Advertisement

Metallurgical and Materials Transactions B

, Volume 50, Issue 2, pp 958–980 | Cite as

A Modeling Approach for Time-Dependent Geometry Applied to Transient Heat Transfer of Aluminum Electrolysis Cells

  • François AllardEmail author
  • Martin Désilets
  • Alexandre Blais
Article
  • 149 Downloads

Abstract

The thermal balance of aluminum electrolysis cells (AEC) have to be rigorously controlled in order to improve the efficiency and sustainability of this industrial process. A new modeling strategy is developed to consider the displacements of solid bodies and moving boundaries in finite element models. The transient thermal-electric modeling of the AEC demonstrates the effect of an increase in operating voltage on both the anode cover and the side ledge. With higher heat generation, the anode cover deteriorates and the side ledge thickness decreases. Since the anode cover is characterized by irreversible transformations, the top heat dissipation remains higher even when the operating voltage comes back to its typical value. For the first time, the transient temperature and electric fields throughout the anode life are simulated and validated by industrial measurements. The modeling predictions have been validated from instrumented anodes and manual measurements, all performed on operating AEC.

Nomenclature

Symbol

A

Area (m2)

cp

Specific heat capacity (J/kg K)

E

Electric field (V/m)

F

View factor

H

Height (cm or m)

h

Convection heat transfer coefficient (W/m2 K)

J

Current density (A/m2)

k

Thermal conductivity (W/m K)

L

Length (cm or m)

q

Heat transfer rate (W)

q″

Heat flux (W/m2)

\( \dot{q} \)

Rate of energy generation per unit volume (W/m3)

t

Time (s, h or day)

T

Temperature (K or °C)

V

Electric potential or voltage (V)

Greek

δij

Kronecker delta

\( \nabla \)

Gradient vector field

ε

Emissivity

ρ

Density (kg/m3)

σ

Electrical conductivity (S/m); Stefan–Boltzmann constant (W/m2 K4)

Abbreviation

ACD

Anode–cathode distance

ACM

Anode cover material

AEC

Aluminum electrolysis cell

BMI

Bath–metal interface

CAD

Computer-aided design

CC

Center channel

CFD

Computational fluid dynamics

CR

Cryolite ratio

HFS

Heat flux sensor

MARE

Mean absolute relative error

OA

On the anode

SC

Side channel

Style

bold

A vector

[brackets]

A matrix or a concentration of a chemical species

Notes

Acknowledgments

This study was supported by Rio Tinto Aluminium, the “Conseil de Recherches en Sciences Naturelles et en Génie du Canada” (CRSNG) and the “Fonds de Recherche du Québec - Nature et Technologies” (FRQNT). The authors wish to thank the staff at Rio Tinto Grande-Baie smelter and Arvida Research & Development Center (ARDC), especially Mr. Jean-François Bilodeau and Mr. Sébastien Guérard from ARDC, for the support provided during the realization of this work.

Conflict of interest

The authors declare that they have no competing interests.

Supplementary material

11663_2019_1510_MOESM1_ESM.pdf (100 kb)
Supplementary material 1 (PDF 100 kb)

Supplementary material 2 (MP4 39624 kb)

Supplementary material 3 (MP4 46052 kb)

References

  1. 1.
    J. Thonstad, P. Fellner, G.M. Haarberg, J. Hives, H. Kvande, A. Sterten: Aluminium Electrolysis: Fundamentals of the Hall-Heroult Process, 3rd ed., Aluminium-Verlag, Düsseldorf, Germany, 2001, pp. 1-8.Google Scholar
  2. 2.
    A.E. Gheribi, S. Poncsák, S. Guérard, J.F. Bilodeau, L. Kiss, P. Chartrand: J. Chem. Phys., 2017, vol. 146, pp. 1-10.  https://doi.org/10.1063/1.4978235.CrossRefGoogle Scholar
  3. 3.
    S. Poncsák, L. Kiss, A. Belley, S. Guérard, and J.F. Bilodeau: Light Met. 2015, Proc. Int. Symp., 2015, pp. 655–59.Google Scholar
  4. 4.
    S. Poncsák, L. Kiss, R. St-Pierre, S. Guérard, and J.F. Bilodeau: Light Met. 2014, Proc. Int. Symp., 2014, pp. 585–89.Google Scholar
  5. 5.
    S. Poncsák, L. Kiss, S. Guérard, J.F. Bilodeau: Metals, 2017, vol. 7, pp. 1-10.  https://doi.org/10.3390/met7030097.CrossRefGoogle Scholar
  6. 6.
    F. Allard, G. Soucy, L. Rivoaland, M. Désilets: J. Therm. Anal. Calorim., 2015, vol. 119, pp. 1303-1314.CrossRefGoogle Scholar
  7. 7.
    A. Fallah-Mehrjardi, P.C. Hayes, E. Jak: Metall. Mater. Trans. B, 2014, vol. 45B, pp. 1232-1247.CrossRefGoogle Scholar
  8. 8.
    J. Liu, A. Fallah-Mehrjardi, D. Shishin, E. Jak, M. Dorreen, M. Taylor: Metall. Mater. Trans. B, 2017, vol. 48B, pp. 3185-3195.CrossRefGoogle Scholar
  9. 9.
    F. Allard, M. Désilets, A. Blais: Thermochim. Acta, 2019, vol. 671, pp. 89-102.CrossRefGoogle Scholar
  10. 10.
    F. Allard, M. Désilets, M. LeBreux, A. Blais: Int. J. Heat Mass Transfer, 2019, vol. 132, pp. 1262-1276.CrossRefGoogle Scholar
  11. 11.
    Q. Zhang, M.P. Taylor, J.J.J. Chen: Metall. Mater. Trans. B, 2015, vol. 46B, pp. 1520-1534.CrossRefGoogle Scholar
  12. 12.
    F. Allard, M. Désilets, M. LeBreux, and A. Blais: Light Met. 2015, Proc. Int. Symp., 2015, pp. 565–70.Google Scholar
  13. 13.
    X. Liu, M. Taylor, and S. George: Light Met. 1992, Proc. Int. Symp., 1992, pp. 489–94.Google Scholar
  14. 14.
    L.N. Less: Metall. Trans. B., 1977, vol. 8B, pp. 219–225.CrossRefGoogle Scholar
  15. 15.
    F. Allard, M. Désilets, M. LeBreux, and A. Blais: Light Met. 2016, Proc. Int. Symp., 2016, pp. 289–94.Google Scholar
  16. 16.
    H. Wijayaratne, M. Hyland, M. Taylor, A. Grama, and T. Groutso: Light Met. 2011, Proc. Int. Symp., 2011, pp. 399–404.Google Scholar
  17. 17.
    X. Shen: PhD thesis, University of Auckland, New Zealand, 2006.Google Scholar
  18. 18.
    K.A. Rye, J. Thonstad, and X. Liu: Light Met. 1995, Proc. Int. Symp., 1995, pp. 441–49.Google Scholar
  19. 19.
    M.A. Llavona, L.F. Verdeja, R. Zapico, F. Alvarez, and J.P. Sancho: Light Met. 1990, Proc. Int. Symp., 1990, pp. 429–37.Google Scholar
  20. 20.
    G. Hatem, M. Llavona, T. Log, J.P. Sancho, and T. Ostvold: Light Met. 1989, Proc. Int. Symp., 1989, pp. 365–70.Google Scholar
  21. 21.
    M.A. Llavona, R. Zapico, P. García, J.P. Sancho, and L.F. Verdeja: Light Met. 1988, Proc. Int. Symp., 1988, pp. 201–06.Google Scholar
  22. 22.
    K.E. Einarsrud, I. Eick, W. Bai, Y. Feng, J. Hua, P.J. Witt: Appl. Math. Modell., 2017, vol. 44, pp. 3–24.CrossRefGoogle Scholar
  23. 23.
    B. Bardet, T. Foetisch, S. Renaudier, J. Rappaz, M. Flueck, and M. Picasso: Light Met. 2016, Proc. Int. Symp., 2016, pp. 315–19.Google Scholar
  24. 24.
    S. Langlois, J. Rappaz, O. Martin, Y. Caratini, M. Flueck, A. Masserey, and G. Steiner: Light Met. 2015, Proc. Int. Symp., 2015, pp. 771–75.Google Scholar
  25. 25.
    M. Ariana, M. Désilets, P. Proulx: Can. J. Chem. Eng., 2014, vol. 92, pp. 1951-1964.CrossRefGoogle Scholar
  26. 26.
    M. Blais, M. Désilets, M. Lacroix: Appl. Therm. Eng., 2013, vol. 58, pp. 439-446.CrossRefGoogle Scholar
  27. 27.
    D. Marceau, S. Pilote, M. Désilets, J.F. Bilodeau, L. Hacini, and Y. Caratini: Light Met. 2011, Proc. Int. Symp., 2011, pp. 1041–46.Google Scholar
  28. 28.
    Y. Safa, M. Flueck, J. Rappaz: Appl. Math. Modell., 2009, vol. 33, pp. 1479-1492.CrossRefGoogle Scholar
  29. 29.
    M. Dupuis and V. Bojarevics: Light Met. 2005, Proc. Int. Symp., 2005, pp. 449–54.Google Scholar
  30. 30.
    T.X. Hou, Q. Jiao, E. Chin, W. Crowell, and C. Celik: Light Met. 1995, Proc. Int. Symp., 1995, pp. 755–61.Google Scholar
  31. 31.
    A.T. Brimmo, M.I. Hassan, Y. Shatilla: Appl. Therm. Eng., 2014, vol. 73, pp. 116-127.CrossRefGoogle Scholar
  32. 32.
    M. Désilets, D. Marceau, and M. Fafard: Light Met. 2003, Proc. Int. Symp., 2003, pp. 247–54.Google Scholar
  33. 33.
    M. LeBreux, M. Désilets, F. Allard, and A. Blais: Numer. Heat Transf. A, 2016, vol. 69A, pp. 128-145.CrossRefGoogle Scholar
  34. 34.
    Q. Wang, L. Gosselin, M. Fafard, J. Peng, B. Li: Metall. Mater. Trans. B, 2016, vol. 47B, pp. 1228-1236.CrossRefGoogle Scholar
  35. 35.
    D. Picard, J. Tessier, G. Gauvin, D. Ziegler, H. Alamdari, and M. Fafard: Metals, 2017, vol. 7, pp. 1–9.  https://doi.org/10.3390/met7090374.CrossRefGoogle Scholar
  36. 36.
    H. Abbas, M.P. Taylor, M. Farid, and J.J. Chen: Light Met. 2009, Proc. Int. Symp., 2009, pp. 551–56.Google Scholar
  37. 37.
    R. Zhao, L. Gosselin, A. Ousegui, M. Fafard, D.P. Ziegler: Numer. Heat Transfer, Part A, 2013, vol. 64A, pp. 317-338.CrossRefGoogle Scholar
  38. 38.
    R. Zhao, L. Gosselin, M. Fafard, J. Tessier, D.P. Ziegler: Int. J. Therm. Sci., 2017, vol. 112, pp. 395-407.CrossRefGoogle Scholar
  39. 39.
    K. Stein, T.E. Tezduyar, R. Benney: Comput. Methods Appl. Mech. Eng., 2004, vol. 193, pp. 2019-2032.CrossRefGoogle Scholar
  40. 40.
    A.A. Johnson and T.E. Tezduyar: Comput. Methods Appl. Mech. Eng., 1994, vol. 119, pp. 73-94.CrossRefGoogle Scholar
  41. 41.
    J.N. Reddy and D.K. Gartling: The Finite Element Method in Heat Transfer and Fluid Dynamics, 3rd ed., CRC Press, Boca Raton, Florida, 2010, pp. 229-235.Google Scholar
  42. 42.
    G. Vidalain, L. Gosselin, M. Lacroix: Int. J. Heat Mass Transfer, 2009, vol. 52, pp. 1753-1760.CrossRefGoogle Scholar
  43. 43.
    ANSYS Inc.: ANSYS Mechanical APDL Theory Reference, Canonsburg, Pennsylvania, 2017, pp. 203–18.Google Scholar
  44. 44.
    M.F. Cohen and D.P. Greenberg: Comput. Graphics, 1985, vol. 19, pp. 31-40.CrossRefGoogle Scholar
  45. 45.
    Y.S. Touloukian and D.P. DeWitt: Thermophysical Properties of Matter - The TPRC Data Series - Volume 8, Plenum Publishing Corporation, New York, NY, 1972, pp. 8-73.Google Scholar
  46. 46.
    C.F. Windisch, B.B. Brenden, O.H. Koski, and R.E. Williford: Final report on the PNL program to develop an alumina sensor, U.S. Department of Energy, Pacific Northwest Laboratory, United States, 1992, pp. 28–29.Google Scholar
  47. 47.
    Hukseflux Thermal Sensors: HF01 High Temperature Heat Flux Sensor (version 1211), Delft, Netherlands, 2003, pp. 15-16.Google Scholar

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2019

Authors and Affiliations

  • François Allard
    • 1
    Email author
  • Martin Désilets
    • 1
  • Alexandre Blais
    • 2
  1. 1.Department of Chemical Engineering and Biotechnological EngineeringUniversité de SherbrookeSherbrookeCanada
  2. 2.Rio Tinto Aluminium (Arvida Research and Development Centre)JonquièreCanada

Personalised recommendations