Abstract

A general multidimensional model for a solidifying columnar eutectic alloy is presented in which a velocity-dependent freezing temperature is coupled with the macroscale energy equation. At solidification rates (∼ 1–10 mm/s) that are representative of gravity permanent mold and die casting processes, near-eutectic alloys freeze with a macroscopically discrete solid-liquid interface at a temperature below the equilibrium eutectic temperature which can impact the heat transfer process.

The model is illustrated with one-dimensional solidification in a finite domain and solved numerically with a Galerkin finite element method. By nondimensionalizing the governing equations the effect of coupled eutectic growth on heat transport is clearly identified so that the model’s sensitivity to important parameters can be investigated. Additionally, the average eutectic spacing can be determined with the temperature field, rather than post-determination from a standard, uncoupled solution of the energy equation. The eutectic coupling results indicate that the eutectic interface location lags behind the uncoupled solution; therefore, decreasing the amount of solid formed, increasing the total solidification time, and increasing the average eutectic spacing.

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