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Proper selection of the stability parameter determines the accuracy of dendrite tip kinetics at a single crystal scale. Recently developed sophisticated phase field modelling of a single grain evolution provides evidence that this parameter is not constant during the process. Nevertheless, in the commonly used micro-macroscopic simulations of alloy solidification, it is a common practice to use a constant value of the stability parameter, resulting from the marginal stability theory. This paper aims to address the issue of how this inaccuracy in modelling crystal growth kinetics can influence numerically predicted zones of columnar and equiaxed dendrites and the macro-segregation formation.

Using the original authors’ micro-macroscopic computer simulation model of binary alloy solidification, the calculations have been performed for the Kurz-Giovanola-Trivedi (KGT) crystal growth kinetics with two different values of the stability parameter, and for two different compositions of Al-Cu alloys. The computational model is based on single domain-based formulation of transport equations, which are discretized on control-volume mesh. To identify zones of different grain structures, developing within the two-phase liquid-solid region, an envelope of columnar dendrite tips is tracked on a fixed non-orthogonal, triangular control volume grid. The models of porous and slurry media are used, along with the concept of the switching function, to account for diverse flow resistances in the columnar and equiaxed crystal zones. The numerical predictions are carefully studied to address the question of how the chosen stability parameter influences macroscopic structures of a cast, the most important issue from the engineering point of view.

The carried-out comprehensive numerical analysis shows that the value of the stability parameter of the KGT-constrained dendrite growth model does not have a direct significant impact on the macrosegregation formation. It, however, visibly influences the undercooling along the front, separating different dendritic structures and the size of the undercooled melt region where the equiaxed grains can develop. It also affects the amount of eutectic phase created.

To the best of the authors’ knowledge, this is the first attempt at estimating the influence of some inaccuracies, caused by possible ambiguities in choosing the stability constant of the KGT law, on numerically predicted macroscopic fields of solute concentration, the developing zones of columnar and equiaxed crystals and the macrosegregation patterns.

The purpose of this paper is to endorse the idea of using a special post-calculating front tracking (FT) procedure, along with the enthalpy-porosity front tracking (EP-FT) single continuum model, in order to identify zones of different dendritic microstructures developing in the mushy zone during cooling and solidification of a binary alloy.

The 2D and 3D algorithms of the FT approach along with different crystal growth laws were implemented in macroscopic calculations of binary alloy solidification with the identification of different dendrite zones developing during the process.

Direct comparison of results predicted by the FT model with that based on the concept of the critical value of the solid volume fraction shows the sensitivity of the latter on an arbitrary assumed value of the dendrite coherency point (DCP). Moreover, for a carefully chosen DCP value the second model provides results that are close to those given by the FT-based approach. It is also observed that the macro-segregation pattern obtained by the proposed method is hardly influenced by chosen dendrite tip kinetics.

To the best authors’ knowledge, for the first time the 3D FT model has been used along with the enthalpy porosity approach to simulate the development of zones of different dendrite morphology during binary alloy solidification. And, a weak influence of assumed different dendrite tip kinetics on the macro-segregation pattern has been proved, what justifies this underlying assumption of the EP-FT method.

This paper aims to tackle the problem of some ambiguity of the momentum equation formulation in the commonly used macroscopic models of two‐phase solid/liquid region, developing during alloy solidification. These different appearances of the momentum equation are compared and the issue is addressed of how the choice of the particular form affects velocity and temperature fields.

Attention is focused on the ensemble averaging method, which, owing to its stochastic nature, is a new promising tool for setting up the macroscopic transport equations in highly inhomogeneous multiphase micro‐ and macro‐structures, with morphology continuously changing in time when the solidification proceeds. The basic assumptions of the two other continuum models, i.e. based on the classical mixture theory and on the volume‐averaging technique, are also unveiled. These three different forms of the momentum equation are then compared analytically and their impact on calculated velocity and temperature distribution in the mushy zone is studied for the selected test problem of binary alloy solidification driven by diffusion and thermal natural convection in a square mould.

It is found that a chosen appearance of the momentum equation mildly affects temporal velocity/temperature, and shapes of the phase interface at longer times of the solidification.

This mainly results from small variations of the liquid fraction across the mushy zone and from a low solidification rate, and it may change drastically when anisotropic properties of the mushy zone, solutal convection, different phase densities and cooling conditions are considered. Therefore, further comprehensive study is needed.

The paper addresses how the different focus of the momentum equation for liquid flow is compared.