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The European Physical Journal Special Topics

, Volume 149, Issue 1, pp 27–41 | Cite as

Computation of solidification problems with hydrodynamic convection resolving energetic anisotropies at the microscale quantitatively

  • R. Siquieri
  • H. Emmerich
  • M. Jurgk
Article

Abstract.

In this work we propose a new numerical approach to solve the solidification of microstructures from a pure melt including hydrodynamic effects in the molten phase. The model is based on the classical sharp-interface model, i.e the solid–liquid interface is tracked and latent heat is released. An enhanced scheme is employed to solve fluid flow in the melt. The no-slip condition is applied on the interface by enforcing the velocities in the solid phase to be zero. The morphology evolution of the solidifying crystal microstructure under the influence of convection is compared with an existing morphology diagram for pure diffusion controlled growth (see Brener et al. [1]). The peculiarity of our approach is that it models the physical anisotropies along the solid–liquid interface with high accuracy. This allows us to report changes in the morphology diagram given by Brener et al. [1] due to the influence of forced flow. Moreover, we present some results on the scaling of the dendritic tip in such cases.

Keywords

European Physical Journal Special Topic Dendritic Growth Dendritic Morphology Interface Point Solid Cell 
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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References

  1. E. Brener, H. Müller-Krumbhaar, D. Temkin, Europhys. Lett. 17, 535 (1992) Google Scholar
  2. M.F. Tomé, S. McKee, J. Comp. Phys. 110, 171 (1994) Google Scholar
  3. T. Ihle, H. Müller-Krumbhaar, Phys. Rev. E 49, 2972 (1994) Google Scholar
  4. B.T. Murray, A.A. Wheeler, M.E. Glicksman, J. Cryst. Growth 154, 386 (1995) Google Scholar
  5. I. Stalder, Diss. ETH Zuerich, No. 13906, 2000 Google Scholar
  6. For a review see E. Brener, V. Melnikov, Adv. Phys. 40, 53 (1991) Google Scholar
  7. A.A. Wheeler, W.J. Bottinger, G.B. McFadden, Phys. Rev. A 45, 7424 (1992) Google Scholar
  8. A.A. Wheeler, B.T. Murray, R.J. Schaefer, Physica D 66, 243 (1993) Google Scholar
  9. R. Kobayashi, Physica D 63, 410 (1993) Google Scholar
  10. C. Beckermann, R. Viskanta, Appl. Mech. Rev. 46, 1 (1993) Google Scholar
  11. A. Karma, W.-J. Rappel, Phys. Rev. E 53, 3017 (1996) Google Scholar
  12. D. Juric, G. Tryggvason, J. Comp. Phys. 123, 127 (1996) Google Scholar
  13. A. Karma, W.-J. Rappel, Phys. Rev. E 57, 4323 (1998) Google Scholar
  14. M.E. Glicksman, M.B. Koss, E.A. Winsa, Phys. Rev. Lett. 73, 573 (1994) Google Scholar
  15. X. Tong, C. Beckermann, A. Karma, Q. Li, Phys. Rev. E 63, 061601 (2001) Google Scholar
  16. C. Beckermann, H.-J. Diepers, I. Steinbach, A. Karma, X. Tong, J. Comp. Phys. 154, 468 (1999) Google Scholar
  17. R. Tönhardt, G. Amberg, J. Cryst. Growth 194, 406 (1998) Google Scholar
  18. R. Tönhardt, G. Amberg, J. Cryst. Growth 213, 161 (2000) Google Scholar
  19. D. Medvedev, K. Kassner, J. Cryst. Growth 275, 1496 (2005) Google Scholar
  20. D. Medvedev, K. Kassner, Phys. Rev. E 72, 056703 (2005) Google Scholar
  21. D. Medvedev, T. Fischaleck, K. Kassner, Phys. Rev. E 74, 031606 (2006) Google Scholar
  22. J.S. Langer, Rev. Mod. Phys. 52, 1 (1980) Google Scholar
  23. C. Fletcher, 2nd edn., Vol. I–II (Berlin, Springer-Verlag, 1991) Google Scholar
  24. M. Griebel, T. Dornseifer, T. Neunhoeffer (SIAM, Philadelphia, 1997) Google Scholar
  25. N. Al-Rawahi, G. Tryggvason, J. Comp. Phys. 180, 471 (2002) Google Scholar
  26. G.P. Ivantsov, Dokl. Akad. Nauk. SSSR 58, 567 (1947) Google Scholar
  27. J.E. Welch, F.H. Harlow, J.P. Shannon, B.J. Daly, Los Alamos Scientific Lab. Report LA-3425, Los Alamos, 1996 Google Scholar
  28. A.A. Amsden, F.H. Harlow, J. Comp. Phys. 6, 332 (1970) Google Scholar
  29. R. Siquieri, H. Emmerich, M. Jurgk (in preparation) Google Scholar
  30. C.Y. Wang, C. Beckermann, Metall. Mater. Trans. A 24, 2787 (1993); Mater. Sci. Eng. 171, 199 (1993); Metall. Mater. Trans. A 25, 1081 (1994) Google Scholar
  31. S.K. Dash, W.N. Gill, Int. J. Heat Mass Transfer 27, 1345 (1984) Google Scholar
  32. D.A. Saville, P.J. Beaghton, Phys. Rev. A 37, 3423 (1988) Google Scholar
  33. M. Ben Amar, Ph. Bouissou, P. Pelce, J. Cryst. Growth 92, 97 (1988) Google Scholar
  34. Ph. Bouissou, B. Perrin, P. Tabeling, Phys. Rev. A 40, 509 (1989) Google Scholar
  35. M. Benamar, Y. Pomeau, C. R. Acad. Sci. Paris 308, 907 (1989) Google Scholar
  36. Ph. Bouissou, P. Pelce, Phys. Rev. A 40, 6673 (1989) Google Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  • R. Siquieri
    • 1
  • H. Emmerich
    • 1
  • M. Jurgk
    • 2
  1. 1.Computational Materials Engineering, Center for Computational Engineering Science, Institute of Minerals Engineering, RWTH Aachen UniversityAachenGermany
  2. 2.Max-Planck-Institute for Physics of Complex SystemsDresdenGermany

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