Physical and Mathematical Simulation of Fluid Flow in a Wide Single-strand Tundish for Slab Continuo

Journal of Metallurgical Engineering (ME) Volume 3 Issue 3, July 2014 www.me‐journal.org doi: 10.14355/me.2014.0303.03

109

Physical and Mathematical Simulation of

Fluid Flow in a Wide Single‐strand Tundish

for Slab Continuous‐casting Zhong Liangcai*1, Hao Ruichao2 Li Junzhe3 Li Lei1 Zhu Yingxiong4 Xu Ninghui5

1‐4 School of Materials and Metallurgy, Northeastern University, Shenyang 110004, China; 5Pinggang Jiujiang

Branch Corporation, Jiujiang 332000, Jiangxi, China.

*[email protected]; [email protected]; [email protected]; [email protected]

Received 16 July, 2013; Accepted 22 September, 2013; Published 9 June, 2014

© 2014 Science and Engineering Publishing Company

Abstract

Molten steel flow in a wide single‐strand tundish with

different flow control devices (FCDs) for slab continuous‐

casting was investigated by physical and mathematical

simulations in this work. The effects of different FCDs on the

flow characteristics and velocity and temperature fields in

the tundish with larger width, shorter length and larger

depth were studied. The results showed that locations and

dimensions of weirs and dams and geometry of turbulence

inhibitors (TIs) have a large effect on the flow characteristics

and velocity and temperature profiles. Adoption of a square

turbulence inhibitor without extending top lips can improve

the molten steel flow better than that with top extending lips

in the tundish. In comparison with the former tundish

configuration, the flow characteristics are improved to a

great extent in the optimum case. A big “spring uprush”

forms on the free surface around the long shroud when

molten steel flows into a turbulence inhibitor with extending

top lips and rushes up reversely out of the TI, while four

small “spring uprushes” appear on the surface when a

square TI without extending top lips is adopted because the

liquid steel flows mainly out of the 4 corners of the square TI.

The flow of liquid steel in the former tundish configuration

is not reasonable and the height of an area where

temperature is less than 1819 K is about half of liquid surface

height at the right side of the stopper, which means that big

dead zone exited in the former tundish configuration. In the

optimum case, the height of such area was only one seventh

of the liquid surface height. The RTD curves obtained from

the mathematical simulation are agreed with those from the

physical modeling and the flow characteristics obtained

from these two methods in this work are coincident with

each other.

Keywords

Slab Continuous‐casting; Wide Single‐strand Tundish;

Mathematical Simulation; Physical Modelling; Fluid Flow

Characteristic; Velocity Field; Temperature Profile; Flow Control

Device

Introduction

Tundishes in continuous casting have very important

effects for steel cleanness. Tundish metallurgy has

been paid more and more attentions.1 It is well known

that molten steel flow characteristics in tundishes have

great effects on non‐metallic inclusion removal from

the liquid steel, slag and air entrainment minimization,

and new inclusion formation prevention. Different

flow control devices (FCDs), such as weirs, dams,

baffles and turbulence inhibitors (TIs), have been

applied in continuous‐casting tundishes for

improvement of the characteristics of molten steel flow.

Many researchers2‐10 have applied TIs with other FCDs

to optimize the tundish configurations since 1990s by

physical modeling and/or mathematical simulation.

Generally, the TIs used have extending top lips in

these researches and good flow characteristics have

been achieved. But not all tundishes are suitable to use

such TIs with extending top lips. What kinds of TIs in

geometry should be adopted in a tundish lies on the

inside profile of tundishes.

The geometry characteristics of the single‐strand slab

tundish profile studied in the present work are larger

width, shorter length and larger depth, being 1513 mm

(upper width)×4035 mm(upper length)×1215(working

liquid surface depth). For such tundish, different TIs

with or without extending top lips were applied to

optimize the tundish configuration together with a

weir and a dam through physical modeling

experiments and mathematical simulation calculations,

www.me‐journal.org Journal of Metallurgical Engineering (ME) Volume 3 Issue 3, July 2014

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and the flow characteristics of the tundish with

different tundish configurations and their velocity and

temperature fields are investigated in this work.

Physical Modeling Method

In order to ensure that the fluid flowing between a

model tundish and a prototype tundish for isothermal

and non‐reactive systems is similar, geometrical and

dynamic similarities must be satisfied between the two

vessels. In the present work, the ratio of geometrical

similarity of model tundish to the prototype, λ was

chosen to be 1:2.5. Dynamic similarity required

simultaneous equality of both turbulent Reynolds and

Froude numbers, but it was impossible to keep the

condition satisfied in reduced scale modeling studies.

The computational work of Sahai and Burval11 and the

experimental work of Singh and Koria12‐13 showed that

the magnitude of turbulent Reynolds number under

turbulent flow range in different tundishes was very

similar. Therefore, Froude number between the model

tundish and the prototype was maintained to be

equivalent in this work. With this condition, the water

flow rate, Qm in the experiments was calculated from

the liquid steel flow rate, Qp by the following equation:

2.5m pQ Q (1)

The experimental apparatus was shown in Fig. 1. 0.2

g/ml NaCl solution of 500 ml was used as the tracer in

the physical modeling experiments. After fluid flow in

the model tundish reached stable, the tracer was

injected into the tundish though the ladle shroud. A

probe was located under the outlets of the tundish to

measure the variation of water conductivity with time,

that is, residence time distribution (RTD) curves. The

probe was connected to a conductivity meter and the

signals were recorded with a data acquisition system

and a computer. From the RTD curves measured, fluid

flow characteristics in a certain tundish configuration

were calculated with the following equations:

Average residence time tav

0

0

n

i i ii

av n

i ii

tc t dt t c t tt

c t tc t dt

(2)

Plug flow volume fraction vp

p min maxp 2

Vv

V

(3)

Dead zone volume fraction vd 14

d ad a1

V Qv

V Q

(4)

Mixing flow volume fraction vm

mm d p1

Vv v v

V (5)

FIG. 1 SCHEMATIC OF EXPERIMENTAL APPARATUS

Mathematical Simulation Method

Governing Equations

The liquid steel flow in the continuous casting tundish

can be considered to be three‐dimensional, turbulent.

The flow is treated as steady by neglecting the

phenomena involved during filling and emptying of

the tundish. The effect of surface slag to the flow is

ignored and the melt surface is assumed to be flat. The

molten steel is Newtonian and incompressible fluid.

Therefore, the governing equations in Cartesian

tensional form for the liquid steel flow in the tundish

can be written as:

Continuity ( ) 0ii

ux

(6)

Momentum

( ) jii j eff i

i i i j i

uupu u g

x x x x x

(7)

where, ρ is the density of melt, u the velocity, p the

pressure, g the gravitation acceleration, and μeff the

effective viscosity. i and j represent the three

coordinate directions. μeff is equal to the sum of

molecular and turbulent viscosity of steel as follows:

eff t (8)

The turbulent viscosity is calculated through its

relationship with the turbulent kinetic energy and its

dissipation rate. The turbulent kinetic energy, k and its

dissipation rate, ε can be expressed with the following

equations:

Turbulent kinetic energy

effi

i i k i

ku k G

x x ο x

(9)

Journal of Metallurgical Engineering (ME) Volume 3 Issue 3, July 2014 www.me‐journal.org

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Dissipation rate of turbulent kinetic energy

1 2eff

ii i i

u C G Cx x x k

(10)

The generation term, G in Equs. (9) and (10) can be

given as: 22

2 ji it t

i j i

uu uG

x x x

(11)

The turbulent viscosity, μt can be written as:

2

t

C k

(12)

C1, C2, Cμ, σk and σε are the empirical constants of the k‐

ε model and were assigned to their standard values

from Launder and Spalding15: 1.44, 1.92, 0.09, 1.0 and

1.30, respectively.

The heat transfer in the tundish is governed by energy

equation as follows:

Peff

( )i

i i i

C u T T

x x x

(13)

where the effective thermal conductivity, λeff, is the

sum of two components:

Prp t

efft

C (14)

here, Prt is the turbulent Prandtl number, λ is thermal

conductivity, Cp is heat capacity and T is temperature.

To calculate the residence time distribution curves of

the molten steel in the tundish with different

configurations and compare them to the RTD curves

obtained from the physical modeling experiments, a

pulse of tracer was introduced into the melt through

the inlet and allowed to flow with the melt. By

monitoring the change in tracer concentration of the

melt at the tundish outlet, the residence time

distribution curve was obtained. The transport of the

tracer and the variation in tracer concentration are

governed by the mass transport equation as follows:

( )ieff

i i i

u cc cD

t x x x

(15)

where c represents the concentration of the tracer, t is

the time and Deff is the effective mass diffusion

coefficient and is the sum of the molecular and

turbulent diffusivity (D+DT). Under the condition

where turbulent Schmidt number is equal to 1, one has:

eff

eff

1D

(16)

Boundary Conditions

The whole volume filled with molten steel in the

tundish was chosen as the numerical calculation

domain. The above continuity, momentum and energy

equations were solved with the equations for k and ε

by using the boundary conditions. Non‐slipping

conditions were applied as boundary conditions to all

solid walls. Frictionless conditions were used to the

free surface of liquid steel. The logarithmic law was

employed to all nodes closest to any solid walls. The

vertical velocity profiles of the liquid steel at the inlet

as well as at the outlet of the tundish were assumed to

be uniform through the cross sections and the other

two velocity components were assumed to be zero.

The values of k and ε at the inlet were calculated from

the inlet average velocity through the well known

equations. A constant mass flow rate of steel from the

ladle to the tundish was 2.98 ton/min for the

mathematical simulation.

For the boundary conditions of temperature field,

uniform and constant heat flow rates were used at

every wall surface of the tundish and liquid surface.

The heat flow rates used in this work were those

recommended by Chakraborty and Sahai16 and related

parameters were listed in Table 1.

TABLE 1 PARAMETERS FOR MATHEMATICAL SIMULATION OF LIQUID

STEEL FLOW IN THE TUNDISH

Parameters Values Parameters Values

Liquid steel

density/kg∙m‐3 7000

Liquid steel

viscosity/kg∙m‐1∙s‐1 0.0067

Liquid steel

conductivity/W∙m‐1∙K‐141

Liquid steel specific

heat /J∙kg‐1∙K‐1 750

Inlet temperature/K 1823 Heat flux at walls

inside tundish/kW∙m‐21.75

Heat flux at

bottom/kW∙m‐2 1.4

Heat flux at liquid

surface/kW∙m‐2 15

Heat flux at transverse

walls /kW∙m‐2 3.8

Heat flux at

longitudinal

walls/kW∙m‐2

3.2

Zero mass transfer fluxes were used at all walls and

liquid surface for mass equation solution. At t=0 s the

mass fraction of tracer at inlet of the tundish was set to

be 0.1. After t=1 s it was given as zero. The

concentration of the tracer at the outlet of the tundish

was monitored from t=0 and the RTD curves would be

obtained from the numerical calculation.

The commercial CFD package FLUENT® was used to

solve the above governing equations with the

boundary conditions. In the numerical solution

scheme Semi Implicit Method for Pressure Linked

Equation (SIMPLE) algorithm was used for pressure


112

and velocity coupling and first order upwind scheme

for momentum and scalar transport equations. Once

the flow and temperature fields were converged to

steady state the problem defined module of the

FLUENT solver was changed to unsteady state for

solving the transient tracer dispersion Eq. (15) with

appropriate initial and boundary conditions.

Results and Discussion

Physical Modeling

FIG. 2 SCHEMATIC OF TUNDISH CONFIGURATIONS IN THE

EXPERIMANTS

TABLE 2 TYPICAL TUNDISH CONFIGURATIONS IN EXPERIMENTS

Case TI S1/mm S2/mm H1/mm H2/mm

C0 TI1 632 108 96 136

C1 TI1 590 108 96 136

C2 TI1 590 200 130 205

C3 TI2 590 150 55 205

C4 TI3 590 150 55 205

C5 TI4 540 200 55 225

C6 ‐ 390 150 55 250

C7 TI1 390 150 55 250

C8 TI5 540 200 55 250

C9 TI5 440 200 55 250

C10 TI5 390 200 55 250

C11 TI5 390 150 55 250

FIG. 3 SCHEMATIC OF SOME TURBULENCE INHIBITORS IN

THE EXPERIMENTS

Different tundish configuration studied in this work is

shown in Fig. 2. The tundish configurations consisted

of different turbulent inhibitors (TIs), different

locations of a weir and a dam (S1 and S2) and their

different heights (H1 and H2). A lot of tundish

configurations had been experimented in the present

work, but for space limited only some typical tundish

configurations are listed in Table 2 where C0 is the

former tundish arrangement. Figure 3 presents some

TIs used in the physical modeling experiments. These

TIs are all square at horizontal cross‐section except TI3

whose horizontal cross‐section is rectangle with 280

mm short sides.

The RTD curves in the tundish with configurations of

C0, C6, C7 and C11are shown in Fig. 4 and the flow

characteristics of different tundish configurations are

given in Table 3. It is known from Table 2 that C0 and

C7 used the same TI, i.e., TI1, and the difference

between these two cases was their weir and dam

locations and heights, i.e., S1, S2, H1 and H2. As shown

in Fig. 4, there are high peaks in the RTD curves for C0

and C7 cases, which indicates that a lot of tracers flow

out of the tundish and large dead zone volumes exit in

the tundish with C0 and C7 configurations, as seen in

Table 3. Even though C7 and C11 have the same

values of S1, S2, H1 and H2, the peak of the RTD curve

in C11 case is lowered apparently due to the different

TI and its RTD curve moves towards right side in Fig.

4. These results indicate that TI1 is not suitable for this

kind of tundish studied in present work. The

difference among C6, C7 and C11 cases in

configuration is that there is no TI in C6 case. It is

known from Fig. 4 that the minimum residence and

peak concentration times in C6 case are short. Short

minimum residence and peak concentration times are

not expected even though its peak concentration is low.

Therefore, the adoption of turbulent inhibitor without

extending top lips, TI5, in this tundish can distribute

molten steel well to larger space of the tundish and

prolong residence time of liquid steel in the tundish,

which is favorable to removal of non‐metal inclusions.

Such result is determined by the characteristic of this

tundish profile.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0

0.5

1.0

1.5

2.0

C/-

/-

C0

C6

C7

C11

FIG. 4 RTD CURVES IN SOME DIFFERENT TUNDISH

CONFIGURATIONS

As shown in Table 3, the fluid flow in the tundish with

the former configuration, C0, is not perfect. Its


113

minimum residence is 64 s, its peak concentration and

average residence times are short and its dead zone

volume is larger, being 35%, which decreases largely

the effective volume of the tundish. The same TI1 was

used in C1 and C2 cases and the locations and heights

of the weir and dam were adjusted, but the flow

characteristics in these two cases change less. Their

average residence times increase a little and their dead

zone volumes decrease less, and all of their fractions

were over 30%.

TABLE 3 FLOW CHARACTERISTICS IN DIFFERENT TUNDISH

CONFIGURATIONS

Case tmin/s tmax/s tav/s vp/% vd/% vm/%

C0 64 81 237 20 35 45

C1 64 81 241 20 34 46

C2 70 108 249 24 32 44

C3 78 113 279 26 24 50

C4 80 130 280 29 23 48

C5 78 134 289 29 21 50

C6 54 91 286 20 21 59

C7 63 99 273 22 25 53

C8 88 121 291 29 20 51

C9 82 139 303 30 17 53

C10 79 141 307 30 16 54

C11 81 163 314 33 14 53

Turbulent inhibitors of TI2, TI3 and TI4 were applied

in tundish configurations of C3, C4 and C5,

respectively. The outlet areas of these three TIs are

incremental. It can be seen from Table 2 and 3 that

flow characteristics in such tundish are improved by

changing TIs and adjusting locations and heights of

the weir and dam. The minimum, peak and average

residence times are increased and the dead zone

volume is lowered, being below 25%.

There was no TI in C6 case and its dead zone volume

is low obviously, lower 40% than that in the former

case C0. The peak and average residence times are

prolonged in some degree, but the minimum residence

time becomes shorter by 10 s due to no TI, as

compared to that in C0 case. When fluid flows into the

tundish, a part of it flows to the dam along the tundish

bottom if no TI is used in the tundish. As a result, the

flowing distance of this part of fluid is short and the

minimum residence time in such tundish

configuration becomes low.

It can be concluded from Table 2 and 3 that reduction

in S1 and H1 and increase in S2 and H2 are favorable to

improvement for fluid flow characteristics in this

tundish. Average residence time is increased and dead

zone volume is decreased. Lowering H1 and S1 and

increasing S2 and H2 can prolong fluid’s flowing

distance, reduce its flowing velocity between the weir

and dam and let fluid flow toward upper part of the

right end wall, which increases residence times and

decreases dead zone volume in the tundish.

C7 case was obtained by applying TI1 to C6 case.

Comparing to C6 case, minimum residence and peak

concentration times in C7 case are prolonged, but its

dead zone volume fraction is enlarged from 21% to

25%, which means that this TI1 is not favorable to

decreasing dead zone volume in this tundish.

Application of TI in C7 case, in comparison with C6,

prolongs distance of fluid flow in the tundish.

Therefore, its minimum residence time increases. But

such TI with extending top lips makes the fluid flow

out of the TI in a concentrative way and can not

transfer the fluid to the whole tundish volume. For

this reason, the tracers added into the tundish with C7

configuration flow out of the tundish quickly due to

its larger width, which makes its RTD curve have

short peak concentration time and high peak

concentration, as shown in Fig. 4. As a result, there is

larger dead zone volume in the tundish with C7 case.

It was found from the experiments that increase in TI’s

outlet area can improve fluid flow characteristics in

this tundish. TI5 was achieved by canceling TI’s

extending top lips. C8, C9, C10 and C11 configurations

consist of TI5 and different locations and heights of a

weir and a dam. It is known from Table 2 and 3 that

the peak concentration and average residence times

are prolonged greatly by using TI5 and moving the

weir and dam towards the direction of the tundish

outlet and the dead zone volume is reduced greatly,

being less 20%. The dead zone volume fraction in the

tundish with C11 case is lowered to 14%, less by 60%

than that in the former tundish configuration C0.

350 400 450 500 550 600 650

15

20

25

30

35

TI: TI5, S2=150 mm, H

1=55 mm, H

2=250 mm

v d /%

S1/mm

TI: TI1, S2=108 mm, H

1=96 mm, H

2=136 mm

FIG. 5 RELATIONSHIP BETWEEN DEADZONE VOLUME

FRACTION IN THE TUNDSIH AND S1


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Fig. 5 presents the variation of dead zone volume

fraction in the tundish with the distance S1 between

the dam and the centre line of the tundish outlet under

the condition of the same TI, S2, H1 and H2. When S1 is

reduced from 632 mm to 390 mm, the dead zone

volume fraction is lowered from 35% to 30% for the

former tundish configuration C0, while the fraction is

decreased from 20% to 14% for the optimum tundish

configuration C11 when S1 is reduced from 540 mm to

390 mm. As described above, the fluid flowing over

the dam can moves towards the end wall at higher

velocity when the weir and the dam are moved to the

side of the tundish outlet. The same effect is also

obtained if the dam’s height is increased. Therefore,

the dead zone at that end wall is reduced.

The research results in this work indicate that FCDs

and their locations in tundishes should be optimized

carefully to determine an optimum tundish

configuration according to tundish inside profile and

molten steel flow rate so that the optimum fluid flow

characteristics in tundishes can be achieved for the

sufficient removal of inclusions from liquid steel.

Mathematical Simulation

0 1 2 3 40.0

0.5

1.0

1.5

C /

-

/ -

Physical result for C6

Nmerical result for C6


Nmerical result for C7

FIG. 6 RTD CURVES FROM MATHEMATICAL AND PHYSICAL

SIMULATIONS IN C6 AND C7 TUNDISH CONFIGURATIONS

0 1 2 3 40.0

0.5

1.0

1.5


Numerical result for C11

Numerical result for C0

C/-

/-


FIG. 7 RTD CURVES FROM MATHEMATICAL AND PHYSICAL

SIMULTIONS IN C0 AND C11 TUNDISH CONFIGURATIONS

RTD curves obtained from physical modeling

experiments and mathematical simulations in different

tundish configurations are given in Figs. 6 and 7. It is

shown in these figures that the RTD curves obtained

from mathematical simulations are agreed basically

with those from corresponding physical modeling

experiments. Only some differences between these

two methods in this work exist in the vicinity of the

peaks of the curves, but the results in the

mathematical simulations can reflect fluid flow

characteristics in different tundish configurations.

Table 4 gives a comparison of flow characteristics from

mathematical simulation to those from physical

modeling. It is obvious in this table that the calculated

flow characteristics from the RTD curves in

mathematical simulations are coincident with those

from the measured RTD curves.

TABLE 4 COMPARISON OF FLUID FLOW CHARACTERISTICS IN DIFFERENT

TUNDISH CASES FROM NUMERICAL AND PHYSICAL SIMULATIONS

Case Method tmin/s tmax/s tav/s vp/% vd/% vm/%

C0 Numerical 68 123 285 26 28 46

Physical 63 76 235 19 35 45

C11 Numerical 86 185 320 37 17 46

Physical 82 165 313 34 14 52

C7 Numerical 70 113 297 25 24 51

Physical 63 99 273 22 25 53

C6 Numerical 54 169 321 31 19 50

Physical 54 91 286 20 21 59

In order to compare the velocity and temperature

fields in the tundish with different configurations, the

former tundish configuration and the optimum one

were chosen to conduct such comparison in the

mathematical simulation. The velocity fields and

streamlines at symmetrical longitudinal plane and

liquid surface in the former tundish configuration are

presented in Figs. 8 and 9, respectively. It is known

from the two figures that the liquid steel flowing out

of the long shroud impinges the bottom of the TI with

extending top lips and then flows out of the TI at the

opposite direction towards the liquid surface. There is

a big recirculation region around the stream entering

the tundish through the long shroud with the

recirculation “eye” near the TI bottom. When the

molten steel reaches the free surface, it forms a big

“spring uprush” and then flows along the surface and

against the long shroud towards to the side walls and

the weir. As the molten steel reaches these solid walls,

it turns downward. There are two other recirculation

zones near the liquid surface in the area between the

left tundish side wall and the weir, as can be seen in

Fig. 8(b). After the melt reach the tundish bottom,

some part of steel flow along the tundish bottom


115

toward the dam. Then this part of liquid steel is forced

to move upwards to the liquid surface due to the

obstruction effect of the dam. The melt flows along the

free surface toward the right side wall. Finally, it turns

down near the stopper and flows toward the tundish

outlet. A large recirculation region is formed between

the dam and the right tundish side wall. A small

recirculation flow exists in the right side of the weir.

Although some recirculation regions are formed on

the free surface near the right tundish side wall, as can

be found in Fig. 9(b), they would not lead to slag

entrapment because the velocity here is very small.

0.5m/s

(a) Velocity field

(b) Streamline

FIG. 8 FLOW FIELD AND STREAMLINES AT VERTICAL

SECTION IN THE FORMER TUNDISH CONFIGURATION

0.5m/s

(a) Flow field

(b) Streamline

FIG. 9 FLOW FIELD AND STREAMLINES AT FREE SURFACE IN

THE FORMER TUNDISH CONFIGURATION

Flow fields and corresponding streamlines in the

tundish with the optimum configuration in the

symmetrical longitudinal plane and on the free surface

are shown in Figs. 10 and 11, respectively. It can be

found from these two figures that the stream from the

long shroud impinges the bottom of the TI without

extending top lips and diverts along its bottom. The

melt rushes reversely up mainly out of the 4 corners of

the TI toward the free surface where 4 small “spring

uprushes” are formed, as can be seen in Fig. 11(b).

Such phenomena could be observed visually in the

physical modeling experiments with the TI without

extending top lips. A recirculation region with small

height is formed around the shroud stream near the

TI’s bottom. The melts reached at the free surface flow

all around along the surface and turn downward at

the around walls and the symmetrical plane of the

tundish when they encounter. No other recirculation

zones are found under the free surface as those in the

former tundish configuration in the vertical

symmetrical plane. Only several very small

recirculation flowing zones can be observed on the

free surface at the left side of the weir. Such flowing

characteristics in the optimum tundish case are

different from those in the former tundish case. With

the reduction in distance between the dam and the

tundish outlet, the recirculation flow region between

the dam and the stopper becomes small, while with

increase in distance between the weir and the dam, the

recirculation zone behind the weir becomes large.

0.5m/s

(a) Flow field

(b) Streamline

FIG. 10 FLOW FIELD AND STREAMLINES AT VERTICAL

SECTION IN THE OPTIMAL TUNDISH CONFIGURATION

0.5m/s

(a) Flow field


116

(b) Streamline

FIG. 11 FLOW FIELD AND STREAMLINES AT FREE SURFACE IN

THE OPTIMAL TUNDISH CONFIGURATION

(a) Vertical symmetrical plane

(b) Free surface

FIG. 12 TEMPERATURE FIELD IN THE FORMER TUNDISH

CONFIGURATION

(a) Vertical symmetrical plane

(b) Free surface

FIG. 13 TEMPERATURE FIELD IN THE OPTIMAL TUNDISH

CONFIGURATION

Temperature distributions in the tundish with the

former and the optimum configurations are presented

in Figs. 12 and 13, respectively. It can be seen from Fig.

12 that larger temperature gradients exist along the

flow direction of liquid steel and its temperature

changes from 1821 K to 1807 K at the right side of the

weir on the free surface. The high temperature region

concentrates around the shroud stream. The molten

steel temperature range in the area of 1/2 height of the

bath near the free surface at the right side of the

stopper varies from 1819 K to 1813 K and the lowest

melt temperatures at the two side walls on the free

surface at the right side of the tundish are only 1807 K

and 1808 K, respectively. Therefore, in such areas the

molten steel flows slowly and dead zones are formed,

resulting in lower temperature regions and reduction

in effective tundish volume and being unfavorable to

making full use of metallurgical functions of tundishes.

It can be known from Fig. 13 that the temperature

gradients along the melt flow direction in the

optimum tundish configuration becomes smaller than

those in the former tundish case. The high

temperature zones disperse at the 4 gushes above the 4

corners of the TI. There are larger areas where the

temperature is between 1822 K and 1821 K in the

vertical symmetrical plane and on the free surface. The

molten steel temperature range in the area of 1/7

height of the bath near the free surface at the right side

of the stopper varies from 1819 K to 1816 K and the

lowest melt temperature at the two side walls on the

free surface at the right side of the tundish is 1813 K. It

is indicated from the above results that the molten

steel flow is reasonable and dead volume and low

temperature regions are reduced in the optimum

tundish configuration.

Conclusions

Molten steel flow in a wide single‐strand tundish with

different FCDs for slab continuous‐casting was

investigated by physical and mathematical

simulations in this work. The following conclusions

can be drawn out from this investigation.

(1) The former tundish configuration and the former

FCDs are not reasonable, resulting in poor flow

characteristics. The residence times are short and the

dead zone volume is large, being 35%. Such tundish

configuration is unfavorable to the inclusion removal.

(2) Adoption of a TI without extending top lips in this

tundish can improve flow characteristics in

comparison to the former TI with extending top lips in

this special tundish. Increase in the height of weir and

dam and movement of the weir and dam toward the

outlet of the tundish can prolong residence times and

reduce dead zone volume.

(3) In comparison with the former tundish

configuration, the flow characteristics in the optimum

tundish case are improved to a great extent; minimum

residence time, peak concentration time and average


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residence time are increased from 64 s, 81 s and 237 s

to 81 s, 163 s and 314s, respectively, and the fraction of

dead zone volume decreases from 35% to 14%, being

reduced by 60%.

(4) Liquid steel flowing out of the long shroud

impinges the bottom of the TI with extending top lips

and then flows out of the TI at the opposite direction

towards the liquid surface. A big recirculation region

around the stream entering the tundish through the

long shroud is formed. A big “spring uprush” appears

around the long shroud on the free surface.

(5) Liquid steel from the long shroud impinges the

bottom of the TI without extending top lips and rushes

reversely up mainly out of the 4 corners of the TI

toward the free surface where 4 small “spring

uprushes” are formed. The recirculation region

around the stream entering the tundish becomes small.

(6) Larger temperature gradients in the former tundish

configuration exist along the flow direction of liquid

steel and its temperature changes from 1821 K to 1807

K at the right side of the weir on the free surface.

There is a larger low temperature zone in the area of

1/2 height of the bath near the free surface at the right

side of the stopper and the lowest melt temperatures

at the two side walls on the free surface at the right

side of the tundish are only 1807 K and 1808 K,

respectively. This indicates that the velocity of liquid

steel in this area is low and large dead zone volume

exists.

(7) The molten steel temperature ranging from 1819 K

to 1816 K in the optimum tundish configuration only

occupies the area of 1/7 height of the bath near the free

surface at the right side of the stopper and the lowest

melt temperatures at the two side walls on the free

surface at the right side of the tundish is 1813 K. The

molten steel flow is reasonable and dead volume and

low temperature regions are reduced.

(8) RTD curves obtained from the mathematical

simulations are in basic agreement with those from the

corresponding physical modeling experiments. The

calculated flow characteristics from the RTD curves in

mathematical simulations are coincident with those

from the measured RTD curves. The results of the

mathematical simulations can reflect fluid flow

characteristics in different tundish configurations.

ACKNOWNLEDGMENTS

The authors are very grateful to National Natural

Science Foundation of China for financial support of

this key research project (No. 61333006).

REFERENCES

Craig K J, Kock de D J, Makgata K W, et al. “Design

Optimization of a Single‐strand Continuous Caster

Tundish Using Residence Time Distribution Data.” ISIJ

International, 2001, 41(10), 1194–1200.

Jha P K, Dash S K, Kumar S. “Fluid flow and mixing in a six

strand billet caster tundish: a parametric study.” ISIJ Int,

2001, 41 (12), 1437‐1446.

Kim H B, Guthrie R I L, Isac M, et al. “The effect of flow

modifiers on the hydrodynamic performance of a delta

shaped, four‐strand tundish.” ISS Tech 2003 Conf Proc:

ISS, Warrendale, 2003, 215‐224.

Kumar A, Mazumdar D, Koria S C. “Modeling of Fluid Flow

and Residence Time Distribution in a Four‐strand

Tundish for Enhancing Inclusion Removal.” ISIJ

International, 2008, 48 (1), 38–47.

Mazumdar D, Guthrie R I L. “The physical and

mathematical modeling of continuous casting tundish

systems. ” ISIJ Int, 1999, 39 (6). 24‐547.

Miki Y, Thomas B G. “Modeling of inclusion removal in a

tundish.” Metall and Mater Trans B, 1999, 30(8), 639‐654.

Morales R D, Barreto J J, Lopez‐Ramirez S, et al. “Melt flow

control in a multistrand tundish using a turbulence

inhibitor.” Metall and Mater Trans B, 2000, 31 (11), 1505‐

1515.

Morales R D, López‐Ramirez S, Palafox‐Ramos J, et al.

“Numerical and Modeling Analysis of Fluid Flow and

Heat Transfer of Liquid Steel in a Tundish with Different

Flow Control Devices.” ISIJ International, 1999, 39 (5),

455‐462.

Palafox‐Rams J, Barreto J, Lopez‐Ramire S, et al. “Melt Flow

Optimization Using Turbulence Inhibitors in Large

Volume Tundishes.” Ironmaking and Steelmaking, 2001,

28(2), 101‐109.

Ramos‐Banderas A, Morales R D, García‐Demedices L, et al.

“Mathematical Simulation and Modeling of Steel Flow

with Gas Bubbling in Trough Type Tundishes, ISIJ

International.” 2003, 43 (5), 653–662

Ray S K, Isac M, Guthrie R I L. “Modelling performance of

four‐strand, 12 t delta shaped continuous casting tundish

fitted with different flow modifying arrangements for

better steel quality.” Ironmaking and Steelmaking, 2011,


118

38 (3), 173‐180.

Sahai Y, Emi T. “Melt flow characterization in continuous

casting tundishes.” ISIJ Int, 1996, 36(6), 667‐672.

Tomasz Merder, Jacek Pieprzyca. “Optimization of Two‐

Strand Industrial Tundish Work with Use of Turbulence

Inhibitors: Physical and Numerical Modeling.” Steel

Research Int, 2012, 83 (11), 1029‐1038.

Zhong Liangcai, Li Baokuang, Zhu Yingxiong, et al. “Fluid

Flow in A Four‐strand Bloom Continuous Casting

Tundish with Different Flow Modifiers.” ISIJ

International, 2007, 47 (1), 88–94.

Zhong Liangcai, Zhang Li, Huang Yaowen, et al.

“Influence of Various Turbulence Inhibitor on Fluid Flow

Behavior in Tundish.” J of Iron and Steel Research, 2002,

14(4), 6‐9.

Physical and Mathematical Simulation of Fluid Flow in a Wide Single-strand Tundish for Slab Continuo

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Transcript of Physical and Mathematical Simulation of Fluid Flow in a Wide Single-strand Tundish for Slab Continuo