Using a Three-Phase Deterministic Model for the Columnar-to-Equiaxed Transition

Wu, Menghuai; Ludwig, Andreas

doi:10.1007/s11661-007-9175-9

Cited by 111 publications

(104 citation statements)

References 20 publications

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“…High volume fractions of equiaxed phase are pronounced in the bottom area of the computed ingot as a result of the sedimentation of equiaxed grains. Nucleation of equiaxed grains is described in this model with a Gaussian function, [9,10,12,13] where the nucleation behavior is dependent of three parameters. The mean undercooling DT N was set to 30 K, the standard deviation DT r to 15 K, and the maximum number density of grains was chosen to be n max = 10 9 m -3 .…”

Section: Resultsmentioning

confidence: 99%

“…The present work is the validation of the recent development and application of the volume averaged multiphase/multicomponent (Fe-C-Cr) model by Ludwig et al [9,10] and Wu et al [11,12] The governing equations of the multiphase approach for solidification and melting processes were presented. The numerical results from a simulation of solidification of a ternary (Fe-C-Cr) alloy have been explained considering the process parameters such as the thermal and solutal convection and the nucleation parameters based on a parameter study by Ko¨no¨zsy et al [13] The multicomponent modeling is one of the most relevant outcomes of the CDL and BEG cooperation coupling solidification kinetics with thermodynamics.…”

Section: Introductionmentioning

confidence: 93%

“…The distance between two cylinder centers represents the primary dendrite arm spacing for which a constant value is assumed. Their growth velocity can also be analytically derived [9][10][11][12] as…”

Section: A Modeling Of the Mass-transfer Ratesmentioning

confidence: 99%

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Validation of a Multiphase Model for the Macrosegregation and Primary Structure of High-Grade Steel Ingots

Tanzer

Schützenhöfer

Reiter

et al. 2008

Metall Mater Trans B

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A mixed columnar-equiaxed solidification model is used to predict the macrosegregation in high grade steel ingots. In this model, three phases are considered: the melt; the columnar phase, which is assumed to be stationary; and the equiaxed phase, which is free to move. With this approach, the model is able to simulate the evolution of the primary solid phase distributions including the columnar-to-equiaxed transition, the melt convection and the grain sedimentation, and their influence on the macrosegregation. Thermodynamic information of a ternary alloy (Fe-C-Cr) is simplified by the piecewise linearization of the phase diagram around the suitable compositions in the ferritic and austenitic regions. As a result, macrosegregation of carbon and chromium has been analyzed. As the first step, the validation of the numerical model was performed on a benchmark ingot of a laboratory scale. Computed macrosegregation and primary structure were compared with measurements and good agreement was obtained.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 93%

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Validation of a Multiphase Model for the Macrosegregation and Primary Structure of High-Grade Steel Ingots

Tanzer

Schützenhöfer

Reiter

et al. 2008

Metall Mater Trans B

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“…A three-phase mixed columnar-equiaxed solidification Modeling of Casting and Solidification Processes -MCSP 2017 CHINA FOUNDRY model was described previously [11,12] . The so-called three phases are the liquid, equiaxed and columnar.…”

Section: Fragmentation Formulationmentioning

confidence: 99%

Role of fragmentation in as-cast structure: numerical study and experimental validation

Zheng

Kharicha

et al. 2017

China Foundry

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M ore and more evidence has shown that the interdendritic fluid flow can facilitate the fragmentation by the mechanism of solute-driven remelting of dendrite arms [1][2][3][4] . On this base, a dendrite fragmentation criterion was proposed [5] . Additionally, the interdendritic flow is also a necessary condition for transport of the fragments out of the (columnar structure) mushy zone, and those fragments act as nuclei of equiaxed crystals [6] . The current authors proposed a formula to incorporate fragmentation into a volume average model [7] . This work is to use this model to investigate the role of fragmentation in the formation of as-cast structure. Abstract:A volume average solidification model is extended to incorporate fragmentation as the source of equiaxed crystals during mixed columnar-equiaxed solidification. This study is to use this model to analyze the role of fragmentation in the formation of as-cast structure. Test simulations are made for the solidification of a model alloy (Sn-10wt.%Pb) with two different geometries. The first one is a 2D rectangular domain (50 × 60 mm 2 ) as cooled from the top boundary. Solidification starts unidirectionally as columnar structure from the top. The solute (Pb) enriched interdendritic melt is heavier than the bulk melt, and sinks downwards, hence leads to solutal convection. Fragmentation phenomenon occurs near the columnar tip front. The fragments are transported out of the columnar region, and they continue to grow and sink, and finally settle down and pile up at the bottom. The growing columnar structure from the top and pile-up of equiaxed crystals from the bottom finally lead to a mixed columnar-equiaxed structure, in turn leading to a columnar-to-equiaxed transition (CET). The second geometry is a 3D plate, 100 × 60 ×10 mm 3 , as cooled laterally from one side. It was cast experimentally and analyzed for the as-cast structure. The equiaxed fragments are produced in the solidification front and transported into the bulk melt, leading to a special pattern of as-cast structure: columnar structure in the cool wall side and equiaxed structure in the upper left corner near the hot wall side, extending downwards to the middle bottom region. Numerically calculated as-cast structures agree with the experiment results.

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“…Herein, the equation of motion of equiaxed grains is solved by using an effective viscosity for the solid/liquid mixture. This approach was used to model pure equiaxed solidification, [13][14][15][16][17][18] mixed columnarequiaxed solidification [19][20][21][22][23][24][25][26] (with predictions on Columnar-to-Equiaxed Transition (CET)), equiaxed solidification with dendritic morphology, 27,28 and mixed columnar-equiaxed solidification with dendritic morphology. 26,[29][30][31] Recently, a four-phase solidification model, i.e., combining the three-phase mixed columnar-equiaxed solidification with the description of shrinkage cavity, is used to calculate the formation of macrosegregation and shrinkage cavity in a 2.45-ton steel ingot (Fig.…”

Section: Flotation/sedimentation Of Equiaxed Crystals During Solidifimentioning

confidence: 99%

Simulation in Metallurgical Processing: Recent Developments and Future Perspectives

Ludwig

Kharicha

2016

JOM

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This article briefly addresses the most important topics concerning numerical simulation of metallurgical processes, namely, multiphase issues (particle and bubble motion and flotation/sedimentation of equiaxed crystals during solidification), multiphysics issues (electromagnetic stirring, electro-slag remelting, Cu-electro-refining, fluid-structure interaction, and mushy zone deformation), process simulations on graphical processing units, integrated computational materials engineering, and automatic optimization via simulation. The present state-of-the-art as well as requirements for future developments are presented and briefly discussed.

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Using a Three-Phase Deterministic Model for the Columnar-to-Equiaxed Transition

Cited by 111 publications

References 20 publications

Validation of a Multiphase Model for the Macrosegregation and Primary Structure of High-Grade Steel Ingots

Validation of a Multiphase Model for the Macrosegregation and Primary Structure of High-Grade Steel Ingots

Role of fragmentation in as-cast structure: numerical study and experimental validation

Simulation in Metallurgical Processing: Recent Developments and Future Perspectives

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