5th International DAAAM Baltic Conference
“INDUSTRIAL ENGINEERING – ADDING INNOVATION CAPACITY OF LABOUR
FORCE AND ENTREPRENEURS”
20-22 April 2006, Tallinn, Estonia
INVESTIGATION OF THE SHELL SOLIDIFICATION IN
HORIZONTAL CONTINUOUS CASTING PROCESS
Bockus, S.
4
Abstract: Horizontal continuous casting is
one of the prominent methods of
production of cast iron billets. Effective
creation
of
continuous
casting
technological process needs complete
analysis of the continuous casting process.
In this paper the influence of basic
technological parameters on the shell
solidification using the numerical analysis
of heat transfer is presented. The results
show that the billet shell thickness an
increase mainly depends on the billet
cooling conditions, the temperature of
molten metal in a crucible and a casting
rate. A nomograph to calculate shell
thickness is developed.
Key words: Continuous casting, cast iron,
solidification, heat transfer, mathematical
modelling.
]. This especially can be seen in the crosssections of the billets, where anomalous,
intermediate and normal structural zones
can be obtained. This is the result of
specific billet cooling and solidification
conditions [5]. The quality of the castings
and productivity of process depend mainly
on the processing conditions. In this
respect, the position and the shape of the
solidification front plays a significant role.
The key to an increase in productivity
remains often in the control of all
operational parameters. Simulation is
convenient and accurate method to
understand and analyse the importance of
each casting parameter [6].
The main aim of the investigation was to
examine the effect of technological, design
and heat physics parameters on the process
of shell solidification in the crystallizer.
1. INTRODUCTION
2. FORMULATION OF THE
SOLIDIFICATION MODEL
The horizontal continuous casting is very
productive and economic method and has a
lot of advantages in comparison with
traditional casting methods: few operations, no waste, stable dimensions of the
billet, better operation service characteristics and personal work conditions. All
these factors force to be find possibilities to
wider implementation of the method.
In the horizontal continuous casting
process the liquid metal issues from
crucible into a water cooled crystallizer.
The liquid metal solidifies in the
crystallizer, and a solid shell is formed.
The solid shell is then withdrawn
periodically in successive strokes [1, 2].
Continuous casting has its peculiarities [3,
Billet solidification in the crystallizer is
investigated by mathematical modelling of
the casting process.
Formation of the billet in continuous
casting process mainly is affected by the
cooling conditions, which predetermine the
parameters
of
it
crystallization
(temperature field, crystallization rate,
etc.). The cooling conditions vary along the
billet length and influence its solidification
character. Solidification of the molten
metal, being supplied into the crystallizer,
is not uniform in the whole volume.
Intense cooling of the peripheral zone of
the billet results higher solidification rate
245
specific crystallization heat;  is the
amount of solid phase in the given billet
element; when = 0 the metal is liquid;
when  = 1 it is completely solid. Suppose
that initial temperature of the billet is
uniformly distributed, i.e.
than in the central zone. Therefore the
following three different zones can be
distinguished: hard shell zone where the
temperature drops below the solidus
temperature; intermediate zone where heat
of phase transformation occurs, and zone
of liquid metal, where heat is transferred
by conductivity and convection. In
common case, in order to describe
mathematically billet solidification during
the continuous casting process, system of
differential equations should be derived,
which consists of: Fourier heat transfer
equations for the solidified part of billet;
convection heat transfer equation, evolving
crystallization heat occurrence in the
intermediate zone, for the liquid part of the
billet; convectional diffusion equation;
molten metal motion equation and
continuity
equation.
To
overcome
difficulties related to the molten metal
hydrodynamics, heat transfer process of the
liquid phase is described by the same type
equation as that for solidified shell, and the
convection effect is evaluated by the heat
conductivity coefficient. It is assumed, that
heat capacity of the half-solidified zone
equals to the effective heat capacity, which
is the sum of both actual heat capacity and
spectral crystallization heat together with
the crystallization heat, occurring in the
given temperature. Taking into account
these assumptions, the problem of both
heat distribution and location of the border
between liquid and solidified phases,
during the billet solidification process, is
solved as heat conductivity differential
equation with the corresponding conditions
of singularity.
In the all three billet zones, the temperature
field is described by one differential heat
conductivity equation:
T r , z, t  t 0  Tcb
(2)
where Tcb is the temperature of metal
coming from the crucible into the
crystallizer. Heat transfer on a surface of
the billet is going according to the
following law:
  T 
Tsf
r

  Tsf  Ten

(3)
where Tsf is the billet surface temperature;
 is a heat transfer coefficient; Ten is an
environment temperature. Continuous
cylindrical billet condition of symmetry is
written in the form:
T
r
r 0
0
(4)
Presented problems can not be solved
analytically. It is solved applying
approximate numerical methods. The
following heat physics values were used in
the calculations:
837 , J /( k g  K );
if T  TL;

T  TS

cef T   700  2 Lcr
if TSTTL;
TL  TS 2

700 , J /( k g  K ).
if T  TS

Lcr = 268000 J/kg;
r(T) = 8590 - 1.4T, kg/m3;
T

(1)
cT 
 div T gradT  Lcr
t
t
18.61, W/(m.K)
if T  TL;

T  TS

if TS  T  TL;
 T   35.0  16.39
T L  TS

35.0, W/(m.K)
if T  TS.
where c(T) is a billet specific heat capacity
as a function of the temperature T; r is a
density of the billet; (T) is an effective
heat transfer coefficient; t is a time; Lcr is a
246
Stability of the horizontal continuous
casting most strongly is affected by the
shell thickness at the moment, when billet
gets out of the crystallizer. Therefore,
values of casting parameters, first of all,
must ensure sufficient duration of the billet
location in the crystallizer tc, which is
related to the drawing regimes by the
relationship:
tc 
L
vt
 tp
1 
 t
d





3. THE INFLUENCE OF DESIGN AND
TECHNOLOGICAL PARAMETERS
ON THE CASTING PROCESS
Aiming to find out the best cooling
conditions of the continuously casting
billets, the influence of the following
parameters on the continuously cast
cylindrical iron billets solidified shell
thickness have been investigated: cooling
intensity of the billet; molten metal
temperature in the crucible; molten metal
liquidus temperature; billet diameter and
casting speed. Simulation of the shell
solidification was performed under the
following initial technological casting
parameters and cooling conditions of a
billet: Tc = 1240 oC, a = 1000 W/(m2.K), TL
= 1190 oC, R = 0.055 m, a = 3.28.10-6, TS =
1150 oC, tc = 30 s.
The cooling intensity is determined by the
heat transfer coefficient. The results of this
investigation show that the heat transfer
coefficient has a significant effect on the
shell thickness which is formed at the end
of crystalliser (Fig. 1).
The effect of liquidus temperature of cast
iron on the shell thickness is negligible
(Fig. 2). Therefore it is possible to use the
same value of liquidus temperature of cast
iron for the shell thickness calculations.
(5)
where L is length of the crystallizer cooling
part; vt is pulling velocity of the billet; tp is
pause duration, and td is drawing duration.
This equation can be rewritten in the form:
vac 
L

tc
vt
;
tp
1
td
(6)
where vac is average casting speed. This
equation shows that average continuous
casting speed depends on vt and ratio tp/td.
Increasing this ratio, average casting
velocity decrease and vice versa. If vt is
constant, proportional increase or decrease
of the values tp and td do not change the
average casting velocity. Thus, when tp and
td values are a few times decreased, time tc
stays constant, and the drawing step
decreases too. A decrease of the ratio tp/td
results an increase of the casting process
productivity. It is recommended to
decrease this ratio by decrease of the pause
duration, because increase of the drawing
time results increment of the drawing step,
which has a negative effect on the billet
quality. At present the tendency is higher
to use drawing frequency and small
drawing step. An average casting speed can
be increased by an increase of the
crystallizer length. The drawing velocity of
the billet can be increased both by a
decrease of the molten metal in the crucible
temperature or by an intensification heat
transfer in the crystallizer.
13
11
,
mm
9
7
800
900
1000
2.
1100
a, W/(m1200
K)
1300
Fig. 1. Effect of heat transfer coefficient α
on the shell thickness .
A temperature of the molten metal in a
crucible has a strong effect on the shell
thickness (Fig. 3).
247
This Figure shows the effect of the time tc
during which the billet is in the crystallizer
on the shell thickness also. Because the
time tc is related to the average casting
speed vac (see Eq. 2) therefore an increase
this speed results the decrease of shell
thickness.
The influence of a billet diameter on the
shell thickness is illustrated in Figure 5,
where it is shown that effect of the billet
diameter is strong in the case of small
values only.
12
11
,
mm
10
9
o
1160 1170 1180 1190 1200 T1210
L, C 1220
Fig. 2. The effect of liquidus temperature
of cast iron TL on the shell thickness .
4. DETERMINATION OF THE SHELL
THICKNESS
20
For graphical interpretation of the solutions
of the heat conductivity equation the
smallest number of criteria and simplexes
characterising the heat transfer process at
certain boundary conditions, was find out.
Method of integral analogs of the theory of
similarity had been used for the analysis.
At constant molten metal temperature in
the holder Equation (1) may be written in
the form:
16
,
mm
12
8
1180
1200
1220
o
1240 T1260
c, C
1280
Fig. 3. Shell thickness  as a function of
the temperature Tc of molten metal in the
crucible.
   Bi, Fo  ;
Figure 4 shows that the shell thickness
which is formed at the end of crystalliser 
= 10 mm at Tc = 1210 oC and tc = 24 s. But
if Tc = 1270 oC then  = 10 mm only at tc =
35 s.
where  
shell;

R
(7)
is relative thickness of the
at
R
 Bi is Bio criterion;
 Fo is

R2
Fourier criterion. Figure 6 shows a net
nomograph for this equation at molten
metal in the crusible temperatures Tc =
1270 0C are developed.
15
,
10
mm
6
5
5,
mm
0
0
10
tc30
, mm
20
1
2
40
4
3
3
0
Fig. 4. Shell thickness  as a function of a
temperature Tc and a time tc: 1 – Tc =
1180 oC; 2 – Tc = 1210 oC; 3 – Tc =
1270 oC.
50
100
150
d,200
mm
250
Fig. 5. The influence of billet diameter d
on the shell thickness  (tc = 5 s).
248
In this nomograph any of variables F0,  or
Bi can be unknown value. It is possible to
define relative thickness  of the solidified
in the crystallizer metal shell, which
corresponds to given Bi and F0, values, or
choose such technological regime, which
results the given shell thickness.
2. Beeley, P.
Foundry
Technology.
Butterworth-Heinemann, Oxford, 2001.
3. Noshadi,
V.,
Schneider,
W.,
Kuznetsov, A.V. Internal flow and
shell solidification in horizontal
continuous casting processes. In
Modeling of Casting, Welding, and
Advanced Solidification Processes
(Thomas, B.G. and Beckermann, C.,
eds.). The Minerals, Metals &
Materials
Society,
San
Diego,
California, 1998, 655-662.
4. Das, S.K. Evaluation of solid-liquid
interface profile during continuous
casting by a spline based formalism.
Bull. Mater. Sci., 2001, 24, 373-378.
5. Cicutti, C., Boeri, R. On the
relationship between primary and
secondary dendrite arm spacing in
continuous casting products. Scripta
Materialia, 2001, 45, 1455-1460.
6. Modelling for casting and solidification
processing (Kuang-O (Oscar) Yu., ed.)
Marcel Dekker, Inc., New York, 2002.
5. CONCLUSIONS
7. CORRESPONDING ADDRESS
Differential equation describing heat
transfer during the ingot solidification in
the crystallizer was established and solved.
Effect of technological, constructional and
heat physics parameters on the ingot
solidification in the crystallizer rate was
investigated. Tests showed that the billet
shell thickness an increase mainly depend
on the billet cooling conditions, the
temperature of the molten metal in crucible
and casting speed. Liquidus temperature
influence is not strong. Effect of billet
diameter is strong at small values of the
diameter only. The nomograph to calculate
shell thickness was developed.
Prof. Dr. Habil. Stasys Bockus
Kaunas University of Technology,
Department of Metals Technology
Kestucio g. 27, 44025 Kaunas, Lithuania
Phone: +370 37 323758,
Fax: +370 37 323461,
E-mail: stasys.bockus@ktu.lt
0.2
0.15

Bi = 4
2
0.8
1.3
0.6
0.1
0.05
0.4
0.25
0.3
0
0.01
0.1
0.2
Fo
1
Fig.6. Nomograph for the shell thickness
determination at Tc =12700 C.
6. REFERENCES
1.
Huespe, A.E., Cardona, A., Fachinotti,
V. Thermomechanical model of a
continuous casting process. Computer
Methods in Applied Mechanics and
Engineering, 182, 2000, 439-455.
249
250