An Extended Similarity Solution for One-Dimensional Multicomponent Alloy Solidification in the Presence of Shrinkage-Induced Flow

체적수축유동이 있는 일차원 다원합금 응고에 대한 확장된 해석해

  • 정재동 (서울대학교 정밀기계설계공동연구소) ;
  • 유호선 (숭실대학교 기계공학과) ;
  • 최만수 (서울대학교 기계항공공학부) ;
  • 이준식 (서울대학교 기계항공공학부)
  • Published : 2000.03.01


This paper deals with a generalized similarity solution for the one-dimensional solidification of ternary or higher-order multicomponent alloys. The present approach not only retains the existing features of binary systems such as temperature- solute coupling, shrinkage-induced flow, solid-liquid property differences, and finite back diffusion, but also is capable of handling a multicomponent alloy without restrictions on the partition coefficient and microsegregation parameter. For an alloy of N-solute species, governing equations in the mushy region reduce to (N+2) nonlinear ordinary differential equations via similarity transformation, which are to be solved along with the closed-form solutions for the solid and liquid regions. A linearized correction scheme adopted in the solution procedure facilitates to determine the solidus and liquidus positions stably. The result for a sample ternary alloy agrees excellently with the numerical prediction as well as the reported similarity solution. Additional calculations are also presented to show the utility of this study. Finally, it is concluded that the present analysis includes the previous analytical approaches as subsets.



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