Skip to main content
SpringerLink
Log in

Bubbling at high flow rates in inviscid and viscous liquids (slags)

  • Published:
Metallurgical Transactions B Aims and scope Submit manuscript

Abstract

The behavior of gas discharging into melts at high velocities but still in the bubbling regime has been investigated in a laboratory modeling study for constant flow conditions. Air or helium was injected through a vertical tuyere into water, zinc-chloride, and aqueous glycerol solutions. High speed cinematography and pressure measurements in the tuyere have been carried out simultaneously. Pressure fluctuations at the injection point were monitored and correlated to the mode of bubble formation. The effects of high gas flow rates and high liquid viscosities have been examined in particular. Flow rates were employed up to 10-3 m3/s and viscosity to 0.5 Ns/m2. In order to attain a high gas momentum, the tuyere diameter was only 3 x 10-3 m. The experimental conditions and modeling liquids were chosen with special reference to the established practice of submerged gas injection to treat nonferrous slags. Such slags can be highly viscous. Bubble volume is smaller than that calculated from existing models such as those given by Davidson and Schüler10,11 due to the effect of gas momentum elongating the bubbles. On the other hand, viscosity tends to retard the bubble rise velocity, thus increasing volumes. To take elongation into account, a mathematical model is presented that assumes a prolate ellipsoidal shape of the bubbles. The unsteady potential flow equations for the liquid are solved for this case. Viscous effects are taken into account by noting that flow deviates from irrotational motion only in a thin boundary layer along the surface of the bubble. Thus, drag on the bubble can be obtained by calculating the viscous energy dissipation for potential flow past an ellipse. The time-dependent inertia coefficient for the ellipsoid is found by equating the vertical pressure increase inside and outside the bubble. This pressure change in the bubble is obtained by assuming that gas enters as a homogeneous jet and then calculating the stagnation pressure at the apex of the bubble.

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

Similar content being viewed by others

References

  1. P. Halsall:Advances in Sulphide Smelting, Proc. Int. Symposium on Sulphide Smelting, H.Y. Sohn, D.B. George, and A.D. Zunkel, eds., TMS-AIME, 1983, pp. 553–82.

  2. J. T. Woodcock:Mining and Metallurgical Practices in Australia, No. 10, The Aust. Inst, of Mining and Metallurgy, Parkville, Victoria, 1980, pp. 177–359.

  3. J. M.Floyd and P.S.Mackey: Extraction Metallurgy ’81, IMM, 1981, pp. 345–71.

  4. E. O. Hoefele and J.K. Brimacombe:Metall. Trans. B, 1979, vol. 10B, pp. 631–48.

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  6. D. W. Ashman, J. W. McKelliget, and J. K. Brimacombe:Can. Met. Quart., 1981, vol. 20, pp. 387–95.

    CAS  Google Scholar 

  7. A.E. Wraith:Chem. Engng. Sci., 1971, vol. 26, pp. 1659–71.

    Article  CAS  Google Scholar 

  8. A. A. Bustos, G. G. Richards, N. B. Gray, and J. K. Brimacombe:Metall. Trans. B, 1984, vol. 15B, pp. 77–89.

    Article  ADS  CAS  Google Scholar 

  9. R. Clift, J. R. Grace, and M. E. Wikes:Bubbles Drops and Particles, Acad. Press, New York, NY, 1978, pp. 322–28.

    Google Scholar 

  10. J. F. Davidson and B. O. G. Schüler:Trans. Inst. Chem. Engrs., 1960, vol. 38, pp. 144–53.

    CAS  Google Scholar 

  11. J. F. Davidson and B. O. G. Schüler:Trans. Inst. Chem. Engrs., 1960, vol. 38, pp. 335–42.

    CAS  Google Scholar 

  12. R. Kumar and N. R. Kuloor:Adv. Chem. Eng., 1970, vol. 8, pp. 320–68.

    Google Scholar 

  13. D.W. Moore:J. Fluid Mech., 1963, vol. 16, pp. 161–73.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  14. M. Nilmani: Ph.D. Thesis, Imperial College, Univ. of London, 1978.

  15. P.E. Anagbo:Can. J. of Chem. Engng., 1982, vol. 60, pp. 220–25.

    Article  CAS  Google Scholar 

  16. J.F. Harper:Chem. Engng. Sci., 1970, vol. 25, pp. 342–43.

    Article  CAS  Google Scholar 

  17. H. Lamb:Hydrodynamics, 6th ed., Dour Publ., New York, NY, 1932, pp. 131–33, 147-55.

    MATH  Google Scholar 

  18. G. N. Abramovitch:The Theory of Turbulent Jets, MST Press, Cambridge, MA, 1963, p. 83.

    Google Scholar 

  19. N. Rajaratnam:Turbulent Jets, Elsevier Publ. Co., Amsterdam, 1976, p. 48.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Métallurgistk Institutt, Technical University of Norway, Trondheim, Norway

    T. Abel Engh (Professor)

  2. Williams Research Laboratory for Extractive Metallurgy Research, Department of Chemical Engineering, University of Melbourne, 3052, Parkville, Victoria, Australia

    M. Nilmani (Lecturer)

Authors
  1. T. Abel Engh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Nilmani
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Engh, T.A., Nilmani, M. Bubbling at high flow rates in inviscid and viscous liquids (slags). Metall Trans B 19, 83–94 (1988). https://doi.org/10.1007/BF02666494

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02666494

Keywords

Search

Navigation