A Similarity Solution for the Directional Casting of Peritectic Alloys in the Presence of Shrinkage-Induced Flow

체적수축유동이 있는 포정합금의 방향성주조에 대한 상사해

  • Published : 2001.04.01


This paper presents a similarity solution for the directional casting of binary peritectic alloys in the presence of shrinkage-induced flow. The present model retains essential ingredients of alloy solidification, such as temperature-solute coupling, macrosegregation, solid-liquid property differences, and finite back diffusion in the primary phase. An algorithm for simultaneously determining the peritectic and liquidus positions is newly developed, which proves to be more efficient and stable than the existing scheme. Sample calculations are performed for both hypo- and hyper-peritectic compositions. The results show that the present analysis is capable of properly resolving the solidification characteristics of peritectic alloys so that it can be used for validating numerical models as a test solution.



  1. Beckermann, C. and Viskanta, R., 1993, 'Mathematical Modeling of Transport Phenomena during Alloy Solidification,' Appl Mech Rev, Vol. 46, pp. 1-27
  2. Ni, J. and Incropera, F. P., 1995, 'Extension of the Continuum Model for Transport Phenomena Occurring during Metal alloy Solidification-Ⅱ. Microscopic Considerations,' Int. J. Heat Mass Transfer, Vol. 38, pp. 1285-1296
  3. Schneider, M. C. and Beckermann, C., 1995, 'Formation of Macrosegregation by Multicomponent Thermosolutal Convection during the Solidification of Steel,' Metall. Trans. A, Vol. 26A, pp. 2373-2388
  4. Swaminathan, C. R. and Voller, V. R., 1997, 'Toward a General Numerical Scheme for Solidification Systems,' Int. J. Heat Mass Transfer, Vol. 40, pp. 2859-2868
  5. Krane, M. J. M., Incropera, F. P. and Gaskell, D. R., 1997, 'Solidification of Ternary Metal Alloys-Ⅰ.Model Development,' Int. J. Heat Mass Transfer, Vol. 40, pp. 3827-3835
  6. Krane, M. J. M. and Incropera, F. P., 1997, 'Solidification of Ternary Metal Alloys-Ⅱ.Predictions of Convective Phenomena and Solidification Behavior in Pb-Sb-Sn Alloys,' Int. J. Heat Mass Transfer, Vol. 40, pp. 3837-3847
  7. Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere Publ., New York
  8. Muehlbauer, J. C., Hatcher, J. D., Lyons, D. W. and Sunderland, J. E., 1973, 'Transient Heat Transfer Analysis of Alloy Solidification,' J. Heat Transfer, Vol. 95, pp. 324-331
  9. Worster, M. G., 1986, 'Solidification of an Alloy from am Cooled Boundary,' J. Fluid Mech., Vol. 167, pp. 481-501
  10. Braga, S. L. and Viskanta, R., 1990, 'Solidification of a Binary Alloy solution on a Cold Isothermal Surface,' Int. J. Heat Mass Transfer, Vol. 33, pp. 745-754
  11. Chung, J. D., Lee, J. S., Ro, S. T. and Yoo, H., 1999, 'An Analytical Approach to the Conduction-Dominated Solidification of Binary Mixtures,' Int. J. Heat Mass Transfer, Vol. 42, pp. 373-377
  12. Voller, V. R., 1997, 'A Similarity Solution for the Solidification a Multicomponent Alloy,' Int. J. Heat Mass Transfer, Vol. 40, pp. 2869-2877
  13. 정재동, 유호선, 이준식, 1998, '혼합물 응고문제에 대한 확장된 해석해,' 대한기계학회논문집(B), 제22권, 제2호, pp. 184-192
  14. Kurz, W. and Fisher, D. J., 1989, Fundamentals of Solidification, Trans. Tech. Publication, Switzerland
  15. Trivedi, R., 1995, 'Theory of Layered-Structure Formation in Peritectic Systems,' Metall. Mater. Trans. A, Vol. 26A, pp. 1583-1590
  16. Zeisler-Mashl, K. L. and Lograsso, T. A., 1997, 'The Occurrence and Periodicity of Oscillating Peritectic Microstructures Developed during Directional Solidification,' Metall. Mater. Trans. A, Vol. 28A, pp. 1543-1552
  17. Park, J.-S. and Trivedi, R., 1998, 'Convection-Induced Novel Oscillating Microstructure Formation in Peritectic Systems,' J. Crystal Growth, Vol. 187, pp. 511-515
  18. Clyne, T. W. and Kurz, W., 1981, 'Solute Redistribution during Solidification with Rapid State Diffusion,' Metall. Trans. A, Vol. 12A, pp. 965-971
  19. Ohno, A., 1976, The Solidification of Metals, Chijin Shokan, Japan
  20. Ni, J. and Beckermann, C., 1991, 'A Volume-Averaged Two-Phase Model for Transport Phenomena during Solidification,' Metall. Trans. B, Vol. 22B, pp. 349-361
  21. Touloukian, Y. S., Powell, R. W., Ho, C. Y. and Klemens, P. G., 1970, Thermophysical Properties of Matter, IFI/Plenum Press, New York/Washington
  22. Kaviany, M., 1998, Principles of Heat Transfer, Curse Pack, University of Michigan
  23. John, D. H. and Hogan, L. M., 1987, 'A simple Prediction of the Rate of the Peritectic Transformation,' Acta Metall., Vol. 35, pp. 171-174