R. PYSZKO et al.: MONITORING AND SIMULATION OF THE UNSTEADY STATES IN CONTINUOUS CASTING
111–117
MONITORING AND SIMULATION OF THE UNSTEADY STATES
IN CONTINUOUS CASTING
OPAZOVANJE IN SIMULACIJA NESTABILNIH POGOJEV MED
KONTINUIRNIM LITJEM
René Pyszko1, Zdenìk Franìk2, Miroslav Pøíhoda1, Marek Veli~ka1, Kamil Sikora1
1V[B – Technical University of Ostrava, Faculty of Metallurgy and Materials Engineering, Department of Thermal Engineering,
17. listopadu 15, 708 33 Ostrava, Czech Republic
2Silesian University in Opava, School of Business Administration, Univerzitní square 1934/3, 733 40 Karviná, Czech Republic
rene.pyszko@vsb.cz
Prejem rokopisa – received: 2016-08-01; sprejem za objavo – accepted for publication: 2017-09-26
doi:10.17222/mit.2016.235
Continuous casting comprises thermal, mechanical and chemical processes running in a complex system that contains a number
of elements, such as a solidifying steel strand, a mould with an oscillation mechanism, a withdrawal mechanism, a water cooling
sub-system with nozzles, several control sub-systems, etc. An external observer might see the process as robust and stable, but
in reality there are fluctuations in the internal thermal and mechanical quantities, reflected in the structure and quality of the
product. The research on unsteady behaviour of the quantities such as a solidifying strand temperature field, solid shell
thickness and metallurgical length was conducted using an industrial diagnostic system DGS complemented with special
measurement equipment and a thermal numerical model. Selected results of the monitoring and simulation of the non-standard
process states are shown and analysed in the paper. Methods for determining the boundary conditions for the numerical model
are also presented. The effect of the Leidenfrost phenomenon on the heat-transfer coefficient during water cooling by nozzles is
also discussed. Since the determination of precise and immediate boundary conditions has technical limits, the model provides
only smoothed values in time and space. As knowledge of the instantaneous state of the fluctuating process is a prerequisite for
achieving quality and defect-free production, it is appropriate to complement the thermal numerical model by on-line
monitoring of the machine’s internal state. The results of the simulations are closely linked to the real process data.
Keywords: continuous casting, monitoring, on-line simulation, boundary conditions
Kontinuirno litje obsega termi~ne, mehanske in kemi~ne procese, ki te~ejo v kompleksnem sistemu, ki vsebuje vrsto elementov,
kot so: strjujo~a se jeklena `ila (gredica), kokila z oscilacijskim mehanizmom, izvle~ni mehanizem, vodno hlajenje s pod-
sistemom hladilnih {ob, ve~ kontrolnih podsistemov itd. Zunanji opazovalec lahko vidi proces kot robusten in stabilen, toda v
resnici imamo vrsto fluktuacij (nihanj) internih termi~nih in mehanskih veli~in in kakovosti produkta (nastajajo~e konti lite
gredice). Raziskave (~asovno) nestabilnega obna{anja veli~in, kot so: temperaturno polje strjujo~e se konti gredice, debelina
trdne skorje in metalur{ka dol`ina, so avtorji prispevka izvajali z industrijskim diagnosti~nim sistemom (DGS), dopolnjenim s
specialno merilno opremo in termi~nim numeri~nim modelom. V ~lanku avtorji predstavljajo izbrane rezultate analiz,
opazovanja in simulacije nestandardni procesnih stanj. Prav tako predstavljajo metode dolo~evanja robnih pogojev za numeri~ni
model. Diskusija obsega tudi t.i. Leidenfrostov fenomen in njegov vpliv na koeficient prenosa toplote med vodnim hlajenjem s
{obami. Za natan~no dolo~itev vsakokratnih robnih pogojev obstajajo tehni~ne omejitve. Zato so v postavljenem modelu
uporabljene le zglajene vrednosti v realnem ~asu in prostoru. Poznavanje trenutnega stanja ves ~as spreminjajo~ega stanja, je
predpogoj za doseganje kvalitetne proizvodnje brez napak. Zato je primerno uporabljati termi~ni numeri~ni model s teko~im
(on-line) oz. neposrednim spremljanjem internega stanja na konti livni napravi. Predstavljeni rezultati so tesno povezani z
realnimi procesnimi podatki.
Klju~ne besede: kontinuirno litje, monitoring, on-line simulacija, robni pogoji
1 INTRODUCTION
Continuous casting (CC) is currently the leading
technology of liquid steel processing into solid semi-
finished products. The process is typically unstable.
Internal state variables change due to operator control
interventions into casting and cooling parameters, but the
variables also fluctuate spontaneously either in a random
or quasi-periodic way. The most effective technique to
predict the process state is based on continuous measure-
ment and evaluation of the internal quantities in the
continuous casting machine (CCM) that helps achieve
quality and defect-free production.1 Modern casters are
also equipped with a numerical model of the strand soli-
dification and cooling, which is functioning as "a soft-
ware sensor" for detecting quantities immeasurable by
other technical means, such as solid shell thickness.2,3
Numerical models require boundary conditions that are
usually determined with data from the monitoring and
control system and data from laboratory measurements.
The aim of the research was to investigate the
behaviour of the CC process based on real process data
as well as results of specific experimental measurements
and simulations. The paper focuses on the kinetics of the
strand temperature field. To achieve the required quality
of the product and to avoid failures such as breakouts, it
is desirable that the temperature field of the solid shell is
stable and uniform, in both the transverse and longitu-
dinal directions. Non-defect billets are a prerequisite for
quality sheets or pipes made from them and conse-
Materiali in tehnologije / Materials and technology 52 (2018) 2, 111–117 111
UDK 621.74.047:67.017:620.163.1 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 52(2)111(2018)
quently for impeccable final products.4 Since the
occurrence of non-standard states due to changes in
casting parameters cannot be eliminated in the actual
casting process, the investigation of their influence on
the strand temperature field kinetics is important in terms
of the quality and safety of production.
2 EXPERIMENTAL AND SIMULATION
RESEARCH
Experimental research was conducted in a real plant
as well as in a laboratory using an extensive experimen-
tal equipment and software. The industrial monitoring
and diagnostic system DGS was utilized for gathering
the values of internal variables in the caster during
experiments. The mould is the most important part of the
CCM, which determines the quality of the final product.
The system DGS has been developed by the company
DASFOS in co-operation with the authors from
V[B – Technical University of Ostrava (both from the
Czech Republic) and was implemented at block and
billet casters of round and rectangular formats in
Tøinecké `elezárny and @elezárny Podbrezová.5 The
algorithms of DGS are based on measurements and
analyses of temperatures in the mould wall and friction
between the strand and the mould.
Up to 30 thermocouples of type E (NiCr-CuNi) were
installed in the round mould with a diameter of 520 mm
in a single horizontal level 390 mm from the mould
upper edge around the mould perimeter for the purpose
of breakout and quality prediction (Figure 1). The sys-
tem DGS also recorded the process variables received
from the caster control system, e.g., cooling water tem-
perature and flow rate, liquid steel level and temperature,
casting speed, etc. All data were stored with a period of
5 s.
During experimental campaigns a special measure-
ment equipment was also used, which complemented the
system DGS. Moulds of the round format 520 mm
were fitted with an additional 12 thermocouples installed
in two vertical lines at distances from the mould upper
edge of (116, 236, 356, 426, 506 and 586) mm. Six sen-
sors were on the side of the outer radius (OR) and
another six sensors on the inner radius (IR) side.6
Below the mould, the strand surface temperatures
were measured by means of optical pyrometers. Three
pieces of ratio pyrometers were used, namely Raytek
Marathon MR1SB (a span of 700–1800 °C) and MR1SA
(a span of 600–1400 °C).
Due to significant delays in the caster caused by the
strand withdrawal, for the purpose of evaluation all the
data were transformed from a database of time series to a
database of the samples belonging to strand virtual cross
sections. Special software was developed for this pur-
pose, which interpolated and integrated the values with
respect to the point or length interval, where the parti-
cular quantity was acting in the caster. The algorithm
was designated as "data aggregation".7,8 Each record in
the aggregated database contained values that characte-
rised the history of the strand section during moving
through the caster.
Off-line and on-line versions of thermal numerical
models were developed at the Department of Thermal
Engineering at V[B – TU Ostrava. The on-line model
was used during the experimental work for evaluating
the strand temperature field, the thickness of the solid
shell and the length of liquid and mushy core of the
strand, called the metallurgical length. A prototype of the
advanced diagnostic system "DGS-DMT" consisting of
the system DGS linked with the thermal numerical mo-
del was developed in the company DASFOS in coopera-
tion with V[B – TU Ostrava. The system was success-
fully tested at the round block caster in Tøinecké
`elezárny.
The thermal model is based on the Fourier-Kirchhoff
Equation (1):
D
d
t
a t
q
c
V
p 
= ⋅∇ +
⋅
2 (K·s–1) (1)
where a (m2 s–1) is the thermal diffusivity of steel, qV
(W m–3) is the volumetric internal heat source of the
latent heat of solidification, cp (J kg–1 K–1) is the spe-
cific heat capacity,  (kg m–3) is the density and Dt/d is
the substantial derivative of temperature by time. All the
thermophysical parameters of the steel are functions of
temperature.
The model uses a 3D explicit finite-volume method.
The calculated volume contains the whole strand from
the steel level in the mould down to the cutting device.
The main result of the model is the strand temperature
field. The liquid, mushy or solid phase of each steel ele-
ment is identified by comparing the element temperature
with the steel liquidus and solidus temperatures. The
numerical model was verified by comparing the cal-
culated temperatures of selected surface elements to
temperatures measured using optical pyrometers.
R. PYSZKO et al.: MONITORING AND SIMULATION OF THE UNSTEADY STATES IN CONTINUOUS CASTING
112 Materiali in tehnologije / Materials and technology 52 (2018) 2, 111–117
Figure 1: Thermocouple leads mounted in the mould (Source:
DASFOS)
To solve the numerical problem, boundary conditions
are required. Besides the initial, geometrical and physi-
cal conditions, surface conditions must be determined.
The average heat flux qm in the mould was derived from
measured cooling water parameters using the following
Equation (2):
q
A
Q c t c tm
m
w p,2 p,1= ⋅ ⋅ ⋅ − ⋅
1
2 1 ( ) (Wm
–2) (2)
where Am (m2) is the area of the mould working surface,
 (kg m–3) is the water density at the position of the
flow rate sensor, Qw (m3 s–1) is the water flow rate, t1,
t2 (°C) are the temperatures of inlet and outlet cooling
water, cp,1, cp,2 (J kg–1 K–1) are the mean specific heats
of water at temperatures t1, t2 calculated by integration
of the immediate heat capacity for the interval from
0 °C to the actual temperature.
Heat flux in a real mould varies along the mould
length and perimeter. The heat flux layout in mould
walls was compiled from the average heat flux qm using
measured temperature layout in a mould wall. Figure 2
shows an example of the vertical temperature profiles on
the sides of the mould outer radius (OR) and the inner
radius (IR) measured during casting the steel with 0.4 %
of mass fractions of C. The temperature profiles in the
graph were evaluated from five of six thermocouples on
each side. The highest placed thermocouples were not
used as they were occasionally above the steel level. The
temperature profiles show that the strand was pushed to
the OR side at the lower part of the mould. This was
individual to the specific mould and casting parameters.
Temperature profiles are influenced by the mould wear,
geometrical adjustment of the casting arc, submerged
nozzle position, etc. Several hundred heats were
measured and an extensive database of temperature
profiles was created.
The demanding task was to determine the 3rd-kind
condition under spraying nozzles in the secondary cool-
ing zone. The condition represents a heat-transfer coeffi-
cient (HTC, ). An original laboratory device was
developed, which utilised special sensors, either a
directly or indirectly heated probe with a stainless-steel
core, which was repeatedly heated by electric current and
then exposed to spraying while temperatures in the core
were sensed. HTC was then obtained by solving an
inverse problem of heat conduction. The nozzle was
mounted opposite to the probe on the arm of the indus-
trial robot, which moved the nozzle to discrete positions
and, step by step, the entire sprayed area was scanned. At
each single position, the dependence of HTC on the
surface temperature for specific water pressure was ob-
tained. An example of such dependences for two values
of pressure is in Figure 3 for the nozzle JATO 3065 at a
distance of 100 mm between the nozzle and the sensor.
The dependences are typically non-linear due to the
Leidenfrost phenomenon. The value of the Leidenfrost
temperature point (400 °C for pressure of 0.4 MPa and
480 °C for 0.8 MPa) depends, apart from the water pres-
sure, on the local spray intensity, size and kinetic energy
of water drops, surface roughness, oxide layer on the
surface, etc.9
Figure 4 represents the obtained distribution of HTC
over a square part of the sprayed area for a surface tem-
perature of 800 °C and a water pressure of 0.4 MPa for
the nozzle type and the distance specified above. This
characteristic is one example of the extensive set of
R. PYSZKO et al.: MONITORING AND SIMULATION OF THE UNSTEADY STATES IN CONTINUOUS CASTING
Materiali in tehnologije / Materials and technology 52 (2018) 2, 111–117 113
Figure 4: Layout of heat transfer coefficient on surfaceFigure 2: Vertical temperature profiles in the mould
Figure 3: Measured dependences of HTC on surface temperature
characteristics obtained with laboratory measurements
for all the nozzles and parameters used in the caster.
In the thermal model of the round format caster, un-
like a slab caster, the influence of the rollers to the heat
removal can be neglected. This is due to the relatively
small number of rollers compared to the slab machine
and the small area of the contact between the rollers and
the strand.
3 RESULTS AND DISCUSSION
Generally, the most influential parameter in CCM is
the casting speed. Simultaneously with the casting speed,
the control system also corrects other quantities such as
the mould oscillation frequency and cooling water flow
rate into nozzles in the secondary cooling zone. There-
fore, the influence of casting speed on other variables is
complex and difficult to predict by simulation without a
simultaneous operational measurement. Based on
measurement and simulation during casting round blocks
of diameter 520 mm, responses to unsteady casting
speed were analysed.
Figure 5 shows a 6-hour interval of casting. Besides
casting speed v, also simulated strand temperatures are
plotted, i.e., the surface temperature ts averaged around a
strand circumference and the centreline temperature tc,
both evaluated at the end of the mould where the strand
is not yet influenced by the secondary cooling zone.
There were two non-standard states, the first at the time
6.03 h and the second at 7.3 h when speed of the strand
withdrawal was reduced and stopped due to the breakout
danger predicted by the system DGS.
The surface temperature response to the change in
casting speed is complicated. Generally, a reduction in
casting speed causes a gradual drop of surface tempera-
ture due to extended time available for cooling. In
contrast, a complete stop of the strand withdrawal causes
a gradual increase in surface temperature as the solid
shell is shrinking, thermal resistance of the gap between
the shell and mould is increasing, heat flux from the
strand surface is decreasing and the solid shell is being
reheated with high enthalpy of the strand liquid core. A
following renewal of withdrawing causes initially an
immediate drop in surface temperature due to a sudden
restoration of the shell contact with the mould, followed
by a steep increase in surface temperature due to shell
shrinkage and reheating. Generally, the temperature peak
after renewal of withdrawing is the higher the longer
lasts the previous withdrawal interruption and the greater
is the step of the casting speed change. Finally, the tem-
perature gradually decreases to a stable value.
Figure 6 shows a detail of the first non-standard state
at 6.03 h. There was a speed reduction followed by three
short stops and a final increase in casting speed which
caused several periods of the surface temperature
oscillation. In Figure 7 is a detail of the second
non-standard state at 7.3 h, which makes it possible to
analyze the general behaviour described above more
clearly. Reduction in casting speed at 7.35 h caused a
drop of the surface temperature due to extending the time
of cooling. The complete stop at 7.41 h caused a gradual
increase in surface temperature due to the shell shrinking
and reheating. The sudden short renewal of withdrawing
at 7.45 h caused an initial rapid drop of the surface tem-
perature followed by a gradual increase during next
stopping at 7.48 h. The second renewal of withdrawing
at 7.61 h caused a temperature drop followed by a steep
increase at 7.63 h and finally a gradual decrease at 7.65 h
down to a stable value reached at 7.75 h.
In Figure 8 are waveforms of casting speed and
measured surface temperatures at three positions in the
tertiary cooling zone where the strand is cooled by free
convection and radiation. Optical pyrometers were
placed at positions 5.3 m (pyrometer P1), 19.6 m (P2)
and 30.5 m (P3) from the steel level. P1 was about 3 m
behind the last cooling nozzle. After stopping at 6.03 h
the signals from all pyrometers were dropping due to the
extended cooling time. As the cooling water flow rate
into nozzles was not reduced enough during stopping,
the part of the strand located in the secondary zone was
R. PYSZKO et al.: MONITORING AND SIMULATION OF THE UNSTEADY STATES IN CONTINUOUS CASTING
114 Materiali in tehnologije / Materials and technology 52 (2018) 2, 111–117
Figure 6: Detailed interval of the first non-standard stateFigure 5: Strand temperatures at the mould exit and casting speed
undercooled. At 6.2 h this part came to P1 and caused
further dropping of the P1 signal. The signal of P2 later
at 7.1 h dropped similarly when the same undercooled
part came to P2. Similarly, would react P3, but the res-
ponse of P3 was simultaneously influenced by the
second non-standard state at 7.3 h.
Undecooling is not favourable in terms of quality.
This meant that the static control algorithm of the secon-
dary zone did not react sufficiently. It should be im-
proved or replaced by an optimal dynamic control
method10. Due to the time shift caused by the strand
movement, the effect of the first non-standard state
collided with the second non-standard state at 7.3 h in
P1–P3 temperatures. Nevertheless, the temperature drop
of P1 at 7.7 h, P2 at 8.8 h and P3 at 9.3 h due to the
strand undercooling is visible.
Figure 9 shows the time dependence of the simulated
solid shell thickness s at the exit of the mould and at the
pyrometer P1. The shell thickness was evaluated as an
average distance between the surface and the node with
100 % of solids. An increase in shell thickness was
greater during the second non-standard state at 7.3 h
when stopping took longer than during the first abnormal
state.
Figure 10 presents a waveform of metallurgical
length based on the simulation. Generally, at steady con-
ditions applies the higher casting speed the longer
metallurgical length. But the behaviour of the metallur-
gical length after a sudden change in casting speed is
more complex. After the stop of withdrawing at 6.03 h
the metallurgical length slowly decreased, which was
caused by extension of the cooling time. After restoring
withdrawing at 6.2 h, metallurgical length initially
remained constant since the velocity of solidification
approximated casting speed. About at 6.6 h, however, the
metallurgical length suddenly decreased. This was
caused by a final solidification of the bounded region
filled with the mushy phase surrounded by the solid
phase, which may be considered as a "mini-ingot". After
this the metallurgical length was slowly increasing up to
the stable value at 7.1 h, which corresponded to the
current casting speed. The same phenomenon of the
"mini-ingot" final solidification occurred at 8.0 h after
the second non-standard state.
Phase maps of the strand at selected significant time
points are pictured in Figure 11. White colour expresses
the liquid phase, light grey colour corresponds to the
mushy phase and dark grey represents the solid phase.
The above mentioned mushy phase areas surrounded by
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Materiali in tehnologije / Materials and technology 52 (2018) 2, 111–117 115
Figure 9: Simulated shell thickness
Figure 8: Surface temperatures measured by optical pyrometers
Figure 7: Detailed interval of the second non-standard state
Figure 10: Simulated metallurgical length
the solid phase after the second non-standard state can be
seen in the phase map of 8.0 h.
The simulated surface temperatures at pyrometers
positions P1, P2 and P3 are in Figure 12. The numerical
model was tuned to calculate 20–30 °C higher surface
temperatures in comparison to the values measured by
the pyrometers to compensate an average temperature
drop due to oxides and casting powder on the surface.
The simulated temperature waveforms were in good
accordance with reality, but it is evident that simulated
surface temperatures are smoother in comparison to the
measured temperatures. The reason is that the simulated
temperatures are responding only to changes in known
casting parameters, e.g., casting speed and cooling water
flow rate, while the surface temperatures in the real
caster oscillate (Figure 8) due to a non-uniform layer of
oxides and casting powder on the surface, and also due
to spontaneous internal oscillation in the caster, either
stochastic or quasi-periodical. Such oscillations are
typical for multidimensional non-linear systems.
Frequency analysis showed that the signals feature
quasi-periods ranging from seconds to several minutes.
A correlation analysis proved occasional relationship
between surface temperature and some variables such as
temperatures in the mould wall or liquid steel level.
It is generally difficult or even impossible to derive
sufficiently detailed immediate boundary conditions for
the numerical model to simulate the exact oscillation of
the temperature field. Therefore, it is appropriate to com-
bine several diagnostic methods based on the thermal
numerical modelling and monitoring temperatures and
other variables of the caster internal state for a purpose
of the process control and quality prediction.
4 CONCLUSIONS
An investigation of the unsteady states of the conti-
nuous casting process has been conducted using the
process diagnostic system DGS, special measurement
devices and a thermal numerical model. The responses in
quantities induced by the casting speed variation were
simulated and analysed, based on real measured data
from a round block caster with a diameter of 520 mm.
The strand surface temperature oscillation was excited
after a change of casting speed. The peak of surface tem-
perature was the higher the longer lasted the withdrawal
interruption and the higher was the casting speed step
change. The metallurgical length behaviour after a tem-
porary stop of withdrawing was also analysed and
creation of "mini-ingots" was predicted. Due to the
multidimensional and non-linear character, the system of
the casting machine tends to be unstable and quantities
in a caster are susceptible to oscillate. Knowledge of the
cause and magnitude of the process variation is import-
ant for the casting control and quality prediction.
Acknowledgements
This paper originated with the financial support of
grants MPO ^R No. FT-TA4/048, GA^R No. GA106/
07/0938 and V[B - TU Ostrava research projects
SV2017/37 and SV2017/58. The authors are also grate-
ful to companies DASFOS, v.o.s. and Tøinecké `ele-
zárny, a.s. for their cooperation in operational
experiments.
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