, Volume 71, Issue 11, pp 4206–4214 | Cite as

Application of Inhomogeneous Discrete Method to the Simulation of Transport, Agglomeration, and Removal of Oxide Inclusions in a Gas-Stirred Ladle

  • Gujun Chen
  • Shengping HeEmail author
Technical Article


The behavior of oxide inclusions in a gas-stirred ladle is characterized by a wide inclusion size distribution that evolves continuously owing to their transport, aggregation, and removal. Due to the high temperature and opacity of the ladle, a computational fluid dynamics-based method coupled with a suitable population balance algorithm is required to analyze this evolution process. In this work, the inhomogeneous discrete method is applied to solve the population balance equations associated with the behavior of Al2O3 inclusions in a gas-stirred ladle, and the effect of the number of subphases is evaluated. The calculated flow and mixing characteristics of molten steel and the size distribution of inclusions in the ladle agree well with measured values reported in literature. The results indicate that the inclusion size distribution for one, two, and three subphases differs from that obtained for four and five subphases, while the refinement from four to five subphases produces a similar distribution, hence use of the inhomogeneous discrete method with four subphases is suggested to study the behavior of inclusions in a gas-stirred ladle.



The authors are grateful for financial support from the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJQN201801413) and the Science and Technology Program of Fuling Science and Technology Commission (Grant No. FLKJ, 2018BBA3043). The Guangxi Natural Science Foundation (Grant No. 2017GXNSFBA198128).


  1. 1.
    L. Zhang and S. Taniguchi, Int. Mater. Rev. 45, 59 (2000).CrossRefGoogle Scholar
  2. 2.
    H. Ling and L. Zhang, JOM 65, 1155 (2013).CrossRefGoogle Scholar
  3. 3.
    J.P. Bellot, J.S. Kroll-Rabotin, M. Gisselbrecht, M. Joishi, A. Saxena, S. Sanders, and A. Jardy, Materials 11, 1179 (2018).CrossRefGoogle Scholar
  4. 4.
    A. Huang, H. Harmuth, M. Doletschek, S. Vollmann, and X. Feng, Steel Res. Int. 86, 1447 (2015).CrossRefGoogle Scholar
  5. 5.
    Q. Cao and N. Laurentiu, JOM 70, 2071 (2018).CrossRefGoogle Scholar
  6. 6.
    M. Haustein, A. Asad, and R. Schwarze, JOM 70, 2943 (2018).CrossRefGoogle Scholar
  7. 7.
    Q. Cao and L. Nastac, Ironmak. Steelmak. 45, 984 (2018).CrossRefGoogle Scholar
  8. 8.
    W. Liu, S.F. Yang, J.S. Li, and H.B. Yang, JOM 70, 2877 (2018).CrossRefGoogle Scholar
  9. 9.
    H. Duan, P.R. Scheller, Y. Ren, and L. Zhang, JOM 71, 69 (2019).CrossRefGoogle Scholar
  10. 10.
    D. Sheng, M. Söder, P. Jönsson, and L. Jonsson, Scand. J. Metall. 31, 134 (2002).CrossRefGoogle Scholar
  11. 11.
    M. Hallberg, P. Jönsson, and L. Jonsson, Scand. J. Metall. 34, 41 (2005).CrossRefGoogle Scholar
  12. 12.
    L. Wang, Q. Zhang, C. Deng, and Z. Li, ISIJ Int. 45, 1138 (2005).CrossRefGoogle Scholar
  13. 13.
    L. Wang, Q. Zhang, S. Peng, and Z. Li, ISIJ Int. 45, 331 (2005).CrossRefGoogle Scholar
  14. 14.
    Y.J. Kwon, J. Zhang, and H.G. Lee, ISIJ Int. 48, 891 (2008).CrossRefGoogle Scholar
  15. 15.
    V.D. Felice, I.L.A. Daoud, B. Dussoubs, A. Jardy, and J.P. Bellot, ISIJ Int. 52, 1273 (2012).CrossRefGoogle Scholar
  16. 16.
    J.P. Bellot, V. Descotes, and A. Jardy, JOM 65, 1164 (2013).CrossRefGoogle Scholar
  17. 17.
    J.P. Bellot, V. Descotes, B. Dussoubs, A. Jardy, and S. Hans, Metall. Mater. Trans. B 45, 13 (2014).CrossRefGoogle Scholar
  18. 18.
    W. Lou and M. Zhu, Metall. Mater. Trans. B 44, 762 (2013).CrossRefGoogle Scholar
  19. 19.
    W. Lou and M. Zhu, ISIJ Int. 54, 9 (2014).CrossRefGoogle Scholar
  20. 20.
    J.D. Lister, D.J. Smit, and M.J. Hounslow, AIChE J. 41, 591 (1995).CrossRefGoogle Scholar
  21. 21.
    L. Claudotte, N. Rimbert, P. Gardin, M. Simonnet, J. Lehmann, and B. Oesterlé, Steel Res. Int. 81, 630 (2010).CrossRefGoogle Scholar
  22. 22.
    L. Claudotte, N. Rimbert, P. Gardin, M. Simonnet, J. Lehmann, and B. Oesterle, AIChE J. 56, 2347 (2010).Google Scholar
  23. 23.
    N. Rimbert, L. Claudotte, P. Gardin, and J. Lehmann, Ind. Eng. Chem. Res. 53, 8630 (2014).CrossRefGoogle Scholar
  24. 24.
    R. McGraw, Aerosol Sci. Technol. 27, 255 (1997).CrossRefGoogle Scholar
  25. 25.
    I.L.A. Daoud, N. Rimbert, A. Jardy, B. Oesterlé, S. Hans, and J.P. Bellot, Adv. Eng. Mater. 13, 543 (2011).CrossRefGoogle Scholar
  26. 26.
    E. Krepper, D. Lucas, T. Frank, H.M. Prasser, and P.J. Zwart, Nucl. Eng. Des. 238, 1690 (2008).CrossRefGoogle Scholar
  27. 27.
    T. Frank, P.J. Zwart, J.M. Shi, E. Krepper, D. Lucas, and U. Rohde, Inhomogeneous MUSIG Model–a Population Balance Approach for Polydispersed Bubbly Flows. Presented at the International Conference on Nuclear Energy for New Europe, Bled, Slovenia, 2005.Google Scholar
  28. 28.
    Y. Liao, R. Rzehak, D. Lucas, and E. Krepper, Chem. Eng. Sci. 122, 336 (2015).CrossRefGoogle Scholar
  29. 29.
    U. Lindborg, Trans. Metall. Soc. AIME 242, 94 (1968).Google Scholar
  30. 30.
    L.I. Zaichik, O. Simonin, and V.M. Alipchenkov, Int. J. Heat Mass Trans. 53, 1613 (2010).CrossRefGoogle Scholar
  31. 31.
    K. Higashitani, K. Yamauchi, Y. Matsuno, and G. Hosokawa, Fluid J. Chem. Eng. Jpn. 16, 299 (1983).CrossRefGoogle Scholar
  32. 32.
    F. Oeters, Metallurgy of Steelmaking (Dusseldorf: Veriog Stahleisen mbH, 1994).Google Scholar
  33. 33.
    L. Zhang, S. Taniguchi, and K. Cai, Metall. Mater. Trans. B 31, 253 (2000).CrossRefGoogle Scholar
  34. 34.
    L. Wang, H.G. Lee, and P. Hayes, ISIJ Int. 36, 7 (1996).CrossRefGoogle Scholar
  35. 35.
    R.H. Yoon and G.H. Luttrell, Miner. Process. Extrac. Metall. Rev. 5, 101 (1989).CrossRefGoogle Scholar
  36. 36.
    W.J. Trahar, Int. J. Miner. Process. 8, 289 (1981).CrossRefGoogle Scholar
  37. 37.
    K. Krishnapisharody and G.A. Irons, Metall. Mater. Trans. B 46, 191 (2015).CrossRefGoogle Scholar
  38. 38.
    L. Schiller and Z. Naumann, Zeit. Ver. Deutsch. Ing. 77, 318 (1935).Google Scholar
  39. 39.
    O. Simonin and P.L. Viollet, Phenomena in Multiphase Flows (Washington: Hemisphere, 1990).Google Scholar
  40. 40.
    R. Bel-Fdhila and O. Simonin, Eulerian prediction of a turbulent bubbly flow downstream of a sudden pipe expansion, Proceedings 5th Workshop on Two-Phase Flow Predictions, 1992.Google Scholar
  41. 41.
    S.E. Elghobashi and T.W. Abou-Arab, Phys. Fluids 26, 931 (1983).CrossRefGoogle Scholar
  42. 42.
    B.E. Launder and D.B. Spalding, Lectures in Mathematical Models of Turbulence (London: Academic, 1972).zbMATHGoogle Scholar
  43. 43.
    J. Aoki, B.G. Thomas, J. Peter, K.D. Peaslee, Assoc. Iron Steel Technology, Warrendale, PA, 2004.Google Scholar
  44. 44.
    Y. Miyashita and K. Nishikawa, Trans. ISIJ 8, 181 (1968).Google Scholar
  45. 45.
    S. Joo and R.I.L. Guthrie, Metall. Mater. Trans. B 23, 765 (1992).CrossRefGoogle Scholar
  46. 46.
    Y. Miki and B.G. Thomas, Metall. Mater. Trans. B 30, 639 (1999).CrossRefGoogle Scholar
  47. 47.
    M. Haustein, A. Asad, and R. Schwarze, JOM 70, 2943 (2018).CrossRefGoogle Scholar
  48. 48.
    K. Wasai, K. Mukai, and A. Miyanaga, ISIJ Int. 42, 459 (2002).CrossRefGoogle Scholar
  49. 49.
    M.A.T. Andersson, L.T.I. Jonsson, and P.G. Jönsson, ISIJ Int. 40, 1080 (2000).CrossRefGoogle Scholar
  50. 50.
    B. Coletti, B. Gommers, C. Vercruyssen, B. Blanpain, P. Wollants, and F. Haers, Ironmak. Steelmak. 30, 101 (2003).CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society 2019

Authors and Affiliations

  1. 1.College of Materials Science and EngineeringYangtze Normal UniversityFulingChina
  2. 2.College of Materials Science and EngineeringChongqing UniversityChongqingChina

Personalised recommendations