Advertisement

Metallurgical and Materials Transactions B

, Volume 49, Issue 5, pp 2343–2356 | Cite as

Similarity Criteria for the Study of Removal of Spherical Non-metallic Inclusions in Physical Models of Continuous Casting Tundishes: A More Fundamental Approach

  • Bernardo Martins Braga
  • Roberto Parreiras Tavares
Article
  • 44 Downloads

Abstract

Physical modeling is widely used for studying steelmaking processes. The accuracy of this technique depends on the use of appropriate similarity criteria during experimental design. The present work deduced rigorously the similarity criteria for the study of spherical non-metallic inclusions in isothermal physical models of tundishes. Initially, macroscopic quantities were used to simplify the multiphase problem. Then, the similarity criteria were obtained from the dimensionless form of the exact equation of motion for an inclusion in Stokes regime. The validity range of these criteria was discussed and they were compared with common literature practice. Some practical considerations were also presented. This work clarifies various implicit assumptions usually adopted in literature. Additionally, a restrictive criterion to choose the density of the inclusion simulating particles was obtained, which can be satisfied, for example, by hollow glass particles in water models. This criterion is necessary to adequately describe the inclusion motion in regions where fluid elements suffer strong acceleration (e.g., inside nozzles, near flow controllers or in the entering fluid jet). Moreover, it was established an upper limit for the concentration of particles injected in the inlet nozzle of physical models, which do not simulate the phenomenon of inclusion aggregation.

Notes

Acknowledgments

The financial support of FAPEMIG – Fundação de Amparo à Pesquisa do Estado de Minas Gerais, Brazil – in the form of a research grant to R. Tavares, Process No. PPM-00118-13, is gratefully acknowledged. The authors also acknowledge the financial support of CAPES/PROEX to the graduate program. The doctoral scholarship, No. 1487157, from CAPES to B. Braga is acknowledged.

References

  1. 1.
    Y. Sahai: Metall. Mater. Trans. B, 2016, vol. 47B, pp. 2095-106.CrossRefGoogle Scholar
  2. 2.
    D. Mazumdar and R. I.. L. Guthrie: ISIJ Int., 1999, vol. 39, pp. 524-47.CrossRefGoogle Scholar
  3. 3.
    K. Chattopadhyay, M. Isac and R. I. L. Guthrie: ISIJ Int., 2010, vol. 50, pp. 331-48.CrossRefGoogle Scholar
  4. 4.
    M. Kruger: Masters Dissertation, UFSC, Brazil, 2010.Google Scholar
  5. 5.
    K. Chattopadhyay, M. Isac and R. I. L. Guthrie: Ironmaking Steelmaking, 2012, vol. 39, pp. 454-62.CrossRefGoogle Scholar
  6. 6.
    J.-S. Cho and H.-G. Lee: ISIJ Int., 2001, vol. 41, pp. 151-7.CrossRefGoogle Scholar
  7. 7.
    J.P. Rogler, L.J. Heaslip and M. Meahvar: Can. Metall. Q., 2005, vol. 44, pp. 357-68.CrossRefGoogle Scholar
  8. 8.
    R.P. Nascimento: Masters Dissertation, UFOP/REDEMAT, Brazil, 2008.Google Scholar
  9. 9.
    Q. Yue, Z.-S. Zou and Q.-F. Hou: J. Iron Steel Res. Int., 2010, vol. 17, pp. 6-10.CrossRefGoogle Scholar
  10. 10.
    V. Seshadri, C.A. Da Silva, I.A. Da Silva and E.S. Araújo Júnior: Tecnol. Metal. Mater. Min., 2012, vol. 9, pp. 22–29.Google Scholar
  11. 11.
    F.D. Machado: Masters Dissertation, UFRGS, Brazil, 2014.Google Scholar
  12. 12.
    H. Kim: Ph.D. Thesis, McGill University, Canada, 2003.Google Scholar
  13. 13.
    A. Chakraborty: Master’s Thesis, McGill University, Canada 2010.Google Scholar
  14. 14.
    A.F.G. Mendonça: Masters Dissertation, UFMG, Brazil, 2016.Google Scholar
  15. 15.
    A. Rückert, M. Warzecha, R. Koitzsch, M. Pawlik and H. Pfeifer: Steel Res. Int., 2009, vol. 80, pp. 568-74.Google Scholar
  16. 16.
    Y. Sahai and T. Emi: ISIJ Int., 1996, vol. 36, pp 1166-73.CrossRefGoogle Scholar
  17. 17.
    B.G. Thomas: Chapter 5 in The Making, Shaping and Treating of Steel, 11th ed., Casting Volume, A.W. Cramb, ed., The AISE Steel Foundation, Warrendale, PA, 2003, pp. 2–5.Google Scholar
  18. 18.
    Y. Sahai and T. Emi: Tundish Technology for Clean Steel Production, 1st ed., Hackensack, NJ, World Scientific Publication Co. Pte. Ltd., 2007, pp. 130–58.Google Scholar
  19. 19.
    V. Seshadri, R.P. Tavares, C.A. Da Silva and I.A. Da Silva: Transport Phenomena: Fundamentals and Applications in Metallurgical and Materials Engineering, 1st ed., São Paulo, Brazil, ABM, 2011, pp. 723-45.Google Scholar
  20. 20.
    L. Zhang and B.G. Thomas: ISIJ Int., 2003, vol. 43, pp. 271-91.CrossRefGoogle Scholar
  21. 21.
    L. Zhang: Steel Res. Int., 2006, vol. 77, pp. 158-69.CrossRefGoogle Scholar
  22. 22.
    R. Dekkers: Doctoral Thesis, KU Leuven, Belgium, 2002.Google Scholar
  23. 23.
    H. Enwald, E. Peirano and A.-E. Almstedt: Int. J. Multiphase Flow, 1996, vol. 22, pp. 21-66.CrossRefGoogle Scholar
  24. 24.
    M.Z. Podowski: Nucl. Eng. Des., 2009, vol. 239, pp. 933-40.CrossRefGoogle Scholar
  25. 25.
    C.T. Crowe, J.D. Schwarzkopf, M. Sommerfeld and Y. Tsuji: Multiphase Flows with Droplets and Particles, 2nd ed., Boca Raton, FL, CRC Press, 2011, pp. 17-100.Google Scholar
  26. 26.
    A. Einstein: Ann. Phys., 1906, vol. 324, pp. 289-306.CrossRefGoogle Scholar
  27. 27.
    A. Einstein: Ann. Phys., 1911, vol. 329, pp. 591-2.CrossRefGoogle Scholar
  28. 28.
    M.R. Maxey and J.J. Riley: Phys. Fluids, 1983, vol. 26, pp. 883-9.CrossRefGoogle Scholar
  29. 29.
    T.R. Auton, J.C.R. Hunt and M. Prud’Homme: J. Fluid Mech., 1988, vol. 197, pp. 241-57.CrossRefGoogle Scholar
  30. 30.
    E.E. Michaelides: Particles, Bubbles & Drops: Their Motion, Heat and Mass Transfer, 1st ed., Hackensack, NJ, World Scientific Publication Co. Pte. Ltd., 2006, pp. 48–79.Google Scholar
  31. 31.
    J.S. Marshall and S. Li: Adhesive Particle Flow: A Discrete-Element Approach, 1st ed., New York, NY, Cambridge University Press, 2014, pp. 130-88.Google Scholar
  32. 32.
    J. Szekely and O.J. Ilegbusi: The Physical and Mathematical Modeling of Tundish Operations, 1st ed., New York, NY, Springer-Verlag, 1989, pp. 34-8.Google Scholar
  33. 33.
    D. Mazumdar and J. W. Evans: Modeling of Steelmaking Processes, 1st ed., Boca Raton, FL, CRC Press, 2009, pp. 99-132.Google Scholar
  34. 34.
    L.B. Torobinz and W.H. Gauvln: Can. J. Chem. Eng.,1959, vol. 37, pp. 129-41.CrossRefGoogle Scholar
  35. 35.
    R. I. L. Guthrie: Engineering in Process Metallurgy, 1st ed., New York, NY, Oxford University Press, Inc., 1992, pp. 99-103.Google Scholar
  36. 36.
    R.B. Bird, W.E. Stewart and E.N. Lightfoot: Transport Phenomena, 2nd ed., New York, NY, John Wiley & Sons, Inc., 2001, pp. 185–88.Google Scholar
  37. 37.
    G.H. Geiger and D.R. Poirier: Transport Phenomena in Metallurgy, 1st ed., Reading, MA, Addison-Wesley Publishing Company, Inc., 1973, pp. 86–88.Google Scholar
  38. 38.
    C.E. Lapple and C.B. Shepherd: Ind. Eng. Chem., 1940, vol. 32, pp. 605-17.CrossRefGoogle Scholar
  39. 39.
    R. Mei, C.J. Lawrence and R.J. Adrian: J. Fluid Mech., 1991, vol. 233, pp. 613-31.CrossRefGoogle Scholar
  40. 40.
    E.J. Chang and M.R. Maxey: J. Fluid Mech., 1994, vol. 277, pp. 347-79.CrossRefGoogle Scholar
  41. 41.
    E.J. Chang and M.R. Maxey: J. Fluid Mech., 1995, vol. 303, pp. 133-53.CrossRefGoogle Scholar
  42. 42.
    J. Magnaudet, M. Rivero and J. Fabre: J. Fluid Mech., 1995, vol. 284, pp. 97-135.CrossRefGoogle Scholar
  43. 43.
    P.G. Saffman: J. Fluid Mech., 1965, vol. 22, pp. 385-400.CrossRefGoogle Scholar
  44. 44.
    P.G. Saffman: J. Fluid Mech., 1968, vol. 31, pp. 624-4.CrossRefGoogle Scholar
  45. 45.
    Q. Yuan, B.G. Thomas and S.P. Vanka: Metall. Mater. Trans. B, 2004, vol. 35B, pp. 703-14.CrossRefGoogle Scholar
  46. 46.
    P.M. Lovalenti and J.F. Brady: J. Fluid Mech., 1993, vol. 256, pp. 561-605.CrossRefGoogle Scholar
  47. 47.
    P.M. Lovalenti and J.F. Brady: J. Fluid Mech., 1993, vol. 256, pp. 607-14.CrossRefGoogle Scholar
  48. 48.
    P.M. Lovalenti and J.F. Brady: Phys. Fluids A, 1993, vol. 5, pp. 2104-16.CrossRefGoogle Scholar
  49. 49.
    R.B. Bird, W.E. Stewart, E.N. Lightfoot and D.J. Klingenberg: Introductory Transport Phenomena, 1st ed., Hoboken, NJ, John Wiley & Sons, Inc., 2014, pp. 153–55.Google Scholar
  50. 50.
    M.J. Assael, K. Kakosimos, R.M. Banish, J. Brillo, I. Egry, R. Brooks, P.N. Quested, K.C. Mills, A. Nagashima, Y. Sato and W.A. Wakeham: J. Phys. Chem. Ref. Data, 2006, vol. 35, pp. 285-300.CrossRefGoogle Scholar
  51. 51.
    W. Pabst and E. Gregorova: Chapter 3 in New Developments in Materials Science Research, 1st ed., B.M. Caruta, ed., Nova Science Publishers, Inc., New York, NY, 2007, pp. 108–11.Google Scholar
  52. 52.
    J.F. Xu, K. Wan, J.Y. Zhang, Y. Chen and M.Q. Sheng: J. South. Afr. Inst. Min. Metall., 2015, vol.115, pp. 767-72.CrossRefGoogle Scholar
  53. 53.
    J. Lee, L.T. Hoai, J. Choe and J.H. Park: ISIJ Int., 2012, vol. 52, pp. 2145-8.CrossRefGoogle Scholar
  54. 54.
    J.V. Sengers and J.T.R. Watson: J. Phys. Chem. Ref. Data, 1986, vol. 15, pp. 1291-314.CrossRefGoogle Scholar
  55. 55.
    D.J. Shaw: Introduction to Colloid and Surface Chemistry, 4th ed., Oxford, UK, Butterworth-Heinemann, 1992, pp. 210-43.CrossRefGoogle Scholar
  56. 56.
    P.C. Hiemenz and R. Rajagopalan: Principles of Colloid and Surface Chemistry, 3rd ed., New York, NY, Marcel Dekker, Inc., 1997, pp. 575-619.Google Scholar
  57. 57.
    A.T. Hjelmfelt Jr. and L.F. Mockros: Appl. Sci. Res., 1966, vol. 16, pp 149-61.CrossRefGoogle Scholar
  58. 58.
    A. Kumar, S.C. Koria and D. Mazumdar: ISIJ Int., 2004, vol. 44, pp. 1334-41.CrossRefGoogle Scholar
  59. 59.
    P. Galpin and G. Scheuerer: Model Selection—Turbulence Models. (ISimQ, 2016), http://library.esss.com.br/modelos-de-turbulencia-tk. Accessed 03 Oct 2017.
  60. 60.
    ANSYS: ANSYS CFX-Solver Theory Guide, R. 14.5, Canonsburg, PA, ANSYS, Inc., 2012, pp. 8-35.Google Scholar
  61. 61.
    L. Neves and R.P. Tavares: Ironmaking Steelmaking, 2017, vol. 44, pp. 559-67.CrossRefGoogle Scholar
  62. 62.
    B.E. Launder and D.B. Spalding: Comput. Methods Appl. Mech. Eng., 1974, vol. 3, pp. 269-89.CrossRefGoogle Scholar
  63. 63.
    P. Ni, M. Ersson, L.T.I. Jonsson and P.G. Jönsson: A Study on the Nonmetallic Inclusion Motions in a Swirling Flow Submerged Entry Nozzle in a New Cylindrical Tundish Design. (Metall. Mater. Trans. B, 2017),  https://doi.org/10.1007/s11663-017-1162-y.CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2018

Authors and Affiliations

  • Bernardo Martins Braga
    • 1
  • Roberto Parreiras Tavares
    • 1
  1. 1.Department of Metallurgical and Materials Engineering, Engineering SchoolFederal University of Minas GeraisBelo HorizonteBrazil

Personalised recommendations