連鑄流動與凝固耦合模擬中糊狀區系數的表征及影響

李少翔; 張曉萌; 李亮; 蘭鵬; 唐海燕; 張家泉

doi:10.13374/j.issn2095-9389.2019.02.006

連鑄流動與凝固耦合模擬中糊狀區系數的表征及影響

doi: 10.13374/j.issn2095-9389.2019.02.006

北京科技大學冶金與生態工程學院, 北京 100083

基金項目:

國家自然科學基金資助項目 U1860111

國家自然科學基金資助項目 51604021

北京市自然科學基金資助項目 2174077

北京科技大學本科教育教學改革資助項目 JG2017M11

詳細信息

通訊作者:
張家泉, E-mail: jqzhang@metall.ustb.edu.cn

中圖分類號: TF777.2
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出版歷程
- 收稿日期: 2018-03-01
- 刊出日期: 2019-02-01

Representation and effect of mushy zone coefficient on coupled flow and solidification simulation during continuous casting

School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083, China

More Information

Corresponding author: ZHANG Jia-quan, E-mail: jqzhang@metall.ustb.edu.cn

摘要

摘要: 分析提出了連鑄流動與凝固耦合數值模擬中, 鋼液在兩相區流動時的糊狀區系數(A_mush)與滲透率的關系; 通過建立大方坯連鑄結晶器三維耦合數值模型, 揭示了不同糊狀區系數對鋼液流動、傳熱與凝固進程的影響, 以及早期相關研究結果差異的源頭.結果表明: 糊狀區系數越大, 鋼液在糊狀區內的流動阻力越強, 凝固時鋼液流動速度降低越快.采用較大的糊狀區系數時, 糊狀區呈較窄的"帶狀"分布在固液相之間; 當糊狀區系數較小時, 糊狀區范圍變大, 鋼液在結晶器內溫降過快, 自由液面處出現過冷現象, 凝固坯殼局部發生重熔.結合實驗數據驗證與模型分析, 認為糊狀區系數取值1×10⁸~5×10⁸ kg·m^-3·s^-1可以較可靠地揭示連鑄結晶器內的實際凝固現象.
- 連鑄 /
- 數值模擬 /
- 流動 /
- 凝固 /
- 糊狀區系數
Abstract: The mushy zone refers to the region of the solid-liquid system where the temperature is between the liquidus and solidus temperatures. In this zone, the turbulence of the interdendritic flow is reduced by blockage of dendrites. The mushy zone coefficient (A_mush) is an important calculating parameter in the continuous casting numerical simulation process, which strongly affects the prediction of fluid flow and solidification behavior in the mold zone. However, most researchers have neglected the influence of the mushy zone coefficient, and the correct expression of this coefficient is rarely found in the literature. Generally, the lower default value of 1×10⁵ kg·m^-3·s^-1 is used in the model, which leads to unrealistic results. In this study, the relationship between the mushy zone coefficient and permeability was analyzed, and the expression of the mushy zone coefficient was proposed. A coupled flow and solidification numerical model was developed to evaluate the effect of the mushy zone coefficient on the melt flow and solidification phenomena in a bloom continuous casting mold. Results show that the higher the value of the mushy zone coefficient, the stronger the damping becomes, and the faster the velocity drops as melt solidifies. A relatively high value of the mushy zone coefficient generates a "banded" form of mushy zone sandwiched between the solid and liquid phases in the mold zone. When the mushy zone coefficient is at a lower value, a wider mushy zone is obtained and the melt cools down rapidly in the mold region. In addition, the temperature at free surface is relatively low with supercooling, and the solidified shell remelts locally. The model is validated through comparison with measurements of shell thickness on a breakout shell. The value of the mushy zone coefficient ranging from 1×10⁸ to 5×10⁸ kg·m^-3·s^-1 is suggested.
- continuous casting /
- numerical simulation /
- fluid flow /
- solidification /
- mushy zone coefficient

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圖 1 二次枝晶間距測量值

Figure 1. SDAS against distance from outer surface of breakout shell

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圖 2 不同糊狀區系數下結晶器寬面中心對稱面上的液相分率分布. (a) 1×10⁵ kg ·m^-3 ·s^-1; (b) 1×10⁶ kg ·m^-3 ·s^-1; (c) 1×10⁷ kg ·m^-3 ·s^-1; (d) 1×10⁸ kg ·m^-3 ·s^-1; (e) 5×10⁸ kg ·m^-3 ·s^-1

Figure 2. Distributions of liquid fraction on central symmetry plane of strand under different cases: (a) 1×10⁵ kg ·m^-3 ·s^-1; (b) 1×10⁶ kg ·m^-3 ·s^-1; (c) 1×10⁷ kg ·m^-3 ·s^-1; (d) 1×10⁸ kg ·m^-3 ·s^-1; (e) 5×10⁸ kg ·m^-3 ·s^-1

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圖 3 不同糊狀區系數下結晶器寬面中心對稱面上的糊狀區示意圖. (a) 1×10⁵ kg ·m^-3 ·s^-1; (b) 1×10⁶ kg ·m^-3 ·s^-1; (c) 1×10⁷ kg ·m^-3 ·s^-1; (d) 1×10⁸ kg ·m^-3 ·s^-1; (e) 5×10⁸ kg ·m^-3 ·s^-1

Figure 3. Diagrams of mushy zone on central symmetry plane of strand under different cases: (a) 1×10⁵ kg ·m^-3 ·s^-1; (b) 1×10⁶ kg ·m^-3 ·s^-1; (c) 1×10⁷ kg ·m^-3 ·s^-1; (d) 1×10⁸ kg ·m^-3 ·s^-1; (e) 5×10⁸ kg ·m^-3 ·s^-1

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圖 4 不同糊狀區系數下結晶器出口處鑄坯橫截面上的液相分率分布云圖. (a) 1×10⁵ kg ·m^-3 ·s^-1; (b) 1×10⁶ kg ·m^-3 ·s^-1; (c) 1×10⁷ kg ·m^-3 ·s^-1; (d) 1×10⁸ kg ·m^-3 ·s^-1; (e) 5×10⁸ kg ·m^-3 ·s^-1

Figure 4. Liquid fraction contour on cross plane at mold exit under different cases: (a) 1×10⁵ kg ·m^-3 ·s^-1; (b) 1×10⁶ kg ·m^-3 ·s^-1; (c) 1×10⁷ kg ·m^-3 ·s^-1; (d) 1×10⁸ kg ·m^-3 ·s^-1; (e) 5×10⁸ kg ·m^-3 ·s^-1

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圖 5 不同糊狀區系數下結晶器出口處液相分率沿鑄坯寬度方向的變化曲線

Figure 5. Variation of liquid fraction along Y direction at mold exit

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圖 6 不同糊狀系區數下結晶器中心線上的鋼液溫度沿拉坯方向的分布

Figure 6. Temperature variations at strand center along casting direction

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圖 7 不同糊狀區系數下彎月面處的鋼液流線圖與液相分率云圖. (a) 1×10⁵ kg ·m^-3 ·s^-1; (b) 1×10⁶ kg ·m^-3 ·s^-1; (c) 1×10⁷ kg ·m^-3 ·s^-1; (d) 1×10⁸ kg ·m^-3 ·s^-1; (e) 5×10⁸ kg ·m^-3 ·s^-1

Figure 7. Liquid fraction contour and streamline around meniscus: (a) 1×10⁵ kg ·m^-3 ·s^-1; (b) 1×10⁶ kg ·m^-3 ·s^-1; (c) 1×10⁷ kg ·m^-3 ·s^-1; (d) 1×10⁸ kg ·m^-3 ·s^-1; (e) 5×10⁸ kg ·m^-3 ·s^-1

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圖 8 不同糊狀區系數下自由液面處的鋼液溫度沿寬面方向的分布

Figure 8. Variation of temperature along Y direction at free surface

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圖 9 不同糊狀區系數下寬面中心線上的坯殼厚度沿拉坯方向的變化情況

Figure 9. Shell thickness at center line of wide face along casting direction

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圖 10 不同糊狀區系數時鋼液流線圖與液相分率云圖. (a) 1×10⁵ kg ·m^-3 ·s^-1; (b) 5×10⁸ kg ·m^-3 ·s^-1

Figure 10. Liquid fraction contour and streamline under different cases: (a) 1×10⁵ kg ·m^-3 ·s^-1; (b) 5×10⁸ kg ·m^-3 ·s^-1

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圖 11 漏鋼凝固坯殼示意圖

Figure 11. Schematic of shell from breakout

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圖 12 坯殼厚度數值計算值與測量值及經驗公式計算值對比

Figure 12. Comparison of shell thickness under different conditions

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表 1 數值模擬方案

Table 1. Cases calculated for this study

方案	糊狀區系數/(kg·m^-3·s^-1)
A	1×10⁵
B	1×10⁶
C	1×10⁷
D	1×10⁸
E	5×10⁸

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表 2 鋼液熱物性參數及模擬參數列表

Table 2. Thermophysical properties and simulation conditions in this study

參數名稱	數值
結晶器工作長度/mm	645
鑄坯斷面/mm²	250×280
拉速/(m·min^-1)	1.05
水口插入深度/mm	100
水口內徑/mm	40
水口外徑/mm	90
鋼液比熱容/(J·kg^-1·K^-1)	680
鋼液導熱系數/(W·m^-1·K^-1)	29
鋼液黏度/(kg·m^-1·s^-1)	0.006
鋼液密度/(kg·m^-3)	7020
固相線溫度/K	1718
液相線溫度/K	1766
凝固潛熱/(J·kg^-1)	270000
熱膨脹系數/K^-1	1×10^-4
過熱度/K	30

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