensive CFD-based modeling of high-speed
twin-roll strip casting was developed on FLUENT
6.3.16 platform.
VOLUME 43B, AUGUST 2012—923
2. The prediction of the model was validated for rapid
cooling and solidification during high speed twin-roll
strip casting of Al-33 wt pct Cu, using Jackson-Hunt
theory.
3. For high casting speed, it is predicted from simulation as well as experimentally observed that the cast
strips have a layered structure. Thus, the current
work proposes high-speed twin-roll casting as a
method for direct production of layered materials,
when the microstructure of the cast material is
dependent on the cooling rate.
ACKNOWLEDGMENT
The authors acknowledge the financial support
provided by Department of Science Technology (DST),
New Delhi, for generously supporting the research
program.
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