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应用投影算法与相场法相结合的数学模型,采用基于非均匀网格的自适应有限元法求解该模型,并对强制流动作用下镍过冷熔体中枝晶生长行为进行模拟。模拟结果表明,强迫对流的引入导致枝晶生长的不对称性。当流速小于临界值时,流动对枝晶的不对称生长影响较小;当流速达到或超过临界值时,枝晶生长的控制因素逐渐从热扩散过渡到对流。随着流速的增大,流动法向的一次枝晶臂朝逆流方向倾斜角度增大。而枝晶生长对熔体流动具有明显的影响。随着枝晶尺寸的增大,在顺流区域产生涡流效应,涡流区逐渐扩大并在枝晶尖端出现重熔现象。此外,非均匀网格的自适应有限元方法的CPU耗费时间比均匀网格方法降低一个数量级,并且加速比与计算域尺寸成正比。
The mathematical model combining the projection algorithm and the phase field method was used to solve the model by using the adaptive finite element method based on non-uniform mesh. The growth behavior of dendrite in the undercooled melt under forced flow was simulated. Simulation results show that the forced convection leads to the asymmetry of dendrite growth. When the flow rate is less than the critical value, the flow has little effect on the asymmetric growth of dendrites. When the flow rate reaches or exceeds the critical value, the controlling factors of dendrite growth gradually transition from thermal diffusion to convection. With the increase of the flow rate, the angle of the primary dendrite arm in the flow direction increases toward the counterflow direction. Dendritic growth has a significant effect on melt flow. With the increase of dendrite size, eddy current is produced in the downstream area, and the eddy current area is gradually enlarged and remelting occurs at the tip of dendrites. In addition, the non-uniform mesh adaptive finite element method consumes an order of magnitude more CPU time than the uniform mesh method, and the speedup ratio is proportional to the size of the computational domain.