ORIGINAL RESEARCH

Prediction of equiaxed grain structure and macrosegregationin an industrial steel ingot: comparison with experiment

Arvind Kumar • Miha Zaloznik • Herve Combeau

� Indian Institute of Technology Madras 2011

Abstract Chemical heterogeneities and grain structures

significantly influence the quality and final properties in

solidified ingots, and the phenomena responsible for their

formation during solidification are closely related. Two

significant issues exist, which make the prediction of

chemical heterogeneities and grain structures in industrial

ingots a difficult task. The first challenge is that develop-

ment of such models combining these two aspects is still at

its beginning, and the second challenge is the size of the

industrial ingots, where a number of phenomena need to be

accounted for. In this article, we present macro-segregation

and grain structures predictions in a 6.2-ton industrial steel

ingot using a multiphase and multiscale model. In the

model used the grain growth model is fully coupled with a

volume-averaged two-phase macroscopic solidification model

that accounts for macroscopic fluid flow, grain transport,

heat transfer, and solute transport. A comparison between

experiment and numerical results is discussed in order to

illustrate the capabilities and limitations of the model.

Notably, it is demonstrated that accounting for grain

motion improves the predictions, compared to the case

where the solid is assumed to be fixed. The model is also

able to predict the globular grain in the bottom part and

dendritic grains in the remaining part of the ingot.

Keywords Multiscale model � Steel ingot casting �Grain morphology � Macrosegregation

1 Introduction

The production of steel ingots with improved structure and

chemical homogeneities is of great concern for steelmak-

ers. Final properties of parts manufactured using these steel

ingots are strongly affected by the metallurgical structures

and chemical homogeneities of the as-cast ingots. With this

view, the prediction of grain structure and chemical het-

erogeneities in industrial half-products (ingots and cast-

ings) during solidification is of great importance.

Solidification involves several physical and chemical

processes. Of particular importance is the difference in

solubility of elements between liquid and solid phases,

which induces an enrichment of solute in residual liquid

steel during solidification. The main phenomena responsi-

ble for the formation of segregations in the casting have

been identified long years ago, and a general framework for

the development of inherent model has been defined since

20 years. The same phenomena and conclusions can be

related to the formation of grain structure during solidifi-

cation [1–7]. However, the development of models com-

bining these two coupled aspects is still at its beginning.

The solute redistribution during the solidification is

governed mainly by two mechanisms: By melt flow

induced by thermosolutal natural convection, shrinkage,

and pouring, and by the transport of solute-lean free-

floating grains. The motion of the grains affects all aspects

of the coupled highly nonlinear transport phenomena, heat

transfer, solute transport, and flow behavior [1–16]. While

we know that free-floating grains appear during the solid-

ification of an ingot [1–19], the co-operation and compe-

tition of the grain-settling effect with that of the melt flow

depends on the morphology of the grains. A fully coupled

multiscale solidification model was used to perform

solidification simulations of a 3.3-ton steel ingot, where

A. Kumar � M. Zaloznik � H. Combeau (&)

Institut Jean Lamour, Nancy-Universite, Ecole des Mines de

Nancy, Parc de Saurupt, 54042 Nancy Cedex, France

e-mail: herve.combeau@ijl.nancy-universite.fr

123

Int J Adv Eng Sci Appl Math

DOI 10.1007/s12572-011-0034-y IIT, MadrasIIT, Madras

either fully dendritic or fully globular grain morphology

has been used [15]. In practice, the grain morphology in

large ingots experiences transitions [1, 2]; we generally

find globular regions at the bottom and dendritic regions in

the central part of the ingot. Therefore, the morphology

transition has to be accounted for in the solidification

model by modeling the evolution of the grain morphology

in order to properly predict the macro-segregation forma-

tion [3]. The equiaxed grain morphology transition was

observed numerically using a three phase model but the

study was limited to the case of one grain [3].

The application of solidification models to processes

like industrial steel ingot production is a challenging

problem mainly due to the size of the products and the

variety of the phenomena to be accounted for [1, 2, 19, 20].

Some of those various phenomena to be accounted for are

thermo-solutal convection [19, 20], grain motion [3–17],

evolution of grain morphology by suitably considering a

coupled grain growth model in the macroscopic solidifi-

cation model [2–4, 7], formation of channel segregates

(mesosegregates) [21–24]. Vannier et al. [20] reported

calculations for a large multicomponent steel ingot,

however, grain motion and evolution of grain morphol-

ogy during solidification was not considered, which

present significant limitations of their study. Some other

researchers have reported applications to small ingots (less

than 10 kg in weight with diameter 66 mm and height

170 mm) and considered only globular equiaxed grains

[13]. In previous work by Combeau and coworkers, sim-

ulation results for a 3.3-ton steel ingot was reported con-

sidering motion of equiaxed grains [4, 7, 15] and evolution

of grain morphology during solidification [4, 7]. It has been

shown that a model with purely globular grains cannot

explain the macro-segregation pattern in the ingot as it does

not properly account for the motion of inter-dendritic liquid

in the packed layer [15]. For this ingot a dendritic grain

structure was observed experimentally. The axial segre-

gation pattern with purely dendritic grains or with fixed

solid is found to resemble similarity as the flow pattern of

purely dendritic grains is similar to that for the case with

fixed solid. In references [4, 7] the evolution of equiaxed

grain morphology and its influence on the macro-segrega-

tion pattern was considered.

In this work, we present simulation results, using a

coupled multiphase and multiscale model reported in [15],

for the macro-segregation and grain morphology formation

during solidification of 6.2-ton industrial steel ingot (shown

in Fig. 1) The model is developed in-house and considers

motion of grains and evolution of the grain morphology

(grain growth). This is one of the first applications of such a

model to an industrial sized production steel ingot. The aim

of this contribution is to illustrate the capabilities and

limitations of the model by comparing the predictions with

the experimental data. For the sake of brevity, the gov-

erning equations (reported in [15]) are not repeated here,

and only a brief description of the model is provided.

2 Model

2.1 Macroscopic considerations

At the macroscopic level, the model [15] accounts for heat,

mass, momentum, solute balance, grain density, and grain

envelope fraction, considering motion of free-floating

grains. Solidification shrinkage is not taken into account.

Depending on the behavior of the solid phase, we consider

two flow regimes. The regime depends on the local volume

fraction of grains, genv, which is defined as the ratio

between the volume of grain envelopes and the total

averaging volume. For dendritic grains genv is different

from the solid fraction gs. If the local volume fraction of

grains is larger than the packing limit, genv [ gpenv

� �the

solid phase in the mushy zone is considered to be blocked

or coalesced and the flow of inter-dendritic liquid through

the porous solid matrix is described by a momentum

equation including a Darcy term to model the drag inter-

actions. In the present study, the packing limit prescribed is

0.4 (i.e. gpenv ¼ 0:4). The permeability of the porous matrix

is modeled by the Kozeny–Carman law, depending on a

microstructural dimension, the secondary dendrite arm

spacing (SDAS). At grain volume fractions smaller than

H = 2.67m

mold

refractory

ingot

Adiabatic condition

Hot top

Adiabatic condition

Deq =0.65m

Perfect contact at all interfaces

External cooling: Fourier condition h = (7.5 + 4×5.67×10-8 T3 ) W/m2/K = 0.9

Text = 20 °C

ε

ε

Fig. 1 Schematic of the model geometry for the steel ingot used to

perform simulations

Int J Adv Eng Sci Appl Math

123

the packing limit genv\gpenv

� �the solid phase is considered

to be in the form of free-floating equiaxed grains and the

motion of the grains is described by transport equations for

the solid phase. The macroscopic transport equations are

derived from local continuum equations using a volume

averaging technique. Two phases, the solid and the liquid,

are considered separately in the model (two-phase model);

each phase is described with an Eulerian approach. In this

way, the behavior of a population of grains is locally

described by the behavior of an averaged grain. To describe

the transport of grains in the free-floating regime, a

momentum equation for the solid phase has been derived.

The motion of the grains is governed by a balance of

buoyancy, drag, and pressure forces and the solid and

liquid phases have locally different velocities. The mac-

roscopic transport equations are solved following FVM and

a splitting technique [5]. The splitting technique consists of

decoupling the transport of different quantities by diffusion

and convection at the macroscopic level, of the growth of

the grains, which is assumed to occur locally at the scale of

control volume. The key feature in the splitting solution

scheme is that the contributions to the solid mass and solute

balances due to transport and due to grain growth are

solved in two stages, applying an operator splitting algo-

rithm. This allows to deal with the nonlinearity of the grain

growth model locally, opposed to the global coupling (over

the whole domain) of the transport.

2.2 Microscopic considerations

2.2.1 Nucleation

The microscopic level is treated locally, which is based on

the finite volume method [15]. This means within each

control volume (CV), the formation of new grains by

nucleation is modeled by an instantaneous uniform volume

nucleation law. Locally, a predefined number of spherical

nuclei N0 (density per unit volume) with a predefined ini-

tial diameter d0 is activated, when the temperature drops

below the local liquidus temperature for the first time.

This strategy is followed for every CV. It may be noted that

nucleation in other CV may occur at different time

depending on the local temperature. Then, later during the

process, it may be possible that all grains locally (i.e.

within a control volume in the discretized representation)

vanish, either due to complete remelting or, more com-

monly, due to the evacuation by grain motion (settling).

This presents a problem since a volume with zero grain

density would never solidify, it would only be able to

undercool infinitely. To remedy this problem, which stems

from the simplified treatment of nucleation, we re-inject

(re-nucleate) N0 grains in a discrete control volume every

time when the local grain density N is zero (in the

numerical implementation we used N \ 1 as a more

practical criterion) and the temperature is below the local

liquidus temperature. We have used this treatment as the

growth of a grain is restricted to a CV and its propagation

to another CV is not accounted for. The first condition

ensures the nucleation of grains in every CV, even when it

already contains grains that were transported from else-

where. The second condition ensures the solidification of

control volumes that are emptied of grains by transport. In

the present work, the second condition for ‘‘renucleation’’

is activated only at the top end of the ingot, which can be

emptied because of grain settling.

2.2.2 Grain growth

We represent a dendritic equiaxed grain by a solid skeleton

that is circumscribed by a grain envelope. For alloys with

cubic lattice symmetry the envelope is supposed to be a

regular octahedron where the six vertices correspond to the

primary dendrite tips [3]. Some researchers assumed other

envelope geometry, e.g. spherical envelopes [14, 25]. The

size of the envelope, i.e. the volume of the whole grain, thus

results from the velocity of the primary dendrite tips. The

volume of the solid skeleton inside the grain, on the other

hand, depends on the phase change kinetics, i.e. on the rate

of solidification or dissolution. We can thus regard the

evolution of the grain morphology as a result of the com-

petition between the dendrite tip velocities and the solidifi-

cation rate.

To describe this competition we simplified the three-

phase model by Appolaire et al. [3] (a multicomponent

model based on the philosophy of Wang and Beckermann

[8]), which considered solid, inter-dendritic liquid, and

extra-dendritic liquid phases, to a two phase model that does

not account for a separate inter-dendritic liquid. The tip

velocity is calculated by the KGT model [26]. It depends

principally on the dendrite tip undercooling, described by

the dimensionless parameter X ¼ ðC�l � ClÞ=C�l 1� kp

� �� �

where Cl* is the concentration at the dendrite tip interface,

supposed to be at thermodynamic equilibrium, Cl is the

composition of the liquid far from the interface, and kp is the

equilibrium partition coefficient. The phase change model is

based on a Stefan problem assuming an equivalent spherical

geometry of the solid phase inside the grain. The phase

change rate is determined by a coupling of the local heat

extraction and of the solute balance at the solid–liquid

interface that accounts for solute diffusion in both solid

and liquid phases and assumes thermodynamic equilibrium

at the interface. The grain morphology is then quantified by

the internal solid fraction of the grain

gsi ¼Vs

Venv¼ gs

genv; ð1Þ

Int J Adv Eng Sci Appl Math

123

where, Vs is the volume of the solid phase in the grain, Venv

the volume of the grain envelope, and gs and genv are the

solid and grain volume fractions, respectively. The grain is

globular as gsi approaches 1 and dendritic as gsi � 1.

In the present model, we quantify the grain morphology

in the solidified ingot by the internal solid fraction at the

instant, when the grains are locally packed, that is when the

local grain fraction reaches genv ¼ gpenv. We will denote this

morphology parameter by gsip . The grain morphology in an

ingot depends on the evolution of the local undercooling

during the solidification. The number of grains, which can

be provoked by the number of nucleation sites or by grain

accumulation due to transport significantly influence the

undercooling. A higher grain density increases the surface

for solute diffusion at the solid–liquid interface. This

facilitates the solute diffusion from the interface into the

liquid. For the given solidification rate, the necessary

concentration gradient around the grain adapts and

decreases; the undercooling therefore becomes smaller.

The velocity of the dendrite tips consequently slows down,

while the solidification rate is maintained. Following from

this mechanism, we expect that a higher grain density

results in more globular grains.

Using the above mentioned macroscopic and microscopic

considerations, we can predict the final composition, the

grain density, and the grain morphology in the solidified

casting. The complete detail of the model and solution

methodology is presented in [5, 15]. It may be noted that the

present model does not account for the columnar-to-equa-

ixed transition (CET). We explicitly impose the thickness of

the columnar zone at the mould walls in order to describe the

columnar grains. Within this zone the solid phase is fixed.

In the present study, we used a columnar zone thickness of

8 cm, based on a post-mortem experimental analysis of the

ingot. It has to be also noticed that with this assumption, the

undercooling at the tip of the columnar primary arms of the

dendrites is neglected. It can affect the growth of the equi-

axed grains in the region ahead of the columnar zone [13].

However, with convection the tip undercooling can become

close to the liquidus temperature. In this case, the CET

occurs when the undercooling at the columnar tip becomes

zero [27]. The present study corresponds to this limiting case

where the tip undercooling at the tip of the columnar primary

arms of the dendrites is neglected.

3 Predictions for a 6.2-ton industrial steel ingot

3.1 Simulation details

The solidification in a large-sized (6.2-ton) industrial pro-

duction steel ingot, in which globular and dendritic zones

were observed experimentally [20], is simulated using an

in-house developed code. A schematic of the model geom-

etry used for the simulations of the steel ingot is shown in

Fig. 1. We consider a simplified 2D rectangular geometry

and assume symmetry along the central axis. In the simpli-

fied domain the steel ingot size is 2.67 9 0.325 m

(height 9 width). As seen in Fig. 1, the model geometry

consists of mold also, where the thermal contact at the

interface between the mold and the metal is supposed to be

perfect. Thanks to a sensitivity study of the results to the

mesh size, a total of 10000 rectilinear computational cells

have been used with *8 mm size in the steel.

For the present case the steel grade and thermo-physical

properties of each element have been reported in [20]. To

model the steel properties, we considered a binary iron-

carbon alloy with a nominal composition of C0 =1.01 wt%

C, neglecting the other alloying elements. This simplifi-

cation is justified by the fact, as also estimated in [15], that

of all the alloy components carbon has the strongest effect

on the solutal buoyancy forces that drive the convection

flow together with the thermal buoyancy. Further, in the

present case the thermo-physical data presented in Table 1,

indicate that, mLbTj j\ bCj j. This means that the solutal

effect dominates over the thermal effect. The other thermo-

physical properties of the alloy, the boundary conditions,

and other main parameters of the model are summarized in

Table 1. The filling stage has been neglected and the initial

temperature and carbon concentration fields are supposed

to be uniform. In the experiment, the filling stage took

about 10 min and the total solidification was completed in

about 2 h. Final compositions were available through

chemical analysis of the solidified ingot on the axis of the

ingot and on several transverse sections of the ingot, which

are used for comparison with the predicted result.

3.2 Results and discussion

3.2.1 Model predictions

The grain morphology depends indirectly on the grain

density that affects the solutal undercooling [4, 7]. As

mentioned earlier, we expect that a higher grain density

results in more globular grains. Following this, we present

results for the macro-segregation and grain morphology

formation by varying the nucleation density in the ingot.

We have chosen three cases, which typically give rise to a

fully dendritic (case B-N0 = 108 m-3), a fully globular

(case D-N0 = 5 9 1010 m-3), and a mixed globular-den-

dritic morphology (case C-N0 =5 9 109 m-3) in the

solidified ingot. The choice of N0 is based on our previous

studies [7, 15]. For comparison purpose and in order to

highlight the role of grain motion, we also present results,

where solid is fixed (case A). It may be noted that the

observation of the typical velocity distribution in the ingot

Int J Adv Eng Sci Appl Math

123

during an intermediate stage of solidification is reported in

[7, 15]. As mentioned, the goal of this contribution is to

illustrate the capabilities and limitations of the model

developed in [15], by comparing the simulation predictions

with the experimental measurement. Therefore, for the

sake of brevity, the results for velocity distribution in the

ingot presented in [7, 15] are recalled in this work in order

to explain the final macro-segregation distribution.

Figure 2 shows the predicted final macro-segregation

(left half) and morphology (right half) in the solidified

ingot for cases B, C, and D with different nucleation

density (N0), where grain motion is considered. Case A

shows only the final macro-segregation in the both left and

right half for the case of fixed solid. Case A shows a

conically shaped negative segregation zone at the bottom

of the ingot and a strong positive segregation of carbon in

the hot top part and a positive segregation in the central

axis of the ingot. This typical segregation pattern observed

with the fixed solid is already discussed in detail in [15, 20]

and therefore for the sake of brevity, we will not repeat the

explanation again here. A striking feature of the numerical

results are the significant differences in the predicted grain

morphology and the macro-segregation pattern for the

cases where grains move (cases B–D). We observe mostly

dendritic morphology for case B (gsip varies from 0.1–0.2 in

the bottom till mid regions to 0.05 in the top of the ingot).

Case D predicts a fully globular morphology in the entire

regions of the ingot. However, case C (with N0 in between

cases B and D) predicts a globular morphology (gpsi ¼ 0:6)

up to 40% height of the ingot and a dendritic morphology

(gpsi ¼ 0:3) in the remaining part of the ingot. As reported

earlier in references [4, 7], the higher grain density results

in more globular grains which can be seen from cases B–D.

It can be noted that the grain morphology observed in case

C, resembles well with the experiment, where a metallo-

graphic analysis has shown the presence of a cone-shaped

sedimentation zone up to 40% height of the ingot com-

posed of globular equiaxed crystals.

Regarding the segregation pattern in the cases B–D,

with a nucleation density of N0 = 108 m-3 (case B) the

dendritic grains quickly form a very permeable sedimen-

tation layer after settling. In this layer, (up to the mid-

height in the ingot) the fluid flow is very similar to that

observed in the case with fixed solid [4, 7, 15] and there-

fore the global segregation pattern is very similar to case A.

It may be recalled that the fluid flow is typically governed

by the solutal buoyancy (which is dominant between the

thermal and the solutal buoyancy) driven flow, descending

at the center and ascending at the surface of the ingot [7,

15]. This results in an increase in carbon concentration

from the center towards the surface (up to the columnar

zone width) [15]. A conically shaped negative segregation

zone at the bottom of the ingot and a strong positive seg-

regation of carbon in the hot top part is again observed in

this case also. In case D, where a fully globular grain

morphology is observed, we find a similar trend of negative

(comparatively low) segregation in the bottom part formed

due to sedimentation of globular grains, and strong positive

segregation in the hot top part of the ingot. Also, globally

the level of segregation is lower than that in other cases. As

discussed in Ref. [7] for the case with fully globular grains,

the solid and liquid move with the same velocity and the

flow is mainly driven by grain movement. It causes a very

uniform distribution of solid fraction in the regions where

grains move. No relative motion between solid and liquid

phases and a uniform distribution of solid fraction in the

regions with moving grains causes a uniform concentration

distribution (very low macro-segregation in the central

regions of the ingot). In case C, which shows similar grain

structure in the ingot as that observed experimentally,

negative segregation in the bottom part extending up to the

height of the globular zone (40% height of the ingot) is

observed. This negative segregation is formed due to sed-

imentation of globular grains. In the remaining part of the

ingot, where the grains are dendritic, we observe the sim-

ilar segregation pattern across the width of the ingot as

observed in case B (i.e. increasing carbon concentration

Table 1 Parameters used in the simulations

Initial conditions

Steel temperature: 1475.077�C (this value corresponds to the

liquidus temperature of the model steel, no superheat is

considered)

Iron mold temperature: 25�C

Refractory material temperature: 25�C

Thermal boundary conditions

Interface between the iron mold and the outside, Fourier

condition: h = (7.5 ? 495.67 9 10-8 e T3) W/m2/K, e = 0.9,

Text = 20�C

Alloy properties

Melting temperature of pure iron: 1538�C

Nominal carbon content: 1.01 wt%

Partition coefficient: 0.358

Liquidus slope: -62.3� C/wt%

Solutal expansion coefficient: 1.4 9 10-2 (wt%)-1

Thermal expansion coefficient: 1.07 9 10-4 K-1

Reference density: 7060 kg/m3

Latent heat: 309000 J/kg

Dynamic viscosity: 0.0042 kg/m/s

SDAS: 500 lm

Thermal conductivity of the solid phase: 40 W/m/K; liquid phase:

30 W/m/K

Specific heat at constant pressure: 500 J/kg/K

Diffusion coefficient of carbon in the liquid: 2 9 10-8 m2/s

Diffusion coefficient of carbon in the solid: 5.187 9 10-11 m2/s

Gibbs–Thomson coefficient: 3.3 9 10-7 K m

Int J Adv Eng Sci Appl Math

123

from the center towards the surface). The explanation for

such segregation pattern is similar as explained earlier for

case B.

It may be noted that the segregation in the hot regions is

very complex for all cases as the thermal conditions in this

region is severely influenced by the adiabatic condition at

the top and presence of insulating refractory material [7].

At the transition to the hot top, there is a strong vertical

concentration gradient. The reason is the insulation of the

hot top. When the ingot is already almost completely

solidified the hot top is still mostly liquid. Due to the lateral

insulation the heat is extracted from the hot top from the

bottom. The grains forming in the hot top are globular and

settle towards the bottom of the hot top. This creates the

typical vertical positive segregation gradient.

3.2.2 Comparison with experiment

Carbon concentration was measured at several locations

along the axis and along some transverse sections in the

solidified ingot. An actual transverse section of the ingot is

a squared geometry; hence, chemical measurements have

been analyzed both on a median and on a diagonal section,

so as to be sure that no important discrepancy would be due

to the actual geometry of the ingot. Note that, as the model

is only a 2D model, calculations have been carried out

considering an axisymmteric geometry.

Figure 3 shows the comparison of the predicted and

experimental segregation patterns along the ingot axis.

Experimentally, we observe a negative segregation in the

bottom region of the ingot, up to the height (40% of the

ingot height), where globular grains were observed in the

experiment, and a strong positive one in the hot top. In

between, the carbon concentration is passing several times

from negative to positive in the upward direction, until it

reaches the strongly positively segregated hot top. A good

agreement is obtained with case C in the top of the ingot

and also at the bottom of the ingot. The formation of a

globular sedimentation zone at the bottom is responsible

for the negative segregation and case C well predicts this

globular sedimentation zone. It can be seen that the cases

with dendritic morphology (case A) and with fully globular

morphology (case D) are not able to predict the typical

segregation profile observed in the experiment. Moreover,

the case with fixed solid (case A) gives a very different

segregation prediction as compared to the experiment.

There is still some discrepancy observed with case C in the

regions just below the hot top and just above the globular

sedimentation zone. However, this case reproduces the

experimentally observed segregation profile in the most

part of the ingot.

Figure 4a shows the transverse sections along which the

comparison of macro-segregation in the traverse sections

are shown. In section H, we can notice that in general, there

is negative segregation due to presence of a sedimented

globular zone (see Fig. 4b). In this negative segregated

zone the carbon concentration increases from centre

towards the ingot surface because of the typical solutally

driven flow as invoked earlier. Case C shows a good

agreement with experiment, while other cases fail to show

a good agreement.

Fig. 2 Predicted final macro-

segregation (left half) and grain

morphology (right half) in the

solidified ingot for cases B, C,

and D where grain motion is

accounted for Case A shows

only the final macro-segregation

in both the left and the right half

for the case of fixed solid

Int J Adv Eng Sci Appl Math

123

We can notice that for sections C and B also case C,

shows a good qualitative trend that observed in the

experiment (see Fig. 4c–d). A good qualitative and quan-

titative agreement between calculation and experiment is

observed in the central part of section B, however some

discrepancy is found towards the centre of the ingot. The

presence of V segregates on the axis of the ingot may partly

be the source of this deviation. Also proximity of this

section to the hot top, where we noted a very complex

segregation pattern, may also be partly responsible for this

deviation. In the hot top regions, the grain size could be

typically more than the control volume size and our

treatment of grain growth, restricted to a CV and not

allowing its propagation to another CV, needs to be

improved. With other case studies (i.e. other than case C)

the comparison with experiment is not good.

4 Conclusion

The aim of this article is to illustrate the capabilities of the

model previously developed by Combeau and coworkers

[5, 15] for simulating grain morphology evolution and

macro-segregation formation of a large industrial-scale

0.0

0.5

1.0

1.5

2.0

2.5

3.0

-20% -10% 0% 10% 20% 30% 40% 50% 60%

(C-C0)/C0

Hei

gh

t (m

)

Experimentcase A

case Bcase Ccase D

Fig. 3 Comparison of the predicted and experimental segregation

patterns at the axis

-14%

-12%

-10%

-8%

-6%

-4%

-2%

0%

2%

4%

6%

8%

10%

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

distance from centre (m)

Exp-medianExp-diagonalcase Acase Bcase Ccase D

Hot top

H = 2.67 m

Section H (0.45 m)

Section C (1.8 m)

Section B (2.1 m)

-14%

-12%

-10%

-8%

-6%

-4%

-2%

0%

2%

4%

6%

8%

10%

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

distance from centre (m)

Exp-medianlExp-diagonalcase Acase Bcase Ccase D

-14%

-10%

-6%

-2%

2%

6%

10%

14%

18%

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

distance from centre (m)

(C-C

0)/C

0

(C-C

0)/C

0

(C-C

0)/C

0

Exp-medianExp-diagonalcase Acase Bcase Ccase D

(a) (b)

(c) (d)

Fig. 4 a Schematic showing the transverse sections used for the comparison of predicted and experimental segregation patterns; Comparison

along, b section H, c section C, d section B

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production steel ingot. In contrast to the case with fixed

solid the study accounting for grain motion and grain

morphology evolution allows to improve the prediction of

the important coupled effects of the phenomena of grain

morphology and macro-segregation formation. A globular

sedimentation zone, consisting of globular grains, observed

experimentally in the cast ingot and the transition to den-

dritic morphology in the remaining part of the ingot are

successfully predicted. Using a nucleation density of

N0 = 5 9 109 m-3 the predicted macro-segregation along

the axial and transverse direction shows good qualitative

and quantitative agreement, except in the upper hot top

regions of the ingot. We noticed that the evolution of the

grain morphology depends significantly on the local grain

density of the free-floating grains. This suggests the need of

more work, both experimental and theoretical, focusing on

the source of these grains e.g. mechanisms of fragmenta-

tion, packing of grains, and improvements in the physical

description of grain growth in the hot top regions. Sup-

plementary work in order to investigate the influence of

spatially-varied denditic arm spacing (DAS) in the mush

permeability model (calculated from some constitutive

laws for DAS variation) on the macro-segregation pattern

is under progress. The other important improvement of the

model can be to account for the evolution of the columnar

zone, which was imposed at a fixed value in the present

work. This will enable an analysis of the CET.

Acknowledgments The work was supported by Ascometal Creas,

ArcelorMittal Industeel Creusot, Aubert & Duval, Erasteel, and Alcan

CRV.

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