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Research Papers: Melting and Solidification

Front Tracking Based Macroscopic Calculations of Columnar and Equiaxed Solidification of a Binary Alloy

[+] Author and Article Information
M. Seredyński

 Warsaw University of Technology, Warsaw 00-665, Polandmsered@itc.pw.edu.pl

J. Banaszek

 Warsaw University of Technology, Warsaw 00-665, Polandbanaszek@itc.pw.edu.pl

J. Heat Transfer 132(10), 102301 (Jul 23, 2010) (10 pages) doi:10.1115/1.4001362 History: Received March 27, 2009; Revised February 22, 2010; Published July 23, 2010; Online July 23, 2010

The paper explores the potential of a recently developed special front tracking method in the identification of the interface between columnar and equiaxed structures formed during a binary alloy solidification, driven by thermosolutal convection. The method, based on theoretical and experimental dendrite tip kinetics, is capable of directly distinguishing between the columnar mush and the undercooled liquid/equiaxed region developing ahead of the dendrite tip curve. A new numerical model and its computational algorithm are proposed, where the classical Eulerian volume averaged description of the transport processes is coupled with the Lagrangian front tracking method on a fixed control-volume grid. Having thus distinguished zones of different dendrite structures, distinct simulation models are used within each of the zones, e.g., the Darcy’s porous medium model in the stationary dendrite region, and a model of slurry with floating dendrites in the equiaxed part of the mush. The calculated temperature and solute concentration fields are compared with the relevant results of the classical enthalpy-porosity model, for an example problem of Pb-48 wt% Sn alloy solidification driven by diffusion and thermosolutal convection. And a good match with both solutions is exhibited. A preliminary validation study is also presented by comparing the available experimental data with the model predictions. Possible reasons for some observed discrepancies between the calculations and the experimental findings are discussed. Finally, the proposed front tracking approach is used to address the question of the impact of dendrites floating in the liquid on the flow pattern and macrosegregation in the solidifying alloy.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Tracking an internal interface via markers on a fixed control-volume grid

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Figure 2

A fragment of the front crossing a control-volume face

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Figure 3

Streamlines after 50 s of solidification, Δψ=3.67×10−6: (a) model of Roux (17), (b) model of Ahmad (25), and (c) the proposed model—Case 1

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Figure 4

Lines of constant solid fraction after 50 s of solidification: (a) model of Roux (17), (b) model of Ahmad (25), and (c) the proposed model—Case 1

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Figure 5

Relative tin concentration in the completely solidified alloy along the selected horizontal lines of the cavity central cross section (measured in (m) from the left cooled wall): solid line—Case 1, dashed line—Case 2, and dots—experimental data by Hebditch and Hunt (26)

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Figure 6

Relative mixture concentration of Sn (in %) after 150 s of solidification: left—Case 1, right—Case 2; a dotted line—the columnar front position

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Figure 7

Stream function after 150 s of solidification: left—Case 1, ψmax=8.8×10−6, right—Case 2, ψmax=1.4×10−4; a dotted line—the columnar front position

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Figure 8

Solid fraction after 150 s of solidification, left—Case 1, right—Case 2; a dotted line—the columnar front position

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Figure 9

Relative mixture concentration of Sn (in %) after 300 s of solidification: left—Case 1, right—Case 2; a dotted line—the columnar front position

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Figure 10

Stream function after 300 s of solidification: left—Case 1, ψmax=2.8×10−6, right—Case 2, ψmax=3.6×10−5; a dotted line—the columnar front position

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Figure 11

Solid fraction after 300 s of solidification: left—Case 1, right—Case 2; a dotted line—the columnar front position

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