• 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.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.12
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• pp.1657-1668
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• 1998

In the analysis of a mushy solidification system with natural convection using a fixed grid method, the enthalpy method has been used to account for the release of latent heat. The variable viscosity, Darcy source, and hybrid methods have been employed for the velocity suppression in a mushy region. The choice of the values of solid viscosity and permeability constant in conjunction with the Darcy source term plays an important role in forming the location and shape of the phase boundaries. In this work the effects of these major parameters related to steady-state behavior in the system of mushy solidification are investigated through a simple test problem. The effective specific heat based on the spatial gradients of the enthalpy and temperature is adopted for the treatment of the release of latent heat. The effects of the Prandtl and Rayleigh numbers on the shape of mushy region are examined using the hybrid method.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.584-595
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• 1991

In the direct rolling processes for the mushy state alloy, a mushy state material which simultaneously contains liquid-solid phase is obtained from the exit port of stirring apparatus with a given solid fraction. This solid fraction is dependent on the temperature of within the solid-liquid range which shows to be controlled accurately by the experimental conditions for a given stirring apparatus. Rolling conditions for fabrication the fine surface strip were obtained from direct rolling experiment with mushy state alloys of Sn-75%Pb and aluminum alloy. Influence of solid fraction, rolling speed and initial roller gap on the state of strip surface and solidified structure was observed. We proposed theoretical model for prediction of rolling force, and we compared calculation result and experimental value measured with load cell.

• 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.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.

• 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.

• Nuclear Engineering and Technology
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• v.41 no.7
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• pp.929-944
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• 2009

The present study is concerned with the extension of the Effective Convectivity Model (ECM) to the phase-change problem to simulate the dynamics of the melt pool formation in a Light Water Reactor (LWR) lower plenum during hypothetical severe accident progression. The ECM uses heat transfer characteristic velocities to describe turbulent natural convection of a melt pool. The simple approach of the ECM method allows implementing different models of the characteristic velocity in a mushy zone for non-eutectic mixtures. The Phase-change ECM (PECM) was examined using three models of the characteristic velocities in a mushy zone and its performance was compared. The PECM was validated using a dual-tier approach, namely validations against existing experimental data (the SIMECO experiment) and validations against results obtained from Computational Fluid Dynamics (CFD) simulations. The results predicted by the PECM implementing the linear dependency of mushy-zone characteristic velocity on fluid fraction are well agreed with the experimental correlation and CFD simulation results. The PECM was applied to simulation of melt pool formation heat transfer in a Pressurized Water Reactor (PWR) and Boiling Water Reactor (BWR) lower plenum. The study suggests that the PECM is an adequate and effective tool to compute the dynamics of core melt pool formation.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.9
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• pp.1166-1174
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• 2000

This work presents a two-dimensional quasi-steady state model to study the fluid flow and heat transfer in high-power density welding process of thin AISI-304 stainless steel plates. The enthalpy method and the finite volume method were used for a numerical analysis of the mushy region phase change as well as the heat flow at the weld pool and the heat-affected zone. The results show that the mushy region distributed around the weld pool becomes wider downstream and the surface heat losses by convection and radiation can be significant factors in welding process especially when a welding speed is relatively low.