Analysis and Application of Soft Reduction Amount for Bloom
Continuous Casting Process
Cheng JI,* Sen LUO and Miaoyong ZHU
School of Materials and Metallurgy, Northeastern University, 3-11, Wenhua Road, Shenyang, Liaoning, 110819 China. (Received on November 24, 2013; accepted on January 7, 2014)
Based on the principle of solidification shrinkage compensation, a soft reduction amount calculation method was derived for bloom continuous casting process, and the bearing steel GCr15 was chosen as specific research steel to describe calculation process in detail. A two-dimensional heat transfer model was built to predict the solidification process of bloom, and the material properties of GCr15 were derived by weighted averaging of the phase fractions. The predicted temperature and shell thickness were verified by a thermal infrared camera and nail shooting results, respectively. The soft reduction amount of typical high carbon alloy steel blooms were calculated and discussed. The plant results showed that after the application of soft reduction to the bloom, centerline segregation and “V” type segregation were improved significantly. The carbon and sulfur ratios of the bloom centerline were reduced from 1.39 to 1.09 and 2.14 to 1.29, respectively.
KEY WORDS: bloom continuous casting; soft reduction; reduction amount; solidification shrinkage; high carbon alloy steel; macro-segregation.
1. Introduction
Soft Reduction (SR) technology has proved to be an effective method to reduce slab and bloom centerline segre-gation and porosity in many industrial practices.1–10) The principle of SR is to impose a reasonable reduction rate/ amount on the solidification end of the strand for compen-sating liquid core shrinkage and preventing the solute-enriched liquid flowing toward the center of the strand without creating internal cracks.1,2,4) In bloom SR process, the reduc-tion is usually executed by 6–10 withdrawal units which are arranged in the air cooling zone with intervals of 1.0–3.5 m. Therefore the reduction interface is discontinuous, and the SR amount is generally selected as the primary control parameter during the bloom SR process.
Since Miyazawa and Schwerdtfeger simulated the macro-segregation caused by bulging on slab continuous casting process in 1981,11) some researchers studied the flow fluid and macro-segregation induced by deformation of the solid skeleton in mushy zone.12–16) Recently, Menghuai Wu and et
al.15,16) developed a two-phase columnar solidification mod-el to describe the effect of shmod-ell deformation, mmod-elt flow, den-drite growth on the macro-segregation behavior, and revealed more detailed mechanism and principles of SR. However, due to the complicated coupled macro and micro
factors and variable industrial process, it is still difficult to precisely quantify the SR amount, and more studies were carried out with industrial trial method. At the same time, because of the different trial conditions, the empirical SR amount was significantly different, for example the 7.5±1.5 mm for bloom thickness of 350 mm,2) 1.54–6.41 mm for bloom thickness of 380 mm,6) and 20–30 mm for bloom thickness of 400 mm.9) Therefore, it is difficult to form com-mon criteria from these industrial trail results only.
In this paper, based on the solidification shrinkage com-pensation principle, a calculation method for SR amount is derived, and bearing steel GCr15 was chosen as specific research steel to illustrate calculation process in detail. A heat transfer model was developed to predict the bloom tem-perature distribution based on the specific parameters of bloom continuous casting machine. In order to improve the accuracy of the calculation results, the material properties of GCr15 were derived by weighted averaging of the phase fractions, and the predicted temperature and shell thickness were verified by thermal infrared camera and nail shooting results, respectively. According to the temperature distribu-tion and shell deformadistribu-tion of GCr15 bloom, the SR amounts under different casting speeds were calculated. The SR amount of two other typical high carbon alloy steel, 82B and 72A, were presented and applied to industrial practice as well. Finally, the plant results without and with SR were compared and discussed.
2. SR Amount Calculation Model
Figure 1 shows the schematic of the bloom SR process, This article is one which was originally scheduled for publication in the
special issue (Vol. 54, No. 2) on “Cutting Edge of Computer Simulation of Solidification, Casting and Refining” and instead was specially published in this regular issue.
* Corresponding author: E-mail: [email protected] DOI: http://dx.doi.org/10.2355/isijinternational.54.504
and the temperature distribution of transverse section on SR start point, SR point under Unit 3 and SR end point corre-spond to the Figs. 2(a) to 2(c), respectively. It is obvious that the liquid core shrinks continuously due to the temperature decrease along the casting direction.
The mass flow rate of strand transverse section along the casting direction at strand point zi could be calculated as:
... (1) Where x, y and z are width, thickness, and length of the bloom, respectively, and ρ(x, y, z) is steel density function which is related to temperature.
In ideal conditions, the liquid core shrinkage, as shown in Fig. 2, would be supplied by free flowing liquid steel, and
dM/dz is constant for the whole strand due to the mass
con-servation along the casting direction. However, according to the research by Takahashi et al.,17) the dendrites begin to form network and block liquid flow when the solid fraction,
fs, becomes equal to 0.31, and the liquid steel could not be supplied deep into the mushy zone completely. In the non-free flowing zone, the mass difference between the ith and
i-1th SR points can be calculated as follow:
... (2) Where, ΔLi is the length between the ith and i-1th strand points, m. The volume of required liquid steel, which is assumed to be supplied for the mass difference between the
ith and i-1th strand points, could be calculated as:
... (3) Where, ρl is steel density at liquidus temperature, kg/m3. On the other hand, because the ΔVi is caused by solidifica-tion shrinkage between the ith and i-1th strand points, it also could be calculated as:
... (4) Where, ΔAi is the shrinkage area between the ith and i-1th
strand points, m2.
In order to reduce centerline segregation and porosity of strand, the liquid core should be compensated with ΔAi as shown in Fig. 3. Combining the Eqs. (2)–(4), ΔAi could be derived by the following equation:
... (5)
The deformation behavior as shown in Fig. 3 is another important factor which influences the SR effect, because most of SR amount is consumed on the bloom deformation process.15,18,19) The SR efficiency η
i is defined to characterize the relationship between SR amount on the strand surface and the required SR amount of the shrinkage volume.18,20) According to the authors’ previous work,19,21) the SR effi-ciency ηi could be expressed as:
... (6) Where, the ΔSi is the surface shrinkage area on ith strand point shown in Fig. 3, m2, and it could be calculated as:
... (7) Where, Ri is the surface SR amount in ith SR point shown in Fig. 3, m; Xi is the bloom width in ith strand point shown in Fig. 3, m.
Combining the Eqs. (5)–(7), the Ri could be expressed as:
.... (8)
3. Heat Transfer Model Description
In the present work, a 4-strand arc bloom continuous cast-ing machine is chosen as specific research objective, and its schematic is shown in Fig. 4. The SR is executed by with-drawal units, which are located between 16.187 m and 24.649 m of the distance from the meniscus as shown in Fig. 4, and the bloom section was 325 mm× 280 mm at room temperature. In order to obtain the shrinkage compensation Fig. 1. The schematic of the bloom SR process.
Fig. 2. The temperature distributions on the bloom transverse sec-tion. dM dz x y z dxdy i i X Yi i =
∫
0∫
0 ρ , ,(
)
ΔM dM Δ dz dM dz L i i i i =⎛ − ⎝ ⎜ ⎞ ⎠ ⎟⋅ −1 ΔVi ΔMi l = ρ ΔVi=ΔAi⋅ΔLiFig. 3. Schematic of the shell deformation during SR process.
ΔA dM dz dM dz x y z dxdy x y z dxdy i i i l i X Y i i i = − =
(
)
−(
)
− −∫
∫
1 0 0 0 1 ρ ρ , , Y XX ρ , , l i i− −∫
∫
1 1 0 ρ ηi i i A S =Δ Δ ΔSi = ⋅R Xi i R A X x y z dxdy x y z dxdy i i i i i X Y i X Y i i i i = ⋅ =∫
∫
(
)
−∫
(
−)
− Δ η ρ , , ρ , , 0 0 0 0 1 1 −−∫
(
)
⋅ ⋅ 1 ρ ηl i Xiof liquid core, ΔAi, a heat transfer model of quarter bloom transverse section was developed to predict the temperature distribution of whole strand under steady casting conditions. Based on some simplified assumptions,22) a two-dimensional transient heat conduction equation was employed to describe the heat transfer behavior as follow:
... (9) Where, T and t are temperature, °C and calculation time, s, respectively. ρ(T ), c(T ), and λ(T) are the density, kg/m3, specific heat, J/(kg·°C), and heat conductivity, W/(m·°C), respectively.
In the present work, a kind of bearing steel, GCr15, was chosen as specific research steel grade, and its main
compo-sition was 1.00 Wt Pct C, 0.25 Wt Pct Si, 0.30 Wt Pct Mn, 0.01 Wt Pct P, 0.01 Wt Pct S, and 1.45 Wt Pct Cr.
3.1. Material Properties
In order to obtain more accurate material properties of GCr15 between the solidus and liquidus temperatures range, a one-dimensional direct finite-difference model was devel-oped to calculate the evolution of phase fraction and the sol-ute redistribution on the basis of the assumption of Ueshima
et al.23) Furthermore, the MnS inclusion precipitation during the solidification process was considered for the accuracy of the calculation results, and the rates of diffusion into solid and liquid phases were determined by diffusion coefficients and equilibrium distribution coefficients of the ele-ments.23,24) The specific parameters and calculation process are described in detail by the present authors’ previous work.25)
Figure 5(a) shows the evolution of phase fraction, inter-dendritic solute segregation ratio during the solidification process of GCr15 with cooling rate of 0.25°C/s. It can be seen that the γ phase generated directly from liquid steel without forming δ phase in the solidification process. The element segregation ratio increases gradually at the initial stage of solidification and then increase rapidly at the end of solidification.
Figures 5(b), 5(c), and 5(d) show the density, enthalpy, and conductivity of GCr15, respectively, which were calcu-lated by weighted phase fraction equations which are described in detail by Li and Thomas.26)
3.2. Boundary Conditions
The finite element method was adopted to calculate Eq. (1), and the initial temperature of all nodes was set as the Fig. 4. The schematic of the bloom continuous casting machine.
ρ T c T T λ λ t x T T x y T T y
( ) ( )
∂∂ = ∂ ∂( )
∂ ∂ ⎛ ⎝⎜ ⎞ ⎠⎟+ ∂∂( )
∂ ∂ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟Fig. 5. Phase fraction, solute segregation and material properties of GCr15: (a) phase fraction and solute segregation, (b) density, (c) enthalpy, and (d) conductivity.
casting temperature, 1 479°C, which is the most common temperature in the industrial practice. The heat flux at the symmetrical sides of the model is assumed to be zero. 3.2.1. In the Mold
A simplified boundary condition equation of the form proposed by Savage and Pritchard was used to calculate the heat flux of the surface center along the casting direction.27) ... (10) where, qcenter is the heat flux on the bloom surface center, MW/m2; t is time in the mold, s; A and B are coefficients which depend on the mold cooling conditions. In the present work, A varied between 1.25–1.45× 106, and B varied between 5.5–6.5× 104.
The heat flux decreases along bloom transverse surface from surface center to corner due to the shell shrinkage, and therefore the heat flux of bloom surface, qmold, should be cal-culated as:
... (11) Where, a1 and a2 are parameters according to different height in mold, for example a1=68.5 and a2=11.7 on the bloom wide surface at the mold exit; x is the position from surface center to corner, m.
3.2.2. In the Secondary Cooling Zones
The equivalent convection coefficients are usually applied to calculate heat transfer in secondary cooling zones. According to the experimental results of Nozaki et
al.,22) the equivalent convection coefficient of cooling water and radiation, hi
ec, is expressed by:
... (12) The right of the Eq. (12) is composed of three parts for calculating heat extraction of spray water, radiation, and roller contact.
In the first part, αi is a modified parameter of ith cooling zone; Tw is cooling water temperature, °C; Wi(x) is the water flux distribution in ith cooling zone, l/(m2·min), where x is the distance from bloom surface center to corner, and Wi(x) was measured by the nozzle characteristics of the testing stand.28) In the second part, σ is Stefan-Boltzmann constant, 5.67× 10–8 W/(m2·K4); ε is steel emissivity; T
surf and Tamb are the surface temperature of the strand and the ambient tem-perature, respectively, K.
In the third part, hci is the heat transfer coefficient between rollers and bloom in ith cooling zone, W/(m2·K); N
Ri is the roller number of ith cooling zone; Ri
L is the contact length between rollers and bloom in ith cooling zone, m; Zi
L is the total length of the ith cooling zone, m. According to the previous research,29,30) h
ci is set as 0.3–3.6 kW(m2· K), and Ri
L is equal to 0.02 m. 3.2.3. In the Air Cooling Zones
In the air cooling zones, the equivalent heat transfer coef-ficient hi
air is composed by radiation and rollers contact, and it is calculated as follows:
... (13)
3.3. Model Validation
The model was verified by plant measured surface tem-perature and shell thickness. The surface temtem-perature was measured by a thermal infrared camera (A40, FLIR), and the shell thickness was measured by nail shooting method. Figure 6 shows the comparison between the predicted and the measured results when the casting speed is 0.8 m/min. The relative error between the predicted and the measured temperature is less than ±0.84%, while the relative error between the predicated shell thickness and nail shooting results is less than 1.86%.
4. SR Amount Calculation and Application Results 4.1. SR Amount Calculation
The SR should act on the area where the liquid steel could not flow freely. So based on the research of Takahashi17) the SR start point was chosen as fs=0.31 at strand centerline. On the other hand, the SR should be applied at the proper posi-tion to squeeze solute-enriched liquid out of the strand cen-ter, and so the SR end point was chosen as fs=0.92 at strand centerline based on the present authors’ previous work.25)
Figure 7 compares the isolines of solid fraction 0.00, 0.31, 0.92 and 1.00 in the bloom thickness direction with different casting speed. It can be seen that the mushy zone and SR zone are both prolonged and move towards the end of the strand with increase of the casting speed, because the time for heat release decreases while the heat release speed in the air cooling zone remains almost unchanged. When the casting speed increases every 0.05 m/min, the SR zone is prolonged by about 0.35 m, while the SR start point moves towards cast end with about 1.18 m.
The shrinkage area, ΔAi, between the SR point (fs=0.31– 0.92) and SR start point (fs=0.31) could be calculated by Eq. (5) and the predicted temperature distribution. The calculat-ed results with different casting specalculat-eds are shown in Fig. 8. It can be seen that ΔAi increased almost linearly in the cast-ing direction with increascast-ing distance from the SR start point. When the casting speed increases, the maximum of ΔAi (at the position of fs=0.92) also increases.
According to the present authors’ previous work,19) a
qcenter = −A B t
qmold =qcenter⋅ −(1 exp(a x1 −a2))
h W x T
T T T T
ec i
i i w
surf amb surf a
= ⋅ ⋅ − + ⋅ ⋅ + ⋅ + α σ ε ( ) ( . ) ( ) ( . 0 55 2 1 0 0075 m mb c i R i L i L i h N R Z 2 )+ ⋅ ⋅
Fig. 6. Comparison between the predicted and measured surface temperature and shell thickness.
h T T T T h N R
Z
ec i
surf amb surf amb c i R i L i L i = ⋅ ⋅σ ε ( + ) (⋅ 2+ 2)+ ⋅ ⋅
three-dimensional thermal mechanical coupled model was built to describe the deformation behavior of continuous casting bloom during SR process, and the relationship between the SR efficiency and non-solidification ratio is shown in Fig. 9. It can be seen that the SR efficiency increases with the increase of non-solidification ratio when the SR amount is same. When the non-solidification is same, the SR efficiency increases rapidly with the increase of SR amount at the beginning, then decrease slowly, and finally tended to relative stability.
Based on the predicted results of temperature distribution, the non-solidification ratio of bloom transverse section with different casting speed was calculated and is shown in Fig. 10. It can be seen that the non-solidification ratio decreases almost linearly along with strand position.
According to above mentioned calculation results of ΔAi, the SR efficiency and the non-solidification ratio, the SR amount of the GCr15 strand surface were calculated from Eq. (8), and the results are listed in Table 1.
Table 1 shows that the total SR amount of 280 mm× 325 mm section GCr15 bloom is 7.3–9.68 mm depending on the casting speeds, while the SR amount of single withdrawal unit is 1.06–5.22 mm. The SR amount of units is decided by both the shrinkage area and the deformation behavior. With increasing casting speed, more withdrawal units participate in SR process due to the prolonged mushy zone, but the total SR amount decreases due to less shell deformation needed. Besides of GCr15, the calculation method also had been Fig. 7. The isolines of different solid fractions on bloom thickness
direction with different casting speed.
Fig. 8. The shrinkage area between SR point and SR start point with different casting speed.
Fig. 9. The SR efficiency with different SR amounts and non-solidification ratios.
Fig. 10. The non-solidification ratio of bloom transverse section with different casting speed.
Table 1. The calculation results of SR amount with typical casting
speeds. Steel
grade Casting speed(m/min)
SR amount of withdrawal units (mm) Unit 1 Unit 2 Unit 3 Unit4 Unit 5 Unit 6 Total
GCr15 0.70 1.06 3.40 5.22 9.68 0.75 1.42 3.08 4.08 8.58 0.80 2.12 2.69 3.41 8.22 0.85 1.79 2.43 3.08 7.30 82B 0.75 2.64 4.36 7.00 0.80 3.13 3.71 6.84 0.85 0.53 2.68 3.32 6.53 0.90 0.69 2.46 3.03 6.18 72A 0.75 1.91 4.94 6.85 0.80 2.32 4.24 6.56 0.85 2.62 3.80 6.42 0.90 2.78 3.50 6.28
used to calculate SR amount of other high carbon alloy blooms, 72A (tire cord steel) and 82B (prestressed strand steel), which main composition are listed in Table 2, and their calculation results of SR amount are listed in Table 1 as well. With the typical casting speed of 0.75–0.90 m/min, the total SR amount of 280 mm× 325 mm section 82B and 72A blooms are 6.18–7.00 mm and 6.28–6.85 mm, respec-tively. The 82B and 72A blooms need less SR amount than that of GCr15 to compensate solidification shrinkage for their lower carbon and alloy content.
4.2. Application Results
The SR amounts listed in Table 1 were applied to the above mentioned bloom continuous casting machine. With the similar casting conditions listed in Table 3, the macro-graphs of the blooms longitudinal and transverse section before and after the SR application were compared in Figs. 11 and 12.
The left column of Fig. 11 is the macrographs of the blooms longitudinal section without SR, and it is clear that the centerline segregation and “V” type segregation are more and more serious with the increase of carbon and alloy content. As shown in the right column of Fig. 11, the blooms center quality improved significantly after the SR applica-tion. There are some internal cracks which are perpendicular to the blooms centerline on the 1/4 location of bloom height after the SR application, and these cracks may be caused by the amplified straightening stress, when the SR was execut-ed by units 1 to 3 which have straightening function besides of withdrawal. Additionally, Fig. 12 shows the huge center porosity with radius greater than 8 mm in the transverse sec-tion of GCr15 bloom was eliminated while the macrostruc-ture of whole section became homogeneous after the SR application.
The carbon and sulfur segregation ratios on the GCr15 bloom centerline were measured quantitatively by the chem-ical analysis of drillings. The sampling positions are shown in Fig. 13.
Figures 14(a) and 14(b) show the carbon and sulfur seg-regation ratios at the GCr15 bloom centerline, respectively. It is clear that the sulfur segregation is more serious com-pared to the carbon segregation. Figure 14(a) shows that the maximum of the carbon segregation ratio decreased from
Table 2. The Ts, Tl and main composition of steel (in mass%).
Steel grade Ts (°C) Tl (°C) C Si Mn P S Cr
GCr15 1 292.7 1 453.9 1.00 0.25 0.30 0.010 0.010 1.45 82B 1 317.3 1 464.5 0.83 0.23 0.80 0.008 0.015 0.28 72A 1 333.6 1 476.8 0.70 0.19 0.50 0.010 0.008 0.02
Fig. 11. Macrographs of longitudinal bloom section without SR: (a), (c) and (e); and with SR: (b), (d) and (f).
Fig. 12. Macrographs of transverse bloom section with (a) and without (b) SR for GCr15.
Fig. 13. Schematic illustration of sampling method. Table 3. Parameters of the casting conditions.
Steel grade Casting speed (m/min) Casting temperature (°C)
Water flowrate of secondary cooling zones (l/min)
Zone 1 Zone 2 Zone 3 Zone 4 Zone 5
I/O L/R I/O L/R I O L/R I O L/R I O L/R
GCr15 0.75 1 476–1 480 23.9 23.9 18.1 15.6 5.9 6.5 10.2 3.3 4.0 5.7 2.1 2.7 3.6
82B 0.80 1 480–1 488 26.3 23.9 29.0 25.0 9.6 10.5 16.5 5.4 6.4 9.2 3.4 4.4 5.9
1.39 to 1.09 after the SR application, and the proportion of the carbon segregation ratio greater than 1.05 decreases from 76.7% to 6.7%. As shown in Fig. 14(b), the sulfur ratio at the bloom centerline fluctuates abruptly with the maxi-mum of 2.14 before the SR application, and this uneven dis-tribution decreased significantly while the peak ratio became 1.29 after the SR application.
5. Conclusions
The SR amount is usually chosen as a control parameter in bloom continuous casting process due to its feature of dis-continues reduction, and in this paper the SR amount calcu-lation method is derived which is based on the principle of solidification shrinkage compensation.
In order to obtain the shrinkage compensation of liquid core, a heat transfer model was developed to predict the temperature distribution with specific equipment parame-ters, and bearing steel GCr15 was chosen as specific research steel. In order to improve the accuracy of calcula-tion results, the material properties of GC15 were calculated by weighted averaging of the phase fractions. The predicted temperature and shell thickness were verified by thermal infrared camera and nail shooting result with the relative error of less than ±0.84% and 1.86%, respectively.
From the temperature predicted results and the deforma-tion behavior of continuous casting bloom, the calculadeforma-tion process of the SR amount under different casting speed was presented and discussed. The total SR amount increases with the increase of carbon and alloy content for different steel grade, and with typical casting speeds the total SR amount of 280 mm× 325 mm section GCr15, 82B and 72A blooms were 7.3–9.68, 6.18–7.00 mm and 6.28–6.85 mm, respectively.
The plant results showed that the centerline segregation and “V” type segregation of high carbon alloy blooms improved significantly after the SR application, and the car-bon and sulfur ratios on the GCr15 bloom centerline were reduced from 1.39 to 1.09 and 2.14 to 1.29, respectively.
Acknowledgments
The present work is financially supported by the National Natural Science Foundation of China No. 50925415 and No. 51004030. The authors sincerely acknowledge helpful com-ments and suggestions of Prof. Yogeshwar Sahai of the Ohio State University. The special thanks are due to the Xingtai Iron & Steel Corporation for industrial trials and application.
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