Best practice for measuring grid convergence in numerical models of alloy solidification

Abstract

Purpose -When a multi component alloy solidifies the redistribution of solute components leads to the formation of macrosegregation patterns. Blending ideas from a number of recent publications the purpose of this paper is to provide a "best practice" on how grid convergence of a given macrosegregation simulation can be measured and determined. Design/methodology/approach -The best practice is arrived at by considering a benchmark problem consisting of a 2D-casting simulation of an idealized Al-4.5%Cu alloy in a side cooled square (76×76 mm) cavity. The model for this simulation is based on a mixture treatment of the relevant heat and mass transfer equations. Simulations are made using three increasingly refined grid sizes. Findings -The best practice to determine grid resolution involves two steps: first, a visual evaluation of predicted segregation images leading to the evaluation of solute profiles along selected transects; and second, the construction of a cumulative distribution function (CDF) of the predicted segregation field. On application to the benchmark problem, it is concluded that current computer resources are insufficient to grid resolve macrosegregation patterns but that the CDF provides a useful signal of the nature of macrosegregation in a given system.Research limitations/implications -The benchmark is chosen to be representative. Exact convergence behavior, however, may depend on the system chosen. Originality/value -In addition to establishing a best practice for measuring grid resolution of macrosegregation simulations the work also highlights, even in the absence of complete grid convergence, how the recently proposed CDF treatment can inform solidification modeling and process understanding.

On macrosegregation in a binary alloy undergoing solidification shrinkage

“…freckles, A-segregates, V-segregates [41]; whereas the first two are believed to form as a consequence of the enrichment of the interdendritic melt with light solute elements, leading to a decrease in the local melt density and the onset of thermosolutal convection [7], a mechanism for the third has still to be determined. Although the formation of channel segregates is a comparatively old problem [3,16,19,24,43], there is still considerable doubt as to whether existing numerical simulations are able to compute them correctly [35,36], as regards mesh independence; this refers primarily to their width, their length and the spacing between them. In particular, the approach adopted here could elucidate when and exactly where in the mushy zone they are initiated; a precursor to this is believed to be when remelting first occurs, i.e.…”

Mathematical modelling of macrosegregation in binary alloys induced by convection

“…In addition, this approach would be well-suited not just to problems involving two moving boundaries, but also when the boundaries are not planar, as was demonstrated in (VYNNYCKY; KIMURA, 2007;VYNNYCKY;KIMURA, 2015) for the two-dimensional problem of the solidification of one-component material in the presence of natural convection in an enclosure. By tracking the solid and liquid interfaces explicitly, it is hoped to be able to avoid the usual issues of numerical dispersion and diffusion that are present in the numerically simulated macrosegregation profiles reported in the literature (DU; ESKIN; KATGERMAN, 2009;VOLLER, 2014;VOLLER, 2016).…”