Optimization Of The Parameters In The Simulation Of Dendrite Growth Of Al-Cu Alloy Using A Phase-field Method

Phase field method is an effective tool to describe the complicate solid-liquid interface in non-equilibrium state. Without explicitly tracking the complex phase boundaries, it is expected to simulate the complex dendritic growth during the solidification processes. It is the frontier domain of the numerical simulation of solidification processes at present. It is significant to development and application of the solidification simulation. In this paper, according to comprehensive analysis of the existing phase field model of the binary alloys, a modified phase-field model for the binary alloys is deduced on the basis of the Ginzberg-Landau theory, and the numerical methods to those governing equations of this model are discussed. The phase equation is solved by coupling solution equation and temperature equation. The primary work is focused on optimizing the meshes to discretize the governing equations. The equations can be processed using Finite Difference Method under the uniform grids. Firstly, we find out that the magnitude of the grids is the key stone to the accuracy and the efficiency, secondly the optimized magnitude of the space meshes and the appropriate time step is investigated. Thirdly since the phase field parameter, the solute field parameter and the temperature change not at the same rate, multi-grid method, especially the double grid method can be applied to save time, which makes the computing time decreasing about 1/3 during the simulation of Al-Cu dendrite growth. Finally, adaptive mesh method based on quarter trees is first put forward in this paper, which can automatically dense or sparse the meshes according the solutions and the soluting area. Therefore, the computation can be performed in the must accuracy and in less time. In order to simulate the dendritic growth realistically, the disturbance and the anisotropy are introduced into the phase-field model. The disturbance intension and the anisotropy intension and interface thickness are three important parameters which greatly influence the simulation results and their effect are investigated and the optimized values are deduced. Experimental study on the solidification process of Al-Cu binary alloy was carried out. Comparing the numerical simulation results with the real casting experiments, we found out that the dendrite morphologies, the solute profile agreed well with each other qualitatively.