Ensemble Averaged Two-Phase Eulerian Model for Columnar/Equiaxed Solidification of a Binary Alloy

Abstract

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 and equiaxed solidification. We present a new set of equations to simulate the segregations during the columnar solidification of a binary alloy. 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. Firstly, the statistical approach does not need the definition of a representative elementary volume. Secondly, it is consistent with the random aspect of the equiaxed grain germination and motion as well as the possible turbulent behaviour of the fluid flow. 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. It may also incorporate the effects of the inhomogeneities of the various scalar fields, e.g., the solute and temperature gradients. First tests of the model are presented in two asymptotic situations, namely the wholly equiaxed and the columnar solidification.

Modélisation numérique des ségrégations lors de la solidification d'alliages Ti-Al

“…Malheureusement une telle résolution n'est pas envisageable. Dans cette optique, un modèle multiphasique de type Euler-Euler a été développé (Ciobanas et al (2005) TAB.1 -Propriétés physiques du TiAl (31.9wt%), Bai et al (2004) 4.2 Influence de la convection sur les ségrégations…”

Comparison between Simulation and Experimental Results of the Effect of RMF on Directional Solidification of Al-7wt.%Si Alloy

“…Accordingly, the segregation patterns are closely related to the flow structure (see [1]- [7] and references within). As far as the effect of rotating magnetic fields (RMF) are concerned, both numerical and experimental investigation were performed so far [6]- [8]. It was shown that for moderate field strength the RMF promoted the formation of large central channels.…”

“…Indeed, the macrosegregation occurs because of convective redistribution of the solute rejected during the solidification, but the most part of the latter is contained in a mushy zone where intensity of the flow can differ significantly from that in pure liquid. Numerical study of solidification processes under the action of RMF for a range of magnetic field was performed in [6] and [7]. The formation of a large central channel was confirmed in [6] for moderate magnetic field strength.…”

“…Numerical study of solidification processes under the action of RMF for a range of magnetic field was performed in [6] and [7]. The formation of a large central channel was confirmed in [6] for moderate magnetic field strength. A macrosegregation in a form of "Christmas tree" was also obtained for Al-7wt.%Si in Ref.…”

Ensemble averaged multiphase Eulerian model for columnar/equiaxed solidification of a binary alloy: I. The mathematical model

“…Such an approach was suggested first by Furmanski [10]. A first preliminary set of equations has been proposed by Fautrelle et al [11] and Ciobanas et al [12] using the statistical phase averaging approach. In the present paper, we extend the idea proposed by Fautrelle et al [11] to propose a complete set of equations which describe both the columnar and the equiaxed solidification.…”