ISIJ International, Vol. 50 (2010), No. 8, pp. 1175–1179

1. Introduction

Sequential casting of different grades of steel is increas-ingly required to meet the customer’s demand for fast deliv-ery of small quantity orders for steel products. Since thissuccessive casting produces undesirable grade-mixed steelswhich should be cut out as scrap, it is important to knowthe exact location of the intermixed region. To minimize thelength of the undesirable intermixing zone and to optimizethe casting conditions, it is necessary to predict the finalcomposition distributions produced within the continuouscast slabs or blooms during the arbitrary grade transition.

The conventional method1–4) of predicting the composi-tion in the intermixed region extracts the prediction func-tion on the basis of experiments such as water model or realplant test. Another method5–9) is the 3-D transient numericalsimulation considering tundish filling and casting speedchanges. Although these methods give us precise data onmixing during the grade transition, they require much effortand time. Even when the geometry or operating conditionof the caster is changed, these methods still call for as muchtime and effort as they used to before.

Pioneers in the area of developing an efficient intermix-ing model to predict the mixed region during a grade transi-tion, Huang and Thomas10,11) have developed a model forpredicting the intermixed region within several seconds asopposed to the conventional methods that used to take sev-eral days or even weeks. Their model is designed to con-sider the mixing within both the tundish and the strand. Itcovers any kinds of casters by introducing eight parameters

which have to be defined according to the geometry of thetundish and the strand. However, this model also requires agreat deal of experimental data to tune its eight parameters.

Recently, Cho and Kim12) have developed a new tundishmixing model which has only one parameter related withthe tundish geometry for convenient replication and effi-ciency. Since their model has only one parameter, it can beeasily tuned after one or two experiments. However, sincethis model is limited to the tundish mixing, it is not capableof predicting the intermixed zone of the final products tocut out.

This article proposes a new mixing model for coveringboth the tundish and the strand by extending Cho and Kim’ssimple tundish mixing model to the strand region.

2. Cho and Kim’s Simple Tundish Mixing Model

Cho and Kim12) have developed a novel tundish mixingmodel designed to minimize the number of parameters toonly one that needs to be tuned for easier application tonew situations. Their model was verified through the casesof the two water models and real bloom casting.

In their mixing model, the composition of the liquid isspecified as a dimensionless “concentration” C:

.............................(1)

where F(t) is the fraction of a given element in the alloy andt represents time. Fold and Fnew are the fraction of that ele-

CF t F

F F≡

( )�

�

old

new old

A Practical Model for Predicting Intermixed Zone During GradeTransition

Myung Jong CHO1) and Sang Joon KIM2)

1) Technical Research Lab., POSCO, 1, Goedong-dong, Nam-gu, Pohang 790-785 Korea.2) GIFT, POSTECH, San 31, Hyoja-dong, Nam-gu, Pohang 790-784 Korea.

(Received on April 7, 2010; accepted on May 19, 2010 )

This article proposes a new mixing model for predicting the composition distribution in continuously caststeel during a grade transition. The transient model consists of two sub-models, one for mixing in thetundish and the other for mixing in the liquid pool of the strand. The Cho and Kim’s simple tundish mixingmodel (which is very efficient and practical) is adopted as the present tundish model. For the mixing modelin the strand, the concept of Cho and Kim’s tundish model was extended to the strand. In order to verify theproposed model, plant tests were conducted on three kinds of casters (slab, bloom and thin slab caster)during the grade transition period of continuous casting under various conditions. The real grade intermixedslabs and blooms were produced and the composition distributions were measured and compared. Whenthe proposed model was applied to several cases of the slab, bloom and thin slab casting, the numerical re-sults were found to be in good agreement of the experimental data. These findings verify that the proposedmodel is capable of tracking mixing phenomena for arbitrary casters and operating conditions.

KEY WORDS: grade transition; continuous casting; intermixed zone.

1175 © 2010 ISIJ

ment measured in the old and new grades, respectively.They assumed that the concentration leaving the tundishCTD is related with the average concentration CTave and theinlet concentration Cin (shown in Fig. 1). The relation be-tween Cin, CTD and CTave is assumed to be

............(2)

where fTD is a scale factor to be determined and is related tothe tundish shape.

And, CTave is calculated as

..........(3)

...........................................(4)

where n is the number of outlets from the tundish, r is thedensity of the molten steel, MTD is the weight of moltensteel within the tundish and Q represents the volume flowrate of molten steel (m3/s).

The main steps of Cho and Kim’s tundish mixing modelare as follows:1. Obtain the starting values MTD(t), Qin(t), Q

jout(t), Cin(t),

CTD(t), CTave(t) and fTD (t�to at the first step). t�t�D t.2. Update the tundish weight MTD(t�D t) by means of Eq.

(4).3. Calculate the average concentration CTave(t�D t) in the

tundish at (t�D t) step by employing Eq. (3).4. Calculate CTD(t�D t) from Eq. (2).5. Update the time t�t�D t. Terminate the iteration, if the

calculation time is enough. Otherwise continue with

step 1.

3. Extending Cho and Kim’s Tundish Model to theStrand

In this article, Cho and Kim’s tundish mixing model isextended to the strand region to predict the intermixed zoneof the final product through a grade transition. During theladle change for grade transition, the casting speed, the flowrate into the tundish, and the molten steel level in thetundish vary with time. Tundish mixing begins when a newladle is opened, and a new grade of steel starts to flow intothe tundish. The behavior of the mixing depends on theshape of the tundish including the shape of the dam and theweir, as shown in Fig. 1, and it also depends on the operat-ing condition such as the time varying inflow Qin, the out-flow Qout, and the molten steel level in the tundish. Afterleaving the tundish, mixing occurs in the strand. Diffusionis negligible in solid shell, including the entire surface ofthe strand below the meniscus. Turbulent flow within theliquid pool may bring mixed molten steel far below the po-sition of the meniscus. Huang and Thomas10,11) have simu-lated the composition difference between the center and thesurface in a section of the mixed zone according to the cast-ing speed. They found that a slower casting speed greatlyreduces the extent of mixing in the strand. At the same timethe slower speed of the shell also decreases the metallurgi-cal length. These investigations revealed that casting speedduring grade transition is greatly decreased to minimize thestrand mixing in the real plant operation. And in general,the same formulation occurs across the cross section of thestrand used in the real caster.1,2)

Based on this background, we assumed that the incomingmixed steel through the tundish outlet is fully mixed in therestricted region (x��L–0, shown in Fig. 1) of the strandand uniformly solidified. Then, the weight MMD of the mix-ing region in the strand can be defined as

...........................(5)

where W is the mold width and H represents mold thick-ness. We assumed that the concentration leaving the re-stricted region (x��L) CMD is related with the average con-centration CMave in the strand and the incoming concentra-tion CTD through tundish (shown in Fig. 1). The relation be-tween CTD, CMD and CMave is assumed to be

...........(6)

where fMD is a scale factor to be determined. The fMD repre-sents the mixing behavior in the strand. The average con-centration CMave in the restricted region of the strand is cal-culated as

...........................................(7)

The main steps of the present mixing model are sketched inFig. 2.

C t t

M C t Q t t C t C t

M

Mave

MD Mave out TD MD

MD

( )

( ) ( ) [ ( ) ( )]

�

�� �

ΔΔ⋅ ⋅ ⋅ ⋅ρ

C t t f C t t

f C t tMD MD Mave

MD TD

( ) ( )

( ) ( )

� � �

� � �

Δ ΔΔ

⋅⋅1

M L W HMD�ρ ⋅ ⋅ ⋅

M t t M t Q t t Q t tj

j

n

TD TD in out( ) ( ) ( ) ( )� � � ��

Δ Δ Δρ ρ⋅ ⋅⎛

⎝⎜

⎞

⎠⎟ ⋅ ⋅∑

1

��

�

Q t t C t

M t t

j

j

n

out TD

TD

( ) ( )

( )

1∑

⎛

⎝⎜

⎞

⎠⎟ ⋅ ⋅ ⋅ρ Δ

Δ

C t tM t C t Q t t C t

M t tTavetd ave in in

TD

( )( ) ( ) ( ) ( )

( )� �

�

�Δ

ΔΔ

⋅ ⋅ ⋅ ⋅ρ

C t t f C t t

f C t tTD TD Tave

TD in

( ) ( )

( ) ( )

� � �

� � �

Δ ΔΔ

⋅⋅1

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Fig. 1. A schematic diagram of the fluid flow in tundish and instrand.

4. Verification

To verify the proposed model, an extensive verificationand calibration was performed on the tundish and strandmixing models, and it was validated with measurementsfrom several different continuous casting machines, includ-ing the slab, bloom and thin slab caster.

A schematic diagram of the first tundish (called boattype) for slab casting is shown in Fig. 3. The tundish hasone inlet (from ladle) and two outlets (to strands). The max-imum inner volume of this tundish is designed to be 70tones. The operation conditions for grade transition includerefilling the tundish from 10.0 to 60.0 tones in 230 s whilethe casting speed ramped back up from 0.0 to 1.2 m/min

over 300 s. To compare the result of the proposed mixingmodel with the actual plant product, a grade intermixedslab of 12 m�1.28 m�0.23 m that includes the mixed por-tion was cut into several slices, and the compositions (Cand Mn) were measured at each cross section of the slice.

The concentration contours and profiles of the measuredcomponents for carbon and manganese, each converted todimensionless composition with Eq. (1), are shown in Figs.4 and 5. These experimental data indicate that the composi-tion difference between the slab surface and the center isnot significant. This result reconfirmed that the molten steelnear the center can not penetrate deep within the liquid poolsince the casting speed during grade transition is greatly de-creased. Figure 5 compares model predictions with compo-

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Fig. 2. Calculation procedure of the present model.

Fig. 3. The boat type tundish of slab caster for verification.

Fig. 4. The measured composition contours in the mixed zonefor the slab caster.

Fig. 5. Comparison of concentration profiles for the slab caster.

Fig. 7. Comparison of concentration profiles for the slab caster.

Fig. 6. Comparison of concentration profiles for the slab caster.

sition measurements in the slab. The zero point on the coor-dinate axis “Distance up slab” represents the position of themeniscus at the time of opening the new ladle. In order tominimize the errors between the experimental data and thepresent model, the parameters, fTD, fMD and L were tuned tothe values of 1.18, 1.0 and 0.7 respectively by the geneticalgorithm.13) In Fig. 5, the predictions of concentrationchange with different sets of model parameters are com-pared to the experimental data. It is found that the values ofparameters were successfully tuned. Figure 5 also showsthat the proposed model predicted well that the compositionwould steeply increase during tundish filling and the gradi-ent of composition increment would decrease after filling.

The calibrated model (fTD�1.18, fMD�1 and L�0) forthe slab caster with the boat type tundish was applied to dif-ferent casting operations. The relevant casting conditionsare given in Table 1. The predicted results are comparedwith the measurement data in Figs. 6 and 7, which showthat the proposed model predicts the concentration historyin the intermixed zone very well, and that its result is ingood agreement with the measurement data. The measure-ments were based on a chemical analysis of drilling chipstaken near the surface and the centerline of the slabs.

In a different case, the bloom caster was investigated totest the proposed mixing model. The tundish (20 tones) ofthis bloom caster has 1-inlet (ladle) and 4-outlets (strandswith 250 mm�330 mm cross section), as shown in Fig. 8.This tundish has already been studied by Cho and Kim in afull scale water model experiment. They found that fTD�1.0is the proper value for this bloom tundish. The comparisonbetween model predictions (fTD�1.0, fMD�1 and L�0.7)and measurements of bloom composition is given in Figs. 9and 10. The casting speed was decreased from 1.0 to0.0 m/min for 300 s, held as a stop for 150 s, and increasedup to 1.0 m/min for 300 s. The measurements were con-ducted along the produced bloom surface and the centerlinefor manganese and chrome alloy contents. Figures 9 and 10indicate that excellent agreement was obtained betweenpredictions and measurements. These also show that fMD�1and L�0.7 (which tuned from the above slab case) werestill proper in this bloom case.

For the final verification, a thin slab caster with two la-dles and one strand was considered as shown in Fig. 11.Two ladles provide the molten steel to the tundish of 50tones in sequence. The molten steel of the tundish flows

into the thin slab mold with a 100 mm�1 200 mm crosssection. During the grade transition, the tundish was filledfrom 22.8 tones to the 50 tones in 305 s at a constant cast-ing speed of 5.0 m/min. As shown in Fig. 12 which com-pares the model prediction (fTD�1.2, fMD�1 and L�0.7)with the composition measurement in the slab, the com-puted results of the proposed mixing model were found to

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Fig. 8. The sketch of the bloom tundish for verification.

Fig. 9. Comparison of predicted and measured concentrationalong the intermixed bloom (TDmin�4 tons).

Fig. 10. Comparison of predicted and measured concentrationalong the intermixed bloom (TDmin�8 tons).

Table 1. Casting conditions of slab caster for model valida-tion.

agree fairly well with the experimental data. The value ofthe tundish mixing related parameter (fTD) was changed incomparison with that of the above slab and bloom cases be-cause the different tundish was used, as Cho and Kim12)

told. However, the same values as the above slab and bloomcases for the strand mixing related parameters (fMD and L)were also proper in this thin slab case.

Although we could set the strand mixing parameters (fMD

and L) to the same values of 1.0 and 0.7 respectively in theabove three verification cases, these parameters are relatedto the mixing in the strand and may be changed according

to the condition of the strand mixing. As an example, if thegrade separator is inserted through the meniscus to com-pletely prevent mixing and decrease the mixing region inthe strand, these two parameters (fMD and L) should bechanged.

5. Conclusion

This paper proposed a novel mixing model for predictingthe intermixed zone during a grade transition by extendingCho and Kim’s tundish simple model to the strand region.To verify the proposed mixing model, the real grade mixedslabs, blooms and thin slabs were produced through a gradetransition continuous casting. When applied to several dif-ferent continuous casting cases, including slab, bloom andthin slab casting operations, the numerical results of theproposed mixing model agreed well with the experimentaldata. In the present verification cases, fMD and L could befixed as constant values whereas the constant parameter fTD

was found to be determined according to the tundish shape.However, for the strand mixing related parameters fMDandL, much further application work is needed.

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Fig. 11. A schematic view of reverse T-type tundish of thin slabcaster.

Fig. 12. Comparison of concentration profiles in the case of thinslab caster.