Role of appropriate permeability model on numerical prediction of macrosegregation

Abstract

A continuum formulation based mathematical model was developed to predict macrosegregation during solidification of alloys and to investigate the role of permeability on macrosegregation. The model is based on the conservation of mass, momentum, energy, and solute. Darcy's law was invoked to model the flow through the mushy region. The anisotropic nature of permeability was considered in the formulation of the model. Using the experimental data from the literature regarding macrosegregation in lead-tin alloys, commonly employed permeability models were assessed, and their inadequacies were demonstrated. The permeability model proposed by West, which is valid up to a very high liquid fraction of the mush and has some limitations, was generalized by incorporating a microstructural parameter into the model. Use of this generalized permeability model showed better agreement with the experimental data on the macrosegregation reported in the literature.

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

“…125,126) A significant body of work, however, has been completed using highly-simplified binary single-phase simulations. [127][128][129][130][131] This is almost certainly because of the complexities and excessive computing times associated with large multiphase simulations, as will be discussed in the following section.…”

“…106) Indeed, many recent studies have resorted to the original treatments by Bennon and Incropera and Beckermann et al to deliver their predictions. [128][129][130][131][132] Reducing the size of the model system can drastically reduce times, and using symmetry is certainly essential, but results can only be scaled up to larger problems with caution (macrosegregation will not normally arise in small ingots, see later). Increasing mesh sizes often means that certain features, such as A-segregates, are not resolved and changes can significantly affect computed segregation patterns, see Fig.…”

“…[71][72][73][74][92][93][94]97,169) Results of macromodels have demonstrated that the use of different mushy-zone permeability functions, and neglection of permeability anisotropy, can have a significant effect on the macrosegregation predicted, including the number, length and orientation of channel segregates. 71,99,127,128,184) The treatments described above have considered only the permeability of mushy zones during columnar solidification, yet it is clear that a significant proportion of solidification (and segregation) in large steel ingots occurs in the equiaxed regime. Wang et al examined the permeability of equiaxed structures in the mid 1990s, finding that fluid drag was a function of various terms including arm spacings and grain densities, but recently this complex subject appears to have received little attention.…”

Influence of process parameters on CET in Ti–Al alloy ingot with consideration of shrinkage cavity formation: A computer simulation

“…The following assumptions and simplifications are made in this model. This set of equations is basically the one proposed in [17]:…”

“…The coupling of the energy and species conservation equations in the mushy zone through the phase diagram provides a method for calculating the solid fraction by solving a nonlinear equation. The meaning of each thermophysical parameter and detailed description of these approaches see, for example, references [17,18].…”