Phase Field Method And Numerical Simulations Of Dendritic Crystal Growth

In the process of metal solidification, the numerical simulations of the dendritic crystal growth is an important part of materials science field. Its result is practical guiding significance to effectively control the growth of metal materials. At the following section, I will briefly introduce the main contents of the paper.(1) We propose the governing equations of phase field and temperature field bas- ed on phase transition theory of Ginzburg-Landau; we use phase field order parameterφto distinguish the solid, the liquid and solid-liquid interface; we use explicit scheme which applys forward Euler in time and centered-differencing in space to the governing equations.(2) Using 2-dimensional scheme simulate the phase field and temperature field, and get 2-dimensional picture of phase field and temperature field;furthermore, we simulate the variations of the dendritic crystal's structures when we change the governing parameter; we simulate the tip radius and the tip velocity of the dendritic crystal by analysis and calculation to qualitatively analyse the variations of the dendritic morphology, get the curves changes with the time, find that the tip radius decreases continuously with the time and remain unchanged at last, and the dendrite tip velocity decreases rapidly and tend to stable at last.(3) We simulate the directional and competitive growth of many isotropic dendrit- es by introducting the so-called"noise", and get that dendrite will select the superior and eliminating the inferior; furthermore, we simulate the dendrite morphology of multiple dendritic directional and competitive growth, and find that the model domain will be filled with the solid of the undercooled melt; we also simulate the solid fraction changed with the time by analysis and calculation to qualitatively analyse the variations of dendritic crystal when we change the governing parameter.(4) In order to simulate the growth of 3-dimensional equiaxial crystal, we improve the 2-dimensional governing equations to be suitable for the 3-dimensional modeling and numerical simulations based on the 2-dimensional modeling and numerical simulations, and using the explicit scheme to apply difference to 2-dimensional phase field and temperature field governing equations; simulate the morphology structure of the isotropic single equiaxial crystal, and simulate the growth of the isotropic multiple equiaxal crystal, and compare the variations of the morphology structure between 2D and 3D dendritic crystal growth, and find that they are almost same with each other.