A multiphase solute diffusion model for dendritic alloy solidification

Wang, C. Y.; Beckermann, C.

doi:10.1007/bf02666283

Cited by 61 publications

(149 citation statements)

References 28 publications

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“…The conservation of mass, momentum solute and energy at the solid-liquid interface A βσ are respectively given by: (10) where w βσ is the velocity of the interface A βσ and n βσ is the unit normal vector pointing from the β-phase to the σ -phase. Thermodynamical equilibrium is considered at A βσ and the local coupling between solid and liquid temperatures (T σ and T β ) and concentration is obtained through the functions g σ and g β that describe the solidus and liquidus lines of the equilibrium phase diagram:…”

Section: Local Conservation Equationsmentioning

confidence: 99%

“…This latter coefficient is found to be mainly dependent on the solute diffusion length [10] while it is actually strongly related to the location within the dendritic layer and therefore to tortuosity and local dispersion phenomena [26].…”

Section: Introductionmentioning

confidence: 96%

“…ing improvement lies in an accurate micro-macroscopic description of transport phenomena within the dendritic mushy zone. In most averaged representations, this region is described as a porous medium and macroscopic conservation equations have been obtained using the mixture theory [4][5][6] or up-scaling procedures [1,[7][8][9][10][11]. Due to its ability to incorporate complex microscopic information in averaged equations and effective transport properties (permeability, conductivity, mass diffusion coefficients, ...), the method of volume averaging has been often chosen for the derivation of the macroscopic models [12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

“…A significant improvement has been performed in this direction by Beckermann and co-authors [9,10] who proposed a three-phase macroscopic solute diffusion model where interfacial species fluxes in phase k are proportional to the difference between the interfacial and volume-averaged concentration such as ϕ k = h k (C * k − C k k ), h k being the mass exchange coefficient. This latter coefficient is found to be mainly dependent on the solute diffusion length [10] while it is actually strongly related to the location within the dendritic layer and therefore to tortuosity and local dispersion phenomena [26].…”

Section: Introductionmentioning

confidence: 99%

“…The objective of this paper is to improve the micro-macroscopic description of the transport processes in columnar dendritic structures by using the volume averaging method with closure problems. According to Wang and Beckermann [10] and Quintard and Whitaker [27] for soil contamination problems, solute transport is based on a macroscale non-equilibrium description leading to a macroscopic representation of interfacial species exchange (active dispersion). All the interfacial area integrals arising from the averaging procedure are explicited and the associated closure problems are derived for the determination of effective transport properties.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Macroscopic modeling of columnar dendritic solidification

Goyeau¹,

Bousquet-Melou²,

Gobin³

et al. 2004

Mat. apl. comput.

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Abstract. This paper deals with the derivation of a macroscopic model for columnar dendritic solidification of binary mixtures using the volume averaging method with closure. The main originalities of the model are first related to the explicit description of evolving heterogeneities of the dendritic structures and their consequences on the derivation of averaged conservation equations, where additional terms involving porosity gradients are present, and on the determination of effective transport properties. These average properties are defined by the associated closure problems taking into account the geometry of the dendrites and the local intensity of the flow. The macroscopic solute transport is obtained by considering macroscale non-equilibrium giving rise to macroscopic dispersion and interfacial exchange phenomena. Mass exchange coefficients are accurately explicited as a function of the local geometry.Mathematical subject classification: 76S05, 76T05, 76R05.

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Section: Local Conservation Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Macroscopic modeling of columnar dendritic solidification

Goyeau¹,

Bousquet-Melou²,

Gobin³

et al. 2004

Mat. apl. comput.

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Directional Solidification and Melting of Eutectic GaIn

Koster

1999

Cryst. Res. Technol.

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Eutectic gallium-indium is studied in a horizontal Bridgman furnace geometry. Differential temperature gradients are applied to solidify and melt the alloy while observing in-situ the interface morphology and the chemical segregation in the melt and in the solid as well. Upon cooling, a wedge-type indiumrich mushy zone develops at the cold wall. The melt is initially stirred by convective flow. After solidification starts the roll cell recedes to be replaced by a chemically layered conductive melt that eventually solidifies with rather uniform eutectic structure. Upon re-melting, the morphology of the interface adopts a profile that is predetermined by the original solid structure. Those patterns, as well as the flow, are different from single element solid melting experiments and have yet to be modeled. Under high thermal gradient the convective flow mixes the binary melt and the visualized density pattern eventually becomes that of a homogeneous melt.

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Implementation and Validation of a Multiphase Multigrain Model of Equiaxed Solidification

Martorano¹,

Arango²,

Ramunno³

2014

TMS 2014 Supplemental Proceedings

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A multiphase and multigrain mathematical model for the solidification of binary alloys is proposed, implemented, and validated. The model equations are derived using the volume averaging method and considering the conservation principles of mass, energy, and chemical species applied to a representative elementary volume. In the present model, grains that nucleate at different temperatures are grouped in different classes and are followed individually, enabling calculations of different growth velocities for globulitic and dendritic grains growing simultaneously. The proposed model is capable of predicting final average grain size, cooling curves during the complete primary and eutectic solidification, and the volume fraction of eutectic. These predictions are compared with experimental results for the solidification of cylindrical bars of Al-Si alloys with different Si concentrations and different amounts of inoculant additions, showing good agreement.

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A multiphase solute diffusion model for dendritic alloy solidification

Cited by 61 publications

References 28 publications

Macroscopic modeling of columnar dendritic solidification

Macroscopic modeling of columnar dendritic solidification

Directional Solidification and Melting of Eutectic GaIn

Implementation and Validation of a Multiphase Multigrain Model of Equiaxed Solidification

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