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Experimental and Numerical Investigation of Fluid Flow and Mixing in Pachuca Tanks

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Abstract

This study reports laboratory and computational work carried out to determine the effect of operating and design parameters on the motion of the liquid and the mixing of a solute in Pachuca tanks. In the laboratory tanks, the liquid velocity field was measured using particle image velocimetry (PIV) and mixing was characterized using a stimulus-response technique. Visualization of the air-water flow suggested the suitability of a one-phase variable density turbulent recirculating flow model coupled to the drift flux model, to describe the motion of the water phase and the gas holdup, in two dimensions (2-D) and in steady state. The dispersion of the solute tracer was simulated by solving the unsteady state turbulent mass transfer equation in three dimensions (3-D). The computational predictions give a good estimate of laboratory measurements of the influence that operating and design variables have on liquid circulation velocity, liquid flow pattern, gas holdup, and mixing evolution and time. Fluid flow simulation of industrial-scale tanks revealed that the recirculating loop that forms in their annular section is more intense and extends over a larger proportion of the reactor height as the draft tube/tank diameters ratio, d d /d t , decreases, at the same time the superficial liquid velocity in the draft tube increases. These features suggest that tanks with d d /d t ∼ 0.1 promote conditions for good particle suspension by hindering the settling of particles in the annulus and favoring their lifting in the draft tube; in laboratory-scale tanks, the flow characteristics that enhance particle suspension are not as apparent. The mathematical model also predicts different solute mixing behavior between the laboratory and industrial-scale tanks. At low superficial gas velocities (u sg  ≤ 0.003 m/s) the effect of the increasing d d /d t on the decreasing mixing time is smaller in the last tanks. Hence, according to the calculations, it should be expected that industrial tanks with d d /d t  = 0.1 have advantages in regard to particle suspension in comparison to tanks with d d /d t  = 0.5 and, at the same time, they should be comparable in respect to solute mixing under low superficial air velocities, at which they also exhibit good energy efficiency.

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Abbreviations

A a , A d :

cross-sectional area of the annulus; cross-sectional area of draft tube

A ct , A cb :

area of the cylindrical surface of height s d on top of the draft tube; area of the cylindrical surface of height s db below the base of the draft tube, m2

B 1, B 2 :

cyclic r-z planes separated by 360 deg

C :

concentration of solute tracer, kg m−3

C 1, C 2, C d :

constants in the turbulence model

d d , d t , d ab :

draft tube diameter; tank tube diameter; thickness of annular section at draft tube base

d at :

thickness of annular section at draft tube top, m

D eff :

effective diffusion coefficient, m2 s−1

g:

acceleration due to gravity, ms−2

G :

rate of generation of k per unit volume, kg m−1 s−3

h d :

height of draft tube, m

h t , h d :

depth of water bath; height of draft tube, m

I s :

intensity of segregation

k :

turbulence kinetic energy, m2 s−2

p :

pressure, kg m−1 s−2

Q g , Q l :

volumetric gas flow rate at orifice conditions; circulation liquid flow rate, m3 s−1

r, r d , r t :

radial coordinate; radius of draft tube; radius of tank, m

E ϕP :

residual of the discretized equation for the flow variable ϕ at node P

s d , s db :

draft tube submergence; draft tube to base separation, m

S ϕ :

source term of flow variable ϕ

t :

time, s

t w :

draft tube wall thickness, m

u :

mean axial velocity component, ms−1

U slip :

terminal rising velocity of a single bubble, m/s

u sg , u sg,d :

superficial gas velocity with respect to the tank diameter; with respect to draft tube diameter, superficial

u sl,d :

liquid velocity in draft tube, ms−1

v :

mean radial velocity component, ms−1

V, V l :

volume of discretization cell; volume of cell occupied by liquid, m3

V o , V ∞ , V(t):

initial voltage across the electrode of the conductivity meter corresponding to an initial solute concentration; voltage corresponding to complete tracer dissolution after a sufficiently long time; voltage corresponding to a certain local tracer concentration at time t, V

Y :

degree of mixing

z :

axial coordinate, m

\( \ifmmode\expandafter\bar\else\expandafter\=\fi{\alpha } \), \( \ifmmode\expandafter\bar\else\expandafter\=\fi{\alpha }_{{{\text{vol}}}} \) :

cross-sectional area averaged gas volume fraction; volume-averaged gas fraction in draft tube

ε :

dissipation rate of turbulence kinetic energy, m2 s−3

ϕ :

flow variable

∇:

gradient operator in terms of r-z coordinates for the continuity, momentum and turbulence equations and in terms of r-θ-z coordinates for the mass solute tracer concentration equation, m−1

∇:

divergence operator in terms of r-z coordinates for the continuity, momentum and turbulence equations and in terms of r-θ-z coordinates for the mass solute tracer concentration equation, m−1

μ, μ τ , μ eff :

molecular, turbulent and effective viscosity, kg m−1 s−1

ρ, ρ l , ρ g :

local density; liquid density; gas density, kg m−3

σ C , σ C,t :

laminar and turbulent Schmidt numbers for concentration

σ k , σ ε :

Schmidt numbers for k and ε

θ :

circumferential coordinate, radians

Γ ϕ :

effective exchange coefficient of the quantity ϕ, kg m−1 s−1

References

  1. N.N. Clark: Miner. Metall. Process., 1984, Nov. pp. 226–32

  2. C.J. Hallet, A.J. Monhemius, D.G.C. Robertson: Extraction Metallurgy 1981, I.M.M., London, 1981, pp. 308–20

  3. R. Shekhar, J.W. Evans: Metall. Trans. B, 1989, vol. 20B, pp. 781–91

    Article  Google Scholar 

  4. A.G.W. Lamont: Can. J. Chem. Eng.,1958, Aug., pp. 153–60

  5. P. Weiland: Ger. Chem. Eng., 1984, vol. 7, pp. 374–85

    Google Scholar 

  6. G.M. Fraser: Aus. I.M.M. Perth and Kalgoorlic Branches, Regional Conf. on Gold-Mining, Metallurgy and Geology, Oct. 1984, pp. 245–56

  7. F.R. Carrillo P., A. Uribe S., and A.H. Castillejos E.: Miner. Eng., 1995, vol. 8, pp. 405–509

  8. M. Zaisha, Y. Shouzhi, and C. Chen: Proc. 3rd Int. Symp. on Hydrometallurgy, Research Development and Plant Practice, K. Osseo-Asare and J.D. Miller, eds., AIME, Atlanta, GA, 1983, pp. 789–806

  9. K. Koide, S. Iwamoto, Y. Takasaka, S. Matsuura, E. Takahashi, M. Kimura, H. Hubota: J. Chem. Eng. Jpn., 1984, vol. 17, pp. 611–18

    Google Scholar 

  10. K. Koide, K. Horibe, H. Kawabata, S. Ito: J. Chem. Eng. Jpn., 1984, vol. 17, pp. 369–74

    Google Scholar 

  11. G.G. Roy, R. Shekhar, S.P. Mehrotra: Metall. Mater. Trans. B., 1998, vol. 29B, pp. 339–49

    Article  Google Scholar 

  12. G.G. Roy, R. Shekhar: Trans. Inst. Min. Metall., 1996, vol. 105, pp. C9–C15

    Google Scholar 

  13. D. Gavroy, C. Joly-Vuillemin, G. Cordier, H. Delmas: Trans. I. Chem. E., 1995, vol. 73, pp. 637–42

    Google Scholar 

  14. G.G. Roy, A. Bera, J.H. Mankar: Trans. Inst. Min. Metall., Sect. C, 2000, vol. 109, pp. 90–96

    Google Scholar 

  15. R. Shekhar: Ph.D. Thesis, University of California, Berkeley, CA, 1988

  16. R. Shekhar, J.W. Evans: Metall. Trans. B, 1990, vol. 21B, pp. 191–203

    Article  Google Scholar 

  17. H. Singh, D. Mazumdar: Metall. Mater. Trans. B, 1997, vol. 28B, pp. 727–31

    Article  Google Scholar 

  18. J.S. Woo, J. Szekely, A.H. Castillejos, J.K. Brimacombe: Metall. Trans. B, 1990, vol. 21B, pp. 269–77

    Article  Google Scholar 

  19. T. DebRoy, A.K. Majumdar, D.B. Spalding: Appl. Math. Model., 1978, vol. 2, pp. 146–50

    Article  Google Scholar 

  20. J.H. Hills: Chem. Eng. J., 1976, vol. 12, pp. 89–99

    Article  Google Scholar 

  21. VISIFLOW System User Manual, AEA Technology, Oxford, United Kingdom, 1987, pp. 9:2–9:5

  22. E.N. Aguilera G: M.Sc., CINVESTAV, Unidad Saltillo, Mexico, 1994

  23. G.G. Murthy, J.F. Elliott: ISIJ, 1992, vol. 32, pp. 190–95

    Google Scholar 

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

    Article  Google Scholar 

  25. G.F. Hewitt: Measurement of Two Phase Flow Parameters, Academic Press Inc., London, 1978, pp. 11–13

    Google Scholar 

  26. R. Clift, J.R. Grace, M.E. Weber: Bubbles, Drops and Particles, Academic Press Inc., NY, 1978, pp. 171–73

    Google Scholar 

  27. N. El-Kaddah, J. Szekely: Ironmaking and Steelmaking, 1981, vol. 8, pp. 269–78

    Google Scholar 

  28. W.P. Jones, B.E. Launder: Int. J. Heat Mass Transfer, 1972, vol. 15, pp. 301–14

    Article  Google Scholar 

  29. B.E. Launder, D.B. Spalding: Comput. Math. Appl. Mech. Eng., 1974, vol. 3, pp. 269–89

    Article  Google Scholar 

  30. PHOENICS 2006, D.B. Spalding, CHAM, Bakery House, London

  31. Esperanza Rodríguez M.: Reporte Interno de Doctorado, CINVESTAV, Feb. 2006

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Acknowledgments

The authors gratefully acknowledge research funding from the National Council for Science and Technology of Mexico through Research Grant No. 4407-A9406. One of the authors (ERM) thanks CONACYT for receipt of a postdoctoral scholarship. The authors appreciate the assistance of E.N. Aguilera G. and D.A. Salinas G. with the laboratory work.

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Authors and Affiliations

  1. CINVESTAV–Unidad Saltillo, 25000, COAH, Saltillo, Mexico

    E. Rodrίguez M. (Postdoctoral Student), A.H. Castillejos E. (Professor) & F.A. Acosta G. (Associate Professor)

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  1. E. Rodrίguez M.
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  2. A.H. Castillejos E.
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  3. F.A. Acosta G.
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Correspondence to A.H. Castillejos E..

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Manuscript submitted April 4, 2007.

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Rodrίguez M., E., Castillejos E., A. & Acosta G., F. Experimental and Numerical Investigation of Fluid Flow and Mixing in Pachuca Tanks. Metall Mater Trans B 38, 641–656 (2007). https://doi.org/10.1007/s11663-007-9079-5

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