金属凝固过程中热动力学相场模型——枝晶过冷生长速度模型的推导

Thermal Kinetics Phase Field Model for Metals' Solidification——Mathematic Derivation of Dendrite Growth Velocity Model in Undercool

相场方程用于模拟枝晶生长,已有近20年的历史。现有的相场方程是直接通过Ginzburg-Landau方程导出的,虽然得到了广泛应用,但方程中各个变量物理意义并没有搞清,国内外研究者甚至都作了许多错误的解读。本文以固相率作为相场变量,在金属凝固热动力学基础理论上,给出了纯金属凝固过程中枝晶过冷生长速度模型及其推导过程。

The phase field equation for the simulation of dendritic growth has a history of near twenty years. The existing phase field equation was directly derived by Ginzburg-Landau equations. However, by widely used, the physical meaning of each variable in the equations is not clear. So the domestic and foreign researchers have made a lot of mistakes and interpretation. Taking the solid fraction as a phase field variables in the field, based on the thermodynamics and heat transfer theory, the solidification velocity model for metal dendrite growth in undercooled and its derivation process were given.