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Metallurgical and Materials Transactions B

, Volume 49, Issue 6, pp 3603–3615 | Cite as

A Phase-Field Lattice-Boltzmann Study on Dendritic Growth of Al-Cu Alloy Under Convection

  • Ang Zhang
  • Jinglian Du
  • Zhipeng GuoEmail author
  • Qigui Wang
  • Shoumei XiongEmail author
Article

Abstract

Effects of convection (forced and natural) on dendritic evolution of the Al-Cu alloy were investigated using a phase-field lattice-Boltzmann approach. The non-linear coupled equations were solved by applying a parallel and adaptive mesh refinement algorithm. Important physical aspects including dendritic fragmentation, splitting, and formation of solute plumes were simulated. Results showed that the dendritic growth patterns under convection exhibited remarkable difference from those without convection. The presence of flow led to variation of solute diffusion and upstream–downstream dendritic growth difference, which further influenced the development of dendritic arms and multi-dendritic competitive growth. When the convection intensity was magnified, the convection-induced anisotropy became dominated, and the growth patterns changed accordingly to accommodate the local thermodynamic variation.

Notes

Acknowledgments

This work was financially supported by the National Natural Science Foundation of China [Grant Numbers U1537202 and 51701104], the Tsinghua-General Motors International Collaboration Project [Grant Number 20153000354], the Tsinghua University Initiative Scientific Research Program (20151080370), and the Tsinghua Qingfeng Scholarship (THQF2018-15). The authors would also like to thank the National Laboratory for Information Science and Technology in Tsinghua University for access to supercomputing facilities.

References

  1. 1.
    J.A. Dantzig and M. Rappaz. Solidification, EPFL Press, Lausanne, 2009.CrossRefGoogle Scholar
  2. 2.
    S. Xiong, J. Du, Z. Guo, M. Yang, M. Wu, C. Bi and Y. Cao, Acta Metall Sin, 2018, vol. 54, pp. 174-92.Google Scholar
  3. 3.
    T.A. Kowalewski and D. Gobin. Phase change with convection: Modelling and validation, Springer-Verlag Wien, New York, 2004.CrossRefGoogle Scholar
  4. 4.
    J. Du, B. Wen, R. Melnik and Y. Kawazoe, Comp Mater Sci, 2015, vol. 103, pp. 170-78.CrossRefGoogle Scholar
  5. 5.
    A. Zhang, S. Liang, Z. Guo and S. Xiong, Exp Therm Fluid Sci, 2017, vol. 88, pp. 472-82.CrossRefGoogle Scholar
  6. 6.
    J. Du, A. Zhang, Z. Guo, M. Yang, M. Li, and S. Xiong: Phys. Rev. Mater., 2018, vol. 2 (8), art. no. 083402.Google Scholar
  7. 7.
    J.C. Ramirez, C. Beckermann, A. Karma, and H.J. Diepers: Phys. Rev. E, 2004, vol. 69 (5 Pt 1), art. no. 051607.Google Scholar
  8. 8.
    H. Nguyen Thi, Y. Dabo, B. Drevet, M.D. Dupouy, D. Camel, B. Billia, J.D. Hunt and A. Chilton, J Cryst Growth, 2005, vol. 281, pp. 654-68.CrossRefGoogle Scholar
  9. 9.
    D.J. Browne, F. Garcia-Moreno, H. Nguyen-Thi, G. Zimmermann, F. Kargl, R.H. Mathiesen, A. Griesche and O. Minster. Overview of In Situ X-Ray Studies of Light Alloy Solidification in Microgravity. In: K.N. Solanki, D. Orlov, A. Singh, N.R. Neelameggham (Eds), Minerals Metals & Materials Series, Springer International Publishing AG, Cham, 2017, pp. 581-90.Google Scholar
  10. 10.
    B. Echebarria, R. Folch, A. Karma, and M. Plapp: Phys. Rev. E, 2004, vol. 70 (6 Pt 1), art. no. 061604.Google Scholar
  11. 11.
    Z. Guo, J. Mi and P.S. Grant, J Comput Phys, 2012, vol. 231, pp. 1781-96.CrossRefGoogle Scholar
  12. 12.
    J. Du, A. Zhang, Z. Guo, M. Yang, M. Li and S. Xiong, ACS Omega, 2017, vol. 2, pp. 8803-09.CrossRefGoogle Scholar
  13. 13.
    A. Karma: Phys. Rev. Lett., 2001, vol. 87 (11), art. no. 115701.Google Scholar
  14. 14.
    R. Folch and M. Plapp: Phys. Rev. E, 2005, vol. 72 (11), art. no. 011602.Google Scholar
  15. 15.
    A. Zhang, Z. Guo and S. Xiong, China Foundry, 2017, vol. 14, pp. 373-78.CrossRefGoogle Scholar
  16. 16.
    J. Hötzer, P. Steinmetz, M. Jainta, S. Schulz, M. Kellner, B. Nestler, A. Genau, A. Dennstedt, M. Bauer, H. Köstler and U. Rüde, Acta Mater, 2016, vol. 106, pp. 249-59.CrossRefGoogle Scholar
  17. 17.
    S. Akamatsu and M. Plapp, Curr. Opin. Solid State Mater. Sci., 2016, vol. 20, pp. 46-54.CrossRefGoogle Scholar
  18. 18.
    W.J. Boettinger, J.A. Warren, C. Beckermann and A. Karma, Annu Rev Mater Res, 2002, vol. 32, pp. 163-94.CrossRefGoogle Scholar
  19. 19.
    I. Steinbach: Model. Simul. Mater. Sci. Eng., 2009, vol. 17 (7), art. no. 073001.Google Scholar
  20. 20.
    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
  21. 21.
    J. Du, C. Dong, R. Melnik, Y. Kawazoe, and B. Wen: Sci. Rep. UK, 2016, vol. 6, art. no. 033672.Google Scholar
  22. 22.
    C. Beckermann, H.J. Diepers, I. Steinbach, A. Karma and X. Tong, J Comput Phys, 1999, vol. 154, pp. 468-96.CrossRefGoogle Scholar
  23. 23.
    X. Tong, C. Beckermann, A. Karma, and Q. Li: Phys. Rev. E, 2001, vol. 63 (6 Pt 1), art. no. 061601.Google Scholar
  24. 24.
    Z. Guo, J. Mi, S. Xiong and P.S. Grant, Metall Mater Trans B, 2013, vol. 44, pp. 924-37.CrossRefGoogle Scholar
  25. 25.
    Z. Guo, J. Mi, S. Xiong and P.S. Grant, J Comput Phys, 2014, vol. 257, pp. 278-97.CrossRefGoogle Scholar
  26. 26.
    A. Zhang, Z. Guo, and S.M. Xiong: Phys. Rev. E, 2018, vol. 97 (5), art. no. 053302.Google Scholar
  27. 27.
    T. Krüger, H. Kusumaatmaja, A. Kuzmin, O. Shardt, G. Silva and E.M. Viggen. The Lattice Boltzmann Method Principles and Practice, Springer, Switzerland, 2017.CrossRefGoogle Scholar
  28. 28.
    S. Chen and G.D. Doolen, Annu Rev Fluid Mech, 1998, vol. 30, pp. 329-64.CrossRefGoogle Scholar
  29. 29.
    A. Fakhari, M. Geier and T. Lee, J Comput Phys, 2016, vol. 315, pp. 434-57.CrossRefGoogle Scholar
  30. 30.
    X. Zhang, J. Kang, Z. Guo, S. Xiong and Q. Han, Comput Phys Commun, 2018, vol. 223, pp. 18-27.CrossRefGoogle Scholar
  31. 31.
    W. Miller, S. Succi and D. Mansutti, Phys Rev Lett, 2001, vol. 86, pp. 3578-81.CrossRefGoogle Scholar
  32. 32.
    W. Miller, J Cryst Growth, 2001, vol. 230, pp. 263-69.CrossRefGoogle Scholar
  33. 33.
    W. Miller and S. Succi, J Stat Phys, 2002, vol. 107, pp. 173-86.CrossRefGoogle Scholar
  34. 34.
    D. Medvedev and K. Kassner: Phys. Rev. E, 2005, vol. 72 (5 Pt 2), art. no. 056703.Google Scholar
  35. 35.
    D. Medvedev, T. Fischaleck, and K. Kassner: Phys. Rev. E, 2006, vol. 74 (3), art. no. 031606.Google Scholar
  36. 36.
    S. Sakane, T. Takaki, R. Rojas, M. Ohno, Y. Shibuta, T. Shimokawabe and T. Aoki, J Cryst Growth, 2017, vol. 474, pp. 154-59.CrossRefGoogle Scholar
  37. 37.
    T. Takaki, R. Rojas, S. Sakane, M. Ohno, Y. Shibuta, T. Shimokawabe and T. Aoki, J Cryst Growth, 2017, vol. 474, pp. 146-53.CrossRefGoogle Scholar
  38. 38.
    S. Sakane, T. Takaki, M. Ohno, Y. Shibuta, T. Shimokawabe and T. Aoki, J Cryst Growth, 2018, vol. 483, pp. 147-55.CrossRefGoogle Scholar
  39. 39.
    R. Siquieri and H. Emmerich, Philos Mag, 2011, vol. 91, pp. 45-73.CrossRefGoogle Scholar
  40. 40.
    D. Raabe, Modelling Simul. Mater. Sci. Eng., 2004, vol. 12, pp. R13-46.CrossRefGoogle Scholar
  41. 41.
    P.L. Bhatnagar, E.P. Gross and M. Krook, Phys. Rev., 1954, vol. 94, pp. 511-25.CrossRefGoogle Scholar
  42. 42.
    Z. Guo, C. Zheng, and B. Shi: Phys. Rev. E, 2002, vol. 65 (4), art. no. 046308.Google Scholar
  43. 43.
    Z. Guo and S.M. Xiong, Comput Phys Commun, 2015, vol. 190, pp. 89-97.CrossRefGoogle Scholar
  44. 44.
    J. Du, Z. Guo, A. Zhang, M. Yang, M. Li, and S. Xiong: Sci. Rep. UK, 2017, vol. 7 (1), art. no. 013600.Google Scholar
  45. 45.
    J. Du, A. Zhang, Z. Guo, M. Yang, M. Li and S. Xiong, Intermetallics, 2018, vol. 95, pp. 119-29.CrossRefGoogle Scholar
  46. 46.
    A. Zhang, Z. Guo, and S.M. Xiong: J. Appl. Phys., 2017, vol. 121 (12), art. no. 125101.Google Scholar
  47. 47.
    M. Berger and I. Rigoutsos, IEEE Trans. Syst. Man Cybern., 1991, vol. 21, pp. 1278-86.CrossRefGoogle Scholar
  48. 48.
    O. Filippova and D. Hänel, J Comput Phys, 1998, vol. 147, pp. 219-28.CrossRefGoogle Scholar
  49. 49.
    O. Filippova and D. Hänel, J Comput Phys, 2000, vol. 165, pp. 407-27.CrossRefGoogle Scholar
  50. 50.
    A. Dupuis and B. Chopard: Phys. Rev. E, 2003, vol. 67 (6), art. no. 066707.Google Scholar
  51. 51.
    C.J. Vreeman, M.J.M. Krane and F.P. Incropera, Int. J. Heat Mass Transf., 2000, vol. 43, pp. 677-86.CrossRefGoogle Scholar
  52. 52.
    C.J. Vreeman and F.P. Incropera, Int J Heat Mass Tran, 2000, vol. 43, pp. 687-704.CrossRefGoogle Scholar
  53. 53.
    R.S. Maier, R.S. Bernard and D.W. Grunau, Phys Fluids, 1996, vol. 8, pp. 1788-1801.CrossRefGoogle Scholar
  54. 54.
    A. Bogno, H. Nguyen-Thi, B. Billia, N. Bergeon, N. Mangelinck-Noel, E. Boller, T. Schenk and J. Baruchel, T Indian I Metals, 2009, vol. 62, pp. 427-31.CrossRefGoogle Scholar
  55. 55.
    N. Shevchenko, O. Roshchupkina, O. Sokolova and S. Eckert, J Cryst Growth, 2015,, vol. 417, pp. 1-08.CrossRefGoogle Scholar
  56. 56.
    S. Karagadde, L. Yuan, N. Shevchenko, S. Eckert and P.D. Lee, Acta Mater, 2014, vol. 79, pp. 168-80.CrossRefGoogle Scholar
  57. 57.
    C.W. Lan and C.J. Shih, J Cryst Growth, 2004, vol. 264, pp. 472-82.CrossRefGoogle Scholar
  58. 58.
    K. Murakami, T. Fujiyama, A. Koike and T. Okamoto, Acta Metallurgica, 1983, vol. 31, pp. 1425-32.CrossRefGoogle Scholar
  59. 59.
    K. Murakami, H. Aihara and T. Okamoto, Acta Metallurgica, 1984, vol. 32, pp. 933-39.CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2018

Authors and Affiliations

  1. 1.School of Materials Science and EngineeringTsinghua UniversityBeijingChina
  2. 2.Materials Technology, GM Global Powertrain EngineeringPontiacUSA
  3. 3.Key Laboratory for Advanced Materials Processing Technology, Ministry of EducationTsinghua UniversityBeijingChina

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