The solidification of a dilute alloy (bismuth-tin) under Bridgman crystal growth conditions is investigated. Computations are performed in two dimensions with a uniform grid. The simulation includes the species concentration, temperature and flow fields, as well as conduction in the ampoule. Fully transient simulations have been performed, with no simplifying steady state approximations. Results are obtained under microgravity conditions for pure bismuth, and for Bi-0.1 at.% Sn and Bi-1.0 at.% Sn alloys, and compared with experimental results obtained from crystals grown in the microgravity environment of space. For the Bi-1.0 at.% Sn case the results indicate that a secondary convective cell, driven by solutal gradients, forms near the interface. The magnitude of the velocities in this cell increases with time, causing increasing solute segregation at the solid/liquid interface. Finally, a comparison between model predictions and results obtained from a space experiment is reported. The concentration-dependence of the alloy melting temperature is incorporated in the model for this case. Satisfactory correspondence is obtained between the predicted and experimental results in terms of solute concentrations in the solidified crystal.

Issue Section:
Heat Transfer in Manufacturing
Keywords:
bismuth alloys, tin alloys, crystal growth from melt, liquid alloys, liquid metals, zero gravity experiments, convection, dilute alloys
Topics:
Alloys, Convection, Crystal growth, Simulation, Temperature, Tin, Tin alloys, Melting, Solidification
1.
Abbaschian, R., Gokhale, A. B., Favier, J. J., and Coriell, S. R., 1992, “In-Situ Monitoring of Crystal Growth Using MEPHISTO,” NASA Science Requirements Document (SRD), NASA.
2.
Abbaschian, R., 1996, In-Situ Monitoring of Crystal Growth Using MEPHISTO: Revised Science Requirements Document (RSRD) for the Re-flight of MEPHISTO aboard USMP-4, NASA.
3.
Yeoh
,
G. H.
,
de Vahl Davis
,
G.
,
Leonardi
,
E.
,
de Groh
, III,
H. C.
, and
Yao
,
M.
,
1997
, “
A Numerical and Experimental Study of Natural Convection and Interface Shape in Crystal Growth
,”
J. Cryst. Growth
,
173
, pp.
492
–
502
.
4.
Yao
,
M.
, and
de Groh
, III,
H. C.
,
1993
, “
Three-Dimensional Finite Element Method Simulation of Bridgman Crystal Growth and Comparison With Experiments
,”
Numer. Heat Transfer, Part A
,
24
, pp.
393
–
412
.
5.
de Groh III, H. C., and Yao, M., 1994, “Numerical and Experimental Study of Transport Phenomena in Directional Solidification of Succinonitrile,” Transport Phenomena in Solidification, ASME HTD-Vol. 284, pp. 227–243.
6.
Yao, M., de Groh III, H. C., and Abbaschian, R., 1997, “Numerical Modeling of Solidification in Space With MEPHISTO-4 (Part 1),” 35th Aerospace Sciences Meeting and Exhibit, Reno, NV, Paper AIAA 97-0449.
7.
de Groh III, H. C., and Nelson, E. S., 1994, “On Residual Acceleration During Space Experiments,” Heat Transfer in Microgravity Systems, ASME HTD-Vol. 290, pp. 23–33.
8.
Yao, M., Raman, R., and de Groh III, H. C., 1995, “Numerical Simulation of Heat and Mass Transport During Space Crystal Growth With MEPHISTO,” NASA Technical Memorandum 107015, NASA.
9.
Kurz, W., and Fisher, D. J., 1989, Fundamentals of Solidification, Trans Tech Publications.
10.
Alexander
,
J. I. D.
,
Ouazzani
,
J.
, and
Rosenberger
,
F.
,
1989
, “
Analysis of the Low Gravity Tolerance of Bridgman-Stockbarger Crystal Growth
,”
J. Cryst. Growth
,
97
, pp.
285
–
302
.
11.
Simpson, J. E., Yao, M., de Groh III, H. C., and Garimella, S. V., 1998, “Numerical Modeling of Solidification in Space With MEPHISTO-4 (Part 2),” NASA Technical Memorandum TM-1998-206630, NASA.
12.
Adornato
,
P. M.
, and
Brown
,
R. A.
,
1987
, “
Convection and Segregation in Directional Solidification of Dilute and Non-Dilute Binary Alloys
,”
J. Cryst. Growth
,
80
, pp.
155
–
190
.
13.
Liang
,
M. C.
, and
Lan
,
C. W.
,
1996
, “
Three-Dimensional Convection and Solute Segregation in Vertical Bridgman Crystal Growth
,”
J. Cryst. Growth
,
167
, pp.
320
–
332
.
14.
Simpson
,
J. E.
, and
Garimella
,
S. V.
,
1998
, “
An Investigation of the Solutal, Thermal and Flow Fields in Unidirectional Alloy Solidification
,”
Int. J. Heat Mass Transf.
,
41
, pp.
2485
–
2502
.
15.
Timchenko
,
V.
,
Chen
,
P. Y. P.
,
Leonardi
,
E.
,
de Vahl Davis
,
G.
, and
Abbaschian
,
R.
,
2000
, “
A Computational Study of Transient Plane Front Solidification of Alloys in a Bridgman Apparatus Under Microgravity Conditions
,”
Int. J. Heat Mass Transf.
,
43
, pp.
963
–
980
.
16.
Zeng
,
X.
, and
Faghri
,
A.
,
1994
, “
Temperature-Transforming Model for Binary Solid–Liquid Phase-Change Problems: Part 1—Mathematical Modeling and Numerical Methodology
,”
Numer. Heat Transfer, Part B
,
25
, pp.
467
–
480
.
17.
Swaminathan
,
C. R.
, and
Voller
,
V. R.
,
1997
, “
Towards a General Numerical Scheme for Solidification Systems
,”
Int. J. Heat Mass Transf.
,
30
, pp.
2859
–
2868
.
18.
Voller
,
V. R.
,
Brent
,
A. D.
, and
Prakash
,
C.
,
1989
, “
The Modeling of Heat, Mass and Solute Transport in Solidification Systems
,”
Int. J. Heat Mass Transf.
,
32
, pp.
1719
–
1731
.
19.
Simpson
,
J. E.
, and
Garimella
,
S. V.
,
2000
, “
The Influence of Gravity Levels on the Horizontal Bridgman Crystal Growth of an Alloy
,”
Int. J. Heat Mass Transf.
,
43
, pp.
1905
–
1923
.
20.
Timchenko, V., Leonardi, E., and de Vahl Davis, G., 1997, “FRECON3V User’s Manual,” University of New South Wales, School of Mechanical and Manufacturing Engineering, Report 1997/FMT/1, and FRECON3V Programmer’s Manual, Report 1997/FMT/2.
21.
Samarskii
,
A. A.
, and
Andreyev
,
V. B.
,
1963
, “
On a High-Accuracy Difference Scheme for an Elliptic Equation With Several Space Variables
,”
USSR Comput. Math. Math. Phys.
,
3
, pp.
1373
–
1382
.
22.
Hirt
,
C. W.
, and
Nichols
,
B. D.
,
1981
, “
Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries
,”
J. Comput. Phys.
,
39
, pp.
210
–
225
.
23.
Ferziger, J. H., and Peric´, M., 1996, Computational Methods for Fluid Dynamics, Springer-Verlag, New York.
24.
Smith
,
V. G.
,
Tiller
,
W. A.
, and
Rutter
,
J. W.
,
1955
, “
A Mathematical Analysis of Solute Redistribution During Solidification
,”
Can. J. Phys.
,
33
, pp.
723
–
743
.
Copyright © 2001
 by ASME
You do not currently have access to this content.