• 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.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1269-1283
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• 2011

Here we consider magneto-convection in a mushy layer which is formed during solidification of binary alloys. The mushy layer is treated as an active porous media with variable permeability. The equations governing the layer are conservation of mass, conservation of heat, conservation of solute, magnetic induction equation, momentum equation governed by the Darcy's law and Maxwell's equations for the magnetic field. To study the second order effects on the flow without solving the second order system, we need to obtain the adjoint system for the flow. This motivates the authors we derive the adjoint system analytically for the mushy layer case. Numerical results of the adjoint system are presented for passive and active mushy layers at the onset of the motion using a set of parameters experimentalists use.

• Korean Chemical Engineering Research
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• v.55 no.6
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• pp.868-873
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• 2017

Natural convection is driven by the compositional buoyancy in solidification of a binary melt. The stabilities of convection in a growing mushy layer were analyzed here in the time-dependent solidification system of a near-eutectic melt cooled impulsively from below. The linear stability equations were transformed to self-similar forms by using the depth of the mushy layer as a length scale. In the liquid layer the stability equations are based on the propagation theory and the thermal buoyancy is neglected. The critical Rayleigh number for the mushy layer increases with decreasing the Stefan number and the Prandtl number. The critical conditions for solidification of aqueous ammonium chloride solution are discussed and compared with the results of the previous model for the liquid layer.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.499-510
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• 2012

Here we consider the inertial effect in a horizontal mushy layer during solidification of a binary alloy. Using perturbation technique, we obtain two systems, one of zero order and the other of first order. We consider a mushy layer with an impermeable mush-liquid interface and of constant permeability. The analysis reveals that the effect of inertial parameter is stabilizing in the sense that the critical Rayleigh number at the onset of motion increases by the inertial effect.

• 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.

• Korean Chemical Engineering Research
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• v.50 no.1
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• pp.61-65
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• 2012

The onset of convection in a mushy layer is analyzed by using linear stability theory in time-dependent solidification of a binary melt. A simplified model of a near-eutectic mush, in which the mush is assumed to be a porous block, is used and the propagation theory is applied to determine the critical conditions for the onset of convection. The present critical Rayleigh number is higher than the existing experimental result and also theoretical results obtained by considering the mushy layer with an overlying liquid layer. The constant pressure (permeable) condition applied on the mush-liquid interface produces a lower critical Rayleigh number, which is closer to the experimental results of aqueous ammonium chloride solution, compared with the impermeable condition.

• Journal of Korea Foundry Society
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• v.6 no.1
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• pp.20-26
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• 1986

In order to investigate the solidification characteristics of CV. graphite cast iron, decantation technique and thermal analysis test were used. Solidification characteristics were studied in the specimens with various compositions and graphite shape. The results were as follows; 1. The first surface solidifcation layer is formed along the mold wall by the growth of austenite dendrites in hypoeutectic composition and thin solid film in hypereutectic composition. 2. The mushy degree of solidifcation of hypereutiectic composition is higher than that of hypoeutectic. 3. In hypoeutectic, the effect of change of the mushy degree of solidification on the graphite shape is small, however, in hypereutectic the mushy degree of solidification becomes higher in order of flake, CV, and spheroidal graphite cast iron.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.11
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• pp.1437-1446
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• 2000

A numerical analysis on the freeze coating process of a non-isothermal finite dimensional plate with a binary alloy is performed to investigate the growth and decay behavior of the solid and the mushy layer of the freeze coat and a complete procedure to calculate the process is obtained in this study. The continuously varying solid and mushy layers are immobilized by a coordinate transform and the resulting governing differential equations are solved by a finite difference technique. To account for the latent heat release and property change during solidification, proper phase change models are adopted. And the convection in the liquid melt is modeled as an appropriate heat transfer boundary condition at the liquid/mushy interface. The present results are compared with analytic solutions derived for the freeze coating of infinite dimensional plates and the discrepancy is found to be less than 0.5 percent in relative magnitude for all simulation cases. In addition the conservation of thermal energy is checked. The results show that the freeze coat grows proportional to the 1.2 square of axial position as predicted by analytic solutions ar first. But after the short period of initial growth, the growth rate of the freeze coat gradually decreases and finally the freeze coat starts to decay. The effects of various non-dimensional processing parameters on the behavior of freeze coat are also investigated.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.18 no.12
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• pp.52-58
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• 2019

This study numerically analyzed the icing process in a U-shaped pipe exposed to the outside by considering the mushy zone of freezing water. Numerical results showed that the flow was pulled outward due to the U-shaped bend in the freezing section exposed to the outside, which resulted in the ice wave formation on the wall of the bended pipe behind. At the same time, the formation of a corrugated ice layer became apparent due to the venturi effect caused by the ice. The factors affecting the freezing were investigated, including the change of the pipe wall temperature, the water inflow velocity, and the pipe bend spacing. It was found that, as a whole, the thickness of the freezing layer increased as the pipe wall temperature decreased. It was also found that the freezing layer became relatively thin when the inflow rate of water was increased, and that the spacing of the pipe bends did not significantly impact the change in the freezing layer.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.17 no.6
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• pp.144-150
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• 2018

In this study, the freezing process of L-shaped pipe exposed to the outside was investigated numerically by considering the mushy zone of freezing water. From the numerical results, it was found that the flow was outwardly directed due to the influence of the L-shaped bending part in the outside exposed part of the pipe, and the ice was formed in the shape of longitudinal corrugation on the wall surface of the pipe after the bending part. It is confirmed that this phenomenon is caused by the venturi effect due to the freezing as seen in connection with the velocity distribution in the pipe. It is found that the remelting phenomenon at the end of the freezing section occur simultaneously during the process of forming the ice in the pipe section. In regard of the factors affecting freezing, it was found that the thickness of the freezing layer is increased as the exposed pipe surface temperature is decreased, and the pipe surface temperature had a significant effect on the change of the freezing layer thickness. At the same time, it was found that the freezing layer becomes relatively thin when the water inflow rate is increased. This phenomenon was caused by reducing the exposure time of freezing water due to the vigorous flow convection of the water fluid.