Simulation of unconstrained solidification of A356 aluminum alloy on distribution of micro/macro shrinkage

In the condition of Newtonian heat transfer, A356 aluminum alloy is solidified with randomly distributed equiaxed dendrites. Ability of interdendritic liquid flow is described by permeability parameter using Darcy's law and this parameter is used to predict the micro-shrinkages. In this study the interdendritic liquid flow during nucleation and grain growth are simulated in a 1 mm × 1 mm domain. Temperature gradient is zero in the initial condition of the unconstrained solidification. The numerical simulation procedure includes two stages; first, numerical evolution of the shape, number, size, and distribution of dendrites during solidification using a novel Cellular Automation Finite Volume (CA-FV) method, and second, numerical determination of the micro-permeability by a Computational Fluid Dynamics (CFD) technique. Subsequently, the effect of Reynolds number, cooling rate and solidification rate on a critical permeability range was investigated in order to predict the micro/macro shrinkage distribution. Results showed that it is possible to propose a mathematical model to relate the Reynolds number and liquid flow rate, in the creeping flow range, on the micro-permeability during unconstrained solidification.