Effect of Shrinkage on Primary Dendrite Arm Spacing during Binary Al-Si Alloy Solidification

Upward and downward directional solidification of hypoeutectic Al-Si alloys were numerically simulated inside a cylindrical container. Undercooling of the liquidus temperature prior to the solidification event was introduced in the numerical model. The finite-volume method was used to solve the energy, concentration, momentum, and continuity equations. Temperature and liquid concentrations inside the mushy zone were coupled with local equilibrium assumptions. An energy equation was applied to determine the liquid fraction inside the mushy zone while considering the temperature undercooling at the solidifying dendrite/liquid interface. Momentum and continuity equations were coupled by the SIMPLE algorithm. Flow velocity distribution at various times, G, R, λ1, and solidification time at mushy zone/liquid interface during solidification were predicted. The effect of shrinkage during solidification on these solidification parameters was quantified. Transient temperature distribution, solidification time for the mushy zone/liquid interface, and λ1 were validated by laboratory experiments. It was found that better agreement could be achieved when the fluid flow due to solidification shrinkage was considered. Considering shrinkage in upward solidification was found to only have a marginal effect on solidification parameters, such as G, R, and λ1; whereas, in the downward solidification, fluid flow due to shrinkage had a significant effect on these solidification parameters. Considering shrinkage during downward solidification resulted in a smaller R, stronger fluid flow, and increased solidification time at the mushy zone/liquid interface. Further, the flow pattern was significantly altered when solidification shrinkage was considered in the simulation. The effect of shrinkage on G and λ1 strongly depended on the instantaneous location of the mushy zone/liquid interface in the computational domain. The numerical results could be validated by experimental data only when both the undercooling of the liquidus temperature prior to solidification and fluid flow in the liquid caused by the effect of shrinkage during solidification were included in the model.