A new model that can quantitatively evaluate the permeability for columnar dendritic structures was developed by modifying the Kozeny constant in Kozeny-Carman's equation. The modified Kozeny constant consists of two terms: one accounting for the flow direction for primary arms of columnar dendrites and the other accounting for the tortuosity of channels in the dendritic structures. The permeability calculated by this new model was compared with that obtained in our previous simulations [Y. Natsume et al.: Tetsuto-Hagané, 99 (2013), 117] and from experiments other researchers [K. Murakami et al.: Acta metall., 31 (1983), 1417, 32 (1984), 1423, Liu et al.: Mater. Sci. Tech., 5 (1989, 1148] and the values were found to be in fairly good agreement with the compared values. In addition, we investigated the obtained quantitative model to determine permeability for use in computational studies of macrosegregation. To evaluate the permeability quantitatively using Kozeny-Carman's equation, the value of the specific surface area for dendrites is required. We introduced an assumption that the inverse of the specific surface area for columnar dendrites is proportional to the secondary arm spacing. By using this assumption in our modified model, the permeability can be determined using only the dendrite arm spacing and liquid volume fraction.
緒言連続鋳造鋳片の中心偏析や大型鋳塊の ・河嶋 佳純3) ・谷川 英司3) ・大笹 憲一 1) Evaluation of Permeability for Columnar Dendritic Structures by Three Dimensional Numerical Flow AnalysisYukinobu Natsume, Daiki takahashi, Kasumi kawashima, Eiji taNigawa and Kenichi Ohsasa Synopsis : Toevaluatethepermeabilityforcolumnardendriticstructures,threedimensional(3D)flowsimulationsofinterdendriticliquidwerecarried out. The 3D columnar dendrites were made by means of the computer aided design (CAD), which were based on two-dimensional dendrite morphologiescalculatedbyaphase-fieldmethod.Theartificial3Dcolumnardendriteswereregularly-arranged,andsixkindsof3Dcolum-nardendriticstructureswereobtained,whichhavedifferentvolumefractionsofliquidbetween0.56and0.95.Forthesecolumnardendritic structures,theflowsparallelandnormaltotheprimarydendritearmswerecalculatedbytheFLUENT,andthepermeabilityforsix3Dco-lumnardendriticstructuresandbothflowdirectionsweredeterminedbyusingtheDarcylaw
In order to evaluate the permeability of columnar dendritic structures, three-dimensional (3-D) flow simulations of interdendritic liquid were carried out. The 3-D columnar dendrite morphologies, created by means of a computer-aided design (CAD) software, were based on two-dimensional dendrite morphologies calculated by a phase-field method. The artificial 3-D columnar dendrites were regularly arranged, and six kinds of 3-D columnar dendritic structures were observed, each with different liquid volume fractions between 0.56 and 0.95. For these 3-D columnar dendritic structures, the flow parallel and normal to the primary arms were calculated using FLUENT, and the permeability of six 3-D columnar dendritic structures for both flow directions were determined using the Darcy law. Tech., 5 (1989), p. 1148]. For both flow directions, our simulated permeability for high liquid volume fractions complemented their experimental permeability for low liquid volume fractions. Therefore, we confirmed the consistency of simulated reading with extrapolations of experimental values of low volume fractions to high volume fractions. In addition, we discussed the limitation of flow within the mushy region, and found that defining the limiting permeability of interdendritic flow, in order to evaluate the relationship between dendritic morphology and the solid volume fraction where interdendritic liquid flow ceases, was effective.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.