Skip to main content
SpringerLink
Log in

Modeling Natural Convection in Copper Electrorefining: Describing Turbulence Behavior for Industrial-Sized Systems

  • Published:
Metallurgical and Materials Transactions B Aims and scope Submit manuscript

Abstract

A computational fluid dynamics (CFD) model of copper electrorefining is discussed, where natural convection flow is driven by buoyancy forces caused by gradients in copper concentration at the electrodes. We provide experimental validation of the CFD model for several cases varying in size from a small laboratory scale to large industrial scale, including one that has not been compared with a CFD model. Previously, the large-scale systems have been thought to be turbulent by some workers and modeled accordingly with k-ε type turbulence models, but others have not considered turbulence effects in their modeling. We find that the turbulence model does not predict turbulence exists; however, we analyze carefully the fluctuation statistics predicted for a transient model, finding that most cases considered do exhibit a type of turbulence, an instability related to the interaction between velocity and copper concentration fields. We provide a comparison of the extent of turbulence for various electrode heights, and gap widths, and we emphasize industrial-sized electrorefining cells.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

Abbreviations

B :

natural convection buoyancy force (N m−3)

C :

Copper concentration (kg m−3)

C ref :

average concentration of copper over the cathode (kg m−3)

D :

diffusion coefficient (m2 s−1)

F :

Faraday’s constant (A s mol−1)

F 2 :

blending function (-)

g :

Gravitational acceleration vector (m/s2)

Gr H :

Grashof number (-)

H :

Height of electrode (mm)

H 0 :

Parameter height of electrode (mm)

h :

width of electrode (mm)

h 0 :

parameter width of electrode (mm)

i :

current density (A m−2)

I :

turbulence intensity (-)

k :

kinetic energy (m2 s−2)

\( \mathop m\limits^{\bullet}{_{\text{Cu}}} \) :

flux of copper at the anode and cathode walls (kg m−2 s−1)

M Cu :

molecular weight of copper (g mol−1)

p :

pressure (Pa)

p’ :

modified pressure (Pa)

Ra H :

Rayleigh number (-)

S :

invariant measure of the strain rate (-)

Sc :

Schmidt number (-)

t + :

transference number (-)

v’ :

RMS turbulence velocity fluctuation (m s−1)

V average :

time averaged vertical velocity (m s−1)

v :

velocity vector (m s−1)

V :

velocity scale in dimensionless numbers (maximum near electrode velocity)

X :

X direction coordinate (m)

Y :

Y direction coordinate (m)

ΔY min :

Y minimum grid cell (mm)

ΔY min :

Y minimum grid cell (mm)

ΔΖ min :

Y minimum grid cell (mm)

ΔΖ min :

Y minimum grid cell (mm)

z :

valency (-)

Z :

Z direction coordinate (m)

α1 :

dimensionless turbulence parameter (-)

β :

coefficient of expansion (L g−1 s−1)

μ :

liquid laminar dynamic viscosity (kg m−1 s−1)

μ T :

turbulent dynamic viscosity (kg m−1 s−1)

υ T :

turbulent kinematic viscosity (m2 s−1)

ρ :

density (kg m−3)

σ T :

turbulence Schmidt number taken (-)

ω :

eddy frequency (s−1)

average:

average used for V average

Cu:

copper

H:

height H dimension

h:

width h dimension

min:

minimum

max:

maximum

ref:

reference

T:

turbulent

+ :

positive

0:

refers to parameter of h, e.g., h 0

T :

transpose

‘ :

modified pressure p’ or average velocity u’

References

  1. A. Eklund, F. Alavyoon, D. Simonsson, R. Karlsson, and F. Bark: Electrochim. Acta., 1991, vol. 36, no. 8, pp. 1345-1254.

    Article  CAS  Google Scholar 

  2. D.A. Bograchev and A.D. Davydov: Russ. J. Electrochem., 2003, vol. 39, no. 9, pp. 967-72.

    Article  CAS  Google Scholar 

  3. F. Alavyoon: Electrochim. Acta., 1992, vol. 37, no. 2, pp. 333-44.

    Article  CAS  Google Scholar 

  4. G. Nelissen, B. Van Den Bossche, J. Deconinck, A. Van Theemsche, and C. Dan: J. Appl. Electrochem., 2003, vol. 33, no. 10, pp. 863-73.

    Article  CAS  Google Scholar 

  5. J.W. Elder: J. Fluid Mech., 1965, vol. 23, pp. 77-98.

    Article  Google Scholar 

  6. J.W. Elder: J. Fluid Mech., 1965, vol. 23, pp. 99-111.

    Article  Google Scholar 

  7. R. Cheesewright: Technical Report No. 05031-8-T, The University of Michigan, Ann Arbor, MI, 1967.

  8. M. Moats, W. Davenport, T. Robinson, G. Karcas, and S. Demetrio: in Electrolytic Copper Refining–2007 World Tankhouse Operating Data, G.E. Houlachi, J.D. Edwards, and T.G. Robinson, eds., CIM, Montréal, Canada, 2007, pp. 195–241.

  9. K. Denpo, S. Teruta, Y. Fukunaka, and Y. Kondo: Metall. Trans. B, 1983, vol. 14B, pp. 633-43.

    Article  CAS  Google Scholar 

  10. S. Kawai, K. Nishikawa, Y. Fukunaka, and S. Kida: in Numerical Simulation of Turbulent Natural Convection Along Vertical Plane Electrodes, G.E. Houlachi, J.D. Edwards, and T.G. Robinson, eds., CIM, Montréal, Canada, 2007, pp. 545–60.

  11. F. Gurniki, F. Bark, and S. Zahari: J. Appl. Electrochem., 1999, vol. 29, pp. 27-34.

    Article  CAS  Google Scholar 

  12. D. Ziegler and J. Evans: J. Electrochem. Soc., 1986, vol. 133, no. 3, pp. 559-66.

    Article  CAS  Google Scholar 

  13. F. Gurniki: Ph.D. Dissertation, Royal Institute of Technology, Stockholm, Sweden, 2000.

  14. Y. Konishi, Y. Tanaka, Y. Kondo, and Y. Fukunaka: Electrochim. Acta, 2000, vol. 46, pp. 681-90.

    Article  CAS  Google Scholar 

  15. ANSYS: CFX-11 Solver, http://www.ansys.com/cfx, 2007.

  16. J. Newman and K. Thomas-Alyea: Electrochemical Systems, 3rd ed., Wiley, New York, NY, 2004, p. 14.

  17. F.R. Menter: Zonal Two Equation k-ω Turbulence Models for Aerodynamic Flows, AIAA Paper 93-2906, 1993.

  18. A. Eklund, D. Simonsson, F. Alavyoon, R. Karlsson, and F. Bark: Theoretical and Experimental Studies of Free Convection in a Copper Refining Cell, Institute of Chemical Engineers Symposium Series, 1989, vol. 112, pp. 47–58.

  19. X. Yang, K. Eckert, A. Heinze, and M. Uhlemann: J. Electroanal. Chem., 2008, vol. 613, pp. 97-107.

    Article  CAS  Google Scholar 

  20. M. Farhangnia, S. Biringen, and L.J. Peltier: Int. J. Numer. Meth. Fluid, 1996, vol. 23, no. 13, pp. 1311-26.

    Article  Google Scholar 

Download references

Acknowledgments

The authors gratefully acknowledge funding from the AMIRA P705 sponsors. The authors also gratefully acknowledge Peter Witt, Graeme Lane, and Darrin Stephens. Mike Nicol is acknowledged for helpful discussions.

Author information

Authors and Affiliations

  1. Division of Earth Sciences & Resource Engineering, Commonwealth Scientific and Industrial Research Organization (CSIRO), Clayton, Victoria, 3168, Australia

    Martin J. Leahy (Research Scientist)

  2. Division of Mathematics, Informatics and Statistics, CSIRO, Clayton, Victoria, Australia

    M. Phillip Schwarz (Program Leader, Computation and Mathematical Modeling)

Authors
  1. Martin J. Leahy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Phillip Schwarz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Martin J. Leahy.

Additional information

Manuscript submitted October 31, 2010.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (AVI 90242 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Leahy, M.J., Phillip Schwarz, M. Modeling Natural Convection in Copper Electrorefining: Describing Turbulence Behavior for Industrial-Sized Systems. Metall Mater Trans B 42, 875–890 (2011). https://doi.org/10.1007/s11663-011-9504-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11663-011-9504-7

Keywords

Search

Navigation