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FIELD OF APPLICATION
The present invention relates to an improved method of cooling a solidifying strand in a continuous slab casting process.
In particular, the present invention relates to the design of such cooling strategy for the continuous casters by extracting heat from solidifying strands in the secondary cooling zone.
BACKGROUND OF THE INVENTION
Continuous slab casting is a process where liquid steel is continuously poured into a copper mould to construct the slabs. The solidification process initiates at the top most level of the liquid steel (the meniscus) within the mould cavity and it propagates as the solidifying strand descends down. The copper mould is cooled by running water. The mould cooling must be sufficient to strengthen the shells in withstanding the ferro static pressure of the liquid core.

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Beneath the mould the solidifying strand travels through banks of nozzle sprays where jets of air-water mixture are impinged on the strand surface, The purpose of this secondary cooling zone is to continue the heat extraction and the solidification that are initiated in the mould, but at a faster rate. The cooling system in this zone should be so designed that the solidification should be complete within this zone and as such without generating tensile stresses of sufficient magnitude which may cause internal defects and cracks.
The strand is further air cooled in the radiation zone, which follows the spray cooling zone and precedes the torch-cutting machine. In the torch-cutting machine the completely solidified strand is cut to slab-sizes and the slabs are fed to the mill.
The heat extraction of the solidifying strands plays a major role in producing quality slabs. In the primary cooling zone (mould cooling), inadequate cooling may develop thinner shell and as a consequence may lead to rupture or breakout of the shell. Excess of cooling, on the other hand, may lead to shape deformation or crack formation.

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In the secondary zone uneven cooling may cause bulging of strands or propagate cracks that are initiated in the mould. Severe bulging may lead to breakage of the strand. Continuous occurrence of bulging and squeezing of strand within the roll gaps may even lead to mould level fluctuation.
It is therefore, important to design appropriate cooling system to reduce such operational nuisances.
Numerous research work related to spray water design are available. Most of the works are performed in the laboratory scale. The workers here have assumed implicitly that the caster operates at steady state and most of their empirical formulation have been applied only in this condition. In reality, steady state in casting speed is rarely achieved. This is due to the operational practices such as start-up; capping off; ladle, tundish or shroud changes; or due to unplanned events such as nozzle blockage.

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If speed changes are unavoidable then the question is how to adjust spray pattern with the speed changes. Common practice is to vary the spray water throughout the secondary zone in direct proportion to the casting speed changes. This method of cooling strategy has been adopted by many steel plants including Tata Steel. Recently commissioned vertical caster and other two casters that are upgraded to higher speeds in Tata Steel follow this practice. This method is simple but fundamentally incompatible with the nature of continuous casting process.
Alternative practice that has been proposed by many researches and also adopted by many steel plants is to adjust the spray water based upon the thermal history or "age" of the slice of the strand. The method is described in brief in the following paragraph.
It has been observed that the temperature distribution in the strand can be computed by considering the transverse slice that descends at the withdrawal rate of the casting machine. It is evident that at constant speeds the strand-slice

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temperature at a specific location in the strand-travel-path is constant and depends on the time the slice takes to reach that point, i.e. the age of the slice, and the spray-cooling condition. At constant speed the age of successive slices passing the location remains unchanged; but with the speed changes the age of the slices passing the point obviously change. An increase in speed would cause the age to decrease while the opposite would occur with decrease in speed.
If the thermal history of any slice is to remain unchanged during this period the spray cooling must be adjusted, not in proportion to speed change, but according to the age of the slices at each location.
Baptista [1] has used this practice to determine the spray adjustment during the shroud change on an operating slab caster of five zones. Water-flux calculated for each of the five zone corresponding to the averaged age of slices has later been compared to that dictated by simple water / speed ratio control. It has been observed that the water flux requirements for a zone during the shroud change are a strong function of distance of the zone from the meniscus.

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Further, the predicted changes in water requirements for the lower zones are almost negligible in 'age-based' cooling and therefore large surface reheats will result if the sprays are adjusted in direct proportion to the casting speeds.
Chakroborty [2] has employed the following governing equation of heat conduction and solidification with the boundary conditions of primary mould cooling and spray water cooling to develop the thermal history of descending slice:

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where,
q = Mould heat flux (Kw / m2 - sec)
htc = spray water heat flux kw / m2 - sec]
w = water flux liter / m2 - sec
The empirical formulation of the boundary conditions are proven formulate which are available in open literature and applied by several researchers- The constants a, b and n are the design factors which are tunable with the operating practices. The model was used in Tata Steel in displaying the thermal profile of the strand but have never been employed to adjust the spray-water. Chakroborty later used the simulator to device "age" based cooling strategies for caster "A" and "B" of Tata Steel. The 'age' based cooling strategy replaced the water / speed cooling control. The author claimed that the 'age' based cooling

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strategy has reduced the thermal shock considerably as the water flow in the strategy does not change abruptly with the speed change as it does with water / speed cooling control. The claims however have never been proven as the thermal shocks are not measurable.
Further, the strand thermal profiles as computed by the simulator have never been checked with the measured plant data so the validity of the governing equations and the boundary conditions that are used in the simulation are under questions.
In the course of the present invention a series of pyrometers was used to measure the strand thermal profile [2]. The simulation results of Chakroborty et.al are then verified with the measured temperature. The graph-plot of the results shows that the simulated profile does not only mismatch with the measured temperature but also differ in 180 degree phase angle. This evidently raises the question of formulation of the heat transfer coefficient.

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Shimada and Mitsutsuka [3] based on their laboratory experimentation on plain carbon steel plate with spray cooling at both sides included the spray water temperature in the heat transfer coefficient formulae. The modified form is as follows:
htc = 1.57 w0.55 (1- 0.0075 Tw) (4)
Shimada et.al. [3] have observed the considerable change in heat transfer coefficient with the change in surface temperature, particularly in the region of Leidenfrost temperature. They have bound n value with the water flux values. The relationship of n with the water flux W is as follows:
0.65 < n < 0.75 for W > 0.08 Liter / m2s
0.005 < n < 0.008 for W > 10-10.3 Liter/ m2s

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Nozaki et.al. [5] have used equations of Shimada and Mitsutsuka with empirical adjustment, a, based on in-plant temperature measurements at the straightener. The modified form of the equation [4] is as follows:
htc= 1.57 w0.55(l-0.0075 Tw) (5)
a
where, a˜4.0
All the formulae in the model were used during the course of the present invention, but the model temperature never matched the pyrometer data.
The 'age' based strategy of the secondary cooling system advocates that the moving strand will observe same temperature repeatedly at a given location and

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at a given speed. The cooling strategies are devised on this fundamental principle. But the statement is ambiguous as the strand will observe different temperature at the same location and the same speed if the cooling pattern is different. So the design of the 'age' based cooling strategy has the dependency on the initial cooling pattern based on which the 'age' calculations are made.
Another drawback of the system is the empirical formulation of the heat-transfer coefficient. In the preceding section it is described how the simulation results that have been obtained by Chakroborty et at. and others have not matched with the measured strand temperature in the plant. This evidence is sufficient to prove that the formulation of the heat-transfer coefficient needs a critical review.
SUMMARY OF THE INVENTION
Since heat extraction from the strand surface is strongly related to the spray-water, the design Of the cooling system depends upon how accurately the co-relationship between the heat transfer coefficient and water flow is established.

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The present invention provides a newly formulated empirical relationship of heat transfer coefficient and spray water flux.
One object of the present invention is to compute the strand surface temperature profile as a whole at every time step instead of computing the 'age' or "residence time' of the descending slice for designing the secondary cooling system.
Another object of the invention is to adjust the water-flux by reducing the difference between the computed strand temperature and the required temperature at each cooling segment instead of selecting cooling curves based on 'age' of descending slice at the cooling segment at the time of selection.
Yet another object of the present invention is to formulate a new equation of heat transfer coefficient such that the model temperature matches with the measured temperature.

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In a casting process with temporal grid points the axis-symmetry geometry of the stab and the shower locations have eased the problem by simplifying the governing equation. Dynamic cooling model has employed the Eqn. 1.0, a typical two-dimensional transient heat conduction equation to compute grid-point temperature at every five seconds.
The required temperature or target temperature profiles of the strand are predefined and have been collected from the suppliers operating manual, In Tata Steel there are three cooling practices the hard cooling is for casting low carbon grades, medium cooling for medium carbon and soft cooling for peritectic and high carbon grades. The required cooling curves for each cooling practice are stored in the dynamic cooling model. The water-flux in each cooling segment is adjusted in a regular interval with an aim to minimize the difference between the computed cooling curve and the required cooling curve.

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Heat transfer coefficient largely depends upon the residence time and surface temperature [6]. LaedenFrost temperature indicates that the heat transfer coefficient changes dramatically if the surface temperature is below the Laedenfrost temperature and the vice-versa.
The empirical formulae of heat transfer coefficient which are described in equation 3.0 to 5.0 have not considered the effect of residence time and the Ladenfrost temperature. The following equation is a modified formulation of equation 5.0 which has been successfully used in Dynamic cooling model of the present invention of the author. The equation is as follows:
htc= 1.57 w0.55 (1 - 0.0075 Tw [1-C0 (Vref-V)] (6)
a
where Co = A constant value ranging from 0 -1
Vref = Casting Speed of Reference (Here 1.0 Meter / Min)
V = Casting Speed

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In a preferred embodiment the present invention provides an improved method of cooling a solidifying strand in a continuous slab casting process, comprising the steps of: computing at every time step the strand surface temperature profile as a whole, in a secondary cooling zone; adjusting water-flux by reducing the difference between the computed strand temperature and the temperature required at each cooling segment in the secondary cooling zone; and formulating a governing equation of heat conduction and solidification with boundary conditions of secondary cooling zone where
spray water heat flux htc- 1.57 w0.55 (1 - 0.0075 Tw) [ 1-Co (Vref - V)]
a [W = water flux liter / m2 - sec; a ˜ 4.0; Co * a constant value ranging from 0-1; Vref = casting speed of reference, here 1.0 mm / min; V = casting speed] so that model temperature matches the measurement.

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BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS
The invention can now be described in detail with the help of the figures of the accompanying drawings in which
Figure 1 shows measured strand temperature and model
(Chakroborty et.al.) predicted temperature over the casting speed.
Figure 2 shows a schematic diagram of a typical slab caster
Figure 3 shows 2D plane of moving strand with temporal grid-points (nodes)
Figure 4 shows strand temperature profile at various casting speed using look up table (VAI designed)
Figure 5 shows strand surface temperature profile at various casting speeds using DSCC cooling strategy

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Figure 6 shows strand temperature measured by pyrometer while running with look up table cooling strategy (VAI designed)
Figure 7 shows strand temperature measured by pyrometer while running with DSCC cooling strategy
Figure 8 shows validation of DSCC model temperature and measured temperature
DESCRIPTION OF THE INVENTION
The strand thermal profile as computed by the simulator of Chakroborty et.al were verified with the measured temperature and the results are shown in Figure 1.

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Figure 2 shows in schematic form the slab casting process with the temporal grid points. The three cooling zones, primary, secondary and radiation zones are shown clearly.
It is evident from the continuous casting operation that the strand geometry, mould cooling and secondary cooling equipment are axis-symmetric by design. This has enabled the selection of 2D heat transfer equation In the present invention as the governing equation (Eqn. 1). In this model the strand is represented by a longitudinal 2D plane (Figure 3) passing through the longitudinal axis of the strand. The origin of the plane is the intersection of plane of meniscus level and the longitudinal axis. The terminal end of the plane is the end of the radiation zone. The top and bottom boundaries of the plane are bounded by the top surface and the longitudinal axis of the strand. The plane is divided into 50 X 300 grid points (nodes) that are equally spaced along each axis but with different space size in two axes. The grid space in transverse direction (referred as x - axis in the model) is 0.0025 m whereas that in the longitudinal direction (referred as z-axis in the model) is 0.05 m.

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The boundary condition in the mould section due to heat extraction by primary cooling is formulated in the model in the following way:

The boundary condition in spray cooling section is used as the equation described in Eqn: 6.
Thermal property of the steel such as the diffusivity, density, conductivity are considered in the model as function of temperature, liquidus and solidus temperature. In the meniscus level high intensity of turbulence occur as the liquid metal is sprayed into the mould through submerged nozzle. At high intensity turbulence thermal property of liquid metal differs discretely from that of solid steel. The thermal conductivity increases in exponential terms in this turbulent zone. The model has considered the impact of the turbulence on the thermal property.

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The model is integrated to the on-line DCS system and retrieve real time process parameters at every five seconds interval. The numerical method termed as the explicit scheme Is used as the solver of the governing equations. The scanned data which includes parameters like casting speed, water flow, chemical composition, strand width etc are used to compute the heat transfer coefficients of the boundary nodes. The solver solves the equation and determines the current nodal temperature based upon the temporal history of the previous time step. This application continues unless it is stopped externally.
Once the nodal temperatures are computed the next step of the model is to compute the difference between the current surface-node temperature and the desired temperature at that location. Consequently it determines the water flows needed to be adjusted such that the gap is minimized. The adjusted water flows become the set-point for the next cycle.

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Figure 4 shows the strand temperature profile at various speeds when water / speed look-up table is used as the cooling strategy. Figure 5 shows the same when DSCC model is used as the cooling strategy. Figure 6 shows the strand temperature sensed by a pyrometer installed in the last cooling segment when water / speed look-up table is used as the cooling strategy. Figure 7 shows the same when DSCC is used as the cooling strategy. Figure 8 shows the validation of Eqn. 6 with the plant measured data.
It is evident from the figures that strand temperature profile at various speeds are more ordered and tend to remain close to the mean under the DSCC cooling strategy in comparison to that of the water / speed cooling strategy. The pyrometer temperature also shows that fluctuation is significantly less under the DSCC cooling Strategy.

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Reference:
1. L,, Baptista; "Spray Cooling in the Continuous Casting of Steel"; MASc. Thesis, University of British Columbia, 1979.
2. S. Chakroborty, R. Kumar "Dynamic Secondary Cooling Control System for the slab Casters", Tata Search, 2000, pp 79 - 84.
3. ML Shimada and M. Mltsutsuka, "On Heat Transfer Coefficient by Forced Water Cooling to Carbon", Tetsu-to-Haguane, Vol 52,1966, p 1643.
4. M. Mitsutsuka "Study on the water spray cooling of Steel Plate at High Temperature", Tetsu-to Haguane. Vol-54,1968, ppl457 - 1471.
5. T. Nozaki, J. Matsuno, K. Murata, H. Ooi and M. Kodama, "A Secondary Cooling Pattern for preventing surface cracks of Continuous Casting Slabs" Trans. ISD, Vol. 18,1978 pp 330 - 338.
6. 1 Brimacombe, P. Agarwal, S. Hibbins, B. Prabhaker, L.A. Baptista, "Control of Spray Cooling in the Continuous Casting of Steel", Continuous Casting Conference, pp 109 - 123.
1.
-24-WE CLAIM
1. An Improved method of cooling a solidifying strand in a continuous slab casting process, comprising the steps of:
computing at every time step the strand surface temperature profile as a whole, in a secondary cooling zone;
- adjusting water-flux by reducing the difference between the computed strand temperature and the temperature required at each cooling segment in the secondary cooling zone;
- and formulating a governing equation of heat conduction and solidification with boundary conditions of secondary cooling zone where
spray water heat flux htc= 1.57 w0.55 (1 -0.0075 Tw) [ 1-Co (Vref - V)]
a [W = water flux liter / m2 - sec; a ˜ 4.0; Co = a constant value ranging from 0-1; Vref = casting speed of reference, here 1.0 mm / min; V = casting speed]
so that model temperature matches the measurement.

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2. The method as claimed in claim 1, wherein the boundary condition in the
mould section for heat extraction by primary cooling is formulated by the
following equation:
_ A Z
htc = qq * e zmax Vmax
where
qq = Heat Extraction by water in mould (KW)
z = Mould Depth from Meniscus (m)
v = Casting Speed (m / min)
3, The method as claimed in claim 1, wherein said time steps, are after
every five seconds.

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4. "The method as claimed in claim 1, wherein cooling curves for different cooling practices can be stored and water flux in each cooling segment can be adjusted at regular intervals for minimizing the difference between computed cooling curve and cooling curve required.
5. An improved method of cooling a solidifying strand in a continuous slab casting process, substantially as herein described and illustrated in the accompanying drawings.
Dated this 2nd day of April 2007.
Since heat extraction from the strand surface is strongly related to the spray-water, the design of the cooling system depends upon how accurately the co-relationship between the heat transfer coefficient and water flow is established.
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The present invention provides a newly formulated empirical relationship of heat transfer coefficient and spray water flux.
One object of the present invention is to compute the strand surface temperature profile as a whole at every time step instead of computing the 'age' or "residence time' of the descending slice for designing the secondary cooling system.
Another object of the invention is to adjust the water-flux by reducing the difference between the computed strand temperature and the required temperature at each cooling segment instead of selecting cooling curves based on 'age' of descending slice at the cooling segment at the time of selection.
Yet another object of the present invention is to formulate a new equation of heat transfer coefficient such that the model temperature matches with the measured temperature.

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In a casting process with temporal grid points the axis-symmetry geometry of the stab and the shower locations have eased the problem by simplifying the governing equation. Dynamic cooling model has employed the Eqn. 1.0, a typical two-dimensional transient heat conduction equation to compute grid-point temperature at every five seconds.
The required temperature or target temperature profiles of the strand are predefined and have been collected from the suppliers operating manual, In Tata Steel there are three cooling practices the hard cooling is for casting low carbon grades, medium cooling for medium carbon and soft cooling for peritectic and high carbon grades. The required cooling curves for each cooling practice are stored in the dynamic cooling model. The water-flux in each cooling segment is adjusted in a regular interval with an aim to minimize the difference between the computed cooling curve and the required cooling curve.

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Heat transfer coefficient largely depends upon the residence time and surface temperature [6]. LaedenFrost temperature indicates that the heat transfer coefficient changes dramatically if the surface temperature is below the Laedenfrost temperature and the vice-versa.
The empirical formulae of heat transfer coefficient which are described in equation 3.0 to 5.0 have not considered the effect of residence time and the Ladenfrost temperature. The following equation is a modified formulation of equation 5.0 which has been successfully used in Dynamic cooling model of the present invention of the author. The equation is as follows:
htc= 1.57 w0.55 (1 - 0.0075 Tw [1 - C0(Vref-V)] (6)
a
where Co = A constant value ranging from 0 -1
Vref = Casting Speed of Reference (Here 1.0 Meter / Min)
V = Casting Speed

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In a preferred embodiment the present invention provides an improved method of cooling a solidifying strand in a continuous slab casting process, comprising the steps of: computing at every time step the strand surface temperature profile as a whole, in a secondary cooling zone; adjusting water-flux by reducing the difference between the computed strand temperature and the temperature required at each cooling segment in the secondary copling zone; and formulating a governing equation of heat conduction and solidification with boundary conditions of secondary cooling zone where
spray water heat flux htc- 1.57 w0.55 (1 - 0.0075 Tw) [ 1-Co (Vref - V)]
a [W = water flux liter / m2 - sec; a ˜ 4.0; Co * a constant value ranging from 0-1; Vref = casting speed of reference, here 1.0 mm / min; V = casting speed] so that model temperature matches the measurement.