Skip to main content
SpringerLink
Log in

Investigation of Bubble-Slag Layer Behaviors with Hybrid Eulerian–Lagrangian Modeling and Large Eddy Simulation

  • Published:
JOM Aims and scope Submit manuscript

Abstract

In ladle metallurgy, bubble–liquid interaction leads to complex phase structures. Gas bubble behavior, as well as the induced slag layer behavior, plays a significant role in the refining process and the steel quality. In the present work, a mathematical model using the large eddy simulation (LES) is developed to investigate the bubble transport and slag layer behavior in a water model of an argon-stirred ladle. The Eulerian volume of fluid model is adopted to track the liquid steel–slag–air free surfaces while the Lagrangian discrete phase model is used for tracking and handling the dynamics of discrete bubbles. The bubble coalescence is considered using O’Rourke’s algorithm to solve the bubble diameter redistribution and bubbles are removed after leaving the air–liquid interface. The turbulent liquid flow that is induced by bubble–liquid interaction is solved by LES. The slag layer fluactuation, slag droplet entrainment and spout eye open–close phenomenon are well revealed. The bubble diameter distribution and the spout eye size are compared with the experiment. The results show that the hybrid Eulerian–Lagrangian–LES model provides a valid modeling framework to predict the unsteady gas bubble–slag layer coupled behaviors.

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

b cri :

Criteria impact parameter (m)

C D :

Drag force coefficient

C VM :

Virtual mass force coefficient

C L :

Lift force coefficient

C S :

Smagorinsky constant

d :

Distance to the closest wall (m)

d pi :

Initial bubble diameter (m)

\( \vec{F}_{\text{VM}} \) :

Virtual mass force (m/s2)

\( \vec{F}_{\text{L}} \) :

Lift force (m/s2)

\( \vec{F}_{\text{PG}} \) :

Pressure gradient force (m/s2)

g :

Gravitational acceleration (m/s2)

n :

Number of bubbles

P :

Pressure (Pa)

Q :

Gas flow rate (m3/s)

r :

Bubble radii (m)

Re :

Relative Reynolds Number

S :

Rate-of-strain tensor (s−1)

t :

Time (s)

u :

Velocity (m/s)

V :

Cell volume (m3)

We :

Collisional Weber number

α :

Volume fraction

ρ :

Density (kg/m3)

σ :

Stress tensor (N/m2)

τ :

Subgrid-scale stress (N/m2)

μ :

Viscosity (kg/m/s)

μ t :

Turbulent viscosity (kg/m/s)

κ :

Von Kármán constant

δ ij :

Dirac function

References

  1. L. Nastac, JOM 56, 43 (2004).

    Article  Google Scholar 

  2. Q. Zheng and A. Yu, Phys. Rev. Lett. 113, 068001 (2014).

    Article  Google Scholar 

  3. L. Zhang, Modell. Simul. Mater. Sci. Eng. 8, 463 (2000).

    Article  Google Scholar 

  4. A. Mukhopadhyay, E.W. Grald, K. Dhanasekharan, S. Sarkar, and J. Sanyal, Steel Res. Int. 76, 22 (2005).

    Google Scholar 

  5. B. Li, H. Yin, C. Zhou, and F. Tsukihashi, ISIJ Int. 48, 1704 (2008).

    Article  Google Scholar 

  6. N. Kochi, Y. Ueda, T. Uemura, T. Ishii, and M. Iguchi, ISIJ Int. 51, 1011 (2011).

    Article  Google Scholar 

  7. L. Li, Z. Liu, B. Li, H. Matsuura, and F. Tsukihashi, ISIJ Int. 55, 1337 (2015).

    Article  Google Scholar 

  8. Z. Liu, L. Li, F. Qi, B. Li, M. Jiang, and F. Tsukihashi, Metall. Mater. Trans. B 46B, 406 (2015).

    Article  Google Scholar 

  9. S.T. Johansen and F. Boysan, Metall. Trans. B 19B, 755 (1988).

    Article  Google Scholar 

  10. D. Guo and G.A. Irons, Metall. Mater. Trans. B 31B, 1457 (2000).

    Article  Google Scholar 

  11. H. Liu, Z. Qi, and M. Xu, Steel Res. Int. 82, 440 (2011).

    Article  Google Scholar 

  12. L. Zhang, J. Aoki, and B.G. Thomas, Metall. Mater. Trans. B 37B, 361 (2006).

    Article  Google Scholar 

  13. S.M. Cho, S.H. Kim, and B.G. Thomas, ISIJ Int. 54, 845 (2014).

    Article  Google Scholar 

  14. K. Jin, B.G. Thomas, R. Liu, S.P. Vanka, and X.M. Ruan, IOP Conf. Ser. Mater. Sci. Eng. 84, 012095 (2015).

    Article  Google Scholar 

  15. L. Li, Z. Liu, M. Cao, and B. Li, JOM 67, 1459 (2015).

    Article  Google Scholar 

  16. J. Klostermann, K. Schaake, and R. Schwarze, Int. J. Numer. Methods Fluids 71, 960 (2013).

    Article  MathSciNet  Google Scholar 

  17. C.W. Hirt and B.D. Nichols, J. Comput. Phys. 39, 201 (1981).

    Article  Google Scholar 

  18. L. Zhang, JOM 64, 1059 (2012).

    Article  Google Scholar 

  19. Y.M. Lau, W. Bai, N.G. Deenn, and J.A.M. Kuipers, Chem. Eng. Sci. 108, 9 (2014).

    Article  Google Scholar 

  20. D. Jain, J.A.M. Kuipers, and N.G. Deen, Chem. Eng. Sci. 119, 134 (2014).

    Article  Google Scholar 

  21. T. Zhang, Z.G. Luo, C.L. Liu, H. Zhou, and Z.S. Zou, Powder Technol. 273, 154 (2015).

    Article  Google Scholar 

  22. Z. Liu, B. Li, M. Jiang, and F. Tsukihashi, ISIJ Int. 53, 484 (2013).

    Article  Google Scholar 

  23. M. van Sint Annaland, N.G. Deen, and J.A.M. Kuipers, Chem. Eng. Sci. 60, 2999 (2005).

    Article  Google Scholar 

  24. J. Smagorinsky, Month. Weather Rev. 91, 99 (1963).

    Article  Google Scholar 

  25. S.A. Morsi and A.J. Alexander, J. Fluid Mech. 55, 193 (1972).

    Article  Google Scholar 

  26. A. Tomiyama, H. Tamai, I. Zun, and S. Hosokawa, Chem. Eng. Sci. 57, 1849 (2002).

    Article  Google Scholar 

  27. D. Darmana, R.L.B. Henket, N.G. Deen, and J.A.M. Kuipers, Chem. Eng. Sci. 62, 2556 (2007).

    Article  Google Scholar 

  28. P.J. O’Rourke, Collective drop effects on vaporizing liquid sprays, Ph.D Thesis, Princeton University, 1981.

  29. A.A. Amsden, P.J. O’Rourke, and T.D. Butler, NASA Sti/Recon Technical Report No. 89, 1989.

  30. X. Gu, S. Basu, and R. Kumar, Int. J. Heat Mass Trans. 55, 5322 (2012).

    Article  Google Scholar 

Download references

Acknowledgements

Authors are grateful to the National Natural Science Foundation of China for support of this research, Grant No. 51574068.

Author information

Authors and Affiliations

  1. School of Materials and Metallurgy, Northeastern University, Shenyang, 110819, People’s Republic of China

    Linmin Li & Baokuan Li

Authors
  1. Linmin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Baokuan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Baokuan Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, L., Li, B. Investigation of Bubble-Slag Layer Behaviors with Hybrid Eulerian–Lagrangian Modeling and Large Eddy Simulation. JOM 68, 2160–2169 (2016). https://doi.org/10.1007/s11837-016-1849-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11837-016-1849-6

Keywords

Search

Navigation