MATHEMATICAL SIMULATION AND EXPERIMENTAL

MATHEMATICAL SIMULATION AND EXPERIMENTAL RESEARCH
OF THERMAL WORK OF A STEELMAKING LADLE
Pavel Hašek
VŠB-Technical University Ostrava, 17. listopadu, 708 33
Department Heat Technology - Institute of Industrial Ceramics and Refractories
Abstrakt
Matematická simulace a experimentální výzkum tepelné práce licí pánve
Matematické modelování tepelných pochodů a změny teploty oceli v pánvi. Tepelná
bilance tekuté oceli. Matematický model tepelných pochodů v pánvi při pánvové metalurgii a
odlévání. Sdílení tepla zářením na pracovním povrchu vyzdívky, který není v kontaktu s
tekutou ocelí. Experimentální stanovení součinitele přestupu tepla z tekuté oceli na vyzdívku
pánve. Příklad použití matematického modelu ke stanovení provozních charakteristik pánví
při zpracování malých množství oceli.
Provozní sledování tepelné práce pánví při mimopecním zpracování a odlévání oceli.
Provozní zkoušky nových druhů žárovzdorných materiálů pro vyzdívky pánví. Technologické
podmínky provozu vyzdívek pánví. Využití výsledků matematické simulace a provozních
experimentů pro přípravu dílčích modelů automatizovaného systému řízení ocelárny. Model
tepelného stavu vyzdívky pánve. Predikce změny teploty oceli v pánvi při mimopecním
zpracování a odlévání.
1.
INTRODUCTION
Attainment of optimum steel-teeming temperature and observance its narrow interval
in the course of casting are of atmost significance for successful casting of liquid steel. The
principal thermal and technical problem faced with the ladle metallurgy and steel casting
consists in determination of change in steel temperature within the period from steel tapping
up to the final casting in which the enthalpy of steel reveals a decreasing tendency due to the
effect of thermal losses. Only a few technological processes of ladle metallurgy provide
additional reheating of the molten steel, especially at a ladle furnace or by the chemical
reheating. This topic should be dealt with so as to enable prediction of the tapping
temperatures for the control system of the steelmaking furnaces and assessment of the
temporal variation in temperature at the extra-furnace processing and casting of steel. The
principal methods used for solution of the thermal processes in a ladle are the mathematical
modelling and experimental research with full-scale facilities.
2.
MATHEMATICAL SIMULATION OF THERMAL PROCESSES IN A LADLE
AT LADLE METALLURGY AND CONTINUOUS CASTING
The mathematical model of thermal processes in a ladle at ladle metallurgy and
continuous casting of steel is based on analytical description of the physical and chemical
phenomena taking place with the technological processes in ladle. The main advantage of
application of a mathematical model consists in possible simulation of various technological
routes by viewing the specific conditions of a metallurgical plant. Equation (1) shows the
thermal balance of liquid steel used as a basis for mathematical modelling of a variation in
enthalpy or in steel temperature. This solution presents the dependence of steel temperature in
ladle or the depedence of variation of steel temperature on the time elapsed from the start of
tapping, see Eqs. (2) and (3).
I steel,1 + Qexo + Qheating = I steel , 2 + Qlining + Qslag + Qstream + Qendo + Qadd. + Qinert
(J)
(1)
Isteel,1; Isteel,2
Qheating
Qlining
Qslag
Qstream
Qinert
Qadd.
t steel = f (τ )
enthalpy of steel at tapping and at the end time,
heat supplied by additional heating of steel,
heat loss through ladle lining,
heat loss trough slag layer,
heat dissipated from the steel stream during tapping,
heat loss at inert gas blowing,
heat loss due to introduction of additions.
∆t steel = f (τ )
( ! C)
(2, 3)
Simultaneously, there should be determined the partial variations in steel temperature as
caused by the individual items of thermal loss or by items of heat delivery.
2.1 Temperature Field of Ladle Lining
The main items of thermal loss are those through the lining and by slag and such items
of thermal loss are active for the entire time of casting i.e. from the start of tapping up to the
end of teeming. To determine the temporal dependence of thermal loss one has to deal with
the non-stationary thermal field as described by the Fourier´s partial differential equation:
∂
(c ⋅ ρ ⋅ t ) = div (λ ⋅ grad t ) + qV
∂τ
t
τ
c
ρ
λ
qV
(W ⋅ m−3 )
(4)
temperature (°C),
time (s),
specific heat (J.kg-1.K-1),
density (kg.m-3),
thermal conductivity (W.m-1.K-1),
thermal source (W.m-3).
For solution of the Fourier´s equation the explicit finite-difference method was chosen.
The conditions of explicit calculation have to be compiled for solution the temperature field;
these conditions include the geometric figure of device and the physical properties of the
materials applied here and the initial as well as the surface conditions. At solution of the
temperature field there is applied a simplified shape of ladle lining incl. of slag layer and of
cover, see Fig. 1. In this respect independent algorithms had to be compiled for application of
the complex surface conditions at the inside surface of lining.
2.2 Mathematical Description of Thermal Radiation at the Inside Surface of Lining
A separate mathematical description is necessary for the thermal radiation at the inside
surface of lining that is not in contact with molten steel. The target of solution is to derive the
depedence of the resulting thermal flow qi, result through the surface of the individual bodies on
their surface temperature. From the energy balance the resultant formulae were derived:
Fig. 1. Simplified shape of ladle lining incl. of slag layer and of cover
Fig. 2. Dependence of heat transfer coefficient ALFA by convection and by conduction from
the liquid steel to the ladle lining on time from tapping
q1,result =


εn
ε1
ε 
ε2
σ o 1 − d11 1 T14 − d12
T24 − ⋅ ⋅ ⋅ − d1n
Tn4  ( W ⋅ m −2 )
1 − ε 1 
1 − ε1 
1− ε2
1− εn

(5)
T surface temperature (K),
ε emissivity (1),
σo Stefan-Boltzmann constant (W.m-2.K-4).
The model of solution of the temperature field of lining gets more precise at
application of the proposed solution of heat transmission at a system consisting
of n isothermal areas. The derived formulae are applied at solution of heat transmission in
the systems:
a) bottom - side wall - cover or environment of ladle without its cover, namely in the coolingdown period of lining after drying, preheating or after the end of casting,
b) slag surface - side wall above the slag level cover or environment in the period when the
liquid steel level in ladle is changed, i.e. immediately at tapping or at the beginning of
teeming.
2.3 Heat Transfer by Convection and Conduction in System Liquid Steel – Ladle Lining
The combined heat transfer by convection and conduction takes place between the
liquid steel and the ladle lining. The steel flowing in ladle is unsteady in view of the time and,
depending on the sequence of the technological processes, even multiple transitions encounter
from the forced convection to free convection and vice versa. The heat transfer coefficient
ALFA by convection and by conduction from the liquid steel to the ladle lining has been
determined from the results of operational measurements in steelplant and its temporal
dependence is shown plotted in Fig. 2.
Apart from the algorithm of solution of the thermal loss through lining and through
slag layer have been elaborated algorithms of solution of further balance items for the
mathematical model as given in Eq. (1). In case of liquid steel homogenization, carried out by
inert-gas bubbling, the specific effect of some thermal loss is registered here. On the basis of
operational measurements there have been modified the relations for determination of the
blast trace at the liquid-steel surface when blasting inert gas and when pushing aside the liquid
slag.
As expample of application of the mathematical model there is presented
determination of the thermal characteristics of ladles when processing small amounts of steel
i.e. when the ladles are not completely filled and when the liquid-steel level is low in the
ladle. This condition is less suitable for two reasons. At first reduction of the volume of steel
in ladle is associated with increase of the ratio of lining surface to steel weight and thus, the
heat loss by lining and slag is increasing. Secondly, the surface of lining above the slag level
is growing with decreasing steel level and thus, the thermal loss from slag surface by radiation
and by convection is higher. Still before start of the full-scale investigation into new
technological system in steelplant the simulation of the course of steel temperature has been
carried out. After pouring the liquid steel from a 30-t transporting ladle into a 50-t refining
ladle the VOD-process (Vacuum-Oxygen-Decarburization) with implementation of chemical
reheating was applied here. The dependences of steel temperature on time are shown in Fig. 3,
namely for two variants of preheating the ladle lining [ 3 ].
Fig. 3. Simulated dependences of steel temperature on time from tapping for two ladles
preheating variants
Fig. 4. Course of measured and calculated temperatures at five heats scanned in several points
situated in half height of the ladle wall.
Ladle lining: corundum – spinel refractory concrete.
3.
EXPERIMENTAL RESEARCH OF THERMAL WORK OF LADLE
Some experimental measurements were carried out in certain steelworks for the sake
of detailed analysis of the thermal processes in liquid steel and in the ladle lining. The
temperature field of liquid steel is developed due to the effect of thermal, hydrodynamical and
physico-chemical processes in the system consisting of liquid steel, ladle lining and slag. The
temperature field is influenced by the metallurgical operations run in the ladle. The continuous
measurement of steel temperature has been made with the help of thermocouple probes
installed in the measuring points. The registration of measured data was made by a trend
logger of Grant Squirell 1203 type installed in a cooled box at the steel mantle of ladle. The
results of measurement of the temperature field in ladle at homogenization performed by
argon bubbling are described in lit. [ 1 ]. The results were used to determine the heat transfer
coefficient from liquid steel to the lining.
The present-day technological systems of ladle metallurgy and of continuous casting of
steel are imposing ever more stringent requirements for the refractory lining of ladles. The
characteristic data on the conditions of ladle operation are listed in Table 1. The technology of
extra - furnace treatment run in a ladle furnace and the continuous casting under conditions
adopted at the NOVÁ HUŤ, a.s. Ostrava makes use of two sorts of refractories, namely the
dolomite bricks and the corundum-spinel refractory concrete.
Tab. 1. Characteristic data on the conditions of ladle operation
ladle lining:
dolomite
PARAMETER
corundum-spinel
MIN
MAX
AVG
MIN
MAX
AVG
tapping temperature
°C
1617
1670
1646
1626
1678
1645
temperature in ladle
°C
1570
1649
1597
1579
1610
1592
temperature in tundish
°C
1525
1548
1536
1535
1547
1540
remain time in ladle
h
2,6
4,2
3,5
3,1
3,8
3,5
heating in ladle furnace
min
17
35
26
23
33
27
teeming time
min
55
94
78
71
99
83
h
4,1
9,3
6,3
4,5
15,3
7,5
tap to tap time for ladle
In the course of solution of the research tasks [ 2 ] and [ 4 ] the temperature field of lining
has been measured during the operational testing. For example, Fig. 4 shows the course of
temperature at five heats scanned in several points situated in half the height of the side wall.
At the same time there is given the course of steel temperature in ladle tsteel and the
temperature of the lining surface t[0], this two parameters were calculated by means of the
mathematical model. For the same case Fig. 5. shows the temporal dependence of some items
of the thermal balance of lining. Comparison of thermal loss through lining with applicatin of
the two refractories is made in lit. [ 5 ].
4.
UTILIZATION OF THE RESULTS OF MATHEMATICAL SIMULATION AND
OF OPERATIONAL EXPERIMENTS FOR THE PURPOSE OF PREPARATION
OF PARTIAL MODELS OF THE AUTOMATIZED SYSTEM OF CONTROL
OF A STEELWORKS
The complex system of steelmaking associated with ladle metallurgy and continuous
casting should be combined with an automatized system of control. The technological models
are significant part of the control system of any steelworks. In the framework of solution of
the research task called „Modernization of the automatized control system of steelworks of the
NOVÁ HUŤ, a.s. Ostrava“ [ 7 ] two partial models were elaborated and arranged among the
technological models of control.
4.1 Model of the Thermal State of a Ladle Lining
The model of the thermal state of ladle lining deals with the alteration of enthalpy of
ladle lining arranged into the working cycle of the steelworks. The ladle cycle consists of
several mutually associated intervals of reheating and cooling. Partial algorithms for
calculation of variations in enthalpy of lining have been composed for such operatios with the
ladles. The results of measurement of temperature fields of the linings were applied especially
at elaboration of algorithms and derivation of the constants for any design of the ladle lining.
[ 2, 4 ].Simultaneously, there has been utilized even the mathematical modelling of the effect
of some parameters on variation in the enthalpy of lining for various technological processes.
The model of thermal state of lining enables to determine the enthalpy of lining either for the
real time or for any time interval optionally set-up. The model is arranged into the
technological model of circulation and high-temperature preheating of ladles [ 6 ].
4.2 Prediction of Variations of Steel Temperature in Ladle at the Secondary
Steelmaking and Continuous Casting of Steel
The model used for determinaton the variations of steel temperature in ladle at the
period from the start of tapping up to final teeming presents also the thermal balance of liquid
steel, namely, on the basis of the entering data characterizing the applied technological
processes of the ladle metallurgy and continuous casting of steel. Solution will provide the
dependence of steel temperature on time. The loss of heat active for the whole period of liquid
steel dwelling in ladle includes the loss through lining and slag. For example, the dependences
of the rate of variation of steel temperature on the starting enthalpy of lining Io were derived
for the purpose of assessment the thermal loss throungh ladle lining. [ 2, 4 ]. The starting
enthalpy of lining is parameter belonging among the outlet data of model of the thermal state
of lining. The comparison of the course of steel temperature calculated with the help of model
and steel temperature measured by the submerged probes, for a single heat, is illustrated in
Fig. 6. The model of variation of steel temperature in the ladle is used in the technological
model of steel ready for teeming and in the models for control of extra-furnace treatment, the
ladle furnace and the steel-casting machine. [ 6, 8 ].
Fig. 5. Thermal balance of ladle lining
Fig. 6. Comparison of the course of steel temperature calculated with help of model and steel
temperature measured by submerged thermocouples.
References
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variation of steel temperature at extra-furnace metallurgy and casting. In: Transactions
VŠB-TU Ostrava. Agricola Volume, 1994, p. 51 - 58
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zpracované v pánvové peci a odlévané na ZPO. [Výzkumná zpráva] VŠB-TU Ostrava,
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quantities ) Hutnické listy, 1996, č. 1, s. 6 - 11
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