Effect of Diffusion Length in Modeling of Equiaxed Dendritic Solidification under Buoyancy Flow in a Configuration of He
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averaging procedures are omitted in the paper, i.e. a field property averaged over its proper phase hWiii is replaced with Wi for simplicity.
I.
INTRODUCTION
MODELING the equiaxed regime for alloy solidification is essential for predicting the structure and composition of solidifying material in the casting process. Indeed, sedimentation or flotation of free equiaxed grains leads to composition inhomogeneity; growth of equiaxed dendrites can block growth of columnar ones either mechanically or by rejected solute and induces columnar to equiaxed transition (CET).[1,2] However, despite
TAO WANG is with Key Laboratory of Electromagnetic Processing of Materials (Ministry of Education), Northeastern University, No. 3-11, Wenhua Road, Shenyang 110004, P.R. China, and with the Univ. Grenoble Alpes, CNRS, Grenoble INP, SIMAP 38000 Grenoble, France, and also with the School of Metallurgy, Northeastern University, Shenyang 110004, P.R. China. SERGEY SEMENOV, YVES DELANNOY, YVES FAUTRELLE and OLGA BUDENKOVA, are with the Univ. Grenoble Alpes, CNRS, Grenoble INP, SIMAP. ENGANG WANG is with Key Laboratory of Electromagnetic Processing of Materials (Ministry of Education), Northeastern University and also with the School of Metallurgy, Northeastern University. Contact e-mail: [email protected] Manuscript submitted April 30, 2019.
METALLURGICAL AND MATERIALS TRANSACTIONS B
serious efforts to develop dedicated numerical models, such simulation remains challenging due to the complexity of coupled multiscale phenomena. Indeed, numerical analysis of equiaxed dendritic solidification accompanied by convective flow basically needs to address the following issues: (1) individual grain growth inside an undercooled melt, which is governed by the mass, heat, and chemical species transfers between phases, which, in turn, are affected by grain growth; (2) motion of liquid and growing grains, and corresponding transport of solute concentration, energy, and grain number density. Contemporary numerical models propose different approaches to resolve these issues. To provide readers with a clear vision of the differences between the models, an extended review regarding treatment of the aforementioned issues is given in the introduction. Based on this analysis, in Section II, we present a three-phase multiscale equiaxed solidification model in which some approximations regarding microscopic scale phenomena are put together and incorporated into macroscopic mass, momentum, energy, and solute transportation equations in a new way. Particular attention is paid to calculation of diffusion length around the dendrite envelope, which is crucial for grain growth kinetics. Furthermore, the choice of momentum exchange coefficient, the improvements to the grain packing method, and a double time step algorithm are also explained in detail. The proposed model is applied to simulation of the Hebditch–Hunt experiment, which
is briefly described in Section III. In Section IV, the results obtained using two approaches to calculate diffusion length are presented and s
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