numerical investigation of fluid flow and heat transfer...

www.steel-research.de

FULL

PAPER
Numerical Investigation of Fluid Flow and Heat
Transfer Phenomenon Inside a Single StrandTundish of Slab Caster

Anurag Tripathi,� Anil Kumar, Satish Kumar Ajmani, J. B. Singh, and Vinay V. Mahashabde

The tundish design is an important factor which governs the steel quality. An effectivetundish design can enhance inclusion flotation through development of required liquid steelflow pattern. The well-shaped bottom is one of the developments in the area of tundishdesign. This tundish is in practice and has significantly contributed towards improving theproductivity of the steel plants. The current work investigates the liquid steel flowphenomenon in this type of tundish. The 3D CFD model was used for present investigation.The results obtained shows that well-shaped bottom tundish produces better performanceas compared to tundishes having flat bottom. The effect of bath height, throughput anddepth of well on flow behavior inside the tundish having well-shaped bottom was studied inthe current work. The results of RTD analysis show the need to optimize these parameters.CFD simulations were also performed to capture the non isothermal phenomenon in awell-shaped bottom tundish.

1. Introduction

The increase in productivity without affecting the

quality is a major challenge among the steel makers.

The separation of inclusion frommolten steel is required

to achieve the superior quality of steel. The tundish is a

steel refining metallurgical vessel used as a buffer during

continuous casting. The liquid steel flow phenomenon

in a tundish governs the inclusion flotation charecter-

istics. RTD (Residence time distribution) characteristic

is an established criterion for predicting the inclusion

separation in the tundish. Ahuja and Sahai[1] have

postulated that surface directed flow enhances the

inclusion separation ratio. It is expected that flow

without hindrances facilitate the inclusion flotation.

Plug volume in RTD analysis represents the hindrances

free flow region of the tundish. Estimation of dead

volume in RTD analysis gives the percentage of

unutilized volume of the tundish. Inclusion trapped in

dead volume can not float out.

There are various studies reported in the literature

about the effect of operating parameters on inclusion

separation characteristics.[2–4] The increase in production

results in an enhanced throughput for tundish. Here,

[�] A. Tripathi, A. Kumar, S. K. Ajmani, J. B. Singh, V. V. MahashabdeResearch and Development, Tata Steel, Jamshedpur 831001, IndiaEmail: [email protected]

DOI: 10.1002/srin.201400530

1558 steel research int. 86 (2015) No. 12

throughput means rate at which the liquid steel flows out

of the tundish. Throughput in steel plant is generally

measured in tonnes/minute (tpm). Hence, increase in

throughput leads to a loss of residence time for fluid

elements inside the tundish. The bath height of liquid steel

in the tundish can drop below optimum level during ladle

change over operation, due to rise in throughput. The

change in throughput can also affect the fluid flow

characteristics of tundish. Thus, metallurgical and refrac-

tory performance of tundish can detoriate with increase in

productivity. The increase in volume of tundish is required

to compensate the loss in residence time. The volume

increase can either be incorporated through change in

shape or dimensions of tundish.

Investigators have reported various studies on fluid

flow behavior using physical and mathematical modeling

in a tundish.[5–9] They came up with the various designs of

tundish, such as rectangular tundish, tundish with

sloping sides, curved shape tundish, wedge shaped

tundish, etc.

The well-shaped bottom is another innovation in the

area of tundish design. It is being used, successfully, by the

steelmakers around the world. However, the different

aspects of this tundish design are still unexplored in the

research community. The merits of the well-shaped

bottom design and its effectiveness at higher throughput

is still an area of research among steel making commun-

ity.[10–12] The investigations were performed in the present

work to understand the flow phenomenon in this type of

tundish. Its comparative analysis was performed with

� 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim


FULL

PAPER

conventional flat bottom tundish, which confirms the

superior performance of former. The parametric inves-

tigation performed for this tundish shows the need to

optimize its dimensions.

Research is currently going on to understand the non-

isothermal flow behavior inside the tundish. Researchers

are trying to capture the effect of change in inlet

temperature on flow behavior.[13,14] Induction heating

inside the tundish is another area where recent research

investigations are being performed.[15,16] Thus, simula-

tions were performed to capture the non-isothermal effect

in the present work.

Figure 1. Top and sectional view for symmetrical half of tundishes


2. Model Development

2.1. Geometrical Description

The current investigation explores the liquid steel flow

phenomenon in a tundish with and without well-shaped

bottom. The CFD simulations were performed for sym-

metricalhalfof thetundish.Figure1showsthetopandvertical

sectional view of symmetrical plane for tundishes with and

without well-shaped bottom. The top view of both the

tundishesare similar. Thedimensionsof tundishcaneasilybe

visualized from Figure 1. The pouring chamber used for

with and without well-shaped bottoms.

steel research int. 86 (2015) No. 12 1559


FULL

PAPER
present simulation and its dimensions can be seen from
differentviewsinFigure2.Table1showsthesetofsimulations

performed for isothermal and non-isothermal cases.

2.2. Governing Equations

The 3D CFD model was used to compute the flow field in

the tundish. The tracer dispersion equation was solved for

Figure 2. Top and sectional view of pouring chamber.


computed velocity field to calculate RTD characteristics.

Table 2 shows the expression for the RTD characteristics

used in the present work. The expression of dead volume

assumes that flow in dead region is almost stagnant and

entry of flowing fluid in this region is negligible. The

calculation of plug volume is done using the expression

shown in Table 2. Dispersed plug volume is another

parameter used in some of the research investigations to


Cases Tundish

shape

Type Throughput

[tpm]

Tundish

bath

height[m]

Well-shaped

bottom

depth[m]

Inlet

Temperature

[K]

Bath

Temperature

[K]

1 Flat bottom Isothermal 3.5 1.13 0.00 Isothermal Isothermal

2 Well-shaped

bottom

Isothermal 3.5 1.13 0.34 Isothermal Isothermal

3 Well-shaped

bottom


4 Well-shaped

bottom


5 Well-shaped

bottom


6 Well-shaped

bottom

Isothermal 2 1.13 0.34 Isothermal Isothermal

7 Well-shaped

bottom


8 Well-shaped

bottom

Isothermal 3 1.13 0.34 Isothermal Isothermal

9 Well-shaped

bottom


9a Well-shaped

bottom

Non-Isothermal 3.5 1.23 0.34 1820 1820

9b Well-shaped

bottom

Non-Isothermal 3.5 1.23 0.34 1840 1818.5

9c Well-shaped

bottom

Non-isothermal 3.5 1.23 0.34 1800 1818.5

10 Well-shaped

bottom


11 Well-shaped

bottom


Table 1. No. of cases chosen for simulation.

Sl. No. RTD characteristics Expressions

1 Theoretical residence time [tr] Volume of tundish/volumetric flow rate

2 Actual mean residence time (tm) tm ¼P

CtDtPCDt

3 Average break through time (tmin) First appearance of tracer at the outlet

4 Fraction of plug volume (VPV) VPV¼ tmin/tr

5 Fraction of dead volume (VDV) VDV¼ 1-tm/tr

6 Fraction of mixed volume (VMV) VMV¼ 1-VPV–VDV

Table 2. Expressions for RTD characteristics.


� 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim steel research int. 86 (2015) No. 12 1561

FULL

PAPER


FULL

PAPER
characterize the plug flow region in the tundish. However,
researchers have recommended the use of dispersed plug

volume in cases where there is a significant deviation from

ideally expected RTD curve.

The RTD analysis in present work was only performed

for isothermal conditions. The details of the model

equation were already published in our previous paper.[8]

The momentum and heat transfer equation for non-

isothermal behavior is added to the previously developed

model. The steady state isothermal equation was solved to

obtain the flow field for RTD analysis. The transient heat

transfer equation was solved to get the thermal response

for hot and cold steel input.

The governing equations solved for simulation are

presented below:

Continuity:

@r

@tþr:r �U ¼ 0 ð1Þ

Isothermal Momentum equation:

rD�U iDt ¼ � @�P

@xi� @

@xjðtlij þ ttijÞ þ rgi þ Si (2)

where laminar shear stress, tlij is given by:

tlij ¼ �m @�U i

@xjþ @

�U j

@xiÞ

�ð3Þ

and Reynolds shear stress, ttij is expressed as:

ttij ¼ � �ru}i u}j ¼ �mt @

�U i

@xjþ @

�U j

@xiÞ

�ð4Þ

Here �U i is the ith component velocity vector, and i & j

vary for x, y,and z direction.

Si in Equation (2) is a momentum source term in ith

direction.

Tracer dispersion:

r@ �C

@tþ r

@ð �U i�CÞ

@xi¼ @

@xi

meff

sC

@ �C

@xi

� �ð5Þ

Turbulent Kinetic energy:

rDk

Dt¼ Dk þ G � re ð6Þ

Rate of dissipation:

rDe

Dt¼ De þ C1G

e

k� C2r

e2

kð7Þ

where


Dw ¼ @

@xjmþ mt

sw

� �@w

@xj

� �ð8Þ

Here w is k for (6) and e for (7)mt ¼ rCmk2

eand G ¼ ttij@

�U i@xj

(9)

Here, C1¼ 1.44, C2¼ 1.92, Cm¼ 0.09, sc¼ 1, sk¼ 1,

se¼ 1.3

Non isothermal momentum equation:

rD�U i

Dt¼ � @�P

@xi� @

@xjðtlij þ ttijÞ þ rgið1� bðT � T ref ÞÞ ð10Þ

Here, b (Thermal expansion coefficient) is 0.0002 (1/K)

Energy equation:

r@h

@tþ r

@ð �U ihÞ@xi

¼ @

@xiKeff

@�T

@xi

� �ð11Þ

2.3. Boundary Conditions

The boundary conditions were similar to one used in

published papers.[8,9] No-slip and standard wall function

was used at the walls. Symmetry boundary condition (zero

gradients for all the variables normal to plane) was applied

at the symmetry plane. The turbulent intensity of 2% was

defined at the inlet. Zero shear stress at the free surface and

pressure of 1 atm at the outlets was fixed for present

simulation. A zero gradient for tracer concentration was

applied on the walls, free surface and outlets.

The heat loss from the outer surface of the tundish wall

and top surface takes place through convection and

radiation. The net heat flux at the wall can be calculated

through Equation (12). Here, TWL and Text represents

tundish wall temperature (outer surface) and ambient

temperature, respectively. The radiation losses from

tundish walls and top surface are neglected in the present

work.

q ¼ hextðT ext � TWLÞ ð12Þ

The heat transfer coefficient in Equation (12) was

obtained by tuning the model with temperature of

liquid steel measured in the plant. The inlet temper-

ature of the liquid steel was taken from the LD2 plant of

Tata Steel Ltd.

2.4. Numerical Procedure

The computational domain was constructed through

gambit software. This domain was then discretized into



FULL

PAPER

small cells. The finite volume technique was used to solve

the set of governing equations in these cells. The

commercial CFD package (FLUENT) was used to solve

the discretized equation. The velocity profile was

generated inside the computational domain. The tracer

dispersion equation was then solved to get the data for

RTD analysis. SIMPLE algorithm was used for pressure–

velocity coupling and higher order schemes were used for

discretization of equations. The density and viscosity of

molten was kept constant at 7100 kgm�3 and 0.006482 kg

ms�1, respectively, throughout the computational

domain for isothermal simulations. The specific heat

and thermal conductivity used for non-isothermal

simulations are 750 J kg-K�1 and 41W m-K�1,

respectively.

3. Model Validation

The validation of the computational method was estab-

lished with the experiment data reported in the literature.

The matching between experiment and computation was

reported in our previous papers.[8]

The model validation was also performed by carrying

out the water modeling experiment for the well-shaped

bottom tundish shown in Figure 1. Figure 3a shows the

experimental set-up used for performing the experi-

ment. The tundish used in the experimental setup is 0.6

scale down model of the industrial tundish. Exper-

imental setup is composed of a model tundish, a ladle,

two water tanks, a water supply, a water pump, a digital

flow meter, a tracer injector, a conductivity meter

probe, a conductivity meter, a data logger interface, and

a desktop computer. Water was transferred from the

water tank to ladle through water pump and then from

ladle to the tundish. Once the readings and tundish

level were stable, 36 g of KCl solution was injected as a

pulse into the inlet stream. The data recorded from

conductivity meter as a function of time were then

converted into concentration profile. The concentra-

tion and time data were converted into their dimen-

sionless form to get RTD curve.

The comparison of computationally obtained results

with experiments was done for throughput of 2.5 tpm.

Figure 3b shows the comparison of predicted and

experimentally obtained RTD curves. The plug volume

and dead volume computed at 2.5 tpm were 19 and 7%,

respectively, however from experiment these volumes

came to be 20 and 6%, respectively. Thus, the predictions

appear to be in good agreement with water modeling

experiments. The plant observation shows 1–2 8C temper-

ature drop between inlet and outlet due to heat losses from

walls and top surfaces. The prediction made by non-

isothermal model was found to be in agreement with the

plant observations.


4. Results and Discussion

The flow patterns were developed through 3D CFD

simulation for all the cases shown in Table 1. The RTD

analysis was then performed for the computed velocity

field. This RTD analysis was correlated with the flow

patterns to conclude the comparative study of tundishes

with and without well-shaped bottom. The analysis was

also done to investigate the effect of tundish dimensions

and throughput. The results obtained from the simulation

are presented in the subsequent steps.

4.1. Comparison of Tundishes With and Without Well-Shaped Bottom

The liquid steel flow inside the tundish is altered by the

change in the shape of tundish. Thus, the analysis was

performed for flow patterns developed in the tundishes

(shown in Figure 1). Simulations were carried out for

Cases 1 and 2 shown in Table 1 to compare the

performance of tundishes with and without well-shaped

bottom. Figure 4a shows the comparison of flow patterns

at vertical symmetrical plane for Cases 1 and 2. The flow

phenomenon for Case 2 appears to be gradual and

smooth as compared to intense flow for Case 1. The

development of circulatory flow near the pouring region

of the tundish is desired in a tundish. However, the type of

large eye circulatory flow developed in the tundish of Case

1 can also lead to dead zone formation. The high velocity

flow vectors occupy comparatively larger region for Case

1 in Figure 4a. The circulatory loop observed for flat

bottom tundish of Case 1 was not seen in tundish of Case

2. The movement of flow vectors towards the pouring

region can be seen for Case 2 in Figure 4a. The flow

vectors appear to be captured in the pouring region for

this tundish. This leads to reduction in velocity magni-

tude of flow vectors moving towards the outlet. The

presence of well-shaped bottom in tundish of Case 2

results in further reduction of flow velocity near the outlet

and leads to smooth discharge of liquid steel.

Figure 4b shows the comparison of flow vectors at

meniscus for tundishes with and without well-shaped

bottom. The velocitymagnitude appears to be quite high in

most of the region for tundish of Case 1 as compared to

that of Case 2. The similarity in the circulatory cell

developed above the outlet for both the tundishes can be

seen from Figure 4b. However, the eye of the circulatory

cell appears to be large for flat bottom tundish of Case 1.

The comparison of flow patterns in Figure 4a,b shows that

flow phenomenon in tundish of Case 2 is comparatively

closer to desired fluid flow characteristics.

The RTD analysis of flow patterns described in

Figure 4a,b was required to draw inferences about the

superior performance of tundish having well-shaped

bottom. Figure 5a shows the comparison of RTD curve

of tundishes with and without well-shaped bottom. The


Figure 3. a) Experimental setup used to perform water modeling experiment for well-shaped tundish. b) Comparison of Predicted RTDcurve with the one obtained from water modeling experiment.


FULL

PAPER

sharp peak for tundish of Case 1 reflects the presence of

short circuiting. The lower tmin for this tundish results in

reduced percentage of plug volume as compared to one

obtained for tundish of Case 2. The shift in peak of the

curve towards the centre for tundish of Case 2 leads to

reduced dead volume as compared to that of Case 1.


Table 3 shows the RTD characteristics of all the cases

described in Table 1. The high ratio of plug to dead volume

for tundish of Case 2 as compared to that of Case 1 can be

noticed from Table 3. Thus, RTD analysis confirms the

superiority of tundish with well-shaped bottom over

conventional flat bottom tundish.


Figure 4. a) Flow pattern at vertical symmetrical plane (Z¼ 0) for tundish (without well-shaped bottom) and tundish (with well-shapedbottom). b) Flow pattern at top surface for tundish (without well-shaped bottom) and tundish (with well-shaped bottom).


FULL

PAPER

4.2. Effect of Well Depth on Flow Patterns in a Tundish

The well-shaped bottom of tundish, acts as a flow

modifier near the outlet. Its strong role in improving the

flow characteristics within well-shaped tundish was


already established in previous section. It was felt that

investigation of well depth is required for further

improvement of flow characteristics in this type of

tundish. The well depth was varied from 0.15 to 0.45m to

explore its effect on flow characteristics. Cases 2–5 in


Figure 5. RTD curves obtained from simulation of different conditions.

Cases

Sl. No. RTD characteristics 1 2 3 4 5 6 7 8 9 10 Case 11

1 Mean residence time [s] 536 475 468 505 384 837 670 552 570 585 557

2 Theoretical residence time [s] 700 500 600 555 480 900 720 600 600 636 671

3 VPV 0.12 0.16 0.13 0.12 0.15 0.19 0.19 0.17 0.15 0.13 0.12

4 VMV 0.64 0.79 0.65 0.79 0.65 0.74 0.74 0.75 0.80 0.80 0.72

5 VDV 0.24 0.05 0.22 0.09 0.20 0.07 0.07 0.08 0.05 0.07 0.16

6 VPV/VDV 0.51 3.2 0.59 1.33 0.73 2.7 2.7 2.1 3 1.9 0.75

Table 3. RTD characteristics for all the isothermal cases.


1566 steel research int. 86 (2015) No. 12 � 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

FULL

PAPER


FULL

PAPER

Table 1 was simulated to investigate the role of well

depth.

Figure 6 shows the comparison of flow patterns at

vertical symmetrical plane (Z¼ 0) for all the four cases. It

was established that the well-shaped bottom breaks large

eye circulatory loop and divides the flow in opposite

directions. The extent of this flow division depends upon

Figure 6. Flow pattern at vertical symmetrical plane (Z¼ 0) for diffe


depth of well. This phenomenon can be understood by the

observation of flow patterns in Figure 6. The increase in

well depth results in increased region of flow division. The

flow vectors inmost of the region for Case 3moves towards

outlet with comparatively higher velocity, as observed in

Figure 6. However, there was a presence of thin region of

low velocity, near tundish bottom for this Case. The

rent well depths in a tundish.



FULL

PAPER
velocity vectors in this region moves towards the pouring
region. The relatively lowmagnitude velocity of this region

can lead to dead zone formation.

The flow pattern developed for Case 4 shows the effect

of increase in well depth. The rise in well depth results in

increased number of flow vectors moving towards the

pouring region. It also leads to reduction in velocity

magnitude of flow vectors towards outlet. The reduced

difference between high and low magnitude velocity can

be noticed for Case 4 as compared to Case 3. Thus, the

dead zone formation will be reduced for this case. Case 2

in Figure 6 shows the flow pattern for further increase in

well depth. The increased well depth again leads to

increase in flow diversion towards the pouring region.

The difference between two extremes of velocity magni-

tude was found to be further reduced for Case 2 in

Figure 6.

The improvement in flow patterns inside the tundish

with rise in well depth inspires us to perform CFD

simulation for further increase in depth. Case 5 in Table 1

presents the well depth simulated for this study. The flow

pattern for Case 5 in Figure 6 confirms our earlier

investigation about flow diversion and velocity magnitude.

However, the velocity magnitude appears to be reduced to

a level of stagnant zone. Hence, the increase in well depth

beyond certain optimum level can lead to enhanced region

of dead volume.

It can be further noticed from the Figure 6 that flow

pattern near the meniscus for Cases 3 and 2 show some

similarity. Cases 4 & 5 in Figure 6 also show some similarity

in flow pattern near meniscus with regard to location of

flow division. The momentum losses of the streams due to

increase in well depth appears to be the reason behind

such type of observation. The drop in velocity with

increase in well depth results in collision of two opposite

streams at the centre as seen for Case 4 in Figure 6. The

further increase in well depth leads to comparatively

higher momentum loss for the stream coming from region

above outlet. Therefore, flow division in Case 2 was

observed farther from the centre (near the outlet). It was

found that even further increase in well depth (Case 5 in

Figure 6) results in comparatively larger drop in momen-

tum for the stream coming from pouring region. Therefore

flow division was again observed at centre for Case 5 in

Figure 6.

The RTD analysis was performed for these four cases to

conclude the well depth investigation. Figure 5b shows the

RTD curve for all the four cases. The RTD characteristic for

these curves can be seen from Table 3. The sharp and high

peak concentration can be noticed for Cases 3and 5 in

Figure 5b. This reflects the presence of larger dead volume

for these cases as compared to Cases 2 and 4. Table 3

confirms our observation. The two peaks in RTD curve for

Case 4 shows the degradation of its flow characteristics as

compared to Case 2. The high ratio of plug to dead volume

for Case 2 in Table 3 confirms its superiority over other

cases simulated for well depth investigation.


4.3. Effect of Throughput on Flow Phenomenon in aTundish Having Well-Shaped Bottom

The steel industry is increasing its productivity to meet the

continuous rise in demand of its product. It is a challenge

for the steel makers to increase production and maintain

the desired steel quality within the existing setup. Thus, the

present designs of metallurgical vessels needs to be

evaluated with respect to throughput.

The fluid flow investigation was performed for through-

put range of 2–3.5 tpm in a tundish having well-shaped

bottom. Cases 2, 6, 7, and 8 in Table 1 were simulated for

this investigation. Figure 7 shows the flow vectors at

meniscus for all the four cases having different through-

puts. Though, the flow pattern appears to be almost similar

for all the cases in Figure 7. However, the small increase in

size of eye developed above outlet was noticed with

increase in the throughputs from 2.0 to 3.5 (Figure 7). The

velocity scale in Figure 7 for different cases represents the

maximum velocity obtained at meniscus for particular

case. The rise in the magnitude of the maximum velocity

with increased throughput can be noticed in Figure 7. The

RTD analysis for different throughputs strengthens our

earlier discussion. The RTD curve in Figure 5c appears to

be almost similar for all the throughputs. The value of RTD

characteristics in Table 3 was found to be close for all the

cases. The minor difference in the ratio of plug to dead

volume was noticed for all the cases. However, there was a

significant difference in the values of theoretical residence

time for different throughputs. The change in velocity

magnitude and theoretical residence time was found to be

the whole effect of throughput.

4.4. Effect of Bath Height on Flow Characteristics inTundish Having Well-Shaped Bottom

The impact of rising demand of steel on its quality was

already discussed in previous section. The loss in

theoretical residence time due to increased throughput

can only be compensated through increase in capacity of

tundish. The superiority of well-shaped bottom tundish

over that of conventional flat bottom tundish was already

discussed. Therefore, it was felt that tundish capacity

should be increased through change in dimensions of well-

shaped bottom tundish. The tundish bath height needs to

be maintained at the desired level during ladle changeover

operation. Hence, bath height was found to be an ideal

parameter to incorporate dimension change. Though,

theoretical residence time will be enhanced through

increased bath height, but flow characteristics of tundish

can be affected.

CFD simulation was performed to investigate the effect

of bath height on flow phenomenon in well-shaped

bottom tundish. Cases 2, 9, 10, and 11 of Table 1 present

the bath height simulated for this study. Figure 8 shows the

flow patterns at vertical symmetrical plane (Z¼ 0) for


Figure 7. Flow pattern at meniscus for different throughputs in a well-shaped bottom tundish.


FULL

PAPER

different bath heights. The major variation in the flow

patterns between different cases can be seen in the vicinity

of the pouring region. Flow vectors generally circulate

within the pouring region, as observed from Figure 8. The

increase in bath height results in diversion of these flow

vectors towards the outlet. The movement of flow vectors

becomes stronger at high values of bath height. The


increase in differences between two extremes of velocity

magnitude with increase in heights can also be noticed

from Figure 8. Thus, the dead zone formation will be

enhanced at bath height above optimum level.

The RTD curve for this study can be seen from

Figure 5d and its characteristics from Table 3. The RTD

curve looks similar for all the cases except Case 11. The


Figure 8. Flow pattern at vertical symmetrical plane (Z¼ 0) for different bath heights of well-shaped bottom tundish.


FULL

PAPER

sharp and high peak concentration for Case 11 reflects the

presence of short-circuiting and dead zone. The RTD

characteristics in Table 3 also show the significant rise in

dead volume at bath height of 1.35m. The ratio of plug to

dead volume was found to be decreased with increase in

bath height. However, the difference in this ratio was


found to be minor for Cases 2 and 6. Thus, the theoretical

residence time can be improved by 100 s without any

major loss in flow characteristics by increasing bath

height up to 1.23m. However, the increase in bath height

beyond certain level can hamper the metallurgical

performance of this tundish.


Figure 9. Thermal response of liquid steel to hot and cold steel input.


FULL

PAPER

4.5. Effect of Heat Transfer on Flow Field Inside theTundish

It was felt that heat transfer can have a role on flow

behavior inside the tundish. Thus 3D steady state

simulation was performed to capture the temperature

drop due to heat losses from wall and top surfaces of the

tundish. The Case 9 of Table 1 was chosen for the heat

transfer analysis.

The results obtained from steady state simulation

shows 2 8C drop in temperature between inlet and

outlet. The plant observation suggest that temperature

drop at any particular instant of time is influenced by

the temperature of incoming steel from the ladle.

Hence, the study was performed to establish the impact

of change in inlet liquid steel temperature on thermal

contours inside the tundish. The simulation was

performed by rising and dropping inlet temperature

by 20 8C. Case 9a–c in Table 1 provides the details of the

simulation for hot and cold steel input inside the

tundish. Figure 9 shows the thermal response at the


outlet after hot and cold steel input. It can be noticed

that it takes 25min (approx) for tundish to attain steady

state temperature. Figure 10 shows the thermal contour

at vertical central plane for hot and cold steel input. It

appears that thermal layer develop due to hot and cold

step input will alter flow field at any particular instant of

time and hence the flow characteristics of tundish might

be changed.

5. Conclusion

The liquid steel flow investigation in tundish having well-

shaped bottom was performed through numerical model-

ing. The results were compared with conventional flat

bottom tundish. The following conclusions are obtained

from this study:

1.
CFD investigation concludes that the fluid flow
characteristics in tundish having well-shaped bottom


Figure 10. Thermal contours at vertical sectional plane for hot and cold steel input.


15

FULL

PAPER

are superior as compared to conventional flat bottom

tundish. The well-shape bottom has an effective role in

the performance of tundish.

2.
CFD investigation shows that the well depth should be
optimized for better performance of tundish.

3.
The flow patterns and RTD curve in well-shaped
bottom tundish were found to be similar for all the

throughputs. It can be concluded that change in

throughput can only alter the velocity magnitude and

theoretical residence time.

4.
It was found that loss in residence time due to increased
throughput in well-shaped bottom tundish can be

recovered through increase in bath height. However,

the increase in bath height beyond certain optimum

level will hamper the flow characteristics inside the

tundish.

5.
The heat transfer analysis of well-shaped bottom
tundish shows that tundish will take sufficient amount

of time to attain a new steady state after step input of

hot and cold steel. The thermal stratification will

result in a flow driven by natural convection. There-

fore the flow field will be influenced by thermal field.

The future investigation will try to quantify the

influence of thermal effect on flow characteristics of

the tundish.


5.1. Nomenclature

�C: Mass fraction of the injected tracer

C Average concentration of tracer from outlet (kg/m3)

H Bath height of the tundish (m)

L Length of half tundish (m)

k Turbulent kinetic energy (m2/s2)

P Pressure (Pascal)

RTD Residence time distribution (s)

t Time (s)

tm Actual mean residence time (s)

tmin Average breakthrough time (s)

tr Theoretical mean residence time (s)�U : Velocity (m/s)

u0 Velocity fluctuation (m/s)

V Volume (m3)

Text External temperature (K)

TWL Outside surface temperature of Tundish wall (K)

hext Heat transfer coefficient (Watt/m2K)

q Heat flux (W/m2)

5.2. Greek Symbols

r Density of steel (kg/m3)

m Molecular viscosity of steel (kg/ms)



FULL

PAPER

mt Turbulent viscosity of steel (kg/ms)

meff Effective viscosity of steel (kg/ms)

sC Turbulent Schmidt number

e Rate of dissipation of turbulent kinetic energy (m2/s3)

tl Laminar shear stress

tt Turbulent shear stress

5.3. Suffix

i, j, k Three Cartesian coordinate directions x, y, and z

DV Dead volume

MV Mixed volume

PV Plug Volume

Received: November 17, 2014;

Published online: February 25, 2015

Keywords: well-shaped bottom; plug volume; dead

volume; mean residence time

References

[1] Y. Sahai, R. Ahuja, Ironmaking Steelmaking 1986, 13, 241.


[2] S. Singh, S. C. Koria, ISIJ Int. 1993, 33, 1228.

[3] S. Singh, S. C. Koria, Ironmaking Steelmaking 1993,

20, 221.

[4] S. Singh, S. C. Koria, ISIJ Int. 1994, 34, 784.

[5] D. Mazumdar, G. Yamanoglu, R. I. L. Guthrie, Steel

Res. 1995, 66, 14.

[6] D. Mazumdar, G. Yamanoglu, R. I. L. Guthrie, Steel

Res. 1997, 68, 293.

[7] Y. He, Y. Sahai, Metall. Trans. 1987, 18B, 81.

[8] A. Tripathi, S. K. Ajmani, ISIJ Int. 2005, 45, 1616.

[9] P. K. Jha, S. K. Dash, S. Kumar, ISIJ Int. 2001, 41,

1437.

[10] A. Cwudzinski, Steel Res. Int. 2014, 85, 902.



[13] A. Zamora, R. D. Morales, M. Diaz_Cruz, J. Palafox-

Ramos, L. Gascia Demedices, Int. J. Heat. Mass Trans.

2003, 46, 3029.

[14] R. D. Morales, S. Lopez Ramirez, J. Palafox-Ramos,

D. Zacharias, ISIJ Int. 1999, 39, 455.

[15] Q. Wang, B. K. Li, F. Tsukihashi, ISIJ Int. 2014, 54,

311.

[16] Q. Wang, F. S. Qi, B. K. Li, F. Tsukihashi, ISIJ Int. 2014,

54, 2796.


numerical investigation of fluid flow and heat transfer...

Documents