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Research Papers: Melting and Solidification

Comparison of Three-Dimensional Multidomain and Single-Domain Models for the Horizontal Solidification Problem

[+] Author and Article Information
M. H. Avnaim, A. Levy, O. Ben-David, A. Azulay

Pearlstone Center for Aeronautical
Engineering Studies,
Department of Mechanical Engineering,
Ben-Gurion University of the Negev,
Be'er Sheva 8410501, Israel

B. Mikhailovich

Pearlstone Center for Aeronautical
Engineering Studies,
Department of Mechanical Engineering,
Ben-Gurion University of the Negev,
P.O. Box 653,
Be'er Sheva 8410501, Israel
e-mail: borismic@bgu.ac.il

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received February 16, 2016; final manuscript received May 12, 2016; published online June 14, 2016. Editor: Portonovo S. Ayyaswamy.

J. Heat Transfer 138(11), 112301 (Jun 14, 2016) (11 pages) Paper No: HT-16-1086; doi: 10.1115/1.4033700 History: Received February 16, 2016; Revised May 12, 2016

In this paper, horizontal solidification of gallium in a rectangular cavity was studied both experimentally and numerically. Two three-dimensional (3D) numerical models related to different numerical approaches were built. The first is a single-domain (SD) model based on the volume-of-fluid (VOF) method. This model also takes into account the presence of a mushy zone. The second model is a multidomain (MD) one; it includes two different meshes for the two phases and uses Stephan's boundary condition to determine the front velocity. The 3D models were tested under various thermal boundary conditions and compared with experimental results obtained in an appropriate experimental setup. The experimental setup included an ultrasonic Doppler velocimeter (UDV) for noninvasive measurements of the velocities in the liquid part of the metal, liquid–solid interface position and profile, its displacement, and longitudinal mean velocity. For determining the boundary influence, both 3D and 2D models were built. The comparison was carried out for the solidification front location and shape and the velocity and temperature fields. In general, the 3D numerical model gave more accurate results than the 2D model with respect to the experiments results. Although the MD model is more complicated to build and requires more computational efforts than the VOF model, the 3D MD model provides the most accurate results in comparison with current experiments.

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Figures

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Fig. 1

Horizontal solidification process scheme for midvertical xy plane (z = 0): (a) VOF and (b) MD

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Fig. 2

Comparison of solidification front in VOF model for grids (a) and (b)

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Fig. 3

Comparison of solidification front in MD model for two calculation methods (c) and (d)

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Fig. 4

Schematic diagram of experimental system: (1) constant temperature bath, (2) Plexiglas walls, (3) thermocouples inside the cavity, (4) heat exchanger, (5) heat exchanger thermocouples, (6) ultrasonic transducers, and (7) and (8) pouring and compensating tubes

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Fig. 5

Solid–liquid front location and shape for different moments of time for 3D VOF and MD models versus experiments for case nos. (a) 1, (b) 2, and (c) 3 (Table 2)

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Fig. 6

Liquid fraction in mid z-plane at t = 1800 s for the 3D VOF model, case 1 (Table 2)

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Fig. 7

Temperature as a function of time in the middle of the container (x = 47 mm and z = 0 mm) for 3D VOF and MD models versus experiments (case 1, Table 2) for different heights: (a) 45 mm, (b) 30 mm, and (c) 15 mm

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Fig. 8

Velocity field during the solidification process for MD. Left—case no. 1 and right—case no. 3 at (a) t = 1000 s and (b) 3000 s.

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Fig. 9

Velocity field during the solidification process for VOF. Left—case no. 1 and right—case no. 3 at (a) t = 1000 s and (b) 3000 s.

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Fig. 10

x-velocity profiles (y = 53 mm and z = 20 mm) along the container length for 3D VOF and MD models versus experimental profiles for case no. 1 (Table 2)

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Fig. 11

x-velocity profiles (y = 7 mm and z = 20 mm) along the container length for 3D VOF and MD models versus experimental profiles for case no. 1

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Fig. 12

Solid–liquid front location and shape at different moments of time for 2D and 3D VOF models versus experiments for cases (a) 1 and (b) 3

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Fig. 13

Solid–liquid front location and shape at different moments of time for the 2D and 3D MD model versus experiments for cases (a) 1 and (b) 3

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