A numerical study of the combined effects of microsegregation, mushy zone permeability and fllow, caused by volume contraction and thermosolutal convection, on macrosegregation and eutectic formation in binary alloy solidification

Abstract Numerical simulations of the columnar dendritic solidification of a Pb-20 wt% Sn alloy in a square cavity cooled from one side and fed by a rectangular riser are reported. Overall macrosegregation patterns predicted using Scheil and lever-rule type microsegregation models are found to be similar, although the predicted eutectic fraction is significantly higher with the Scheil-type model. The choice of mushy zone permeability function significantly affects the predicted number, length and orientation of segregated channels. The inclusion of shrinkage-driven flow leads to the prediction of the well-known inverse macrosegregation pattern. However, macrosegregation caused by thermosolutal convection readily masks the inverse segregation. The microsegregation models predict different solid concentrations and eutectic fractions, leading to different solid density distributions which, in turn, cause differences in the extent of contraction-driven flow.

[1]  F. Incropera,et al.  Three-Dimensional Considerations of Unidirectional Solidification in a Binary Liquid , 1993 .

[2]  Vijay K. Garg,et al.  A variable property analysis of alloy solidification using the anisotropic porous medium approach , 1992 .

[3]  Christoph Beckermann,et al.  Mathematical Modeling of Transport Phenomena During Alloy Solidification , 1993 .

[4]  Frank P. Incropera,et al.  Numerical simulation of a solidifying Pb-Sn alloy: The effects of cooling rate on thermosolutal convection and macrosegregation , 1991 .

[5]  H. Exner,et al.  Numerical calculation of microsegregation in coarsened dendritic microstructures , 1986 .

[6]  V. Voller,et al.  Dual scale model of segregation phenomena , 1994 .

[7]  R. Trivedi,et al.  Primary dendrite spacing of lead dendrites in Pb-Sn and Pb-Au Alloys , 1980 .

[8]  Chaoyang Wang,et al.  A multiphase solute diffusion model for dendritic alloy solidification , 1993, Metallurgical and Materials Transactions A.

[9]  R. Viskanta,et al.  Effect of anisotropic permeability on the transport process during solidification of a binary mixture , 1992 .

[10]  J. Drummond,et al.  Laminar viscous flow through regular arrays of parallel solid cylinders , 1984 .

[11]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[12]  W. Kurz,et al.  Fundamentals of Solidification , 1990 .

[13]  V. Voller,et al.  The modelling of heat, mass and solute transport in solidification systems , 1989 .

[14]  S. Felicelli,et al.  Simulation of freckles during vertical solidification of binary alloys , 1991 .

[15]  Andreas Acrivos,et al.  Slow flow past periodic arrays of cylinders with application to heat transfer , 1982 .

[16]  D. R. Poirier.  Permeability for flow of interdendritic liquid in columnar-dendritic alloys , 1987 .

[17]  Frank P. Incropera,et al.  Analysis of the effect of shrinkage on macrosegregation in alloy solidification , 1995 .

[18]  G. Amberg,et al.  On the formation of macrosegregations in unidirectionally solidified Sn-Pb and Pb-Sn alloys , 1992 .

[19]  H. Tsai,et al.  Modeling of solute redistribution in the mushy zone during solidification of aluminum-copper alloys , 1993 .

[20]  H. Tsai,et al.  Inverse segregation for a unidirectional solidification of aluminum-copper alloys , 1993 .

[21]  Qing-chun Li,et al.  NUMERICAL METHOD FOR SOLUTION OF STRONGLY COUPLED BINARY ALLOY SOLIDIFICATION PROBLEMS , 1991 .

[22]  Y. S. Touloukian.  Thermophysical properties of matter , 1970 .

[23]  David R Poirier,et al.  The energy and solute conservation equations for dendritic solidification , 1991 .

[24]  F. Weinberg,et al.  Macrosegregation during solidification resulting from density differences in the liquid , 1974, Metallurgical and Materials Transactions B.

[25]  F. Incropera,et al.  Effect of rotation on fluid motion and channel formation during unidirectional solidification of a binary alloy , 1993 .

[26]  H. Tsai,et al.  Interaction between shrinkage-induced fluid flow and natural convection during alloy solidification , 1992 .

[27]  Frank P. Incropera,et al.  The evolution of macrosegregation in statically cast binary ingots , 1987 .

[28]  D. R. Poirier.  Densities of Pb-Sn alloys during solidification , 1988 .

[29]  Vaughan R Voller.  Development and application of a heat balance integral method for analysis of metallurgical solidification , 1989 .

[30]  C. Beckermann,et al.  Effects of simplified enthalpy relations on the prediction of heat transfer during solidification of a lead-tin alloy , 1991 .

[31]  Vaughan R Voller,et al.  On the numerical solution of continuum mixture model equations describing binary solid-liquid phase change , 1989 .

[32]  Qingchun Li,et al.  GRAVITY- AND SOLIDIFICATION-SHRINKAGE-INDUCED LIQUID FLOW IN A HORIZONTALLY SOLIDIFIED ALLOY INGOT , 1991 .

[33]  H. Thresh,et al.  The viscosities of lead, tin, and Pb-Sn alloys , 1970 .