Hybrid Cellular Automaton - Parabolic Thick Needle model for equiaxed dendritic solidification

Abstract

• The growth of a dendritic equiaxed grain is modeled using a CA-PTN approach. • Evolution of solute field in the liquid phase is computed using a FE method. • Dendritic branches are approximated by needles to mimic the interfacial evolution. • Advantages of the approach are shown including solutal interaction between branches. • The solidification simulation of an Al-Si droplet highlights heat and solute transfer. A hybrid Cellular Automaton (CA) - Parabolic Thick Needle (PTN) model is developed for the simulation of an equiaxed dendritic grain. It is implemented by solving conservation equations with the Finite Element (FE) method at two scales. At the scale of the microstructure, dendritic branches are approximated by a network of PTN. The solute field is computed in the liquid using a FE mesh with minimum size smaller than the diffusion length ahead of the dendrite tips, giving access to a detailed description of each dendrite tip growth velocity as well as solutal interactions between branches. At the simulation domain scale, volume averaged heat and solute transfers are solved on a coarser FE mesh. The average volumetric fraction of phases is deduced from a field giving the fraction of dendritic microstructure together with a microsegregation model. Because the PTN themselves grow on CA cells, the dendrite tip growth velocity is transferred to the vertices of the polygon associated to the CA growth shape. Similarly, the field giving the fraction of dendritic microstructure is deduced from the fraction of CA cells part of the mushy zone, which include cells containing PTN network. Advantages of the new multiple scale CAPTN model include solutal interaction between dendrite branches together with long range transfer of heat and solute mass, together with the role of latent heat release on equiaxed solidification.