Experiments were performed with binary metal alloys to validate a continuum mixture model for alloy solidification. Ingots of two compositions, Pb-20%Sn and Pb-40%Sn, were cast in a permanent mold, and the solidification process was simulated. Temperature histories were measured during casting, and composition profiles were found in the solidified ingot. Dendritic arm spacings were found from optical micrographs of the alloy microstructure and used to determine a constant in the Blake-Kozeny submodel for the mushy zone permeability in the liquid-solid interaction term of the momentum equations. Scaling analysis from a previous work and a large uncertainty in the permeability constant suggested that predictions of the composition are extremely sensitive to the choice of a permeability model. Three simulations of each casting were performed using the permeability constant as a parameter, and measured temperatures and compositions were compared with predictions based on different model constants. In the region of the liquidus interface, where all of the significant advection of solute takes place, the results suggest that the Blake-Kozeny model based on measured dendritic arm spacings significantly underpredicts the resistance of the dendritic array to fluid flow.

1.
Asai
 
S.
, and
Muchi
 
I.
,
1978
, “
Theoretical Analysis and Model Experiments on the Formation Mechanism of Channel-Type Segregation
,”
Trans. ISIJ.
, Vol.
18
, pp.
90
98
.
2.
Bennon
 
W. D.
, and
Incropera
 
F. P.
,
1987
a, “
A Continuum Model for Momentum, Heat and Species Transport in a Binary Solid-Liquid Phase Change System: I. Model Formulation
,”
Int. J. Heat Mass Trans.
, Vol.
30
, pp.
2161
2170
.
3.
Bennon
 
W. D.
, and
Incropera
 
F. P.
,
1987
b, “
A Continuum Model for Momentum, Heat and Species Transport in a Binary Solid-Liquid Phase Change System: II. Application to Solidification in a Rectangular Cavity
,”
Int. J. Heat Mass Trans.
, Vol.
30
, pp.
2171
2187
.
4.
Bird, R. B., Stewart, W. E., and Lightfoot, E. N., 1960, Transport Phenomena, John Wiley & Sons Inc., New York.
5.
Flemings, M. C., 1974, Solidification Processing, McGraw-Hill Inc., New York.
6.
Hills
 
R. N.
,
Loper
 
D. E.
, and
Roberts
 
P. H.
,
1983
, “
A Thermodynamically Consistent Model of a Mushy Zone
,”
Q. J. Mech. Appl. Math.
, Vol.
36
, pp.
505
539
.
7.
Krane, M. J. M., 1996, “Transport Phenomena During the Solidification of Binary and Ternary Metal Alloys,” Ph.D. dissertation, School of Mechanical Engineering, Purdue University, West Lafayette, IN.
8.
Krane
 
M. J. M.
, and
Incropera
 
F. P.
,
1996
, “
A Scaling Analysis of the Unidirectional Solidification of a Binary Alloy
,”
Int. J. Heat Mass Trans.
, Vol.
39
, pp.
3567
3579
.
9.
Piwonka
 
T. S.
, and
Flemings
 
M. C.
,
1966
, “
Pore Formation in Solidification
,”
Trans. Met. Soc. AIME
, Vol.
236
, pp.
1157
1165
.
10.
Prescott, P. J., 1992, “Convective Transport Phenomena During Solidification of Binary Metal Alloys and the Effect of Magnetic Fields,” Ph.D. dissertation. School of Mechanical Engineering, Purdue University, West Lafayette, IN.
11.
Prescott, P. J., and Incropera, F. P., 1996, “Convection Heat and Mass Transfer in Alloy Solidification,” Advances in Heat Transfer, J. P. Hartnett, T. Irvine, Jr., Y. I. Cho, and G. A. Green, eds., Vol. 28, Academic Press, New York, pp. 231–338.
12.
Prescott
 
P. J.
,
Incropera
 
F. P.
, and
Bennon
 
W. D.
,
1991
, “
Modelling of Dendritic Solidification Systems: Reassessment of the Continuum Momentum Equation
,”
Int. J. Heat Mass Trans.
, Vol.
34
, pp.
2351
2359
.
13.
Prescott
 
P. J.
,
Incropera
 
F. P.
, and
Gaskell
 
D. R.
,
1994
, “
Convective Transport Phenomena and Macrosegregation During Solidification of a Binary Metal Alloy: II—Experiments and Comparisons With Numerical Predictions
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
116
, pp.
742
749
.
14.
Reddy
 
A. V.
, and
Beckermann
 
C.
,
1993
, “
Measurements of Metal-Mold In-terfacial Solidification of Sn and Sn-Pb Alloys
,”
Exp. Heat Transfer
, Vol.
6
, pp.
111
129
.
15.
Schneider
 
M. C.
, and
Beckermann
 
C.
,
1995
, “
A Numerical Study of the Combined Effects of Microsegregation, Mushy Zone Permeability and Flow, Caused by Volume Contraction and Thermosolutal Convection, on Macrosegregation and Eutectic Formation in Binary Alloy Solidification
,”
Int. J. Heat Mass Trans.
, Vol.
38
, pp.
3455
3473
.
16.
Shahani
 
H.
,
Amberg
 
G.
, and
Fredriksson
 
H.
,
1992
, “
On the Formation of Macrosegregations in Unidirectional Solidified Sn-Pb and Pb-Sn Alloys
,”
Met. Trans. A
, Vol.
23
A, pp.
2301
2311
.
17.
West
 
R.
,
1985
, “
On the Permeability of the Two-Phase Zone During Solidification of Alloys
,”
Met. Trans. A
, Vol.
16A
, p.
693
693
.
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