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IntroductIonManufacture of large steel ingots is a strong assurance of com-mon economic development. So, it’s of great significance to im-prove quality of large steel ingots and to raise productivity in production. Heat transfer is a fundamental premise of solidifica-tion and has vital effect on solidification of a large steel ingot. During solidification process of an ingot, heat transfer through the outer wall of the mould is the main heat transfer section which is easily to control. Therefore, it’s feasible in practice to the control solidification process of a steel ingot by control of cooling conditions at the outer wall of mould.With development of computer technology, numerical simulation is being increasingly applied to manufacture of steel ingot, es-pecially study of heat transfer process during solidification and formation of shrinkage porosity in steel ingot[1-3]. Z. Radovic and M. Lalovic [4] developed a two-dimensional numerical model of ingot solidification based on the Fourier’s differential equation. Temperature distribution, temperature gradient, distribution solid and liquid phase and increment of solid fraction were calculated. Heui-Seol Roh[5] proposed a statistical thermodynamic trans-port theory for heat transfer, and he demonstrated the validity of the heat transfer theory for internal convection and external conduction by examining the solidification processes at the in-terface of two different phase materials. Heui-Seol Roh[6] also proposed a statistical thermodynamic transport theory which is applicable to the heat transfer mechanisms for non-equilibrium, quasi-equilibrium, and equilibrium to overcome limits on the heat diffusion equation. Jiaqi Wang et al. [7] proposed a criterion which can be used to reproduce precisely the experimental size

and distribution of the shrinkage porosity in heavy steel ingots through FEM simulation in combination with the experimental sectioning investigation of 100-ton ingot. Lu Nan et al.[8] put for-ward a new cooling method, gradient cooling process, in which the upper part of the ingot is air cooled and the lower part is spray cooled. And they found that gradient cooling can efficiently reduce shrinkage porosity of the jumbo slab ingot by optimizing the solidification sequence, and making the position of shrinkage porosity move from near the middle height of the ingot (under air cooling condition) towards the head of the ingot; and the secondary shrinkage is diminished.Through many researchers have investigated solidification and heat transfer of steel ingot, there’re few reports on water-cooled mould casting, especially on influence of different cooling condi-tions on solidification of steel ingots. In this paper, heat transfer

Influence of cooling condition on solidification of large steel ingot

c. Zhang, Y. Bao, M. Wang, L. Zhang

Influence of cooling conditions such as air cooling, forced air cooling, air mist cooling and water cooling on characteristic of solidi-fication of large steel ingot was investigated by numerical simulation. Numerical simulation of solidification of a 19 ton steel ingot was conducted and simulation results were validated by the method of temperature surveying. Cooling rate, solidification time and shrinkage porosity of large steel ingot solidified under different cooling conditions were investigated. The ingot solidified under air cooling condition has the smallest cooling rate and longest solidification time. It’s expected the restricted heat transfer section during ingot solidification is heat transfer through outer wall of the mould under air cooling condition. However, under forced air cooling, air mist cooling and water cooling conditions, the restricted heat transfer sections during ingot solidification are heat transfer processes through ingot/mould interface and mould. Soft wind cooling condition with the heat transfer coefficient on outer wall of mould being 450 W/(m2K) is the critical cooling condition with the 19 ton steel ingot.

KeYWords: LARgE STEEL INgoT - NuMERICAL SIMuLATIoN - CooLINg CoNDITIoN - CooLINg RATE

chaojie Zhang, Yanping Bao, Min Wang, Lechen Zhang

State Key Laboratory of Advanced Metallurgy, university of Science and Technology Beijing,

Beijing 100083, China

Corresponding author: E-mail: zcj_ustb@163.com

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Diecastingcharacteristic during solidification and shrinkage porosity in a 19 ton ingot were investigated by numerical simulation. Influence of cooling conditions such as air cooling, forced air cooling, air mist cooling and water cooling on cooling rate, solidification time and shrinkage porosity were investigated. It was found that the ingot solidified under air cooling condition has the smallest cooling rate and longest solidification time compared with that under forced air cooling, air mist cooling and water cooling conditions. While cooling rates and solidification times of ingots solidified under forced air cooling, air mist cooling and water cooling con-ditions are very close. under air cooling condition, the restricted heat transfer section during ingot solidification is heat transfer through the outer wall of the mould. However, under conditions of forced air cooling, air mist cooling and water cooling, the re-stricted heat transfer sections during ingot solidification are heat transfer processes through ingot/mould interface and mould. It was also found that the amount of shrinkage porosities of the ingot solidified under air cooling is the largest compared with that under forced air cooling, air mist cooling and water cooling conditions.

experIMentaLcharacteristic of heat transfer during solidification of a large steel ingot

Fig. 1 - Schematic of temperature distribution during solidifica-tion of large steel ingot, (a) Schematic of temperature distribu-

tion, (b) geometry of a 19 ton steel ingot

During solidification of large steel ingots, latent heat and sensi-ble heat of steel are extracted outside through solidified shell, in-got/mould interface, mould and outer wall of mould successively as shown in Fig. 1. In solidified shell and mould heat transfer section, conduction is the main heat transfer method. However, in the ingot/mould interface heat transfer section, heat trans-fer method varies with the formation of gap between ingot and mould. At filling stage and early stage of solidification, the solidi-

fied shell was in complete contact with the inner wall of mould without any gap between them, and the heat transfer resistance is very small. With the shrinkage of the ingot and the expansion of the mould, a gap forms between the ingot and the mould. Then, heat transfer through this section is mainly by radiation and slight conduction and advection. In the outer wall of mould heat transfer section, radiation and advection are the main heat transfer methods. During filling, temperature on the outer wall of mould increases rapidly, consequently radiation is the dominant heat transfer method in this section. Besides, there is slight heat transfer by advection due to air flow.At different stages of solidification of steel ingots, heat transfer resistances of each section are different and vary with time. At early stage of solidification, solidified shell is thin and the ingot/mould interface gap has not formed yet. In addition, temperature of the outer wall of the mould is low. At this stage, cooling of molten steel mainly depends on heat absorption of the mould. At mid stage of solidification, solidified shell has grown thick and ingot/mould interface gap has formed. What’s more, temperature of outer wall of mould has increased to about 650 °C. At this stage, heat transfer resistances are large. At a late stage of so-lidification, solidified shell is thick and heat transfer resistances are quite large.After filling, temperature of the mould increases rapidly and temperature of the outer wall of mould can increase to about 650 °C within 100 minutes. At this moment, the thermal re-sistance of outer wall of mould is about 0.02 m2K/W, which is evaluated according to radiation and advection heat transfer. This value is equivalent to the thermal resistance of the solidi-fied shell with thickness of 200 mm, and is about half of the total thermal resistance at mid and late stages of solidification. The existence of this thermal resistance prolongs the solidifi-cation time of steel ingot to a great extent. Furthermore, the longtime liquid status and flow of molten steel in the ingot can lead to serious macro-segregations such as A-segregates and V-segregates and shrinkage porosities[9, 10]. However, if the outer wall of the mould is cooled under intensive cooling conditions such as forced air cooling or water cooling condi-tions, heat transfer resistance of outer wall of mould can be significantly decreased. Consequently solidification time can be reduced and quality of steel ingot can be improved. Following are details about influence of different cooling conditions on solidification of large steel ingots.

numerical simulation of solidification of 19 ton steel in-gots with different cooling conditionsA three dimensional model of solidification of a 19 ton steel in-got was developed based on Fourier’s equation, the continuity equation, the Navier-Stokes equation, the transport equations for the standard k-ε model. And the solidification processes of the steel ingot were performed using finite element method in ProCAST 2013.0 package. During the solidification, the shrink-age porosity is formed and the Nyiama criterion[11] g·L-0.5(g is temperature gradient, L is cooling rate) was used to predict the shrinkage porosity in the ingot.

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PressocolataThe metal/mould interface heat transfer coefficient varies with time [12-14]. The heat transfer coefficients of both the metal/in-sulation brick interface and the mould/insulation brick interface were assigned as 30 W/(m2K). Here the mould/insulation brick is used for heat insulation in the hot top as shown in Fig. 2. The

heat transfer coefficient of hot top was calculated according to temperature measurement. In this paper, different cooling condi-tions as shown in Table 1 on the outer wall of the mould were investigated.

tab. 1 - Heat transfer coefficients of outer wall of mould under different cooling conditions

Cooling condition Description Heat transfer coefficient[15], W/(m2K)

Air cooling Natural convection 80

Forced air cooling Forced convection 800

Air mist cooling Air mist by spray nozzles 2000

Water cooling Forced water convection in the mould 4000

Initial temperatures of the mould and insulation brick were as-signed as 50 °C. Pouring temperature is 1555 °C, and filling time is 30 minutes. Compositions of the ingot and the mould are

shown in Table 2. Physical properties of steel ingot and mould were calculated with the Scheil model[16].

tab. 2 - Compositions of the steel ingot and the mould

material codeComposition (Wt, %)

C Mn Si P S Cr Ni Mo

melt 1.2738 0.35~0.4 1.3~1.6 0.2~0.4 ≤0.02 ≤0.02 1.8~2.1 0.9~1.2 0.15~0.25

mould Ductile iron 3.2~3.8 0.8~1.2 - ≤0.05 ≤0.05 - - -

geometric models of the 19 ton steel ingot and the mould are shown in Fig. 2. In consideration of the axial symmetry, a quarter was modeled. Finite element mesh of the mould and the ingot

is shown in Fig. 3, which consists of 22968 nodes and 104838 tetrahedral elements. The mesh was selected based on several mesh refinements.

Fig. 2 - geometric models of the 19 ton steel ingot and the mould

Fig. 3 - Finite element mesh of the 19 ton steel ingot and the mould

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DiecastingexperIMentaL procedureIn order to check the accuracy of the results by numerical simu-lation, the melting and casting process of the 19 ton steel ingot was conducted in company ANSTEEL. During solidification of the ingot, temperature measurement was carried out on the mid-point on outer wall of mould as shown in Fig. 4 with an infrared radiation thermometer. Fig. 5 shows a comparison of the calculated temperatures with the measured ones. It can be seen that the calculated values are in good agreement with the measured ones.

Fig. 4 - Temperature measurement

Fig. 5 - Comparison of the calculated temperatures with the measured ones

resuLts and dIscussIonsInfluence of cooling condition on cooling rate and so-lidification time of a large steel ingotNumerical simulations of solidification of 19 ton steel ingots under cooling conditions of air cooling, forced air cooling, air mist cooling and water cooling were conducted, and cooling rates of these ingots were obtained as shown in Fig. 6. It can be seen that the cooling rate of marginal side parts of ingot is the largest, followed by that of center parts, and that of the 1/2 position parts is the smallest. on the whole, cooling rate of ingot solidified under air cooling condition is the smallest compared with that under forced air cooling, air mist cooling and water cooling conditions. Moreover, cooling rates of ingot solidified under forced air cooling, air mist cooling and water cooling conditions are almost the same. Ingot solidification times under different cooling conditions are shown in Fig. 7. It can be seen that solidification time of ingot solidified under air cooling condition is the longest compared with that under forced air cooling, air mist cooling and water cooling con-ditions. Solidification times of ingots solidified under forced air cooling, air mist cooling and water cooling conditions are nearly the same.

Fig. 6 - Ingot cooling rates under different cooling conditions

Fig. 7 - Ingot solidification times under different cooling conditions

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Fig. 8 - Temperature distributions of ingot and mould under different cooling conditions at mid stage of solidification

Temperature distributions of middle position of ingot and mould under different cooling conditions at mid stage of solidification are shown in Fig. 8. It can be seen that temperature on outer wall of mould is the lowest, while temperature in the center of ingot is

the highest. Inside ingot and mould, temperature shows continu-ous variation. However, there’s a sudden change of temperature about 250 to 500 °C at ingot/mould interface. This is due to the gap between the ingot and the mould. Heat transfer through this gap is mainly by radiation and slight conduction and advec-tion. It also can be seen that, at mid stage of solidification, tem-perature distributions of ingot under different cooling conditions are almost the same. Table 3 shows temperature characteristics of ingot and mould under different cooling conditions at mid stage of solidification. It can be seen that temperature on outer wall of the mould under air cooling condition is far higher than that under forced air cooling, air mist cooling and water cooling conditions, which imply that further increasing cooling intensity on outer wall of mould in case of forced air cooling condition can enhance heat transfer during solidification process. Both the temperature gradient of mould and temperature difference of ingot/mould interface under forced air cooling, air mist cooling and water cooling conditions are twice that under air cooling condition. Therefore, conclusions can be drawn that thermal re-sistances of ingot/mould interface and mould are dominant at mid stage of solidification of steel ingot under forced air cooling, air mist cooling and water cooling.

tab. 3 - Temperature characteristics of ingot and mould under different cooling conditions at mid stage of solidification

Item Air cooling Forced air cooling, air mist cooling and water cooling

Temperature of mould, °C 660-870 50-600

Average temperature on outer wall of mould, °C 660 40-100

Average temperature gradient of mould, 103 °C /m 1.2 2.7

Average temperature difference of ingot/mould interface, °C 240 490

So, it’s made clear from these simulation results that when in-tensity of cooling on the outer wall of the mould is higher than that of forced air cooling condition, there’s little difference of heat transfer processes between them during solidification. un-der air cooling condition, the restricted heat transfer section dur-ing ingot solidification is heat transfer through the outer wall of mould. However, under forced cooling, air mist cooling and water cooling conditions, the restricted heat transfer sections during the ingot solidification are heat transfer processes through the ingot/mould interface and mould. In other words, under air cool-ing condition the best measure to improve cooling rate of an ingot is to further enhance intensity of cooling on outer wall of mould. While under condition of forced air cooling or water cool-ing, measures to improve cooling rate of ingot should be dimin-ishing thickness of mould, or improving heat transfer coefficient of mould and ingot/mould interface.In order to further investigate influence of cooling intensity of the outer wall of mould on cooling rate of an ingot, numerical simu-

lations of solidification of 19 ton ingot under forced air cooling conditions of several levels were conducted. Heat transfer coef-ficients of outer wall of mould under soft wind cooling conditions of different levels are shown in Table 4. Fig. 9 shows ingot cool-ing rates under forced air cooling conditions of different levels. It can be seen that cooling rate of the ingot increases obviously with increase of intensity of forced air cooling until it reaches level of ‘soft wind cooling 3’. However, cooling rates of ingot un-der ‘soft wind cooling 3’ and ‘4’ are very close, which are almost the same to that under forced air cooling. Solidification time of ingots solidified under ‘soft wind cooling 1’, ‘soft wind cooling 2’, ‘’soft wind cooling 3’ and ‘soft wind cooling 4’ are 278.8 min, 270.0 min, 267.2 min and 265.9 min, respectively. Solidification times of ingots solidified under ‘soft wind cooling 3’ and ‘soft wind cooling 4’ are very close. These results demonstrate that ‘soft wind cooling 3’ is the critical cooling condition on outer wall of mould during solidification of 19 ton ingot.

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Diecastingtab. 4 - Heat transfer coefficients of outer wall of mould under

soft wind cooling conditions of different levels

Cooling condition Heat transfer coefficient, W/(m2K)

‘Soft wind cooling 1’ 150

‘Soft wind cooling 2’ 300

‘Soft wind cooling 3’ 450

‘Soft wind cooling 4’ 600

Fig. 9 - Ingot cooling rates under forced air cooling conditions of different levels

Increasing cooling rate of a steel ingot not only shorten solidifica-tion time and raise production, but also refine grains and reduce macro-segregations in ingot. Ingot with fine grains has uniform structures and few defects such macro-segregations and cracks inside. It has been known that secondary dendrite arm spacing is mainly depend on cooling rate[17-19]. From Fig. 6 and Fig. 9 it can be seen that cooling rate of an ingot has a great deal to do with cooling condition on the outer wall of mould. Therefore, in order to improve quality of an ingot and to raise productivity in produc-tion, enhancing intensity of cooling on outer wall of mould is a method. According to the earlier analysis that ‘soft wind cooling 3’ is the critical cooling condition on outer wall of mould during solidification of a 19 ton ingot, measures should be taken to enhance intensity of cooling on outer wall of mould up to ‘soft wind cooling 3’ as shown in Table 4 in practice.

Influence of cooling condition on shrinkage porosity in large steel ingotShrinkage porosity is a significant factor that deteriorates the properties of large steel ingot, especially when porosities in an ingot are too big that they can’t be healed by the following forg-ing process. Distribution of shrinkage porosity in 19 ton ingots under cooling conditions of air cooling, forced air cooling, air mist cooling and water cooling are shown in Fig. 10. It can be seen that amount of shrinkage porosities of the ingot solidified under air cooling is the largest compared with that under forced

air cooling, air mist cooling and water cooling conditions. Distri-bution of shrinkage porosity of ingots solidified under forced air cooling, air mist cooling and water cooling conditions are very close.

Fig. 10 - Distributions of shrinkage porosity in 19 ton ingot under different cooling conditions, (a) air cooling, (b) forced air

cooling, (c) air mist cooling, (d) water cooling

Shrinkage porosity forms when there’s insufficient molten steel compensating the contraction of solidification, which is mainly due to the upper part of ingot solidifies earlier than the lower part. It can be known from Fig. 6 and Fig. 9 that the solidifica-tion rate can be controlled by cooling condition on outer wall of mould. So solidification consequence from below to above can be strengthened by different cooling conditions on the outer wall of mould, and the shrinkage porosity defects can be diminished.

concLusIonsNumerical simulations of solidification of 19 ton steel ingot un-der different cooling conditions of air cooling, forced air cooling, air mist cooling and water cooling were conducted, and influ-ence of cooling condition on cooling rate, solidification time and shrinkage porosity was investigated. Conclusions are drawn as followings:1) Ingot solidified under air cooling condition has the smallest

cooling rate and longest solidification time compared with that under forced air cooling, air mist cooling and water cool-ing conditions. While cooling rates and solidification times of ingots solidified under forced air cooling, air mist cooling and water cooling conditions are very close. Soft wind cool-ing condition with heat transfer coefficient on outer wall of mould being 450 W/(m2K) is the critical cooling condition of 19 ton ingot.

2) under air cooling condition, the restricted heat transfer sec-tion during ingot solidification is heat transfer through the

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Pressocolataouter wall of mould. However, under forced air cooling, air mist cooling and water cooling conditions, the restricted heat transfer sections during ingot solidification are heat transfer processes through ingot/mould interface and mould.

3) The amount of shrinkage porosities of the ingot solidified un-der air cooling is the largest compared with that under forced air cooling, air mist cooling and water cooling conditions.

acKnoWLedgeMentsThis work was supported by the National Natural Science Foun-dation of China under grant No. 51274029. The authors are thankful to ANSTEEL for the support on the field test.

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