Modeling of marangoni-induced droplet motion and melt convection during solidification of hypermonotectic alloys
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10/30/03
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Modeling of Marangoni-Induced Droplet Motion and Melt Convection during Solidification of Hypermonotectic Alloys MENGHUAI WU, ANDREAS LUDWIG, and LORENZ RATKE A two-phase volume averaging approach to model Marangoni-induced droplet motion of the minority liquid phase and the convection in the parent melt during solidification of the hypermonotectic alloys is presented. The minority liquid phase decomposed from the parent melt as droplets in the miscibility gap was treated as the second-phase L2. The parent melt including the solidified monotectic matrix was treated as the first phase L1. Both phases were considered as different and spatially interpenetrating continua. The conservation equations of mass, momentum, solute, and enthalpy for both phases, and an additional transport equation for the droplet density, were solved. Nucleation of the L2 droplets, diffusion-controlled growth, interphase interactions such as Marangoni force at the L1-L2 interface, Stokes force, solute partitioning, and heat release of decomposition were taken into account by corresponding source and exchange terms in the conservation equations. The monotectic reaction was modeled by adding the latent heat on the L1 phase during monotectic reaction, and applying an enlarged viscosity to the solidified monotectic matrix. A two-dimensional (2-D) square casting with hypermonotectic composition (Al-10 wt pct Bi) was simulated. This paper focused on Marangoni motion, hence gravity was not included. Results with nucleation, droplet evolution, Marangoni-induced droplet motion, solute transport, and macrosegregation formation were obtained and discussed.
I. INTRODUCTION
ALLOYS with a miscibility gap in the liquid state, especially those with an alloy composition above the monotectic point (hypermonotectic), are potential bearing materials for the automotive industry, if the soft minority phase (normally in droplets) can be well dispersed in the hard matrix.[1,2] However, the spatial separation of the minority phase from the parent melt seems unavoidable regardless of whether the alloy solidifies under normal terrestrial conditions[3] or in a reduced gravity situation.[4,5] The reasons are sedimentation due to gravity and Marangoni (thermocapillary)-induced droplet motion. The former is easily understood, because the two liquid phases have generally a different density. The Marangoni-induced droplet motion is due to the temperature gradient established during solidification, which leads to the droplet moving from cold toward hot regions. The surface tension at the liquid-liquid interface decreases with temperature. Great efforts have been made[6,7,8] in the last few decades to understand Marangoni-induced droplet motion of single droplets. How to model Marangoni motion of multiple droplets in a macroscopic system, especially in the presence of a complicated solidification process, still remains an open subject. Modeling of solidification and phase separation is part of a multiphase problem. A multiphase volume-averaging
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