Equiaxed dendritic solidification with convection: Part II. Numerical simulations for an Al-4 Wt pct Cu alloy
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I.
INTRODUCTION
IN recent years, numerical modeling of equiaxed dendritic solidification without convection has experienced considerable progress: ~,2J Nucleation and growth kinetic laws have been coupled with transient heat conduction calculations to determine the solidification microstructure. However, simulations of equiaxed dendritic solidification, taking melt convection and solid movement into account, have not been attempted in the literature, with the exception being the numerical study by Ni and Beckermann, [3] which includes both liquid convection and solid transport but deals with globulitic structures only (as opposed to dendritic). This second article of the series describes a first attempt toward predicting equiaxed dendritic microstructures in the presence of melt convection and solid movement using the multiphase model developed by Wang and Beckermannt4] (hereinafter referred to as part I). The microstructural features of particular interest include the grain size and the intemal solid fraction, which is an index measuring how dendritic the grains are. In addition, it is of interest to predict the macrosegregation pattern as a result of combined melt convection and grain movement. In the following, the multiphase model is briefly outlined for completeness. This is then followed by a description of the numerical procedures. Representative numerical results are finally presented to shed light on the complicated solidification and multiphase flow phenomena occurring during equiaxed alloy solidification.
tion of 4 wt pet copper. The walls are impermeable and adiabatic, except for the west wall which is subject to convective cooling for t > 0. The coolant temperature is fixed at 293 K, and the convective heat-transfer coefficient between the coolant and the mold wall is chosen as 250 W/mZK in all simulations presented subsequently. This set of parameters is representative of practical casting conditions and falls into the range of equiaxed dendritic solidification, as given by Kurz and Fisher: 51 The multiphase approach to the modeling of equiaxed dendritic solidification has been thoroughly discussed in part I, and the model equations together with the supplementary relations presented therein are again summarized in Tables I and II, respectively. All symbols are defined in the Nomenclature, with the averaging symbols dropped for convenience. An overbar denotes an interfacial quantity. The model distinguishes three phases: the solid (es), the interdendritic liquid (ed), and the extradendritic liquid (el); and two interfaces: the solid/interdendritic liquid interface (St) and the dendrite envelope (Sr separating the inter- and extradendritic liquids. One of the important assumptions made in the present multiphase model is that there exists a certain flow partitioning between the inter- and extradendritic regions. Hence, the relative portions of the mass flow rates through each region can be quantified by introducing an isotropic flow partition coefficient r v. This coefficient
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