Abstract
The results of the experiments with solidification in space imply that the effect of gravity conditions should be included into the theoretical and computational models of solidification processes. The paper presents the results of computational simulation of binary-alloy solidification where the gravity acts as the driving force of chemical diffusion. A simplified version of a complex theoretical model constructed by the same authors was implemented on a computer and used to simulate the solidification of a two-dimensional sample of the pseudo-binary mercury-cadmiumtelluride alloy. The computational model was used to study the influence of gravity on the chemical diffusion in the sample. The results of our simulations have shown that the influence of gravity on the diffussion of the solute is a second-order effect only. Therefore, to describe the influence of the gravitational field on solidification processes adequately we would need a more complex model involving convective phenomena in the melt as well. In addition, a series of numerical experiments were performed to consider how the accuracy with which the material parameters had been determined affects the computed temperature and concentration fields. The results imply that the simulation of this kind could be seriously biased by insufficient accuracy in determining the primary material properties. Moreover, the results show that neglecting the thermal diffusion and the temperature and concentration dependence of the material parameters may lead to serious errors.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alexiades V., Wilson D. G., Solomon A. D.: Quart. Appl. Math.43 (1985) 143.
Solomon A. D., Alexiades V., Wilson D. G.: SIAM J. Sci. Stat. Comput.6 (1985) 911.
Alexiades V., Geist G. A., Solomon A. D.: Res. Rep. ORNL-6127. Oak Ridge National Laboratory, Oak Ridge, 1985.
Vodák F., Černý R., Přikryl P.: Int. J. Heat Mass Transfer, in the press.
Vodák F.: A Model of the Discontinuity Surface in a Continuum and its Application to Solidification Processes (Thesis for the DrSc Degree). Czech Technical University, Prague, 1982 (in Czech).
Zienkiewicz O. C.: The Finite Element Method in Engineering Science. McGraw-Hill, London, 1971.
Finlayson B. A.: The Method of Weighted Residuals and Variational Principles. Academic Press, New York-London, 1972.
Connor J. J., Brebbia C. A.: Finite Element Techniques for Fluid Flow. Newnes-Butterworths, London, 1976.
Přikryl P., Vodák F.: The Influence of Gravity and Convection on the Stability of a Phase Interface (Res. Rep.). Inst. of Physics, Czechosl. Acad. Sci., Prague, 1984 (in Czech).
Chalmers B.: Principles of Solidification. Krieger, New York, 1977.
Flemings M. C.: Solidification Processing. McGraw-Hill, New York, 1974.
Woodruff D. P.: The Solid-Liquid Interface. Cambridge University Press, Cambridge, 1973.
Crowley A. B., Ockendon J. R.: Appl. Sci. Res.44 (1987) 1.
Lacey A. A., Tayler A. B.: IMA J. Appl. Math.30 (1983) 303.
Fasano A., Primicerio M.: IMA J. Appl. Math.41 (1988) 31.
Černý R., Přikryl P., Vodák F.: Czech. J. Phys.40 (1990) 301.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Černý, R., Přikryl, P. & Vodák, F. A two-dimensional model of binary-alloy solidification with a Mushy-zone. Czech J Phys 42, 411–430 (1992). https://doi.org/10.1007/BF01598739
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01598739