Metallurgical and Materials Transactions B

, Volume 47, Issue 1, pp 508–521 | Cite as

Physical Modeling of Slag ‘Eye’ in an Inert Gas-Shrouded Tundish Using Dimensional Analysis

Article
First Online:

Abstract

The formation of an exposed eye in the gas-stirred metallurgical vessels such as ladle or tundish is a common observation. Although gas stirring results in proper homogenization of melt composition and temperature, the resulting exposed eye leads to higher heat losses, re-oxidation of liquid steel, and formation of inclusions. Most of the previous research related to slag eye were carried out explicitly for ladles. In the present work, a large number of experiments were performed to measure the slag eye area in full scale and one-third scale water models of an inert gas-shrouded tundish under various operating conditions. Based on the polynomial regression of experimental data, and the method of dimensional analysis, correlations for diameter of gas bubbles and plume velocity were developed. Subsequently, these results were used to obtain correlations for the slag eye area, and critical gas flow rate in an inert gas-shrouded tundish in terms of the operational parameters viz., gas flow rate, thickness of the slag and melt baths, along with the physical properties of the liquids viz., kinematic viscosity and density. It was observed that the dimensionless slag eye area can be expressed in terms of dimensionless numbers such as the density ratio, Froude number, and Reynolds number.

Keywords

LLDPE Nozzle Diameter Bubble Diameter Slag Layer Bubble Plume 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

Q

Gas flow rate (m3 s−1)

H

Depth of bulk fluid phase (m)

h

Depth of upper fluid phase (m)

Ae

Area of the slag eye (m2)

ρl

Density of bulk fluid phase (kg m−3)

Δρ

Density difference between lower and upper fluid phases (kg m−3)

vs

Kinematic viscosity of upper fluid phase (m2 s−1)

Up

Plume velocity (average rise velocity of the gas-liquid mixture) (m s−1)

g

Acceleration due to gravity (m s−2)

db

Diameter of the gas bubbles (m)

ρb

Density of the gas bubbles (kg m−3)

µl

Viscosity of the lower fluid phase (kg m−1 s−1)

db*

Non-dimensional gas bubble diameter

Q*

Non-dimensional gas flow rate

Up*

Non-dimensional plume velocity

Ae*

Non-dimensional plume velocity

Qc

Critical gas flow rate

Qc*

Non-dimensional critical gas flow rate

LLDPE

Linear low-density polyethylene

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References

  1. 1.
    S. Chatterjee and K. Chattopadhyay, ISIJ Int., 2015, vol. 55, pp. 1416–1424.CrossRefGoogle Scholar
  2. 2.
    K. Chattopadhyay, M. Isac, and R. I. L. Guthrie, ISIJ Int., 2011, vol. 51, pp. 573–580.CrossRefGoogle Scholar
  3. 3.
    M. Peranandhanthan and D. Mazumdar, ISIJ Int., 2010, vol. 50, pp. 1622–1631.CrossRefGoogle Scholar
  4. 4.
    K. Krishnapisharody and G. A. Irons, Metall. Mater. Trans. B Process Metall. Mater. Process. Sci., 2006, vol. 37, pp. 763–772.CrossRefGoogle Scholar
  5. 5.
    K. Chattopadhyay, H. Mainul, M. Isac, and R. I. L. Guthrie, Metall. Mater. Trans. B Process Metall. Mater. Process. Sci., 2010, vol. 41, pp. 225–233.CrossRefGoogle Scholar
  6. 6.
    K. Chattopadhyay: Modelling of Transport Phenomena for Improved Steel Quality in a Delta Shaped Four Strand Tundish, McGill University, 2011.Google Scholar
  7. 7.
    D. Mazumdar, H. Nakajima, and R. I. L. Guthrie, 1988, vol. 19, pp. 507–511.CrossRefGoogle Scholar
  8. 8.
    Z. Lin and R. I. L. Guthrie, Metall. Mater. Trans. B, 1994, vol. 25, pp. 855–864.CrossRefGoogle Scholar
  9. 9.
    Z. Iguchi, M., Ilegbusi O. J., Ueda H., Kuranaga T. and Morita, Metall. Mater. Trans. B, 1996, vol. 27, pp. 35–41.CrossRefGoogle Scholar
  10. 10.
    10. K. Krishnapisharody and G. A. Irons: ISIJ Int. (2008) 48(12):1807–1809.CrossRefGoogle Scholar
  11. 11.
    P. Valentin, C. Bruch, and J. Gaule: Steel Res. Int., 2009, vol. 80, pp. 746–52.Google Scholar
  12. 12.
    D. Mazumdar and R. I. L. Guthrie, Metall. Mater. Trans. B Process Metall. Mater. Process. Sci., 2010, vol. 41, pp. 976–989.CrossRefGoogle Scholar
  13. 13.
    L. T. Khajavi and M. Barati, ISIJ Int., 2010, vol. 50, pp. 654–662.CrossRefGoogle Scholar
  14. 14.
    A. N. Conejo, S. Kitamura, N. Maruoka, and S. J. Kim, Metall. Mater. Trans. B Process Metall. Mater. Process. Sci., 2013, vol. 44, pp. 914–923.CrossRefGoogle Scholar
  15. 15.
    D. Mazumdar and R. I. L. Guthrie, ISIJ Int., 1995, vol. 35, pp. 220–222.CrossRefGoogle Scholar
  16. 16.
    M. Hirasawa, K. Mori, M. Sano, Y. Shimatani, and Y. Okazaki, Trans. ISIJ, 1987, vol. 27, pp. 283–290.CrossRefGoogle Scholar
  17. 17.
    S.H. Kim, R.J. Fruehan, and R.I.L. Guthrie: in Proc. Steelmak. Conf. (1986), pp. 107–118.Google Scholar
  18. 18.
    M. Iguchi, J. Yoshida, T. Shimizu, and Y. Mizuno, ISIJ Int., 2000, vol. 40, pp. 685–691.CrossRefGoogle Scholar
  19. 19.
    P. Valentin, C. Bruch, Y. Kyrylenko, H. Köchner, and C. Dannert: Steel Res. Int., 2009, vol. 80, pp. 552–58.Google Scholar
  20. 20.
    J. Savolainen, T. Fabritius, and O. Mattila, ISIJ Int., 2009, vol. 49, pp. 29–36.CrossRefGoogle Scholar
  21. 21.
    J.M. Harman and A.W. Cramb: in, Steelmak. Conf. Proc. (Warrendale, 1996), p. 773.Google Scholar
  22. 22.
    R. Hagemann, H.-P. Heller, S. Lachmann, S. Seetharaman, and P. R. Scheller, Ironmak. Steelmak., 2012, vol. 39, pp. 508–513.CrossRefGoogle Scholar
  23. 23.
    M. Sano and K. Mori, Trans. JIM, 1976, vol. 17, pp. 345–352.Google Scholar
  24. 24.
    G. A. Irons and R. I. L. Guthrie, Metall. Trans. B, 1978, vol. 9, pp. 101–110.CrossRefGoogle Scholar
  25. 25.
    L. Davidson and E. H. J. Amick, AIChE J., 1956, vol. 2, pp. 337–342.CrossRefGoogle Scholar
  26. 26.
    E. O. Hoefele and J. K. Brimacombe, Metall. Trans. B, 1979, vol. 10, pp. 631–648.CrossRefGoogle Scholar
  27. 27.
    Y. Sahai and R. I. L. Guthrie, Metall. Trans. B, 1982, vol. 13, pp. 193–202.CrossRefGoogle Scholar
  28. 28.
    A. Mersmann: VDI Research Bulletin, Association of German Engineers, Dusseldorf, 1962.Google Scholar
  29. 29.
    K. Mori, M. Sano, and T. Sato, Trans. ISIJ, 1979, vol. 19, pp. 553–558.Google Scholar
  30. 30.
    L. Zhang and S. Taniguchi, Int. Mater. Rev., 2000, vol. 45, pp. 59–82.CrossRefGoogle Scholar
  31. 31.
    M. Iguchi, T. Chihara, N. Takanashi, Y. Ogawa, N. Tokumitsu, and Z.-I. Morita, ISIJ Int., 1995, vol. 35, pp. 1354–1361.CrossRefGoogle Scholar
  32. 32.
    D. Mazumdar, R. I. L. Guthrie, and Y. Sahai, Appl. Math. Model., 1993, vol. 17, pp. 255–262.CrossRefGoogle Scholar
  33. 33.
    D. Mazumdar, Metall. Mater. Trans. B, 2002, vol. 33, pp. 937–941.CrossRefGoogle Scholar
  34. 34.
    M. A. S. C. Castello-Branco and K. Schwerdtfeger, Metall. Mater. Trans. B, 1994, vol. 25, pp. 359–371.CrossRefGoogle Scholar
  35. 35.
    F. Oeters, Metallurgy of Steelmaking (VSHD, Berlin, 1994).Google Scholar

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2015

Authors and Affiliations

  1. 1.Process Metallurgy and Modeling Group, Department of Materials Science and EngineeringUniversity of TorontoTorontoCanada
  2. 2.Process Metallurgy and Modeling Group, Department of Materials Science and Engineering, Faculty of Applied Science & EngineeringUniversity of TorontoTorontoCanada

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