Computer modelling of solidification of pure metals and alloys.

Two numerical models have been developed to describe the volumetric changes
during solidification in pure metals and alloys and to predict shrinkage defects in the
castings of general three-dimensional configuration. The first model is based on the
full system of the Continuity, Navier-Stokes and Enthalpy Equations. Volumetric
changes are described by introducing a source term in the Continuity Equation
which is a function of the rate of local phase transformation. The model is capable
of simulating both volumetric shrinkage and expansion.
The second simplified shrinkage model involves the solution of only the Enthalpy
Equation. Simplifying assumptions that the feeding flow is governed only by
gravity and solidification rate and that phase transformation proceeds only from
liquid to solid allowed the fluid flow equations to be excluded from consideration.
The numerical implementation of both models is based on an existing proprietary
general purpose CFD code, FLOW-3D, which already contains a numerical
algorithm for incompressible fluid flow with heat transfer and phase transformation.
An important part of the code is. the Volume Of Fluid (VOF) algorithm for tracking
multiple free surfaces. The VOF function is employed in both shrinkage models to
describe shrinkage cavity formation.
Several modifications to FLOW-3D have been made to improve the accuracy and
efficiency of the metal/mould heat transfer and solidification algorithms.
As part of the development of the upwind differencing advection algorithm used in
the simulations, the Leith's method is incorporated into the public domain twodimensional
SOLA code. It is shown that the resulting scheme is unconditionally
stable despite being explicit.