陈开来等：钢中液态夹杂物聚并行为的数学物理模拟 ·1287· 式中：y为两相间界面张力，4.和u分别为连续相和 (徐迎铁，陈兆平，杨宝权.轴承钢Ds类大颗粒夹杂物研究 分散相的黏度，P。为连续相的密度，ε为湍动能耗散 炼钢，2016,32(4)：49) 率，d为液滴直径，B为范德华常数，其数量级为 [4]Zhu T H,Chen H,Liu Y,et al.Effect of Al on stomata,inclusion and impact toughness in rail surfacing weld.Weld Join,2011(8):25 10-28Jm,E为液膜的量纲一曲率直径，它是界面活 (朱藤辉，陈辉，刘艳.等.A1对钢轨堆焊焊缝中气孔，夹杂 动性系数M的函数： 物及冲击韧性的影响.焊接，2011(8)：25) E=12.61+2.166 arctg(28) (11) [5]Pamnani R,Jayakumar T,Vasudevan M,et al.Investigations on M=1.12(my)2 the impact toughness of HSLA steel are welded joints.I Manuf Lp.e2d丽) (12) Processes,2016,21:75 结合式(10)、(11)和(12)可知，在其他参数均 [6]Taniguchi S,Kikuchi A,Ise T,et al.Model experiment on the coagulation of inclusion particles in liquid steel.ISI/Int,1996, 不变的条件下，界面活动性系数M随两相界面张力 36(Suppl):S117 的升高而增大，随分散相黏度的增大而减小，相应 [7]Zheng S G,Zhu M Y.Physical modeling of inclusion behavior in 的，液滴的理论聚并时间则随两相界面张力的升高 ladle with eccentric bottom blowing argon.J fron Steel Res,2008, 而缩短，随分散相黏度的增大而延长.这与本文中 20(6):18 数学物理模拟实验的研究结果具有很高的一致性. (郑淑国，朱苗勇.偏心底吹氩钢包内夹杂物行为的物理模 拟.钢铁研究学报，2008,20(6)：18) 3结论 [8]Arai H,Matsumoto K,Shimasaki S,et al.Model experiment on inclusion removal by bubble flotation accompanied by particle co- (1)采用水模拟钢液，密度接近的三组有机试 agulation in turbulent flow.ISI/Int,2009.49(7):965 剂模拟液态夹杂物，在相同实验条件下，三者的钢包 [9]Cho J S,Lee H G.Cold model study on inclusion removal from 模拟实验平均上浮去除率分别为81.1%、74.5%和 liquid steel using fine gas bubbles.IS//Int,2001,41(2):151 65%.结果表明，夹杂物液滴的聚合趋势与其自身 [10]Mhatre S,Deshmukh S,Thaokar R M.Electrocoalescence of a 的物理性质有紧密联系 drop pair.Phys Fluids,2015,27(9):092106 [11]Lou W T,Zhu M Y.Numerical simulations of inclusion behavior (2)液滴与连续相之间的界面张力对聚并过程 in gas-stirred ladles.Metall Mater Trans B,2013,44(3):762 影响显著.随着界面张力的增大，聚并进行中液滴 [12]Chen G J.He S P,Li Y G.et al.Modeling dynamies of agglom- 对受到的附加压力增加，界面收缩速率升高，总体聚 eration,transport,and removal of AlO clusters in the Rhein- 并进程被加快.在本计算条件下，聚并时间由10mN sahl-Heraeus reactor based on the coupled computational fluid dy- m1时的240us缩短至90mNm-1时的27us. namics-population balance method model.Ind Eng Chem Res, 2016,55(25):7030 (3)其他条件均不变时，增加液滴的动力学黏 [13]Guo L F,Li H,Wang Y,et al.Simulation on agglomeration of 度会减缓聚并进行过程中液滴间的相互传质，从而 liquid inclusion particles in steel based on VOF model.Adr Mater 降低界面的收缩速度，阻碍液滴对的聚并过程 Res,2012,538-541:525 因此，为了实现钢液中液态夹杂物的无害化控 [14]Demond A H,Lindner A S.Estimation of interfacial tension be- 制，可以考虑促使其聚合上浮去除或者无害化残留 tween organic liquids and water.Environ Sci Technol,1993,27 (12):2318 的两种不同的控制思路.通过改变液态夹杂物与高 [15]Peters F,Arabali D.Interfacial tension between oil and water 温钢液之间的界面参数以及黏度参数，调整两液态 measured with a modified contour method.Colloids Suf A. 夹杂物的聚合时间，有望达到液态夹杂物聚合或分 2013.426:1 散的控制目标 [16]Sahai Y,Emi T.Criteria for water modeling of melt flow and in- clusion removal in continuous casting tundishes.IS/J Int,1996, 参考文献 36(9):1166 [1]Zhu M Y,XiaoZQ.Physical and Numerical Simulation of Refining [17]Liu S P,Li T M,Jia S Y.Coalescence between two small liquid Process of Molten Steel.Beijing:Metallurgical Industry Press,1998 drops.Acta Phys-Chim Sin,1995,11(11):997 (朱苗勇，萧泽强.钢的精炼过程数学物理模拟.北京：治金 (刘世平，李佟茗，贾绍义.两个液滴之间的聚并.物理化学 工业出版社，1998) 学报，1995,11(11)：997) [2]Yao J,Qu X H.He X B,et al.Effect of inclusion size on the [18]Liu S P,Li T M,Zhang T Y.Drop coalescence in turbulent dis- high cycle fatigue strength and failure mode of a high V alloyed persions.CIESC J.1998.49(4):409 powder metallurgy tool steel.Int J Miner Metall Mater,2012,19 (刘世平，李佟茗，张腾燕。湍流分散系统中的液滴聚并.化 (7):608 工学报，1998,49(4)：409) [3]Xu Y T.Chen Z P.Yang B Q.Study of large size Ds type inclu- [19]Liu S P,Li D M.Drop coalescence in turbulent dispersions. sions in bearing steel.Steelmaking,2016,32(4):49 Chem Eng Sci,1999,54(23):5667陈开来等: 钢中液态夹杂物聚并行为的数学物理模拟 式中:酌 为两相间界面张力,滋c和 滋d分别为连续相和 分散相的黏度,籽c为连续相的密度,着 为湍动能耗散 率,d 为液滴直径,B 为范德华常数,其数量级为 10 - 28 J·m,E 为液膜的量纲一曲率直径,它是界面活 动性系数 M 的函数: E = 12郾 61 + 2郾 166arctg(2M 0郾 8 ) (11) M = 1郾 12 滋c 滋 ( d 仔酌 籽c着 2 / 3 d 5 / 3 ) 1 / 2 (12) 结合式(10)、(11)和(12)可知,在其他参数均 不变的条件下,界面活动性系数 M 随两相界面张力 的升高而增大,随分散相黏度的增大而减小,相应 的,液滴的理论聚并时间则随两相界面张力的升高 而缩短,随分散相黏度的增大而延长. 这与本文中 数学物理模拟实验的研究结果具有很高的一致性. 3 结论 (1)采用水模拟钢液,密度接近的三组有机试 剂模拟液态夹杂物,在相同实验条件下,三者的钢包 模拟实验平均上浮去除率分别为 81郾 1% 、74郾 5% 和 65% . 结果表明,夹杂物液滴的聚合趋势与其自身 的物理性质有紧密联系. (2)液滴与连续相之间的界面张力对聚并过程 影响显著. 随着界面张力的增大,聚并进行中液滴 对受到的附加压力增加,界面收缩速率升高,总体聚 并进程被加快. 在本计算条件下,聚并时间由 10 mN ·m - 1时的 240 滋s 缩短至 90 mN·m - 1时的 27 滋s. (3)其他条件均不变时,增加液滴的动力学黏 度会减缓聚并进行过程中液滴间的相互传质,从而 降低界面的收缩速度,阻碍液滴对的聚并过程. 因此,为了实现钢液中液态夹杂物的无害化控 制,可以考虑促使其聚合上浮去除或者无害化残留 的两种不同的控制思路. 通过改变液态夹杂物与高 温钢液之间的界面参数以及黏度参数,调整两液态 夹杂物的聚合时间,有望达到液态夹杂物聚合或分 散的控制目标. 参 考 文 献 [1] Zhu M Y, Xiao Z Q. Physical and Numerical Simulation of Refining Process of Molten Steel. Beijing: Metallurgical Industry Press, 1998 (朱苗勇, 萧泽强. 钢的精炼过程数学物理模拟. 北京: 冶金 工业出版社, 1998) [2] Yao J, Qu X H, He X B, et al. Effect of inclusion size on the high cycle fatigue strength and failure mode of a high V alloyed powder metallurgy tool steel. Int J Miner Metall Mater, 2012, 19 (7): 608 [3] Xu Y T, Chen Z P, Yang B Q. Study of large size Ds type inclu鄄 sions in bearing steel. Steelmaking, 2016, 32(4): 49 (徐迎铁, 陈兆平, 杨宝权. 轴承钢 Ds 类大颗粒夹杂物研究. 炼钢, 2016, 32(4): 49) [4] Zhu T H, Chen H, Liu Y, et al. Effect of Al on stomata, inclusion and impact toughness in rail surfacing weld. Weld Join, 2011(8): 25 (朱藤辉, 陈辉, 刘艳, 等. Al 对钢轨堆焊焊缝中气孔、夹杂 物及冲击韧性的影响. 焊接, 2011(8): 25) [5] Pamnani R, Jayakumar T, Vasudevan M, et al. Investigations on the impact toughness of HSLA steel arc welded joints. J Manuf Processes, 2016, 21: 75 [6] Taniguchi S, Kikuchi A, Ise T, et al. Model experiment on the coagulation of inclusion particles in liquid steel. ISIJ Int, 1996, 36(Suppl): S117 [7] Zheng S G, Zhu M Y. Physical modeling of inclusion behavior in ladle with eccentric bottom blowing argon. J Iron Steel Res, 2008, 20(6): 18 (郑淑国, 朱苗勇. 偏心底吹氩钢包内夹杂物行为的物理模 拟. 钢铁研究学报, 2008, 20(6): 18) [8] Arai H, Matsumoto K, Shimasaki S, et al. Model experiment on inclusion removal by bubble flotation accompanied by particle co鄄 agulation in turbulent flow. ISIJ Int, 2009, 49(7): 965 [9] Cho J S, Lee H G. Cold model study on inclusion removal from liquid steel using fine gas bubbles. ISIJ Int, 2001, 41(2): 151 [10] Mhatre S, Deshmukh S, Thaokar R M. Electrocoalescence of a drop pair. Phys Fluids, 2015, 27(9): 092106 [11] Lou W T, Zhu M Y. Numerical simulations of inclusion behavior in gas鄄stirred ladles. Metall Mater Trans B, 2013, 44(3): 762 [12] Chen G J, He S P, Li Y G, et al. Modeling dynamics of agglom鄄 eration, transport, and removal of Al2O3 clusters in the Rhein鄄 sahl鄄Heraeus reactor based on the coupled computational fluid dy鄄 namics鄄population balance method model. Ind Eng Chem Res, 2016, 55(25): 7030 [13] Guo L F, Li H, Wang Y, et al. Simulation on agglomeration of liquid inclusion particles in steel based on VOF model. Adv Mater Res, 2012, 538鄄541: 525 [14] Demond A H, Lindner A S. Estimation of interfacial tension be鄄 tween organic liquids and water. Environ Sci Technol, 1993, 27 (12): 2318 [15] Peters F, Arabali D. Interfacial tension between oil and water measured with a modified contour method. Colloids Surf A, 2013, 426: 1 [16] Sahai Y, Emi T. Criteria for water modeling of melt flow and in鄄 clusion removal in continuous casting tundishes. ISIJ Int, 1996, 36(9): 1166 [17] Liu S P, Li T M, Jia S Y. Coalescence between two small liquid drops. Acta Phys鄄Chim Sin, 1995, 11(11): 997 (刘世平, 李佟茗, 贾绍义. 两个液滴之间的聚并. 物理化学 学报, 1995, 11(11): 997) [18] Liu S P, Li T M, Zhang T Y. Drop coalescence in turbulent dis鄄 persions. CIESC J, 1998, 49(4): 409 (刘世平, 李佟茗, 张腾燕. 湍流分散系统中的液滴聚并. 化 工学报, 1998, 49(4): 409) [19] Liu S P, Li D M. Drop coalescence in turbulent dispersions. Chem Eng Sci, 1999, 54(23): 5667 ·1287·