mathematical modelling of flow control in a tundish using electro-magnetic forces

Applied Mathematical Modelling 35 (2011) 5075–5090

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Applied Mathematical Modelling

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Mathematical modelling of flow control in a tundish usingelectro-magnetic forces

Anurag TripathiResearch & Development, Tata Steel, Jamshedpur 831001, India

a r t i c l e i n f o

Article history:Received 7 October 2010Received in revised form 14 April 2011Accepted 15 April 2011Available online 24 April 2011

Keywords:Slab casterTundishPlug volumeMean residence timeInclusion flotationElectro-magnetic forces

0307-904X/$ - see front matter � 2011 Elsevier Incdoi:10.1016/j.apm.2011.04.028

E-mail address: [email protected]

a b s t r a c t

The control of flow in a tundish is important for improving the quality of the steel. Dams,Wiers and Pouring chamber are some of the devices used for controlling the flow in thetundish. The investigation about the role of electromagnetic forces as a replacement forthese devices is an objective for the present work. Thus, 3-D MHD simulation was per-formed to study the effect of electromagnetic forces on flow behaviour in the tundish.The MHD model developed for carrying out the simulation was validated with the analyt-ical solution of the Hartman problem. The results obtained shows improvement in thedesired characteristics for inclusion flotataion with magnetic flow modifier of optimumstrength of magnetic field.

� 2011 Elsevier Inc. All rights reserved.

1. Introduction

The quality of the steel is becoming an important parameter for maximising the profit in the steel market. The separationof inclusion from the molten steel is a way to achieve the superior quality of steel. Tundish metallurgy is a step in the processof steel making for removal of inclusion and thus improving the quality of steel. Inclusion flotation inside the tundish de-pends upon the establishment of flow behaviour in the tundish. RTD characteristics is an establish criteria for predictingthe inclusion separation in the tundish. Ahuja and Sahai have postulated certain RTD characteristics for achieving the max-imum inclusion separation ratio [1–3]. The control of fluid flow is a way to achieve the desired characteristics of RTD in thetundish. The fluid flow in the tundish is controlled by different types of flow modifiers. The traditional flow modifiers usedinside the tundish are dams and weirs. Dams and weirs have improved the flow characteristics, but resulted in a reduction ofeffective volume.

The design of effective flow modifier is a recent area of research in tundish metallurgy. The understanding of flow phe-nomenon inside the tundish is pre-requisite for designing of flow modifiers. Fluid flow phenomenon inside the tundish wasinvestigated by various researchers. The studies done by various researchers have suggested the strong influence of pouringregion on the flow behaviour in the tundish. The latest designs of flow modifiers are based on suppressing the flow near thepouring region of the tundish. RD. Morales et al. has discussed the role of turbulence inhibitor in suppressing the turbulencein the incoming stream [4]. Pouring chamber designed by Foseco is a latest development in this direction. The pouring cham-ber is the device designed to inhibit the turbulence near the pouring region and thus achieving the required RTD character-istics. The turbulent inhibitors are mechanical devices and depend on the optimum location of other parameters (such asshroud position, submergence depth and design of tundish) for giving desired flow characteristics. The replacement of thesemechanical devices with external forces can restrict the dependence on various other parameters of the tundish.

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Nomenclature

C mass fraction of the injected tracerCav i average concentration of tracer from ith outletH bath height of the tundishL length of half tundishk turbulent kinetic energyP pressureRTD residence time distributiont timetm actual mean residence timetmin average breakthrough timetr theoretical mean residence timeU velocityu0 velocity fluctuationV volumeB magnetic field strengthZ Hartmann number

Greek symbolsH density of steell molecular viscosity of steellt turbulent viscosity of steelleff effective viscosity of steelrC turbulent Schmidt numbere rate of dissipation of turbulent kinetic energysl laminar shear stressst turbulent shear stressr electrical conductivity

Suffixi, j, k three Cartesian co-ordinate directions x, y and zDV dead volumeMV mixed volumePV plug volume

5076 A. Tripathi / Applied Mathematical Modelling 35 (2011) 5075–5090

The use of external forces in controlling the flow in the tundish is an innovative concept in designing the flow modifier.Thus, the objective of the present work is to explore the use of electromagnetic forces as a replacement for existing mechan-ical devices. The use of electro-magnetic forces is limited to mould in the present practices adopted by various steel makers.It was felts that electro-magnetic forces can be used to direct the flow in the tundish. Thus, the present work of using elec-tromagnetic forces as a flow modifier in a tundish is also an investigation for increasing the application of these forces inprocessing of steel making.

2. Model development

2.1. Geometrical description

Simulations were performed for the symmetrical half of tundish. Figs. 1a and 1b show the top and vertical sectional viewof the symmetrical half of delta shaped tundish. The dimensions of tundish are shown in Figs. 1a and 1b. The dimension ofthe pouring chamber used for simulation can be seen from Figs. 2a and 2b. The location of the electromagnetic forces incor-porated in the mathematical model for carrying out MHD simulation of tundish can be seen from Fig. 1b. Table 1 shows theoperating parameters for the tundish. Table 2 shows the set of simulation performed for this study.

2.2. Mathematical formulation and assumptions

The flow field in the tundish was computed by solving the continuity and momentum conservation equation in three-dimensional. The model was developed for isothermal condition and uniform steel temperature of 1600 �C was assumedfor the whole bath of tundish. The standard k–e model was solved to incorporate the turbulence near the incoming and out-going stream. The free surface of the liquid in the tundish was assumed to be flat and the slag depth was considered to beinsignificant. The electromagnetic force was incorporated as a volumetric source term in the momentum equation. Natural

A. Tripathi / Applied Mathematical Modelling 35 (2011) 5075–5090 5077

convection effect was neglected while computing the velocity field. The equation for dispersion of tracer in the tundish wassolved to capture the variation of tracer concentration in the tundish and then RTD analysis was performed. Table 3 showsthe expression for the RTD characteristics.

Governing equationsContinuity:

@ui

@xi¼ 0: ð1Þ

Fig. 1a. Vertical sectional view of the tundish at symmetrical plane (Z = 0 m).

Fig. 1b. Top view of half tundish about symmetrical plane (Y = 1.1 m).

Fig. 2a. Top view of the pouring chamber used for carrying out simulation for the tundish.

Fig. 2b. View of the pouring chamber for section BB0 .

Table 1Operating parameters of tundish of slab casters used for simulation.

S. no. Parameter Values

1 Base length (m) 1.12 Submergence depth of shroud (m) 0.353 Shroud diameter (m) 0.0854 Outlet nozzle diameter 0.0815 Throughput (ton/min) 3.5

Table 2No. of cases chosen for simulation.

S. no. Flow control devices used inside the tundish Magnetic field strength (T)

1 Existing pouring chamber 02 No flow control device 03 Magnetic flow control device 0.14 Magnetic flow control device 0.55 Magnetic flow control device 1

Table 3Expressions for RTD characteristics.

S. no. RTD characteristics Expressions

1 Theoretical residence time (tr) volume of tundish/volumetric flow rate2 Actual mean residence time (tm) tm ¼

PCavi

tDtPCavi

Dt, i = 1, 2, and 3 (for the three outlets)

3 Average break through time (tmin) First appearance of tracer at the outlet4 Fraction of plug volume (VPV) VPV = tmin/tr

5 Fraction of dead volume (VDV) VDV = 1 � tm/tr

6 Fraction of mixed volume (VMV) VMV = 1 � VPV � VDV


Momentum equation:

qDUi

Dt¼ � @P

@xi� @

@xjðsl

ij þ stijÞ þ qgi þ Si; ð2Þ

where, laminar shear stress, slij is given by

slij ¼ �lt

@Ui

@xjþ @Uj

@xi

!ð3Þ

and Reynolds shear stress, stij is expressed as

stij ¼ �qu0iu

0j � lt

@Ui

@xjþ @Uj

@xi

!: ð4Þ

Here Ui is the ith component velocity vector, and i and j vary for x, y and z direction and Si is the volumetric source termincorporated in the momentum equation for Lorentz force.

Lorentz force:

Fi ¼ Ji � Bi: ð5Þ


Here Ji is a current density and Bi is strength magnetic field in X, Y & Z direction.Using Ohm’s law with Ei = 0

Ji ¼ rðEi þ Ui � BiÞ ¼ rðUi � BiÞ: ð6Þ

Tracer dispersion:

q@C@tþ q

@ðUiCÞ@xi

¼ @

@xi

leff

rC

@C@xi

!: ð7Þ

Turbulent kinetic energy:

qDkDt¼ Dk þ G� qe: ð8Þ

Rate of dissipation:

qDeDt¼ De þ C1G

ek� C2q

e2

k; ð9Þ

where

D/ ¼@

@xjðlþ lt

r/Þ @/@xj

� �: ð10Þ

Here / is k for (6) and e for (7).

lt ¼ qClj2

eand G ¼ st

ij@Ui

@xj: ð11Þ

Here, C1 = 1.44, C2 = 1.92, Cl = 0.09, rC = 1, rk = 1, re = 1.3.

2.3. Boundary conditions

The boundary conditions for the momentum and the continuity equations can be easily visualised by referring to Fig. 1b.No-slip condition was set for all the walls of the tundish and the standard wall function was used to incorporate the variationdue to turbulence. Symmetry boundary condition was applied at the symmetry plane, which implies a zero gradient condi-tion for all the variables normal to that plane. Inlet velocity of 1.45 m/s was set for the incoming jet with a turbulent intensityof 2% [3]. Zero shear stress boundary condition was applied for the free surface of the tundish according to Ref. [3]. Pressureboundary condition of 1 atm was fixed at the outlets of the tundish. The tracer concentration was considered to be imper-vious for the walls of the tundish, hence a zero gradient or flux boundary condition was applied on the walls for the tracerdispersion equation. Zero gradient condition for the tracer was also applied at the free surface and the outlets of the tundish.

Mass fraction of tracer at the inlet was set to 0.11 till 1.2 s, after which it was kept to zero. 1.2 s is very small as comparedto the mean residence time of the tundish, and thus the influx of the tracer is not expected to affect the local velocity field.This inlet boundary condition of tracer mass fraction was decided based on the procedure of tracer injection adopted bySingh and Koria, while carrying out the experiment for a slab caster tundish.

2.4. Numerical procedure

The computational domain inside the half tundish was discretized into 1.5 lacs cells. The set of governing equations withboundary conditions were solved for each cell in the computational domain using the finite volume technique. The commer-cial CFD package (FLUENT) was used for solving the equation. The Tet/Hybrid mesh and Fluent 5/6 solver was adopted forpresent simulation. The momentum equation with electromagnetic forces and turbulence was solved to get the steady stateprofile. The unsteady equation for tracer concentration was then solved to get the data for RTD analysis. SIMPLE algorithmwas used for pressure-velocity coupling. The higher order schemes were used for discretization of momentum equation. Thedensity and viscosity of molten was kept constant at 7100 kg/m3 and 0.006482 kg/ms, respectively, throughout the compu-tational domain.

3. Model validation

The validation of the momentum equation with electromagnetic forces was done with analytical solution of the Hartmanproblem. The rest of the model equations were already validated with experiments of Singh and Koria and published [5,6,3].Hartman flow is a steady flow of an electrically conducting viscous fluid between parallel non conducting channels with anapplied transverse magnetic field. The configuration for this problem can be seen from Fig. 3a. The Lorentz force (i.e. the totalelectromagnetic force) acts against the motion of the fluids. The similar type of analogy is incorporated in the model equa-tion for tundish. This is the reason for selecting Hartman problem for validation. The governing equation for this problem is

Fig. 3a. Schematic view of the Hartman problem used for MHD validation.

0

1

2

3

4

-0.0005 -0.0004 -0.0003 -0.0002 -0.0001 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005

Channel width (m)

Vel

oci

ty M

agn

itu

de

(m/s

)

z=0Z=2z=5z=10z=25

Fig. 3b. Velocity profile for the Hartman problem for different Hartman number.


similar to Eqs. (1)-(11). The inlet velocity for this problem was kept at 2 m/s. No slip condition was applied at the walls of theproblem. The simulation was performed for certain range of Hartman no. from 0 to 50. Hartman no. is defined as the ratio ofelectromagnetic forces to non electromagnetic forces. The results obtained were compared with the analytical solution ofHartman problem [7,8]. Fig 3b shows the velocity profile computed from simulation results with increasing Hartman num-ber. The similar type of trend in the velocity profile was reported in the literature for increase in the Hartman no. [7,8]. Fig. 3cshows the comparison of simulation versus analytical results of velocity profile. The maximum deviation of 3.3% was notedbetween simulated and analytical values of velocity in Fig. 3c. Hence, the performance of model appears to be reasonablyaccurate according to Figs. 3b and 3c.

4. Results and discussion

The 3-D MHD simulation was performed for the tundish with magnetic flow modifier of varied magnetic field strengths.3-D simulation was also performed for the tundish with and without flow modifier and comparative analysis was done withthe results obtained for magnetic flow modifier. The role of increase in the strength of magnetic field on the flow patternsinside the tundish was investigated in present simulation. The RTD analysis was performed for all the flow patterns and re-sults obtained can be seen from the RTD curve in Figs. 4a and 4b. The results obtained from the simulation are presented inthe subsequent steps.

4.1. Comparison of pouring chamber with magnetic flow modifier

The comparative study was performed by analysing the flow patterns obtained from the simulation results of tundishwith pouring chamber and magnetic flow modifier. The simulation was also performed for the bare tundish with similar

1

2

3

4

0 10 20 30 40 50

Hartman Number

Vm

ax (m

/s)

SimulatedAnalytical

Fig. 3c. Comparison of the simulated versus analytical velocity for different Hartman number.

No Flow ModifierPouring ChamberMagnetic flow

modifier (Strength 0.5 T)

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

00 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

dimensioniess time

dim

ensi

onie

ss c

once

ntra

tion

Fig. 4a. Comparison of RTD curve for different types of flow modifiers.

Fig. 4b. Comparison of RTD curve for magnetic flow modifier of varied strength of magnetic field.



operating parameters. The results obtained for the bare tundish was analysed and compared with that of pouring chamber.This analysis was done to understand the flow patterns obtained from the pouring chamber. Fig. 4a shows the comparison ofthe RTD curve for different flow modifier. The results of the RTD analysis can be seen from Table 4. The correlation of the RTDcurve with velocity patterns for different flow modifiers will be presented in a sequence.

4.1.1. Flow patterns for the tundish without flow modifiersThe simulation was performed for the tundish without any flow modifiers. The flow patterns obtained from the simula-

tion results were correlated with the results obtained from the RTD analysis. Fig. 5a shows the flow pattern in a top view ofthe tundish (at Y = 1.1 m). Figs. 5b and 5c show the flow pattern in transversal and vertical sectional view (at X = 3.4 m and

Table 4RTD characteristics for various sets of simulation.

S. no. Problems Mean residence time VP (plug volume) (%) VD (dead volume) (%) VMix (mixed volume) (%)

1 Tundish with existing pouring chamber 566 13 7.7 79.32 Tundish without pouring chamber 524 3 19 783 Tundish with magnetic field of 0.1 T 595 12 8.4 79.64 Tundish with magnetic field of 0.5 T 618 15.4 4.9 79.75 Tundish with magnetic field of 1 T 601 12.3 7.5 80.2

Fig. 5a. Velocity profile at top surface (Y = 1.1 m) for the tundish without any flow modifier.

Fig. 5b. Velocity profile at vertical transversal plane (X = 3.4 m) for the tundish without any flow modifier.

Fig. 5c. Velocity profile at Z = 0 m (symmetrical plane) for the tundish without any flow modifier.

Fig. 6a. Velocity profile at top surface (Y = 1.1 m) for the tundish with pouring chamber.


Z = 0 m) of the tundish, respectively. The movement of flow vector towards the centre can be visualised from Fig. 5a. Themagnitude of the velocity was found to be higher in the region of the incoming stream and decreases significantly in theregion above the outlet. The downward movement of the flow was the reason for the development of low velocity regionabove the outlet. This development of low velocity zone contributes significantly to the high value of dead volumes shownin Table 4. The movement of flow towards the centre also contributes toward the development of dead zones. This down-ward directed flow can be clearly seen from the flow patterns in Fig. 5c. The flow patterns for transversal section plainthrough the inlet shroud can be seen from Fig. 5b. The recirculation cell in the anticlockwise direction of re-circulation cellwas one of the reasons for bottom directed flow in tundish without any flow modifier. The low value of plug volume reportedin Table 4 was evident from the significantly low value of tmin in the RTD curve shown in Fig. 4a.

4.1.2. Flow patterns for the tundish with pouring chamberThe set of flow patterns were obtained from the simulation results of the tundish using pouring chamber as a flow mod-

ifier. These flow patterns were analysed and compared with the one obtained without any flow modifier to understand therole of pouring chamber. The flow patterns in the top view of the tundish (at Y = 1.1 m) can be seen from Fig. 6a. The velocityprofile was found to be more uniform as compared to one shown in Fig. 5a. The movement of the flow was straight and wasdirected towards outlet as compared to the movement of flow vector towards centre plane in Fig. 5a. Figs. 6b and 6c showthe flow pattern in transversal plane (at X = 3.4 m) and vertical centre plane (at Z = 0 m), respectively. The development ofthe circulatory loop above the pouring chamber can be easily visualised from the flow patterns in the plane (Z = 0 m). It canbe seen from Fig. 6c that the incoming stream is rotated towards the surface in the region above pouring chamber. This rota-tion of flow towards the surface imparts momentum to the stream moving towards the outlet at the surface plane. Thus, themagnitude of the velocity at the surface plane was increased due to momentum transfer by the rotating flow. The reason forthe development of rotating flow can be obtained by observing the flow pattern in Fig. 6b for transversal plane. The rotationof the flow within the pouring chamber can be observed from the flow patterns in Fig. 6b. This circulatory flow within thepouring chamber acts as an agent in applying the brake and circulating the flow moving in vertical plane at the centre. Theimportant observation noted from the flow patterns in Figs. 6a and 6c was the slow movement of the flow in the centre re-gion of the tundish. The momentum loss in the centre region was imparted to the stream at the top and the corner region ofthe tundish. Thus, the re-distribution of the stream towards the top and corner region of the tundish results in an increase in

Fig. 6b. Velocity profile at vertical transversal plane (X = 3.4 m) for the tundish with pouring chamber.

Fig. 6c. Velocity profile at Z = 0 m (symmetrical plane) for the tundish with pouring chamber.


plug and loss in dead volume. The increase in tmin for the RTD curve in Fig. 4a reflects the increase in plug volume for thetundish with pouring chamber.

4.1.3. Flow patterns for the tundish with magnetic flow modifierThe simulation was performed for flow modifiers of varied strengths of magnetic field. The results obtained were ana-

lysed and compared with simulation results derived in previous cases. The location and dimension of the region for electro-magnetic forces can be seen from Fig. 1b. The simulation was performed for varied strength of magnetic field in the range of0.1 T–1 T. The electromagnetic forces act as a hypothetical wall to suppress the turbulence in a region of incoming stream.Fig. 7a shows the flow patterns in the top view (at Y = 1.1 m) for magnetic strength of 0.1 T. The flow patterns for magneticstrengths of 0.1 T in transversal (at X = 3.4 m) and vertical centre plane (at Z = 0 m) can be visualised from Figs. 7b and 7c,respectively. The flow profile in Fig. 7a looks similar but more uniform as compared to the one obtained with out any flowmodifier as shown in Fig. 5a. The uniformity in the flow pattern in Fig. 7a can be explained by careful investigation of theflow phenomenon in Fig. 7c. The turbulence in the incoming stream was suppressed and captured with in the region sur-rounded by electromagnetic forces. The contour shape flow profile moving towards the zone surrounded by electromagneticforces can be seen from Fig. 7c. The suppression of turbulence restricts the down ward movement of the flow as observed inFig. 5c. The restriction of downward movement results in the redistribution of the momentum and hence the flow profilebecomes more uniform. The circulation loop developed above the region of pouring chamber in Fig. 6c was not observedin flow pattern with magnetic flow modifier in Fig. 7c. The RTD analysis shows the considerable improvement in the ratioof plug to dead volume as compared to that obtained without any flow modifier. The RTD characteristics for magnetic flowmodifier shows improved performance but not compatible with pouring chamber.

Fig. 7a. Velocity profile at top surface (Y = 1.1 m) for the tundish with magnetic flow modifier (B = 0.1 T).

Fig. 7b. Velocity profile at vertical transversal plane (X = 3.4 m) for the tundish with magnetic flow modifier (B = 0.1 T).

Fig. 7c. Velocity profile at symmetrical plane (Z = 0 m) for the tundish with magnetic flow modifier (B = 0.1 T).


4.2. Effect of strength of magnetic field on flow patterns inside the tundish

The results obtained from magnetic flow modifier with magnetic strength of 0.1 T were not good enough to replace thepouring chamber. The increase in the strength of magnetic field can be alternative for improving the performance of

Fig. 8a. Velocity profile at top surface (Y = 1.1 m) for the tundish with magnetic flow modifier (B = 0.5 T).

Fig. 8b. Velocity profile at vertical transversal plane (X = 3.4 m) for the tundish with magnetic flow modifier (B = 0.5 T).

Fig. 8c. Velocity profile at symmetrical plane (Z = 0 m) for the tundish with magnetic flow modifier (B = 0.5 T).


Fig. 9a. Velocity profile at top surface (Y = 1.1 m) for the tundish with magnetic flow modifier (B = 1 T).

Fig. 9b. Velocity profile at vertical transversal plane (X = 3.4 m) for the tundish with magnetic flow modifier (B = 1 T).

Fig. 9c. Velocity profile at symmetrical plane (Z = 0 m) for the tundish with magnetic flow modifier (B = 1 T).


magnetic flow modifier. It was also felt that the magnetic flow modifier should be designed in such a way that it should affectonly the small portion of the tundish. Hence, there was a need to limit the magnetic field zone and increase the performance.The objective to achieve superior performance by applying magnetic field in small region in the tundish inspired us to inves-tigate the effect of magnetic field strength up to 1 T.


The simulation was performed by increasing the strength of magnetic field to 0.5 T and 1 T. Figs. 8a–8c show the threedifferent views of the flow pattern obtained from the simulation for magnetic field of 0.5 T. Simulation results for magneticfield of 1 T can be seen from the simulation from the flow patterns in Figs. 9a–9c. The flow patterns for magnetic field of 0.5 T

Fig. 10a. Contour of velocity at the meniscus for magnetic field strength of 0.1 T.

Fig. 10b. Contour of velocity at the meniscus for magnetic field strength of 0.5 T.

Fig. 10c. Contour of velocity at the meniscus for magnetic field strength of 1 T.

0

0.04

0.08

0.12

0.16

0 1 2 3 4Length of Tundish (m)

Velo

city

Mag

nitu

de (m

/s)

Magnetic Field = 0.1 TMagnetic Field = 0.5 TMagnetic Field = 1 T

Fig. 11. Plot of velocity magnitude at the meniscus with length of tundish for different strengths of magnetic field.


in Figs. 8a–8c looks similar to the one obtained with the magnetic field of 0.1 T in Figs. 7a–7c. The RTD characteristics shownin Table 4 reflect improvement in the performance of magnetic flow modifier with the magnetic field of 0.5 T. The drastic fallin the flow characteristics for inclusion flotation can be noticed from the Table 4 for magnetic field strength of 1 T. The reasonfor the drop in the value of the RTD characteristics for magnetic field of 1 T can be obtained by correlating the flow patternswith the RTD curve.

The flow patterns in Figs. 9a and 9c (for planes at Y = 1.1 m and Z = 0 m, respectively) looks similar to one obtained formagnetic field of low strengths. The flow phenomenon in Fig. 9b (for plane at X = 3.4 m) shows dissimilarity with the oneobtained for magnetic field of low strengths. The circulation loop in Fig. 9b shows higher intensity and is confined to smallerregion as compared to the patterns in Figs. 7b and 8b. The flow velocity in the tundish should be of optimum value for gettingthe best inclusion flotation characteristics. The higher velocity in the tundish can lead to formation of circulation cells andreduction in velocity magnitude beyond certain limit results in formation of stagnant zone. Hence, the challenge was to pro-duce optimum flow velocity through controlling device. The increase in the magnetic filed strength beyond certain extentenhances the controlling forces to such a level that the magnitude of the flow velocity goes below the optimum level. Figs.10a–10c show the contour of the velocity at the meniscus for the magnetic filed strength of 0.1 T, 0.5 T and 1 T, respectively.The slight fall in velocity can be noticed for magnetic field of 0.5 T as compared to 0.1 T. This fall in velocity brings the flowvectors close to the optimum value. However, the further fall in the velocity magnitude for the magnetic filed of 1 T lead tosignificant deviation from optimum value. Fig. 11 shows the plot of velocity magnitude at the meniscus with the length ofthe tundish for different strengths of magnetic field. The velocity magnitude at 1 T was found to be significantly low as com-pared to magnetic filed of 0.1 and 0.5 T in Fig. 11. The comparison of the RTD curve for the flow patterns of different strengthsof magnetic field can be seen from Fig. 4b.

5. Conclusion

The role of electromagnetic forces in controlling the flow in the tundish was investigated by using 3-D MHD simulation.The conclusions drawn from the study are reported in sequence:

� The comparative study was performed for the tundish with and without pouring chamber. The suppression of turbulenceby the pouring chamber in the region of incoming stream was established from the simulation study.� The role of pouring chamber in directing the flow towards the surface was established from the study. The surface direc-

ted flow results in an improvement of flow characteristics for inclusion flotation.� The role of magnetic flow modifier as an alternative for pouring chamber was investigated. The results obtained show the

certain similarity in the flow characteristics with the one obtained with pouring chamber.� The RTD analysis done for different sets of simulation reflects the need to optimise the strength of magnetic field for

improving the performance of magnetic flow modifier� The magnetic flow modifier can be used as an alternative flow modifier in the tundish.

Acknowledgements

The author would like to thanks Dr. S.K. Ajmani and Dr. S.K. Choudhary for their constant encouragement. The supportextended by management of R&D, Tata Steel Ltd. is highly acknowledged.


References

[1] Y. Sahai, R. Ahuja, Ironmak. Steelmak. 13 (1986) 241.[2] P.K. Jha, S.K. Dash, Sanjay Kumar, ISIJ Int. 41 (2001) 1437.[3] Anurag Tripathi, S.K. Ajmani, ISIJ Int. 45 (2005) 1616.[4] R.D. Morales, J. Palafox-Ramos, J.deJ. Barreto, S. Lopez-Ramirez, D. Zacharias, Metall. Mater. Trans. B 31 (2000) 1505.[5] S. Singh, S.C. Koria, ISIJ Int. 33 (1993) 1228.[6] S. Singh, S.C. Koria, ISIJ Int. 34 (1994) 784.[7] M. Hughes, K.A. Pericleous, M. Cross, Appl. Math. Model. 18 (1994) 150.[8] Tony W.H. Sheu, R.K. Lin, Int. J. Numer. Method Fluids 45 (2004) 1209.

Further reading

[9] D. Mazumdar, R.I.L. Guthrie, ISIJ Int. 39 (1999) 524.[10] S. Govindarajan, S.K. Ajmani, A. Chatterjee, T. Mukherjee, in: Proc. Int. Symp. on Modern Developments in Continuous Casting, New Delhi, 1988, p. 153.[11] D.B. Spalding, Int. J. Numer. Math. Eng. 4 (1972) 551.[12] O. Levenspiel, Chemical Reaction Engineering, John Wiley & Sons Inc., New York, 1972.[13] S.V. Patankar, D.B. Spalding, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, 1980.

mathematical modelling of flow control in a tundish using electro-magnetic forces

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