考虑凝固收缩作用的凝固过程及其液相流动的有限元计算模型

On the Solidification Process in Consideration of Shrinkage and the FEM model for Interdentric Flow in Liquid State

当要考虑凝固收缩作用所带来的密度变化时，至今所提出的凝固过程及其液相流动数学模型在应用有限元方法进行计算机模拟时有困难。通过建立Ａ变量及与速度的关系，提出了以固液两相区微元体守恒性分析为基础，建立了质量、动量、能量方程式。计算时用这同一个方程组处理液相、固相和固液两相区。由于各偏微分方程内已消去场变量密度与场变量速度（或温度）的乘积项的微分，使得该形式的偏微分方程组适合于用有限元方法进行非定常包括凝固收缩作用的凝固过程及其液相流动的计算机模拟。

It is,so far,difficult to simulate on computers with FEM the solidification processes and to propose their mathematical models describing the interdentric flow in liquid state if the density changes caused by the solidification shrinkage are taken into account. In this paper,a set of equations comprising mass,momentum and energy has been put forward on the principle of conservation of microelements in solid and liquid states,given a variable A and its relation to the velocity known.During calculation,this set of equations is used to deal with the liquid state,solid state and the solid - liquid state.Having cancelled the differentials of the products of the field quantity density and the field quantity velocity(or temperature),these partial differential equations are applicable to the computer-aided FEM simulation of the unstable time-dependent so-lidification processes in consideration of solidification shrinkage and the interdentric flow in liquid state.