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JOURNAL OF IRON AND STEEL RESEARCH, INTERNATIONAL. 2013, 20(3) : 06-17

Multiphase Flow and Thermo-Mechanical Behaviors of Solidifying Shell in Continuous Casting Mold

ZHU Miao-yong, CAI Zhao-zhen, YU Hai-qi (School of Materials and Metallurgy, Northeastern University, Shenyang 110819, Liaoning, China)

Abstract: The metallurgical phenomena occurring in the continuous casting mold have a significant influence on the performance and the quality of steel product. The multiphase flow phenomena of molten steel, steel/slag interface and gas bubbles in the slab continuous casting mold were described by numerical simulation, and the effect of electro­magnetic brake (EMBR) and argon gas blowing on the process were investigated. The relationship between wavy fluctuation height near meniscus and the level fluctuation index F , which reflects the situation of mold flux entrap­ment, was clarified. Moreover, based on a microsegregation model of solute elements in mushy zone with 8/7 trans­formation and a thermo-mechanical coupling finite element model of shell solidification, the thermal and mechanical behaviors of solidifying shell including the dynamic distribution laws of air gap and mold flux, temperature and stress of shell in slab continuous casting mold were described. Key words : continuous casting mold; multiphase flow; heat transfer; solidification; numerical simulation

The continuous casting mold has been taken as the heart of continuous casting machine due to its important roles of heat transfer with high efficiency, cleaning molten steel and controlling strand quality during casting performance. The molten steel flow in the continuous casting mold has a great influence on the important phenomena related to product qual­ity, including the entrapment of inclusions and ar­gon gas bubbles on the solidified shell and the tem­perature distribution of molten steel. Electromag­netic brake (EMBR) and argon gas injection as the concerned molten steel flow-control technologies in the mold for improving the quality of continuous casting slab at high casting speed are of great help and significance. So it is necessary to have an in-depth understanding that the flow and steel/slag in­terface behaviors particularly in the case of applying different in-mold flow-control methods to achieve the perfect metallurgical objectives. Numerical sim­ulation as an economical and effective method has been developed and applied widely to study the flow and interfacial behavior in continuous casting mold'-1-9-'. However, the steel/slag interface charac­

teristics as various flow-control means are applied, especially in the case of coupling the EMBR and ar­gon gas injection, has been rarely considered.

Thermal and mechanical behaviors of the solidi­fying shell in continuous casting mold are linked to the performance of continuous casting and the quali­ty of slab, which are controlled mainly by the inter­face thermal resistance between shell and mold cop­per plate and mechanical loads. Therefore, the be­haviors of mold flux such as state, thickness distri­bution and heat transfer characteristics, air gap dis­tribution, cooling structure of mold and cooling sys­tem , as well as mold taper setting have a great effect on the progress of steel solidification in mold. Be­cause of the limitation of detection and measure­ment, most of the studies on shell thermal and me­chanical behaviors in mold also have been carried out by computer simulation without considering the effect of mold flux film between solidifying shell and mold on shell heat transfer or just assuming the uni­form distribution of mold fluxDo-17]. Actually, the thickness of mold flux along the circumference and the height of mold are not uniform since the thermal

Foundation Item:Item Sponsored by National Outstanding Young Scientist Foundation of China (50925415) ; Fundamental Research Funds for Central Universities of China (N100102001)

Biography:ZHU Miao-yong(1965—), Male, Doctor, Professor; E-mail: myzhu@mail.neu.edu.cn; Received Date: September 3, 2012

I s sue 3 M u l t i p h a s e F l o w a n d T h e r m o - M e c h a n i c a l Behav io r s of Sol idifying Shel l in C o n t i n u o u s C a s t i n g M o l d · 7 ·

contraction of initially solidified shell changes dy­namically in mold, and both the mold flux state and mold/flux interfacial thermal resistance also vary with the temperature of shell.

In this paper, the multiphase flow phenomena of molten steel, steel/slag interface and gas bubbles in the slab continuous casting mold were described by numerical simulation, and the effects of EMBR and argon gas blowing on the process were investi­gated. The relationship between wavy fluctuation height near meniscus and level fluctuation index F reflecting the situation of mold flux entrapment was clarified. Based on a microsegregation model of sol­ute elements in mushy zone with 8/y transformation and a thermo-mechanical coupling finite element model of shell solidification, the thermal and me­chanical behaviors of solidifying shell including the dynamic distribution laws of air gap, mold flux, shell temperature and stress in slab continuous cast­ing mold were analyzed.

1 Mathematical Model and Procedure 1.1 Multiphase flow in mold

Fig. 1 shows the schematics of one quarter mold geometry model with EMBR device and the mesh di-

Fig. 1 Schematics of geometrical model of mold with EMBR (a) and grid division of mold (b)

vision of the mold. There is a liquid slag layer on top of molten steel in the mold. The detailed geome­try and simulation process parameters are given in Table 1. In the present study, additional magnetic field produced by the molten steel flow in the mold, and the influence of the solidified shell and the oscil­lation of mold on the molten steel flow are ignored. The gas bubbles are assumed to be spherical with a uniform size.

Table 1 Process and physical parameters Parameters Valu

Mold size ( width X thickness)

SEN submergence dep th /mm

SEN port angle/ C )

Casting speed t i c / ( m · m i n - 1 )

Molten steel dens i ty / (kg · m - 3 )

Molten steel viscosity/(Pa · s)

Molten steel electric conductivity/( S · m - 1 )

Molten steel magnetic conductivity/ ( H · m - 1 )

Armature core magnetic conductivity/( H · m - 1 )

Copper mold electric conductivity/(S · m _ 1 )

Argon gas bubble diameter /mm

Argon gas dens i ty / (kg · m - 3 )

Argon gas flow rate vJCL· · m i n _ 1 ) ( 1 0 1 . 325 kPa , 298 K)

Liquid slag dens i ty / (kg · m - 3 )

Liquid slag viscosity/(Pa · s)

Thickness of liquid slag layer/mm

Steel/slag interface tension coefficient/(N · m - 1 )

Contact angle of steel/slag i n t e r f a c e / O

Circle number of coils/loops

Upper coil current of EMBR i u / A

Lower coil current of EMBR J L / A

1150 mmX224 mm

170

- 1 5

2 . 1

7100

0.005 5

7. 14X10 5

1 .257X10-«

1. 2 5 7 X 1 0 ~ 3

4. 7 X 1 0 7

1

0 .32

2 , 4 , 6

2 700

0 .2

20

1.6

60

80

0, 100, 200, 300

500, 600, 700, 850

1.1.1 Governing equations and boundary conditions The governing equations include the electromagnetic

field equations, the VOF model equation for tracking the

steel/slag interface, the Lagrangian discrete phase model (DPM) equation for predicting the influence of argon gas injection, and the three-dimensional Navier-Stokes

• 8 · Journal of Iron and Steel Research, International Vol. 20

equations. The detailed descriptions have been ex­pressed in the published papers1-8-9-1.

For three-dimensional calculation, only a quarter of the EMBR device and mold are analysed because the twofold symmetry of the mold and the static magnetic field is produced by the EMBR. For the boundary conditions of electromagnetic field calculation based on ANSYS, the boundary conditions in the symme­try planes and the air surfaces need only to be set with the magnetic flux parallel condition. For the boundary conditions of flow field and steel/slag in­terface calculation based on FLUENT, the inlet of SEN and the outlet of the mold as the velocity-inlet have the same mass flow rate corresponding to the specified casting speed, and the volume fraction of molten steel at the inlet was set to 1 ; normal gradi­ents of all variables at the symmetry planes were set to zero; the wall was set to non-slip boundary condi­tion with zero normal velocity and the standard "wall functions" near the wall were used to capture the steep gradients with accuracy on a coarse grid. For the boundary conditions of discrete phases calcula­tion based on FLUENT, the gas bubbles were as­sumed to "escape" at the steel/slag interface and the outlet of the mold, and to "reflect" at the mold walls. The initial locations of bubbles were assumed to be uniformly distributed within the inlet surface and the initial velocity was the same as the inlet ve­locity of molten steel.

For the boundary conditions of electric potential calculation based on FLUENT, the mold walls were set to insulating wall boundary condition with zero normal component of current density; the normal gradient of current density was set to be zero at the inlet and outlet surfaces. 1.1.2 Solution procedure

Solution process was divided into two parts. Firstly, during the calculation procedure of electro­magnetic field based on ANSYS, a magnetic vector po­tential method was used to solve the Maxwell equations and obtain the electromagnetic field for different cur­rent intensities of coils1-8-1. Then, the data files of the magnetic induction intensity in the mold region were exported to a data file according to a certain file form. Secondly, all other fields were solved by FLUENT. All coupled fields including flow field, steel/slag interface, trajectories of argon gas bubbles and magnetic field were solved, in which its own MHD module needed to be activated and the magnet­ic field data file was loaded to the flow region in the mold with a certain required data format. The pres­

sure-velocity coupling algorithm was PISO algorithm, The trajectories of bubbles were solved using the Random Walk model of DPM, and the influence of turbulent fluctuation of velocity field on the turbu­lent diffusion effect of bubbles was considered. The geometric reconstruction approach was used to re­present the steel/slag interface shape in order to ob­tain the most accurate interface pattern and the con­tinuum surface force (CSF) model was employed to describe the effect 'θί surface tension1-9-1.

1. 2 Thermo-mechanical behaviors of solidifying shell in mold 1.2.1 Microsegregation model

The physical properties of solidifying steel asso­ciated with the chemical composition and reflecting the actual process of shell solidification in mold with δ/γ transformation are very important for describing the solidifying characteristics of steel at high temper­ature precisely. In previous work1-18-1, based on the regular hexagon transverse cross-section of dendrite shape proposed by Y Ueshima et alCl9], a microseg­regation model of solute elements in mushy zone with δ/γ transformation during steel solidification was established by finite difference method. The dendrite arm spacing of steel in the model was cho­sen as the primary dendrite arm spacing formula, λ = Κν"τυο(λ is dendrite arm spacing, K, a, b are con­stants, v is cooling rate, and wc is carbon content), proposed by M El-Bealy and B G ThomasC20] since it is related to cooling rate and carbon content during practical continuous casting. The average cooling rate of mold, 10 °C/s, was applied for the parameter of cooling rate in the model.

Based on relationship of phase fraction and tem­perature obtained from the microsegregation model, the properties of the peritectic steel such as thermal conductivity, enthalpy, density and linear thermal expansion coefficient in mushy zone with tempera­ture were determined by the formulas proposed by C Li and B G Thomascl3] as shown in previous work1-21·1. It is noteworthy that the conductivity of liquid steel was amplified 6. 0 times for accounting the effect of convection heat transfer of strand in liq­uid zone and the arbitrary reference temperature of linear thermal expansion, Tref, was defined as LIT (Liquid Impenetrable Temperature) that the fraction of solid phase equals 0. 884 determined by the previ­ous work1-18-1. 1. 2. 2 Mold/shell inter facial heat transfer model

The determination of heat flux boundary be-

Issue 3 Multiphase Flow and Thermo-Mechanical Behaviors of Solidifying Shell in Continuous Casting Mold · 9 ■

tween shell and mold precisely is the basis and key step for numerically investigating the shell thermal and mechanical behavior. Fig. 2 schematically shows the process of shell solidifying and heat transfer in mold. With the thermal contraction action of solidif­ying shell and mold flux, the air gap forms between the interface of solidifying shell and mold flux.

Therefore, the components of heat transfer between shell and mold mainly consisted of shell/mold flux interfacial heat transfer, mold flux heat transfer, air gap heat transfer, and mold flux/copper plate inter-facial heat transfer. The thickness of every heat trans­fer medium layer changes dynamically for shell contrac­tion along the circumference and height of mold.

Mold

Air gap

Mold Interface (liermal

resistance

Interface Mold flux

Shell

Shell

Fig. 2 Schematic diagram of copper/shell interface and heat transfer process in mold

In order to establish the model more conveniently, some assumptions were made as follows : 1 ) the composition change between glassy layer and crys­talline layer in solid flux was ignored, and the mold flux just consists of liquid with very good fluidity and solid; 2) the state of mold flux is determined by the shell surface temperature, copper plate hot face temperature and its solidus temperature, and thick­ness of the flux is just dependent on shell surface temperature and gap thickness between mold and shell; 3) the deformation of mold flux due to solidi­fication was neglected, and its effect was treated by introducing the interfacial thermal resistance be­tween mold and flux in the model. The formula of interfacial heat flux between mold and shell can be given as follows;

T —T J?Uq "T^so l "Γ-Rair T-Rint

where, q is the interfacial heat flux between mold and shell; Ts and Tm are shell surface temperature and copper hot face temperature, respectively; and ■Riiq > -Rsoi > -Rair and RiM , are the thermal resistances of the liquid flux, solid flux, air gap and mold/flux in­terface, respectively, which have been expressed in previous publication1-213. Therefore, a new shell/mold interfacial heat flux model considering conduction heat transfer and radiation heat transfer was devel­

oped based on the displacement between shell sur­face and mold hot face as shell shrinkage, the dy­namic distributions of mold flux and air gap, and the temperature distributions of shell surface and mold hot face in the present work. The modelling process of the model was shown in previous work[21]. The thermo-physical properties of heat transfer medium are given in Table 2C22_24]. 1.2. 3 Finite element model

1) Heat transfer model Based on the symmetrical assumption of shell

solidification in mold, a two-dimensional transient heat transfer model for shell and mold was modeled, and the governing equations can be expressed as fol­lows respectively:

dH(T) dt 3T

("It"

dx

~dx

AS(T)|̂ 1 +^,U(T) 3T dy

rr dx By

dT) Am 'i

3y

(2)

(3)

where H(T) and AS(T) are the enthalpy and thermal conductivity of the peritectic. steel obtained from chapter 1. 2. 1 with temperature that the chemical composition is shown in Table 3. p, c and Xm are the density, heat capacity and thermal conductivity of copper respectively as shown in Table 4. In the present study, 1. 0% was chosen for the mold nar­row face taper, while the two wide faces were parallel,

• 10 · J o u r n a l of I r o n a n d S tee l R e s e a r c h , I n t e r n a t i o n a l Vol . 20

Table 2 Thermal physical properties of flux

Description Item Unit Valu

Shell

Liquid slag layer

Solid slag layer

Air gap layer

Mold

Emissivity

Thermal conductivity, &iiq

Absorption coefficient, δ

Refractive index, nu,

Thermal conductivity, kmi

Extinction coefficient, E^Ì

Emissivity, esol

Refractive index, n80i

Solidus temperature , T«,!

Thermal conductivity, £ajr

Emissivity, emoid

W - m " 1 · K " 1

W · m " 1 · K 1

W · m " 1 · K-

0 .8

0.26

51

1.58

1.625

1356

0 .9

1.59

1409

0.06

0 .4

Table 3 Chemical composition of peritectic steel

( m a s s p e r c e n t , % )

c 0.15

Table 4

Material

Si Mn

0. 25 1. 5

Thermal properties of Thermal

conductivity/ ( W · m " 1 · K " 1 )

P

0.015

copper plate

(J

Specific heat /

kg^ 1 · K~

and

')

S

0.008

cooling water

Density/ (kg · m ~ 3 )

Copper Copper Copper Nickel Water

335 (298 K) 315 (393 K) 310 (623 K)

82.9 0.597

410 410 410

460.6 4187

8 940 8 940 8 940 8 910 998

namely no taper. The boundary conditions of heat transfer were

treated as : 1) heat flux at cold face of steel backup and symmetrical plane of slab and mold is 0; 2) shell surface and copper hot face loaded the heat flux by mold/shell interfacial heat transfer model dynamically; 3) the heat transfer between mold and cooling water is determined by heat transfer coefficient, hw , as fol­lows"23

Aw

= 0.023 μ·»

^w/*w

Aw

(4)

where, λ„ is the heat conductivity coefficient of wa­ter; d„ is the hydraulic diameter of the water slots; pw, ww, μ„ and cw are the density, velocity, viscosity and specific heat of cooling water, respectively.

2) Stress model Since the shell solidification in the mold subjects

to the deformations of elastic, thermal and plastic, as well as the creep during practical continuous cast­ing, a rate dependent constitutive equation proposed by L AnandC25] and S B Brown et alC26] was adopted in this work, which can be written as follows:

e i e=Aexp — [ QA T

sinh * '

(5)

The evolution equations for s is 5

; = {h0 1-

Lexp T

s i g n ^ x p

QA }< (6)

The meaning and value of the parameters in the formula are listed in Table 5E27]. The elastic modulus and Poison s ratio were determined by formulas re­gressed from the data measured by H Mizukami et alC28] and M Uehara et al[29], respectively.

Table 5 Specification for constitutive equation parameters

Parameter Meaning Unit Valu

io Initial value of s, deformation resistance

QA Activation energy/gas constant

A Pre-exponential factor

ξ Multiplier of stress

m Strain rate sensitivity of stress

ho Hardening/softening constant

3" Coefficient for deformation resistance saturation value

n Strain rate sensitivity of saturation value

a Strain rate sensitivity of hardening or softening

ς Time derivative of deformation resistance

MPa

K

s " 1

MPa

MPa

43

32514

1 . 0 X 1 0 "

1.-15

0.147

1329

147.6

0.068 69

1

MPa

Issue 3 Multiphase Flow and Thermo-Mechanical Behaviors of Solidifying Shell in Continuous Casting Mold · 11 ·

T h e boundary conditions for s t ress model were given as · 1) the contact between shell surface and mold hot face was rigid-to-flexible; 2 ) the effect of mold narrow face taper was t reated as displacement increment as a function of height from steel bath level to mold exit ; 3) ferro-static pressure was loaded on solidification front at solid phase / , = 0. 884 with an algori thm tha t reject the "liquid element" dynamically as solidification proceeded1-21-1. T h e value of the p res ­sure P was determined as

P=pmgvct ( 7 ) w h e r e , pm is densi ty of mo l t en s t ee l , k g / m 3 ; t is

t ime , s.

2 Results and Discussion 2 . 1 Simulation results verification

Fig. 3 shows the comparison of water model ex­perimental and simulated resul ts in the mold. It is obvious tha t the flow fields and bubble trajectories both are in a good agreement in the two cases.

Fig. 4 shows the predicted mold copper tempera­ture dis tr ibut ions at the positions of thermocouples and corresponding measured tempera ture at the con­ditions of casting speed of 1. 4 m/min and solidus tem-

Vc~2. 1 m/min, vt = 6 L/min. Fig. 3 Comparison of experimental (a) and predicted (b) flow and bubble trajectories in mold

180

160

140

120

100

80

(a)

1

-

Thermocouple

"—'« 7 ^ - 1 «"""i *~~, l * ^ ! ,»_ I*·*. ' K'J · < - . ' ««■«· ' . - . 1 \

\ \ t \ t 1

» 1 i i l 1 \ 1

Upper row thermocouple ' \ - - Down row thermocouple , \

I I 1 l

(b)

Thermocouple A - - Thermocouple B ■-· ThermocoupleC

-o— Thermocouple A' -o— Thermocouple B' -*— Thermocouple C

0 100 300 500 700 Distance from mold wide face centerline/mm

160

140

120

100

(c) Thermocouple

■ D y^~ D'

* " " " ■ - - . . - " "

Upper row thermocouple - - - - Down row thermocouple

1 I I

•1

m *

2:26:00

(d)

^ V % r ^

2:27:40 2:29:20 Time

Thermocouple D —o— Thermocouple D'

I 1

0 15 45 75 105 Distance from narrow centerline of slab/mm

2:26:00 2:27:40 Time

2:29:20

Fig. 4 Comparison of predicted temperature of mold copper plate at position of thermocouple installations and corresponding measured temperature of wide face (a) , (b) and narrow face (c) , (d)

• 12 · Journal of Iron and Steel Research, International Vol. 20

perature of mold flux of 1136 'C. The calculated re­sults show that the temperature distributions both in wide face and narrow face of mold copper plates are in a good agreement.

2. 2 Behaviors of multiphase flow in mold 2. 2. 1 Basic characteristics of multiphase flow in mold

Fig. 5 shows the flow fields at the center sym­metry planes of the mold. The free surface is defined as the calm steel/slag interface, and black colour in the tops of planes represents the liquid slag. It is very influential on the flow pattern as the argon gas flow rate is 4 L/min. Most of molten steel from the SEN port directly flows upwards with the argon gas bubbles, the eddy eye of the upper re-circulation zone disappears and the re-circulating velocity is ob­

viously reduced as shown in Fig. 5 ( b ) . Fig. 5 (c) shows the case with EMBR, and it can be seen that the flow velocity of molten steel wholly decreases, especially near the steel/slag interface and the me­niscus, and the area of re-circulation zones also de­creases. A small vortex flow opposite to the upper re-circulating flow direction at the interface near the side of SEN can be found. Fig. 5 (d) shows the case with the double actions of EMBR and argon gas in­jection, where the re-circulating velocity in the up­per re-circulation zone and the vortex velocity of vortex flow zone near the SEN increase evidently. Obviously, argon gas injection could aggravate the vortex intensity, thus the appropriate argon gas flow rate with EMBR is crucial for keeping the sta­bility of steel/slag interface and preventing the oc­currence of slag entrapment.

uW>0))

(a) Without argon gas injection and EMBRs (b) With argon gas injection ( » , = 4 L/min) ; (c) With EMBR ( Ju = 200 A, iL = 700 A) ; (d) With argon gas injection and EMBR.

Fig. 5 Velocity fields at half thickness symmetric planes of mold for different flow control means ( vc = 2 . 1 m/min)

2. 2. 2 Wavy fluctuation height in mold and level fluctuation index

Since the flow and steel/slag interface behaviors in the mold particularly in the case of applying dif­ferent in-mold flow-control methods have a very close relation to the quality of slab and the perform­ance of casting, the flow pattern and the steel/slag interface profiles for difierent flow-control means have been numerically investigated1-8-9]. T Teshima et al1-30-1 presented the level fluctuation index of F value to reflect the situation of mold flux entrapment quantitatively by both water model and actual meas­urements in plant, which can be rewritten as

rr—/QmQLfeQ —sing) 1 . . . F ~ 4 'D ( 8 )

where, QL is flow rate of molten steel, m 3 / s ; ve is penetrating velocity of main steel stream, m / s ; D is the distance between penetrating point at the wall and free surface, m; and Θ is the steel stream pene­trating angle, (°).

The physical meaning of each symbols of Eqn. (8) is shown in Fig. 6.

In the present work, the F was employed to study the effect of different flow-control methods and parameters in mold.

W—Mold wide face width; a—Port angle of SEN. Fig. 6 Physical meaning of symbols in Eqn. (8)

Issue 3 Multiphase Flow and Thermo-Mechanical Behaviors of Solidifying Shell in Continuous Casting Mold · 13 ·

Fig. 7 shows the relationship between F value and argon gas flow rate or the maximum level fluc­tuat ion near meniscus in mold wi th EMBR. It shows that the value of F increases linearly wi th the argon gas flow r a t e , and with the increase of F va lue , the maximum level fluctuation height of s tee l / s lag inter­face near meniscus turns upward to downward, which shows the linearly decreasing relat ionship. T h a t is to say , the thickness of liquid flux near meniscus in­creases wi th the F value as argon gas flow rate in­creases. Th i s figure indicates that as the value of F is in the range of 12 — 1 6 , the maximum level fluctu­ation near meniscus is no more than 4 m m and the s tee l /s lag interface will not expose to the air. T h e relationship between F value and casting speed or the maximum level fluctuation near meniscus wi th EMBR and argon gas bubbling in mold is shown in Fig. 8. It is obvious that the value of F increases lin­early with casting speed. With the increase of F value, the maximum level fluctuation height of steel/slag inter­face near meniscus tu rns downward to upward , which shows the linearly increasing relationship. That is to say, with the increase of casting speed, the F value

I' Ì 2

• Gas flow rate o Level fluctuation

10

-2Ü

14 16 /"value

20

vc = 2. 1 m/min, Ιυ = 200 A, iL = 700 A. Fig. 7 Relationship between F value and argon |

flow rate or maximum level fluctuation near meniscus in mold with EMBR

2.7 r A 2.1 111

1.8

1.5 ϋ

1.2

• Casting speed ° Level fluctuation

-10 12 15

F value 18 21

». = 4. 0 L/min, Iu = 200 A, IL = 700 A. Fig. 8 Relationship between F value and casting speed or

maximum level fluctuation near meniscus with EMBR and argon gas bubbling

increases and the thickness of liquid flux near menis­cus becomes thinner. As the value of F is in the range of 15 — 2 1 , the maximum level fluctuation near meniscus is also no more than 4 m m and the s lag/ steel interface will not expose to the air.

Fig. 9 shows the relationship between F values and upper / lower coil current or the maximum level fluctuation near meniscus in mold with EMBR and argon gas bubbling. This figure shows that the value of F increases linearly wi th the upper or lower coil cur­r en t , and wi th the increase of F value, the maxi­m u m level fluctuation height of s tee l /s lag interface near meniscus tu rns from upward to downward , which shows the semi-parabolic decreasing relation­ship. T h e thickness of liquid flux near meniscus in­creases wi th the F value as coil current increases. As the value of F is in the range of 14 — 16 , the maximum level fluctuation near meniscus is no more than 4 m m and the s tee l / s lag interface will not ex­pose to the air.

F r o m the above analysis , it is clear tha t the F value linearly increases approximately with argon gas

400

< 300

1 1 200

1 | 100

0

(a)

•

• y / \ .

• Upper coil current o Level fluctuation

-

/ ·

s>

14 15 16 17

Ί I

F value

900

< 800 Ì 1 700

wer

coil

Z 500

Μ Θ ^

•

• s^\.

• Lower coil current o Level fluctuation

/m

.

X 14 15 16 17

0 I s sa

-4l

18

(a) vc = 2. 1 m/min, JL = 700 Ai (b) vc = 2. 1 m/min, iu = 200 A. Fig. 9 Relationship between F values and coil current or maximum level fluctuation near meniscus in

mold with EMBR and argon gas bubbling (4. 0 L/min)

• 14 · Journal of Iron and Steel Research, International Vol. 20

flow r a t e , casting speed or coil current intensity, and the F value can reflect effectively the fluctuation of s lag/s tee l interface near meniscus in the mold wi th EMBR and argon gas blowing. It is meaningful to control the F value in the proper range for avoiding violent fluctuation of s tee l /s lag interface and the en­t rapment of slag in mold.

2 .3 Thermal behaviour of shell solidification in mold 2. 3. 1 Air gap distribution

Fig. 10 shows the air gap distr ibution around shell corner along the direction of mold height and shell circumference. Under the casting condit ions, air gap foremost appears at the height of 160 mm be­low steel ba th level at the shell corner in mold , and presents different distr ibution characters from shell wide face and narrow face as shown in Fig. 10 ( a ) .

On the wide face, the air gap grows continuously in the casting direction and spreads to the direction of the wide face midst as the solidifying shell is moving d o w n , because the compensation by mold taper for shell shr inkage is lack and the mold flux at this re­gion solidifies relatively early. However, the thick­ness of air gap from the narrow face (wide face corner) to the midst of wide face decreases ra ther rapidly as the shell is moving down as shown in Fig. 10 ( b ) . T h e reason is tha t the surface tempera ture of solidif­ying shell at the off-corner region of wide face is rel­atively h igh , as shown thereinafter , which makes the solidification of mold flux lag , and therefore the formation of air gap is impeded. Compared to the wide face, the air gap evolution on the narrow face is quite different. A t the initial solidification s tage , the air gap increases rapidly since the heat contraction is

0.8

0.6

•§0.4

0.2

(a) a Wide face corner — Narrow face corner

200 400 600 Distance from steel bath level/mm

o 300 mm below steel bath level o 500 mm below steel bath level Δ Mold exit

10 20 30 40 Distance from shell narrow face/mm

Fig. 10 Air gap thickness distribution at shell corner along mold height (a) and around shell circumference (b)

larger than the compensation by the mold taper of narrow face. However, the thickness of air gap turns to decrease at the height of 300 mm from the steel bath level because the shell contraction decreases and the mold narrow face taper compensates continuously until it moves down to 500 mm below steel bath level, and then after the air g a p , it becomes stable. 2. 3. 2 Mold flux distribution in slag channel

T h e mold flux distr ibution around shell corner along the direction of mold height and shell circum­ference is shown in Fig. 11. T h e thickness of mold flux changes gently at the height of 0 — 50 mm below steel ba th level as the shell contracts gently for i ts high temperature . As the shell moves down , the in­creasing contraction of the shell due to its decreasing temperature makes more liquid flux flow into the slag channel between solidifying shell and mold copper plate, and reaches maximum at the height of 160 mm below steel bath level at shell corner firstly. As shell moves down cont inuously , the thickness nearby the corners

1.2

Î0.8 -

«0.4 •a o

Wide face corner Wide (ace off-corner Narrow face corner Narrow face off-corner

0 200 400 600 800 Distance from steel bath, level/mm

Fig. 11 Mold flux distribution along mold height

of wide face and narrow face becomes stable gradually because the surface tempera ture of solidifying shell decreases below the mold flux solidus. However , in the region of shell off-corner, the mold flux thick­ness increases continuously since the tempera ture in this region is higher than that of the corner and the liquid flux still can infiltrate the contraction gap un­til the shell moves to the height of 650 mm below

Issue 3 Multiphase Flow and Thermo-Mechanical Behaviors of Solidifying Shell in Continuous Casting Mold · 15 ·

the steel bath level. Such phenomena lead to the thickness of mold flux firstly increasing and then de­creasing from shell corner to the midst. It is also ob­vious that the thickness of mold flux in shell narrow face is wholly thicker than that of the wide face, which will have a negative effect on the heat transfer of narrow face. 2. 3. 3 Shell surface temperature distribution

Fig. 12 shows the surface temperature distribu­tions of the solidifying shell near the corner along the height of mold. At the initial solidification stage, the surface temperatures of the shell on wide face and narrow face are uniform. However, on the shell corner, it decreases rapidly since the heat trans­fer is two-dimensional. As the cooled solidifying shell is moving down then, the thermal contraction begins to work. Under the function of mold oscilla­tion, mold flux infiltrates the gaps continuously be-

2. 4 ■ Mechanical behaviour of shell solidification Fig. 13 shows the maximum principal stress dis­

tributions in the solidifying shell at the distance be­low steel bath level of 100, 300, 500 mm and mold exit, respectively. The deformed geometries of shell were magnified by 5 times for clearly showing the difference. Under the typical peritectic steel casting conditions, stress in shell surface layer is tensile stress, while it is compressive stress in the solidifi­cation front. From shell surface to the solidification front, the absolute value of the stress decreases firstly and then increases. At the initial solidification stage, the stress of solidifying shell is caused mainly by thermal stress and concentrates in shell corner. However, as the shell moves down, it deforms seri­ously due to the unsuitable mold taper adopted. The taper of mold narrow face is linearly decreased along

fore shell surface temperature falls below the melt­ing point of the flux, and the thermal resistance of mold/shell interface increases in this region, there­fore the drop of temperature slows down. As the shell moves down to 200 mm below steel bath level, some hot spots form in the region of 10—20 mm off the shell corner. The longer the shell moves from the bath level, the more remarkable the hot spots are. The space of the hot spots expands from 10 — 20 mm initially to 60 — 75 mm finally along shell circumfer­ence from its corner. The maximum temperature difference between the off-corner and the wide face midst or narrow face midst reaches 120 and 61 °C at mold exit, respectively. It is worth to note that the temperature of wide face off-corner surface comes to fluctuate at 200 mm above the mold exit, and it is one of the most important factors leading to the slab surface defects.

the casting direction, which is not enough to com­pensate the contraction of solidified shell fully. So, the mechanical stress becomes the main factor at the height of 300 mm below steel bath level, and the stress in shell distributes non-uniformly, as shown in Fig. 13 (b) . Such a mold taper is not suitable for peritectic steel continuous casting and a nonlinear mold taper is necessary.

3 Conclusions 1) Both the argon gas blowing and EMBR have

great influences on flow and steel/slag interface in continuous casting mold. Appropriate argon gas flow rate with EMBR is crucial for keeping the sta­bility of steel/slag interface.

2) The level fluctuation index F can reflect the situation of mold flux entrapment during continuous

Fig. 12 Shell surface temperature distribution at wide face (a) and narrow face corner (b)

• 16 · Journal of Iron and Steel Research, International Vol. 20

0.12

0.08 -

| 0.04 S e

•a

I 0.12

0.08 -

0.04 -

0.52 0.54 0.56 0.58 0.60 0.62 0.50 0.52 0.54 Distance from slab wide face center/m

0.56 0.58 0.60 0.62

Fig. 13 Maximum principal stress.of shell at various distances below steel bath level of 100 mm (a) , 300 mm (b) , 500 mm (c) and mold exit (d)

cast ing, and it has a linear relationship with operat­ing conditions such as argon gas flow ra te , casting speed and coil current in tensi ty , which would be helpful to the development and application of on-line monitoring model for flux ent rapment in mold.

3) Air gap in mold firstly forms at shell corner and mainly concentrates in the region of 0 — 20 mm nearby the corner. T h e air gap in wide face corner grows cont inuously, and its thickness is wholly thic­ker than that of narrow face. Mold flux firstly solid­ifies at shell corner and distr ibutes from corner to the midst of wide face and narrow face wi th increas­ing firstly and then decreasing. T h e thickness of mold flux in narrow face is thicker than that of the wide face. Shell hot spots form in the region of 10 — 20 m m nearby the corner at 200 mm below steel bath level firstly and expand to 75 and 60 m m of wide face and narrow face nearby corner at mold exit respec­tively. T h e maximum tempera ture difference be­tween shell off-corner and its wide face midst and narrow face midst reaches 120 and 61 *C , respectively.

4) Stress in the shell surface layer and solidifi­cation front is tensile s t ress and compressive s tress respectively, and the absolute value decreases firstly and increases then from shell surface to the solidifi­cation front. T h e s t ress of shell at initial solidifica­tion stage is governed by thermal s t r e s s , while the mechanical s t ress becomes the main factor at lower part of mold.

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