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Thermal and grain-structure simulation in a land-based turbine blade directionally solidified with the liquid metal cooling process

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Abstract

The thermal field and the grain structure of a cored superalloy turbine blade, which has been directionally solidified with the liquid metal cooling (LMC) process, has been simulated in three dimensions using a cellular automaton (CA) coupled with finite-element (CAFE) model. The cooling induced by the liquid aluminum bath has been replaced by a heat-transfer coefficient, whose temperature- and time-dependence has been adjusted on the basis of natural convection simulations and dimensionless analyses. The simulated grain structure and crystallographic texture have been compared with the microstructure, and the electron back-scattered diffraction (EBSD) results were obtained for a real blade. In both the experiment and the simulation, it has been found that the grains do not exhibit a well-defined <001> texture, even near the top of the blade, mainly as a result of a concave liquidus surface. In order to improve the texture and decrease the number of stray crystals, the LMC process was then optimized by changing several parameters. The baffle geometry, the liquid bath level, and the thermal conductivity of the ceramic mold were found to be the dominant parameters. Using the optimized design, the effect of the withdrawal rate on the resulting grain structure was investigated.

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Abbreviations

a 2, a 3 :

growth kinetics parameters (m s−1 °C−2, m s−1 °C−3)

β :

volumetric expansion of the liquid metal (°C−1)

c :

pseudobinary concentration (wt pct)

c i :

concentration of the element i (wt pct)

c p :

specific heat (J kg−1 °C−1)

D i :

diffusion coefficient of the element i in the liquid (m2 s−1)

ΔT :

temperature difference between the mold surface and the bath (°C)

ΔT :

undercooling (°C)

ΔT m :

mean undercooling of the Gaussian nucleation distribution (°C)

ΔT σ :

standard deviation of the Gaussian nucleation distribution (°C)

h :

heat-transfer coefficient (W m−2 °C−1)

g :

gravitation vector (m s−2)

Gr:

Grashof number (—)

k :

thermal conductivity (W m−1 °C−1)

ҟ:

pseudobinary partition coefficient (—)

k i :

partition coefficient of the element i (—)

L :

characteristic length (m)

L f :

latent heat of fusion (J kg−1)

μ :

dynamic viscosity (kg m−1 s−1)

\(\bar m\) :

pseudobinary liquidus slope (°C wt pct−1)

m i :

liquidus slope of the element i (°C wt pct−1)

n max :

maximum density of nuclei (m−2 or m−3)

Nu:

Nusselt number for natural convection (—)

Pr:

Prandtl number (—)

ρ :

specific mass (kg m−3)

t :

time (s)

t 0 :

time at which each element of the mold surface enters the bath level (s)

T :

temperature (°C)

T L :

liquidus temperature (°C)

T S :

solidus temperature (°C)

T b :

mean temperature of the liquid metal bath (°C)

ν:

withdrawal rate (mm min−1)

References

  1. R.F. Singer: in Materials for Advanced Power Engineering, Part II, D. Coutsouradis et al., eds., Kluwer Academic Publishers, Dordrecht, Netherlands, 1994, pp. 1707–29.

    Google Scholar 

  2. T.J. Fitzgerald and R.F. Singer: Metall. Mater. Trans. A, 1997, vol. 28A, pp. 1377–83.

    Article  CAS  Google Scholar 

  3. R.E. Shalin and V.A. Pankratov: Metall. Sci. Technol., 1992, vol. 10, pp. 3–9.

    CAS  Google Scholar 

  4. F. Hugo, H. Mayer, and R.F. Singer: 42nd Annual Technical Meeting 1994, Investment Casting Institute, Atlanta, GA, 1994, pp. 9:1–9:12.

    Google Scholar 

  5. J. Großmann, J. Preuhs, W. Eßer, and R.F. Singer: Int. Symp. on Liquid Metal Processing and Castings, Santa Fe, NM, Investment Casting Inst., Dallas TX, USA, 1994, 1999, pp. 31–40.

    Google Scholar 

  6. F. Hugo, U. Betz, J. Ren, S.-C. Huang, J.A. Bondarenko, and V. Gerasimov: Int. Symp. on Liquid Metal Processing and Castings, Santa Fe, NM, 1999, Vacuum Metallurgy Division of AVS (American Vacuum Soc., New York, 1999), pp. 16–30.

  7. A.F. Giamei and J.G. Tschinkel: Metall. Trans. A 1976, vol. 7A, pp. 1427–34.

    CAS  Google Scholar 

  8. S.L. Cockcroft, M. Rappaz, A. Mitchell, J. Fernihough, and A.J. Schmalz: in Materials for Advanced Power Engineering, Part II, D. Coutsouradis et al., eds, Kluwer Academic Publishers, Dordrecht, Netherlands, 1994, pp. 1145–54.

    Google Scholar 

  9. PROCAST User’s Manual and Technical Reference, Version 3.1.1, UES, Inc., Annapolis, MD, 1997.

  10. CALCOMOS User’s Manual and Technical Reference, Version 2.5.1, Calcom SA, Lausanne, Switzerland, 1997.

  11. C.-A. Gandin and M. Rappaz: Acta Mater., 1997, vol. 45, pp. 2187–95.

    Article  CAS  Google Scholar 

  12. C.-A. Gandin, J.-L. Desbiolles, P. Thévoz, and M. Rappaz: Metall. Mater. Trans. B 1999, vol. 30B, pp. 3151–65.

    Google Scholar 

  13. P. Magnin: Ph.D. Thesis, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland, 1985.

    Google Scholar 

  14. C.-A. Gandin, M. Rappaz, D. West, and B.L. Adams: Metall. Mater. Trans. A, 1995, vol. 26A, pp. 1543–52.

    CAS  Google Scholar 

  15. S. Henry, P. Jarry, P.-H. Jouneau, and M. Rappaz: Metall. Mater. Trans. A, 1997, vol. 28A, pp. 207–13.

    CAS  Google Scholar 

  16. MESHCAST User’s Manual and Technical Reference, Version 1.3.0, UES, Inc., Annapolis, MD, 1997.

  17. S.S. Kutateladze, V.M. Borishanskii, I.I. Novikov, and O.S. Fedynskii: Liquid Metal Heat Transfer Media, 1st ed., Chapman & Hall Ltd., London, 1959, pp. 82–86.

    Google Scholar 

  18. W. Kurz, B. Giovanola, and R. Trivedi: Acta Metall., 1986, vol. 34, pp. 823–30.

    Article  CAS  Google Scholar 

  19. M. Bobadilla, J. Lacaze, and G. Lesoult: J. Cryst. Growth, 1989, 531–44.

  20. M. Rappaz, S.A. David, J.M. Vitek, and L.A. Boatner: Metall. Trans. A, 1990, vol. 21A, pp. 1767–82.

    CAS  Google Scholar 

  21. J.L. Murray, L.H. Bennett, and H. Baker: Binary Alloys Phase Diagrams, ASM, Metals Park, OH, 1986, vol. 1–2.

    Google Scholar 

  22. H.P. Wang, J. Zou, E.M. Perry, and R. Doherty: AFS Trans., 1993, pp. 771–79.

  23. A. Kermanpur, N. Varahram, E. Engilei, M. Mohammadzadeh, and P. Davami: “Directional Solidification of IN 738LC Ni Base Superalloy to Improve Creep Properties”, Mater. Sci. Tech., 2000, 16(5), pp. 579–86.

    CAS  Google Scholar 

  24. M. Rappaz, C.-A. Gandin, J.-L. Desbiolles, and P. Thévoz: Metall. Mater. Trans. A, 1996, vol. 27A, pp. 695–705.

    CAS  Google Scholar 

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Authors and Affiliations

  1. the Materials Department, Ecole Polytechnique Federale de Lausanne, CH-1015, Lausanne, Switzerland

    A. Kermanpur (Postdoctoral Candidate and Fellow) & M. Rappaz (Professor)

  2. the Department of Materials Science and Engineering, Sharif University of Technology, Tehran, Iran

    N. Varahram (Assistant Professor) & P. Davami (Professor)

Authors
  1. A. Kermanpur
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  2. M. Rappaz
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  3. N. Varahram
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  4. P. Davami
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Kermanpur, A., Rappaz, M., Varahram, N. et al. Thermal and grain-structure simulation in a land-based turbine blade directionally solidified with the liquid metal cooling process. Metall Mater Trans B 31, 1293–1304 (2000). https://doi.org/10.1007/s11663-000-0017-z

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