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Convective instabilities during the solidification of an ideal ternary alloy in a mushy layer

Published online by Cambridge University Press:  18 March 2010

DANIEL M. ANDERSON ,
GEOFFREY B. McFADDEN ,
SAM R. CORIELL  and
BRUCE T. MURRAY
DANIEL M. ANDERSON*
Affiliation:
Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA Mathematical and Computational Sciences Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
GEOFFREY B. McFADDEN
Affiliation:
Mathematical and Computational Sciences Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
SAM R. CORIELL
Affiliation:
Metallurgy Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
BRUCE T. MURRAY
Affiliation:
Mathematical and Computational Sciences Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA Department of Mechanical Engineering, State University of New York at Binghamton, Binghamton, NY 13902, USA
*
†Email address for correspondence: danders1@gmu.edu
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Abstract

We consider a model for the solidification of an ideal ternary alloy in a mushy layer that incorporates the effects of thermal and solutal diffusion, convection and solidification. Our results reveal that although the temperature and solute fields are constrained to the liquidus surface of the phase diagram, the system still admits double-diffusive modes of instability. Additionally, modes of instability exist even in situations in which the thermal and solute fields are each individually stable from a static point of view. We identify these instabilities for a general model in which the base-state solution and its linear stability are computed numerically. We then highlight these instabilities in a much simpler model that admits an analytical solution.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 647: Dedicated to Professor S. H. Davis on his 70th birthday , 25 March 2010 , pp. 309 - 333
Copyright
Copyright © Cambridge University Press 2010

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References

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