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Fluid Flow and Solidification Simulation in Beam Blank Continuous Casting Process With 3D Coupled Model
Available online at www.sciencedirect.com
JOURNAL OF IRON AND STEEL RESEARCH, INTERNATIONAL. 2006, 13(4) : 17-21
Fluid Flow and Solidification Simulation in Beam Blank Continuous Casting Process With 3D Coupled Model YANG Jian-wei' ,
DU Yan-ping' ,
S H I Rong'
,
CUI Xiao-chao'
(1. School of Mechanical and Electronic Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, 2. School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, Hebei, China) Shanxi, China;
Abstract: Based on turbulent theory, a 3D coupled model of fluid flow and solidification was built using finite difference method and used to study the influence of superheating degree and casting speed on fluid flow and solidification, analyze the interaction between shell and molten steel, and compare the temperature distribution under different technological conditions. The results indicate that high superheating degree can lengthen the liquid-core depth and make the crack and breakout possible, so suitable superheating should be controlled within 35 *C according to the simulation results. Casting speed which is one of the most important technological parameters of improving production rate, should be controlled between 0.85 m/min and 1.05 m/min and the caster has great potential in the improvement of blank quality. Key words: beam blank continuous casting; flow field; temperature distribution; coupled model; solidification Symbol List
C1 , Cz , C,-Empirical constants; F,-Volumetric force, N ; h-Heat transfer coefficient, (W m-' K-' ) ; k-Turbulent kinetic energy, (mZ s-' ) ; p-Pressure, Pa; Pr, Pr,-Prandtl number of laminar flow and turbulent flow, respectively; q-Heat flow density, (kW s-' ) ; &-Source term; t-Casting time. s ; T-Temperature, OC ; T.-Air temperature, OC ; T,-Casting temperature; T.---Surface temperature of blank, *C; T,-Cooling water temperature, 'C ;
The heat transfer of continuous casting blank is a complex 3D problem, which strictly includes convection, transfer and radiation. When establishing the model of the solidification and heat transfer of continuous casting blank, an effective coefficient of
u, , u,-Velocity
along i and j directions, (m s-' ) ; of water spraying, ( L m-' s-' ) ; coordinates in i and j directions, m; rate of turbulent kinetic energy,
W-Intensity I , ,z,-Node E-Dissipation (m2 s P 3 ) ; E'-Emission ratio, E' =0. 8 ; p , p,-Viscosity coefficient of laminar flow and turbulent flow, respectively, (Pa s) ; p.ff-Effective viscosity coefficient, (Pa s) ; T F l u i d density, (kg m - 3 ) ; Petf-Effective mass diffusion coefficient; r b l t z m a n constant. a= 5.765 X lo-' ( W . m--z Oc-4);
.
u,
, u.-Empirical
constants.
heat conductivity was usually adopted to express the convection of liquid steel. For example, the effective coefficient of heat transfer presented by Mizikar was applied to simulate the fluid flow in the liquidoid areaC1-51.However, due to different flow pattern and
Foundation Item: Item Sponsored by National Key Scientific and Technological Brainstorm Project for Ninth FiveYear Plan of China (95-528-0301-03c) and Provincial Youth Foundation of Shanxi Province of China (2006021028) Biogrnphy:YANG Jian-wei(l971-), Male. Doctor, Associate Professor1 E-mail: railyjwBl63. comi Revised Date: September 29, 2005
18
Journal of Iron and Steel Research, International
heat transfer in the molten steel, the calculated res u l t is not satisfactory, and it is impossible to study in depth the effect of the molten steel movement on temperature distribution. Furthermore, the generated blank shell can also affect the molten steel movement. In order to describe process precisely, the fluid flow and solidification should be considered in one system. Therefore, a 3D model for flow field and heat transfer was set upcs1, which can predict not only the changes of shell with the casting time and the molten steel movement, but also the changes of shell on the section. It is meaningful to prevent molten steel from breakout. T h e growing regularity of the shell in the process of slab continuous casting was computed with consideration of convection, and was compared with measured data and the simulated data from the effective coefficient of heat conductivit y method; which shows a good agreement between measured and calculated data with considering convectionC7]. For the complex shape of beam blank, the fluid flow of molten steel is different from that of the slab and billet. Furthermore, the change of the casting speed and the superheating may bring new problems to the fluid stability in the meniscus and the shape of uniform shell. So the coupled research in the beam blank mould is of great importance. Based on the beam blank continuous caster at Ma'anshan Iron and Steel Company Ltd, a 3D coupled model for the fluid flow and solidification in the beam blank mold is established according to turbulent theory to determine the optimum parameters of casting.
1 3D Coupled Mathematical Model The schematic of beam blank transverse section and immersed nozzle is shown in Fig. 1. Only 1/4 of the whole blank was taken to calculate due to the symmetry.
1. 1 Control equation Continuity equation is a P u i )-0
axi
(1)
Momentum equation is
where peff=p+pt. Energy equation is (3)
Wing end
Vol. 13
Inside Immersed edge Ventro-board nozzle
edge
B '
Fig. 1 Schematic of beam blank transverse section and immersed nozzle
T h e turbulence model adopts kc double equations[*]. Turbulent kinetic energy ( k ) equation is
Dissipation rate ic energy is
(E)
equation of turbulent kinet-
(5) where pt =pC,,k2/E; C1 = 1 . 4 4 , Cz = 1. 92, C,,= 0.09, o k = l . 0 and u r = l . 3['].
1 . 2 Initial and boundary conditions (1) T h e initial condition is t = O , x=O, T=T, (6) (2) On the symmetrical section, the heat flow is zero. aT/az=o, aT/ay=o (7) (3) On surface of casting blank According to the operational characteristics of continuous casting, the heat transfer of blank is divided into three parts, i. e. mold part, secondary cooling part and radiation part. In every part, the boundary condition is different. T h e heat flow in mold is calculated by adopting the Savage and Pritchard's heat flow formulaC101.By regression, the heat flow in beam blank mold is deduced as follows, q = 2 688-236&
kW
m-'
(8)
Fluid Flow and Solidification Simulation in Beam Blank Continuous Casting Process
No. 4
The heat flow for secondary cooling part is calculated by following Ishiguro's empirical equationr1']. h=O. 581W0.451(1-0.007 5T,) (9) The heat transfer in radiation zone is calculated by the following equation"". q=U*E'* (E-E) (10) ( 4 ) Slip boundary condition During iteration calculation, molten steel flows into solidified shell unceasingly, and the solidified shell changes continuously. Therefore, irregular boundary should be considered. In present study, trapezoid grid is adopted. If the solid phase proportion of a controlled node is bigger than 0. 7 , the controlled node is regarded as solid node. T o the controlled node in the solid, its speed is equal to the casting speed. The influence of shell movement on the flow field must be considered since the blank moves at a casting speed. T h e sketch of a two-dimensional slip boundary is shown in Fig. 2. In Fig. 2 , the dashed area represents that the solid boundary moves to right at casting speed u o . u (velocity along x direction) comes back a half grid, and 'u (velocity along y direction) comes down a half grid. T o the controlled node in solid, its speed is equal to casting speed, and to the node near the solid node in the liquid field, its velocity is dealt with adopting the wall function.
Numeric solution method T h e control volume method put forward by Patankar is adopted to disperse basic equation and boundary conditionrg1; in other words, computation area is divided into many non-overlapping control volume, and differential equations should be integral in each control volume that enclose a node, then discrete equation is obtainedr". '*I. T h e SIMPLER method is adopted in present study. 1.3
2
Results and Analysis
19
and size, casting speed, etc. 1 of Ma' anshan Iron and Steel Co Ltd, the coupled temperature and flow field distribution of beam blank (500 mm X 300 mm X 120 mm) were analyzed, which is basically consistent with the practical situation.
Non-coupled and coupled flow field distribution T h e non-coupled and coupled flow field distribution at A-A section is shown in Fig. 3. From Fig. 3 , it can be seen that the back flow is obviously reinforced in the mold when the effect of shell is considered, which results from decreased flowing space, strengthened turbulent flow and increased flowing rate with solidifying of molten steel. General speaking, the flowing trend of non-coupled molten steel is consistent with that of coupled molten steel. 2.1
2 . 2 Influence of superheating 2.2.1 Influence on coupled temperature distribution T h e temperature distribution in beam blank with different superheating degree is shown in Fig. 4. From Fig. 4 , it is clear that the temperature a t mold meniscus rises obviously with the superheating degree increasing. Raising superheating degree with 10 C , the temperature at mold meniscus is increased by 3-4 C averagely and the temperature at liquid-core bottom is increased about 6 %. 2.2.2 Influence on shell shape Fig. 5 shows the flow field distribution and the shell shape at cross section of the mold outlet. T h e arc area is always the thinnest of the whole cross section at following two conditions. When the superheating is improved, the shell thickness in the whole section becomes thinner and more non-uniform, Length of beam blanWm (a) 0
0.1 0.2 0.3 0.4 0.:5 0
@I
0.1
0.2
0.3 0.4 0.5
According to the practical parameters (nozzle shape
c-
1-l
,c
-7 I
................ . . . .... a,-..
................ . . . . . .._._ .....
. . . ........ ...C
Fig. 2
Sketch map of move boundary
Superheating degree-30 *C,Casting speed-0.9 m min-' Fig. 3 Contrast between non-coupled flow field distribution (a> and coupled flow field distribution (b)
Journal of Iron and Steel Research, International
20
Vol. 13
-
0
0.1 0.2
0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.6 Lenglh of beam blanWm
(a) Superheating degree-10 Y: 1
(b) Superheating degree-30 ‘C
Fi& 4 Influence of superheatingdegree on tempera-
(a) Superheating degree-10 Y: 1
distribution
(b) Superheating degree-30 Y:
(a) Casting speed-0.9 m min-I ; (b) Casting speed- 1 . 1 m * min-I
Fig. 6
Influence of casting speed on flow field distribution
naked steel and slag entrapment, and make the crack of the shell possible. 2 . 3 . 2 Influence on coupled temperature distribution T h e influence of casting speed on temperature distribution is shown in Fig. 7. It can be seen that with the casting speed increasing, t h e temperature change a t the top of mold is not obvious, and the temperature at blank center is raised remarkably because the molten steel at the center of mold renews quickly. T h e temperature increase makes liquid-core length long so that longitudinal crack appears easily on the surface of web plate. In order to improve caster capacity and blank quality, casting speed should be controlled between 0. 85 m/min and 1 . 0 5 m/min according to the simulation results, and the maximum casting speed should not exceed 1. 1 m/min.
Fig. 5 Influence of superheating degree on shell shape at c r o ~ ssection of mold outlet n.
which is one factor leading to the longitudinal crack on the surface of the web plate. At the same time, the fusion of shell is aggravated, and breakout may occur. Superheating should be controlled within 35 *C according to the requirement of shell thickness.
2 . 3 Influence of casting speed 2. 3.1 Influence on coupled f l o w f i e l d distribution Fig. 6 shows the coupled flow field distribution at A-A section with different casting speed. When casting speed is increased from 0.9 m / m h to 1 . 1 m/min, the fluid flow speed is evidently improved, and the back flow in the mold is violent and the meniscus is fluctuating, which is easy to bring some defects such as
0
0.1
0.2 0.3 0.4 0.6 0 0.1 0.2 Length of blankh
0.3 0.4 0.5
-
(a) Casting speed-0. 9 rn min-’ I (b) Casting speed-1. 1 m min-l
Fig. 7
Influence of casting speed on temperature distribution
No. 4
3
Fluid Flow and Solidification Simulation in Beam Blank Continuous Casting Process
Conclusions
(1) A 3 D model is built t o describe accurately heat transfer and flow field inside casting blank by considering flow and solidification synchronously, ( 2 ) The model can predict temperature distribution, flow field distribution, shell thickness, width of dual-phase area and liquid-core length t o prevent breakout. T h e quality of casting blank can be guaranteed, and the caster capacity can be fully realized. ( 3 ) The movement trend of non-coupled molten steel is consistent with that of coupled molten steel, but the back flow is obviously reinforced in the mold when the effect of shell is considered. ( 4 ) The slag-melting capacity of molten steel is intensified when the superheating degree is increased, which can reduce slag entrapment, and raise the temperature at the mold meniscus obviously. The calculated results indicate that when superheating degree is raised by 10 "C , the temperature at the mold meniscus will be raised by 3-4 'C averagely, and the temperature at the bottom of liquid core will be raised by about 6 %. So the increase of superheating degree will lead the increase of liquid-core depth, thus make the crack and breakout possible. According to the simulation results, suitable superheating should be controlled within 35 "C in order to reduce defect. ( 5 ) With the increase of casting speed, the liquid-core length is lengthened and the temperature difference inside casting blank is increased, which can increase difficulty of molten-slag to float and result in cracking. According to the simulation results, suitable casting speed should be controlled between 0 . 8 5 m/min and 1. 05 m/min t o realize caster capacity and improve blank quality, and t h e maximum casting speed should not exceed 1.1 m/min.
21
References: Thomas B G , Mika L J , Naijar F M. Simulation of Fluid Flow Inside a Continuous Slab-Casting Machine [J]. Metal1 Trans, 1990, 21B(2) : 387-399. Samarasekera I V. Brimacombe J K. Thermal and Mechanical C2l Behavior of Continuous-Casting Billet Moulds [J]. Ironmaking and Steelmaking, 1982, 9(1): 1-15. Chaver Federico J , Arturo Celaya, Barron Miguel A, et al. C3l Heat Transfer in Mold Flux-Layers During Slab Continuous Casting [A]. Iron and Steel Society, eds. 1996 Steelmaking Conference Proceedings [C]. Pittsburgh, USA: Iron and Steel Society, 1996. 321-329. C41 Hoseok Nam, Hwa-soo Park, Yoon J K. Numerical Analysis of Fluid Flow and Heat Transfer in the Funnel Type Mold of a Thin Slab Caster [J]. ISIJ International, 2000, 40(9): 886892. c51 YAN BO, WEN Guang-hua, ZHANG Pei-yuan. Numerical Simulation of Solidification in Slab Continuous Casting Caster [J]. Chinese Journal of Applied Mechanics, 1998, 15(4): 4348 (in Chinese). Herbertson J , He Q L, Flint P J , et al. Modeling of Metal De C6l livery to Continuous Casting Moulds [A]. Iron and Steel Socie ty, eds. 1991 Steelmaking Conference Proceedings [C]. Washington DC, USA: Iron and Steel Society, 1991. 171-185. c71 YANG Hong-liang , ZHAO Lian-gang , ZHANG Xing-zhong , et al. Mathematical Simulation on Coupled Flow, Heat and Solute Transport in Slab Continuous Casting Process [J]. Metallurgical and Materials Transactions, 1998, 29B(12) : 13451356. ZHU Miao-yong, XIAO Zeqiang. Maths-Physics Simulation of C8l Steel Refining [MI. Beijing: Metallurgical Industry Press, 1998 (in Chinese). C91 Launder B E , Spalding D B. Mathematical Models of Turbulence [MI. London: Academic Press, 1972. 101 CAI Kai-ke. Continuous Casting [MI. Beijing: Science Press, 1990 (in Chinese). Clll YANG Jian-wei, DU Yan-ping, SHI Rong, et al. Effect of SEN Parameters on 3D Flow Field in Mould of Beam Blank Continuous Caster [J]. Journal of Iron and Steel Research, International, 2004, 11(6) : 20-24. DU Yan-ping, YANG Jian-wei, LIANG Ai-sheng, et al. 3D C12l Numerical Simulation for Flowing Field Coupled With Temperature Field in Strip Rolling Casting Mould [J]. Special Casting and Nonferrous Alloys, 2004, 1: 41-43 (in Chinese).
c11
c
JOURNAL OF IRON AND STEEL RESEARCH, INTERNATIONAL. 2006, 13(4) : 17-21
Fluid Flow and Solidification Simulation in Beam Blank Continuous Casting Process With 3D Coupled Model YANG Jian-wei' ,
DU Yan-ping' ,
S H I Rong'
,
CUI Xiao-chao'
(1. School of Mechanical and Electronic Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, 2. School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, Hebei, China) Shanxi, China;
Abstract: Based on turbulent theory, a 3D coupled model of fluid flow and solidification was built using finite difference method and used to study the influence of superheating degree and casting speed on fluid flow and solidification, analyze the interaction between shell and molten steel, and compare the temperature distribution under different technological conditions. The results indicate that high superheating degree can lengthen the liquid-core depth and make the crack and breakout possible, so suitable superheating should be controlled within 35 *C according to the simulation results. Casting speed which is one of the most important technological parameters of improving production rate, should be controlled between 0.85 m/min and 1.05 m/min and the caster has great potential in the improvement of blank quality. Key words: beam blank continuous casting; flow field; temperature distribution; coupled model; solidification Symbol List
C1 , Cz , C,-Empirical constants; F,-Volumetric force, N ; h-Heat transfer coefficient, (W m-' K-' ) ; k-Turbulent kinetic energy, (mZ s-' ) ; p-Pressure, Pa; Pr, Pr,-Prandtl number of laminar flow and turbulent flow, respectively; q-Heat flow density, (kW s-' ) ; &-Source term; t-Casting time. s ; T-Temperature, OC ; T.-Air temperature, OC ; T,-Casting temperature; T.---Surface temperature of blank, *C; T,-Cooling water temperature, 'C ;
The heat transfer of continuous casting blank is a complex 3D problem, which strictly includes convection, transfer and radiation. When establishing the model of the solidification and heat transfer of continuous casting blank, an effective coefficient of
u, , u,-Velocity
along i and j directions, (m s-' ) ; of water spraying, ( L m-' s-' ) ; coordinates in i and j directions, m; rate of turbulent kinetic energy,
W-Intensity I , ,z,-Node E-Dissipation (m2 s P 3 ) ; E'-Emission ratio, E' =0. 8 ; p , p,-Viscosity coefficient of laminar flow and turbulent flow, respectively, (Pa s) ; p.ff-Effective viscosity coefficient, (Pa s) ; T F l u i d density, (kg m - 3 ) ; Petf-Effective mass diffusion coefficient; r b l t z m a n constant. a= 5.765 X lo-' ( W . m--z Oc-4);
.
u,
, u.-Empirical
constants.
heat conductivity was usually adopted to express the convection of liquid steel. For example, the effective coefficient of heat transfer presented by Mizikar was applied to simulate the fluid flow in the liquidoid areaC1-51.However, due to different flow pattern and
Foundation Item: Item Sponsored by National Key Scientific and Technological Brainstorm Project for Ninth FiveYear Plan of China (95-528-0301-03c) and Provincial Youth Foundation of Shanxi Province of China (2006021028) Biogrnphy:YANG Jian-wei(l971-), Male. Doctor, Associate Professor1 E-mail: railyjwBl63. comi Revised Date: September 29, 2005
18
Journal of Iron and Steel Research, International
heat transfer in the molten steel, the calculated res u l t is not satisfactory, and it is impossible to study in depth the effect of the molten steel movement on temperature distribution. Furthermore, the generated blank shell can also affect the molten steel movement. In order to describe process precisely, the fluid flow and solidification should be considered in one system. Therefore, a 3D model for flow field and heat transfer was set upcs1, which can predict not only the changes of shell with the casting time and the molten steel movement, but also the changes of shell on the section. It is meaningful to prevent molten steel from breakout. T h e growing regularity of the shell in the process of slab continuous casting was computed with consideration of convection, and was compared with measured data and the simulated data from the effective coefficient of heat conductivit y method; which shows a good agreement between measured and calculated data with considering convectionC7]. For the complex shape of beam blank, the fluid flow of molten steel is different from that of the slab and billet. Furthermore, the change of the casting speed and the superheating may bring new problems to the fluid stability in the meniscus and the shape of uniform shell. So the coupled research in the beam blank mould is of great importance. Based on the beam blank continuous caster at Ma'anshan Iron and Steel Company Ltd, a 3D coupled model for the fluid flow and solidification in the beam blank mold is established according to turbulent theory to determine the optimum parameters of casting.
1 3D Coupled Mathematical Model The schematic of beam blank transverse section and immersed nozzle is shown in Fig. 1. Only 1/4 of the whole blank was taken to calculate due to the symmetry.
1. 1 Control equation Continuity equation is a P u i )-0
axi
(1)
Momentum equation is
where peff=p+pt. Energy equation is (3)
Wing end
Vol. 13
Inside Immersed edge Ventro-board nozzle
edge
B '
Fig. 1 Schematic of beam blank transverse section and immersed nozzle
T h e turbulence model adopts kc double equations[*]. Turbulent kinetic energy ( k ) equation is
Dissipation rate ic energy is
(E)
equation of turbulent kinet-
(5) where pt =pC,,k2/E; C1 = 1 . 4 4 , Cz = 1. 92, C,,= 0.09, o k = l . 0 and u r = l . 3['].
1 . 2 Initial and boundary conditions (1) T h e initial condition is t = O , x=O, T=T, (6) (2) On the symmetrical section, the heat flow is zero. aT/az=o, aT/ay=o (7) (3) On surface of casting blank According to the operational characteristics of continuous casting, the heat transfer of blank is divided into three parts, i. e. mold part, secondary cooling part and radiation part. In every part, the boundary condition is different. T h e heat flow in mold is calculated by adopting the Savage and Pritchard's heat flow formulaC101.By regression, the heat flow in beam blank mold is deduced as follows, q = 2 688-236&
kW
m-'
(8)
Fluid Flow and Solidification Simulation in Beam Blank Continuous Casting Process
No. 4
The heat flow for secondary cooling part is calculated by following Ishiguro's empirical equationr1']. h=O. 581W0.451(1-0.007 5T,) (9) The heat transfer in radiation zone is calculated by the following equation"". q=U*E'* (E-E) (10) ( 4 ) Slip boundary condition During iteration calculation, molten steel flows into solidified shell unceasingly, and the solidified shell changes continuously. Therefore, irregular boundary should be considered. In present study, trapezoid grid is adopted. If the solid phase proportion of a controlled node is bigger than 0. 7 , the controlled node is regarded as solid node. T o the controlled node in the solid, its speed is equal to the casting speed. The influence of shell movement on the flow field must be considered since the blank moves at a casting speed. T h e sketch of a two-dimensional slip boundary is shown in Fig. 2. In Fig. 2 , the dashed area represents that the solid boundary moves to right at casting speed u o . u (velocity along x direction) comes back a half grid, and 'u (velocity along y direction) comes down a half grid. T o the controlled node in solid, its speed is equal to casting speed, and to the node near the solid node in the liquid field, its velocity is dealt with adopting the wall function.
Numeric solution method T h e control volume method put forward by Patankar is adopted to disperse basic equation and boundary conditionrg1; in other words, computation area is divided into many non-overlapping control volume, and differential equations should be integral in each control volume that enclose a node, then discrete equation is obtainedr". '*I. T h e SIMPLER method is adopted in present study. 1.3
2
Results and Analysis
19
and size, casting speed, etc. 1 of Ma' anshan Iron and Steel Co Ltd, the coupled temperature and flow field distribution of beam blank (500 mm X 300 mm X 120 mm) were analyzed, which is basically consistent with the practical situation.
Non-coupled and coupled flow field distribution T h e non-coupled and coupled flow field distribution at A-A section is shown in Fig. 3. From Fig. 3 , it can be seen that the back flow is obviously reinforced in the mold when the effect of shell is considered, which results from decreased flowing space, strengthened turbulent flow and increased flowing rate with solidifying of molten steel. General speaking, the flowing trend of non-coupled molten steel is consistent with that of coupled molten steel. 2.1
2 . 2 Influence of superheating 2.2.1 Influence on coupled temperature distribution T h e temperature distribution in beam blank with different superheating degree is shown in Fig. 4. From Fig. 4 , it is clear that the temperature a t mold meniscus rises obviously with the superheating degree increasing. Raising superheating degree with 10 C , the temperature at mold meniscus is increased by 3-4 C averagely and the temperature at liquid-core bottom is increased about 6 %. 2.2.2 Influence on shell shape Fig. 5 shows the flow field distribution and the shell shape at cross section of the mold outlet. T h e arc area is always the thinnest of the whole cross section at following two conditions. When the superheating is improved, the shell thickness in the whole section becomes thinner and more non-uniform, Length of beam blanWm (a) 0
0.1 0.2 0.3 0.4 0.:5 0
@I
0.1
0.2
0.3 0.4 0.5
According to the practical parameters (nozzle shape
c-
1-l
,c
-7 I
................ . . . .... a,-..
................ . . . . . .._._ .....
. . . ........ ...C
Fig. 2
Sketch map of move boundary
Superheating degree-30 *C,Casting speed-0.9 m min-' Fig. 3 Contrast between non-coupled flow field distribution (a> and coupled flow field distribution (b)
Journal of Iron and Steel Research, International
20
Vol. 13
-
0
0.1 0.2
0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.6 Lenglh of beam blanWm
(a) Superheating degree-10 Y: 1
(b) Superheating degree-30 ‘C
Fi& 4 Influence of superheatingdegree on tempera-
(a) Superheating degree-10 Y: 1
distribution
(b) Superheating degree-30 Y:
(a) Casting speed-0.9 m min-I ; (b) Casting speed- 1 . 1 m * min-I
Fig. 6
Influence of casting speed on flow field distribution
naked steel and slag entrapment, and make the crack of the shell possible. 2 . 3 . 2 Influence on coupled temperature distribution T h e influence of casting speed on temperature distribution is shown in Fig. 7. It can be seen that with the casting speed increasing, t h e temperature change a t the top of mold is not obvious, and the temperature at blank center is raised remarkably because the molten steel at the center of mold renews quickly. T h e temperature increase makes liquid-core length long so that longitudinal crack appears easily on the surface of web plate. In order to improve caster capacity and blank quality, casting speed should be controlled between 0. 85 m/min and 1 . 0 5 m/min according to the simulation results, and the maximum casting speed should not exceed 1. 1 m/min.
Fig. 5 Influence of superheating degree on shell shape at c r o ~ ssection of mold outlet n.
which is one factor leading to the longitudinal crack on the surface of the web plate. At the same time, the fusion of shell is aggravated, and breakout may occur. Superheating should be controlled within 35 *C according to the requirement of shell thickness.
2 . 3 Influence of casting speed 2. 3.1 Influence on coupled f l o w f i e l d distribution Fig. 6 shows the coupled flow field distribution at A-A section with different casting speed. When casting speed is increased from 0.9 m / m h to 1 . 1 m/min, the fluid flow speed is evidently improved, and the back flow in the mold is violent and the meniscus is fluctuating, which is easy to bring some defects such as
0
0.1
0.2 0.3 0.4 0.6 0 0.1 0.2 Length of blankh
0.3 0.4 0.5
-
(a) Casting speed-0. 9 rn min-’ I (b) Casting speed-1. 1 m min-l
Fig. 7
Influence of casting speed on temperature distribution
No. 4
3
Fluid Flow and Solidification Simulation in Beam Blank Continuous Casting Process
Conclusions
(1) A 3 D model is built t o describe accurately heat transfer and flow field inside casting blank by considering flow and solidification synchronously, ( 2 ) The model can predict temperature distribution, flow field distribution, shell thickness, width of dual-phase area and liquid-core length t o prevent breakout. T h e quality of casting blank can be guaranteed, and the caster capacity can be fully realized. ( 3 ) The movement trend of non-coupled molten steel is consistent with that of coupled molten steel, but the back flow is obviously reinforced in the mold when the effect of shell is considered. ( 4 ) The slag-melting capacity of molten steel is intensified when the superheating degree is increased, which can reduce slag entrapment, and raise the temperature at the mold meniscus obviously. The calculated results indicate that when superheating degree is raised by 10 "C , the temperature at the mold meniscus will be raised by 3-4 'C averagely, and the temperature at the bottom of liquid core will be raised by about 6 %. So the increase of superheating degree will lead the increase of liquid-core depth, thus make the crack and breakout possible. According to the simulation results, suitable superheating should be controlled within 35 "C in order to reduce defect. ( 5 ) With the increase of casting speed, the liquid-core length is lengthened and the temperature difference inside casting blank is increased, which can increase difficulty of molten-slag to float and result in cracking. According to the simulation results, suitable casting speed should be controlled between 0 . 8 5 m/min and 1. 05 m/min t o realize caster capacity and improve blank quality, and t h e maximum casting speed should not exceed 1.1 m/min.
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