Abstract
A mixed model for micro-macroscopic computer simulation of binary alloy solidification is proposed. It involves a two-domain approach to solute conservation equations in the liquid and solid phases, whereas transport of momentum and energy in the two-phase region is modelled using the phase mixture theory. To distinguish regions of columnar and equiaxed crystal structures evolving in a cast during solidification, the special front tracking technique on non-structural triangular grids is included in the model. In this two-domain approach, solute conservation equations are averaged across solid and liquid phases, and the solute transport at the phase interface is included. Additionally, the microstructure evolution is modelled to capture the development of various complex grain structures and more accurately describe the solute transport between the phases. The accuracy of the proposed model is first verified by a grid refinement analysis, and then the model is used to predict the solute concentration and macro-segregation in the example problem of Pb-48%wt Sn alloy solidification in a 2D mould. The results obtained are next compared with the relevant ones predicted by the fully single-domain model, earlier developed by authors. Thus, the role of finite diffusion in liquid and solid phases is identified and discussed.
Highlights
Solidification of binary alloys is a complex process, which involves multiscale transport phenomena and formation of a complex tiny tree-like microstructure of the solid phase
Their model took into account micro- and macroscopic transport of solute, equilibrium growth of solid grains in the undercooled liquid, blocking of growth of columnar dendrites with equiaxed grains, and it replaced the commonly used coherency point model (e.g. Ilegbusi and Mat [7]) by more exact distinguishing the zones of different dendrite structures [5]
Since the model is based on the mixture theory, where local thermal and solutal equilibrium is assumed, many microscale phenomena are beyond its scope, like nucleation, globular/equiaxed growth, solute transport rate at the phase boundary related to evolving grain shape, etc
Summary
Solidification of binary alloys is a complex process, which involves multiscale transport phenomena and formation of a complex tiny tree-like microstructure of the solid phase. The important part of micromacroscopic modelling of alloy solidification is the identification of zones of different grain morphology by tracing of a moving hypothetical interface separating these zones In their advanced multi-phase model Wang and Beckermann [1] used a simple one-dimensional approach of the single point tracking of the liquidus isotherm, justified only for diffusive heat and mass transport. The line, consisting of connected linear segments, being a locus of the envelope of columnar dendrite tips, represented by mass-less markers moving across the domain according to prescribed kinetics This approach was further extended to the cases involving thermal natural convection (Banaszek and Browne [3]), thermosolutal natural convection (Seredyński and Banaszek [4,5]) and non-structural triangular control volume grids (Seredyński and Banaszek [6]). Its accuracy is verified by the grid independency study, and its predictions of solute concentration fields and macrosegregation with potential channeling are compared with the relevant results obtained from the fully equilibrium mixture model, for the selected example problem of Pb48%wt Sn alloy solidification in a 2D mould
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