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A Simple Model of the Mold Boundary Condition in Direct-Chill (DC) Casting of Aluminum Alloys

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Abstract

An accurate thermofluids model of aluminum direct-chill (DC) casting must solve the heat-transfer equations in the ingot with realistic external boundary conditions. These boundary conditions are typically separated into two zones: primary cooling, which occurs inside the water-cooled mold, and secondary cooling, where a film of water contacts the ingot surface directly. Here, a simple model for the primary cooling boundary condition of the steady-state DC casting process was developed. First, the water-cooled mold was modeled using a commercial computational fluid dynamics (CFD) package, and its effective heat-transfer coefficient was determined. To predict the air-gap formation between the ingot and mold and to predict its effect on the primary cooling, a simple density-based shrinkage model of the solidifying shell was developed and compared with a more complex three-dimensional (3-D) thermoelastic model. DC casting simulations using these two models were performed for AA3003 and AA4045 aluminum alloys at two different casting speeds. A series of experiments was also performed using a laboratory-scale rectangular DC caster to measure the thermal history and sump shape of the DC cast ingots. Comparisons between the simulations and experimental results suggested that both models provide good agreement for the liquid sump profiles and the temperature distributions within the ingot. The density-based shrinkage model, however, is significantly easier to implement in a CFD code and is more computationally efficient.

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Abbreviations

A, B, C, D :

thermoelastic model coefficients

C f :

empirical coefficient for nucleate boiling

C p :

specific heat at constant pressure

E :

Young’s modulus

f :

mass fraction

g :

gravitational acceleration

H :

enthalpy

H fg :

latent heat of evaporation

h :

heat-transfer coefficient

K :

conductivity

K 0 :

permeability coefficient

K μ :

permeability of mushy zone

L :

ingot cross section length

\( \hat{n} \) :

unit normal vector at solid phase

p :

pressure

q :

heat flux

Q ′ :

water flow rate per unit perimeter

T :

temperature

u :

velocity

W :

ingot cross section width

α :

thermal expansion coefficient of solid phase

β :

thermal expansion coefficient of liquid phase

γ :

surface tension

Γ:

water flow rate

δ :

cooling-induced shrinkage

\(\epsilon\) :

strain tensor

μ:

viscosity

ν :

Poisson’s ratio

ρ :

density

σ :

stress tensor

air:

air

boil:

boiling

coh:

coherency

cont:

contact

conv:

convective

disp:

displacement

eff:

effective

ext:

external

gap:

air gap

in:

inlet

incip:

incipient boiling

l:

liquid phase

liq:

liquidus

lubr:

lubricating film

mold:

mold inner wall

ref:

reference value

s:

solid phase

sat:

water saturation point

sol:

solidus

surf:

ingot surface

wat:

water

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Acknowledgments

The authors acknowledge the financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC), Novelis Global Technology Centre (NGTC), Ontario Centres of Excellence (OCE), and Emerging Materials Knowledge (EMK).

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Authors and Affiliations

  1. Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Amir R. Baserinia (Postdoctoral Fellow), H. Ng (Research Assistant), D. C. Weckman (Professor) & M. A. Wells (Professor)

  2. Novelis Global Technology Centre, Kingston, K7L 3N6, ON, Canada

    S. Barker (Metallurgist) & M. Gallerneault (Director of Research)

Authors
  1. Amir R. Baserinia
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  2. H. Ng
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  3. D. C. Weckman
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  4. M. A. Wells
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  5. S. Barker
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  6. M. Gallerneault
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Correspondence to Amir R. Baserinia.

Additional information

Manuscript submitted May 14, 2011.

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Baserinia, A.R., Ng, H., Weckman, D.C. et al. A Simple Model of the Mold Boundary Condition in Direct-Chill (DC) Casting of Aluminum Alloys. Metall Mater Trans B 43, 887–901 (2012). https://doi.org/10.1007/s11663-012-9658-y

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