Solidification Simulation of Binary Al-Si Alloys: Prediction of Primary Dendrite Arm Spacing with Macro-Scale Simulations (~1mm Length Scale)

Abstract

A new and improved algorithm and numerical method has been developed and validated to simulate the solidification of binary alloys considering optimized thermophysical material properties, undercooling of the liquidus temperature prior to solidification event of the primary phase, fluid flow induced by natural convection and shrinkage during solidification in the solidifying domain. The simulation was for a two dimensional unsteady state solidification process inside a cylindrical container. The validation was carried out with reliable experiment results for both upward and downward solidification modes. An additional advantage of the present numerical algorithm is the estimation of the instantaneous primary dendrite arm spacing at any location in the solidified component. It has been shown that the Bouchard-Kirkaldy model (unsteady state solidification) to evaluate the primary dendrite arm spacing in an unsteady solidification process coupled with the Lehmann model to evaluate the primary arm spacing with the effect of fluid velocity in the liquid phase is accurate within acceptable error. The results from simulations using these models have a good agreement with experiment results for instantaneous primary dendrite arm spacing in the solidified microstructure. The effect of fluid flow on the evaluation of primary arm spacing is pronounced during downward solidification. However, the effect of primary arm spacing on fluid flow is insignificant, so it is acceptable to apply average primary arm spacing during macro-scale solidification simulations. To obtain a valid simulation, the thermophysical material properties of the solid phase should be considered as function of temperature and that of the liquid can be considered as an average constant value. The inclusion of solidification shrinkage in the simulation has negligible effect on the solidification parameters during the upward solidification mode. However, significantly changes the direction and magnitude of the fluid velocity in the liquid phase and the magnitude of primary arm spacing in the downward solidification mode. A valid solidification simulation of binary alloys to estimate accurate primary dendrite arm spacing could be achieved only with the consideration of the undercooling of the liquidus temperature. Optimized thermophysical properties, and fluid flow in the domain caused by both solidification shrinkage and natural convection effects.