• Journal of Mechanical Science and Technology
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• v.15 no.8
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• pp.1188-1195
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• 2001

A numerical analysis has been carried out to investigate the influences of thermosolutal convection on the heat and mass transfer and solute segregation in crystals grown by the vertical Bridgman technique. The governing equations are solved by a finite-volume method using the power law scheme and the SIMPLE algorithm in which body-fitted coordinate system has been used. A primary convective cell driven by thermal gradients forms in the bulk of the domain, while a secondary convective cell driven by solutal gradients forms near interface. As the solutal Rayleigh number increases, secondary cell becomes to be stronger and has a great influence on the radial concentration along the interface.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.10
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• pp.1337-1345
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• 2001

Numerical investigation is made to study the effects of thermosolutal convection on the formation of macrosegregation in a Pb-Sn alloy solidification process in a two dimensional confined rectangluar mold. The basic equations are sovled using the Contrinum Model theory with the SIMPE algorithm during the solidification process. In addition, to track the liquid-solid interface with time variations, the moving boundary condition was adopted and moving irregular interface shapes were treated with the time-dependent, boundary-fitted coordinate system. As the temperature reduces from the liquidus to the solidus, the liquid concentration of Sn, the lighter constituent, increases. Then the buoyancy-driven flow due to temperature and liquid composition gradients occurs in the mushy region and forms the complicated macrosegregation maps. belated to this phenomena, effects on the macrosegregation formation depending on the cooling condition and gravity values are examined.

• Proceedings of the KSME Conference
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• 2000.04b
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• pp.37-44
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• 2000

Numerical investigation is made to study the effects of natural convection on the formation of macrosegregation of a Pb-Sn alloy solidification process in a 2-D confined rectangle mold. The governing equations are calculated using previous continuum models with SIMPLE algorithm doring the solidification process. In addition. to track the solid-liquid interface with time variations. the moving boundary condition Is adopted and irregular interface shapes are treated with Boundary-Fitted Coordinate system. As the temperature reduce from the liquidus to the solidus, the liquid concentration of Sn. the lighter constituent, increases. Then the buoyancy-driven flow due to temperature and liquid composition gradients, called thermosolutal convection or double diffusion, occurs in the mushy region and forms the complicated macrosegregation maps. Related to this phnomena, effects on the macrosegregation formation depending on the cooling condition and gravity values are described.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.51-66
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• 2007

A layer of compressible, rotating, elastica-viscous fluid heated & soluted from below is considered in the presence of vertical magnetic field to include the effect of Hall currents. Dispersion relation governing the effect of viscoelasticity, salinity gradient, rotation, magnetic field and Hall currents is derived. For the case of stationary convection, the Rivlin-Erickson fluid behaves like an ordinary Newtonian fluid. The compressibility, stable solute gradient, rotation and magnetic field postpone the onset of thermosolutal instability whereas Hall currents are found to hasten the onset of thermosolutal instability in the absence of rotation. In the presence of rotation, Hall currents postpone/hasten the onset of instability depending upon the value of wavenumbers. Again, the dispersion relation is analyzed numerically & the results depicted graphically. The stable solute gradient and magnetic field (and corresponding Hall currents) introduce oscillatory modes in the system which were non-existent in their absence. The case of overstability is discussed & sufficient conditions for non-existence of overstability are derived.

• Journal of Korea Foundry Society
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• v.17 no.1
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• pp.76-84
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• 1997

An investigation of the effects of transverse magnetic field on melt convection and macrosegregation in vertical Bridgman growth of Te doped InSb was carried out by means of microstructure observation, the measurement of Te distribution by Hall measurement, electrical resistivity measurement and X-ray analysis. Prior to the experiments, interface stability, convective instability and suppression of convection by magnetic field were examined. A thermosolutal convection in the Te doped InSb melt occurred in the examined growth condition without magnetic field. The effective distribution coefficient, $K_{eff}$, was about 0.35 without magnetic field, 0.45 with magnetic field of 2kG, and 0.7 at 4kG. It was found that the stronger the applied magnetic field was, the more the convection was suppressed.

• Proceedings of the Korea Association of Crystal Growth Conference
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• 1996.06a
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• pp.522-522
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• 1996

An investigation of the effects of transverse magnetic field and Peltier effect on melt convection and macrosegregation in vertical Bridgman crystal grosth of Te doped InSb was been carried out by means of microstructure observation, Hall measurement, electrical resistivity measurement and X-ray analysis. Before the experiments, Interface stability, convective instability and suppression of convection by magnetic field were calculated theoretically. After doping 1018, 1019 cm-3 Te in InSb, the temperature of Bridgman furnace was set up at $650^{\circ}C$. The samples were grown in I.D. 11mm, 100mm high quartz tube. The velocity of growth was about 2${\mu}{\textrm}{m}$/sec. In order to obtain the suppression of convection by magnetic field in the middle of growth, 2-4KG magnetic field was set on the melt. For searching of the shape of solid-liquid interface and the actual velocity of crystal growth, let 2A current flow from solid to liquid for 1second every 50seconds repeatedly (Peltier effect). The grown InSb was polycrystal, and each grain was very sharp. There was no much difference between the sample with and without magnetic field at a point of view of microstructure. For the sample with Peltier effect, the Peltier marks(striation) were observed regularly as expected. Through these marks, it was found that the solid-liquid interface was flat and the actual growth velocity was about 1-2${\mu}{\textrm}{m}$/sec. On the ground of theoretical calculation, there is thermosolutal convection in the Te doped InSb melt without magnetic field in this growth condition. and if there is more than 1KG magnetic field, the convection is suppressed. Through this experiments, the effective distribution coefficients, koff, were 0.35 in the case of no magnetic field, and 0.45 when the magnetic field is 2KG, 0.7 at 4KG. It was found that the more magnetic field was applied, the more convection was suppressed. But there was some difference between the theoretical calculation and the experiment, the cause of the difference was thought due to the use of some approximated values in theoretical calculation. In addition to these results, the sample with Peltier effect showed unexpected result about the Te distribution in InSb. It looked like no convection and no macrosegregation. It was thought that the unexpected behavior was due to Peltier mark. that is, when the strong current flew the growing sample, the mark was formed by catching Te. As a result of the phenomena, the more Te containing thin layer was made. The layer ruled the Hall measurement. The values of resistivity and mobility of these samples were just a little than those of other reference. It was thought that the reason of this result was that these samples were due to polycrystal, that is, grain boundaries had an influence on this result.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.1
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• pp.162-171
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• 1993

This paper deals with the anisotropy of the mushy region during solidification process of a binary mixture. A theoretical model which specifies a permeability tensor in terms of pricipal values is proposed. Also, the governing equations are modified into convenient forms for the numerical analysis with the existing algorithm. Some test computations are performed for soeidification of aqueous ammonium chloride solution contained in a square cavity. Results show that not only the present model is capable of resolving fundamental characteristics of the tranport phenomena, but also the anisotropy significantly affects the interdendritic flow structure, i.e., double-diffusive convection and macrosegregation patterns.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.33 no.3
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• pp.110-115
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• 2023

During the Hg₂Br₂ physical vapor transport process, with increasing the partial pressure of component B, P_B from 40 Torr to 200 Torr, a unicellular convective flow structures move from the crystal growth region to the center region in the vapor phase. The boundary layer flow is dominant for P_B = 40 Torr, and the core region flow is dominant for P_B = 200 Torr. The flow in the vapor phase shows a three-dimensional convective flow structure with a single cell (unicellular) for P_B = 40 Torr and 200 Torr, exhibits an asymmetrical flow with respect to the x, y central axis under the horizontally oriented configuration with an aspect ratio (length-to-width) of 3 and linear conducting walls. The critical temperature difference between the source and crystal region is about 30 K. The total molar flux of Hg₂Br₂ increases with the temperature difference until the total molar flux reaches the critical value. At the critical total molar flux, the total molar flux abruptly decreases.