Modeling of Solidification and Filling of Thin-Section Castings

A finite element model for simulating dendritic solidification of multicomponent-alloy castings is used to study the filling and solidification of castings of thin cross section. The model solves the conservation equations of mass, momentum, energy, and alloy components and couples the solution with the thermodynamic of the multicomponent alloy through a phase diagram equation. The transport of mass and energy in the mushy zone is done considering the mushy zone as a porous medium of variable porosity. The same set of conservations equations are used for the liquid, solid and mushy zones, in which the volume fraction of liquid acts as the variable that makes the equations transition continuously from one zone to another (Felicelli et al. [1]). During filling, the model tracks the advancing front as the metal flows into the thin mold, and solidification is calculated as the metal loses energy by convection and radiation to the mold, including the dynamic calculation of view factors. The code supports two fluid models that emulate the flow behavior under equiaxed or columnar solidification. In the former case a slurry fluid model is used in which the viscosity is determined by the volume fraction of solid. In this slurry state, the solid and liquid move at the same velocity. For the case of columnar solidification, the solid is fixed and the liquid flows through a porous structure of dendrictic solid. The model development is based on the work by Felicelli et al. [2], to which several features were added, including a front-tracking technique (Gao [3]) and thermal radiation boundary conditions. Calculations for Ni and Al alloys were performed to illustrate the effect of several physical and operation parameters in the filling of a horizontal channel of thin thickness. A wide range of process parameters was tested in order to determine how much of the channel length could be filled before blockage of flow by solidification occurred. In a separate section, the effect of alloy concentration on the fluidity was studied using a Pb-Sn hypoeutectic system, and the importance that the dendrite breaking phenomenon can have on the results is shown. Conclusions about the parameters that most influence the filling process are presented, as well as recommendations on which experimental data are more critical in order to conduct a proper validation of this type of models.