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ISIJ International, Vol. 54 (2014), No. 2, pp. 359–365

Simulation of the Center-Line Segregation Generated by the Formation of Bridging

Takemasa MURAO,1) Toshiyuki KAJITANI,1) Hideaki YAMAMURA,1)* Koichi ANZAI,2) Katsunari OIKAWA2) and Tomoki SAWADA3)

1) Process Research Laboratories, Nippon Steel & Sumitomo Metal Corporation, 20-1 Shintomi, Futtsu, Chiba, 293-8511 Japan.2) Graduate School of Engineering Tohoku University, 6-6-11-1008 Aramaki Aza Aoba, Aoba-ku, Sendai, Miyagi, 980-8579Japan. 3) Formerly Graduate School of Engineering Tohoku University. Now at Japan Steel Works, 4, Chatsumachi,Muroran-shi, Hokkaido, 051-8505 Japan.

(Received on July 26, 2013; accepted on November 11, 2013; originally published in Tetsu-to-Hagané,Vol. 99, 2013, No. 2, pp. 94–100)

The macrosegregation model that heat transfer, solidification, liquid flow and solute movement wereconsidered was developed to simulate the generation of the center-line segregation in the casting ofsteel. The classical model which considers only the liquid flow caused by solidification shrinkage leads thenegative segregation which contradicts the fact. In order to explain the contradiction, the bulging of thecast slab has been claimed to be important factor to form the positive segregation at the center of thecast. However, some experimental data show that the bulging has not been necessarily formed during thegeneration of center-line segregation. In this case, the bridging with the solidification shrinkage has beenfound to be formed instead of the bulging. In this paper, the macrosegregation model is developed con-sidering, thus, three driving forces of fluid flow; solute concentration, thermal expansion and solidificationshrinkage. This simulation results show that the primary driving force which results in the center-line seg-regation is the solidification shrinkage with the bridge. In addition to that, the mechanism of generatingthe center-line segregation is discussed based on the simulation results.

KEY WORDS: macrosegregation; bridging; solidification; fluid flow; simulation.

1. Introduction

Center-line segregation in continuous casting of steeldegrades the quality of products such as hydrogen-inducedcrackling.1) It is known that the generation of center-linesegregation in continuous casting is caused by the fluid flowof the liquid phase in the mushy zone at the final stage ofsolidification.2) In order to generation of positive segrega-tion in the center fluid flow of liquid steel among dendritesis needed.3) Both bulging and solidification shrinkage havebeen considered as the principal cause for such flow. Theflow of liquid steel by bulging occurs because the bulgedshell due to the static pressure of the molten steel is reducedby rolls, and thus the liquid steel among dendrites is pushedout toward the center.3,4) Some numerical study on the center-line segregation by bulging are performed.3–5) For preventingbulging, such as shortened roll pitches using rolls of smallerdiameter, intensified secondary cooling, and maintained rollalignment have been considered and performed.6–10)

Fluid flow of liquid steel by solidification shrinkage isoccurred because the liquid steel among dendrites is suckedout by shrinkage during solidification. The effects of this flu-id flow on segregation have been variously discussed.11–14)

The effects of the solidification shrinkage on center-linesegregation are examined using the numerical analyses.However, solidification shrinkage create negative segrega-tion because solidification shrinkage creates the flowtoward the solidification shell from the center.3,4) It followsthat it is indispensable for forming positive segregation togenerate bulging. By contrast, Suzuki, et al.11) claim in theirreport that fluid flow by solidification shrinkage generate Vshape segregation by experimental method using molds ofvarious shapes. Suzuki12) studies the effects of bridging byobserving solidification structure in the continuous castingof billets. In this study, bridging is formed by the equiaxeddendrite that is accumulated at some convex parts of solid-ification shell. And thus, center-line segregation is createdby suction of liquid steel among dendrites around the bridg-ing due to solidification shrinkage. Asano, et al.2) say thatcontribution rate of metallurgical factor for center segrega-tion (i.e. Solidification shrinkage) is 33% and a mechanicalfactor (i.e. bulging) is 25%. They say that the metallurgicfactor has a large effect on the generated center-line segre-gation.

In addition, Uchimura, et al.15) show the positive segre-gation by using constricted mold made of refractries. Thisexperiment of Cu addition during solidification indicatesthat the positive segregation is generated below the bridgingby suction from above the bridging as the permeability of

* Corresponding author: E-mail: murao.8d2.takemasa@jp.nssmc.comDOI: http://dx.doi.org/10.2355/isijinternational.54.359

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constricted section increases. As in this experiment, the pos-itive segregation occurs without bulging. In our work, themacrosegregation model is developed considering threedriving forces of fluid flow; solute concentration, thermalexpansion and solidification shrinkage. By using this simu-lation model, it is analyzed the effect of bridging for the pos-itive segregation formation. In addition, the effect of thedriving forces of fluid flows for the formation of positivecenter-line segregation is discussed.

2. Calculation Methods

2.1. Calculation ModelThe basic calculation formulas used for the present model

are shown in Formulas (1)–(4).

...... (1)

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

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

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

Where, t, u, ρ, p, ν, K, Δρ, g, β, T, c, q, L, fs, CL, and krespectively denote time, flow velocity, density, pressure,kinetic viscosity coefficient, permeability coefficient,change in density accompanying varying temperature andsolute content, gravity, solidification shrinkage rate, tem-perature, specific heat, heat flux, latent heat, solid fraction,liquid phase solute content, and equilibrium distributioncoefficient.

Formulas (1)–(4) denote each momentum equation forliquid, continuation equation, solute conservation equation,and energy conservation equation. In this model, fluid flowby solidification shrinkage, thermal convection, and soluteconvection are taken into consideration. Thermal convectionand solute convection are calculated by translating fromtemperature difference and solute content difference to den-sity change by using Boussinesq approximation. Fluid flowby solidification shrinkage is taken into consideration byformula (2). Microsegregation model is used the Guilliver-Scheil model.

Solidification is calculated by using the temperature-recovering method. By using this method, temperature andsolid fraction are calculated separately. And thus the changeof solid fractions with change in solute contents can be cal-culated. The progress of solidification is calculated by For-mula (5). The first term of the right side of Formula (5)denotes the change in solid fractions by changing in temper-ature and the second term denotes the change in solid frac-tions by changing in solute contents.

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

Liquidus temperature TL and equilibrium distributioncoefficient k are obtained by calculation using Thermo-Calcwhich is a thermo-dynamic calculation software. The for-

mulas for calculating TL and k are expressed in Formulas(6)–(7). Coefficients used for calculating Formulas (6)–(7)are listed in Table 1.

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

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

Fluid flow of liquid steel in the mushy zone is calculatedby Darcy’s law. The relationship between solid fraction andpermeability coefficient is obtained by the Kozeny-Carmanmodel as shown in Formula (8). K0 denotes permeabilitycoefficient.

............................ (8)

Calculation is conducted using the FLUENT6.3.26 whichis the commercial CFD software. Fluid flow in Darcy flowsis calculated using the SIMPLE Method. Density, tempera-ture, momentum, and solute content are discretized by usingthe linear upwind difference method. Liquidus temperatureand solid fraction are calculated as UDF (User-definedFunction). The physical properties of the materials used forcalculations are listed in Table 2. Segregation is investigat-ed for a binary Fe–C alloy with the two-dimensional calcu-lation. Calculation ingot size is a width of 0.5 m and a heightof 2.0 m. The mesh size is 0.002 m, and the time step inter-val is 0.5 sec. The distance from the ingot center is taken asthe x axis and that from the bottom is the y axis. Cooling isconsidered on the side wall only, and the bottom and upperwall are adiabatic condition. The temperature condition ofthe side wall is shown in Formula (9).

∂∂ ρ

νν ρ ρ

ρu

u u u u gt

p

K+ ⋅∇ = −

∇+ − +

+Δ

Δ

∇ ⋅ =u β∂∂f

ts

∂∂

∂∂

C

tC

f

t

k C

fL

Ls L

s

+∇ ⋅ =−( )−

( )u1

1

∂∂ ρ

∂∂

T

tT

c

L

c

f

ts+∇ ⋅( ) = − ∇ ⋅ +u q

1

∂∂

=∂∂

∂∂

+∂∂

∂∂

f

t

f

T

T

t

f

C

C

tS S S

i

i

Table 1. Coefficients for calculation of liquidus temperature anddistribution coefficient.

Coefficient

TL0 +1 806.17406845176

TL1 –6 377.00457652378

TL2 –53 628.2351524308

k0 +2.005459854223230×102

k1 –2.259675594486650×10–1

k2 +6.370543316188730×10–5

Table 2. Physical properties of material.

units

Initial carbon content 0.1 mass%

Initial temperature 1 900 K

Kinetic viscosity 0.0056 Kg/(m·s)

Liquid density 7 000 Kg/m3

Specific heat 808 J/(kg·K)

Thermal conductivity 41 J/(s·m·K)

Gravity 9.81 m/s2

Heat convection coefficient 0.00003 –

Solidification shrinkage 0.04 –

Latent heat 251 000 J/(kg·K)

Permeability coefficient 5.7×10–11 m2

T T T C T CL L L L= + × + ×0 1 22

k k k C k C= + × + ×0 1 22

K Kf

fS

S

=−( )

0

3

2

1

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..................... (9)

It is assumed that the temperature of the side wall iscooled at a constant rate from the initial temperature shownby Formula (9). In this calculation, the value α is 1 500. Inorder to compensate for changing volume by solidificationshrinkage, an inlet for liquid steel is set at the top of theingot. The liquid steel with the initial temperature and theinitial carbon content is supplied from the inlet when a pres-sure becames 0 Pa and over.

2.2. Procedure to Form BridgingBridging is generated by the temperature gradient of the

initial temperature on the side wall. T(y)= –50×y+1 900 isgiven on the side wall in order to set the temperature gradi-ent which is a low temperature at the upper part of the walland a high temperature at the lower part. The distribution ofthe initial wall temperature is shown in Fig. 1(a). It is report-ed that the fluid flow of liquid steel is blocked when a solidfraction reaches 0.3 or beyond. Accordingly, the bridgingsection is defined the part that solid fraction at the centerreached 0.3 most quickly and there is the site at the belowthat solid fraction is under 0.3. Figures 1(b) and 1(c) showa bridging by the broken line. Bridging is formed at theslightly upward from the middle height of the ingot. This isbecause the solidification in the upper ingot is delayed bysupplying hot liquid steel from the top of the ingot. By con-trast, for no bridging, T(y)=70×y+1 900 is given on the sidewall in order to set temperature gradient which is a hightemperature at the upper part of the wall and a low temper-ature at the lower part.

3. Analyses Results

3.1. Effect of the Bridging on Positive Center-line Seg-regation

Figure 2(a) show the carbon distributions of carbon con-tent without bridging when the center solid fraction at the1.8 m height reaches 1.0. And Fig. 2(b) show the carbon dis-tribution with bridging when he center solid fraction at thebottom reached 1.0. In both cases, calculations are takinginto consideration three driving forces of fluid flow; thermal

convection, solutal convection, solidification shrinkage.Figure 3 show the carbon distribution at the center. Figure3 show that if no bridging is formed, negative segregationwould be generated at the center, similar to the conventionalnumerical results of the center-line segregation. Carbon con-tent at the center of ingot is 0.102%, while the averaged car-bon content in ingot is 0.103%, and thus the segregationratio is 0.99. The reason why the average carbon content in

Fig. 1. Distribution of initial surface temperature and solid fraction with bridging.

T y t T y t, exp( ) = ( ) −( )α

Fig. 2. Distribution of carbon content with or without bridging.

Fig. 3. Solute content in the center of ingots.

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the ingot is higher than its initial stage is that the moltensteel is supplied from the top of ingot because of the solid-ification shrinkage. On the other hand, with bridging, nega-tive segregation with a minimum carbon content of 0.08%is generated above the bridging and positive center-line seg-regation with a maximum carbon content of 0.12% is gen-erated below the bridging, and thus the segregation ratio is1.2. The lower end of the negative segregation and the upperend of the positive segregation are connected one anotherwith the interface of the bridging section. This fact signifiesthat the positive center-line segregation is generated whenbridging is formed.

3.2. Effect of the Fluid Flow by Thermal Convection,Solute Convection and Solidification Shrinkage

Figures 4(a)–4(c) show the distributions of the carboncontent with bridging after solidification, which are takinginto consideration the separate single fluid flow for eachthermal convection, solute convection, and solidificationshrinkage. Figure 5 shows the distribution of solute contentin the 1.0 m height of ingot. As shown in Fig. 5, no positivesegregation is generated around the thickness center, whilethere is small variation of carbon distribution between0.099% and 0.101% in the carbon content for single soluteconvection, and between 0.095% and 0.101% for singlethermal convection. This result shows that thermal convec-tion and solute convection don’t contribute to the center-linesegregation generation. On the other hand, by considering

only solidification shrinkage, positive segregation is gener-ated in the center with maximum carbon content of 0.135%.Segregation ratio is 1.35. This result shows that the positivesegregation is generated by solidification shrinkage.

Figure 6 demonstrates the solid fractions in the center inthe following two cases; all of the three driving force of flu-id flow have been taken into consideration, the only solidi-fication shrinkage fluid flow has been taken into account.This result shows that the thermal convection and soluteconvection occur the difference in the bridging position andthe timing. Thereby, it is considered that thermal convectionand solute convection don’t contribute to the generation ofpositive center-line segregation, while they contribute tobridging generation.

4. Discussions

4.1. Transition of the Distribution of Carbon Content,Pressure, Velocity Vector and Solid Fraction

In Figs. from 7 to 10, the distribution of pressure, the car-bon content, the velocity vector and the solid fraction withbridging are respectively shown in a chronological order,i.e., immediately before bridging occurrence, at 20 s, at 30s, and at 35 s each after bridging occurrence, as well as aftersolidification.

Right before forming the bridging, the pressure of theingot in the lower section is higher than in the upper sectionas shown in Fig. 7(a). At this moment, the molten steelmoves toward the direction of solidifing shell as shown inFig. 8(a), and thus no solute concentration is generated asshown in Fig. 9(a).

According to Fig. 7(b), 20 seconds after forming thebridging, negative pressure is generated in the section belowthe bridging. The pressure is to be minimum (–5.8×104 Pa)slightly below the bridging. This reveals that the fluid flowsorienting downward in the section below the bridging occuras shown in Fig. 8(b). As shown in Fig. 9(b), carbon contentis concentrated in the section below the bridging, and thecarbon content is reduced in the section over the bridging.

Along with the further progression of the solidification(30 s after bridging), the pressure decreases to –1.2×107 Paat below the bridging. It means that the position where theminimum pressure is found moves rather downward withtime elapsing than just after bridging. In addition to thedownward flow, Fig. 8(c) shows the fluid flow toward theFig. 4. Distribution of carbon content with bridging.

Fig. 5. Cardon content in the 1.0 m height of ingot. Fig. 6. Solid fraction in the center of ingots.

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center is also observed at the section below the bridging.This still increases the solute content in the section belowthe bridging, which results in further center-line positive

segregation. On the other hand, in the section over the bridg-ing, the fluid flow of molten steel directing toward the loweroutside is generated.

35 seconds after bridging, one can observe the increase of

Fig. 7. Transitional change of pressure: (a) before bridging, (b) 20 safter bridging, (c) 30 s after bridging, (d) 35 s after bridging,(e) after solidification.

Fig. 8. Transitional change of velocity vector: (a) before bridging,(b) 20 s after bridging, (c) 30 s after bridging, (d) 35 s afterbridging, (e) after solidification.

Fig. 9. Transitional change of solute content: (a) before bridging,(b) 20 s after bridging, (c) 30 s after bridging, (d) 35 s afterbridging, (e) after solidification.

Fig. 10. Transitional change of solid fraction: (a) before bridging,(b) 20 s after bridging, (c) 30 s after bridging, (d) 35 safter bridging, (e) after solidification.

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negative pressure in the section below the bridging, theincrease of the molten steel fluid towards the center andincrease in the carbon content in the center. For the bettervisibility, the distribution of the solid fractions at thismoment is magnified in Fig. 10(d). The solidification speedis more rapid in the zone surrounding the center of thebridging zone than the inside, which reads the larger perme-ability in the outside of the center than in the center. Hence,the molten steel is easy to flow in the outside the center. Asshown in the enlarged figure of Fig. 8(d), the molten steelflow stream is formed in the bridging zone because the flowvelocity in the center of the bridging is slower than in sur-roundings. The velocity of molten steel flow in the lowersection of bridging at that moment is at most 0.0001 m/s. Itindicates that the concentrated solute at this moment can notcome from above the bridging but, possibly, flows in fromthe outside of the center section of the ingot. As mentionedabove, in the upper side of the bridging area, the negativesegregation occurs because of the flow toward outer-bottom,whereas in the bottom side, the positive segregation occursbecause of the flow toward inner-top.

4.2. The Mechanism of Generation of the Center-lineSegregation

In this section, we analyse the mechanism of forming thecenter-line segregation.

As we have seen above, molten steel flows from upstreamto downstream around the thickness center section towardsolidifying shell in the vicinity of the solidification front bysolidification shrinkage until the bridging begins to form,which agrees with the classical notion. As shown in Fig.11(a), if bridging of fs>0.3 is formed due to nonuniformsolidification, the shortage of molten steel to the sectionbelow the bridging caused by the negative pressure occursdue to solidification shrinkage. The negative pressure alsocauses the downward stream of molten steel derived fromthe zone where the solute is concentrated among the den-drites and where the liquid fraction is relatively high (seeFig. 11(b)). As the molten steel with a low solute concen-tration flows in the center of bridging section from above,the solid fraction increases compared to outside of the centersection, and hence the downward flow of the molten steel isprevented at the center section. Along with the solidifica-tion, the negative pressure increases in the section below thebridging. Then, as demonstrated in Fig. 11(c), as magnitudeof the negative pressure in the section below the bridginglevel increases, the flow intensifies from solidifying shell tothe thickness center. As demonstrated by Mehrabian, et al.,16)

a molten steel flow toward the center from solidifying shell

side is necessary for the generation of positive segregation.The flow accelerates the solute concentration by absorbingthe molten steel among dendrites toward the center, and atthe same time, the molten steel is supplied to the bottomside, which also contributes to the growth of the center-linesegregation. In the this calculation, solid fraction fs in thebridging section is 0.95, and a permeability coefficient is7.9×10–15 m2 by Eq. (8). This permeability coefficient coin-cides with that of the fluid flow limit of 2.1×10–15 m2,obtained by Takahashi, et al.17) Following the above proce-dure, the priority flow can be found in Fig. 11(d), in a sec-tion with a lower solid fraction. The molten steel entails alower solid fraction at a position where the concentratedmolten steel flows in. As a result, the flow stream of themolten steel forms and keeps its shape supplying steadyamount of molten steel. In the present calculation, the solidfraction fs in the molten steel flow stream is always notmore than 0.98, whereas the permeability coefficient is notless than 4.8×10–16 m2.

We conclude here that, negative segregation is formed inthe section over the bridging, whereas positive center-linesegregation is formed in the section below the bridging. Theflow channel of the concentrated molten steel in the sectionbelow the bridging results in V shape segregation; the con-clusion appears to be good agreement with the experimentalresults by Uchimura, et al.15)

5. Conclusions

Changes in solid fractions due to temperature variation aswell as those due to solute concentrating is concurrentlydeal with, the simulation model of center-line segregationtaking into account solidification shrinkage fluid flow, ther-mal convection, and solute convection are created, and anal-yses are performed on the effects of bridging on center-linesegregation. Following results are obtained.

(1) Positive segregation is generated in the center sec-tion by bridging formation and solidification shrinkage fluidflow.

(2) The center-line segregation at the moment of bridg-ing formation is generated according to these steps: i) bridg-ing formation, ii) negative pressure generation, iii) genera-tion of the molten steel flow, iv) formation of flow channelto supply molten steel in the outside of core of bridging, andv) positive segregation generation caused by supplying con-centrated molten steel from the solidifying shell side towardthe thickness center.

(3) Generation of fluid flows directing from the solidi-fying shell side toward the thickness center is needed for

Fig. 11. Schematic views of center-line segregation generation mechanism.

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positive segregation generation in the section below bridg-ing level. For generation such flow, molten steel flow chan-nel is formed in the outside of core and molten steel is sup-plied downward from the above section of bridging. Theformation of these flow channel involves taking consider-ation of varying solid fractions due to the changing of soluteconcentrations.

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