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Natural Convection and Columnar-to-Equiaxed Transition Prediction in a Front-Tracking Model of Alloy Solidification

  • Symposia: Solidification Modeling and Microstructure ZFormation
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Abstract

A meso-scale front-tracking model (FTM) of nonequilibrium binary alloy dendritic solidification has been extended to incorporate Kurz, Giovanola, and Trivedi (KGT) dendrite kinetics and a Scheil solidification path. Model validation via comparison with thermocouple measurements from a solidification experiment, in which natural convection is limited by design, is presented. Via solution of the flow field due to natural thermal buoyancy, it is shown that resultant liquid-phase convection creates conditions in which equiaxed solidification is favored. Comparison with simulations in which casting solidification is diffusion controlled show that natural convection has greatest effect at intermediate times, but that at early and late stages of columnar solidification, the differences are relatively small. It is, however, during the time of greatest divergence between the simulations that the authors’ predictive index for equiaxed zone formation is enhanced most by convection. Finally, the columnar-to-equiaxed transition is directly simulated, in directional solidification controlled by diffusion.

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Abbreviations

c :

specific heat

D l :

mass diffusivity in liquid

E a :

source term accounting for front advection

E t :

source term accounting for dendrite thickening

f :

mass fraction

G :

temperature gradient

g :

internal volumetric fraction

g i :

component of gravity vector

H :

specific enthalpy

h :

heat-transfer coefficient

K 0 :

morphological constant

K 1 :

coefficient of KGT model

K 2 :

coefficient of KGT model

k :

thermal conductivity

L :

latent heat term, L=(c s -c l )T ref +L ref

L ref :

latent heat at reference temperature

ni :

component of outward normal

Q v :

Darcy’s source term

r :

volumetric fraction

S :

surface

T :

temperature

T env :

ambient temperature

T init :

initial temperature

T ref :

reference temperature

T t :

dendrite tip temperature

T L :

liquidus temperature

T M :

melting point of pure metal

t :

time

V :

volume

V m :

volume of columnar mush

v :

apparent velocity

v l :

liquid velocity

x i :

Cartesian coordinate

β T :

thermal expansion coefficient of liquid

ΔT :

temperature difference

Δt :

time-step

Γ :

Gibbs-Thomson coefficient

κ p :

partition coefficient

μ l :

dynamic viscosity of liquid

ρ :

density

ρ ref :

reference density in Boussinesq model

Subscripts:

 

CV :

pertinent to control volume

i, j :

Cartesian coordinate direction

l :

liquid

m :

pertinent to columnar mush

s :

solid

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Acknowledgments

The authors are grateful to the European Space Agency for funding via the CETSOL (columnar-equiaxed transition in solidification processing) Microgravity Applications Promotion project (Contract No. CCN002-14313/01/NL/SH). We also thank Mr. M. Seredynski, Warsaw University of Technology, for performing some of the calculations.

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Authors and Affiliations

  1. Warsaw University of Technology, 00-665, Warsaw, Poland

    J. Banaszek (Dean)

  2. University College Dublin, Belfield, Dublin 4, Ireland

    S. McFadden (Postdoctoral Researcher) & D.J. Browne (Senior Lecturer)

  3. ACCESS e.V, D-52072, Aachen, Germany

    L. Sturz (Research Scientist) & G. Zimmermann (Senior Scientist)

Authors
  1. J. Banaszek
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  2. S. McFadden
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  3. D.J. Browne
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  4. L. Sturz
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  5. G. Zimmermann
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Corresponding author

Correspondence to D.J. Browne.

Additional information

This article is based on a presentation made in the symposium entitled “Solidification Modeling and Microstructure Formation: in Honor of Prof. John Hunt,” which occurred March 13–15, 2006 during the TMS Spring Meeting in San Antonio, Texas, under the auspices of the TMS Materials Processing and Manufacturing Division, Solidification Committee.

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Banaszek, J., McFadden, S., Browne, D. et al. Natural Convection and Columnar-to-Equiaxed Transition Prediction in a Front-Tracking Model of Alloy Solidification. Metall Mater Trans A 38, 1476–1484 (2007). https://doi.org/10.1007/s11661-007-9140-7

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  • DOI: https://doi.org/10.1007/s11661-007-9140-7

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