Fe-C合金凝固过程流动、传热、传质的耦合数值模拟

NUMERICAL SIMULATION ON FLUID FLOW, HEAT AND MASS TRANSFER IN SOLIDIFICATION OF Fe-C ALLOYS

通过耦合求解凝固过程质量、动量、能量和溶质守恒方程,对Fe-C二元合金凝固过程中的流动、传热、传质现象进行了数值模拟.基于控制容积的有限差分法（CV-FDM）建立了微分方程的隐式离散格式,采用SIMPLE方法求解.代数方程的求解采用交替方向隐式（ADI）和三对角矩阵算法（TDMA）相结合的方法.对一个上下边界绝热、左右边界对流换热的二维矩形区域的模拟计算表明,凝固初期排出的溶质主要被凝固前沿的液相流动带入液相区.在固液两相区中,由于枝晶骨架造成的流动阻力很大,在不考虑凝固收缩的条件下,两相区中的液相流动速度一般较纯液相区的流速小2-3个数量级.

The fluid flow, heat and mass transfer phenomena in solidification of Fe-C alloys are numerically simulated by simultaneously solving the coupled macroscopic mass, momentum, energy, and species conservation equations. The control volume-based finite-difference method is used in establishing the discrete scheme of the conservation equations, and the alternate direction implicit procedure and tridiagonal matrix algorithm are employed in solving the algebraic equations. The velocity-pressure coupling in the momentum equations is treated using the SIMPLE algorithm. The simulation on the solidification of a Fe-C alloy in a two-dimensional rectangular domain with insulated boundaries at top and bottom sides and symmetric cooling boundaries at left and right sides shows that in early solidification stage of the alloy, the rejected solute species is mainly brought into bulk liquid by the convection near the solidifying front. Moreover, because of the large resistance of the dendritic skeleton to the liquid flow, the liquid velocities in the mushy zone are about 2-3 orders of magnitude. lower than those in the bulk liquid without considering the effect of solidification shrinkage.