.1654 工程科学学报，第43卷，第12期 到了较好的模拟，随着计算能力和模型方法的进 [13]Liu W,Yang S F,Li J S.Calculation of static suspension depth 步，模拟结果将更为准确. and meniscus shape of a solid spherical inclusion at the steel-slag (3)目前采用的水模型、原位观察等方法，可 interface.Metall Mater Trans B,2020,51(2):422 [14]Soder M,Jonsson P,Jonsson L.Inclusion growth and removal in 以间接揭示夹杂物在钢-渣界面的运动行为，但由 gas-stirred ladles.Steel Res Int,2004,75(2):128 于尺度、可视角度等限制，还需要更先进的方法来 [15]Zhu M Y,Zheng S G,Huang ZZ,et al.Numerical simulation of 进一步还原夹杂物界面行为 nonmetallic inclusions behaviour in gas-stirred ladles.Steel Res (4)目前已有的受力分析模型、流体力学模型、 m,2005,76(10):718 原位观察实验以及水模型实验等表明，界面分离 [16]Miki Y,Thomas B G,Denissov A,et al.Model of inclusion 是夹杂物去除过程中的关键环节，主要受到夹杂 removal during RH degassing of steel.Iron Steelmaker,1997, 物和熔渣两者物性参数影响，但目前物性参数与 24(8):31 界面分离两个环节的关联性尚未完全建立，随着 [17]Miki Y,Thomas B G.Modeling of inclusion removal in a tundish. Metall Mater Trans B.1999,30(4):639 物性预测模型与界面运动模型的完善，有望进 [18]Wang L T,Zhang Q Y,Deng C H,et al.Mathematical model for 步揭示工艺参数对夹杂物去除过程的影响机理. removal of inclusion in molten steel by injecting gas at ladle shroud.SJ1m,2005,45(8):1138 参考文献 [19]Thomas B G,Zhang L F.Mathematical modeling of iron and steel [1]Nakajima K.Okamura K.Inclusion transfer behavior across making processes.mathematical modeling of fluid flow in molten steel-slag interface /The 4th International Conference on continuous casting./S///nt,2001,41(10):1181 Molten Slags and Fluxes.Sendai,1992:505 [20]Cho S M,Thomas B G,Hwang J Y,et al.Modeling of inclusion [2]Liu C,Yang S F,Li J S,et al.Motion behavior of nonmetallic capture in a steel slab caster with vertical section and bending. inclusions at the interface of steel and slag.part I:Model Metals,.2021,11(4):654 development,validation,and preliminary analysis.Metall Mater [21]Geng D Q,Zheng J X,Wang K,et al.Simulation on TasB,2016,47(3):1882 decarburization and inclusion removal process in the ruhrstahl- [3] Xuan C J,Persson E S,Sevastopolev R,et al.Motion and heraeus (RH)process with ladle bottom blowing.Metall Mater detachment behaviors of liquid inclusion at molten steel-slag TasB,2015,46(3:1484 interfaces.Metall Mater Trans B,2019,50(4):1957 [22]Chattopadhyay K,Isac M,Guthrie R I L.Considerations in using [4]Liu W,Yang S F,Li J S,et al.Numerical model of inclusion the discrete phase model (DPM).Steel Res Int,2011,82(11):1287 separation from liquid metal with consideration of dissolution in [23]Duan H J.Ren Y,Zhang L F.Inclusion capture probability slag.J Iron Steel Res Int,2019,26(11):1147 prediction model for bubble floatation in turbulent steel flow [5] Yang S F,Liu W,Li J S.Motion of solid particles at molten Metall Mater Trans B,2019,50(1):16 metal-liquid slag interface.JOM,2015,67(12):2993 [24]Chen K L,Wang D Y,Qu T P,et al.Physical and numerical [6] Bouris D,Bergeles G.Investigation of inclusion re-entrainment simulation of the coalescence of liquid inclusion particles in from the steel-slag interface.Metall Mater Trans B,1998,29(3): molten steel.Chin J Eng,2019,41(10):1280 641 (陈开来，王德永，屈天鹏，等.钢中液态夹杂物聚并行为的数学 [7]Shannon G N.Sridhar S.Modeling Al,O,inclusion separation 物理模拟.工程科学学报，2019,41(10)：1280) across steel-slag interfaces.Scand J Metall,2005,34(6):353 [25]Xu Y G,Ersson M,Jonsson P.Numerical simulation of single [8]Valdez M,Shannon G S,Sridhar S.The ability of slags to absorb argon bubble rising in molten metal under a laminar flow.Steel solid oxide inclusions./S//Int,2006,46(3):450 Res Int,2015,86(11):1289 [9]Strandh J,Nakajima K,Eriksson R,et al.A mathematical model to [26]Xuan C J,Persson E S,Jensen J,et al.A novel evolution study liquid inclusion behavior at the steel-slag interface.ISI/Int, mechanism of Mg-Al-oxides in liquid steel:Integration of 2005,45(12):1838 chemical reaction and coalescence-collision.J Alloys Compd, [10]Strandh J,Nakajima K,Eriksson R,et al.Solid inclusion transfer 2020,812:152149 at a steel-slag interface with focus on tundish conditions.ISI/Int. [27]Liu W,Yang S F,Li J S,et al.Numerical simulation of the three- 2005,45(11):1597 phase flow of a bubble interacting with the steel-slag interface [11]Shannon G,White L,Sridhar S.Modeling inclusion approach to during the secondary refining process.Metall Mater Trans B. the steel/slag interface.Mater Sci Eng A,2008,495(1-2):310 2019,50(4):1542 [12]Yang S F,Li J S,Liu C,et al.Motion behavior of nonmetal [28]Liu W,Liu J,Zhao H X,et al.CFD modeling of solid inclusion inclusions at the interface of steel and slag.part II:Model motion and separation from liquid steel to molten slag.Metall application and discussion.Metall Mater Trans B,2014,45(6): Mater Trans B,2021,52(4):2430 2453 [29]Huang A,Wang HZ,Gu HZ,et al.A study on water modeling of到了较好的模拟，随着计算能力和模型方法的进 步，模拟结果将更为准确. （3）目前采用的水模型、原位观察等方法，可 以间接揭示夹杂物在钢−渣界面的运动行为，但由 于尺度、可视角度等限制，还需要更先进的方法来 进一步还原夹杂物界面行为. （4）目前已有的受力分析模型、流体力学模型、 原位观察实验以及水模型实验等表明，界面分离 是夹杂物去除过程中的关键环节，主要受到夹杂 物和熔渣两者物性参数影响，但目前物性参数与 界面分离两个环节的关联性尚未完全建立，随着 物性预测模型与界面运动模型的完善，有望进一 步揭示工艺参数对夹杂物去除过程的影响机理. 参    考    文    献 Nakajima  K,  Okamura  K.  Inclusion  transfer  behavior  across molten steel–slag interface // The 4th International Conference on Molten Slags and Fluxes. Sendai, 1992: 505 [1] Liu  C,  Yang  S  F,  Li  J  S,  et  al.  Motion  behavior  of  nonmetallic inclusions  at  the  interface  of  steel  and  slag.  part  I:  Model development,  validation,  and  preliminary  analysis. Metall Mater Trans B, 2016, 47（3）: 1882 [2] Xuan  C  J,  Persson  E  S,  Sevastopolev  R,  et  al.  Motion  and detachment  behaviors  of  liquid  inclusion  at  molten  steel−slag interfaces. Metall Mater Trans B, 2019, 50（4）: 1957 [3] Liu  W,  Yang  S  F,  Li  J  S,  et  al.  Numerical  model  of  inclusion separation  from  liquid  metal  with  consideration  of  dissolution  in slag. J Iron Steel Res Int, 2019, 26（11）: 1147 [4] Yang  S  F,  Liu  W,  Li  J  S.  Motion  of  solid  particles  at  molten metal−liquid slag interface. JOM, 2015, 67（12）: 2993 [5] Bouris  D,  Bergeles  G.  Investigation  of  inclusion  re-entrainment from the steel−slag interface. Metall Mater Trans B, 1998, 29（3）: 641 [6] Shannon  G  N,  Sridhar  S.  Modeling  Al2O3 inclusion  separation across steel−slag interfaces. Scand J Metall, 2005, 34（6）: 353 [7] Valdez M, Shannon G S, Sridhar S. The ability of slags to absorb solid oxide inclusions. ISIJ Int, 2006, 46（3）: 450 [8] Strandh J, Nakajima K, Eriksson R, et al. A mathematical model to study liquid inclusion behavior at the steel−slag interface. ISIJ Int, 2005, 45（12）: 1838 [9] Strandh J, Nakajima K, Eriksson R, et al. Solid inclusion transfer at a steel−slag interface with focus on tundish conditions. ISIJ Int, 2005, 45（11）: 1597 [10] Shannon  G,  White  L,  Sridhar  S.  Modeling  inclusion  approach  to the steel/slag interface. Mater Sci Eng A, 2008, 495（1-2）: 310 [11] Yang  S  F,  Li  J  S,  Liu  C,  et  al.  Motion  behavior  of  nonmetal inclusions  at  the  interface  of  steel  and  slag.  part  II:Model application  and  discussion. Metall Mater Trans B,  2014,  45（6）: 2453 [12] Liu  W,  Yang  S  F,  Li  J  S.  Calculation  of  static  suspension  depth and meniscus shape of a solid spherical inclusion at the steel−slag interface. Metall Mater Trans B, 2020, 51（2）: 422 [13] Söder M, Jönsson P, Jonsson L. Inclusion growth and removal in gas-stirred ladles. Steel Res Int, 2004, 75（2）: 128 [14] Zhu M Y, Zheng S G, Huang Z Z, et al. Numerical simulation of nonmetallic  inclusions  behaviour  in  gas-stirred  ladles. Steel Res Int, 2005, 76（10）: 718 [15] Miki  Y,  Thomas  B  G,  Denissov  A,  et  al.  Model  of  inclusion removal  during  RH  degassing  of  steel. Iron Steelmaker,  1997, 24（8）: 31 [16] Miki Y, Thomas B G. Modeling of inclusion removal in a tundish. Metall Mater Trans B, 1999, 30（4）: 639 [17] Wang L T, Zhang Q Y, Deng C H, et al. Mathematical model for removal  of  inclusion  in  molten  steel  by  injecting  gas  at  ladle shroud. ISIJ Int, 2005, 45（8）: 1138 [18] Thomas B G, Zhang L F. Mathematical modeling of iron and steel making  processes.  mathematical  modeling  of  fluid  flow  in continuous casting. ISIJ Int, 2001, 41（10）: 1181 [19] Cho S M, Thomas B G, Hwang J Y, et al. Modeling of inclusion capture  in  a  steel  slab  caster  with  vertical  section  and  bending. Metals, 2021, 11（4）: 654 [20] Geng  D  Q,  Zheng  J  X,  Wang  K,  et  al.  Simulation  on decarburization  and  inclusion  removal  process  in  the  ruhrstahl￾heraeus  (RH)  process  with  ladle  bottom  blowing. Metall Mater Trans B, 2015, 46（3）: 1484 [21] Chattopadhyay K, Isac M, Guthrie R I L. Considerations in using the discrete phase model (DPM). Steel Res Int, 2011, 82（11）: 1287 [22] Duan  H  J,  Ren  Y,  Zhang  L  F.  Inclusion  capture  probability prediction  model  for  bubble  floatation  in  turbulent  steel  flow. Metall Mater Trans B, 2019, 50（1）: 16 [23] Chen  K  L,  Wang  D  Y,  Qu  T  P,  et  al.  Physical  and  numerical simulation  of  the  coalescence  of  liquid  inclusion  particles  in molten steel. Chin J Eng, 2019, 41（10）: 1280 （陈开来, 王德永, 屈天鹏, 等. 钢中液态夹杂物聚并行为的数学 物理模拟. 工程科学学报, 2019, 41（10）：1280） [24] Xu  Y  G,  Ersson  M,  Jönsson  P.  Numerical  simulation  of  single argon  bubble  rising  in  molten  metal  under  a  laminar  flow. Steel Res Int, 2015, 86（11）: 1289 [25] Xuan  C  J,  Persson  E  S,  Jensen  J,  et  al.  A  novel  evolution mechanism  of  Mg−Al−oxides  in  liquid  steel:  Integration  of chemical  reaction  and  coalescence-collision. J Alloys Compd, 2020, 812: 152149 [26] Liu W, Yang S F, Li J S, et al. Numerical simulation of the three￾phase  flow  of  a  bubble  interacting  with  the  steel−slag  interface during  the  secondary  refining  process. Metall Mater Trans B, 2019, 50（4）: 1542 [27] Liu W, Liu J, Zhao H X, et al. CFD modeling of solid inclusion motion  and  separation  from  liquid  steel  to  molten  slag. Metall Mater Trans B, 2021, 52（4）: 2430 [28] [29] Huang A, Wang H Z, Gu H Z, et al. A study on water modeling of · 1654 · 工程科学学报，第 43 卷，第 12 期