| Summary: | 碩士 === 國立臺灣大學 === 化學工程學研究所 === 90 === Adaptive phase field simulation based on a finite volume method is carried out for both nonisothermal dendritic growth and directional solidification in a nickel/cooper system. The adaptive nature of the present scheme allows the calculation to cover different length scales for interface thickness, solute diffusion, and heat conduction.
In the case of isothermal dendritic growth, our calculated dendrite tip speed agrees very well with that by Warren and Boettinger [Acta. Metall. Mater. 43 (1995) 689]. For nonisothermal growth, our results also agree reasonably well with those by Loginova et al. [Acta. Mater. Mater. 49 (2001) 573]. However, the domain size used in their calculation was too small for heat conduction, so that the asymptotic tip speed was domain dependent. By choosing an extremely large domain being 4a/Vss in width, the domain-independent tip speed has been obtained here, where a is the thermal diffusivity and Vss the steady tip speed. This tip speed is found much smaller than that obtained by using a small domain.
In the case of directional solidification at high speed, we have performed extensive comparison with previous calculations [Boettinger and Warren, J. Crystal Growth 200 (1999) 583] using the frozen temperature approximation, and reasonably agreement is found. Besides, our calculations are further performed for low speeds, which require a very large domain due to the much larger solute boundary layer and cell wavelength. For the same domain size, the calculated results without using the frozen temperature approximation remain about the same, even though the effect of heat of fusion lowers the steady interface position and the thermal gradient at the interface in the melt side.
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