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Numerical Simulation of Gas and Liquid Two-Phase Flow in Gas-Stirred Systems Based on Euler–Euler Approach

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Abstract

Based on the Euler–Euler approach, a mathematical model is established to describe gas and liquid two-phase flow in the gas-stirred system for steelmaking, and the influences of the interphase force including turbulent dispersion force, drag force, and lift force are investigated. The modified k–ε model with extra source terms to account for the bubble-induced turbulence is adopted to model the turbulence in the system, and the simulation results of gas volume fraction, liquid velocity, and turbulent kinetic energy are compared with the measured data. The results show that the turbulent dispersion force dominates the bubbly plume shape and is responsible for successful prediction of the gas volume fraction. The bubble-induced turbulence has a significant influence on the liquid turbulence, and the conversion coefficient C b, which denotes the fraction of bubble-induced energy converted into liquid turbulence, should be in the range of 0.8 and 0.9. The drag force also strongly influences the bubbly plume dynamics, and the coefficient model proposed by Kolev performs the best for determining the drag force; however, the lift force and bubble diameter do not have much effect on the current bubbly plume system. For different gas flow rates, the current Euler–Euler approach predictions are more consistent with the measured data than the Euler–Lagrange approach and the early Euler–Euler model.

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Abbreviations

C A :

Virtual mass force coefficient (–)

C b :

Turbulent conversion coefficient (–)

C D :

Drag force coefficient (–)

C L :

Lift force coefficient (–)

D tgl :

Turbulent dispersion coefficient (–)

e R :

Total rate of pressure energy lost by the bubble (kg m2/s3)

e D :

Rate of energy converted into turbulence and spent in viscous dissipation (kg m2/s3)

Eo :

Eötvös number (–) \( Eo = {{g\left( {\rho_{\text{l}} - \rho_{\text{g}} } \right)d_{\text{g}}^{2} } \mathord{\left/ {\vphantom {{g\left( {\rho_{\text{l}} - \rho_{\text{g}} } \right)d_{\text{g}}^{2} } \sigma }} \right. \kern-0pt} \sigma } \)

F D :

Drag force per unit volume (N/m3)

F L :

Lift force per unit volume (N/m3)

F VM :

Virtual mass force per unit volume (N/m3)

F TD :

Turbulent dispersion force per unit volume (N/m3)

G k,l :

Production of turbulent kinetic energy due to liquid mean velocity gradients (m2/s3)

G b :

Bubble-induced turbulent kinetic energy (m2/s3)

d g :

Diameter of the bubbles (m)

d 0 :

Diameter of the nozzle (m)

dt i :

Residence time of the ith bubble in the control cell volume (s)

\( \bar{g} \) :

acceleration due to gravity (m2/s)

H :

Bath liquid height (m)

k l :

Liquid turbulent kinetic energy (m2/s2)

\( \overline{M}_{\text{k}} \) :

interphase momentum exchange term (N/m3)

M Wg :

Molecular weight of gas phase (kg/kmol)

N :

Number of bubbles particle released from the gas-inlet (–)

P :

Static pressure (Pa)

P op :

Operating pressure (Pa)

Q g :

Gas flow rate (m3/s)

R :

Universal gas constant (J/(mol K))

Re:

Local bubble Reynolds number (–) \( \text{Re} = {{\rho_{l} \left( {u_{g} - u_{l} } \right)d_{g} } \mathord{\left/ {\vphantom {{\rho_{l} \left( {u_{g} - u_{l} } \right)d_{g} } {\mu_{l} }}} \right. \kern-0pt} {\mu_{l} }} \)

\( \bar{u}_{\text{l}} \) :

liquid velocity (m/s)

\( \bar{u}_{g} \) :

gas velocity (m/s)

u drift :

D

drift velocity between liquid and gas (m/s)

V :

Liquid velocity magnitude (m/s)

V cell :

Grid cell volume (m3)

V bub,pi :

Volume of the ith bubble in the control cell volume (m3)

We :

Webber number (–) \( We = {{\rho_{l} \left( {u_{l} - u_{g} } \right)^{2} d_{g} } \mathord{\left/ {\vphantom {{\rho_{l} \left( {u_{l} - u_{g} } \right)^{2} d_{g} } \sigma }} \right. \kern-0pt} \sigma } \)

z :

Height far from the bath bottom (m)

α :

Volume fraction (–)

ρ l,ρ g :

Liquid and gas density (kg/m3)

μ l, μ t, μ eff :

Liquid molecular viscosity, turbulent viscosity, effective viscosity (kg/(m s))

σ :

Gas–liquid surface tension coefficient (N/m)

ω gl :

Dispersion Prandtl number (–)

τ tgl :

Bubble turbulent characteristic time (s)

τ Fgl :

Characteristic time of particle entrainment by the continuous fluid motion (s)

τ tl :

Characteristic time of the energetic turbulent eddies (s)

θ :

Angle between the mean particle velocity and the mean relative velocity (rad)

ɛ l :

Turbulent dissipation rate (m2/s3)

Π k,l , Π ɛ,l :

Influence of the dispersed phases turbulence on the continuous phase turbulence in Eqs. [25] and [26][50,51]

g:

Gas phase

l:

Liquid phase

References

  1. J.S. Joo, J. Szekely, A.H. Castillejos, and J.K. Brimacombe: Metall. Trans. B, 1990, vol. 21B, pp. 269-77.

    Google Scholar 

  2. D. Mazumdar, R.I.L. Guthrie, and Y. Sahai: Appl. Math. Model., 1993, vol. 17, pp. 255-62.

    Article  Google Scholar 

  3. D. Mazumdar and R.I.L. Guthrie: Metall. Trans. B, 1985, vol. 16B, pp. 83-90.

    Article  CAS  Google Scholar 

  4. A.H. Castillejos, M.E. Salcudean, and J.K. Brimacombe: Metall. Trans. B, 1989, vol. 20B, pp. 603-11.

    Article  Google Scholar 

  5. J.S. Joo and R.I.L. Guthrie: Metall. Trans. B, 1992, vol. 23B, pp. 765-78.

    Article  CAS  Google Scholar 

  6. M.Y. Zhu, T. Inomoto, I. Sawada, and T.C. Hsiao: ISIJ Int., 1995, vol. 35, pp. 472-79.

    Article  CAS  Google Scholar 

  7. M.Y. Zhu, I. Sawada, N. Yamasaki, and T.C. Hsiao: ISIJ Int., 1996, vol. 36, pp. 503-11.

    Article  CAS  Google Scholar 

  8. J.H. Grevet, J. Szekely, and N. El Kaddah: Int. J. Heat Mass Trans., 1982, vol. 25, pp. 487–97.

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

    Article  CAS  Google Scholar 

  10. A.H. Castillejos, M. Salcudean, and J.K. Brimacombe: Metall. Trans. B, 1989, vol. 20B, pp. 603-11.

    Article  Google Scholar 

  11. S.T. Johansen and F. Boysan: Metall. Trans. B, 1988, vol. 19B, pp. 755-64.

    Article  CAS  Google Scholar 

  12. Y. Sheng and G. Irons: Metall. Trans. B, 1993, vol. 24B, pp. 695-705.

    Article  CAS  Google Scholar 

  13. Y. Sheng and G. Irons: Metall. Mater. Trans. B, 1995, vol. 26B, pp. 625-35.

    Article  CAS  Google Scholar 

  14. D. Guo and G. Irons: Metall. Mater. Trans. B, 2000, vol. 31B, pp. 1457-64.

    Article  CAS  Google Scholar 

  15. D. Mazumdar and R.I.L. Guthrie: ISIJ Int., 1994, vol. 34, pp. 384-92.

    Article  CAS  Google Scholar 

  16. H. Turkoglu and B. Farouk: ISIJ Int., 1991, vol. 31, pp. 1371-80.

    Article  CAS  Google Scholar 

  17. H. Turkoglu and B. Farouk: Metall. Trans. B, 1990, vol. 21B, pp. 771-81.

    Article  CAS  Google Scholar 

  18. O.J. Ilegbusi and J. Szekely: ISIJ Int., 1990, vol. 30, pp. 731-39.

    Article  CAS  Google Scholar 

  19. O.J. Ilegbusi, J. Szekely, M. Iguchi, H. Takeuchi, and Z. Morita: ISIJ Int., 1993, vol. 33, pp. 474–78.

    Article  CAS  Google Scholar 

  20. O.J. Ilegbusi, M. Iguchi, K. Nakajima, M. Sano, and M. Sakamoto: Metall. Mater. Trans. B, 1998, vol. 29B, pp. 211-22.

    Article  CAS  Google Scholar 

  21. G. Venturini and M.B. Goladschmit: Metall. Mater. Trans. B, 2007, vol. 38B, pp. 461-75.

    Article  CAS  Google Scholar 

  22. D.Y. Sheng, M. Söder, P. Jönsson, and L. Jonsson: Scand. J. Metall., 2002, vol. 31, pp. 134-47.

    Article  CAS  Google Scholar 

  23. T. Qu, M. Jiang, C. Liu, and Y. Komizo: Steel Res. Int., 2010, vol. 81, pp. 434–45.

    Article  CAS  Google Scholar 

  24. Fluent Inc.: FLUENT 6.3 User’s Guide, Fluent Inc., Lebanon, NH, 2006.

  25. P.J. Smith, F. Thomas, and L.D. Smoot: Eighteenth Symposium (International) on Combustion, vol. 18, 1981, pp. 1285–93.

  26. A.S. Abbas, S.S. Koussa, and F.C. Lockwood: Eighteenth Symposium (International) on Combustion, vol. 18, 1981, pp. 1427–38.

  27. O. Simonin: Fifth Workshop on Two-Phase Flow Predictions, Proc. LSTM, Erlangen, Germany, 1990, pp. 156-66.

  28. O. Simonin and P.L. Viollet: Numerical Methods for Multiphase Flows, FED, vol. 91, ASM International, Materials Park, OH, 1990, pp. 65–82.

  29. O. Simonin, E. Deutsch, and J.P. Minier: Appl. Sci. Res., 1993, vol. 51, pp. 275–83.

  30. N. Huda, J. Naser, G. Brooks, M.A. Reuter, and R. Matusewicz: Metall. Mater. Trans. B, 2010, vol. 41B, pp. 35–50.

    Article  CAS  Google Scholar 

  31. N. Huda, J. Naser, G. Brooks, M.A. Reuter, and R. Matusewicz: Metall. Mater. Trans. B, 2012, vol. 43B, pp. 39–55.

    Article  Google Scholar 

  32. R.F. Mudde and O. Simonin: Chem. Eng. Sci., 1999, vol. 54, pp. 5061–69.

    Article  CAS  Google Scholar 

  33. E. Delnoij, J.A.M. Kuipers, and W.P.M. van Swaaij: Chem. Eng. Sci., 1997, vol. 52, pp. 1429–58.

  34. R. Djebbar, M. Roustan, and A. Line: Trans. IChemE, 1996, vol. 74, pp. 492–98.

    CAS  Google Scholar 

  35. A. Tomiyama, I. Kataoka, and I. Zunb: JSME Int. J. Ser. B, 1998, vol. 41, pp. 472-79.

    Article  Google Scholar 

  36. A. Tomiyama, H. Tamaia, and I. Zunb: Chem. Eng. Sci., 2002, vol. 57, pp. 1849–58.

    Article  CAS  Google Scholar 

  37. M. Ishii and N. Zuber: A.I.Ch.E. J., 1979, vol. 25, pp. 843–55.

    Article  CAS  Google Scholar 

  38. J.T. Kuo and G.B. Wallis: Int. J. Multiphas. Flow, 1988, vol. 14, pp. 547–64.

    Article  CAS  Google Scholar 

  39. N. Boisson and M.R. Malin: Int. J. Numer. Methods Fluid, 1996, vol. 23, pp. 1289–310.

    Article  CAS  Google Scholar 

  40. N.I. Kolev: Multiphase Flow Dynamics 2: Thermal and Mechanical Interactions, 2nd ed., Springer, Berlin, Germany, 2005.

  41. K. Kuwagi and H. Ozoe: Int. J. Multiph. Flow, 1999, vol. 25, pp. 175–82.

    Article  CAS  Google Scholar 

  42. Y. Murai and Y. Matsumoto: JSME Int. J. Ser. B, 1998. vol. 41, pp. 568–74.

  43. M. Lopez de Bertodano, R.T. Lahey, Jr., and O.C. Jones: Int. J. Multiph. Flow , 1994, vol. 20, pp. 805–18.

  44. A. Tomiyama: Proceeding of the Third International Conference on Multiphase Flow, Lyon, France, 1998.

  45. J. Grienberger and H. Hofmann: Chem. Eng. Sci., 1992, vol. 47, pp. 2215–20.

    Article  CAS  Google Scholar 

  46. H.F. Svendsen, H.A. Jakobsen, and R. Torvik: Chem. Eng. Sci., 1992, vol. 47, pp. 3297–304.

    Article  CAS  Google Scholar 

  47. D. Pfleger and S. Becker: Chem. Eng. Sci., 2001, vol. 56, pp. 1737–47.

    Article  CAS  Google Scholar 

  48. B.M. Lopez, R.T. Lahey, and O.C. Jones: J. Fluid Eng., 1994, vol. 116, pp. 128–34.

    Article  Google Scholar 

  49. M. Sano and K. Mori: Trans. Jpn. Inst. Met., 1976, vol. 17, pp. 344–52.

    Google Scholar 

  50. D. Zhang, N.G. Deen, and J.A.M. Kuipers: Chem. Eng. Sci., 2006, vol. 61, pp. 7593–608.

    Article  CAS  Google Scholar 

  51. J.B. Joshi: Chem. Eng. Sci., 2001, vol. 56, pp. 5893–933.

    Article  CAS  Google Scholar 

  52. M. Lopez de Bertodano, S.J. Lee, and R.T. Lahey, Jr.: J. Fluid Eng., 1990, vol. 112, pp. 107–13.

  53. R. Bel F’Dhila and O. Simonin: Sixth Workshop on Two-Phase Flow Predictions, Erlangen, Germany, 1992.

    Google Scholar 

  54. S. Elgobashi and T. Abou-Arab: Phys. Fluid., 1983, vol. 26, pp. 931–38.

    Article  Google Scholar 

  55. A.H. Castillejos and J.K. Brimacombe: Metall. Trans. B, 1987, vol. 18B, pp. 659–71.

    Article  CAS  Google Scholar 

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Acknowledgments

The authors wish to express thanks to the National Outstanding Young Scientist Foundation of China (Grant No. 50925415) and the National Natural Science Foundation of China (Grant No. 51134009) for supporting this work.

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Authors and Affiliations

  1. School of Materials and Metallurgy, Northeastern University, Shenyang, 110819, P.R. China

    Wentao Lou (Ph.D. Candidate) & Miaoyong Zhu (Professor)

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  1. Wentao Lou
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  2. Miaoyong Zhu
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Correspondence to Miaoyong Zhu.

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Manuscript submitted March 28, 2012.

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Lou, W., Zhu, M. Numerical Simulation of Gas and Liquid Two-Phase Flow in Gas-Stirred Systems Based on Euler–Euler Approach. Metall Mater Trans B 44, 1251–1263 (2013). https://doi.org/10.1007/s11663-013-9897-6

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