工程科学学报，第41卷，第2期：199-208,2019年2月 Chinese Journal of Engineering,Vol.41,No.2:199-208,February 2019 DOI:10.13374/j.issn2095-9389.2019.02.006;http://journals.ustb.edu.cn 连铸流动与凝固耦合模拟中糊状区系数的表征及影响 李少翔，张晓萌，李亮，兰鹏，唐海燕，张家泉⑧ 北京科技大学冶金与生态工程学院，北京100083 区通信作者，E-mail:jqzhang(@metall.usth.edu.cn 摘要分析提出了连铸流动与凝固耦合数值模拟中，钢液在两相区流动时的糊状区系数(A)与渗透率的关系：通过建立 大方坯连铸结晶器三维耦合数值模型，揭示了不同糊状区系数对钢液流动、传热与凝固进程的影响，以及早期相关研究结果 差异的源头.结果表明：糊状区系数越大，钢液在糊状区内的流动阻力越强，凝固时钢液流动速度降低越快.采用较大的糊状 区系数时，糊状区呈较窄的“带状”分布在固液相之间：当糊状区系数较小时，糊状区范围变大，钢液在结晶器内温降过快，自 由液面处出现过冷现象，凝固坯壳局部发生重熔.结合实验数据验证与模型分析，认为糊状区系数取值1×103~5×103kg· m3·s可以较可靠地揭示连铸结晶器内的实际凝固现象 关键词连铸：数值模拟；流动：凝固；糊状区系数 分类号TF777.2 Representation and effect of mushy zone coefficient on coupled flow and solidification simulation during continuous casting LI Shao-xiang,ZHANG Xiao-meng,LI Liang,LAN Peng,TANG Hai-yan,ZHANG Jia-quan School of Metallurgical and Ecological Engineering,University of Science and Technology Beijing,Beijing 100083,China Corresponding author,E-mail:jqzhang@metall.ustb.edu.en 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)is an important calculating parameter in the continuous casting numerical simulation process,which strongly affects the predic- tion 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 x 10 kgmsis used in the model,which leads to unrealistic results.In this study,the relationship between the mushy zone coeffi- cient 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 be- comes,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 rel- atively 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 1x10 to 5x10 kgm.sis suggested. KEY WORDS continuous casting;numerical simulation;fluid flow;solidification;mushy zone coefficient 收稿日期：2018-03-01 基金项目：国家自然科学基金资助项目(U1860111,51604021):北京市自然科学基金资助项目(2174077)：北京科技大学本科教育教学改革资 助项目(JG2017M11)工程科学学报,第 41 卷,第 2 期:199鄄鄄208,2019 年 2 月 Chinese Journal of Engineering, Vol. 41, No. 2: 199鄄鄄208, February 2019 DOI: 10. 13374 / j. issn2095鄄鄄9389. 2019. 02. 006; http: / / journals. ustb. edu. cn 连铸流动与凝固耦合模拟中糊状区系数的表征及影响 李少翔, 张晓萌, 李 亮, 兰 鹏, 唐海燕, 张家泉苣 北京科技大学冶金与生态工程学院, 北京 100083 苣通信作者, E鄄mail: jqzhang@ metall. ustb. edu. cn 摘 要 分析提出了连铸流动与凝固耦合数值模拟中,钢液在两相区流动时的糊状区系数(Amush )与渗透率的关系;通过建立 大方坯连铸结晶器三维耦合数值模型,揭示了不同糊状区系数对钢液流动、传热与凝固进程的影响,以及早期相关研究结果 差异的源头. 结果表明:糊状区系数越大,钢液在糊状区内的流动阻力越强,凝固时钢液流动速度降低越快. 采用较大的糊状 区系数时,糊状区呈较窄的“带状冶分布在固液相之间;当糊状区系数较小时,糊状区范围变大,钢液在结晶器内温降过快,自 由液面处出现过冷现象,凝固坯壳局部发生重熔. 结合实验数据验证与模型分析,认为糊状区系数取值 1 伊 10 8 ~ 5 伊 10 8 kg· m - 3·s - 1可以较可靠地揭示连铸结晶器内的实际凝固现象. 关键词 连铸; 数值模拟; 流动; 凝固; 糊状区系数 分类号 TF777郾 2 收稿日期: 2018鄄鄄03鄄鄄01 基金项目: 国家自然科学基金资助项目(U1860111,51604021);北京市自然科学基金资助项目(2174077);北京科技大学本科教育教学改革资 助项目(JG2017M11) Representation and effect of mushy zone coefficient on coupled flow and solidification simulation during continuous casting LI Shao鄄xiang, ZHANG Xiao鄄meng, LI Liang, LAN Peng, TANG Hai鄄yan, ZHANG Jia鄄quan 苣 School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083, China 苣Corresponding author, E鄄mail: jqzhang@ metall. ustb. edu. cn ABSTRACT The mushy zone refers to the region of the solid鄄鄄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 (Amush ) is an important calculating parameter in the continuous casting numerical simulation process, which strongly affects the predic鄄 tion 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 伊 10 5 kg·m - 3·s - 1 is used in the model, which leads to unrealistic results. In this study, the relationship between the mushy zone coeffi鄄 cient 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 be鄄 comes, and the faster the velocity drops as melt solidifies. A relatively high value of the mushy zone coefficient generates a “banded冶 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 rel鄄 atively 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 伊10 8 to 5 伊10 8 kg·m -3·s -1 is suggested. KEY WORDS continuous casting; numerical simulation; fluid flow; solidification; mushy zone coefficient