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A correlation to describe interfacial heat transfer during solidification simulation and its use in the optimal feeding design of castings

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Abstract

It is known from experimental data that for pure aluminum castings manufactured via the gravity die casting process, the interfacial heat-transfer coefficient can vary in the range 500 to 16,000 W/m2 K. These coefficients are of significant importance for the numerical simulation of the solidification process. The experimentally determined variation of interfacial heat-transfer coefficients with respect to time has been recalculated to highlight the variation with respect to casting temperature at the interface. This variation was observed to be of an exponential nature. Also, the pattern of variation was found to be similar in all the experimental results. It has been found that all these patterns of interfacial heat-transfer coefficient variation can be matched by a unique equation that has been proposed as a correlation to model the metal-mold interfacial heat transfer. The benefit of this correlation is in its ability to approximate the combined effects of geometry variation, insulation, chills, die coatings, air gap formation, etc. during the numerical simulation and its use in the optimal design of heat transfer at the metal-mold interface.

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Abbreviations

ρ :

density (kg/m3)

c :

specific heat (J/kg °C)

k :

conductivity of the metal (W/m °C)

H :

enthalpy (J/kg °C)

t :

time (s)

t f :

freezing time (s)

T :

temperature (°C)

Ω:

domain

Γ:

domain boundary

Γ q :

flux boundary

Γ h :

convection boundary

Γ t :

fixed temperature boundary

q :

prescribed flux at the boundary Γ q

h c :

convection heat-transfer coefficient (W/m2 °C)

h :

metal-mold interfacial heat-transfer coefficient (W/m2 °C)

C :

heat capacity matrix

K :

conductivity matrix

F :

load vector

N :

standard finite element shape function

l :

length of interface element

k a :

conductivity of air

δ ag :

macroscopic air gap

r :

vector from casting’s geometric center to casting-mold interface

n :

vector of interface normal

α :

linear thermal expansion coefficient

u s and T sol :

solidus temperature (°C)

u :

average temperature over solidified metal

T L :

liquidus temperature (°C)

T int :

casting temperature at the interface (°C)

x :

intermediate variable

a 1, a 2, a 3 :

coefficients or constants in the correlation

n :

number of user-defined feed metal flow paths

s n :

number of points in the nth user-defined feed metal flow path

p :

penalty term

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Authors and Affiliations

  1. the Mechanical Engineering Department, University of Wales Swansea, SA2 8PP, Swansea, United Kingdom

    R. W. Lewis (Professor) & R. S. Ransing (Postdoctoral Research Fellow)

Authors
  1. R. W. Lewis
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  2. R. S. Ransing
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Lewis, R.W., Ransing, R.S. A correlation to describe interfacial heat transfer during solidification simulation and its use in the optimal feeding design of castings. Metall Mater Trans B 29, 437–448 (1998). https://doi.org/10.1007/s11663-998-0122-y

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