Barman Tambunan, Solidification Analysis…

SOLIDIFICATION ANALYSIS OF BISMUTH BASED ALLOY

IN CONTINUOUS CASTING PROCESS

Barman Tambunan

Pusat Pengkajian dan Penerapan Teknologi Material

P3TM – BPPT, Gedung BPPT II, Lantai 22
Jl. M.H. Thamrin No. 8 Jakarta 10340
Email: barman@webmail.bppt.go.id

ABSTRACT

Continuous Casting is a manufacturing process for producing billets, slabs and flat
products. It is used for casting non-ferrous and steel production to produce high quality
products of slab or billet cast at reduced cost. A thin solidified metal shell is formed
initially during continuous casting due to the intense cooling from the water cooled mould.
Once the cast leaves the mould it goes through various cooling processes and in solid state
will proceed to the further forming processes. To exploit the benefit of continuous casting
process it is essential to develop close control of the production process. This is achieved
through a good understanding of the influence of the various compositional and
operational variables. The objective of the mathematical analysis presented here is to
model the heat transfer during continuous casting of low melting point Bismuth alloy cast
billets material for predicting the surface temperature. Good quality of the cast in
conjunction with the surface quality of the cast is relied on the solidification temperature
during continuous casting. In fact by simulating the solidification temperature of the
continuous casting process through applying different operational casting parameters, the
result are crucial for identifying the best operational casting parameters.

Keywords: Continuous Casting, Solidification, Enthalpy Method, Simulation

Makalah diterima 17 September 2005

1. INTRODUCTION is used as an indicator of the relative

sophistication of any steel industry among
Continuous casting has been producing countries. The operation of
introduced to replace the discrete production continuous casting process consists of many
of first solidified form of metal blocks so complex stages. In continuous casting,
called ingots in a continuous manner, with molten metal is poured continuously from
subsequent rolling process. Various shapes tarnish into water cooled copper mould,
such as blooms, billets or slabs are cooled into a semi finished solid shape and
manufactured directly from the molten metal withdrawing a continuous length of casting.
steel which produced by the electric arc The strand is continuously pulled from the
furnace (EAF) or basic oxygen furnace bottom of the mould under the support rolls
(BOF) directly. Blooms are usually used to where heat from the solidify cast is further
produce rails and heavy sections, billets are removed through subsequent cooling zones
used for making bars, rods and wire; and and finally the casting is cut up into a
slabs are produced for making flat products required length for further manufacturing
of various dimensions. Nowadays, process. The mould oscillates in vertical
continuous casting is the technique applied direction as the solidify strand is
in the majority of steelmaking industries and continuously withdrawn from the mould.

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Berkala MIPA, 15(3), September 2005.

Thin solidified metal shell is formed parameters have been considered during
due to the intense cooling from the water simulation to determine solidification
cooled mould. Inside the shell large molten temperature of the strand and to predict the
core remain and solidify during the shell thickness of the billet from the
withdrawal of the strand. The operating meniscus region throughout the mould exit
conditions for the mould during casting are in continuous casting process.
the most critical for the whole process for
producing a crack-free surface cast. Several
parameters controls the shell development in 2. HEAT TRANSFER PROCESS IN
the mould such as the temperature of the THE MOULD
incoming hot liquid material, the dimensions
of the mould, the oscillating mould, mould The first continuous casting analysis
lubrication, the cooling water flow rate and concerns the heat transfer solidification of
the speed of the solid strand. The quality of the molten metal in the mould region. During
the slab casting production depends on the operation of the casting various variable can
solidification phase during casting process. influence the solidification of the product
Therefore, by developing a mathematical such as the incoming metal temperature,
heat transfer model of the solidification molten properties, mould geometry, mould
process, one may identify the optimal lubricant and the mould cooling system. The
operational parameters during continuous formation of the casting shell is shown in
casting to obtain a high quality slab. Fig. 1. V m is the mould oscillation speed, Vs
In order to gain further insight into is the casting speed and CL is the centre line
continuous casting it is important to of the mould geometry since the profile of
understand the solidification process which the mould is always symmetry. As depicted
is strongly influenced by the temperature and in Fig. 1, the Meniscus zone where the shell
flow of molten metal. This can only be begins to form the liquid metal is separated
obtained by carefully study and pinpoint by the lubricant layers. Three different
various operational casting parameters that phases of metal cast exist in the mould zone
can affect the quality of the continuous during solidification process of the cast
casting product. Most of theoretical consists of solid, liquid and mushy zone
modeling available (Takeuchi, et.al, 1991; (Huang, et.al., 1992; Shy, et.al., 1992). The
Takeuchi and Brimacombe, 1984) have been mushy zone is the solid-liquid interface
compared either with data from a where part of the metal becomes solid and
commercial production process using part of them is liquid. Casting factors such as
sophisticated equipment or using water flow heat extraction process accompanying by the
to verify their analysis (Sheng and Jonnson, solidification has shown an important role to
2000). Economically, it is not feasible to perform a good quality cast product. The
obtain a wide range of data from an casting design and operational parameter
industrial continuous casting to build a better during continuous casting at the meniscus
understanding of the process. To identify mould region is important since the surface
parameters that improve the process require of the cast is initiated and built in this region
changes in production parameters, addition (Mahapatra, et.al., 1991).
of new sensors or measurement devices to a Heat from the liquid metal is
commercial casting process. This may cause extracted to the mould trough various heat
interruption in production and flow sinks consisted of conduction,
inconveniences for the organization. convection and radiation heat transfer,
The present study is concerned with initiated from the liquid pool to the mould-
the review of mathematical model and water cooling interface. To help prevent the
development of numerical simulation of heat strand sticking to the surface of mould,
transfer solidification of the molten low lubricant is poured from the top of the mould
melting point Bismuth alloy in order to and flows into the gap with the help of the
predict the surface temperature of the billet oscillation motion (Darle, et.al., 1993).
cast product. Different operational casting Samarasekara et al., 1978 have reported that

34
 Barman Tambunan, Solidification Analysis…

in steel continuous casting, the heat transfer strand. Inside the mould liquid steel
at the flux channel constitutes the largest solidifies against mould surface controlled
contribution to the heat extraction in the by the water cooling mechanism at the back
mould while the mould wall has the lowest of the surface of the mould. In addition
contribution. Thus heat removal in the casting speed and the geometry of the mould
continuous casting mould is dependent also influence the solidification process
largely to the gap between the solidified during the formation of the shell. The steel
strand and the water cooled copper mould. shell must be thick and strong enough to
contain the molten steel during cast
withdrawal.
y
Mould Lubricant layer
CL
x
Molten Metal

Vm
Shell
Mushy

Vs

Figure 1. Physical System for initial

solidification in continuous casting mould
Figure 2. Several heat transfer and
The molten metal pool in steel temperature distribution in Continuous
Casting mould 4)
continuous casting process is controlled by
different heat transfer removal process such
3. CONTIN UOUS CASTING
as heat in the liquid molten steel, latent heat
of solidification in the mushy zone and heat EXPERIMENTAL RIG
conduction from the solid shell (Mizikar,
A new continuous casting
1967). On the last heat removal process heat
experimental rig has been developed at
is conducted away from the solidification Manufacturing Laboratory at RMIT
boundary front to the cooler surface of the
University, Melbourne, Australia. In
steel shell. At the front surface of the strand
development of this continuous casting rig
in the mould region heat is removed by the
three criteria have been taken into account;
water cooled copper mould which picks up
firstly, the rig should represent the real
the heat to form the solidified skin shell on
situation. Secondly, the rig should be
the outer surface of the cast material. Fig. 2
instrumented with a measurement system for
shows the heat transfer process in more obtaining the require data and thirdly, the
details from the liquid pool to the surface of
continuous casting rig should be easy to
the mould.
operate and to control. Experiments can be
Several operational casting
readily undertaken using this continuous
parameters control the heat transfer and
casting rig (shown in Fig. 3) without the
solidification process of the shell in the
limitations associated with disrupting
mould (Birat, et.al., 1991; Thomas, et.al.,
industrial continuous casting operations or
1997). As shown here, the temperature in the
without costly plant trials.
mould decrease dramatically from the liquid
pool measured above 1500 °C to less than
100 °C at the copper surface far from the

35
 Berkala MIPA, 15(3), September 2005.

33 mm and the outer diameter is 74 mm and

Funnel
the length is 400 mm. These two cylinders
Lubricant were welded together at bases to form a
Plate space for water circulation in the mould and
to produce adequate cooling for the molten
metal to solidify.
Water
Outlet 3.1 Operation of the Experimental Rig

Bismuth based alloy called Wood’s

Oscillation Copper
metal was used as cast material. This metal
Plate Mould
replaces the high melting temperature casting
material such as steel or aluminium. Wood’s
metal has a low melting point temperature of
71°C which is ideal for the experimental rig.
Water Inlet Wood’s metal can be continuously poured
and withdrawn from the mould and mimics
Oscillation arm
LVDT the characteristics of continuous casting of
connected with steel very well. For this reason, Wood’s
the Load Cell metal was selected as cast material in this
work.
Figure 3. Experimental Continuous Casting Rig. The metal was heated in a furnace to
82 °C and let to cool at room temperature to
just above its melting point and then poured
The continuous casting rig uses an into the mould. This melted material was
oscillatory mould with variable oscillation introduced from the top of the mould through
speed and amplitude. During casting, the the available funnel. Underneath the funnel a
mould oscillates in the vertical direction with lubricant plate was placed to lubricate the
adjustable amplitudes of up to 20 mm. The mould wall during casting.
function of mould oscillation with proper
lubrication in continuous casting is to 4. THE MATHEMATICAL MODEL
prevent sticking of the strand to the mould’s OF THE HEAT TRANSFER
wall. Instead of using supported rolls to pull SOLIDIFICATION
the solidify cast located underneath of the
mould, a wire was connected to the dummy Mathematical modelling for
block and pulled down at a controllable predicting the solidification front, heat
speed. A motor driven-wire mechanism was transfer and the temperature distribution of
used to withdraw the solidifying cast from the liquid steel pool in the mould region of a
the mould. continuous casting process have been
Water required for mould cooling is reported. Modelling of the top surface flux
supplied continuously from the inlet channel layers in continuous casting process has been
at the bottom of the mould and exits through indicated by McDavies and Thomas, 1996.
the outlet on the top of the mould. This water The model has reported to include the
inlet and outlet system will deliver thermal conductivity dependent temperature
continuous cooling into the mould during and the enthalpy variations over a range a
casting. Water supplied into the system has temperature for analyzing the flux flow and
an average temperature of 22 °C. thermal behaviour of the mould flux.
The billet mould was made from Modelling of the liquid metal flow through
copper which is also used in industrial bifurcated nozzles in continuous casting is
continuous casting moulds. The mould is reported by Najjar et al., 1995. Modelling of
tubular (1 mm thick) and cylindrical in pouring temperature for investigating the
shape; formed of two concentric cylinders. superheat dissipation in steel continuous
The inner diameter of the mould cylinder is

36
Barman Tambunan, Solidification Analysis…

casting has been reported by Huang et al., 1980; Cliff and Dain, 1967) the density ρ(T)
1992. Thomas et al., 1997 have investigated is assumed constant in this analysis The
numerically the heat transfer and temperature density is less dependent on temperature
distribution in the solidifying shell of steel including in the region where the phase
slab using the 1-D transient heat conduction transformation occur. The specific heat cp (T)
equation by assuming negligible axial heat and the conductivity k(T) of bismuth alloy at
conduction. Mizikar, 1967 described a a range of temperature from the liquid phase
mathematical model of heat transfer to the solid state are strongly varied. The
solidification in continuous casting mould temperature dependent thermophysical
and predicted the slab shell thickness during properties are the subject of further
casting. His approach was to solve a 1-D discussion in the next section.
unsteady state heat conduction equation by When solidification is occurring, the
using an “artificially” high effective thermal associated latent heat L constitutes a heat
conductivity and a “simplify” effective source which is taken care by the internal
specific heat versus temperature relationship heat generated term q * . This heat source term
over a wide range of temperature up to the q * as indicated by Laitinen and
liquid region. Neittaanmaki, 1988 can be obtained from the
From Mizikar, 1967 analysis it is time rate of change of solid fraction f s during
evident that he has assumed a constant value solidification which is expressed as,
for the latent heat release in the mushy zone.
In this work a constant value for the latent  ∂f ∂T  (2)
q * = ρ L s 
heat release in the mushy zone is applied to  ∂T ∂t 
enhance more accurate prediction of the
strand thickness in the mould region of where the parameter L is the latent heat of
continuous casting process. fusion and f s denotes the fraction of solid.
The fraction of solid f s = f s (T) describes how
4.1 Theory of Thermal Analysis the solid phase fraction varies with
temperature T. The release of latent heat is
Due to the latent heat release during difficult to describe mathematically because
solidification the heat transfer equation is of the complexity of solidification in multi
non-linear. The basic equation for two component alloy system. However, it was
dimensional nonlinear heat conduction assumed in this model that no convective
equations in an isotropic medium can be mass and energy transport in the liquid phase
written in the form and mushy zone was considered. The liquids
and the solidus temperatures were defined at
∂T
div (k (T )∇T ) = ρ (T )c p (T ) − q* (1) an exact range of temperature to permit
∂t solidification process at the mushy region to
be specified on the basis of point
where ?(T) is the density of the medium, ∇ is temperature.
the Laplace differential operator, cp (T)
denotes the specific heat, T is the 4.2 The Solid Fraction Relationship
temperature which is a function of position
and time, and k(T) is the thermal In order to solve Eq. (2) the fraction
conductivity. Furthermore q* denotes the of solid f s and temperature T relationship
internal heat generated term involves the must be defined. In practice, the solid
energy removed due to the latent heat of fraction f s versus temperature curve depend
fusion during solidification in continuous on local solute redistribution and this
casting process. The internal heat generated relationship exhibit a strong non-linearity as
term q * is equal to zero everywhere except in indicated by Clyne , 1984. Different methods
the mushy region where the latent heat is have been introduced to describe the fraction
released. As has been reported by many of solid and temperature relationship (Chen
workers (Mizikar, 1967; Davies and Shin, and Tsai, 1990). On equilibrium solidify-

37
Berkala MIPA, 15(3), September 2005.

cation it is assumed that that complete 4.4 Material Property Data of Bismuth
diffusion occur between the solid and liquid Based Alloy Material
states during solidification. In non-
equilibrium solidification the liquid is A low melting point Bismuth based
assumed to reach complete diffusion while alloy, called Wood’s metal (Handbook of
diffusion in the solid state is negligible. The Industrial Materials, 1992) was chosen as the
easiest way to descript this relationship is by casting material to suit our laboratory
assuming that latent heat is released linearly facilities. The melting point temperature of
between the solidus and liquids temperature. the Wood’s metal is 71 °C. During
continuous casting Wood’s metal have
4.3 The Enthalpy Formulation successfully been used to cast a billet shape
material. It was noticed that Wood’s metal
A popular variation for solving Eq. 1 satisfies the condition of a low melting point
with the latent heat release during temperature of 71 °C. This is regarded as the
solidification has been reported by Lally et proper material for conducting the
al., 1999; Voller and Swaminathan, 1991; experimental work. Properties of the bismuth
and Voller and Peng, 1994. They have based alloy are shown in Table 1 (Igor, et.al.,
suggested including the latent heat as an 1997).
enthalpy source term and then considering
the latent heat as a dependent variable which Tabel 1. Thermal Properties of Bismuth
is known as the enthalpy method. By Eq. 1 Based Alloy
and Eq. 2 we get the heat transfer model with No. Properties Parameter
the latent heat and fraction of solid variables, 1. Thermal Conductivity Conductivity
∂f  ∂T
at Various Temperature (W/m °K)

ρ  cp (T ) − L s  = div(k (T )∇T ) (7) ( °K)
 ∂T  ∂t
4 4
The relationship between the enthalpy and 10 11
temperature the is defined by 20 18
40 20
80 23
H = c p (T )T + ∆H , 0 ≤ ∆H ≤ L (8) 100 24
2 Specific Heat at Specific Heat
where H is the total enthalpy, cp (T)T is the Temperature (°K) (J/gr °K)
sensible heat and ?H is the latent heat. At the 278 – 423 0.147
solid and liquid interface the total Enthalpy
H is determined as, The thermal conductivity of bismuth
alloy in continuous casting is temperature
∂f s
T T
H = ∫ ρ c dT − ∫ ρ L dT (9) dependent and its value varies according to
T0 T0
∂T the material composition and thermal
The heat transfer equation in terms of history. Representations of material
enthalpy after applying the chain rule to properties data as a function of elevated
?H/?t can be written as temperature are one of the most severely
limiting constrains for a successful
∂H ∂ T
ρ = div(k (T )∇ T ) (10) simulation and usually these data are hard to
∂T ∂t find or sometimes conflicting. The specific
The sensible heat H1 in Eq. 8 can be obtained heat per unit mass cp is required to solve the
by integration the specific heat while to enthalpy formulation. The latent heat has
determine the heat latent heat H2 the fraction been treated using an apparent
of solid and temperature relationship must be enthalpy/specific heat method where the heat
defined which has been described in generation term has been eliminated. During
previous section. this transformation the latent heat fusion and
the sensible heat (specific heat time’s
temperature) are released simultaneously. It

38
Barman Tambunan, Solidification Analysis…

is thus necessary to treat the sensible heat metal, the mould heat flux as a function of
and latent heat of solidification mould dwell time is required to be
simultaneously which has been included in established. This function covers a wide
the enthalpy formulation. range of casting conditions for different
mould lubricants. This function is applied as
4.5 Enthalpy - Temperature the heat flux boundary condition for the
Relationship finite element analysis. The lack of boundary
condition information will undermine the
An enthalpy-temperature relation- ability of any previous or current analysis to
ship is used to simulate the temperature predict the solidification temperature
distribution of the solidification cast. To variation during the process of billet
define the enthalpy of the material at solidification.
different range of temperature and account
the latent heat during solidification the
Billet Top
enthalpy which has units of heat/volume is
determined by the integral of density times
specific heat with respect to temperature 16.5
defined in Eq. 10. mm
Symmetry
Line

Symmetry Line
Billet Cast
400 mm

16.5 mm
5. SOLUTION METHODOLOGY Heat Flux
Boundary
Conditions
This section present the solution
methodology of the heat transfer
solidification temperature of the billet during
2 Dimensional Modeled
continuous cast Wood’s metal with the finite Transverse Slice
element analysis simulation. The details of
the Wood’s metal billet model simulated Billet Bottom
using the finite element method is shown in
Fig. 4. 33
During billet cast withdrawal, heat
from the billet surface is conducted to the Figure 4. Transverse slice area of the Wood’s metal
surface copper mould’s wall. From the round billet cast model to be analyzed
experimental work, it was noted that the
temperature decreases sharply when the The boundary condition for the
liquid metal is poured into the mould. The mould cooling zone requires a knowledge of
sudden drop of temperature is hindered after the longitudinal variation of heat flux in the
the temperature reaches the melting point mould, preferably, as a function of time.
temperature of the Wood’s metal. The Unfortunately, insufficient data from
temperature decreases in the mushy region at literatures are available to formulate a mould
a lower rate in comparison to the liquid zone heat flux boundary condition. This has
region. During billet withdrawal, the heat been also reported by Savage and Pritchard,
from the billet surface is conducted to 1954 in their analysis for continuous casting
surface copper mould’s wall. The process of steel. Therefore, the mould heat
temperature fall when the cooling water is flux function for continuous casting of
circulated around the mould wall which will Wood’s metal is calculated from
take place in about 20 second depends on the measurement of mould wall temperatures
casting withdrawal speed. Outside the mould using embedded thermocouples as shown in
region, the radiation will enhance the Fig. 5.
completion of billet solidification. It involves the placement of pairs of
To apply the solidification analysis closely spaced thermocouple pairs at each
for the continuous casting process of Wood’s measurement position in the mould wall. At
each position, the two temperature

39
 Berkala MIPA, 15(3), September 2005.

measurements are used to calculate the local Tabel 2 . Input data for finite element
heat flux with the integrated form of analysis of Wood’s metal billet
Fouries’s heat conduction equation (Holman,
1976) given as,
No. Parameters Values Unit
qm = mw (T1 − T2 )
k (11) 1. Wood’s Metal Igor et al., 1997
Lt
Parameters and Bejan, 1993
Conductivity (Kw) 12.8 W/m.°C
where kmw is the copper mould thermal Specific Heat (cp ) 147 J/Kg.°C
conductivity, Lt , is the distance between two Latent Heat ( Lf ) 32567 J/Kg
thermocouples, T1 and T2 are the two Density (?) 1056 Kg/m3
measured temperatures. The thermal Fraction of Solid (Fs ) Linear -
conductivity of the commercial copper Pouring Temperature 77 °C
material at 20 °C is 372 W/m °K. By taking ( Tp )
the value of the heat flux, q, at each position Melting point 69-71 °C
across the length of the mould, a longitudinal temperature ( Tm )
heat flux profile can be generated.
2. Casting Parameter Data from
Experimental Rig
Mould Top
Billet Diameter ( D ) 33 mm
Withdrawal time ( t ) 35 sec
Mould Length (Lm ) 400 mm
Length between 0.01 m
Thermocouple (Lt )
Thermocouple 0.2 °C (Fig.
Temperature (T1 – T2 ) 6.15)
Casting Speed (Vc) 3.7 mm/sec
Hot Face

Cold Face

Oscillation Speed (Vm ) 36.77 mm/sec

Thermocouples 3. Copper Mould Bejan 28)

Position Parameters
Conductivity ( Km ) 372 W/m.°C
T1
T2 LT = 10
T3 mm 6. TYPICAL RESULT AND
DISCUSSION
Mould Bottom
Figure 6 shows the temperature
distribution of the solidified Wood’s metal in
continuous casting obtained by applying the
Figure 5. Schematic diagram of the placement finite element simulation analysis. The
of the thermocouple at the hot surface of solidification analysis of the Wood’s metal
mould wall required for the calculation of the was considered when the mould was cooled
heat flux.
by the water circulation around the mould’s
wall.
The flux boundary condition was As shown in Fig. 6 the blue colour
measured during the continuous cast of the area is denoted for the lowest temperature
Wood’s metal. The value of the heat flux while the red colour area represents the
was used as the input data for the ANSYS highest temperature. At 5th second
finite element analysis. The other required solidification time the temperature range is
input data applied to the finite element still in the mushy region which means no
analysis of the Wood’s metal solidification solid skin is formed during the withdrawal
process in continuous casting, conducted by process. In the 15th second solidification
the experimental rig, is shown in Table 2. time, the outer skin of the billet starts to

40
Barman Tambunan, Solidification Analysis…

become solid but the core of the billet 72.5

remains liquid. Finally, at the 35th second 72

solidification time, the remaining liquid core 71.5

becomes smaller and the solid metal is 71

Temperature ( C )
progressed towards the middle of the billet. 70.5

The temperature distribution of the 70

solidified billet along the symmetry line of 69.5

the finite element billet model as represented 69

in Fig. 4, is shown in Fig. 7. At the centre of 68.5

the billet, the temperature of the metal is 68

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

71.8 °C for time t is 20 seconds, which is Distance from the middle of the billet (mm)

thus in the liquid region. The temperature

decreases further to 69 °C, which is become Figure 7. The temperature distribution of the
solid at 15.3 mm from the centre of the billet. Wood’s metal along the symmetry line at time
The thickness of the billet solid shell, d, t = 20th second.
determined by this finite element analysis is
1.2 mm. 7. CONCLUSIONS
Out side the mould wall region the
components of heat transfer are radiations to Continuous casting solidification
the surrounding and free convection. simulations are performed in this work and
Accurate assessments of the strand surface are used to investigate temperature
boundary conditions represented by the heat distribution and solidification time. It has
flux for the radiation cooling zones and for been demonstrated that the heat transfer
the mould are critical to the validity of the solidification with the consideration of the
model under development. The effect of the latent heat can be performed based on the
radiation to the solidification temperature of enthalpy formulation of the energy equation.
the continuous casting Wood’s metal billet is Further the application of the finite element
not considered for this analysis. method simulation using the commercial
package ANSYS with the ability to simulate
solidification process of bismuth based alloy
is shown to be practical. The freezing range
of the metal cast had been demonstrated
which shows the effect on temperature of
5 sec latent heat release in the mushy region. It has
been shown in the present work the
relationship between temperature, location
and time of the solidification process which
Solidification Time :
has been represented by the finite element
method.
15 sec

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41
Berkala MIPA, 15(3), September 2005.

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