ENSEMBLE AVERAGED TWO-PHASE EULERIAN MODEL FOR COLUMNAR / EQUIAXED SOLIDIFICATION OF A BINARY ALLOY. SIMULATION OF THE COLUMNAR-TO-EQUIAXED TRANSITION

摘要

A new two-phase Eulerian model for the columnar and equiaxed dendritic solidification has been developed. The mean conservation equations are derived by means of a statistical phase averaging technique, and the mathematical formulation of the model can be used for both columnar (c), equiaxed (e) and mixed c/e solidification. The use of such an averaging procedure has several advantages compared with the volume averaging technique which has been widely used during the last decade. However, the most important one is that, owing to the statistical nature of the model, one is able to treat rigorously the coexistence of equiaxed and columnar structures and consequently the CET phenomena. The averaged equations are closed by means of the cell model approximation. This technique can be successfully used to model the various interactions between the liquid and the solid. In addition, in a similar way as Rappaz et al. and Wang et al., an envelope model is used to parameterize the small scales, i.e., the dendrite scale. Here we present simulations of AlCu quasi-steady solidifications in order to obtain the corresponding CET maps. The model is able to reproduce mixed columnar/equiaxed zones within the CET maps and put forth a "double mechanical blockage" of the columnar structures produced by the equiaxed zone ahead of the columnar front. Moreover, the solutal blockage mechanism is intrinsically taken into account by the model. In this respect the new ensemble averaged model unifies rigorously both the mechanical and the solutal blockage mechanism producing the CET.