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Mathematical modeling of mixing phenomena in a gas stirred liquid bath

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Abstract

A macroscopic, steady state energy balance model has been formulated to describe mixing phenom-ena in a liquid bath stirred by injecting gas through a straight nozzle fitted axially at the bottom of the vessel. This, along with experimental data on a water model previously reported, was employed to make predictions. Input energy terms considered in the model consist of buoyancy energy and empirically determined fraction of gas kinetic energy. Dissipation of energy was attributed to liquid circulation and bubble slip. The two-phase plume was assumed to be a truncated cone whose dimen-sions depended upon operating conditions. Numerical solution of model equations gave liquid velocity and gas hold-up inside the plume as well as liquid circulation rate and liquid velocity in the region outside the plume. Influence of process variables, e.g., gas flow rate, bath height, and nozzle diameter, have been predicted. Validity of the model has been established by comparing some pre-dicted entrainment ratios with those experimentally measured by other investigators. Empirical cor-relations to predict circulation time and circulation number have been proposed. Circulation number was found to vary between 2 and 12 in contrast to the existing assumption in the literature of a con-stant value of 3. Usefulness of these correlations in predicting mixing time for industrial vessels has been demonstrated.

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References

  1. L.H. Lehrer:I & EC Proc. Des. Dev., 1968, vol. 7, pp. 226–39.

    Article  CAS  Google Scholar 

  2. O. Haida and J. K. Brimacombe:SCAN1NJECT III, Proc. Intl. Conf. on Injection Metallurgy, Jernkontoret, Sweden, 1983, pp. 5:1–5:17.

    Google Scholar 

  3. G.G. Krishna Murthy, S.P. Mehrotra, and A. Ghosh:Proc. of 6th Proc. Technology Conf., TMS-AIME (ISS), 1986, pp. 401-07.

  4. G. G. Krishna Murthy, S. P. Mehrotra, and A. Ghosh:Metall. Trans. B, 1988, vol. 19B, pp. 839–50.

    Article  Google Scholar 

  5. D. Mazumdar and R. I. L. Guthrie:Metall. Trans. B, 1986, vol. 17B, pp. 725–33.

    Article  CAS  Google Scholar 

  6. T. C. Hsiao, T. Lehner, and B. Kjellberg:Scand. J. Metallurgy, 1980, vol. 9, pp. 105–10.

    CAS  Google Scholar 

  7. J. Szekely and S. Asai:Trans. ISIJ, 1975, vol. 15, pp. 270–85.

    Google Scholar 

  8. M. Sano and K. Mori:Trans. ISIJ, 1983, vol. 23, pp. 169–75.

    Google Scholar 

  9. K. Mori and M. Sano:Tetsu-to-Hagané, 1981, vol, 67, pp. 672–95.

    CAS  Google Scholar 

  10. M.J. McNallan and T. B. King:Metall. Trans. B, 1982, vol. 13B, pp. 165–73.

    Article  CAS  Google Scholar 

  11. Y. Ozawa and K. Mori:Trans. ISIJ, 1983, vol. 23, pp. 759–68.

    Google Scholar 

  12. G. G. Krishna Murthy, A. Ghosh, and S. P. Mehrotra:Proc. Intl. Conf. on Progress in Metallurgical Research: Fundamental and Applied Aspects, S. P. Mehrotra and T. R. Ramachandran, eds., Tata McGraw-Hill, New Delhi, 1986, pp. 307–15.

    Google Scholar 

  13. G. G. Krishna Murthy, A. Ghosh, and S. P. Mehrotra:Metall. Trans. B, 1988, vol. 19B, pp. 885–92.

    Article  Google Scholar 

  14. J.B. Joshi and M.M. Sharma:Trans. Inst. Chem. Eng., 1979, vol. 57, pp. 244–51.

    CAS  Google Scholar 

  15. A.G.W. Lamount:Can. J. Chem. Engg., 1958, vol. 36, p. 153.

    Google Scholar 

  16. J. W. McKelliget, M. Cross, R. D. Gibson, and J. K. Brimacombe: inHeat and Mass Transfer in Metallurgical Systems, D. B. Spald- ing and N. H. Afgan, eds., Hemisphere, New York, NY, 1981, pp. 349–72.

    Google Scholar 

  17. J.F. Davidson and D. Harrison:Chem. Engg. Sci., 1966, vol. 21, pp. 731–38.

    Article  CAS  Google Scholar 

  18. D.J. Nickiin:Chem. Engg. Sei., 1962, vol. 17, pp. 693–702.

    Article  Google Scholar 

  19. Y. Sahai and R.I.L. Guthrie:Metall. Trans. B, 1982, vol. 13B, pp. 193–202 and pp. 203-11.

    Article  CAS  Google Scholar 

  20. R. Clift, J. R. Grace, and M. E. Weber:Bubbles, Drops and Parti- cles, Acad. Press, New York, NY, 1978, pp. 203–11.

    Google Scholar 

  21. N.B. Ballal and A. Ghosh:Metall. Trans. B, 1981, vol. 12B, pp. 525–34.

    Article  CAS  Google Scholar 

  22. O. Haida and J.K. Brimacombe:Trans. ISIJ, 1985, vol. 25, pp. 14–20.

    CAS  Google Scholar 

  23. He. Qinglin, Y. Pen, and T. C. Hsiao:Proc. of Shenyang Symp. on Injection Metallurgy and Secondary Refining of Steel, China, 1984, pp. 98-113.

  24. K. Nakanishi, T. Fujii, and J. Szekely:Ironmaking and Steelmaking, 1975, vol. 2, pp. 193–97.

    CAS  Google Scholar 

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Authors and Affiliations

  1. Department of Materials Science and Engineering, Massachusetts Institute of Technology, 02139, Cambridge, MA

    G. G. Krishna Murthy (Postdoctoral Fellow)

  2. Department of Metallurgical Engineering, Indian Institute of Technology, 208016, Kanpur, India

    A. Ghosh (Professor) & S. P. Mehrotra (Professor)

Authors
  1. G. G. Krishna Murthy
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  2. A. Ghosh
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  3. S. P. Mehrotra
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Additional information

Formerly a Graduate Student in the De-partment of Metallurgical Engineering at the Indian Institute of Technol-ogy, Kanpur

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Murthy, G.G.K., Ghosh, A. & Mehrotra, S.P. Mathematical modeling of mixing phenomena in a gas stirred liquid bath. Metall Trans B 20, 53–59 (1989). https://doi.org/10.1007/BF02670349

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  • DOI: https://doi.org/10.1007/BF02670349

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