Metal Process Simulation Laboratory Department of Mechanical and Industrial EngineeringUniversity of Illinois at Urbana-ChampaignUrbana, IL 61801

Transient Flow Structures in ContinuousCasting of Steel

By

S.Sivaramakrishnan, H. Bai,

B.G. Thomas, S.P. Vanka,(University of Illinois)

and

P.H. Dauby, M. B. Assar (LTV Steel)

Continuous Casting Consortium

Report

Submitted to

Allegheny LudlumAK Steel

Columbus StainlessInland Steel

LTVStollberg, Inc.

December 20, 1999

83rd Steelmaking Conference Proceedings, (Pittsburgh, PA, March 26-29, 2000), Vol. 83, Iron and SteelSociety, Warrendale, PA, 2000.

1

Transient Flow Structures inContinuous Casting of Steel

Sivaraj Sivaramakrishnan* , Hua Bai*,Brian G. Thomas*, S. Pratap Vanka*, andPierre H. Dauby†, Mohammad B. Assar†

*Dept. of Mechanical and Industrial EngineeringUniversity of Illinois at Urbana Champaign1206 West Green Street, Urbana IL 61801

Ph: 217-333-6919 Fax: 217-244-6534

†LTV Steel Technology CenterIndependence, OH 44131

Ph: 216-642-7255; Fax: 216-642-4599

Key Words: steel, water model, transient fluid flow,MFC, sensor, numerical models, particle imagevelocimetry

ABSTRACT

Transient flow events can be very important tothe generation of quality problems during thecontinuous casting of steel. In this work, severaldifferent tools are applied to investigate thesephenomena. Transient flow is computed usingLarge Eddy Simulation (LES) models, whileconventional K-ε models yield time-averagedresults. Particle Image Velocimetry (PIV) is appliedto measure quantitatively the transient velocityfields in a water model of the nozzle and moldregion. Electromagnetic (MFC) sensors on thewideface of an actual slab caster are used tomeasure the liquid steel velocity at four locations.Results using all four methods compare favorablyfor single-phase flow and give new insight into theflow phenomena.

The slide gate creates a strong swirl at the outletports of the nozzle, which is also predicted using theK-ε model. This swirl is seen to persist more thanhalfway across the mold, causing a characteristicstaircase velocity vector pattern in the PIVmeasurements when viewed in a plane parallel tothe wide faces. Flow across the top surface wasfound in PIV to contain periods of 5-10s when thevelocities were three to four times their meanvalues. This is likely related to inlet conditions andwould likely exacerbate shear entrainment of theliquid flux at the top surface and level fluctuations.Simulations of the MFC output indicate thataccurate flow prediction is not possible unless thesensors are located in a region of relatively uniformflow, such as near the top surface. In both LES andPIV, the upper roll structure evolves chaoticallybetween a single large recirculation structure and aset of distinct vortices. The lower rolls in PIV aresignificantly asymmetric for very long periods oftime (~ 1-hour) and go through a repeatingsequence of features. One of these features involvesa short circuit between the upward and downwardflow in the lower roll, which is also seen in thesimulation. This appears to be inherent to theturbulent nature of the flow and is likely importantto inclusion particle and bubble entrapment.

INTRODUCTION

Flow in the mold region during the continuouscasting of steel is of great interest because itinfluences many important phenomena, which havefar-reaching consequences on strand quality. Theseinclude the flow and entrainment of the top surfacepowder / flux layers, top-surface contour and levelfluctuations, and the entrapment of subsurfaceinclusions and gas bubbles.

Flow in the mold can be studied usingmathematical models, physical water models, andplant measurements. The turbulent flow through the

2

nozzle and in the mold of the continuous caster hasbeen studied extensively using computationalmodels based on the Reynolds Averaged NavierStokes (RANS) approach [1-3]. The most popular ofthese are steady models using the K-ε turbulencemodel. In this work, the detailed evolution of theflow structures is also studied using the Large EddySimulation (LES) approach. LES is computationallymuch more intensive than K-ε, but offers a newlevel of insight into transient phenomena.

Scale water models have been applied with greatsuccess in previous work to study the flow ofmolten steel, owing to the similar kinematicviscosity of the two fluids, which governs much ofthe flow behavior. To better visualize and quantifythe flow in these water models, Particle ImageVelocimetry (PIV) has been applied recently tomeasure the instantaneous velocity fields [4-6]. Inthis work, measurements are performed on a watermodel at the LTV Technology Center(Independence, OH) using a PIV system installedby DANTEC [7].

Finally, velocities in the molten steel flowing inthe continuous casting mold can be measuredindirectly from electromagnetic (MFC) sensorsembedded in the mold walls. In this work, MFCsensors developed by AMEPA GmbH [8] wereinstalled on the LTV Steel No. 1 slab caster inCleveland to produce velocity histories at fourlocations [5].

In this paper, recent results using all four of thesemethods are compared and applied to yield newinsights into transient flow phenomena in thecontinuous casting nozzle and mold. This work ispart of an ongoing effort to develop mathematicalmodels of the continuous casting process and toapply them to increase understanding and solveproblems of practical interest.

WATER MODEL AND PIV SETUP

The flow from the tundish passes through a slidegate, which moves at right angles to the wide faceto restrict the opening in the nozzle and thereby

control the flow rate. The flow then enters the moldcavity through the downward-angled square ports ofthe bifurcated nozzle, shown in Figure 1. Flow exitsthe bottom of the water model through three pipesattached to circular outlets in the bottom plate.Figure 2 shows a sketch of the experimental moldmodel, which is nominally symmetric with respectto the centerline shown in the figure. Table I liststhe main dimensions and casting conditions for thenozzle and mold models. The thickness of thewater model tapers from top to bottom in order tosimulate only the liquid portion of the steel caster.

Flow visualization and velocity measurementswere made using 0.4-scale Plexiglas water modelsof the tundish, nozzle and mold of the caster at LTVSteel Technology Center. Sequences ofinstantaneous velocity measurements were obtainedusing the PIV system [5]. The positions of tracerparticles are recorded digitally when twoconsecutive pulses of laser light illuminate a planarsection through the water. Knowing the timeinterval between pulses (1.5 x 10-3s) and thedistances moved by the particles (from imageprocessing), a complete instantaneous velocity fieldis obtained. This procedure is usually repeatedevery 0.2s and the results from at least 50 suchexposures are averaged to obtain the time-averagedvelocity field. In order to get good resolution in thePIV measurements, the domain was divided intofour regions: the vicinity near the nozzle ports, thetop region of the mold containing the jet and theupper roll, the middle region containing both thelower rolls and the bottom region containing part ofthe lower roll.

NUMERICAL MODELS

Two different numerical flow models weredeveloped for this work at the University of Illinois.Each satisfies mass and momentum conservation inthe computational domain by solving the continuityequation and the conservative form of the NavierStokes equations for isothermal incompressibleNewtonian fluids.

3

Liquid Inlet

Gas Injection

Outlet Ports

z,w

x,uy,v

��

Fixed normal gas velocityGas fraction=1

Fixed pressure, Zero normal gradientsof u,v,w,K,ε

Fixed normal liquidvelocity, K,εLiquid fraction=1

SlideGate

UTN

SEN

Fig. 1. Outline of slide gate nozzle and boundaryconditions

∂∂

v

xj

j

= 0 (1)

∂∂

ρ ∂∂

ρ ∂∂

∂∂

µ∂∂

∂∂t

vx

v vP

x x

v

x

v

xij

j ii j

effj

i

i

j

+ = − + +

(2-4)

The solution yields the pressure and velocitycomponents at every point in the three-dimensionaldomain. At the high flow rates involved, thesemodels must account for turbulence.

Table I – Water model conditions

Dimension / Condition Value

Tundish bath depth 400~410 mmNozzle length (total) 510 mmUTN diameter 28 mmSlide-gate diameter 28 mmSlide-gate thickness 18 mmSlide-gate orientation 90°Slide-gate opening (FL) 52%SEN submergence depth(top of port to top surface)

77± 3 mm

Bore (SEN) diameter 32 mmPort width x height 31mm x 32mmPort thickness 11 mmPort angle, lower edge 15o downPort angle, upper edge 40o downBottom well recess depth 4.8 mm

Port opening 31 x 31 mm

Water model length 950 mmWater model width(steel caster width)

735 mm(72 in. full scale)

Water model thickness 95 mm (top) to65 mm (bottom)

(steel caster thickness) (9. in. full scale)Outlets at bottom of mold

domain (both halves)3 round 35mmdiameter outlets

Casting speed (model top) 0.633 m/minLiquid flow rate through

each port3.53x10-4 m3/s(5.6gal/min)

Average velocity at port 424 mm/s

Average jet angle at port 30o

Liquid kinematic viscosity 1.0 x10-6 m2/sGas injection 0%

Large Eddy Simulation (LES) Model

Large Eddy Simulation (LES) uses a fine grid toaccurately capture details of the large-scalestructures of the flow. For high velocities, aturbulence model is often used at the sub-grid scalein order to diffuse the kinetic energy of these scales,although this was not needed in the present work.

4

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Fig. 2. Water model geometry

The equations in the LES model are discretizedusing the Harlow-Welch fractional step procedure[9] on a staggered grid. Second order centraldifferencing is used for the convection terms andCrank Nicolson scheme [9] is used for the diffusionterms. The Adams-Bashforth scheme [9] is used todiscretize in time with second order accuracy. Theimplicit diffusion terms are solved for usingAlternate Line Inversion. The Pressure Poissonequation is solved using a direct Fast FourierTransform solver. For parallelization, 1-D domaindecomposition with MPI (Message PassingInterface) is used. A computational grid with 1.5million nodes was used with a time step of 0.001s.The LES simulations are quite slow and take 18CPU s per time step or 13 days (total CPU time) onan Origin 2000 for 60s of flow simulation. Tosimplify the computational domain, only the moldwas simulated without the taper and rigid boundaryfor the free surface. The inlet was a fully-developedturbulent flow from a square duct at a downwardangle of 30o [10].

K-ε Model

For improved computational efficiency using acourser grid, the conventional K-ε model averagesthe effect of turbulence using an increased effectiveviscosity field. To model two-phase flow, anadditional set of momentum conservation equationswas solved for the argon gas phase. Interphasecoupling terms were added to account for the dragin proportion to the relative velocities of the liquidand bubble phases, which were generally in theStokes or Allen regimes. The equations weresolved using the CFX v4.2 finite-difference package[11]. The nozzle domain used 10620 nodes andtypically required 2.5 hours of computation.Further details are provided elsewhere [12].

NOZZLE RESULTS (SEN)

Flow Pattern Observations

Flow patterns observed in the experiments can bedirectly compared to the numerical simulation withthe model described above under the sameoperation conditions. Simulations were conductedfor the conditions in Table I, except that 5.8% gaswas injected, and 1mm bubble diameter wasassumed. The results were compared with PIVwater model experiments using the same gasinjection. In both the water experiments and modelpredictions, three main recirculation zones areobserved inside the slide-gate nozzle: in the cavityof the middle gate plate, below the throttling gateplate, and at the nozzle ports. High gasconcentration collects in these recirculation zones.Figure 3.1 shows an example of the predicted flowpattern looking into the left nozzle port. In both thesimulation and the water experiments, the jet exitsthe ports with a single strong vortex or swirl. Thevortex rotational direction is relatively stable withclockwise direction at the plane of the port exit. Thejet is directed approximately 29° down, as seen inthe photograph, Figure 3.2. This is very close to thevalue of 27.8° down calculated from the simulationresults using a weighted-average method over allnodes on the port plane [13]. No obvious “back-

5

flow” at the nozzle port was observed during theexperiments. It is noted that the observation of noback-flow differs from many previous findings fortypical nozzles [2, 3].

Fig. 3.1. Swirl patternat nozzle port

The lack of any back-flow-zone in the experi-ments is mainly due tothe special design of theSEN ports of this nozzle,which had a muchsteeper angle of theupper port edges (40°down) than the lowerport edges (15° down).

Velocity Comparison (PIV and K-ε)

Quantitative comparisons between the PIVmeasurements and the K-ε simulation results weremade on the jet at the nozzle port exit. An exampleis shown in Figure 4. Unfortunately, the flow fieldinside the plastic nozzle could not be reliablymeasured, due to the curvature of the nozzle walland partial opacity from the machining cut. Figure4 a) shows a vector plot of the PIV-measured flowfield around the nozzle port in the plane parallel to

the wide face of the mold. The predicted flowvector plots (b) are plotted side by side for directvisual comparison. The magnitudes of the liquidvelocity at the port for measurements and predictionare then extracted and plotted together in (c). The“overall jet angle”, defined as the weighted-averageover the whole 3-D jet [3], should not be comparedwith the 2-D jet angle calculated from a single sliceof the PIV measurements, or “slice jet angle”. Theslice jet angle is a simple arithmetic average of thejet angles for all measuring points (PIV) orcomputational cells (K-ε) at the slice of the nozzleport. The time-averaged values of the “slice jetangle” are marked on Figure 4 c).

The upper part of Figure 4 is for the slicethrough the nozzle center-plane (y=0), and thelower part for the slice that is away from andparallel to the center-plane (at y=12mm). The matchof the velocity magnitude and the slice jet anglebetween the PIV measurement and the modelprediction is satisfactory except that the velocitypredictions are consistently slightly larger than themeasurements. This is likely due to fact that thepulsed laser light sheet location was manuallyadjusted during the PIV experiments, and thusmight not lie exactly in the desired position.

Fig. 3.2. Flow pattern and the average jet angle measurement in water model experiment

6

PredictedMeasured

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m (

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Slice (y=12mm) away from the center-plane of the nozzle, parallel to the wide face of the mold

(A) PIV measurements (B) CFX prediction (C) Speed comparison

Slice jet angle:

Predicted: 26.9° upMeasured: 22.8° up

Dis

tanc

e fr

om th

e po

rt b

otto

m (

mm

)

Liquid velocity (u2+w2)

1/2 (m/s)

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Predicted: 42.8° downMeasured: 40.3° down

Fig. 4. Comparison of PIV measurements and K-ε model predictions, showing downward flow from portcenterline and upward flow at port edges due to swirl.

MOLD REGION RESULTS

Figure 5 shows a side to side comparison of atypical instantaneous vector plot along the centerplane of the water model, parallel to the wide faces,obtained from the simulation (a) and PIVmeasurements (b) for the conditions in Table I.

Figure 6 compares the corresponding timeaveraged vector plots. The simulation vector plot istime averaged over 60s. The PIV vector plot is acomposite containing three time-averaged parts.

The three parts are the top region containing theupper roll and the jet which has been averaged over10s (50 snapshots), the middle region containing thelower roll (0.25-0.65m below water surface)averaged over 200s (200 snapshots), and the bottomregion extending from 0.65m - 0.77m averaged over40s (200 snapshots). The middle region is also aspatial average of the right and left half regions ofthe water model, in order to average theconsiderable differences which arose due toasymmetry between sides.

7

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Fig. 6. Time averaged velocity vector plot of(a) simulation and (b) PIV measurement

The LES simulation and PIV experimentalresults generally match very well. Both the LES andPIV jets bend slightly upwards, as they traverseacross the mold towards the narrow face. Thebiggest discrepancy is that the upward-movingvelocities in the region directly below the SEN inthe numerical simulation are larger than in theexperiment.

LES and PIV in the Upper Mold

Figure 7 shows a sample plot of time variation ofvelocity at a typical point 20 mm below the topsurface, halfway between the SEN and the narrowface. The PIV points are spaced 0.2s apart ascompared to 0.001s increments in the simulation.The PIV velocity variation shows the existence oftwo time scales. The short time scale is about 0.7sand is predicted well by the simulation. The longertime scale is at least 45s. It results in times of 5s ormore when the velocity close to the top surface isthree to four times the mean. This period of high

velocity could shear the molten flux layer and causeits entrainment deep into the caster. These longtime-scale variations caused by the wide variationsin the depth of penetration of the experimental jetare not seen in the simulation.

Figure 8 shows a schematic of the flow from theport that illustrates the swirling jet. Theperpendicular movement of the slide gate flowcontrol positioned high in the nozzle tube, (relativeto the wide face) allows flow through only 41% ofthe nozzle bore area. This causes stronger flowdown the inner-radius wide-face side of the nozzle.This bias in flow over the cross section continuescausing the experimental jet to swirl as it exits thenozzle ports. This persists into the mold cavity,where the jet centerline moves along a helix, asdepicted in the figure. The overall jet movesdownward at an angle of 30o and the swirl graduallydiffuses. The swirling experimental jet moves bothup-down and in-out of the center plane. As a resultof the helical motion, strong regions of the flow

8

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Fig. 7. Typical history of U velocity component in simulation and PIV (about 2 cm below water surface).

have either a stronger upward or downwardcomponent, depending on the radial location.Motion of the jet in and out of the plane results inthis vertical component of flow to often occur in theplane of the PIV measurements. This results in anet instantaneous jet angle that is significantlydifferent from 30o. This results in the staircasepattern seen in Figure 9.

362m

m

Port (31x31mm)

Fig. 8. Schematic of swirling flow in the PIV jet

As the jet moves in and out of the center plane ata given point, either the upward or downwardmoving portion of the spiral flow will be present.This causes the staircase shape to alternate. Thetime scale of this fluctuation, and corresponding in-out of plane motion is of the order of 0.2s. Inaddition, the entire jet chaotically alternatesbetween shallow and deep penetration. The jet alsohas an in-out motion on a large time scale, resultingin the frequent intermittent disappearance of vectorsclose to the narrow face, for periods of about 7s.The simulation jet also has miniature staircase

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9

patterns which result from jet wobble due solely toturbulence, which is consistent with previous work[14]. However the deviation from 30o is muchsmaller than the PIV measurement and the differentstaircases are out of phase.

This finding implies that the inlet swirl persistsmore than halfway across the mold. This maysignificantly affect the flow features in otherregions of the mold and explain some of thediscrepancies in the results. Thus it is necessary toincorporate the swirling inlet condition along withthe in-out of plane motion in future simulations.

LES Simulation of Electromagnetic MFC Sensor

Figure 10 shows location of two MFC velocitysensors on half of the wideface of the mold. Thesensors can be used to determine whether the flowpattern in the molten steel has only a single roll or alower and upper (double) roll [5, 8]. The signals canalso provide a measure of the strength of thevelocities close to the top surface.

Each MFC sensor consists of two probes locatedclose to each other behind the copper mold plates.Both probes emit a magnetic field. The flow ofconducting steel through this magnetic field inducesan electrical signal in each of the probes, accordingto Faraday's third law of electromagnetism. Thetime shift between prominent features of the twosignals is a measure of the time taken by the flow toconvect from one probe to the other. The averagevelocity in the region between the probes is then thedistance between the probes divided by this timeshift.

To enable comparisons of the MFC sensorsignals with the numerical model, simulation resultswere extracted to predict the output of the probes.The horizontal velocity component convects theflow structures from one probe to the other.Prominent flow features appear in both signals, witha time shift corresponding to the average horizontalvelocity between the probes. Thus, the horizontalvelocity components calculated within the cells inthe area beneath each probe head were first

averaged in each plane parallel to the wideface.Next, the attenuation of the magnetic field strengthwith distance into the flow was taken into accountby assuming that the induced signal strengthdecreased inversely with the square of the distancefrom the wideface, according to Figure 11. Thus,the overall simulated signal was calculated bytaking a weighted average of the horizontalvelocities calculated in the different planes beneaththe probe head. Weighting factors were taken fromFigure 11. The average of the two signals predictedat each probe indicates the best possible sensoroutput.

915 mm

Meniscus413 mm

518 mm69 mm

183 mm

40 mm

SEN Narrowface

190 mm

18 mm x 18 mmActive area

Sensor B

Sensor A

1 2

1 2Probe

Fig. 10. MFC sensor location on water model

Figures 12 a) and (b) show typical simulatedprobe signals predicted for sensors A and B. Thepositions were scaled from Figure 10 dimensions tocorrespond with the 0.4 scale water model. Atposition A, near the liquid surface, the two probesignals are very similar, except for an obvious timeshift. Thus, it is quite feasible that the average ofthe two signals could be extracted by the signalprocessing logic, without knowing the absolutevelocities shown on the y axis. At position B,however, the two probe signals are very different.They are clearly not always the same basic signaloffset in time, so it is likely that large errors mightarise in predicting their average by the signalprocessing. The reason for this difference in

10

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behavior of the signals at A and B can beunderstood by looking at the flow fields near thetwo sensors.

Figure 13 shows samples of instantaneousvelocity-vector plots taken in two planes parallel tothe wideface in the top region of the simulation. Theupper roll at this instant is seen to consist of a set ofdistinct vortex structures, as opposed to the singlelarge recirculation structure seen in the time averagevector plot. The upper roll alternates chaoticallybetween these two extremes.

Flow at position A near the top surface is seen tobe relatively consistent, as velocities are mainlyhorizontal and similar at both probes. ComparingFigures 13a) and b) shows that variations throughthe mold thickness are less significant than the timevariations, so the attenuation of the electromagneticsignal should not be important.

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11

Flow at position B is very different, however.The mean convection of vortices is not nearlyhorizontal. Flow past one probe often does not evenreach the other probe. Thus, the probe signals maynot always correlate (Figure 12 b). Figure 13 alsoshows how vortex structures traverse almostrandomly across the caster, especially near thecenter of the roll. For Sensor A, the fluctuationsappear to reverse the time shift for a few seconds

(Figure 12 a) 70-72s). Velocities predicted at someprobes indicate a real change in the direction offlow for several seconds (Sensor B Figure 12 b)122-125s and 152-155s). Either of these situationsmight be falsely interpreted as a change betweensingle and double roll patterns. In conclusion, thisanalysis suggests that the MFC sensor probesshould be placed in regions of steady horizontalflow, such as found near the top surface.

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12

Comparison of LES, K-ε, PIV, and MFC

Figure 14 a) shows an example of the screenoutput of the MFC sensor located on the caster atthe LTV Steel plant. The gradually fluctuatingshape of the signal is similar to the shape of thesimulated probe signal in Figure 12 a). Figure 14 b)shows MFC output at A near the surface as afunction of casting speed for Table I conditions.Each point is a 10s time average. The significantscatter has several potential causes, includingvariations in casting conditions between the 61slabs in the plant trial.

Fig. 14 a) MFC sensor output (1.8m wide slab;0% argon, 1.25 m/min casting speed)

Qualitatively, all four of the flow analysis toolsagree. The conditions under investigation alwaysproduce a classic double roll flow pattern, such asshown in Figure 6. Maximum velocities along thetop surface are found midway between the SEN andnarrow face, and fluctuations are great. Top surfacevelocities increase with casting speed.

The K-ε, LES, and PIV results are comparedquantitatively in Figure 14 c) for flow along the topsurface of the water model. The K-ε predictionsagree very well with the PIV data. The LESpredictions are low, perhaps due to differences inthe inlet conditions assumed in the simulation. TheLES sensor predictions are slightly lower than LESpredictions along the top surface.

It is difficult to compare the MFC sensor datadirectly with the water model results due in part to

the 0.4 scale factor. However, assuming Froudesimilarity means that the 0.63 m/min casting speedin the water model scales up by a factor of

1 0 0 4. / . to 1.0 m/min. in the caster. The averagesurface speed from the MFC sensor signal at 1.0m/min is 0.20 m/s (Figure 14b). This agrees verywell with the K-ε and PIV value of 0.19 m/s (scaledup from the maximum of 0.12 m/s in Figure 14c).This agreement is very encouraging, but furthervalidation is needed to reconcile the LES model andto investigate conditions where argon gas is present.

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0.8 0.9 1 1.1 1.2 1.3 1.4

MF

C V

elo

city

(m

/s)

Casting Speed (m/min)

Least squares linear fitR=0.71

Fig. 14 b) MFC sensor output sorted by casting speed

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

PIV (0.791 m/min)

PIV (0.554 m/min)

K-e (0.633 m/min)

LES (0.633 m/min)

To

p S

urf

ace

Sp

eed

(m

/sec

)

Distance from SEN (m)

NF

Casting speed in water model

based on flow rate(See Table I)

SEN NF

Fig. 14 c) Variation of time-average speed along topsurface comparing PIV, K-ε, and LES

13

LES and PIV in the Lower Mold

Figure 15 is a 30-min time averaged vector plotof the velocities measured in the lower rolls of thewater model. Considerable asymmetry can be seenbetween the left and right rolls, which persist evenover this long time period.

0.3

0.4

0.5

0.6

00.10.20.3

0.05 m/s

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3

Z X

Y

Fig. 15. Velocity vector in both of the lower rolls(30 min. time average).

There are two main features of this asymmetrythat are especially significant. The first is the regionof very low velocity below the impingement pointon the right, which contrasts with the higherdownward flow on the left. The second is thedifference in the shapes and flow in the two lower

rolls. The first was likely caused by an angularmisalignment of the nozzle of the order of 1o in theX-Z plane resulting in the jet on the right movingout of the center plane. Dye injection study for thesame configuration, without change in the flowsettings is consistent with this angularmisalignment. The second is the upward movingflow below the SEN being directed towards the left.This suggests a period of time when the right roll islarger than the left. Study of the transient flowfeatures over this 30-min. period reveals a repeatingsequence of three features when: 1) Both rolls areabout the same size for about 17s; 2) Right roll islarger than the left for about 30s and 3) A short-circuited structure forms and merges into the lowerroll over about 10s, while both rolls are about thesame size.

The simulation enforces symmetry by simulatingonly half of the domain with a symmetry boundarycondition. The presence of this significantasymmetry necessitates the simulation of bothhalves of the water model / caster in future work.Figures 5 a) and (b) show an instant when the shortcircuit between the upward and downward flows ofthe lower roll has taken place and the downwardmotion of the location of the short circuit has begun.

0.2�

0.3�

0.4�

0.5�

0.6�

0.7�

-0.3�-0.2�-0.1�0�0.1�0.2�0.3�

X�

Y�

Z�

0.05�m/s�

0.2�

0.3�

0.4�

0.5�

0.6�

0.7�

-0.3�-0.2�-0.1�0�0.1�0.2�0.3� X�

Y�

Z�

0.05�m/s�

Fig. 16. Instantaneous PIV vector plot of lowerrolls when both rolls are about the same size

Fig 17. Instantaneous PIV vector plot of lowerrolls when right roll is larger than the left

14

a)

0�0.05�0.1�0.15�0.2�0.25�0.3�0.35�

0.3�

0.35�

0.4�

0.45�

0.5�

X�

Y�

Z�

0�.1�m/s�Time�=�0.0s�

b)

0�0.05�0.1�0.15�0.2�0.25�0.3�0.35�

0.3�

0.35�

0.4�

0.45�

0.5�

X�

Y�

Z�

0�.1�m/s�Time�=�2.5s�

c)

0�0.05�0.1�0.15�0.2�0.25�0.3�0.35�

0.3�

0.35�

0.4�

0.45�

0.5�

X�

Y�

Z�

0�.1�m/s�Time�=�5.0s�

d)

0�0.05�0.1�0.15�0.2�0.25�0.3�0.35�

0.3�

0.35�

0.4�

0.45�

0.5�

X�

Y�

Z�

0�.1�m/s�Time�=�7.5s�

Fig. 18. Sequence of PIV images (a-d) showing formation and downward motion of the short-circuitedstructure over a time period of 7.5s

The transient sequence in the lower roll of boththe simulation and PIV progresses as follows.Initially, both left and right rolls are about the samesize, as shown in the instantaneous snapshot inFigure 16. This symmetrical configuration lasts forabout 12s. This is followed by a period of around17s when the right roll is larger than the left, asindicated in Figure 17 by the upward flow belowthe nozzle directed to the left. This in turn isfollowed by the sequence of instantaneous PIVvector plots shown in Figures 18 (a-d) which span7.5s. Here the downward flow along the NF fromthe impingement point of the left jet turns sharply tothe right, to form a short- circuited roll structure (a).This might be caused by pressure instabilities in the

flow field. This structure then expands downwardover a 7.5s period (b-d). This sequence repeatsevery 1 min.

Parts of this repeating sequence are seen in thesimulation as well. Figure 19 shows an instant whenthe lower roll in the simulation is a single largerecirculation region. Figure 20 shows a sequenceidentical to that in the PIV, where a short circuitstructure is formed which expands downward. Thetime scale for this phenomenon is the same for PIVand simulation. This suggests that this short circuitstructure is probably caused by turbulence and notby changes at the inlet or other disturbances whichmay be present in the PIV but not in the simulation.

15

This phenomenon is important when studyingbubble or particle entrapment because it changes thetransport phenomena in the lower roll.

0.2�

0.25�

0.3�

0.35�

0.4�

0.45�

0.5�

0.55�

0.6�

0.65�

0.7�

0.75�

0.8�

0.85�

X�

Y�

Z�

0.1�m/s�

Fig. 19. Instantaneous simulation vector plot whenlower roll is a large recirculation region

CONCLUSIONS

The turbulent flow of liquid steel in a continuouscasting mold has been investigated with K-ε andLES computational models, water models, and plantmeasurements. Model predictions generally agreeboth qualitatively and quantitatively with velocitiesmeasured using PIV (Particle Image Velocimetry)on a 0.4-scale water model and with MFC sensorsin a steel caster. The LES simulation slightlyoverpredicts velocity beneath the nozzle and under-predicts it along the top surface, likely due tooversimplified inlet conditions. Together, thenumerical simulations, PIV and MFC results reveal

deeper insight into flow in the continuous castingprocess, especially transient phenomena.

The inlet condition is very influential on flow inthe mold. Strong swirl is generated at the port outletby the 90o oriented slide gate nozzle. This causesconsiderable in and out of plane motion, whichpersists at least halfway across the mold. This wasnot captured in the current LES simulation, whichhas a simple inclined fully-developed turbulentsquare duct flow as its inlet condition.

Flow across the top surface in the physical modelvaries by more than 100% of its mean value. Thisvariation has a high frequency component (~1.5 Hz)which is also seen in the simulation. It alsoincludes a low frequency component (time period ofthe order of 45s) with times of more than 5s whenthe horizontal velocities are 3-4 times larger thantheir mean values. This component is not seen inthe simulation, so might be caused by fluctuationsin the inlet conditions. This feature is likelysignificant to shear entrainment of liquid flux.

The LES simulation of the MFC sensor signalsillustrates the great importance of locating thesensor in a stable region of the flow if accuratevelocities are to be extracted. Sensors positioned inthe current location near the top surface shouldaccurately output both the direction and velocityhistory. The individual probes of sensors positioneddeep in the recirculation zone experience verydifferent transient flow fields, so cannot be reliedupon to produce accurate velocities.

Although the entire geometry including the inletnozzle and its port were symmetric, there wasconsiderable, persistent, asymmetry between thetwo lower rolls. Flow in this region alternatesthrough a sequence of flow phenomena, whichrepeats chaotically. One of the flow featuresinvolving short circuiting is seen in both thephysical model and the simulation, suggesting thatit is inherent to the turbulence and is not causedsolely by the inlet conditions. This feature isimportant for particle motion and bubbleentrapment, which are responsible for defects in thefinal product.

16

0.2�

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0.3�

0.35�

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0.0s�

0.1�m/s�

0.2�

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a) b)

0.2�

0.25�

0.3�

0.35�

0.4�

0.45�

0.5�

0.55�

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X�

Y�

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0.2�

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c) d)

Fig. 20. Sequence of simulation images (a-d) showing formation and downward motion of the short-circuitedstructure over a time period of 7.5s

17

ACKNOWLEDGEMENTS

The authors would like to thank the NationalScience Foundation (NSF - Grant # DMI - 98-00274) and the Continuous Casting Consortium(CCC) at the University of Illinois at UrbanaChampaign (UIUC) for their support of thisresearch, the National Center for SupercomputingApplications (NCSA) at the UIUC for computingtime, AEA technology for use of the CFX 4.2program, and LTV Steel for use of the PIV systemand access to PIV and MFC measurements.

REFERENCES

1. L.M. Mika, B.G. Thomas and F. Najjar:"Simulation of Fluid Flow Inside a ContinuousSlab Casting Machine", Meta l lurg ica lTransactions B, 1990, vol. 21B, pp. 387-400.

2. D.E. Hershey, B.G. Thomas and F.M. Najjar:"Turbulent Flow through Bifurcated Nozzles",International Journal for Numerical Methodsin Fluids, 1993, vol. 17, pp. 23-47.

3. F.M. Najjar, B.G. Thomas and D.E. Hershey:"Turbulent Flow Simulations in BifurcatedNozzles: Effects of Design and CastingOperation", Metallurgical Transactions B,1995, vol. 26B (4), pp. 749-765.

4. D. Xu, W.K. Jones and J.W. Evans: "PIVPhysical Modeling of Fluid Flow in the Moldof Continuous Casting of Steel", in Processingof Metals and Advanced Materials: Modeling,Deisgn and Properties, B.Q. Li, eds., TMS,Warrendale, PA, San Antonio, TX, 1998, pp.3-14.

5. M.B. Assar, P.H. Dauby and G.D. Lawson:"Opening the Black Box: PIV and MFCMeasurements in a Continuous Caster Mold",in Steelmaking Conference Proceedings, vol.83, ISS, Warrendale, PA, 2000,

6. M. Gharib and C.E. Willart: "Digital ParticleImage Velocimetry", Experiments in Fluids,1991, vol. 10, pp. 181-193.

7. Dantec Flow Technology: User's Guide, V.2.01, 777 Corporate Drive, Mahwah, NewJersey 07430, 1998.

8. K.U. Kohler, P. Andrzejewski, E. Julius and H.Haubrich: "Steel Flow Velocity Measurementand Flow Pattern Monitoring in the Mould", inSteelmaking Conference Proceedings, vol. 78,ISS, Warrendale, PA, 1995, pp. 445-449.

9. J. Tannehill, D. Anderson and R. Pletcher:Computational Fluid Dynamics and HeatTransfer, Taylor and Francis, Washington, DC,1997.

10. R. Madabushi and S.P. Vanka: "Large EddySimulation of Turbulence-Driven SecondaryFlow in a Square Duct", Physics of Fluids,1991, vol. 3 (11), pp. 2734-2475, Nov. issue.

11. AEA Technology: CFX 4.2 Users Manual,1700 N. Highland Rd., Suite 400, Pittsburgh,PA 15241, 1998.

12. H. Bai and B.G. Thomas: "Two-phase flow intundish nozzles during continuous casting ofsteel slabs", Materials Processing in theComputer Age III, V. Voller and H. Henein,eds., Nashville, TN, TMS, Warrendale, PA,March 12-16, 2000.

13. B.G. Thomas: Mathematical Models ofContinuous Casting of Steel Slabs, ContinuousCasting Consortium, University of Illinois atUrbana-Champaign, Report, 1998.

14. R.V. Wilson and A.O. Demuren: "Numericalsimulation of turbulent jets with rectangularcross section", ASME J of Fluids Eng, 1998,vol. 120 (Jun), pp. 285-290.

For further information on this paper, please contactBrian G. Thomas at 1206 West Green Street,Urbana, IL, 60801; Ph: 217-333-6919; Fax: 217-244-6534; email: bgthomas@uiuc.edu