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Modeling of solute redistribution in the mushy zone during solidification of aluminum-copper alloys

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Abstract

A mathematical model has been established to predict the formation of macrosegregation for a unidirectional solidification of aluminum-copper alloys cooled from the bottom. The model, based on the continuum formulation, allows the calculation of transient distributions of temperature, velocity, and species in the solidifying alloy caused by thermosolutal convection and shrinkage-induced fluid flow. Positive segregation in the casting near the bottom (inverse segregation) is found, which is accompanied by a moving negative-segregated mushy zone. The effects of shrinkage-induced fluid flow and solute diffusion on the formation of macrosegregation are examined. It is found that the redistribution of solute in the solidifying alloy is caused by the flow of solute-rich liquid in the mushy zone due to solidification shrinkage. A higher heat-extraction rate at the bottom increases the solidification rate, decreasing the size of the mushy zone, reducing the flow of solute-rich liquid in the mushy zone and, as a result, lessening the severity of inverse segregation. Comparisons between the theoretical predictions from the present study and previous modeling results and available experimental data are made, and good agreements are obtained.

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Abbreviations

c :

specific heat

C :

coefficient, defined in Eq. [9]

c l :

permeability coefficient, defined in Eq. [8]

d :

dendrite arm spacing

D :

mass-diffusion coefficient

f :

mass fraction

g :

volume fraction or gravitational acceleration

h :

enthalpy

H :

latent heat

k :

thermal conductivity

k p :

equilibrium partition ratio

K :

permeability

p :

pressure

t :

time

T :

temperature

T m :

fusion temperature at zero solute concentration

u :

velocity in thex-direction

v :

velocity in they-direction V velocity vector Vr relative velocity vector (Vl — Vs)

x, y :

Cartesian coordinates

β S :

solutal expansion coefficient

β T :

thermal expansion coefficient

ε:

rate of temperature change

μ:

dynamic viscosity

ρ:

density

0:

initial value

c :

chill

e :

eutectic

l :

liquid phase

m :

fusion

r :

relative to solid velocity

s :

vsolid phase

α :

constituent of alloy

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering and Engineering Mechanics, University of Missouri-Rolla, 65401, Rolla, MO

    Q. Z. Diao (Graduate Student) & H. L. Tsai (Associate Professor of Mechanical Engineering)

Authors
  1. Q. Z. Diao
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  2. H. L. Tsai
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Diao, Q.Z., Tsai, H.L. Modeling of solute redistribution in the mushy zone during solidification of aluminum-copper alloys. Metall Trans A 24, 963–973 (1993). https://doi.org/10.1007/BF02656518

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