22 ✦✦ IIrroonn && SStteeeell TTeecchhnnoollooggyy

AABBSSTTRRAACCTTThe quality of continuously cast steel is greatly influ-enced by fluid flow in the mold, particularly at themeniscus. Recent examples of computational modelapplications at the University of Illinois are presentedto investigate the formation of several different typesof defects related to flow phenomena. The amount ofgas injection into the tundish nozzle to avoid air aspi-ration is quantified by modeling. Computationalmodel calculations of superheat transport and surface-level fluctuations are presented. Meniscus defects,such as subsurface hooks and their associated inclu-sions, may form if the superheat contained in the steelis too low, or if top-surface-level fluctuations are toolarge. A thermal stress model has been used to com-pute the distortion of the meniscus during a level fluc-tuation. Gas bubbles and inclusion particles may enterthe mold with the steel flowing through the sub-merged nozzle. In addition, mold slag may beentrained from the top surface. These particles may beremoved safely into the slag layer, or may becomeentrapped into the solidifying shell, to form sliver orblister defects in the rolled product. Transient, turbu-lent flow models have been applied to simulate thetransport and entrapment of particles from both ofthese sources. The insights gained by these modelingefforts aid greatly in the development of processingconditions to avoid the formation of these defects.

IINNTTRROODDUUCCTTIIOONNIn the continuous casting of steel, the task of the flowsystem is to transport molten steel at a desiredflowrate from the ladle into the mold cavity and todeliver steel to the meniscus area that is neither toocold nor too turbulent. In addition, the flow conditionsshould minimize exposure to air, avoid the entrain-

ment of slag or other foreign material, aid in theremoval of inclusions into the slag layer, and encour-age uniform solidification. Achieving these somewhatcontradictory tasks needs careful optimization.

Fluid flow in the mold is controlled by many designparameters and operating conditions. Nozzle geome-try is the most important and includes the bore size,port angle, port opening size, nozzle wall thickness,port shape (round, oval, square), number of ports(bifurcated or multiport), and nozzle bottom design.The flow pattern also depends on parameters thatgenerally cannot be adjusted to accommodate theflow pattern, such as the position of the flow controldevice (slidegate or stopper rod), nozzle clogging,casting speed, strand width and strand thickness.Fortunately, other parameters besides nozzle geome-try can be adjusted to maintain an optimal flow pat-tern. These include the injection of argon gas, nozzlesubmergence depth and the application of electro-magnetic forces. In choosing optimal settings forthese parameters, it is important to understand howthey act together to determine the flow characteris-tics. An increase in casting speed, for example, mightbe compensated by a simultaneous increase in sub-mergence depth (or electromagnetic force), in orderto maintain the same surface flow intensity. Thus, allthe flow-control parameters must be optimizedtogether as a system.

In designing the flow system, it is important to con-sider transients. Sudden changes are the main causeof the flow instabilities that generate surface turbu-lence and other problems. Because flow parametersare more easily optimized only for steady operation,each of the parameters that affects fluid flow must becarefully controlled. It is especially important to keepnearly constant the liquid steel level in the mold, pow-der feeding rate (to keep a constant liquid slag layer

MMooddeelliinngg ooff CCoonnttiinnuuoouuss CCaassttiinnggDDeeffeeccttss RReellaatteedd ttoo MMoolldd FFlluuiidd FFllooww

BBrriiaann GG.. TThhoommaass,, Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, Ill. (bgthomas@uiuc.edu)

Vol. 3, No. 5

JJuullyy 22000066 ✦✦ 33

thickness), casting speed, gas injection rate, slidegateopening, and nozzle position (alignment and submer-gence). It is also important to choose flow conditionsthat are resistant to transients and their detrimentaleffects, although this is difficult to predict.

Many quality problems that originate during thecontinuous casting of steel can be directly attributedto poor control of fluid flow conditions in the mold.1

In order to optimize these flow design and operationconditions, it is crucially important to understand howdefects arise and how changes in the flow patternaffect those defects. This paper summarizes some ofthese problems and illustrates the use of computa-tional flow models in gaining insight into them, usingrecent examples developed through the ContinuousCasting Consortium at the University of Illinois.

DDEEFFEECCTTSS RREELLAATTEEDD TTOO FFLLUUIIDD FFLLOOWWA schematic of the continuous casting process is givenin Figure 1, which illustrates some of the phenomenathat lead to defects due to fluid flow in the moldregion of the process. Jets of molten steel are directedinto the liquid by the nozzle ports and traverse acrossthe mold cavity to impinge on the solidifying steel shellnear the narrowfaces. Gas bubbles in the jet lower itsdensity, providing lift, which may alter the flow pat-tern. The jets impinging against the narrowface maycause shell thinning, and even breakouts, if the super-heat is too high and the interfacial gap is excessive.2

The momentum of the upward flow along the nar-rowfaces can raise the meniscus level there, causing anonlinear profile along the top surface. Where thislevel is too high, the infiltration of liquid mold flux intothe interfacial gap becomes more difficult, which canlead to nonuniform meniscus heat flux, longitudinalcracks and other surface defects.

Excessive surface turbulence may cause rapid fluctu-ations of the surface level. This can disrupt stablesolidification at the meniscus, leading to deep oscilla-tion marks, surface depressions, surface cracks andlocal entrapment of mold slag leading to delaminationdefects. In addition, high-speed flow across the topsurface may shear droplets of liquid mold slag into theflow, where they may become entrained in the liquidsteel.

On the other hand, if the surface velocities are insuf-ficient, or if the local superheat contained in themolten steel near the meniscus is too low, then themeniscus may partially freeze to form deep oscillationmarks and meniscus “hooks.” These hooks are detri-mental because they may entrap particles into thesolidifying meniscus. Superheat also affects the nucle-ation and growth of equiaxed grains, which controlsthe solidification structure, and defects such as cen-

terline segregation. The transport of solute with thefluid is also of crucial importance to macrosegregationproblems, especially toward the final solidificationpoint lower in the strand.

In addition to steel and superheat, the jets carrybubbles and inclusion particles into the mold cavity. Ifthe flow pattern enables the particles to reach the topsurface, they should be harmlessly removed into theliquid slag layer, so long as the slag is not saturatedand the surface tension forces are not excessive.Alternatively, inclusions and bubbles may becomeentrapped in the solidifying steel shell, where theycause slivers, “pencil pipe” blisters and other costlydefects. Inclusion particle behavior is complicated bytheir attachment to the surface of bubbles, whichencourages removal, but also creates potentially dan-gerous large clusters, which may also be createdthrough collisions.

CCOOMMPPUUTTAATTIIOONNAALL MMOODDEELLIINNGG OOFFFFLLUUIIDD FFLLOOWW

GGoovveerrnniinngg EEqquuaattiioonnssComputational models to simulate fluid flow phe-nomena in three dimensions generally start by solvingthe continuity equation and Navier-Stokes equations

FFiigguurree 11Flow phenomena in the continuous casting mold region.

44 ✦✦ IIrroonn && SStteeeell TTeecchhnnoollooggyy

for incompressible Newtonian fluids, which are basedon conserving mass (one equation) and momentum(three equations) at every point in a computationaldomain. This yields the pressure and velocity compo-nents at every point in the domain. The domain is dis-cretized into small computational cells, which shouldexactly match the true shape of the flow region of theprocess, in this case the nozzle and liquid pool of thecontinuous casting mold and upper strand. When thisis performed with a sufficiently refined grid to directlycapture the details of the transient fluid flow pattern,this is called “direct numerical simulation.” Becausethis generally leads to excessive execution times, thecomputational grid is generally coarsened, and a “sub-grid scale model” is used to account for the effects ofturbulence that occur at time and length scales small-er than an individual computational volume. Thispaper contains many examples using this method,which is called “large eddy simulation.”3–4 To achieveeven more efficient computation on coarse grids ormeshes, the effects of turbulence can be treated as anartificial increase in the fluid viscosity, which is deter-mined by solving additional transport equations forthe time-averaged flow pattern. The most popular ofthese Reynolds Averaged Navier Stokes, or “RANS,”methods is the k-ε turbulence model, which solvestwo additional transport equations for the turbulentkinetic energy, k, and its dissipation, ε.5 The relativeadvantages and accuracies of these approaches forcontinuous casting are compared elsewhere.5–6

Unless solidification is modeled together with theflow, then the shape of the liquid domain must beobtained through other means (such as a heat con-duction model of shell solidification — CON1D7). Inaddition, flow through the boundaries of this domainmust be imposed to satisfy the solidification rate, byspecifying fixed velocity boundary conditions at thewalls, as explained elsewhere.3,8 When course-gridRANS models are used, the thin boundary layer of theliquid is smaller than the computational cells at thewalls, so they are taken into account using “turbulentwall functions.”6

To obtain accurate flow solutions, it is often neces-sary to couple the flow equations together with simul-taneous solution of other equations, in order toincorporate other phenomena,9 such as gas injectionor electromagnetic stirring/braking. For example, whena significant amount of gas is injected with the steel, itsbuoyancy requires a multiphase model. Many differentcomputational approaches are possible to simulate thisbehavior.9 Ultimately, it is of crucial importance to val-idate the flow model predictions through comparisonwith measurements as much as possible, such as PIVmeasurements in water models.10

MMoolldd GGeeoommeettrryy aanndd CCaassttiinngg CCoonnddiittiioonnss SSttuuddiieeddTo illustrate the application of some of these modelsused to understand continuous casting defects, exam-ples are taken from simulations conducted at theUniversity of Illinois. For simplicity, almost all the exam-ples involve the same thin-slab caster using thedomain in Figure 2. The tapered nozzle has two 15°downward, 75 x 32 mm ports, a third round portdirected straight downward, and 127-mm submer-gence. The straight-walled mold cavity and upperstrand is 132 mm thick x 984 mm wide, cast at 1.5m/minute with 58°C of superheat, 434 stainless steeland no gas injection. Further details are given else-where on the casting conditions,11 computationalmodel equations3,12 and experimental measure-ments.11–12

A typical example of the fluid flow velocities in thenozzle and mold region of this thin-slab continuouscaster is presented in Figure 3.3 Note the significant

FFiigguurree 22Schematic of the computational domain of the thin-slab steel caster,including tundish nozzle.3

JJuullyy 22000066 ✦✦ 55

asymmetry in the instantaneous snapshot of the flowpattern in the nozzle, both around the stopper rod(Figure 3a) and at the nozzle ports (Figure 3b). Flowvaries chaotically between sides, in spite of the per-fectly symmetrical domain. This is characteristic of the“pseudo-steady” state of this turbulent flow, evenafter long-time operation. The chaotic flow continuesinto the mold region, as Figure 3c shows differencesfrom the time average (Figure 3d). Generally, thisexample is a reasonably stable classic double-roll flowpattern. Flow impinges on the narrowfaces, splitsupward and downward, and traverses the top surfaceback toward the SEN.

MMOODDEELLIINNGG OOFF PPHHEENNOOMMEENNAA RREELLAATTEEDDTTOO DDEEFFEECCTTSSAlthough it is a challenging task to compute, it mustbe remembered that the average flow pattern itself isof no practical interest. Rather, it is a necessary firststep in the simulation of related phenomena, which

depend on the fluid flow and cause defects in the steelproduct. With the tremendous increases in computingpower and modeling sophistication, computationalmodels are increasingly more able to simulate theseimportant related phenomena.

One important phenomenon is the effect of argongas injection on the pressure distribution, buoyancy,direction and pattern of the fluid flow, in both thenozzle13–15 and mold.16–17 The transport of superheatwith the flow,18 and solidification of the steel shell,7,19

are important phenomena to meniscus hook forma-tion, shell thinning, breakouts, internal microstructureand macrosegregation. Solute transport governs inter-mixing during grade changes20–21 and also affectssegregation. Inclusion particle transport with the flowdirectly controls cleanliness of the product.22 Particlesin the flow are subject to many forces — especially inthe boundary layers near the solidification front, andat the slag-metal interface12 — that govern entrap-ment of the particles into the solidification front. A

FFiigguurree 33Computed flow pattern in the centerline between wide faces: (a) nozzle near stopper rod, (b) nozzle near exit ports, (c) instantaneous flow in themold and (d) time-averaged flow in the mold.

(a)

(b)(c) (d)

new entrapment criterion has recently been developedand is presented elsewhere by Yuan and Thomas.12

Other important phenomena include bulging (for theliquid pool shape changes that affect segregation) andmetallurgical thermodynamics (which affects inclusionprecipitation, nozzle clogging and solidificationmicrostructure). Finally, the model must be applied inparametric studies to learn something useful aboutthe real process.

AAIIRR EENNTTRRAAIINNMMEENNTT DDEEFFEECCTTSSExposure to air at any stage after steel refining leadsto detrimental oxide inclusions in the steel product.This problem is worst at the final stage of flow in themold, because there is little opportunity to prevent the

reoxidation products from becoming entrapped in thefinal product as catastrophic large inclusions.

Open-stream pouring produces the worst airentrainment problems, which is the reason for sub-merged entry nozzles and mold flux operation. Airentrainment is still possible, however, if there areleaks, cracks, inadequate sealing between the nozzlejoints or if the nozzle material becomes porous. If theinternal pressure in the nozzle drops below atmos-pheric pressure, air tends to aspirate through thesepathways into the nozzle. This can be identified bynitrogen pickup and dendritic inclusions from reactionin a high-oxygen environment.

Pressure in the nozzle is always lowest just belowthe flow control device, due to the Venturi effect ofthe downward-flowing metal stream. Whenever high-speed flow leaves a restricted region, such as the flow-control passage, the expanding jet tends to suck inand entrain surrounding fluid, so the pressure drops.As shown in Figure 4, the large pressure drop acrossthe slidegate leads to a minimum-pressure region justbelow the slidegate, where air aspiration is most like-ly. For a given steel flowrate, the pressure drop (andcorresponding tundish height needed to maintain thecasting speed) increases as the opening is restricted, asshown in Figures 4 and 5 for a typical slidegate noz-zle.15 The results in these figures were computedusing a three-dimensional multiphase flow of a typicalbifurcated nozzle with 15° downward, 78-mm squareports.15 The “Eulerian-Eulerian” model solves twocomplete sets of mass and momentum balance equa-tions for the gas and liquid phases, which are fullycoupled together through the phase fractions. Themodel was run many times with varying argon injec-tion rate under feasible conditions (i.e., varying slide-gate opening and casting speed togetherappropriately for a given tundish depth).

Air aspiration into the nozzle can be discouraged byproper introduction of an inert gas flow, which is oneof the ways in which argon gas acts to prevent nozzle

66 ✦✦ IIrroonn && SStteeeell TTeecchhnnoollooggyy

FFiigguurree 44Pressure drop calculated down nozzle: (a) pressure contours in centerplane showing that major variations are in the vertical direction, and(b) effect of slidegate opening on vertical pressure distribution.24

(a)

(b)

FFiigguurree 55Optimizing argon gas injection (for a 78-mm bore nozzle with 90°slidegate).24

JJuullyy 22000066 ✦✦ 77

clogging.23 The addition of argon gas can replace air infeeding leaks around seals. Argon injection can alsoraise the minimum pressure in the nozzle above ambi-ent.15 Note that this occurs because the slidegate mustopen up to accommodate the gas (shown in the top ofFigure 5), in addition to the pressurizing effect of thegas. The minimum gas flowrate calculated to avoid apartial vacuum is shown at the bottom of Figure 5.When the slidegate opening is either very small or verylarge, the pressure never drops below 1 atmosphere(zero gauge pressure), so gas injection is not needed toprevent aspiration. Less gas is needed at low castingspeed and at low tundish level, when the pressuredrops are lower. Maintaining a high gas flowrate dur-ing these times may disrupt flow in the mold andthereby be detrimental to steel quality. Further insightgained from models on optimizing argon injection toavoid air entrainment is given elsewhere.13–15

SSUUPPEERRHHEEAATT TTRRAANNSSPPOORRTT,, SSHHEELLLLTTHHIINNNNIINNGG AANNDD BBRREEAAKKOOUUTTSSImpingement of the molten steel jets onto the solidi-fying shell in the mold can cause problems if the jet iseither too hot or too cold. A jet with insufficient super-heat can deliver steel to the top surface that is toocold, which leads to surface skulling, freezing of themeniscus and related surface defects, as discussed inthe next section. This section focuses on problemsarising if the jet is too hot. Breakouts occur when thesteel shell at mold exit is not strong enough to contain

the liquid steel, and they have many causes. One pos-sible cause is local thin and hot regions of the solidify-ing shell, which can result from high superheatdissipation at the region where an excessively hot jetimpinges on the inside of the shell.18,25 Problems ariseonly if this local superheat dissipation is combinedwith slow heat extraction from the corresponding shellexterior. This problem is most likely in the off-cornerregions, where the hot jet may impinge and the shellshrinkage also creates a larger gap.

A computational model of superheat transport hasbeen developed for the 132-mm thin-slab caster inFigure 2.6,26 This computation is challenging becausethe thermal boundary layer has steep gradients, espe-cially in the critical impingement region, whichrequires a very fine grid. The temperature contourspresented in Figure 6 reveal the temperature distribu-tion in various horizontal sections. The jet leaving thenozzle ports is hottest, and it quickly dissipates itssuperheat and drops in temperature as it movesthrough the mold. Measurements of temperaturefrom a probe inserted into the top surface (Figure 8)agree with the predictions that roughly 70 percent ofthe superheat is gone at this location, which providespartial validation of the model. The predicted temper-ature fluctuations, indicated with the error bars, alsobracket the variation in the probe measurements.Most (65 percent) of the superheat is dissipated to the

FFiigguurree 66Temperature distribution in liquid pool (based on flow conditions inFigure 3).26

FFiigguurree 77Superheat removal distribution (based on temperatures in Figure6).26

88 ✦✦ IIrroonn && SStteeeell TTeecchhnnoollooggyy

shell in the mold (Figure 7), with most of the remain-der dissipated just below mold exit.26 As is common inslab casting with bifurcated nozzles, the impingementregion on the narrowface absorbs the most superheat(12 percent) and has double the average heat flux perunit area to the wide face. Each wide faces removes26 percent of the superheat, but its area is more thanseven times larger. This high-impact region on the nar-rowface extends to the off-corner region of the widefaces. Heat losses through the top slag layer are small.

Figure 9 shows how shell growth depends on thecombined effects of superheat input from jet impinge-ment and heat removal to the mold walls.27 Modelpredictions were made using CON1D — a compre-hensive heat-flow solidification model of the mold,interface and shell — which features momentum,mass and force (friction) balances on the liquid fluxlayer.7,19 Jet impingement produces a thinner shell onthe narrowface, compared with classic parabolic shellgrowth on the wide face, as shown in both the com-putations and measurements in Figure 9.27 The impor-tance of this shell-thinning effect increases with highercasting speeds, higher superheats and lower gap heattransfer.18,25 Asymmetric flow, such as that caused bynozzle clogging, may aggravate the effect.

SSUURRFFAACCEE DDEEFFEECCTT FFOORRMMAATTIIOONNMost surface defects in the steel product originate inthe mold at the meniscus, where the solidifying steelshell is very thin. The most obvious source of surfacedefects is the capture of foreign particles into thesolidifying shell at the meniscus. Particles come frommany sources, including argon bubbles, oxide inclu-sions generated by prior processes that are carried inwith the steel entering the mold cavity, and slagentrainment. If they are not removed by scale forma-tion or during surface scarfing, these surface inclu-sions will lead to line defects or slivers in the finalproduct. Other problems include deep oscillation

marks and surface depressions, which lower the localheat transfer, leading to a hotter local shell tempera-ture, strain concentration and crack formation.Transverse cracks often form during unbending at theroot of the deep oscillation marks. Longitudinal cracksoften initiate at local hot spots around the meniscusperimeter. All these defects are worsened by largefluctuations in the top surface liquid level, whichdepend on the flow pattern in the mold.

Many surface defects form at the meniscus due tovariations in the level of the liquid steel on the top sur-face of the mold cavity. These variations take twoforms: a relatively steady contour across the moldwidth known as a “standing wave,” and “level fluctu-ations,” where the local level changes with time.While the standing wave can cause chronic problemswith liquid slag feeding, the time-varying level fluctu-ations cause the most serious surface defects.

TToopp--ssuurrffaaccee--lleevveell PPrrooffiilleeThe top-surface level is important because it affectsthe feeding of liquid flux into the interfacial gapbetween the mold and shell, which is important toheat transfer. Insufficient liquid flux consumption tothe interfacial gap leads to increased thermal resist-ance, variable heat transfer, thermal stresses, stressconcentration and ultimately cracks. A steep surface-level profile poses difficulty for complete coverage ofthe liquid flux over the steel surface. If the liquid fluxlayer becomes so thin that the steel surface touchesthe mold powder, it can become contaminated withelements such as carbon, which can cause surfacequality problems such as cracks and segregation inultralow-carbon steels.

Figure 10 shows a typical instantaneous profile ofthe transient top-surface level obtained from the flowfield in Figure 3.3,28 This computation was achieved by

FFiigguurree 88Comparison of simulated temperature profile and plant measure-ments (#3 – 295 mm from centerline).17,26

FFiigguurree 99Breakout shell thickness profiles and corresponding model predic-tions, showing the thin region near location of jet impingement onnarrowface, relative to steady shell growth down the wide face.27

JJuullyy 22000066 ✦✦ 99

performing a balance between kinetic energy andpotential energy on the results of pressure along thetop surface. The predictions in a water model com-pared well with measured top-surface levels.3 Theresults in Figure 10 also compare with measurementsof the top-surface level in the steel caster, obtained bydipping thin steel sheets. The results match within theuncertainty in the measurements (error bars), whichexists regarding possible rotation of the sheets. Thelevel is always higher near the narrowfaces, by 2 mmin the water model and by 4–6 mm in the steel caster.This is because the steel upward momentum near thenarrowfaces lifts the liquid level there, displacing someof the molten flux. The flux layer must be thickenough to cover the steel, in order to provide a steadysupply of molten flux into the interfacial gap to lubri-cate the steel. Thus, the height of the surface standingwave is important to steel quality.

TToopp--ssuurrffaaccee--lleevveell FFlluuccttuuaattiioonnss Controlled oscillation of the mold generates ripplesacross the liquid level but does not present an inher-ent quality problem, because the liquid near the moldwall tends to move with the wall. Large, sudden jumpsor dips in liquid level are much more serious.

A sudden jump in local level can cause molten steelto overflow the meniscus. In the worst case, the steelcan stick to the mold wall and start a sticker breakout.Alternatively, a sudden change in level can cause anirregular extended frozen meniscus shape, or a“hook.” This defect is discussed in the next section.Variations of more than the oscillation stroke over atime interval on the order of 1 second are the mostdetrimental. Even low-frequency variations (over peri-ods of more than 60 seconds) may cause defects if the

meniscus overflows and the solid slag rim is imprintedon the shell or captured.29

A sudden severe drop in liquid level exposes theinside of the solidifying shell to the mold slag and alsoleads to surface depressions. Relaxing the temperaturegradient causes cooling and bending of the top of theshell toward the liquid steel. When the liquid level risesback, the solidification of new hot solid against thiscool, solid surface layer leads to even more bendingand stresses when the surface layer reheats.30 Thissequence of events is illustrated on a 20-mm-long sec-tion of shell in the thermal-stress model results inFigure 11, for a 20- to 30-mm level drop lasting 0.6second.30 When liquid steel finally overflows themeniscus to continue with ordinary solidification, asurface depression is left behind, such as that shownin Figure 11.

The microstructural changes and surface depres-sions associated with level variations are seriousbecause they initiate other quality problems in thefinal product. These problems include surface cracksand segregation. Surface cracks allow air to penetratebeneath the steel surface, where it forms iron oxide,leading to line defects in the final product. Thesedefects are difficult to distinguish from inclusion-relat-ed defects, other than by the simpler composition oftheir oxides.

Figure 12 shows the time variation of the horizon-tal velocity toward the SEN at the center pointsbetween the SEN and the narrowface on the top sur-face. This result was obtained from the transient largeeddy simulation.3 The velocity fluctuations are verylarge — similar to the velocity magnitude. Figure 12shows a strong component with high frequency (e.g.,flow velocity drops from ~0.4 m/second toward the

FFiigguurree 1100Comparison of predicted and measured top-surface liquid levels in steel (Figure 3 flow field).3

1100 ✦✦ IIrroonn && SStteeeell TTeecchhnnoollooggyy

SEN to a velocity in the opposite direction within 0.2second).

This prediction compares favorably with previousPIV measurements on a 0.4-scale water model.10

Simulations with and without flow across the center-line reveal that interaction between the two sides ofthe caster is an important cause of the large high-fre-quency fluctuations. This agrees with findings basedon water modeling.31 These velocity variations are sig-nificant, because the level fluctuations that accompa-ny them are a major cause of defects in the process.This is revealed in time-dependent animations of theprofile in Figure 10.3

HHooookk FFoorrmmaattiioonnSubsurface hook formation at the meniscus during thecontinuous casting of steel slabs is an important causeof surface defects, owing to their easy entrapment ofmold flux and inclusion-laden gas bubbles. Figure 13shows a typical hook, which is always associated withan oscillation mark and especially plagues ultralow-carbon steels.32–33 Recent work has shown thatcurved hooks, such as this one, form when the menis-cus freezes and later overflows.34 Hook shape is alsoaffected by thermal distortion and other mecha-nisms.35–36 Hook formation is greatly affected by steelgrade, superheat, level fluctuations and oscillationconditions.32–33

The effect of superheat is investigated by closeexamination of the superheat results, shown in Figure6,26 and further application of computational modelsto the meniscus region. As the steel flows throughthe mold cavity, it continuously drops in temperature.The coldest liquid is found at the meniscus, aroundthe perimeter of the top surface, especially near the

FFiigguurree 1111Events during a severe level drop (20 mm for 0.6 second) that lead toa transverse surface depression.30

FFiigguurree 1122Time variations of the horizontal velocity toward SEN at the center point of the top surface of steel (see Figures 2 and 3).

JJuullyy 22000066 ✦✦ 1111

narrowface, the wide-face centerline near the inletnozzle, and the corners. The fluid is coldest in theseplaces because it is both far from the inlet and stag-nant. Liquid in these regions can become super-cooled, causing meniscus freezing upon nucleation.In addition to forming hooks, in extreme cases, thiscan cause skull formation, and even “bridging,”where steel or slag freezes across the shortest dis-tance between the nozzle and meniscus of the wideface, often leading to a breakout.

The heat flux corresponding to superheat delivery tothe solidifying steel shell in the critical meniscus regionis shown in Figure 14 (for slightly different castingconditions chosen to match the hook in Figure 1337).The lowest superheat flux is found at the corner andnear the nozzle, which coincides with the locationswhere the deepest meniscus hooks are observed inpractice. Hooks also tend to be deeper on wide slabswith low superheat and low casting speed, for thesame reasons.

Using a best estimate for superheat flux at themeniscus, the solidification of the initial shell wascomputed with CON1D, and the thickness comparedwith the measured hook shell thickness in Figure13.33 For the calculation, the meniscus locationwhere the hook shell starts is taken at one theoreticaloscillation mark pitch above the measured deepestpart of the oscillation mark at the hook. This suggeststhat the hook shape revealed by etching was created

by a change in heat flow conditions that occurred dueto metal overflow of the initial shell at the meniscusat the instant the oscillation mark formed. The pre-dicted shell profile roughly matches the measuredprofile. The modeling results suggest that the top of

FFiigguurree 1133Typical hook shape (left) and comparison of hook-shell thickness with shell thickness prediction from CON1D (right).33

FFiigguurree 1144Variation of superheat flux (kW/m2) in meniscus region aroundstrand perimeter.37

1122 ✦✦ IIrroonn && SStteeeell TTeecchhnnoollooggyy

the original hook shell was truncated, likely due tobreaking off or melting of the shell tip during the liq-uid overflow event. Recent metallographic evidencehas proved this to indeed be the case.38 Further com-putational efforts are being conducted to simulate thecoupled phenomena governing behavior of the menis-cus region, including transient fluid flow, motion ofthe steel/slag interface, oscillation of the mold walland the attached slag rim, slag consumption into thegap, heat transfer in the region, and thermal distor-tion of the solidifying steel shell.39 The results arebeing combined with metallographic examination andplant trails to investigate the fundamental formationmechanism of these hooks and their associateddefects.

IINNCCLLUUSSIIOONN PPAARRTTIICCLLEE EENNTTRRAAPPMMEENNTTThe entrapment of inclusions, bubbles, slag and otherparticles during solidification of steel products is acritical quality concern. They require expensiveinspection, surface grinding and even rejection of thefinal product. Furthermore, if undetected, large parti-cles lower the fatigue life, while captured bubblesand inclusion clusters cause slivers, blisters and othersurface defects in rolled products. These particleshave two main sources: bubbles and inclusions gen-erated during upstream processing that enter themold through the submerged entry nozzle, and theentrainment of mold slag from the top surface, dis-cussed in the next section.

Particles leaving the tundish can either stick to thenozzle walls (where they lead to clogging), travel withthe recirculating flow to be safely removed into themold slag at the top surface, or become entrapped inthe solidifying shell (where they lead to productdefects). The fraction of particles going to each ofthese destinations is being quantified using a newcomputational model. This model first calculates thetransient turbulent flow field in the mold region usinglarge eddy simulation, with a sub-grid-scale k model.3

Next, the transport and capture of many individualparticles are simulated using a Lagrangian approach totrack the trajectories.4 The results presented here arefor 30,000 particles, in order to achieve reasonablestatistics. The transport equation includes the effectsof six hydrodynamic forces: drag, shear lift, pressuregradient, stress gradient, added mass, and Basset his-tory and buoyancy. The model features a new criteri-on to determine particle entrapment, which considersthe effects of four more forces that are important inthe fluid boundary layer adjacent to the solidificationfront. Further details on the model, including equa-tions for the forces, are given elsewhere.8,12

Instantaneous snapshots of the trajectories of 100-µm alumina inclusion particles at different times afterentering in the mold region are shown in Figure 15,based on the flow pattern in Figure 3.

Note that the domain includes the 1.11-m sub-merged entry nozzle and the top 2.40 m of the steel

FFiigguurree 1155Transport of 100-µm inclusions in a strand at different times (red =final entrapment location, based on flow pattern in Figure 3).4

FFiigguurree 1166Final entrapment location of inclusions on stopper rod and nozzlewalls (flow conditions in Figure 3).

JJuullyy 22000066 ✦✦ 1133

strand. Particles that touch the top surface areassumed to be removed into the slag layer (and arethen colored red). Note that significant asymmetryexists in the flow, which directly affects the particles,especially in the lower regions of the strand. Manymore particles leave from the right side of the domain,although investigation revealed that there was no sig-nificant asymmetry at the nozzle port exit. This behav-ior is attributed solely to the chaotic nature ofturbulence.

NNoozzzzllee EEnnttrraappmmeenntt ((CCllooggggiinngg))The inclusion trajectories themselves are of much lesspractical interest than their final entrapment locations.Inclusions attaching to the nozzle walls contribute toclogging, which is detrimental to steel quality in sev-eral ways: the clogging slows production, large clogscan suddenly break off and enter the mold, and theflow pattern becomes unstable.15

An example of the predicted locations of inclusionstouching the nozzle walls is shown in Figure 16.About 10 percent of the particles exiting the tundishtouched the stopper rod, and a further 16 percent

touched an inner wall of the nozzle.8 These inclusionsmight stick to cause nozzle clogging in a real caster,depending on the properties of the nozzle materialand thermodynamic reactions at the interface. Notethat the bottom portion of the stopper rod and near-by walls of the upper nozzle have the most inclusionentrapment, which agrees with plant experience.Some particles touched the bottom of the SEN nearthe outlet ports.

SSttrraanndd EEnnttrraappmmeenntt ((SSlliivveerr DDeeffeeccttss aanndd BBlliisstteerrss))Particles traveling in the liquid pool may becomeentrapped in the solidifying shell to form defects.Using the new entrapment criterion, particles touch-ing the solidification front were assumed always tobecome entrapped if they are smaller than the primarydendrite arm spacing. Larger particles are subjected toa force balance that considers the effects of transversefluid flow on washing the particles away from theinterface, the angle of the reaction forces between thedendrite tips, and the other hydrodynamic forces. Inaddition, this force balance includes the effects of thesurface tension gradient, such as those caused by sul-fur rejection at the solidification front, the lubricationforce, and Van der Waals forces. All three of theseforces tend to encourage particle entrapment andshould be explored in further work. Further details onthe entrapment criterion are given elsewhere.12

Inclusion entrapment locations in the final solidifiedstrand were computed from the trajectory resultsshown in Figure 15 and are presented in Figure 17.More than 84 percent of the 100-µm inclusions werecaptured in the shell, including 51 percent in theupper 2.4 m of the strand. Only 8 percent touched thetop slag surface, while the remaining 8 percenttouched the outside of the nozzle refractory walls andmight be removed. After injecting larger, 400-µminclusions, only 30 percent were entrapped in thesolidified shell. This is due both to their increasedchances of flotation from their higher buoyancy, andto their smaller likelihood of capture into the solidifi-cation front.

The particles were injected through the nozzle portsduring a 9-second time period, which corresponds to0.23 m of travel of the meniscus down with thestrand, and is labeled on Figure 17. The entrapmentlocations in the strand are distributed both upstreamand downstream about this location. The side and topviews (Figure 17a and b) show that the captured par-ticles concentrate in a thin band around the strandperimeter and especially near the narrowfaces. Theredoes not appear to be any significant concentration ofparticles associated with flow from the central port.Figure 17d reveals strong asymmetry in the particle

FFiigguurree 1177Particle entrapment locations predicted in the final solidified strand(based on trajectories in Figure 15): (a) wide face view, (b) narrowfaceview, (c) top view, and (d) top view at time of exit from domain.

(c)

(a) (b)

(d)

1144 ✦✦ IIrroonn && SStteeeell TTeecchhnnoollooggyy

trajectories through the liquid, as many more particlesexit the left side of the domain into the lower strand.However, this asymmetry appears to be greatly dimin-ished in the final entrapment locations, as Figure 17cshows much less bias toward the left side. This isbecause faster-moving flow across the solidificationfront makes capture more difficult. Capture is mostlikely along those regions of flow along the solidifica-tion front that move slowly downward near the cast-ing speed. It is important to emphasize that theasymmetry is chaotic and, although the stronger flowto the left persisted for a long time interval (greaterthan 30 seconds), it could change to the opposite sideat any time.

By reprocessing the results to model continuousinclusion injection, it is possible to compute theexpected distribution of total oxygen content in anaverage section through the final solid strand.4 Figure18 presents the results for 10 ppm total oxygen con-tent entering from the nozzle ports in the form of100-µm particles. Figure 18 shows that the entrap-ment is concentrated from 10 to 25 mm beneath thestrand surface at the centerline. Considering the shellthickness profile down the strand, this region corre-sponds to a capture region of ~0.5–2.5 m below themeniscus. Local spikes in total oxygen in this banddepend on sample size but are predicted to exceed 60ppm, owing to grouping together of captured parti-cles simply due to chaotic turbulence. The final entrap-ment position in the lower strand is uncertain, so thisregion is represented as a dashed line. Its average oxy-gen content is 6 ppm, indicating that relatively fewerparticles penetrate deeper than 2.5 m below themeniscus into the lower regions of the strand.

The caster simulated here has straight vertical walls.In a curved caster, large particles in the lower recircu-lation zone tend to spiral toward the inner radius, withincreased entrapment rates. Entrapped solid oxide

particles eventually lead to surface slivers or internaldefects, which act as stress concentration sites toreduce fatigue and toughness properties of the finalproduct. Gas bubbles captured in this way eventuallymay cause blister defects such as “pencil pipe,” whichappear as streaks in the final rolled product. When theslab is rolled, the subsurface bubbles elongate and thelayer of metal separating them from the surfacebecomes thinner. Later during annealing, they canexpand to raise the surface of the sheet locally, espe-cially if the steel is weak, as with ultralow-carbongrades, or if hydrogen is present.40 Further computa-tions are needed to quantify the expected benefits oflowering the casting speed, or using a vertical moldand the upper strand.

These results suggest that most of the inclusionsthat enter the mold become entrapped in the finalproduct. Thus, nozzle design and mold operationshould focus on controlling flow at the meniscus toavoid the further entrainment of new inclusions,rather than altering the flow pattern to encourage theremoval of inclusions entering the mold. Upstreamoperations should focus on inclusion removal andreoxidation prevention.

MMOOLLDD SSLLAAGG EENNTTRRAAIINNMMEENNTTMold slag can be entrained into the solidifying shelldue to vortexing, high-velocity flow that shears slagfrom the surface, and turbulence at the meniscus. Thecapture of large inclusions into the solidifying shellthen leads to obvious line defects or slivers in the finalproduct.

Vortexing most often occurs during conditions ofasymmetrical flow, where steel flows rapidly throughthe narrow passage between the SEN and the mold.This creates swirling just beside the SEN, as shown inFigure 19.26 This swirl or vortex may draw mold slagdownward, near the sides of the nozzle. If it is thenentrained with the jets exiting the nozzle ports, thisslag will be dispersed everywhere and create defects,as discussed in the previous section. In addition todrawing in slag, the vortex is detrimental because ithastens erosion of the nozzle refractory walls. Visibleerosion patterns at the locations near the off-cornerand center of the wide, thin-slab nozzle have beenobserved in practice. In addition to the vortex, slagmay also be drawn downward by the recirculationpattern that accompanies flow from the nozzle ports.Thus, slag entrainment is most likely with shallow noz-zle submergence and high casting speed.

The entrainment of mold slag also occurs when thevelocity across the top surface becomes high enoughto shear mold slag fingers down into the flow, wherethey can be entrained. The breakup of the slag fingers

FFiigguurree 1188Oxygen content along the slab centerlines (100-µm inclusions).

JJuullyy 22000066 ✦✦ 1155

into particles is a complex process governed by surfacetension, fluid properties and flow conditions. Figure20 illustrates the transport and fate of these slag par-ticles after they have formed.12 Many float quicklyback into the slag layer, owing to their greater buoy-ancy. However, many slag particles disperse into theflow and behave the same as inclusions that enteredthrough the nozzle, eventually becoming entrapped asinternal inclusion defects. Initial entrainment is easierfor deeper slag layers, lower slag viscosity and lowerslag surface tension.41 To avoid shearing slag in thismanner, the top-surface velocity must be kept belowa critical maximum value, suggested to be 0.3 or 0.4m/second.42 The critical velocity may also be exceededwhen the standing wave becomes too severe and theinterface emulsifies.43 The critical velocity alsodepends on the relative densities of the steel and fluxphases and the mold geometry.43

High-velocity surface flows also may cause emulsifi-cation of the slag, where slag and steel intermix andeven create a foam if too much argon gas is present.44

This allows easy capture of particles via vortexing orsurface shearing flow. Meniscus turbulence related tolevel variations is another mechanism for slag entrain-ment, as discussed previously.

CCOONNCCLLUUSSIIOONNSSFluid flow in the continuous casting process can gen-erate many different types of defects in the finalproduct. Computational models of fluid flow coupledwith other important phenomena can be useful toolsto study and quantify these problems. Several differ-ent examples of insights into defects are presentedhere, based on simulations conducted at theUniversity of Illinois. These include air aspiration intothe nozzle, shell thinning and breakouts from exces-sive superheat, surface defects from a steep “stand-ing wave,” level fluctuations, subsurface hookformation and the associated deep oscillation marksand particle entrapment, and the entrapment into thesolidifying shell of inclusion particles and bubbles

entering the nozzle or from mold slag entrainment atthe top surface.

AACCKKNNOOWWLLEEDDGGMMEENNTTSSThe author wishes to thank his former students, espe-cially Q. Yuan, B. Zhao and H. Shin, and research sci-entist L. Zhang for their efforts generating the resultssampled in this paper. This work was supported bythe National Science Foundation (Grant #DMI-01-15486) and the Continuous Casting Consortium at

FFiigguurree 1199Velocity streamlines showing vortexing near the SEN (in-plane 38.5 mm below the top surface, flow conditions in Figure 3).26

FFiigguurree 2200Instantaneous snapshot of the distribution of 100-µm slag particles,just after entrainment into the top surface (red indicates particles thatrefloated, while blue indicates particles that are still moving, flow con-ditions in Figure 3).

1166 ✦✦ IIrroonn && SStteeeell TTeecchhnnoollooggyy

the University of Illinois. Thanks are also given to theNational Center for Supercomputing Applications atthe University of Illinois for computing time.

RREEFFEERREENNCCEESS11.. Thomas, B.G., “Chapter 14: Fluid Flow in the Mold,” The

Making, Shaping and Treating of Steel: Continuous Casting,edited by A. Cramb, AISE Steel Foundation, Pittsburgh,Pa., 2003, pp. 14.1–14.41.

22.. Thomas, B.G.; Moitra, A.; and McDavid, R., “Simulationof Longitudinal Off-corner Depressions in ContinuouslyCast Steel Slabs,” ISS Transactions, Vol. 23 (4), 1996, pp.57–70.

33.. Yuan, Q.; Thomas, B.G.; and Vanka, S.P., “Study ofTransient Flow and Particle Transport DuringContinuous Casting of Steel Slabs, Part 1: Fluid Flow,”Metall. & Material Trans. B., Vol. 35B (4), 2004, pp.685–702.

44.. Yuan, Q.; Thomas, B.G.; and Vanka, S.P., “Study ofTransient Flow and Particle Transport DuringContinuous Casting of Steel Slabs, Part 2: ParticleTransport.,” Metall. & Material Trans. B., Vol. 35B (4),2004, pp. 703–714.

55.. Thomas, B.G.; Yuan, Q.; Sivaramakrishnan, S.; Shi, T.;Vanka, S.P.; and Assar, M.B., “Comparison of FourMethods to Evaluate Fluid Velocities in a ContinuousCasting Mold,” ISIJ International, Vol. 41 (10), 2001, pp.1266–1276.

66.. Yuan, Q.; Zhao, B.; Vanka, S.P.; and Thomas, B.G., “Studyof Computational Issues in Simulation of Transient Flowin Continuous Casting,” Steel Research International, Vol.76 (1), 2005, pp. 33–43.

77.. Meng, Y., and Thomas, B.G., “Heat Transfer andSolidification Model of Continuous Slab Casting:CON1D,” Metall. & Material Trans., Vol. 34B (5), 2003,pp. 685–705.

88.. Yuan, Q., “Transient Study of Turbulent Flow and ParticleTransport During Continuous Casting of Steel Slabs,”Ph.D. thesis, University of Illinois at Urbana-Champaign,Ill., 2004.

99.. Thomas, B.G., and Zhang, L., “Review: MathematicalModeling of Fluid Flow in Continuous Casting,” ISIJInternational, Vol. 41 (10), 2001, pp. 1181–1193.

1100.. Yuan, Q.; Sivaramakrishnan, S.; Vanka, S.P.; andThomas, B.G., “Computational and Experimental Studyof Turbulent Flow in a 0.4-scale Water Model of aContinuous Steel Caster,” Metall. & Material Trans., Vol.35B (5), 2004, pp. 967–982.

1111.. Thomas, B.G.; O’Malley, R.J.; and Stone, D.T.,“Measurement of Temperature, Solidification, andMicrostructure in a Continuous Cast Thin Slab,”Modeling of Casting, Welding, and Advanced SolidificationProcesses, edited by B.G. Thomas and C. Beckermann, SanDiego, Calif., TMS, Warrendale, Pa., Vol. VIII, 1998, pp.1185–1199.

1122.. Yuan, Q., and Thomas, B.G., “Transport and Entrapmentof Particles in Continuous Casting of Steel,” ICS 2005 —3rd International Congress on Science and Technology ofSteelmaking, Charlotte, N.C., May 9–12, 2005.

1133.. Bai, H., and Thomas, B.G., “Turbulent Flow of LiquidSteel and Argon Bubbles in Slide-Gate Tundish Nozzles,

Part I: Model Development and Validation,” Metall. &Material Trans. B., Vol. 32B (2), 2001, pp. 253–267.

1144.. Bai, H., and Thomas, B.G., “Turbulent Flow of LiquidSteel and Argon Bubbles in Slide-Gate Tundish Nozzles,Part II: Effect of Operation Conditions and NozzleDesign,” Metall. & Material Trans. B., Vol. 32B (2),2001, pp. 269–284.

1155.. Bai, H., and Thomas, B.G., “Effects of Clogging, ArgonInjection and Continuous Casting Conditions on Flowand Air Aspiration in Submerged Entry Nozzles,” Metall.& Material Trans. B., Vol. 32B (4), 2001, pp. 707–722.

1166.. Thomas, B.G.; Huang, X.; and Sussman, R.C.,“Simulation of Argon Gas Flow Effects in a ContinuousSlab Caster,” Metall. Trans. B., Vol. 25B (4), 1994, pp.527–547.

1177.. Shi, T., “Effect of Argon Injection on Fluid Flow andHeat Transfer in the Continuous Slab Casting Mold,”master’s thesis, University of Illinois at Urbana-Champaign, 2001.

1188.. Huang, X.; Thomas, B.G.; and Najjar, F.M., “ModelingSuperheat Removal During Continuous Casting of SteelSlabs,” Metall. Trans. B., Vol. 23B (6), 1992, pp.339–356.

1199.. Meng, Y., and Thomas, B.G., “Interfacial Friction-relatedPhenomena in Continuous Casting With Mold Slags,”Metall. & Material Trans. B., Vol. 34B (5), 2003, pp.707–725.

2200.. Huang, X., and Thomas, B.G., “Intermixing Model ofContinuous Casting During a Grade Transition,” Metall.Trans. B, Vol. 27B (4), 1996, pp. 617–632.

2211.. Thomas, B.G., “Modeling Study of Intermixing inTundish and Strand During a Continuous Casting GradeTransition,” Iron & Steelmaker, Vol. 24 (12), 1997, pp.83–96.

2222.. Sussman, R.C.; Burns, M.; Huang, X.; and Thomas,B.G., “Inclusion Particle Behavior in a Continuous SlabCasting Mold,” Iron & Steelmaker, Vol. 20 (2), 1993, pp.14–16.

2233.. Rackers, K.G., and Thomas, B.G., “Clogging inContinuous Casting Nozzles,” Continuous Casting Vol. 10:Tundish Operations, Iron & Steel Society, Warrendale,Pa., 2003, pp. 264–274.

2244.. Bai, H., “Argon Bubble Behavior in Slide-Gate TundishNozzles During Continuous Casting of Steel Slabs,”Ph.D. thesis, University of Illinois at Urbana-Champaign,2000.

2255.. Lawson, G.D.; Sander, S.C.; Emling, W.H.; Moitra, A.;and Thomas, B.G., “Prevention of Shell ThinningBreakouts Associated With Widening Width Changes,”Steelmaking Conference Proceedings, Vol. 77, Chicago, Ill.,1994, Iron & Steel Society, Warrendale, Pa., pp.329–336.

2266.. Zhao, B., “Numerical Study of Heat Transfer inContinuous Casting of Steel,” master’s thesis, Universityof Illinois at Urbana-Champaign, 2003.

2277.. Thomas, B.G.; O’Malley, R.; Shi, T.; Meng, Y.; Creech,D.; and Stone, D., “Validation of Fluid Flow andSolidification Simulation of a Continuous Thin SlabCaster,” Modeling of Casting, Welding, and AdvancedSolidification Processes, Vol. IX, Shaker Verlag GmbH,Aachen, Germany, Aug. 20–25, 2000, pp. 769–776.

JJuullyy 22000066 ✦✦ 1177

2288.. Yuan, Q.; Thomas, B.G.; and Vanka, S.P., “TurbulentFlow and Particle Motion in Continuous Slab CastingMolds,” ISSTech 2003 Process Technology Proceedings, Vol.86, Indianapolis, Ind., April 27–30, 2003, Iron & SteelSociety, Warrendale, Pa., pp. 913–927.

2299.. Thomas, B.G.; Jenkins, M.; and Mahapatra, R.B.,“Investigation of Strand Surface Defects Using MoldInstrumentation and Modeling,” Ironmaking &Steelmaking, Vol. 31, 2004, pp. 485–494.

3300.. Thomas, B.G., and Zhu, H., “Thermal Distortion ofSolidifying Shell in Continuous Casting of Steel,”Proceedings of Internat. Symposia on Advanced Materials &Tech. for 21st Century, Honolulu, Hawaii, edited by I.Ohnaka and D. Stefanescu, TMS, Warrendale, Pa., 1996,pp. 197–208.

3311.. Honeyands, T., and J. Herbertson, “Flow Dynamics inThin Slab Caster Moulds,” Steel Research, Vol. 66 (7),1995, pp. 287–293.

3322.. Shin, H-J.; Lee, G.G.; Choi, W.Y.; Kang, S.M.; Park,J.H.; Kim, S.H.; and Thomas, B.G., “Effect of MoldOscillation on Powder Consumption and HookFormation in Ultralow-carbon Steel Slabs,” AISTech 2004Proceedings, Nashville, Tenn., Sept. 15–17, 2004, AIST,Warrendale, Pa.

3333.. Shin, H-J.; Thomas, B.G.; Lee, G.G.; Park, J.M.; Lee,C.H.; and Kim, S.H., “Analysis of Hook FormationMechanism in Ultralow-carbon Steel Using CON1DHeat Flow Solidification Model,” MS&T’04, NewOrleans, La., Sept. 26–29, 2004, TMS, Warrendale, Pa.,Vol. II, 2004, pp. 11–26.

3344.. Sengupta, J.; Thomas, B.G.; Shin, H-J.; Lee, G.G.; andKim, S.H., “Mechanism of Hook Formation DuringContinuous Casting of Ultralow-carbon Steel Slabs,”Metallurgical and Materials Transactions A (in press),2006.

3355.. Sengupta, J., “Effect of a Sudden Level Fluctuation onHook Formation During Continuous Casting ofUltraLow Carbon Steel Slabs,” Modeling of Casting,Welding, and Advanced Solidification Processes XI, Opio,France, May 28–June 2, 2006, edited by C.A. Gandin andJ.E. Allison, TMS, Warrendale, Pa., 2006.

3366.. Sengupta, S., and Thomas, B.G., “ThermomechanicalEffects Near the Meniscus During Continuous Casting ofUltralow-carbon Steel,” MS&T’05, Pittsburgh, Pa., Sept.26, 2005, TMS, Warrendale, Pa.

3377.. Zhang, L.; Sengupta, J.; and Thomas, B.G., “Investigationof Meniscus Hook Formation Using ComputationalModels,” final report to Postech, University of Illinois,2004.

3388.. Sengupta, J.; Shin, H-J.; Thomas, B.G.; and Kim, S.H.,“Micrograph Evidence of Meniscus Solidification andSubsurface Microstructure Evolution in Continuous CastUltralow-carbon Steels,” Acta Materialia, Vol. 54 (4),2005, pp. 1165–1173.

3399.. Ojeda, C.; Sengupta, J.; Thomas, B.G.; Barco, J.; andArana, J.L., “Mathematical Modeling of Thermal FluidFlow in the Meniscus Region During an OscillationCycle,” AISTech 2006 Conference Proceedings, May 1–4,2006, Cleveland, Ohio, AIST, Warrendale, Pa.

4400.. Abbel, G.; Damen, W.; de Gendt, G.; and Tiekink, W.,“Argon Bubbles in Slabs,” ISIJ Internaitonal., Vol. 36,1996, pp. S219–S222.

4411.. Harman, J.M., and Cramb, A.W., “A Study of the Effectof Fluid Physical Properties Upon DropletEmulsification,” Steelmaking Conference Proceedings,Dallas, Texas, Vol. 79, Iron & Steel Society, Warrendale,Pa., 1996, pp. 773–784.

4422.. Kubota, J.; Okimoto, K.; Shirayama, A.; and Murakami,H., “Meniscus Flow Control in the Mold by TravellingMagnetic Field for High-speed Slab Caster,” MoldOperation for Quality and Productivity, edited by A.W.Cramb and E. Szekeres, Iron & Steel Society, Warrendale,Pa., 1991.

4433.. Theodorakakos, A., and Bergeles, G., “NumericalInvestigation of the Interface in a Continuous SteelCasting Mold Water Model,” Metall. & Material Trans.B., Vol. 29B (6), 1998, pp. 1321–1327.

4444.. Emling, W.H.; Waugaman, T.A.; Feldbauer, S.L.; andCramb, A.W., “Subsurface Mold Slag Entrainment inUltralow-carbon Steels,” Steelmaking ConferenceProceedings, Chicago, Ill., Vol. 77, Iron & Steel Society,Warrendale, Pa., 1994, pp. 371–379. ✦✦

The original version of this paper was presented at ICS 2005 — The 3rd International Congress on the Science andTechnology of Steelmaking, Charlotte, N.C., and published in the ICS 2005 Proceedings.