注塑流动与传热分析的四边形单元控制体积法

Quadrilateral control-volume method for flow and heat transfer simulation of injection molding

阐述了注塑分析的基于Hele-Shaw假设四边形单元控制体积法。由于四边形控制体积法会产生不对称矩阵的方程组,求解压力时把方程不对称的部分移到方程右边,这样方程转化为对称的线性方程组。在求解转化后的线性方程组时,只在压力求解区域改变时更新方程的右边。注塑分析的时间步长进行自动调整,并大致保证流动前锋在两个时间步内向前流动大略一单元层。与现有文献的计算结果比较表明四边形单元控制体积法可以有效地模拟中面模型的注射过程,该方法并可以与三角形单元混合使用,且可应用于基于表面的注塑分析方法。

Control-volume method based on quadrilateral mesh was proposed for injection molding simulation with Hele-Shaw approximation. Since control-volume method will generate asymmetric matrix for quadrilateral mesh, the asymmetric parts of matrix were moved to the right-hand side of equations to transform the equations into the symmetric equations, and then pre-conditioned conjugate gradient （PCG）method was applied. To solve the pressures, the right-hand sides were updated only when the solved region had changed. The time steps of injection molding simulation were adjusted in order to fill about one element-size layer within two time steps; the gap-direction was discretized bY the Chebyshev collocation method. To reduce the computing efforts, the flow front was checked for each 10 PCG iterationsto determine the filled domain. The comparison with the well-documented results showed that the control-volume method based on the quadrilateral mesh was effective for injection molding simulation, the quadrilateral mesh was able to mix with the triangular mesh, the mass imbalance of the quadrilateral mesh was very low and decreased along with the increasing of mesh size, and the computing performance of the quadrilateral mesh slightly exceeded the one of the triangular mesh. The proposed method is applicable for the injection molding simulation based on the surface model.