Skip to main content
SpringerLink
Log in

A Mathematical Modeling Study of Bubble Formations in a Molten Steel Bath

  • Published:
Metallurgical and Materials Transactions B Aims and scope Submit manuscript

Abstract

The bubble formation during gas injection into liquids was studied using a water model and a three-dimensional numerical model. In the experiment, a high-speed camera was used to record the bubble formation processes. Nozzle diameters of 0.5, 1, and 2 mm were investigated under both wetting and non-wetting conditions. The bubble sizes and formation frequencies as well as the bubbling regimes were identified for each nozzle size and for different wettabilities. The results show that the upper limits of the bubbling regime are 7.35, 12.05, and 15.22 L/h under wetting conditions for the 0.5, 1, and 2 mm nozzle diameters, respectively. Meanwhile, the limits are 12.66, 13.64, and 15.33 L/h for the non-wetting conditions. In the numerical model, the volume-of-fluid method was used to track the interface between the gas and liquid. The simulation results were compared with the experimental observations in the air–water system. The comparisons show a satisfactory good agreement between the two methods. The mathematical model was then applied to simulate the argon-steel system. Simulation results show that the effect of nozzle size is insignificant for the current studied metallurgical conditions. The upper limits of the bubbling regime are approximately 60 and 80 L/h for a 2-mm nozzle for the wetting and non-wetting conditions, respectively. In addition, a poor wettability leads to a bigger bubble and a lower frequency compared with a good wettability, for the same gas flow rate.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Abbreviations

\( \alpha_{\text{l}} \) :

Value of liquid volume fraction (−)

\( \rho \) :

Density (kg m−3)

\( \mu \) :

Viscosity (kg m−1 s−1)

\( \sigma \) :

Surface tension coefficient (N m−1)

\( \kappa \) :

Curvature (m−2)

t:

Time (s)

F s :

Surface tension force (N m−3)

θ :

Contact angle (°)

d B :

Bubble diameter (m)

d N :

Nozzle diameter (m)

f :

Bubble formation frequency (s−1)

T :

Bubble formation period (s)

V B :

Bubble volume (m3)

References

  1. L. Davidson and E.H. Amick: AIChE J., 1956, vol. 2, pp. 337-42.

    Article  Google Scholar 

  2. S. Ramakrishnan, R. Kumar and N.R. Kuloor: Chem. Eng. Sci., 1969, vol. 24, pp. 731-47.

    Article  Google Scholar 

  3. A.A. Kulkarni and J.B. Joshi: Ind. Eng. Chem. Res., 2005, vol. 44, pp. 5873-931.

    Article  Google Scholar 

  4. G.Q. Yang, B. Du and L.S. Fan: Chem. Eng. Sci., 2007, vol. 62, pp. 2-27.

    Article  Google Scholar 

  5. R.J. Andreini, J.S. Foster and R.W. Callen: Metall. Trans. B, 1977, vol. 8B, pp. 625-31.

    Article  Google Scholar 

  6. K.G. Davis, G.A. Irons and R.I.L. Guthrie: Metall. Trans. B, 1978, vol. 9B, pp. 721-22.

    Article  Google Scholar 

  7. G.A. Irons and R.I.L. Guthrie: Metall. Trans. B, 1978, vol. 9B, pp. 101-10.

    Article  Google Scholar 

  8. G.A. Irons and R.I.L. Guthrie: Can. Metall. Q., 1980, vol. 19, pp. 381-87.

    Article  Google Scholar 

  9. K. Mori, Y. Ozawa and M. Sano: Trans. Iron Steel Inst. Jpn., 1982, vol. 22, pp. 377-84.

    Article  Google Scholar 

  10. M. Iguchi, T. Chihara, N. Takanashi, Y. Ogawa, N. Tokumitsu and Z.i. Morita: ISIJ Int., 1995, vol. 35, pp. 1354-61.

    Article  Google Scholar 

  11. M. Iguchi, H. Kawabata, K. Nakajima and Z.I. Morita: Metall. Mater. Trans. B, 1995, vol. 26B, pp. 67-74.

    Article  Google Scholar 

  12. M. Iguchi and T. Chihara: Metall. Mater. Trans. B, 1998, vol. 29B, pp. 755-61.

    Article  Google Scholar 

  13. W. Lou and M. Zhu: Metall. Mater. Trans. B, 2013, vol. 44B, pp. 762-82.

    Article  Google Scholar 

  14. S.T. Johansen and F. Boysan: Metall. Trans. B, 1988, vol. 19B, pp. 755-64.

    Article  Google Scholar 

  15. Y. Xu, M. Ersson, and P. Jönsson: Steel Res. Int., 2015. DOI: 10.1002/srin.201400355.

  16. R.I.L. Guthrie: International Conference on Injection Metallurgy, Jernkontoret, Sweden, 1980, pp. 6:1–31.

  17. Y. Sahai and R.I.L Guthrie: Metall. Mater. Trans. B, 1982, vol. 13B, pp. 125-27.

    Article  Google Scholar 

  18. M. van Sint Annaland, N.G. Deen, and J.A.M. Kuipers: Chem. Eng. Sci., 2005, vol. 60, pp. 2999- 3011.

    Article  Google Scholar 

  19. C.W. Hirt and B.D. Nichols: J. Comput. Phys., 1981, vol. 39, pp. 201-25.

    Article  Google Scholar 

  20. J. Brackbill, D.B. Kothe and C. Zemach: J. Comput. Phys., 1992, vol. 100, pp. 335-54.

    Article  Google Scholar 

  21. Y. Zhang, M. Liu, Y. Xu and C. Tang: Chem. Eng. Sci., 2012, vol. 73, pp. 55-78.

    Article  Google Scholar 

  22. R.I. Issa: J. Comput. Phys., 1986, vol. 62, pp. 40-65.

    Article  Google Scholar 

  23. V.V. Buwa, D. Gerlach, F. Durst and E. Schlücker: Chem. Eng. Sci., 2007, vol. 62, pp. 7119-32.

    Article  Google Scholar 

  24. Z. Wang, K. Mukai and D. Izu: ISIJ Int., 1999, vol. 39, pp. 154-63.

    Article  Google Scholar 

  25. A. Alexiadis: Appl. Math. Model., 2007, vol. 31, pp. 1534-47.

    Article  Google Scholar 

  26. H.P. Liu, Z.Y. Qi and M.G. Xu: Steel Res. Int., 2011, vol. 82, pp. 440-58.

    Article  Google Scholar 

Download references

Acknowledgments

Yonggui Xu would like to extend his sincere appreciation to the CSC (China Scholarship Council) for financial support of his PhD studies at KTH-Royal Institute of Technology, Sweden.

Author information

Authors and Affiliations

  1. Division of Applied Process Metallurgy, Department of Materials Science and Engineering, KTH-Royal Institute of Technology, Brinellvägen 23, 100 44, Stockholm, Sweden

    Yonggui Xu (Ph.D. Student), Mikael Ersson (Assistant Professor) & Pär Göran Jönsson (Professor)

Authors
  1. Yonggui Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mikael Ersson
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pär Göran Jönsson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yonggui Xu.

Additional information

Manuscript submitted March 24, 2015.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xu, Y., Ersson, M. & Jönsson, P.G. A Mathematical Modeling Study of Bubble Formations in a Molten Steel Bath. Metall Mater Trans B 46, 2628–2638 (2015). https://doi.org/10.1007/s11663-015-0423-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11663-015-0423-x

Keywords

Search

Navigation