Modelling of macrosegregation during solidification processes using an adaptive domain decomposition method

Abstract

A numerical method for the simulation of buoyancy-induced macrosegregation during solidification processes is presented. The physical model is based on volume averaged conservation equations for energy, mass, momentum, and solute. The resulting partial differential equations are solved by a finite element method, which considers two different length-scales: on the one hand, the scale of the overall process, on the other, a small critical zone near the solidification front where solutal inhomogeneities are initiated and the fluid velocity is non-zero. A domain decomposition method using two adapted grids has been developed. The overall computational domain is discretized using a 'coarse' finite element mesh adapted to the process scale. At each time step, the energy conservation equation is solved using this discretization and new values of temperature and solid fraction are calculated at each finite element node. Based on these values, the computational domain is subdivided into three subdomains: the so-called solid, mushy, and liquid regions. The mushy subdomain corresponds to the critical zone near the solidification front and is adaptively discretized with a finer finite element mesh, whereas the liquid domain uses the initial coarse grid and the solid is no longer considered. The fluid flow and solute transport equations are then solved on the different meshes using a Dirichlet-Neumann substructuring iterative method, together with the mortar technique to deal with the non-conforming discretizations at the subdomain interfaces. The method is applied to several test problems such as the Hebditch-Hunt macrosegregation experiment or the prediction of freckles, and the performances and limits of the approach are pointed out and discussed.

Modeling Macrosegregation during Direct-Chill Casting of Multicomponent Aluminum Alloys

“…Unstructured meshing allows good spatial resolutions without increasing the mesh number, which is important for the accuracy of calculations, especially in areas such as the place close to the liquidus line, where chemical inhomogeneities are initiated and the relative movement between the liquid and solid is present. [13] B. Microscopic Model…”

Solidification of a binary alloy: Finite-element, single-domain simulation and new benchmark solutions

“…First, H n+1 and C n+1 are computed implicitly from (4) and (7), using the following approximations for the liquid enthalpy and the liquid concentration [32,7]:…”

“…Nevertheless, using the scaling of solidification problems, the ratio between the non-linear and linear drag terms is proportional to √ Da/(1 − ) 2 : provided the Darcy number is very small (which is usually the case in solidification), non-linear terms could only play a role around the liquid-mush interface = 1, where all drag terms rapidly disappear, the flow being controlled by the standard fluid advective and viscous terms. That is why the non-linear drag is not included in the present simulation (see also for instance [18,32,7]). …”

Modeling Freckle Segregation with Mesh Adaptation

“…Recently, articles on the use of adaptive mesh refinement to predict channel segregation began to appear in the literature. Ka¨mpfer and Rappaz [20] employed an adaptive domain decomposition method to carry out mesh adaptive freckle simulations. The initial coarse mesh with rectangular elements was refined based on the volume fraction of solid at the nodes.…”