Metallurgical and Materials Transactions B

, Volume 44, Issue 4, pp 924–937 | Cite as

Phase Field Simulation of Binary Alloy Dendrite Growth Under Thermal- and Forced-Flow Fields: An Implementation of the Parallel–Multigrid Approach

Article
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Abstract

Dendrite growth and morphology evolution during solidification have been studied using a phase field model incorporating melt convection effects, which was solved using a robust and efficient parallel, multigrid computing approach. Single dendrite growth against the flow of the melt was studied under a wide range of growth parameters, including the Lewis number (Le) and the Prandtl number (Pr) that express the relative strengths of thermal diffusivity to solute diffusivity and kinematic viscosity to thermal diffusivity. Multidendrite growths for both columnar and equiaxed cases were investigated, and important physical aspects including solute recirculation, tip splitting, and dendrite tilting against convection have been captured and discussed. The robustness of the parallel–multigrid approach enabled the simulation of dendrite growth for metallic alloys with Le ~ 104 and Pr ~ 10−2, and the interplay between crystallographic anisotropy and local solid/liquid interfacial conditions due to convection on the tendency for tip splitting was revealed.

Keywords

Convection Phase Field Dendrite Growth Lewis Number Dendrite Morphology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Notes

Acknowledgments

The authors would like to thank the Natural Science Foundation of China (Project No. 51205229), the U.K. Royal Academy of Engineering/Royal Society through Newton International Fellowship Scheme, and the EPSRC Centre for Innovative Manufacture: Liquid Metal Engineering (EP/H026177/1) for financial support, and the Oxford Supercomputer Centre, and the National Laboratory for Information Science and Technology in Tsinghua University for granting access to the supercomputing facilities and support for the parallel programming.

References

  1. 1.
    M. Asta, C. Beckermann, A. Karma, W. Kurz, R. Napolitano, M. Plapp, G. Purdy, M. Rappaz and R. Trivedi, Acta Mater. 2009, vol. 57, pp. 941–71.CrossRefGoogle Scholar
  2. 2.
    W. J. Boettinger, J. A. Warren, C. Beckermann and A. Karma, Annu. Rev. Mater. Res. 2002, vol. 32, pp. 163–94.CrossRefGoogle Scholar
  3. 3.
    L.-Q. Chen, Annu. Rev. Mater. Res. 2002, vol. 32, pp. 113–40.CrossRefGoogle Scholar
  4. 4.
    L. Granasy, T. Pusztai and J. A. Warren (2004) J. Phys. Condens. Matter 16: R1205–R1235.CrossRefGoogle Scholar
  5. 5.
    T. Haxhimali, A. Karma, F. Gonzales and M. Rappaz, Nat Mater. 2006, vol. 5, pp. 660–64.CrossRefGoogle Scholar
  6. 6.
    N. Moelans, B. Blanpain and P. Wollants, CALPHAD 2008, vol. 32, pp. 268–94.CrossRefGoogle Scholar
  7. 7.
    A. Badillo, D. Ceynar and C. Beckermann, Journal of Crystal Growth 2007, vol. 309, pp. 216–24.CrossRefGoogle Scholar
  8. 8.
    C. Giummarra, J. C. LaCombe, M. B. Koss, J. E. Frei, A. O. Lupulescu and M. E. Glicksman, J. Cryst. Growth 2005, vol. 274, pp. 317–30.CrossRefGoogle Scholar
  9. 9.
    C. W. Lan, C. M. Hsu and C. C. Liu, J. Cryst. Growth 2002, vol. 241, pp. 379–86.CrossRefGoogle Scholar
  10. 10.
    C. W. Lan and C. J. Shih, J. Cryst. Growth 2004, vol. 264, pp. 472–82.CrossRefGoogle Scholar
  11. 11.
    A. Karma, Phys. Rev. Lett. 2001, vol. 87, p. 115701.CrossRefGoogle Scholar
  12. 12.
    J. C. Ramirez and C. Beckermann, Acta Mater. 2005, vol. 53, pp. 1721–36.CrossRefGoogle Scholar
  13. 13.
    J. C. Ramirez, C. Beckermann, A. Karma and H. J. Diepers, Phys. Rev. E 2004, vol. 69, p. 051607.CrossRefGoogle Scholar
  14. 14.
    C. Beckermann, H. J. Diepers, I. Steinbach, A. Karma and X. Tong, J. Comput. Phys. 1999, vol. 154, pp. 468–96.CrossRefGoogle Scholar
  15. 15.
    X. Tong, C. Beckermann, A. Karma and Q. Li, Phys. Rev. E 2001, vol. 63, p. 061601.CrossRefGoogle Scholar
  16. 16.
    D. M. Anderson, G. B. McFadden and A. A. Wheeler, Physica D 2000, vol. 135, pp. 175–94.CrossRefGoogle Scholar
  17. 17.
    D. M. Anderson, G. B. McFadden and A. A. Wheeler, Physica D 2001, vol. 151, pp. 305–31.CrossRefGoogle Scholar
  18. 18.
    R. Tönhardt and G. Amberg, J. Cryst. Growth 2000, vol. 213, pp. 161–87.CrossRefGoogle Scholar
  19. 19.
    C.W. Lan, C.J. Shih and M.H. Lee, Acta Mater. 2005, vol. 53, pp. 2285–94.CrossRefGoogle Scholar
  20. 20.
    R. Siquieri and H. Emmerich, Philos. Mag. 2011, vol. 91, pp. 45–73.CrossRefGoogle Scholar
  21. 21.
    Z. Guo, J. Mi and P. S. Grant, J. Comput. Phys. 2012, vol. 231, pp. 1781–96.CrossRefGoogle Scholar
  22. 22.
    L. Beltran-Sanchez and D. Stefanescu: Metall. Mater. Trans. A 2004, vol. 35A, pp. 2471–85.CrossRefGoogle Scholar
  23. 23.
    M. F. Zhu and D. M. Stefanescu, Acta Mater. 2007, vol. 55, pp. 1741–55.CrossRefGoogle Scholar
  24. 24.
    S.P. Vanka, J. Comput. Phys. 1986, vol. 65, pp. 138–58.CrossRefGoogle Scholar
  25. 25.
    U. Trottenberg, C. Oosterlee, and A. Schuller: Multigrid, Academic Press, London, U.K., 2001.Google Scholar
  26. 26.
    A. Karma and W.-J. Rappel, Phys. Rev. E 1999, vol. 60, pp. 3614–25.CrossRefGoogle Scholar
  27. 27.
    L. Arnberg and R. Mathiesen (2007) JOM 59:20–26.CrossRefGoogle Scholar
  28. 28.
    D. Ruvalcaba, R. H. Mathiesen, D. G. Eskin, L. Arnberg and L. Katgerman, Acta Mater. 2007, vol. 55, pp. 4287–92.CrossRefGoogle Scholar
  29. 29.
    B. Utter, R. Ragnarsson and E. Bodenschatz, Phys. Rev. Lett. 2001, vol. 86, pp. 4604–07.CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2013

Authors and Affiliations

  1. 1.School of Materials Science and EngineeringTsinghua UniversityBeijingP.R. China
  2. 2.Department of EngineeringUniversity of HullEast YorkshireUK
  3. 3.Department of MaterialsUniversity of OxfordOxfordUK

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