• 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.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.16 no.5
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• pp.203-209
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• 2006

For $P_B=50,\;{\Delta}T=10K$, Ar=5, Pr=2.36, Le=0.015, Pe=1.26, Cv=1.11, the intensity of solutal convection (solutal Grashof number $Grs=3.44x10^4$) is greater than that of thermal convection (thermal Grashof number $Grt=1.81x10^3$) by one order of magnitude, which is based on the solutally buoyancy-driven convection due to the disparity in the molecular weights of the component A($Hg_2Cl_2$) and B(He). With increasing the partial pressure of component B from 10 up to 200 Torr, the rate is decreased exponentially. The convective transport decreases with lower g level and is changed to the diffusive mode at 0.1 $g_0$. In other words, for regions in which the g level is 0.1 $g_0$ or less, the diffusion-driven convection results in a parabolic velocity profile and a recirculating cell is not likely to occur. Therefore a gravitational acceleration level of less than 0.1 $g_0$ can be adequate to ensure purely diffusive transport.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.32 no.1
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• pp.16-24
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• 2022

A computational study of combined thermal and solutal convection (double diffusive convection) in a sealed crystal growth reactor is presented, based on a two-dimensional numerical analysis of the nonlinear and strongly coupled partial differential equations and their associated boundary conditions. The average Nusselt numbers for the source regions are greater than those at the crystal regions for 9.73 × 10³ ≤ Gr_t ≤ 6.22 × 10⁵. The average Nusselt numbers for the source regions varies linearly and increases directly with the thermal Grashof number form 9.73 × 10³ ≤ Gr_t ≤ 6.22 × 10⁵ for aspect ratio, Ar (transport length-to-width) = 1 and 2. Additionally, the average Nusselt numbers for the crystal regions at Ar = 1 are much greater than those at Ar = 2. Also, the occurrence of one unicellular flow structure is caused by both the thermal and solutal convection, which is inherent during the physical vapor transport of Hg₂Br₂. When the aspect ratio of the enclosure increases, the fluid movement is hindered and results in the decrease of thermal buoyancy force.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.14 no.2
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• pp.50-57
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• 2004

Mercurous Bromide ($Hg_2Br_2$) crystals hold promise for many acousto-optic and opto-electronic applications. This material is prepared in closed ampoules by the physical vapor transport (PVT) growth method. We investigate the effects of solutal convection on the crystal growth rate in a horizontal configuration for diffusive-convection conditions and purely diffusion conditions achievable in a low gravity environment. Our results show that the growth rate is decreased by a factor of one-fourth with a ten reduction of gravitational acceleration near y = 2.0 cm. For 0.1 $g_O$ the growth rate pattern exhibits relatively flat which is intimately related to diffusion-dominated processes. The growth rate nonuniformity is regardless of aspect ratio across the interfacial positions from 0 to 1.5. Also, the effect of a factor of the ten reduction in the gravitational acceleration is same to both Ar = 5 and 2. The enlargement in the molecular weight of B from 50 to 500 by a factor 4 causes a decrease in the maximum growth rate by the same factor, indicative of the effect of solutal gradients.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.14 no.6
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• pp.450-455
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• 2002

Convective instability driven by surface tension is analyzed in an initially quiescent water absorbing ammonia gas using the linear stability theory. The propagation theory is adapated to find the critical conditions of the onset of solutal Maragoni convection. In this theory, the solutal penetration depth is chosen as the length scale factor. The results show that the liquid layer becomes more stable with decreasing the Schmidt number It is interesting that for a smaller Biot number than 100, the system becomes stable with decreasing Bi but for a larger Bi, it becomes unstable with decreasing Bi.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.4
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• pp.525-540
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• 1997

The effect of mold rotation on the transport process and resultant macrosegregation pattern during solidification of an Al-Cu alloy contained in a vertical axisymmetric annular mold cooled from the inner wall is numerically investigated. The mold initially at rest starts to rotate at a prescribed angular velocity simultaneously with the beginning of cooling. Computed results for a representative case show that the mold rotation essentially suppresses the development of both thermal and solutal convections in the melt, creating distinct characteristics such as the liquidus front, flow pattern and temperature distribution from those for the stationary mold. Thermal convection which develops at the early stages of cooling is soon extinguished by the rotating flow induced during spin-up, and thus does not effectively remove the initial superheat from the melt. On the other hand, solutal convection, though it weakens considerably and is confined within the mushy zone, still predominates over the solute redistribution process. With increasing the angular velocity, the solute transport in the axial direction is enhanced, whereas that in the radial direction is reduced. The final macrosegregation formed in the mold rotating at moderate angular velocities appears to be favorable in comparison with the stationary casting, in that not only relatively homogenized composition is achieved, but also a severely positive-segregated channel is restrained.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.5 no.2
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• pp.111-121
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• 1993

Double-diffusive convection during solidification process of the binary mixture was studied numerically. Enthalpy method and finite element method were implemented in the analysis. Calculation carried out for $R{\alpha}_T=10^3-10^4$ and $R{\alpha}_T=0-10^5$. The results show that the variation of thermal Rayleigh number changes the fields of velocity, temperature and concentration, but the variation of solutal Rayleigh number gives little effects on those. In conclusion, concentration gradient can be negligible compared with temperature gradient in macroscopic point of view, although concentration gradient plays a role in forming dendrite.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.3
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• pp.445-456
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• 1997

Continuous casting process is numerically analyzed using the continuum model in a non-orthogonal coordinate system. Flow damping in the mush is modeled by combining the viscosity dependence on liquid fraction in dilute mush and the permeability dependence on liquid fraction in concentrated mush. The effect of turbulence is indirectly considered by effective diffusivity determined elsewhere by experiment. The main objective is to investigate the effects of casting parameters such as casting speed and tundish superheat on the distribution of surface temperature, shell thickness, metallurgical length and centerline segregation. Some of the computed results are compared with available experiments, and reasonable agreements are obtained.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.19 no.4
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• pp.172-183
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• 2009

For the effects of the nonlinear temperature profiles and reduced-gravity conditions we conduct a two-dimensional numerical modeling and simulations on the physical vapor transport processes of $Hg_2Cl_2-Xe$ system in the horizontal orientation position. Our results reveal that: (1) A decrease in aspect ratio from 5 to 2 leads to an increasingly nonuniform interfacial distribution and enhances the growth rate by one-order magnitude for normal gravity and linear wall temperature conditions. (2) Increasing the molecular weight of component B, Xenon results in a reduction in the effect of solutal convection. (3) The effect of aspect ratio affects the interfacial growth rates significantly under normal gravity condition rather than under reduced gravitational environments. (4) The transition from the convection-dominated regime to the diffusion-dominated regime ranges arises near at 0.1g$_0$ for operation conditions under consideration in this study.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.7
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• pp.1731-1740
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• 1995

Experimental investigations have been made to study the double-diffusive nature of convection of an initially stratified salt-water solution due to heating from below in a rotating cylindrical cavity. The objective is to examine the flow phenomena and the heat transfer characteristics according to the changes in temperature gradient, concentration gradient and rotating velocity of cavity. Thermal and solutal boundary conditions at side wall are adiabatic and impermeable, respectively. The top and bottom plate are maintained each at constant temperature and concentration. The cavity is put into a state of solid body rotation. Like the stationary case, the types of initially-formed flow pattern are classified into three regimes depending on the effective Rayleigh number and Taylor number; stagnant flow regime, single mixed-layer flow regime and successively formed multi-mixed layer flow regime. At the same effective Rayleigh number, the number of initially-formed mixed layer and its growth rate decrease as the effect of rotation increases. The temperature and concentration profiles are both uniform in each layer due to convective mixing in the layered-flow regime, but look both liner in stagnant flow regime and single mixed-layer flow regime. At the interface between adjacent layers, the temperature changes smoothly but the concentration changes rapidly.