Analysis of macroscopic momentum equation in a columnar mushy zone

Analysis of macroscopic momentum equation in a columnar mushy zone Purpose – This paper aims to tackle the problem of some ambiguity of the momentum equation formulation in the commonly used macroscopic models of two‐phase solid/liquid region, developing during alloy solidification. These different appearances of the momentum equation are compared and the issue is addressed of how the choice of the particular form affects velocity and temperature fields. Design/methodology/approach – Attention is focused on the ensemble averaging method, which, owing to its stochastic nature, is a new promising tool for setting up the macroscopic transport equations in highly inhomogeneous multiphase micro‐ and macro‐structures, with morphology continuously changing in time when the solidification proceeds. The basic assumptions of the two other continuum models, i.e. based on the classical mixture theory and on the volume‐averaging technique, are also unveiled. These three different forms of the momentum equation are then compared analytically and their impact on calculated velocity and temperature distribution in the mushy zone is studied for the selected test problem of binary alloy solidification driven by diffusion and thermal natural convection in a square mould. Findings – It is found that a chosen appearance of the momentum equation mildly affects temporal velocity/temperature, and shapes of the phase interface at longer times of the solidification. Research limitations/implications – This mainly results from small variations of the liquid fraction across the mushy zone and from a low solidification rate, and it may change drastically when anisotropic properties of the mushy zone, solutal convection, different phase densities and cooling conditions are considered. Therefore, further comprehensive study is needed. Originality/value – The paper addresses how the different focus of the momentum equation for liquid flow is compared. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Numerical Methods for Heat & Fluid Flow Emerald Publishing

Analysis of macroscopic momentum equation in a columnar mushy zone

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Publisher
Emerald Publishing
Copyright
Copyright © 2008 Emerald Group Publishing Limited. All rights reserved.
ISSN
0961-5539
DOI
10.1108/09615530810853718
Publisher site
See Article on Publisher Site

Abstract

Purpose – This paper aims to tackle the problem of some ambiguity of the momentum equation formulation in the commonly used macroscopic models of two‐phase solid/liquid region, developing during alloy solidification. These different appearances of the momentum equation are compared and the issue is addressed of how the choice of the particular form affects velocity and temperature fields. Design/methodology/approach – Attention is focused on the ensemble averaging method, which, owing to its stochastic nature, is a new promising tool for setting up the macroscopic transport equations in highly inhomogeneous multiphase micro‐ and macro‐structures, with morphology continuously changing in time when the solidification proceeds. The basic assumptions of the two other continuum models, i.e. based on the classical mixture theory and on the volume‐averaging technique, are also unveiled. These three different forms of the momentum equation are then compared analytically and their impact on calculated velocity and temperature distribution in the mushy zone is studied for the selected test problem of binary alloy solidification driven by diffusion and thermal natural convection in a square mould. Findings – It is found that a chosen appearance of the momentum equation mildly affects temporal velocity/temperature, and shapes of the phase interface at longer times of the solidification. Research limitations/implications – This mainly results from small variations of the liquid fraction across the mushy zone and from a low solidification rate, and it may change drastically when anisotropic properties of the mushy zone, solutal convection, different phase densities and cooling conditions are considered. Therefore, further comprehensive study is needed. Originality/value – The paper addresses how the different focus of the momentum equation for liquid flow is compared.

Journal

International Journal of Numerical Methods for Heat & Fluid FlowEmerald Publishing

Published: May 22, 2008

Keywords: Solidification; Numerical analysis; Simulation; Flow

References

  • Average momentum equation for interdendritic flow in a solidifying columnar mushy zone
    Bousquet‐Melou, P.; Goyeau, B.; Quintard, M.; Fichot, F.; Gobin, D.

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