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Heat Transfer Model of Directional Solidification by LMC Process for Superalloy Casting Based on Finite Element Method

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Abstract

With the rapid development of the aviation industry, the turbine blade, a critical component of the aeronautical engine, has come to be widely produced by liquid-metal cooling (LMC) process. A temperature- and time-dependent heat transfer coefficient was used to represent the heat convection between the shell and the cooling liquid, and an improved Monte Carlo ray-tracing approach was adopted to handle the boundary of radiation heat transfer. Unstructured mesh was used to fit the irregular shell boundary, and the heat transfer model of directional solidification by LMC process based on finite element method (FEM) was established. The concept of local matrix was here proposed to guarantee computational efficiency. The pouring experiments of directional solidification by LMC process were carried out, then simulation and experimental results were compared here. The accuracy of the heat transfer model was validated by the cooling curves and grain morphology, and the maximum relative error between simulation and experimental cooling curve was 2 pct. The withdrawal rate showed an important influence on the shape of solidification interface, and stray grain is liable to be generated on the bottom of platform at an excessive withdrawal rate.

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References

  1. G. A. Chadwick: Corros. Eng. Sci. Technol., 1984, vol. 19, no. 4, pp. 154–55.

    Google Scholar 

  2. D. X. Ma: Acta. Metall. Sin., 2015, vol. 51, no. 10, pp. 1179–90.

    Google Scholar 

  3. H. Fu, X. Geng: Sci. Technol. Adv. Mat., 2001, vol. 2, no. 1, pp. 197–204.

    Article  Google Scholar 

  4. N. Tang, Y. L. Wang, Q. Y. Xu, X. H. Zhao and B. C. Liu: Acta. Metall. Sin., 2015, vol. 51, no. 4, pp. 499–512.

    Google Scholar 

  5. C. H. Lund, J. Hockin: Superalloys, Wiley, New York, 1972, pp. 403–25

    Google Scholar 

  6. M. Konter, M. Thumann: J. Mater. Process. Technol., 2001, vol. 117, no. 3, pp. 386–90.

    Article  Google Scholar 

  7. J. Zhang, T. W. Huang, L. Liu and H. Z. Fu: Acta. Metall. Sin., 2015, vol. 51, no. 10, pp. 1163–78.

    Google Scholar 

  8. A. F. Giamei, J. G. Tschinkel: Metall. Mater. Trans. A, 1976, vol. 7A, no. 9, pp. 1427–34.

    Article  Google Scholar 

  9. J. H. Liu, L. Liu, T. W. Huang, B. M. Ge, J. Zhang, H. Z. Fu, B. Yu, G. Q. Su, P. H. Wang and X. F. Liu: Foundry, 2010, vol. 59, no. 8, pp. 822–25.

    Google Scholar 

  10. A. J. Elliott, S. Tin, W. T. King, S. C. Huang, M. F. X. Gigliotti and T. M. Pollock: Metall. Mater. Trans. A, 2004, vol. 35A, no. 10, pp. 3221–31.

    Article  Google Scholar 

  11. A. J. Elliott, G. B. Karney, M. F. X. Gigliotti and T. M. Pollock: Superalloys, TMS, Warrendale, 2004, pp. 421–30

    Google Scholar 

  12. J. Zhang, L. H. Lou: J. Mater. Sci. Technol., 2007, vol. 23, no. 3, pp. 289–300.

    Article  Google Scholar 

  13. G. Liu, L. Liu, X. B. Zhao, W. G. Zhang, T. Jin, J. Zhang and H. Z. Fu: Acta. Metall. Sin., 2010, vol. 46, no. 1, pp. 77–83.

    Article  Google Scholar 

  14. C. L. Brundidge, D. Vandrasek, B. Wang and T. M. Pollock: Metall. Mater. Trans. A, 2012, vol. 43A, no. 3, pp. 965-76.

    Article  Google Scholar 

  15. J. D. Miller, T. M. Pollock: Metall. Mater. Trans. A, 2012, vol. 43A, no. 7, pp. 2414–25.

    Article  Google Scholar 

  16. R. E. Napolitano, R. J. Schaefer: J. Mater. Sci., 2000, vol. 35, no. 7, pp. 1641–59.

    Article  Google Scholar 

  17. A. Kermanpur, N. Varahram, P. Davami and M. Rappaz: Metall. Mater. Trans. B, 2000, vol. 31, no. 6, pp. 1293–304.

    Article  Google Scholar 

  18. A. J. Elliott, T. M. Pollock: Metall. Mater. Trans. A, 2007, vol. 38A, no. 4, pp. 871–82.

    Article  Google Scholar 

  19. Y. Z. Lu, D. W. Wang, J. Zhang and L. H. Lou: Foundry, 2009, vol. 58, no. 3, pp. 245–48.

    Google Scholar 

  20. Y. Z. Lu, H. J. Xi, J. Shen, W. Zheng, G. Xie, L. H. Lou and J. Zhang: Acta. Metall. Sin., 2015, vol. 51, no. 5, pp. 603–11.

    Google Scholar 

  21. X. W. Yan, N. Tang, X. F. Liu, G. Y. Shui, Q. Y. Xu and B. C. Liu: Acta. Metall. Sin., 2015, vol. 51, no. 10, pp. 1288–96.

    Google Scholar 

  22. A. R. Mitchell, D. F. Griffiths: The Finite Difference Method in Partial Differential Equations, Wiley, Hoboken, 1980.

    Google Scholar 

  23. H. K. Versteeg, W. Malalasekera: An Introduction to Computational Fluid Dynamics: The Finite Volume Method, Pearson Education, New York, 2007.

    Google Scholar 

  24. G. Dhatt, E. Lefrançois and G. Touzot: Finite Element Method, Wiley, Hoboken, 2012.

    Book  Google Scholar 

  25. G. Vladimir: Materials in technology, 2009, vol. 43, no. 5, pp. 233–37.

    Google Scholar 

  26. T. Chen, D. M. Liao and J. X. Zhou: Materials Science Forum, 2013, vol. 762, pp. 224–29.

    Article  Google Scholar 

  27. S. Perron, S. Boivin and J. Hérard: Comput. Fluids, 2004, vol. 33, no. 10, pp. 1305–33.

    Article  Google Scholar 

  28. W. Gao, Y. L. Duan and R. X. Liu: J. Hydrodyn., 2009, vol. 21, no. 2, pp. 201–11.

    Article  Google Scholar 

  29. T. Chen: PhD Thesis, Huazhong University of Science and Technology, 2013.

  30. L. Cao, D. M. Liao, L. M. Cao, H. P. Gu, T. Chen and S. Y. Pang: Foundry, 2014, vol. 63, no. 12, pp. 1235-40.

    Google Scholar 

  31. X. C. Wang: Finite Element Method, Tsinghua University Press, Beijing, 2003.

    Google Scholar 

  32. K. Cui, Q. Y. Xu, J. Yu, B. C. Liu, A. Kimatsuka, Y. Kuroki and F. Yokoyama: Acta. Metall. Sin., 2007, vol. 43, no. 5, pp. 465–71.

    Google Scholar 

  33. J. Yu, Q. Y. Xu, J. R. Li, H. L. Yuan, S. Z. Liu and B. C. Liu: Acta. Metall. Sin., 2007, vol. 43, no. 10, pp. 1113–20.

    Google Scholar 

  34. D. Pan, Q. Y. Xu and B. C. Liu: Acta. Metall. Sin., 2010, vol. 46, no. 3, pp. 294–303.

    Article  Google Scholar 

  35. S. S. Kutateladze, V. M. Borishanskii: Liquid-Metal Heat Transfer Media, Consultants Bureau, New York, 1959.

    Book  Google Scholar 

  36. X. F. Sun, T. Jin, Y. Z. Zhou and Z. Q. Hu: Mater. China, 2012, vol. 31, no. 12, pp. 1–11.

    Google Scholar 

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Acknowledgments

This research is financially supported by the Program for New Century Excellent Talents in University (No. NCET-13-0229, NCET-09-0396), the National Science & Technology Key Projects of Numerical Control (No. 2012ZX04010-031, 2012ZX0412-011), and the National High Technology Research and Development Program (“863” Program) of China (No. 2013031003).

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Correspondence to Yuzhang Lu.

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Manuscript submitted January 20, 2016

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Cao, L., Liao, D., Lu, Y. et al. Heat Transfer Model of Directional Solidification by LMC Process for Superalloy Casting Based on Finite Element Method. Metall Mater Trans A 47, 4640–4647 (2016). https://doi.org/10.1007/s11661-016-3619-z

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