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Tundish Open Eye Formation: A Trivial Eventwith Dire Consequences

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Saikat Chatterjee, Donghui Li, and Kinnor Chattopadhyay�

Inert gas shrouding is a traditional practice in tundish metallurgy and has several benefitssuch as, protecting the melt stream from air aspirations, aiding inclusion flotation withargon bubbles, and also possible thermal and chemical homogenization. On the down side,it displaces the protective slag layer on the top of the melt, and exposes the steel to theambient atmosphere. This region is often referred to as the slag eye or open eye. Thisexposed area leads to higher radiative heat losses, reoxidation of the liquid steel, nitrogenpickup, and subsequent inclusion formation. Although perceived as a trivial event by many,Tundish Open Eye (TOE) has dire consequences. In the present work, TOE formation and itsconsequences have been investigated. The mathematical modeling of this turbulentmultiphase system is performed using the Volume of Fluid (VOF) method, and discretephase method (DPM), coupled with the standard k-e turbulence model. The mathematicalmodel is compared with the water model results and plant trials. The main objective is toensure that the steelmaking tundish acts as a refiner and not as a contaminator.[1]

1. Introduction

The injection of argon gas into the ladle shroud is a

commonpractice during continuous casting to prevent the

melt stream from reoxidation by the aspiration of

surrounding air. The benefits that result from shrouding

the melt stream are manifold. Despite these benefits, too

much argon gas should be avoided, because it forms an

exposed eye of steel around the ladle shroud by sweeping

off the tundish slag layer, making the region prone to

oxidation and nitrogen pickup. Chattopadhyay et al.[2]

have studied slag eye formation since 2009 and simulated

inert gas shrouding practices using a full-scale, four-strand

water model of a 12-tonne, delta-shaped tundish. Com-

pressed air was aspirated into the ladle shroud to model

volumetric flow rates that range between 2 and 10%of steel

entry flows. Bubble trajectories, slag layer movements, and

flow fields, were visualized. Flow fields were visualized

using particle image velocimetry (PIV). A 2D numerical

model[2] was also developed using discrete phasemodeling

(DPM)[3] along with the standard k-e turbulence model[4]

with two-way turbulence coupling. Predicted flow fields

[�] S. Chatterjee, D. Li, K. ChattopadhyayDepartment of Materials Science and Engineering, University ofToronto, 184 College Street, Toronto, Ontario,Canada M5S 3E4Email: [email protected]

DOI: 10.1002/srin.201600436

� 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

and bubble trajectories corresponded with the water

model experiments. Chattopadhyay et al.[5] in 2011 also

developed a 3D model to efficiently predict bubble tracks

and flow fields in the tundish, and compared it with water

model experiments. In terms of quantitative measure-

ments, the mathematical model was quite robust and the

error with respect to experimental measurements was less

than 15% in all cases. The 3Dmodel takes into account the

delta shape of the tundish, and gives a better picture of the

bubble tracks as compared to the previous 2D model.

The spread of the bubble column can be correlated to the

area of the exposed eye, using the 3D model. This was not

possible with the 2D model. While it is very true that the

amount of shroud gas should be optimized, it is very

difficult in practice. From the results, it is seen that at high

gas flow rates, the area of the exposed eye is more and so

are the chances of greater reoxidation. Also, higher gas flow

rates will increase slag-metal interactions and the slag

droplets, thereby, formed, may become entrained into the

final product, by passing through the SENs. Recently,

Chatterjee and Chattopadhyay[6] compared the tundish

open eye water model results with the estimates obtained

from the correlations for ladle open eye, and concluded

that the mechanism of slag eye formation in a tundish is

different from that in ladles, and hence, a new correlation

needs to be developed for predicting the size of slag eye in a

tundish. They studied the formation of slag eye in an inert

gas shrouded tundish systematically using physical and

mathematical modeling. Their mathematical model pre-

dicted the slag eye area quite well, the error being �17% of

steel research int. 87 (2017) No. 9999 (1 of 12) 1600436


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the experimental measurements. Coupling of the VOF
method with the discrete phase method is a robust

technique to simulate complex three phase flows occur-

ring in inert gas shrouded tundishes. The difference of

non-dimensional area of the slag eye obtained from the

plant trials compared to those obtained from their model

increases with increasing gas flow rates. Chatterjee and

Chattopadhyay[7] performed a large number of experi-

ments to measure the slag eye area in full scale and one-

third scale water models of an inert gas-shrouded tundish

under various operating conditions. Based on the polyno-

mial regression of experimental data, and the method of

dimensional analysis, correlations for diameter of gas

bubbles and plume velocity were developed. Subse-

quently, these results were used to obtain correlations

for the slag eye area, and critical gas flow rate in an inert

gas-shrouded tundish in terms of the operational param-

eters viz., gas flow rate, thickness of the slag and melt

baths, along with the physical properties of the liquids viz.,

kinematic viscosity and density. It was observed that the

dimensionless slag eye area can be expressed in terms of

dimensionless numbers such as the density ratio, Froude

number, and Reynolds number. Chatterjee and Chatto-

padhyay[8] also developed a mechanistic model to predict

open eye size in tundishes and compared them with water

model results.

Some people believe it is a trivial event and has little or

no effect on the performance of the continuous casting

process and final slab or billet product quality. In fact,

most people do not even consider it as a phenomenon to

study or investigate. Some operators believe that there is a

protective layer of argon on top of the TOE because the

argon bubbles escape through the TOE. However,

analyzing the densities and concentrations of the argon

and air at high temperatures above the TOE raises doubts

about the claim of a protective inert layer. In the present

study, the authors have analyzed the formation of open

eyes in tundishes using water modeling and mathemati-

cal modeling, and then compared it with plant trials.

Another model was developed to study the relative

concentration of air and argon gases in the region just

above the open eye. The observations prove that the

tundish open eye event is a serious cause of steel

contamination in tundishes. It is, in fact, a trivial event

but has dire consequences.

2. Experimental Section

2.1. Plant Trials

Plant trials were carried out in two different plants A and B

to analyze the tundish open eye phenomenon. The areas of

the Tundish Open Eye (TOE) were measured using a High

definition video camera. Snapshots were considered from

the video at different time intervals followed by precise

analysis and measurement by using an image analysis

1600436 (2 of 12) steel research int. 87 (2017) No. 9999

software named Image JTM. Other details about the plant

measurements are given below:

1.
Plant A: A four strand delta shaped tundishwith a height
of roughly 1m was analyzed. The steady state liquid

steel flow rate through ladle shroud was 1.2 tonnes

min�1 whereas the steady state liquid steel level in the

tundish was 0.5–0.6m covered with slag. The injection

rate of argon was varied from 5 to 35 SLPM.

2.
Plant B: A much bigger two strand slab caster tundish
was under observation this time. It had a total steel

throughput rate of 5–8 tonnesmin�1. The steady state

liquid steel level in the tundish was roughly 0.8–1.3m

covered with tundish powder which partially melted to

form a slag layer. The sealing of slide gates and ladle

nozzles are not perfect on account of being refractory

structures. Ambient air can easily get sucked in through

these gaps and result in reoxidation of steel. Hence, the

usual practice is to flood argon gas in these regions so as

to create a protective blanket, which prevents any

possible reoxidation. On the downside, argon gas

bubbles themselves can get aspirated inside the tundish

and result into open eyes. Variation of TOE areas could

be observed during the trials indicating aspiration of

varying amounts of argon.

2.2. Physical Modeling

The technique of usingwater tomimic the behavior of steel

has been used extensively in the past to investigate fluid

flows in continuous casting units such as tundish or

mold.[9] Since the kinematic viscosities of water at 298K

and steel at 1873K are almost equal, water can replicate the

flow patterns observed in molten steel. A one-third scale

water model was used to physically simulate the process of

TOE formation in a billet caster tundish. A schematic

diagram of the physical model is shown in Figure 1. The

liquid steel and argon gas were simulated by using water

and compressed air, respectively, whereas the slag phase

was simulated using motor oil. The layer of motor oil was

0.01m thick whose density and viscosity were 851 kgm�3

and 0.196Pa.s, respectively. The top slag layer in the

present water model experiments was chosen based on an

earlier study performed by Chatterjee and Chattopad-

hyay.[7] It was observed in their study that the density ratio

term, “r/Dr,” largely impacts the area of TOE. On the other

hand, the effects of viscosity and surface tension are

meagre. The density ratio for water-motor oil combination

was found to be closest to that of steel-slag combination.

As a result, motor oil was chosen as the top slag layer in the

present experiments.

The steady state height of water was kept at a fixed level of

0.167m.BasedonFroude U2

gL

� �similitude,thewaterinflowrate

was 0.01m3min�1. The immersion depth of the ladle shroud

was 0.02m. Compressed air was injected from the top of the


Figure 1. Schematic diagram showing experimental setup of water model experiments.


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ladleshroud,atvolumetricflowratesrangingbetween2to20%

of water entry flows. High definition video photography was

performedtovisualizethesizesofopeneyes, thus, formed.The

eye areameasurement was performed in away similar to that

of the plant data.

3. Mathematical Modeling

In the present mathematical model, the phenomena

considered were: fluid flow, turbulence, discrete phase

motion, and multiphase flow. The two major assumptions

considered during the mathematical modeling of the three

phase gas-liquid-oil flows in the tundish were:

1.

� 2

The liquid (water) in the calculation domain was an

incompressible and Newtonian fluid.

2.

Sl.

No. Component

Density

[kgm�3]

Viscosity

[Pa-s]

1 Steel 7000 0.007

2 Slag 2560 [10] 0.6 [10]

3 Argon gas� 0.267 –

Interfacial tension between steel and slag¼ 1.16Nm�1 [10]

�Calculated at 1823K considering ideal gas

Table 1. Physical properties of liquid steel, slag and argon phasesat 1823K.

The fluid flow within the shroud was predominantly

bubbly and the formation of discrete bubbles was

observed in the water model experiments. Hence,

bubble breakup or coalescence were neglected, and a

constant bubble diameter of 5mm was considered

(based on ref.[7]).

The entire calculation domain was divided into three

hundred thousand (0.3� 106) hexahedral cells. The usual

practice of performing a grid independency test becomes

unviable in cases of complex flows with steep gradients,

large computational domains or multiphase flows with

complicated interactions between different phases. The

total number of cells has to be increased to an

impractically high value in order to attain grid indepen-

dence, thereby, drastically increasing the computational

time. In the present work, the aforementioned problem

has been dealt with by refining the mesh locally where

changes in flow gradients and effects of multiphase flow

interactions are expected, while using a coarser mesh in

regions of steady flows. Specific cells were marked for

refinement by using two types of adaptation techniques

available in ANSYS FLUENT, namely region adaptation

017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

and boundary adaptation. Inflation layers were used in the

vicinity of the ladle shroud and at the walls of the tundish

to properly resolve the fluid flow near the boundaries. As a

result, the mesh near the top surface was refined using

“region adaptation.” The “boundary adaptation” tool

allowed us to mark cells for refinement up to a specific

distance in the normal direction from the free surface. As a

no-slip condition near the free surface can result in large

gradients, refinement near the free surface is necessary to

capture the effect of boundary flows on the overall

solution. Specifying a certain number of cells created a

“register” which was refined. It also helped to patch the

slag layer on top of the liquid steel in the tundish.

A small time step of 10�4 s was chosen to efficiently

track the formation of the exposed eyes. Gas injections of 2,

4, and 6% by volume through the ladle shroud were

considered, and were modeled as discrete gas bubbles

using the discrete phase model. For the VOF model, steel

and slag phases were chosen as the primary and secondary

phases, respectively. A very thin slag layer of 0.01m was

simulated. The properties of the steel, slag, and argon

phases used are shown in Table 1.

The standard k-e model of Launder and Spalding[4] with

standard wall functions was used to model turbulence,

whereas the Volume of Fluid (VOF),[11] and the discrete

phasemethods[3] were used to track steel/slag interface and

trajectories of gas bubbles in steel, respectively. As a result,



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equations related to these models had to be solved along
with the equations for conservation of mass and momen-

tum. The SIMPLE[12,13] algorithm for pressure–velocity

coupling and first order upwind scheme was adopted for

momentum, k and e equations to obtain the initial steady

state solution. This result was used as an initial value for the

subsequent transientcalculationswhere thePISOalgorithm

was used along with the second order upwind scheme.

3.1. Turbulence Modeling

The standard k-e model was used in the present work to

model the turbulence. Here, e is the rate of turbulent

energy dissipation, while k stands for the kinetic energy of

turbulence per unit mass, and is related to the time

averaged-velocity u0i as follows:

k ¼ 1

2

Xu0i2 ð1Þ

The two extra equations for k and e that need to be

solved are as follows:

Dk

Dt¼ nt

skr2k þ Gk � e ð2Þ

DeDt

¼ nt

ser2eþ e

kðC1Gk � C2eÞ ð3Þ

The parameter Gk is the rate of production of k and is

given by the following equation:

Gk ¼ nt@ui@xj

þ @uj@xi

� �@ui@xj

ð4Þ

Finally, the turbulent and the effective viscosities are

calculated by making use of the following relations:

mt ¼Cmrk

2

eð5Þ

meff ¼ mþ mt ð6Þ

The values for the constants in the standard k-e model

recommended by Launder and Spalding,[4] which are

C1¼ 1.44,C2¼ 1.92,Cm¼ 0.09, sk¼ 1, and se¼ 1.3, and were

used in the present work without any modification.

3.2. Multiphase Flow Modeling

The VOF formulation[11] relies on the fact that two or more

fluids (or phases) are not interpenetrating. For each


additional phase added in the system, a variable, the volume

fractionof thephase, is introducedinthecomputationalcell.

The volume fractions of all phases sum to unity in each

control volume.Thefields for all variables andpropertiesare

represented as volume-averaged values. Thus, the variables

and properties in any given cell are either purely represen-

tative of one of the phases, or representative of a mixture of

the phases, depending upon the volume fraction values.

For tracking interfaces between phases, continuity

equations such as Equation. 7 for the volume fraction of

one or more phases are solved.[14]

1

rq

@

@tðaqrqÞ þ r:ðaqrq~uqÞ� ¼ Saq

�ð7Þ

The volume fraction for the primary phase is not solved,

rather it is computed based on the following constraint:

Xn

q¼1aq ¼ 1 ð8Þ

3.3. Discrete Phase Modeling

The dispersed phase is solved by tracking a large number of

particles, bubbles, or droplets, through the previously

calculated flow field in a Lagrangian frame of reference.

Theparticle or droplet trajectories are computed individually

at specified intervals during the fluid phase calculation. The

exchange of momentum, mass, and energy of the dispersed

phase with the fluid phase is taken into account by

considering two-way turbulence coupling. The basic equa-

tions involved in discrete phase modeling are as follows[14]:

dup~

dt¼ 18mCDRe

24rpd2p

urel~þ~gðrp � rÞ

rpþ 1

2

r

rp

d

dturel~ ð9Þ

Re ¼ rdpurelj j~m

ð10Þ

urel~¼~u� up~ ð11Þ

CD ¼ a1 þ a2Re

þ a3

Re2ð12Þ

3.4. Mass Transport in the Gas Phase

3.4.1. Species Transport ModelingThe region above the open eye in tundish consists of a gas

mixture of O2, N2 and Ar. The local mass fraction Cm of



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each species in O2-N2-Ar gas mixture was predicted by

solving the species transport equation:

@

@xiruiCmð Þ ¼ @

@xirDi;m þ mt

Sct

� �@Cm

@xi

� �þ Si ð13Þ

where the subscript m stands for the species of O2 and Ar,

respectively. Sct is the turbulent Schmidt number, Di,m is

the mass diffusion coefficient for species m in the mixture.

Si is the source term that arises due to chemical reaction. At

first, the species transport equations for O2 and Ar are

solved to get their respective concentrations. N2 is set as

the primary species, so its concentration can be calculated

from the following equation: CN2þ CO2

þ CAR ¼ 1.

3.4.2. Energy EquationThe equation of conservation of energy is solved to obtain

the variation of temperature throughout the calculation

domain:

@

@xiruihð Þ ¼ @

@xiKeff

@T

@xi

� �ð14Þ

Here, Keff is the effective thermal conductivity and h is total

sensible enthalpy of the ideal gas mixture, calculated from

the correlation: h ¼ CpT whereCp is the specific heat of the

mixture.

4. Results and Discussion

4.1. Formation and Evolution of the Open Eye

4.1.1. Plant ObservationsThe formation of exposed eyes in a twin slab caster tundish

and a four strand billet caster tundish are shown in

Figure 2a–f. The observations from Plant A, as shown in

Figure 2e–f, depicts that the TOE area increases with the

increase in argon injection. The trend observed in Plant B

results, as shown in Figure 2a–d, was similar to that of Plant

A.However,nodirectcorrelationcouldbeachievedbetween

the TOEareas and argon gas flow rates as it was not possible

to control the argonflow into the tundish steel onaccount of

indirect argon aspiration. Another interesting phenomenon

is the eccentricity of the TOEs. On careful observation of the

plant pictures, one can notice that all of them depict

formationofTOEs thatarenotconcentricwith respect to the

ladle shroud. From their modeling work, Chatterjee et al.[15]

were able to conclude that even small angular displacement

of ladle shroud relative to the vertical direction can result in

misaligned bubble plume and surface velocity patterns,

leading to eccentric open eyes.

4.1.2. Physical Modeling ResultsThe observations from the one-third scale water model

experiments are depicted in Figure 3. The exposed areas


are seen to increase proportionately with increase in the

gas injection rate. As the gas injection rate increases, the

number density of gas bubbles increase resulting into

higher incoming momentum. As the gas bubbles move

away from the ladle shroud, their momentum gradually

decrease. The buoyancy forces dominate at locations

away from the shroud. Finally, there is a complete

reversal of the bubble flow direction due to the effect of

buoyancy. A balance between the downward convective

flow and upward buoyant flow determines the distance

till which the gas plume penetrates, known as the

“penetration depth”. A greater gas fraction generates

stronger buoyant plume which translates into a bigger

size of the open eye.

4.1.3. Mathematical Modeling ResultsThe change in the shape and size of TOEs predicted from

themathematicalmodel can be seen from the Figure 4 and

5 below. The primary liquid phase is steel, whereas the

overlying phase is slag. The volume fraction of the slag

phase is shown in the entire domain. The regions

consisting completely of the slag phase is shown in red

signifying a volume fraction of 1; while the regions with

liquid steel are shown in blue. The stable shape and size of

TOEs obtained at gas flow rates varying from 2 to 6 percent

of steel flows are shown in Figure 4. The TOE sizes increase

with increasing gas flow rates, showing a pattern similar to

the that observed in plants and water model experiments.

In order to better understand the change in morphology of

the TOEs, its temporal evolution for a gas flow rate of 6% is

depicted in Figure 5. The figure shows how exactly the TOE

changes its shape and size over time. The cause of this

variation is the random oscillation of the bubble plume

underneath, which displaces the slag layer both radially

and vertically. Since the slag layer used in the present

simulation is very thin (� 0.01m thick), it was relatively

easier for the bubble plume to displace it and give rise to

exposed regions of liquid steel which were quite big.

4.1.4. Comparison of ResultsAll the photographs and/or figures obtained from plant

trials, water model experiments and mathematical model-

ing were analyzed using an image analysis software named

Image JTM. The results are shown Figure 6 below. Since the

results obtained from various sources were associated with

tundishes of different scales, both the gas flow rates and

TOE area were non-dimensionalized based on the follow-

ing two relationships.[7]

Non-dimensionalgas f low rate;Q� ¼ Q=g0:5H2:5 ð15Þ

Non-dimensional TOE area;A�e ¼ Ae=hH ð16Þ

The results from the one-third scale mathematical

model agree quite well with the corresponding water


Figure 2. Pictures showing observation of TOE in plants with corresponding exposed areas: a–d): slab caster tundish and e–f): billet castertundish.


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model results.[6] The similarity in results stems from the

fact that the same system, water/mineral oil/compressed

air was considered in both the water modeling and

mathematical modeling cases. Following a similar logic,

the difference in results of the one-third scale mathemati-

cal model predictions from water model results (with

motor oil) can be explained. It can be attributed to the

difference in physical properties, such as density and

viscosity, of the upper slag layers in two cases. The effect of

properties of upper phase on TOE has been explained in

details in one our previous works.[7]

The mathematical model for the full-scale steel/slag

system over predicts the TOE area as the slag layer

thickness considered in the model was very small. A very

thin slag layer of 0.01m was used in the mathematical

model. In such a case, the plume can expand easily as there

is not much resistance from the overlying thin slag phase.

As a result, the oscillating plume easily displaced the thin

slag layer, resulting into TOEs of quite large sizes.

4.2. The Myth of a Protective Argon Layer

Since the flow rate of argon entering into tundish inlet was

unknown, different percentages of the total argon flow rate

at the ladle slide gate were considered in the model. The


argon flow rates considered in this work were under

standard state (298.15K and 1 atm). The liquid steel

temperature at the TOE is 1823K, and the temperature of

argon exiting from the TOE surface was assumed to have

the same temperature as that of the liquid steel. Therefore,

the real argon volume flow rates applied on the TOE

boundary could be calculated based on the ideal gas laws.

The typical temperature contour and density field near

the ladle shroud at the symmetrical plane of the transverse

cross section of the tundish are shown in Figure 7 and 8.

The outer circular diameter of the slag eye was considered

to be 600mm. The argon flow rate at slag eye interface was

set to be 20 SLPM. Although the argon density at standard

state is 1.784 kgm�3, which is greater than that of air

(1.275 kgm�3), the argon temperature at the slag eye

interface was 1823K, resulting in a decreased density of

0.267 kgm�3. As the temperature of air (mixture of O2 and

N2) near the tundish lid region was around 773–973K, its

density became 0.4–0.7 kgm�3, which is heavier than that

of hot argon gas. Therefore, once the hot argon gas was

released from the open eye surface due to bubble bursting,

it would float up immediately because of the buoyancy

force. The hot ladle shroud surface would also help in

raising the temperature of the gas mixture.

The predicted velocity fields of gas mixture at the

symmetrical plane of the tundish longitudinal and


Figure 3. Pictures showing variation of TOE area with gas flow rate in a one-third scale water model. Note: percent signifies percentvolume flow rate of water.


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transversal cross-sections are shown in Figure 9 and 10,

respectively. It was found that the gas flow above the

tundish slag layer was mostly in the horizontal direction.

The ambient air entered the tundish through the tundish

sampler opening and stopper rod opening on the tundish

lid. On reaching the hot TOE region, the air gets heated-up

and moves upwards vertically while mixing with the

released argon gas (argon gas released from the eye due to

bubble bursting). The velocity of the gas mixture increases

until it touches the bottom of ladle, where the flow

direction switches to horizontal.


The calculated contour of the argonmole fraction at the

transverse symmetrical plane of the tundish is shown in

Figure 11. The argonmole fraction above the TOE region is

only around 0.05–0.1, which is clearly not enough to form a

protective layer to cover the liquid steel and prevent it from

getting re-oxidized. The TOE surface in reality is highly

turbulent and oscillating on account of vigorous bubble

bursting on its surface. This factor would further increase

the contact area of liquid steel with oxygen present in air

and enhance oxygen pickup. In the case of lower argon

flow rates of 5 SLPM and 10 SLPM, the calculated argon


Figure 4. Variation of TOE areawith gas flow rate in full-scale billetcaster tundish, obtained from CFD modeling (color map showsvariation of volume fraction of slag phase).

Figure 5. Temporal variation of TOE area for a gas flow rate of 6%of steel flow in full-scale billet caster tundish (area reaches aplateau after simulating for certain time).

Figure 6. Comparison of TOE areas obtained from plant trials,water model experiments and mathematical modeling. Mathe-matical modeling in one-third scale and water model results withmineral oil as upper phase fluid (slag)[6] have been included forcomparison.


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mole fraction above tundish TOE was observed to be less

than 0.05–0.1. As a result, it can be clearly stated that the

argon bubbles released at the TOE is not able to protect the

liquid steel from reoxidation.

The TOE is more or less circular around the ladle

shroud. In order to evaluate the maximum amount of

oxygen which may come into contact with liquid steel and

react, a thin layer of 10mm thickness was defined as the

Slag Eye Reaction Zone (SERZ). Once the oxygen enters the

SERZ, it was considered to react or dissolve into liquid

steel. Therefore, a thin layer of liquid steel of 10mm

thickness above the open eye was setup in the modeling.

The choice of the thickness was based on plant observa-

tions, which showed that the oscillations on the TOE

surface were of similar amplitudes.

It is clearly seen in Figure 9 that the gas mixture’s

velocity near the TOE is in the horizontal direction and

point into the SERZ. All the air coming into contact with

the boundary of the SERZ was considered to be absorbed

by liquid steel in the mathematical model. The corre-

sponding amount of oxygen gas getting absorbed could be

easily obtained by tracking its integral mass flow rate going

into the SERZ boundary. Thus, the total oxygen entering


the SERZ can be determined. This also gives us the total

amount of oxygen involved in reoxidation of liquid steel.

Various diameters of circular TOE with argon flow rates

of 5 SLPM, 10 SLPM and 20 SLPM were considered during

the modeling. The calculated values of total oxygen

entering the SERZ are displayed in Figure 12. With

increase of TOE diameter, the total oxygen amount

entering the SERZ increased linearly. It was also observed

that the total oxygen amount was not sensitive to the argon


Figure 7. Temperature field at transversal cross section.

Figure 9. Local velocity field at the symmetrical plane of the tundish longitudinal cross section.

Figure 8. Density field at transversal cross section.


� 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim steel research int. 87 (2017) No. 9999 (9 of 12) 1600436

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Figure 10. Velocity field at the symmetrical plane of the tundish transversal cross section.


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flow rate when the TOE size was kept constant. As the hot

argon gas possess less density, it always floated upwards.

5. Practical Considerations

It is clear from the above observations that avoiding the

formation of a TOE in an inert gas-shrouded tundish is very

difficult and that will always give rise to oxygen pickup and

higher inclusion counts. The question then is, how to

tackle the problem in real plant practice. The authors have

presented their results in different forums and discussed

with operators. One of the key parameters is the gas

shrouding system. There are various types of shrouding

arrangements, and one of them is the direct injection

Figure 11. Contour of the argon mole fraction field, flow rate of 20


system. In the direct injection system, argon goes directly

into the liquid steel stream, and that is not ideally serving

the purpose of shrouding. However, injecting a critical

amount of argon gas for which there is no TOE formation

can solve the problem. Based on their rigorous water

modeling study, Chatterjee and Chattopadhyay[7] sug-

gested a critical gas flow rate for TOE-free operation as

follows:

Q�c ¼

Qc

g0:5H2:5¼ 4:961� 10�5 ð17Þ

where,Qc�,Qc,H, and g represent non-dimensional critical

gas flow rate, critical gas flow rate, depth of bulk fluid

phase, and acceleration due to gravity, respectively.

SLPM.


Figure 12. Calculated oxygen pickup at different argon flow ratesand various open eye sizes.


FULL

PAPER

However, this correlation needs to be fine-tuned by

considering factors such as temperature and pressure,

which is possible by carrying out more experiments in

metallic systems such as Ga-In, Sn-Bi, etc. followed by

subsequent analyses.

A better arrangement is to have a refractory ring around

the shroud and inject argon through it. A tight gasket seal

should be present to ensure minimal entrapment of argon

into the melt stream. However, even with the refractory

ring system, sometimes argon gets aspirated into the steel

stream, resulting in TOE formation. It is essential to check

if the shroud is seating correctly on the collector nozzle,

and no gaps are present. However, operators also

suggested having corrective measures, which include the

presence of cameras below the ladle so that they can

monitor the size of the eye in the pulpit. Once it reaches a

critical size, the operators can throw in new bags of tundish

powder, to close the open eye and minimize reoxidation.

6. Conclusions

The formation and evolution of open eyes in tundishes are

studied usingmathematical modeling and water modeling,

along with plant trials. Modeling liquid steel/slag/argon

flows using VOFþDPM approach gives satisfactory com-

parisonwithwatermodel andplant data. Physicalmodeling

of a reduced scale tundish using water/oil/air allows us to

properly visualize the transient variation of TOE phenome-

non very well. The trends obtained from both water model

and mathematical model match those observed during

plant trials. Finally, modeling with “Species transport

model”allowsus topredict thevariationofoxygen,nitrogen,

and argon gas concentration over the TOE region. The

calculations help us to refute the claim of presence of any

protective argon atmosphere over the exposed eye region.


Nomenclature

k Kinetic energy of turbulence per

unit mass, m2 s�2

u0i Time averaged-velocity in the

direction xi, m s�1

xi Cartesian space coordinate

e Rate of energy dissipation, m2 s�3

vt Kinematic viscosity of fluid,

m2 s�1

C1, C2, Cm, sk and se Empirical Constants

GK Rate of production of k, kgms�3

mt Turbulent viscosity, kgm�1 s�1

r Density of the bulk fluid phase,

kgm�3

Dr Density difference between lower

and upper phase fluids, kgm�3

meff Effective viscosity, kgm�1s�1

m Viscosity of the fluid, kgm�1 s�1

up Particle velocity, m s�1

CD Drag coefficient

dp Particle diameter, m

urel Fluid velocity relative to the par-

ticle, m s�1

rP Density of the particle, kgm�3

a1, a2, a3 Constants

u mean fluid phase velocity

u0ðtÞ fluctuating fluid phase velocity

component

z normally distributed random

number

r uniform random number, 0< r

< 1

te time scale

t particle relaxation time

TL fluid Lagrangian integral time

Le eddy length scale

Re Reynolds number, rdLm

U Characteristic velocity, m s�1

L Characteristic length, m

Qc� Non-dimensional critical gas flow

rate

Qc critical gas flow rate, m3 s�1

H depth of bulk fluid phase, m

g acceleration due to gravity, m s�2

SERZ Slag Eye Reaction Zone

TPM Tonnes Per Minute

SLPM Standard Liters Per Minute

DPM Discrete Phase Modelling

TOE Tundish Open Eye

steel research int. 87 (20

Acknowledgements

The authors would like to thank ANSYS Inc., SimuTech

Group for their support towards the mathematical

modeling research performed in this study.

17) No. 9999 (11 of 12) 1600436


FULL

PAPER

Received: November 1, 2016; Revised: December 19, 2016

Keywords: mathematical modeling; physical modeling;

reoxidation; steelmaking; tundish open eye

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