• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.5 no.1
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• pp.35-43
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• 1993

A numerical model for the solidification of binary mixture is proposed. Numerical model, which employs enthalpy method, is modified from Continuum model, that is, improved relation is proposed for the Enthalpy - Temperature - Concentration - Liquid Mass Fraction. One dimensional example was selected to verify the proposed model. The results show that the new relation can be applied successfully to the solidification or melting of binary mixture.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.12
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• pp.3926-3937
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• 1996

In recent years there has been increased interest in the continuum model associated with the solidification of binary mixtures. A review of the literature, however, shows that the model verification was not sufficient or only qualitative. Present work is conducted for the reassessment of continuum model on the solidification problems of binary mixtures widely used for model validation. In spite of using the same continuum model, the results do not agree well with those of Incropera and co-workers which are benchmark problems typically used for validation of binary mixture solidification. Inferring from the agreement of present results with the analytic, experimental and other model's numerical results, this discrepancy seems to be caused by numerical errors in applying continuum model developed by Incropera and co-workers, not by the model itself. Careful examination should be preceded before selecting validation problems.

• Korean Chemical Engineering Research
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• v.52 no.2
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• pp.199-204
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• 2014

In binary solidification compositional convection in a porous mushy layer influences the quality of the final products. We consider the mushy layer solidifying from below with a constant solidification velocity. The disturbance equations for the mushy layer are derived using linear stability theory. The basic-state temperature fields and the distribution of the porosity in the mushy layer are investigated numerically. When the superheat is large, the thickness of the mushy layer is relatively small compared to the thickness of the thermal boundary layer. With decreasing the superheat the critical Rayleigh number based on the thickness of the mushy layer increases and the mushy layer becomes stable to the compositional convection. The critical Rayleigh number obtained from the continuity conditions of temperature and heat flux at the mush-liquid interface is smaller than that from the isothermal condition at the upper boundary of the mushy layer.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.4
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• pp.440-451
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• 1998

An experimental study has been conducted to investigate solidification of NH$_{4}$CI-H$_{2}$0 mixtures inside a vertical rectangular enclosure. Solidification process is visualized by the shadowgraph method. Emphasis is placed on the effect of solidification parameters such as the aspect ratio, cooling wall temperature and initial composition. The aspect ratio shows a dominant effect on the number and developing time of the double diffusive layers which reveals the relative strength of solutal convection to thermal convection. Similar flow pattern is observed when the concentration difference between interdendritic liquid and the pure liquid which drives solutal convection is the same regardless of the different cooling wall temperature and initial concentration.

• 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.20 no.11
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• pp.3655-3665
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• 1996

An analytical solution is presented for the conduction-dominated solidification of a binary mixture in a semi-infinite medium. The present approach differs from that of other solution by these four characteristics. (1) Solid fraction is determined from the phase diagram, (2) thermophysical properties in mushy zone are weighted according to the local solid fraction, (3) non-equilibrium solidification can be simulated and (4) the cooling condition of under-eutectic temperature can be simulated. Up to now, almost all analyses are based on the assumption of constant properties in mushy zone and solid fraction linearly with temperature or length. The validation for these assumptions, however, shows that serious error is found except some special cases. The influence of microscopic model on the macroscopic temperature profile is very small and can be ignored. But the solid fraction and average solid concentration which directly influence the quality of materials are drastically changed by the microscopic models. An approximate solution using the method of weighted residuals is also introduced and shows good agreement with the analytical solution. All calculations are performed for NH$_{4}$Cl-H$_{2}$O and Al-Cu system.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.4
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• pp.1437-1448
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• 1996

This paper presents a simplified model for approximate analysis of the solute redistribution in coarsening dendrite arms during solidification of binary metal alloys. By introducing a quadratic concentration profile with a time-dependent coefficient, the integral equation for diffusion in the solid phase is reduced to a simple differential relation between the coefficient and the solid-liquid interface position. The solid fraction corresponding to the system temperature is readily determined from the relation, phase equilibrium and the overall solute balance in which the liquid phase is assumed to be completely mixed. In order to validate the developed model, calculations are performed for the directional solidification of Al-4.9 mass Cu alloy. The predicted eutectic fractions for a wide range of the cooling rate reasonably agree with data from the well-known experiment as well as sophisticated numerical analyses. Also, the results for the back diffusion limits are consistent with available references. Additional calculations show that the characteristic parameters such as the coarsening, density variation and nonlinarity in the phase diagram significantly affect the microsegregation. Owing to the simplicity, efficiency and compatibility, the present model may be suitable for the micro-macroscopic solidification model as a microscopic component.

• Journal of the Korean Society for Heat Treatment
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• v.29 no.5
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• pp.227-233
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• 2016

Phase transformation phenomenon at high temperature was investigated by using designed TiAl-Nb alloys with addition of the ${\beta}$ stabilizer. Examination of dendritic morphologies in arc-melted button ingot could reveal the crystallography of the primary solidification phase. It was found that the addition of ${\beta}$ stabilizer(Nb) shifted the high temperature region of the binary Ti-Al phase diagram to the high Al composition side so that ${\beta}$ phase forms as a primary crystal even at higher Al composition compared with the binary Ti-Al system. The ${\beta}$ was found to be the primary solidification phase for alloys with Al content less than about 52 at.%. The composition of ${\beta}$ solidification in Ti-Al-Nb ternary system could be determined from the partial liquidus projection which was constructed by observing the microstructure of arc-melted buttons. The Ti-46Al-(6, 8)Nb composition was selected for ${\beta}$ solidification and the directional solidification was performed by a floating zone-type DS apparatus at the growth rate 30 mm/hr respectively.

• Korean Chemical Engineering Research
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• v.47 no.2
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• pp.174-178
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• 2009

A mushy layer of dendritic crystals is often formed during solidification of a binary mixture. Natural convection in the mushy layer is analyzed by using the propagation theory we have developed. The critical Rayleigh numbers for the onset of convection are evaluated numerically using the self-similar stability equations based on Emms and Fowler's model. The present results approach those from quasi-static stability analysis in the limit of a large superheat or a small growth rate of the mushy layer.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.7
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• pp.2367-2374
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• 1996

A generalized Scheil equation for the solute redistribution in the absence of the back diffusion during the dendritic solidification of binary alloys is derived, in which coarsening of the secondary dendrite arms is taken into account. The obtained equation essentially includes the original Scheil equation as a subset. Calculated results for typical cases show that the coarsening affects the microsegregation significantly. The eutectic fraction predicted for coarsening is considerably smaller than that for fixed arm spacing. The most important feature of the present equation in comparison with the Scheil equation lies in the fact that there exists a lower limit of the initial composition below which the eutectic is not formed. Based on the generalized Scheil equation and the lever rule, a new regime map of the eutectic formation on the initial composition-equilibrium partition coefficient plane is proposed. The map consists of three regimes: the eutectic not formed, conditionally formed and unconditionally formed, bounded by the solubility and diffusion controlled limit lines.