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Research Papers

Study of Freckles Formation During Directional Solidification Under the Influence of Single-Phase and Multiphase Convection

[+] Author and Article Information
Prodyut R. Chakraborty

German Aerospace Center,
Institute of Materials Physics in Space,
Linder Höhe,
Köln 51147, Germany

Pradip Dutta

Department of Mechanical Engineering,
Indian Institute of Science,
Bangalore 560012, India
e-mail: pradip@mecheng.iisc.ernet.in

1Corresponding author.

Manuscript received October 13, 2012; final manuscript received January 30, 2013; published online May 17, 2013. Assoc. Editor: Lili Zheng.

J. Thermal Sci. Eng. Appl 5(2), 021004 (May 17, 2013) (13 pages) Paper No: TSEA-12-1172; doi: 10.1115/1.4023601 History: Received October 13, 2012; Revised January 30, 2013

Formation of freckles during directional solidification of hypereutectic aqueous ammonium-chloride in a bottom cooled cavity is studied numerically. The system studied is thermally stable but solutally unstable, which causes plume type convection and formation of channels in the growing solid mush. Solidification of hypereutectic solutions is usually characterized by detached and drifting solid crystals, thus resulting in multiphase convection. The numerical simulation is performed using a fixed grid single domain approach with single-phase and multiphase convection phenomena. For the multiphase convection modeling in the solidifying system under consideration, the mushy region is assumed to consist of an immobile coherent zone containing packed equiaxed crystals and a mobile noncoherent zone where the solid crystals are able to move. The two zones are demarcated by a critical solid fraction criterion, referred to as the coherency point. The overall effects of drifting solid phase on the freckles formation are compared with the results from conventional single-phase convection model.

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References

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Figures

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Fig. 1

Experimental observation by Tan [15] showing advection of solid phase during channel type solid front growth

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Fig. 2

Schematic diagram of the model system

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Fig. 3

Liquid fraction and flow pattern in the domain at different times for case 1, (a) t = 1770 s, VMAX = 0.632 mm/s, (b) t = 1800 s, VMAX = 0.623 mm/s, (c) t = 1825 s, VMAX = 0.617 mm/s, (d) t = 3500 s, VMAX = 0.313 mm/s, (e) t = 5000 s, VMAX = 0.089 mm/s. *The gray scale represents the variation of liquid fraction in the domain.

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Fig. 4

Macrosegregation in terms of water concentration at different times for case 1, (a) t = 1770 s, (b) t = 1800 s, (c) t = 1825 s, (d) t = 3500 s, (e) t = 5000 s. *The gray scale represents the variation of composition of water in the domain.

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Fig. 5

Zoomed out mushy region between two channels for case 1 at time t = 3500 s, (a) liquid fraction, (b) isotherms, (c) macrosegregation in terms of composition of water. *The color-bars in figure (a), (b), and (c) represent the variation of liquid fraction, temperature and composition of water, respectively.

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Fig. 6

Temperature contour at different times for case 1, (a) t = 1770 s, (b) t = 1800 s, (c) t = 1825 s, (d) t = 3500 s, (e) t = 5000 s. *The gray scale represents the variation of temperature in Kelvin.

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Fig. 7

Stream function at different times for case 1, (a) t = 1770 s, (b) t = 1800 s, (c) t = 1827 s, (d) t = 3500 s, (e) t = 5000 s. *The gray scale represents the variation of stream function value ψ with the unit m2/s.

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Fig. 8

Liquid fraction and flow pattern in the domain at different times for case 3, (a) t = 1770 s, VMAX = 0.618 mm/s, (b) t = 1800 s, VMAX = 0.621 mm/s, (c) t = 1825 s, VMAX = 0.623 mm/s, (d) t = 3500 s, VMAX = 0.337 mm/s, (e) t = 5000 s, VMAX = 0.034 mm/s. *The gray scale represents the variation of liquid fraction in the domain.

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Fig. 9

Macrosegregation in terms of water concentration at different times for case 3, (a) t = 1770 s, (b) t = 1800 s, (c) t = 1825 s, (d) t = 3500 s, (e) t = 5000 s. *The gray scale represents the variation of composition of water in the domain.

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Fig. 10

Temperature contour at different times for case 3, (a) t = 1770 s, (b) t = 1800 s, (c) t = 1825 s, (d) t = 3500 s, (e) t = 5000 s. *The gray scale represents the variation of temperature in Kelvin.

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Fig. 11

Stream function at different times for case 1, (a) t = 1770 s, (b) t = 1800 s, (c) t = 1825 s, (d) t = 3500 s, (e) 5000 s. *The gray scale represents the variation of stream function value ψ with the unit m2/s.

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Fig. 12

Comparison of time evolution of maximum velocity scale for single-phase and multiphase simulation (velocity unit m/s). We show early onset and late decline of convection for single-phase case study, and late onset and early decline of convection for multiphase study.

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Fig. 13

Average height (mm) of mushy zones in between the channels in terms of position of 1% solid fraction with respect to the time

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Fig. 14

Evolution of average maximum width (mm) of the channels near the channel mouth with respect to the time

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