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

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 School of Materials and Metallurgy, Northeastern University, Shenyang 110004, China; 5Pinggang Jiujiang Branch Corporation, Jiujiang 332000, Jiangxi, China.

1‐4

*1

zhonglc@126.com; 2ohaoruichaoo0203@126.com; 3why873936932@126.com; 4lileineu2008@163.com

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,

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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.

Mixing flow volume fraction vm

vm 

Vm  1  vd  vp (5) V

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: Qm   2.5Q p

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:

(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:

Continuity Momentum

 p    (  ui u j )    eff xi xi xi 

tav 

 tc  t  dt

0 

 c  t  dt

0

 ti c  ti  ti i

n

 c  ti  ti

(2)

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:

i

Plug flow volume fraction vp Vp   min   max  vp    (3) V  2  Dead zone volume fraction vd 14 V  Q  vd  d  1  a  a  (4) V  Q 

110

     gi (7)  

eff    t (8)

n



 u u j  i   x j xi 

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:

Average residence time tav 

 (  ui )  0 (6) xi

Turbulent kinetic energy     k    ui k    eff   G   (9) xi xi  οk xi 

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Dissipation rate of turbulent kinetic energy

Boundary Conditions

         ui     eff    C1G  C2   (10) xi xi   xi  k

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.

The generation term, G in Equs. (9) and (10) can be given as:  u u j  u  G  2 t  i    t  i    xi   x j xi 2

2

  (11)  

The turbulent viscosity, μt can be written as:

t 

C  k 2



(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:  (  CP uiT )   T    eff  (13) xi xi  xi 

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.

where the effective thermal conductivity, λeff, is the sum of two components: C p t eff    (14) Prt

TABLE 1 PARAMETERS FOR MATHEMATICAL SIMULATION OF LIQUID STEEL FLOW IN THE TUNDISH

here, Prt is the turbulent Prandtl number, λ is thermal conductivity, Cp is heat capacity and T is temperature.

Parameters Values Liquid steel 7000 density/kg∙m‐3 Liquid steel 41 conductivity/W∙m‐1∙K‐1

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:

1823

Heat flux at bottom/kW∙m‐2

1.4

Heat flux at transverse walls /kW∙m‐2

3.8

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.

c  (ui c)   c     Deff  (15) t xi xi  xi 

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:

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

 Deff  1 (16) eff

Inlet temperature/K

Parameters Values Liquid steel 0.0067 viscosity/kg∙m‐1∙s‐1 Liquid steel specific 750 heat /J∙kg‐1∙K‐1 Heat flux at walls 1.75 inside tundish/kW∙m‐2 Heat flux at liquid 15 surface/kW∙m‐2 Heat flux at 3.2 longitudinal walls/kW∙m‐2

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TIs are all square at horizontal cross‐section except TI3 whose horizontal cross‐section is rectangle with 280 mm short sides.

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.

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.

Results and Discussion Physical Modeling

FIG. 2 SCHEMATIC OF TUNDISH CONFIGURATIONS IN THE EXPERIMANTS TABLE 2 TYPICAL TUNDISH CONFIGURATIONS IN EXPERIMENTS

Case C0 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11

TI TI1 TI1 TI1 TI2 TI3 TI4 ‐ TI1 TI5 TI5 TI5 TI5

S1/mm 632 590 590 590 590 540 390 390 540 440 390 390

S2/mm 108 108 200 150 150 200 150 150 200 200 200 150

H1/mm 96 96 130 55 55 55 55 55 55 55 55 55

H2/mm 136 136 205 205 205 225 250 250 250 250 250 250

2.0

1.5

C0

C/-

C7

FIG. 3 SCHEMATIC OF SOME TURBULENCE INHIBITORS IN THE EXPERIMENTS

C11

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

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C6

1.0

0.5

0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

/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

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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.

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%.

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.

TABLE 3 FLOW CHARACTERISTICS IN DIFFERENT TUNDISH CONFIGURATIONS

Case C0 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11

tmin/s 64 64 70 78 80 78 54 63 88 82 79 81

tmax/s 81 81 108 113 130 134 91 99 121 139 141 163

tav/s 237 241 249 279 280 289 286 273 291 303 307 314

vp/% 20 20 24 26 29 29 20 22 29 30 30 33

vd/% 35 34 32 24 23 21 21 25 20 17 16 14

vm/% 45 46 44 50 48 50 59 53 51 53 54 53

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.

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.

35

vd /%

30

25

20

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

TI: TI1, S2=108 mm, H1=96 mm, H2=136 mm

TI: TI5, S2=150 mm, H1=55 mm, H2=250 mm

15 350

400

450

500

550

600

650

S1/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.

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.

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.

TABLE 4 COMPARISON OF FLUID FLOW CHARACTERISTICS IN DIFFERENT TUNDISH CASES FROM NUMERICAL AND PHYSICAL SIMULATIONS

Case C0 C11

Mathematical Simulation

C7 C6

Physical result for C6 1.5

C/-

Nmerical result for C6

Nmerical result for C7 0.5

0.0 0

1

2

/ -

3

4

FIG. 6 RTD CURVES FROM MATHEMATICAL AND PHYSICAL SIMULATIONS IN C6 AND C7 TUNDISH CONFIGURATIONS

Physical result for C0 1.5

Numerical result for C0 Numerical result for C11

1.0

C/-

Physical result for C11

0.5

0.0 0

1

2

/-

3

4

FIG. 7 RTD CURVES FROM MATHEMATICAL AND PHYSICAL SIMULTIONS IN C0 AND C11 TUNDISH CONFIGURATIONS

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tmin/s 68 63 86 82 70 63 54 54

tmax/s 123 76 185 165 113 99 169 91

tav/s 285 235 320 313 297 273 321 286

vp/% 26 19 37 34 25 22 31 20

vd/% 28 35 17 14 24 25 19 21

vm/% 46 45 46 52 51 53 50 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

Physical result for C7

1.0

Method Numerical Physical Numerical Physical Numerical Physical Numerical Physical

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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.

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

0.5m/s

(b) Streamline FIG. 8 FLOW FIELD AND STREAMLINES AT VERTICAL SECTION IN THE FORMER TUNDISH CONFIGURATION 0.5m/s

(a) Flow field

(a) Flow field

(b) Streamline FIG. 10 FLOW FIELD AND STREAMLINES AT VERTICAL SECTION IN THE OPTIMAL TUNDISH CONFIGURATION 0.5m/s

(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

(a) Flow field

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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.

(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

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.

(a) Vertical symmetrical plane

(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.

(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

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(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%.

this key research project (No. 61333006).

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ACKNOWNLEDGMENTS

four‐strand, 12 t delta shaped continuous casting tundish fitted with different flow modifying arrangements for

The authors are very grateful to National Natural Science Foundation of China for financial support of

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