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A new transient method for analysis of solidification in the continuous casting of metals

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Abstract

Solidification processes involve complex heat and mass transfer phenomena, the modelling of which requires state-of-the art numerical techniques. An efficient and accurate transient numerical method is proposed for the analysis of phase change problems. This method combines both the enthalpy and the enhanced specific heat approaches in incorporating the effects of latent heat released due to phase change. The sensitivity and accuracy of the proposed method to both temporal and spatial discretization is shown together with closed-form solutions and the results from the enhanced specific heat approach. In order to explore the proposed method fully, a non-linear heat release, as is the case for binary alloys, is also examined. The number of operations required for the new transient approach is less than or equal to the enhanced heat capacity method depending on the averaging method adopted. To demonstrate the potential of this new finite-element technique, measurements obtained on operating machines for the casting of zinc, aluminum and steel are compared with the model predictions. The death/birth technique, together with the proper heat-transfer coefficients, were employed in order to model the casting process with minimal error due to the modelling itself.

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Abbreviations

[A]:

conductance matrix

[B]:

matrix containing the derivative of the element shape functions

c, C p :

specific heat (J kg−1°C−1)

\(\bar c\) :

effective specific heat (J kg−1°C−1)

f(T) :

local liquid fraction

f :

thermal load vector

H :

enthalpy (J kg−1)

[H]:

capacitance matrix

h, h r,h c :

heat transfer coefficient (W m−2°C−1)

K :

thermal conductivity (W m−1°C−1)

L :

latent heat of solidification (J kg−1)

l :

overall length (m)

N i :

shape functions

Q :

rate of heat generation per unit volume (J m−3)

q :

heat flux (W m−2)

R :

residual temperature (°C)

T :

temperature (°C)

T s :

solidus temperature (°C)

T l :

liquidus temperature (°C)

T pouring :

pouring temperature (°C)

T top :

temperature at the top of the mould (°C)

T w :

temperature of the water spray (°C)

\(\tilde T\) :

approximated temperature (°C)

T ∞ :

surrounding temperature (°C)

\(\dot T\) :

cooling rate (°C/s)

t :

time (seconds)

x i,x, y, z :

spatial variables (m)

Δt :

time step (s)

Δx :

element size (m)

α :

diffusivity (m2s−1)

ρ :

density (kg m−3)

θ :

time marching parameter

ν n :

direction cosines of the unit outward normal to the boundary

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Authors and Affiliations

  1. Institute for Research in Construction, National Research Council Canada, K1A0R6, Ottawa, Ontario, Canada

    S. E. Chidiac

  2. The Centre for Metallurgical Process Engineering, University of British Columbia, V6T 1Z4, Vancouver, B.C., Canada

    J. K. Brimacombe & I. V. Samarasekera

Authors
  1. S. E. Chidiac
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  2. J. K. Brimacombe
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  3. I. V. Samarasekera
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Chidiac, S.E., Brimacombe, J.K. & Samarasekera, I.V. A new transient method for analysis of solidification in the continuous casting of metals. Appl. Sci. Res. 51, 573–597 (1993). https://doi.org/10.1007/BF00868001

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