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Modeling Study of Metallurgical Slag Foaming via Dimensional Analysis

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Abstract

A procedural model is urgently required for optimization of slag foaming in metallurgical processes. Through physical modeling following the similarity criterion of the Morton number (Mo), this paper investigates the effects of superficial gas velocity, dynamic viscosity, and surface tension on the foaming height. From the physical modeling results, several dimensionless numbers relevant to the slag foaming were identified, and this includes the Reynolds number (Re), Weber number (We), Froude number (Fr), and Mo. In addition, the relationships between Mo and Re for the various types of slag foaming were derived via dimensional analysis. Furthermore, assuming that these dimensionless numbers follow a power law, correlations of foaming height as a function of the slag physical properties and the superficial gas velocity were obtained based on the physical modeling results. Consequently, this study proposes a dynamic mathematical model for predicting the liquid height variation with time during slag foaming according to the gas balance.

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References

  1. [1]A. Kozhukhov: Metall., 2013, vol. 57, pp. 33–40.

    CAS  Google Scholar 

  2. [2]G. Qiu, C. Shan, X. Zhang and X. Lv: Ironmaking Steelmaking, 2017, vol. 44, pp. 246–254.

    Article  CAS  Google Scholar 

  3. [3]Y. Zhang and R. J. Fruehan: Metall. Mater. Trans. B, 1995, vol. 26, pp. 813–819.

    Article  CAS  Google Scholar 

  4. [4]T. M. Kipepe and X. Pan: J. Energy South Afr., 2015, vol. 26, pp. 64–73.

    Article  Google Scholar 

  5. [5]A. Chychko, L. Teng and S. Seetharaman: Metall. Mater. Trans. B, 2012, vol. 43, pp. 1078–1085.

    Article  CAS  Google Scholar 

  6. [6]A. Chychko, L. Teng and S. Seetharaman: Arch. Metall. Mater., 2010, vol. 55, pp. 1089–1095.

    Article  CAS  Google Scholar 

  7. [7]K. Ito and R. J. Fruehan: Metall. Trans. B, 1989, vol. 20, pp. 515–521.

    Article  CAS  Google Scholar 

  8. [8]Y. Zhang and R. J. Fruehan: Metall. Mater. Trans. B, 1995, vol. 26, pp. 803–812.

    Article  CAS  Google Scholar 

  9. [9]Y. Ogawa, D. Huin, H. Gaye and N. Tokumit: ISIJ Int., 1993, vol. 33, pp. 224–232.

    Article  CAS  Google Scholar 

  10. [10]S. S. Ghag, P. C. Hayes and H. Lee: ISIJ Int., 1998, vol. 11, pp. 1201–1207.

    Article  Google Scholar 

  11. [11]S. S. Ghag, P. C. Hayes and H. Lee: ISIJ Int., 1998, vol. 38, pp. 1208–1215.

    Article  CAS  Google Scholar 

  12. [12]S. S. Ghag, P. C. Hayes and H. Lee: ISIJ Int., 1998, vol. 38, pp. 1216–1224.

    Article  CAS  Google Scholar 

  13. [13]M. Y. Zhu and S. C. Du: Steel Res., 2000, vol. 3, pp. 76–82.

    Article  Google Scholar 

  14. [14]M. Y. Zhu, J. Ticora and S. C. Du: Scand. J. Metall., 2010, vol. 30, pp. 51–56.

    Article  CAS  Google Scholar 

  15. [15]L. Pilon and R. Viskanta: Chem. Eng. Process., 2004, 43, pp. 149–160.

    Article  CAS  Google Scholar 

  16. [16]L. Pilon, A. G. Fedorov and R. Viskanta: J. Colloid Interface Sci., 2001, vol. 242, pp. 425–436.

    Article  CAS  Google Scholar 

  17. [17]D. Lotun and L. Pilon: ISIJ Int., 2005, vol. 45, pp. 835–840.

    Article  CAS  Google Scholar 

  18. [18]L. S. Wu, G. J. Albertsson and S. C. Du: Ironmaking Steelmaking, 2013, vol. 37, pp. 612–619.

    Article  Google Scholar 

  19. [19]J. Wang, A. V. Nguyen and S. Farrokhpay: Adv. Colloid Interface Sci., 2016, vol. 228, pp. 55–70.

    Article  CAS  Google Scholar 

  20. [20]S. J. Neethling, H. T. Lee and P. Grassia: Colloids Surf. A, 2005, vol. 263, pp. 184–196.

    Article  CAS  Google Scholar 

  21. [21]N. Barbian, E. Ventura-Medina and J. J. Cilliers: Miner. Eng., 2003, vol. 16, pp. 1111–1116.

    Article  CAS  Google Scholar 

  22. [22]J. Martinsson, B. Glaser and S. C. Du: Ironmaking Steelmaking, 2017, vol. 46, pp. 1–5.

    Google Scholar 

  23. [23]R. F. Wang, B. Zhang, C. J. Liu and M. F. Jiang: Exp. Therm. Fluid Sci, 2020, vol. 113, art. no. 110041.

    Article  CAS  Google Scholar 

  24. [24]S. Hara, M. Kitamura and K. Ogino: ISIJ Int., 1990. vol. 30, pp. 714–721.

    Article  Google Scholar 

  25. [25]S. A. C. Stadler, J. J. Eksteen and C. Aldrich: Miner. Eng., 2007, vol. 20, pp. 1121–1128.

    Article  CAS  Google Scholar 

  26. [26]S. Hara and K. Ogino: ISIJ Int., 1992, vol. 32, pp. 81–86.

    Article  CAS  Google Scholar 

  27. [27]A. P. Luz, T. A. Ávila, P. Bonadia and V. C. Pandolfelli: Refract. Worldforum, 2011, vol. 3, pp. 1–8.

    Google Scholar 

  28. [28]M. Novák, J. Straka and M. Pribyl: In: Proc. UNITECR Salvador, Brazil, 2009, pp. 1–4.

    Google Scholar 

  29. [29]A. P. Luz, T. A. Ávila, P. Bonadia and V. C. Pandolfelli: Ceram. Int.,. 2011, vol. 37. pp. 2947–2950.

    Article  CAS  Google Scholar 

  30. [30]A. Kapilashrami, M. Görnerup, A. K. Lahiri and S. Seetharaman: Metall. Mater. Trans. B, 2006, vol. 37, pp. 109–117.

    Article  CAS  Google Scholar 

  31. [31]R. D. Morales, H. Rodríguez-Hernández, A. Vargas-Zamora and A. N. Conejo: Ironmaking Steelmaking, 2002, vol. 29, pp. 445–453.

    Article  CAS  Google Scholar 

  32. [32]L. Pilon, A. G. Fedorov and R. Viskanta: Chem. Eng. Sci., 2002, vol. 57, pp. 977–990.

    Article  CAS  Google Scholar 

  33. C. W. Nexhip: The University of Melbourne, Melbourne, 1997.

  34. [34]S. J. Neethling and J. J. Cilliers: Powder Technol., 1999, vol. 101, pp. 249–256.

    Article  CAS  Google Scholar 

  35. [35]C. Cicutti, M. Valdez, T. Pérez, R. Donayo and J. Retroni: Lat. Am. Appl. Res., 2002, vol. 32, pp. 237–240.

    CAS  Google Scholar 

  36. [36]S. Nexhip, S. Y. Sun and S. Jahanshahi: Int. Mater. Rev., 2004, vol. 49, pp. 286–298.

    Article  CAS  Google Scholar 

  37. [37]B. Deo, A. Overbosch, B. Snoeijer, D. Das and K. Srinivas: Trans. Indian Inst. Met., 2013, vol. 66, pp. 543–554.

    Article  Google Scholar 

  38. [38]K. Takamura, H. Fischer, N. R. Morrow: J. Pet. Sci. Eng., 2012, vol. 98–99, pp. 50–60.

    Article  Google Scholar 

  39. [39]A. Satyanarayan, R. Kumar and N. R. Kuloor: Chem. Eng. Sci., 1969, vol. 24, pp. 749–761.

    Article  CAS  Google Scholar 

  40. [40]M. Martín, F. J. Montes and M. A. Galán: Chem. Eng. Sci., 2015, vol. 61. pp. 5196–5203.

    Article  Google Scholar 

  41. [41]A. Kozhukhov: Steel Transl., 2014, vol. 44, pp. 15–18.

    Article  Google Scholar 

  42. [42]S. Barella, A. Gruttadauria, C. Mapelli and D. Mombelli: Ironmaking Steelmaking, 2010, vol. 39, pp. 463–469.

    Article  Google Scholar 

  43. [43]S. Ramakrishnan, R. Kumar and N. R. Kuloor: Chem. Eng. Sci., 1969, vol. 24, pp. 731–747.

    Article  CAS  Google Scholar 

  44. [44]W. Siemes and J. F. Kaufmann: Chem. Eng. Sci., 1956, vol. 5, pp. 127–139.

    Article  CAS  Google Scholar 

  45. [45]S. Tcholakova, Z. Mitrinova, K. Golemanov, N. D. Denkov, M. Vethamuthu and K. P. Ananthapadmanabhan: Langmuir, 2011, vol. 27, pp. 14807–14819.

    Article  CAS  Google Scholar 

  46. [46]D. Skupien and D. R. Gaskell: Metall. Mater. Trans. B, 2000, vol. 31, pp. 921–925.

    Article  CAS  Google Scholar 

  47. [47]M. J. Rosen: Surfactants and interfacial phenomena, John Wiley, New York, 1978.

    Google Scholar 

  48. [48]K. H. Soo, M. D. Joon and P. J. Hyun: ISIJ Int., 2001, vol. 41, pp. 317–324.

    Article  Google Scholar 

  49. [49]S. Hara and K. Ogino: ISIJ Int., 1992, vol. 32, pp. 81–86.

    Article  CAS  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Key R & D Program of China, China (Grant No. 2017YFC0805100); National Natural Science Foundation of China, China (Grant No. 51774087); Liaoning Provincial Natural Science Foundation of China, China (Grant No. 2019-MS-123); and Fundamental Research Funds for the Central Universities, China (Grant No. N180725008).

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Authors and Affiliations

  1. Key Laboratory for Ecological Metallurgy of Multimetallic Ores (Ministry of Education), Northeastern University, Wenhua Road, Heping District, Shenyang, 110819, Liaoning Province, P. R. China

    Ruifang Wang, Bo Zhang, Chao Hu, Chengjun Liu & Maofa Jiang

  2. School of Metallurgy, Northeastern University, Wenhua Road, Heping District, Shenyang, 110819, Liaoning Province, P. R. China

    Ruifang Wang, Bo Zhang, Chao Hu, Chengjun Liu & Maofa Jiang

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  1. Ruifang Wang
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  2. Bo Zhang
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  3. Chao Hu
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Correspondence to Bo Zhang.

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Manuscript submitted October 30, 2020; accepted March 5, 2021.

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Wang, R., Zhang, B., Hu, C. et al. Modeling Study of Metallurgical Slag Foaming via Dimensional Analysis. Metall Mater Trans B 52, 1805–1817 (2021). https://doi.org/10.1007/s11663-021-02147-0

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