• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.9
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• pp.2404-2412
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• 1994

A mathematical model has been developed for predicting kinematic, thermal, and solidification histories of atomized droplets during flight. Liquid droplet convective cooling, recalescence, equilibrium-state solidification, and solid-phase cooling were taken into account in the analysis of the solidification process. The spherical shell model was adopted where the heterogeneous nucleation is initiated from the whole surface of a droplet. The growth rate of the solid-liquid interface was determined from the theory of crystal growth kinetics with undercooling caused by the rapid solidification. The solid fraction after recalescence was obtained by using the integral method. The thermal responses of atomized droplets to gas velocity, particle size variation, and degree of undercooling were investigated through the parametric studies. It is possible to evaluate the solid fraction of the droplet according to flight distance and time in terms of a dimensionless parameter derived from the overall energy balance of the system. It is also found that the solid fraction at the end of recalescence is not dependent on the droplet size and nozzle exit velocity but on the degree of subcooling.

• Proceedings of the Korea Association of Crystal Growth Conference
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• 1996.06a
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• pp.139-156
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• 1996

The phase field model is becoming the model of choice for the theoretical study of the morphologies of crystals growth from the melt. This model provides an alternative approach to the solution of the classical (sharp interface) model of solidification by introducing a new variable, the phase field, Ø, to identify the phase. The variable Ø takes on constant values in the bulk phases and makes a continuous transition between these values over a thin transition layer that plays the role of the classically sharp interface. This results in Ø being governed by a new partial differential equation(in addition to the PDE's that govern the classical fields, such as temperature and composition) that guarantees (in the asymptotic limit of a suitably thin transition layer) that the appropriate boundary conditions at the crystal-melt interface are satisfied. Thus, one can proceed to solve coupled PDE's without the necessity of explicitly tracking the interface (free boundary) that would be necessary to solve the classical (sharp interface) model. Recent advances in supercomputing and algorithms now enable generation of interesting and valuable results that display most of the fundamental solidification phenomena and processes that are observed experimentally. These include morphological instability, solute trapping, cellular growth, dendritic growth (with anisotropic sidebranching, tip splitting, and coupling to periodic forcing), coarsening, recalescence, eutectic growth, faceting, and texture development. This talk will focus on the fundamental basis of the phase field model in terms of irreversible thermodynamics as well as it computational limitations and prognosis for future improvement. This work is supported by the National Science Foundation under grant DMR 9211276

• Journal of Korea Foundry Society
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• v.8 no.4
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• pp.453-458
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• 1988

Al-Si alloy powder produced by the gas atomizer showed fine eutectic structure between ${\alpha}-dendrites$, that was grown by coupled growth, and there remained small amount of ${\alpha}$ in Al - 20 wt% Si alloy. The morphology of Si in the eutectic structure was largely influenced by the recalescence caused by solidification latent heat, and that was thought to be due to decrement of the surface energy of Si. In modified eutectic Si by rapid solidification, fine twin about $0.01\;{\mu}m$ was observed and growth direction of eutectic Si was <112>. This fact implied that the growth mechanism of eutectic Si in rapid solidification was related to TPRE mechanism. Due to rapid solidification Si was soluble in ${\alpha}-phase$ in Al - 12.6wt%Si alloy up to about 3.4wt%, and the solubility of Si in ${\alpha}-phase$ reaches the equilibrium solubility stare after 60min, holding when it was held isothermally at $253-296^{\circ}C$.