Mathematical Modeling of Shrinkage in Metals Casting

"A fixed grid numerical model for phase change problems is proposed. The model solves for heat transfer and fluid flow, via the coupled solution of the energy, continuity and momentum equations. In addition, the numerical scheme accounts for temperature varying thermophysical properties and determines the shrinkage profile resulting from phase and density change. Simulations are run to determine the effect of varying model parameters and wall cooling rates on the location and shape of the shrinkage void formation in cylindrical casts. Results are shown for both aluminum and magnesium.IntroductionThe mathematical modeling of phase change processes (be they solidification or melting problems) entails solving for many interrelated phenomena. A comprehensive numerical simulation of the casting of a metal, for example, would have to account for: (a) heat transfer in both the solid and liquid portions of the metal and in the mold, (b) the release of latent heat during phase change, (c) fluid flow behavior in the liquid portion of the metal, (d) temperature induced shrinkage caused by liquid contraction and solidification contraction, and (e) the development of thermal stresses with accompanying shrinkage in the solid portion of the cast and mold. A schematic of the relationships that exist between the coupled equations which govern solidification is shown in Figure 1."