• Banaszek, Jerzy
• Seredyński, Mirosław

Abstract

Solidification of non-eutectic binary alloys is a complex process due to formation of highly developed microstructures ofa solid phase and therefore the presence of multi-scale transport processes at the complex solid-liquid interface. Usually,two different dendrite morphologies appear during the process. At the initial stage of solidification, equiaxed grainsnucleated at the cooled walls transform into columnar dendrites and continue their growth towards interior of a mould.They form a tree-like shape stiff solid matrix, which behaves as a porous medium immersed in a liquid. In the front ofcolumnar dendrites the undercooled liquid region appears where solid grains can grow starting from tiny nuclei orfragments of columnar dendrites detached from the matrix. Behaviour of this part of the domain can be described with aslurry model of solid equiaxed grains floating in the liquid.The existence of these two different regions evolving in time, where various transport models should be introduced, needsaccurate and physically justified procedure for their distinction. Recently, the Front Tracking Approach (FTA) has beenproposed in modelling dendritic zones developing during binary alloy solidification, [1,2,3,4]. A virtual surface is definedto represent an envelope of columnar dendrite tips, which is treated as the separating interface of slurry and porousregions forming the so-called mushy zone. Dendrite tip kinetics, based on theoretical analysis or experimental findings,is used to determine the growth of columnar grains. Knowledge of a temporary position of the front is put in themomentum transport equation by using a special switching function, which excludes or activates those source terms,which model flow resistance in different dendritic structures of the mushy zone.So far the FTA has been successfully implemented and positively verified and validated only on 2D rectangular staggeredcontrol volume grids [1,2,3,4]. Since a real cast is characterized by complex geometrical shapes, the extension of the FTAto unstructured triangular control volume grids is, for the first time, presented in the paper. Completely new algorithms are introduced to computational model details, such as mesh and moving front handling procedures, pressure-velocitycoupling, time advancing etc.In particular, Rhie and Chow’s scheme [5] for velocity interpolation is utilized to avoid artificial pressure oscillations, and the fractional step method [6] is applied for modelling unsteady flow on non-staggered unstructured grids. Additionally,the definition of the switching function is modified to meet new arrangements of a paved mesh related to a moving front structure.The proposed model is verified and validated by comparing its results with the well known benchmarks, based on both:the experimental findings of Hebditch and Hunt [7] and the calculations founded on the computational models developedby several authors, i.e. Ahmad et al. [8].The distribution of solid fraction after 30s. of cooling shows the dominant thermal convection and solid grains transport if the FTA is used (Fig. 1) and dominant solutal convection if the Enthalpy-Porosity approach (EP) with stationary solidphase is considered. Just behind the front, marked with a red line solutal convection appears and transports lighter solute to the top of the cavity. In result the solid phase growth is more pronounced in upper part of the mould.AcknowledgementsThis work was supported by Polish Ministry of Science and Higher Education (Grant No. N N512 457840).

Topics

• porous
• impedance spectroscopy
• surface
• grain
• phase
• forming
• porosity
• solidification