A Comparative Study of Quantitative Models in Phase Field Simulation of Alloy Solidification

The phase field method has been regarded as one of the many methods used to simulate free-boundary problems. It has been four years that our laboratory used the two-dimensional adaptive phase field model to deal with the solidification process, and many fruitful results have been reported. However, due to the numerical nature of this method, it does not support accurate quantitative measurements when simulating the alloy solidification process. The key factors affecting the quantitative modeling, have been clearly identified in recent works (A. Karma, Phys. Rev. Lett. 87, 115701, 2001). The so-called ‘thin-interface analysis’ methodology has consequently been developed to tackle these difficulties, and the feasibility of which has been justified very recently (J. C. Ramirez, C. Beckermann, A. Karma, and H-J. Diepers, Phys. Rev. E 69, 051607, 2004).

In this thesis, we successfully developed a quantitative phase field model by adopting the ‘thin-interface analysis’ methodology. Through careful examinations, we find that results from the present model not only match closely with analytic solutions but are highly identical to other researchers' results. Moreover, we tested the practicability of the Simple-Interface-Model (SIM), proposed by Shih (C. J. Shih, M.S. Diss., National Taiwan University, 2004), on the solute trapping effect. In addition to comparison with sharp-interface model, a comparative study of SIM and ATC model is also reported. The simulated results indicate that SIM is indeed a viable alternative method when suppressing the solute trapping effect. What's more, a full physical explanation of SIM is given for the first time in this thesis.

The last part of this thesis considers the impact that thermalsolutal convection has on the morphological change of the directional solidification process. Preliminary simulation results show that the buoyancy does significantly change the melt/solid interface morphology, due to the lateral change of the concentration profile. This is the first research that uses the phase field simulation method to investigate this phenomenon.