基于ALE描述的压缩流动三维粘弹性数值模拟

3D viscoelastic simulation for compressible flow based on ALE description

塑料熔体压缩流动中在主流动平面及厚度方向均有速度变化,结合了剪切和拉伸两种流动特征。为了准确描述和模拟塑料熔体的压缩流动,本文基于粘弹性及ALE原理建立了熔体三维流动理论模型,构造了有限元求解的变分方程。为了避免整体求解计算量大、稳定性差的缺陷,提出了两重迭代解耦合算法分别求解耦合的连续方程、动量方程、本构方程、能量方程,开发了模拟程序。开展了等厚度板及变厚度板的注压成型实验及相应的数值模拟,结果表明:压缩过程中出现压力变化小于4.57%的平台现象;温度呈指数规律下降;塑料入口、流动末端第一法向应力差比平均值分别高1.73MPa、0.87MPa,变厚度区域第一法向应力差比平均值高1.16MPa。本文提出的理论模型和数值算法能够较好地表征压缩过程中熔体的压力、温度变化、应力演化。

Velocity changes in both dominated flow plane and thickness direction lead to melt compression flow combing shear and extensional flow characteristics. In order to describe and simulate this kind of polymer flow, the 3D flow model based on viscoelastic and ALE principle is built, and the corresponding variational equations are constructed for finite element method. To avoid the shortages of poor stability and huge computational costs of integral method, a new approach involving two twofold iterations is proposed to decouple the interdependence of velocity, temperature and stress in governing and constitutive equations. Both experiments and numerical simulation are carried out with injection/compression molding for iso-thick and var-thick plates. The results of this study demonstrate that, the pressure profile displays a plateau where the pressure difference is within 4.57%, temperature declines according to exponential law during compressing, and the first normal stress differences are 1.73 MPa, 0.87 MPa higher than the average value respectively in the flow start and end regions. Meanwhile, this value in the variable thickness region is 1.16 MPa higher than the average. The good agreement betweensimulations and experiments indicates the proposed model and numerical method are valid to predict the flow characteristics during compressing.