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Article
Publication date: 22 May 2008

Dominique Gobin and Benoit Goyeau

This paper aims to provide a limited, but selective bibliography on modelling heat and mass transfer in composite fluid‐porous domains.

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Abstract

Purpose

This paper aims to provide a limited, but selective bibliography on modelling heat and mass transfer in composite fluid‐porous domains.

Design/methodology/approach

Since the pioneer study by Beavers and Joseph, the problem of interface continuity and/or jump conditions at a fluid‐porous interface has been of interest to the fluid mechanics and heat and mass transfer community. The paper is concerned both with numerical simulations of heat and fluid flow in such systems, and with the linear stability problems.

Findings

The one‐ and two‐domain formulations are equivalent. Using the Darcy‐Brinkman extension instead of the Darcy model reduces the number of ad hoc parameters in this configuration.

Research limitations/implications

The problem of double diffusive convection has still to be solved and analyzed.

Practical implications

The discussion on the interface conditions is of great relevance to many industrial and practical situations.

Originality/value

The important question of the macroscopic formulation of the problem is tackled in the paper.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 18 no. 3/4
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 2 November 2010

Mohamed Rady, Eric Arquis, Dominique Gobin and Benoît Goyeau

This paper aims to tackle the problem of thermo‐solutal convection and macrosegregation during ingot solidification of metal alloys. Complex flow structures associated with the…

362

Abstract

Purpose

This paper aims to tackle the problem of thermo‐solutal convection and macrosegregation during ingot solidification of metal alloys. Complex flow structures associated with the development of channels segregate and sharp gradients in the solutal field call for the implementation of accurate methods for numerical modeling of alloy solidification. In particular, the solute transport equation is convection dominated and requires special non‐oscillarity type high‐order schemes to handle the regions of channels segregates.

Design/methodology/approach

In the present study, a time‐splitting approach has been adopted to separately handle solute advection and diffusion. This splitting technique allows the application of accurate total variation dimensioning (TVD) schemes for solution of solute advection. Applications of second‐order Lax‐Wendroff TVD SUPERBEE and fifth‐order weighted essentially non‐oscillatory (WENO) schemes are described in the present article. Classical numerical solution of solute transport using hybrid and central‐difference schemes are also employed for the purpose of comparisons. Numerical simulations for solidification of Pb‐18%Sn in a two‐dimensional rectangular cavity have been carried out using different numerical schemes.

Findings

Numerical results show the difficulty of obtaining grid‐independent solutions with respect to local details in the region of channels. Grid convergence patterns and numerical uncertainty are found to be dependent on the applied scheme. In general, the first‐order hybrid scheme is diffusive and under predicts the formation of channels. The second‐order central‐difference scheme brings about oscillations with possible non‐physical extremes of solute composition in the region of channel segregates due to sharp gradients in the solutal field. The results obtained using TVD and WENO schemes contain no oscillations and show an excellent capture of channels formation and resolution of the interface between solute‐rich and depleted bands. Different stages of channels formation are followed by analyzing thermo‐solutal convection and macrosegregation at different times during solidification.

Research limitations/implications

Accurate prediction of local variation in the solutal and flow fields in the channels regions requires grid refinement up to scales in the order of microscopic dendrite arm spacing. This imposes limitations in terms of large computational time and applicability of available macroscopic models based on classical volume‐averaging techniques.

Practical implications

The present study is very useful for numerical simulation of macrosegregation during ingot casting of metal alloys.

Originality/value

The paper provides the methodology and application of TVD schemes to predict channel segregates during columnar solidification of metal alloys. It also demonstrates the limitations of classical schemes for simulation of alloy solidification.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 20 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

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