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Reduced complexity solidification models
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DOI：10.1016/j.ijheatmasstransfer.2021.120923.png)
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Abstract
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The solidification of a binary alloy, flowing between two cooled parallel plates is considered. A two-dimensional model for this system, involving the conservation equations of heat, solute, mass, and momentum, is constructed - the hi-fidelity model. Through a depth integration, a Reduced Complexity Model (RCM), in terms of one-dimensional advection equations, expressing the transient conservation of heat and solute, is obtained- the transient- RCM. For thermo-physical data, consistent with a dilute Al-Cu binary alloy, numerical predictions from the transient- RCM are shown to be in close agreement with predictions obtained from a numerical solution of the hi fidelity model. The RCM is reduced further, to a model formed as a single initial value problem, predicting the steady-state axial temperature and liquid fraction profiles between the plates - the steady-RCM. Analysis and numerical solutions of the transient-RCM and steady-RCM, provide a means of modeling, evaluating, and illustrating the role of solid phase motion in the timing and pattern of a binary alloy solidification. (C) 2021 Elsevier Ltd. All rights reserved.
Keywords:
EQUIAXED DENDRITIC SOLIDIFICATION
FREE-FLOATING DENDRITES
CAST-ALUMINUM ALLOYS
PHASE-CHANGE
MUSHY REGION
AL-CU
CONVECTION
TRANSPORT
MACROSEGREGATION
HEAT
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