China Foundry

, Volume 16, Issue 5, pp 326–335 | Cite as

Global heat transfer model and dynamic ray tracing algorithm for complex multiple turbine blades of Ni-based superalloys in directional solidification process

  • Wen Wang
  • Jian-xin Zhou
  • Zhao GuoEmail author
  • Ya-jun Yin
  • Xu Shen
  • Xiao-yuan Ji
Research & Development


High-quality solidification microstructure during directional solidification relies on precise temperature gradient control, so accurate calculation of the temperature field is critical. In this study, a 3D transient global heat transfer model of directional solidification by the Bridgman method based on the finite difference method is developed. The radiation heat in this model is calculated by the discrete transfer method, and a modified method of external surface area for irregular geometric models is proposed to reduce the zigzag shape caused by finite difference grids. Considering the radiative heat transfer between any surface elements of all materials in the directional solidification furnace, a dynamic ray tracing algorithm is developed to simulate the entire process of directional solidification. Then, the simulated results are compared with the theoretical results and experimental results, respectively. Finally, based on the present model and method, the simulation program developed is applied to the directional solidification of actual castings. The simulated results are in good agreement with the experimental results, which indicate that the model and method developed in this study is effective and practical.

Key words

radiative heat transfer ray tracing turbine blade directional solidification numerical simulation 

CLC numbers




  1. [1]
    Rezaei M, Kermanpur A, Sadeghi F. Effects of withdrawal rate and starter block size on crystal orientation of a single crystal Ni-based superalloy. J. Cryst. Growth, 2018, 485: 19–27.CrossRefGoogle Scholar
  2. [2]
    Wang F, Ma D, Zhang J, et al. Effect of solidification parameters on the microstructures of superalloy CMSX-6 formed during the downward directional solidification process. J. Cryst. Growth, 2014, 389: 47–54.CrossRefGoogle Scholar
  3. [3]
    Szeliga D, Kubiak K, Sieniawski J. Control of liquidus isotherm shape during solidification of Ni-based superalloy of single crystal platforms. J. Mater. Process Technol., 2016, 234: 18–26.CrossRefGoogle Scholar
  4. [4]
    Lian Y, Li D, Zhang K. Effects of the location of a cast in the furnace on flatness of the solidification front in directional solidification. J. Cryst. Growth, 2016, 451: 33–41.CrossRefGoogle Scholar
  5. [5]
    Thomas B G, Goettsch D D. Modeling the directional solidification process. In: Proc. the 5th International Conference on Modeling of Casting, Welding and Advanced Solidification Processes (MCWASP), edited by Rappaz M, Ozgu M R, Mahin K W. The Minerals, Metals and Materials Society, 1991.Google Scholar
  6. [6]
    Galantucci L M, Tricarico L. A computer-aided approach for the simulation of the directional-solidification process for gas turbine blades. J. Mater. Process. Technol., 1998, 77: 160–164.CrossRefGoogle Scholar
  7. [7]
    Elliott A J, Pollock T M. Thermal analysis of the Bridgman and Liquid-Metal-Cooled directional solidification investment casting processes. Metall. Mater. Trans. A, 2007, 38: 871–882.CrossRefGoogle Scholar
  8. [8]
    Miller J D. Heat extraction and dendritic growth during directional solidification of single-crystal nickel-base superalloys. University of Michigan, M1-Doctor, 2011.Google Scholar
  9. [9]
    Yu J, Xu Q Y, Cui K, et al. Numerical simulation of solidification process on single crystal Ni-based superalloy investment castings. J. Mater. Sci. Technol., 2007, 23: 47–54.Google Scholar
  10. [10]
    Yan X W, Zhang H, Tang N, et al. Multi-scale simulation of single crystal hollow turbine blade manufactured by liquid metal cooling process. Prog. Nat. Sci. Mater. Int., 2018, 28: 78–84.CrossRefGoogle Scholar
  11. [11]
    Pan D, Xu Q Y, Liu B C. Modeling on directional solidification of superalloy blades with furnace wall temperature evolution. Acta Metall. Sin., 2010: 294–303.CrossRefGoogle Scholar

Copyright information

© Foundry Journal Agency and Springer Singapore 2019

Authors and Affiliations

  • Wen Wang
    • 1
  • Jian-xin Zhou
    • 1
  • Zhao Guo
    • 1
    Email author
  • Ya-jun Yin
    • 1
  • Xu Shen
    • 1
  • Xiao-yuan Ji
    • 1
  1. 1.State Key Laboratory of Materials Processing and Die & Mould TechnologyHuazhong University of Science and TechnologyWuhanChina

Personalised recommendations