Ensemble averaged multi-phase Eulerian model for columnar/equiaxed solidification of a binary alloy: II. Simulation of the columnar-to-equiaxed transition (CET)

Abstract

A new multi-phase Eulerian model for the columnar and equiaxed dendritic solidification has been developed. In this paper we first focus on the numerical simulation of quasi-steady solidification experiments in order to obtain corresponding CET maps. We have identified three main zones on the CET map: the pure columnar, the pure equiaxed zone and finally the mixed columnar+equiaxed zone. The mixed c/e zone was further quantified by means of a columnar fraction εc which quantifies in a rigorous way the two coexisting structures. Since it intrinsically includes the solutal and the mechanical blocking effects, the new ensemble model unifies the semi-empirical Hunt's approach (pure mechanical blocking mechanism) and the Martorano et al approach (pure solutal blocking mechanism). Secondly the present model was used to simulate unidirectional solidification experiments. It was found that the columnar front evolved in a quasi-steady state until a time very close to the critical CET moment. It is also found that the equiaxed nucleation undercooling is close to the maximum columnar dendrite tip undercooling and that the CET is virtually independent of the equiaxed zone ahead of the columnar front. If the equiaxed zone is not taken into account it is observed that the columnar front velocity exhibits a sudden increase at the beginning of the solidification followed by a quasi-plateau corresponding to a quasi-state at the columnar tips and finally, above a critical time, an oscillatory evolution. The beginning of the oscillatory evolution of the columnar front was well correlated with the CET position measured in the experiments. We also find that this oscillatory evolution of the columnar front is very favourable for the fragmentation of the columnar dendrites and thus for the CET. In this respect, it seems that the unsteady regime of the columnar front with respect to the local cooling conditions represents the main cause for the CET phenomena, at least for the non-refined alloys.

Macrosegregation in Steel Ingots: The Applicability of Modelling and Characterisation Techniques

“…Beckermann highlighted the need for such research in 2000, 101) and it is certainly key for the prediction of negative base segregation in ingots. One would suppose that such models would also be an essential starting point for the prediction of V-segregation, and would be useful to those pre- Investigations during the 21st century included the extension of two-phase models 29,31,102) for instance to account for the different behaviours of globular and dendritic equiaxed grains, as well as generation of new formulations, 103,104) such as the three-phase treatment of Ludwig, Wu et al (the phases were stationary columnar solid, equiaxed solid and parent melt). [105][106][107] Martorano et al examined the viability of a CET criterion based on the arrest of columnar solidification by the solute field of growing equiaxed grains ahead (so-called 'soft-blocking').…”

Influence of Forced/Natural Convection on Segregation During the Directional Solidification of Al-Based Binary Alloys

“…All numerical results were obtained from the model developed by Ciobanas et al, [27,28] which is devoted to the prediction of solidification phenomena on the macroscale. The model is Euler-Euler, multiphase, and based on a statistical averaging method.…”

“…Some differences exist [30] in regard to the treatment of the diffusion length involved in the mass transfer between the inter and extradendritic liquid. [28] The global system is detailed in Table AI below.…”

Flow, heat and mass transfers during solidification under traveling/rotating magnetic field

“…A numerical model has been developed to accomplish two objectives: first, to better understand the underlying physical properties of the solidification mechanism, taking into account micro-scale crystal growth, meso-scale segregation, and the macro-scale momentum transport effects in a coupling manner; this study has been elaborated by Ciobanas and Fautrelle via numerical modeling, a multiphase Eulerian model for columnar and equiaxed dendritic solidification has been developed by those authors [10,11]; and second, to investigate the ability of the periodically reversed Lorentz force on the improvement of solutal segregations at the interface of the solid/liquid interface [5].…”