Optimization of Secondary Cooling Water Distribution for Improving the Billet Quality for a Small Caster

Abstract

In order to eliminate internal cracks and other defects of billet caused by improper secondary cooling water distribution for a small caster, a mathematical heat transfer model for billet continuous casting has been presented and solved by finite volume method. For calibrating model better, the surface temperature of billet has been measured by using high resolution CCD measurement system, which can effective eliminate the influence of randomly generated oxide scales for the surface temperature measurement. Then, the existing problems of the secondary cooling water distribution have been discussed and the secondary cooling water distribution of each zone has been optimized at key casting speeds. A new secondary cooling water distribution has been regressed and analyzed. This secondary cooling water distribution can increase the casting speed, minimize the reheating of billet, and minimize the wide fluctuations of secondary cooling water at higher casting speed region. This can improve the billet quality. Finally, the new secondary cooling water distribution has been applied on an actual small caster, it has shown that the billet defects have been decreased greatly and the quality of billet has been obviously improved.

1. Introduction

The continuous casting is the predominant technique for the solidification of molten steel to form billet, slab, or bloom. In this process, the liquid steel is poured in the mould, which is cooled by water so that to form a shell of sufficient thickness. Below the mould, the partially solidified strand enters the secondary cooling zone, where the solidifying strand is further cooled by the water sprays. After the secondary cooling zone, the strand is cooled by air naturally in the radiation zone until fully solidification. Then the solidified strand is straightened, cut, and transported for further processing. As shown in Fig. 1.

Fig. 1.

The schematic of the continuous casting process.

Continuous casting is also a continuous heat extraction process. The defects of strand, especially the internal cracks and shrinkage cavity, are closely related with heat transfer and the distribution of thermal stress, which is mainly affected by the inappropriate casting operation and secondary cooling water distribution.^1,2,3,4,5) In order to produce the strand as little defect as possible, many scholars have researched on the formation mechanism of internal cracks and other defects, which offers theoretical foundation for preventing the occurrence of defects and optimizing the secondary cooling water distribution for improving the strand quality.^6,7,8) The accurate control of the secondary cooling water distribution can obviously improve the quality of the strand. There are mainly three strategies of secondary cooling water distribution in internal casters.⁹⁾

The first strategy is manual control method, in which the secondary cooling water distribution is according to the experience of the operator. This method is rarely used at present. The secondary strategy is equal ratio control method, in which the relationship between the secondary cooling water and the casting speed is simple linear, and the secondary cooling water automatically varies according to the casting speed. This type of secondary cooling water control can work well when the casting speed and the superheat don’t change. However, this has an obvious disadvantage when the casting parameters change, such as the casting speed or superheat. A sudden change of casting speed leads to a corresponding proportion change of the secondary cooling water flow. This results in significant variation in surface temperature and excessive reheating of billet, especially near the bottom of secondary cooling zone, which has a strong influence on the formation of cracks and other defects. The third strategy is parameter control method, in which the secondary cooling water distribution is optimized by heat transfer model at key casting speeds and superheat, and water flow rate-casting speed parabola of going upwards is obtained by data regression. This curve of secondary cooling water distribution is more commonly used than the others. However, the secondary cooling water distribution of this strategy is difficult to simultaneously meet all casting speed region, especially the caster radius is small. In order to ensure complete solidification before straightening zone, the secondary cooling water is often unreasonable without heat transfer model guidance. The secondary cooling water can’t avoid wide fluctuations when the casting speed varies frequently at higher casting speed region. This easily induces excessive thermal stress in the billet solidification front and caused internal cracks. Then some quality defects of strand can be produced and the casting speed is limited.

In this paper, in order to increase the casting speed and eliminate the defects of billet caused by improper secondary cooling water distribution for a small caster, a mathematical heat transfer model for billet continuous casting has been established and validated by measuring the shell thickness and the surface temperature. For calibrating model better, the surface temperature of billet has been measured by using high resolution CCD measurement system, which can effectively eliminate the influence of randomly generated oxide scales for the surface temperature measurement. To eliminate internal cracks and other defects as much as possible, the secondary cooling water distribution should be in such a way that the surface temperature profile of billet is closed to the desired profile as much as possible. At the same time, the billet is entirely solidified before straightening, and the billet surface temperature is avoided entering the embrittlement temperature area at the straightening point. Considering the defect of the water flow rate-casting speed conic curve for some small casters, the secondary cooling water distribution has been optimized at key casting speeds and the secondary cooling water flow rate-casting speed cubic equation has been obtained by data regression. This new secondary cooling water distribution can increase the casting speed and can better avoid the excess reheating of each cooling zone, and it can also avoid the wide fluctuations of secondary cooling water when the casting speed varies frequently at higher casting speed region. The results of billet test indicate the new secondary cooling water distribution can increase the casting speed and can decrease greatly the billet defects. The quality of billet has been obviously improved.

2. Mathematical Heat Transfer Model and Secondary Cooling Water Spray Strategy

In order to simulate the billet continuous casting process of heat transfer and solidification, some assumptions have been made in the present mathematical models.^6,7,8,9,10)

(1) Compared to the heat transfer in the cross direction, the heat transfer in the casing direction can be ignored.

(2) The latent heat of steel solidification is converted into an equivalent specific heat capacity in the mushy zone.

(3) The convective heat flow in the liquid pool and mushy zone can be taken into account by an increased effective thermal conductivity.

(4) The density, specific heat and thermal conductivity of steel are the temperature-dependent properties.

Thus the solidification with phase change and the temperature distribution inside the billet can be described by the two-dimensional heat conduction equation:   

$$\rho c\frac{\partial T}{\partial t}=\frac{\partial }{\partial \mathrm{x}}\left(\lambda \frac{\partial T}{\partial x}\right)+\frac{\partial }{\partial \mathrm{y}}\left(\lambda \frac{\partial T}{\partial y}\right)+S$$(1)

where T is the billet temperature, t is the time, x, y is the rectangular coordinates, λ is the thermal conductivity of steel, c is the specific heat capacity of steel, ρ is the density of steel, and S is the latent heat source.

(1) Initial condition

The initial condition of model is assumed to be the same as the pouring or casting temperature.   

$$T=T_0$$(2)

(2) Boundary condition

In the mould   

$$-\lambda \frac{\partial T}{\partial n}=a-b\sqrt{t}$$(3)

In the secondary cooling zone   

$$-\lambda \frac{\partial T}{\partial n}=h\left(T-T_{\text{war}}\right)$$(4)

In the radiation zone   

$$-\lambda \frac{\partial T}{\partial n}=\epsilon \sigma \left(T^4-T_{\text{air}}^4\right)$$(5)

where T₀ is the steel casting temperature, a, b are constants, h is the heat transfer coefficient (W/m²/K),^11,12) T is the strand surface temperature, T_war is the cooling water temperature, T_air is the air temperature, n is the exterior normal of cooling boundary, ε is the emissivity and σ is the Stefan-Boltzman constant.

The heat transfer coefficient h is calculated by the following equation:   

$$h=\frac{1\mathrm{\hspace{0.17em} }570w^{0.55}\left(1-0.0075T_{\text{war}}\right)}{{\alpha }_i}$$(6)

where h is the heat transfer coefficient (W/m²/K), w is the water flow density (L/m²/s), α_i is the machine-dependent calibration factor of each spray zone.

Due to symmetry heat transfer in square sections, only a quadrant of billet cross-section is selected for the heat transfer analysis. The grid division and boundary conditions for cross-section of the billet are presented in Fig. 2. In the time interval (t, t + Δ t), the heat transfer model is discretized by finite volume method as follow:   

$$\begin{array}{l}{\int }_t^{t+\mathrm{\Delta }t}\iint \rho c_{Pe}\frac{\partial T}{\partial t}dxdydt={\int }_t^{t+\mathrm{\Delta }t}\iint \frac{\partial }{\partial x}\left(\lambda \frac{\partial T}{\partial x}\right)dxdydt\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+{\int }_t^{t+\mathrm{\Delta }t}\iint \frac{\partial }{\partial y}\left(\lambda \frac{\partial T}{\partial y}\right)dxdydt\end{array}$$(7)

Fig. 2.

Schematic diagram of calculation area and grid division.

Then, an implicit form of Eq. (6) is obtained as Eq. (7), and the discrete equations of nodes can be solved by tridiagonal matrix method.¹³⁾   

$$a_{i,j}{T}_{i,j}^{n+1}=a_{i+1,j}{T}_{i+1,j}^{n+1}+a_{i-1,j}{T}_{i-1,j}^{n+1}+a_{i,j+1}{T}_{i,j+1}^{n+1}+a_{i,j-1}{T}_{i,j-1}^{n+1}+b$$(8)

where   

$$a_{i+1,j}=\frac{{\lambda }_{i+1,j}\mathrm{\Delta }y}{\mathrm{\Delta }x},\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }{a}_{i-1,j}=\frac{{\lambda }_{i-1,j}\mathrm{\Delta }y}{\mathrm{\Delta }x}$$(9)

  

$$a_{i,j+1}=\frac{{\lambda }_{i,j+1}\mathrm{\Delta }x}{\mathrm{\Delta }y},\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }{a}_{i,j-1}=\frac{{\lambda }_{i,j-1}\mathrm{\Delta }x}{\mathrm{\Delta }y}$$(10)

  

$$a_{i,j}=a_{i+1,j}+a_{i-1,j}+a_{i,j+1}+a_{i,j-1}+a_{i,j}^0$$(11)

  

$$a_{i,j}^0=\frac{\rho c_{pe}\mathrm{\Delta }x\mathrm{\Delta }y}{\mathrm{\Delta }t},\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }b=a_{i,j}^0{T}_{i,j}^n$$(12)

where ‘n’ and ‘n+1’ are the temperatures before and after the incremental time interval Δt; ‘i’ and ‘j’ are the element position according to ‘x’ and ‘y’ axes, respectively, c_pe is the equivalent heat capacity of steel; Δt is the time step.

As known, the quality of the billet is closely related with the secondary cooling process, and the reasonable distribution of secondary cooling water is very important. In order to obtain a target cooling pattern, the secondary cooling segment of caster is spread over several zones with independently controlled water sprays. The secondary cooling water flow rate depends on the steel grade, section size of billet, casting speed, and so on. In most industrial applications, the relationship between the secondary cooling water flow rate and the casting speed is conic equation, and this type of secondary cooling water distribution can work very well to some caster.^9,14) However, this secondary cooling water distribution may cause some quality defects at higher casting speed region to some small casters. In order to ensure the complete solidification before straightening, this secondary cooling water distribution curve often causes excess reheating of air cooling zone at higher casting speed. Meanwhile, this water distribution curve can’t avoid the wide fluctuations of secondary cooling water when the casting speed varies frequently at higher casting speed, and the billet solidification front is extremely unstable. This easily induces excessive thermal stress in the billet solidification front and caused internal cracks. Then some quality defects of strand can be produced and the casting speed is limited.

In this study, in order to avoid this defect of secondary cooling water spray strategy, a cubic curve between secondary cooling water flow rate and casting speed has been presented. This secondary cooling water distributions can not only response timely at low casting speed region, but also reduce the surface reheating of air cooling zone at higher casting speed region. In ensuring complete solidification before straightening, the increment of secondary cooling water rate of this new cubic curve is relatively little than the conic curve with the casting speed at higher casting speed region, which may minimize fluctuations of secondary cooling water when the casting speed varies frequently. The secondary cooling water distribution should be in such a way that the surface temperature profile of billet is closed to the desired profile as much as possible, and the billet surface temperature is avoided entering the embrittlement temperature area at the straightening point. At the same time, the billet is entirely solidified before straightening. The water distribution of secondary cooling zones has been optimized in some key casting speeds and superheat. Then, the cubic curve between the secondary cooling water and casting speed has been regressed by the following equation:   

$$Q_i=a_i{v}^3+b_i{v}^2+c_{i}v+d_i+k_i\mathrm{\Delta }T$$(13)

where Q_i is the water flow rate of respective spray cooling zones (Mg/h), ν is the casting speed (m/min), a_i, b_i, c_i, d_i are water distribution coefficients, k_i is the superheat coefficient, ΔT is the change of superheat and i is the number of zones in the secondary cooling segment.

3. Results and Discussion

3.1. Model Calibration

This new secondary cooling water distribution has been applied to an actual caster in a steel plant of Pingxiang Iron&Steel Company of China. The caster radius is only 6 m. It has three cooling segments (mould, second and radiation cooling segment), and the secondary cooling segment has three zones with independently controlled water sprays. The geometry parameters of the billet caster and the nozzle configuration are summarized in Table 1. Steel grade is HRB335 and the chemical composition of the steel (in mass%) and the thermo-physical properties are shown in Tables 2 and 3, respectively. The casting speed range is 0–2.5 m/min during regular production, however, some quality defects were occurred at higher casting speed region. For producing as little casting defects as possible, the casting speed was limited no more than 2.2 m/min in the previous secondary cooling water distribution. In order to increase the casting speed and eliminate these defects of the billet, a heat transfer and solidification model was developed. The machine-dependent calibration factor of each spray zone as described in the model is crucial to the accuracy of the model, and it’s difficult to be measured directly. In this study, the machine-dependent factors of secondary cooling zone were calibrated by measured surface temperature, so accurate measurement of surface temperature was most important. In order to eliminate the influence of randomly generated oxide scales to the surface temperature measurement, the surface temperature was measured by using high resolution CCD measurement system, which is different from the traditional infrared thermometer. Because of plane measuring with CCD measurement system, the influence of randomly generated oxide scales for temperature measurement can be effectively eliminated through peak filter. Figure 3 showed the randomly generated oxide scales of billet surface. Figure 4 showed the measured temperature at the secondary cooling exit (5.75 m) using CCD measurement system and infrared thermometer. The influence of oxide scales to temperature measurement was greatly eliminated by using CCD measurement system. The machine-dependent calibration factors of each spray zone were obtained by minimizing the objective equation as follow:   

$$J({\alpha }_i)=\sum _{k=1}^n\frac{\left|T_{\text{k}}^{\text{cal}}-T_{\text{k}}^{\text{meas}}\right|}{T_{\text{k}}^{\text{meas}}}$$(14)

where T^cal is the calculated surface temperature and T^meas is the corresponding measured surface temperature, k is the index of measurement position.

Table 1. Geometry of the billet caster.

Parameter	Value	Nozzle type	Nozzle configuration
Section size (m × m)	0.17×0.17
Max metallurgical length (m)	9.42
Mold length (m)	0.8
Spray zone lengths (m)
Zone I	0.35	HH15	5 × 4
Zone II	2.15	460644	16 × 4
Zone III	2.45	460644	9 × 4

Table 2. Chemical composition of steel (in mass%).

Parameter	value
C	0.20
Si	0.60
Mn	1.4
P	0.045
S	0.045

Table 3. Main simulation parameters and thermo-physical properties.

Parameter	Value
Density (kg/m3)	7600−0.325 T
Thermal conductivity (W/m/K)	13.86+0.01075 T
Specific heat (kJ/kg/K)	417.42+0.19 T
Emissivity	0.85
Liquidus temperature (°C)	1505
Solidus temperature (°C)	1464
Latent heat (kJ/kg)	265

Fig. 3.

The oxide scales of billet surface.

Fig. 4.

Comparsion between CCD measurement system and infrared thermometer.

To valid the accuracy of the model after calibration, the center temperature of billet surface at 5.75 m out of secondary cooling zones was measured by using a CCD temperature measurement system, and the shell thicknesses were measured at 3.3 m and 5.75 m from the meniscus by using shooting nails under specific casting condition.¹⁵⁾ From Table 4, the numerical results can be agreed with the available experimental data.

Table 4. Comparison between calculated and measured data of HRB335 steel.

Casting speed (m/min)	Secondary cooling water flow (Mg/h)			Shell thickness (mm)				Temperature (°C)
	Zone 1	Zone 2	Zone 3	3.3		5.75		5.75
				measured	calculated	measured	calculated	measured	calculated
1.9	14.38	14.62	5.37	42	40	62	59	955	962

3.2. Application in a Small Caster

The previous relationship between the secondary cooling water and the casting speed was conic curve, the secondary cooling water flow was varied automatically according to the casting speed, the cracks and some defects of billet were mainly occurred when the casting speed was higher. Based on the analysis of defects and the results of model simulation, the main reason was that the caster radius was too small. The preset excess secondary cooling water was to ensure the billet completely solidification before straightening point. This caused the reheating of air cooling zone too high at higher casting speed region, and it induced excessive tensile strain in the billet solidification front, then the internal cracks were formed in the interior of the billet.²⁾ In addition, the excessive fluctuation of secondary cooling water will resulted in the billet solidification front unstable. This can also cause some defects. Therefore, the excessive secondary cooling water should be avoided at higher casting speed region.

In order to increase the casting speed and improve the billet quality at the same time, this new secondary cooling water distribution was based on target temperature. The secondary cooling water distribution should be in such a way that the surface temperature profile of billet was closed to the desired profile as much as possible, and the fluctuation of secondary cooling water should be decreased as possible. So by controlling the secondary cooling water, the reheating of billet was lower than 100°C, and the billet surface temperature was between 900°C and 1050°C at the straightening area.⁶⁾ The water distribution of secondary cooling zones was optimized at key casting speeds, and the cubic curve between the secondary cooling water and the casting speed was obtained by data regression. Figures 5, 6, 7 showed the comparison the relationship between casting speed and secondary cooling water before and after adjusted, and the new secondary cooling water distribution can be considered to be a composite curve. The region I of curve can be seen a part of parabola opens upward, the secondary cooling water flow rate can keep up with the casting speed change timely. The region II of curve can be seen as a part of parabola opened downward. The increment of secondary cooling water rate is slowly with the increment of casting speed compare with parabola opened upward. This characteristic of new secondary cooling water distribution can meet the reheating limit of each cooling zone well. Meanwhile, it may minimize fluctuations of secondary cooling water when the casting speed varies frequently at higher casting speed region. Furthermore, it can be very good to ensure the billet quality.

Fig. 5.

The secondary cooling water distribution before and after adjusted at zone I.

Fig. 6.

The secondary cooling water distribution before and after adjusted at zone II.

Fig. 7.

The secondary cooling water distribution before and after adjusted at zone III.

Figure 8 showed the surface center temperature, center temperature and shell thickness before and after applying the new secondary cooling water distribution at v=2.4 m/min. The surface reheating was greatly reduced at radiation segment, and the surface temperature of billet in secondary cooling and straightening area was in plastic area, thereby some internal cracks and defects of billet were obviously eliminated. Figure 9 showed the surface center temperature, center temperature and shell thickness that distribute along the direction of casting speed after applying this new secondary cooling water distribution at higher casting speed region. The billet was entirely solidified before straightening and the billet surface temperature was avoided entering the embrittlement temperature area at the straightening point. The reheating of billet was obviously reduced, and then the tensile stress near the billet solidification front was reduced at the secondary cooling zones, so the internal defects were reduced. This new secondary cooling water distribution can be applied on some small casters, and the quality of billet can be obviously improved. Figure 10 shows the micrographs before and after applying the new secondary cooling water distribution.

Fig. 8.

Comparison of calculated results before and after adjusted at v=2.4 m/min.

Fig. 9.

The strand surface temperature, center temperature and shell thickness profile after adjusted at higher casting speed.

Fig. 10.

Macrographs before (a) and after (b) applying new secondary cooling water distribution.

4. Conclusion

In this paper, in order to increase the casting speed and improve the billet quality for some small casters, a mathematical heat transfer model for billet solidification process has been developed. For calibrating model parameters better, the surface temperature of billet has been measured by using high resolution CCD measurement system. The influence of randomly generated oxide scales on the surface temperature measurement has been effectively eliminate by plane measure and peak filter. A cubic curve between the secondary cooling water and the casting speed has been obtained by data regression. This secondary cooling water distribution can increase the casting speed, minimize the reheating of billet, and minimize the wide fluctuations of secondary cooling water when the casting speed varies frequently at higher casting speed region. At the same time, the billet surface temperature was avoided entering the embrittlement temperature area at the straightening point. This new secondary cooling water distribution has been applied on an actual small caster. The result showed that the quality of billet has been obviously improved.

Acknowledgement

The authors would like to gratefully acknowledge the financial support of the Fundamental Research Funds for the Central Universities (N150304003), The authors also wish to thank the research supported by China Postdoctoral Science Foundation funded project (2015M570252), the Doctoral Scientific Research Foundation of Liao Ning Province (N0.201501055, N0.20141004).

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