支化高分子熔体黏弹性本构行为数值模拟和实验研究

The investigation of rheological behavior of branched polymer melts will be focused on the viscoelastic constitutive model, i.e. S-MDCPP model, in the present work, in order to verify the reproducing ability of the model for several rheological experiments, such as steady uniaxial elongational, simple shear and transient elongational flows. Moreover, the predictive capability and numerical stability in the complex processing status, along with the cases of high Weissenberg number are to be discussed in this study. The experimental data of various flows for polymer melts are obtained by the rheometers, and compared with the predictive results of the S-MDCPP, XPP and PTT-XPP models. Furthermore, the finite element models of the complex processing flows are constructed. The finite increment calculus (FIC) procedure is introduced to reformulate the mass conservation equation, so as to apply the equal low-order interpolation approximation for velocity-pressure-stress variables in the finite element scheme and to ensure the stability of pressure field due to incompressibility of fluids. As for the convection dominated case, geometry and stress singularities, the momentum equation and viscoelastic constitutive model are solved by the pressure-stabilized iterative fractional step algorithm and the discrete elastic-viscous stress splitting(DEVSS) using the inconsistent streamline-upwind(SU) method. The numerical results are compared with those observed in the visual experiments, in order to confirm the ability to rheological behavior of polymer melts predicted by the S-MDCPP model proposed recently by the investigator and to achieve better understanding of the viscoelastic flow behavior of polymer melts, together with providing the scientific bases for the extrusion swell flow instabilities to be eliminated.

本项目将围绕支化高分子熔体的黏弹性本构模型：S-MDCPP模型展开研究，旨在考察该模型对高分子熔体在多种流变实验（稳态单轴拉伸、剪切流动和瞬态拉伸流动）的重现能力和在复杂加工流场中以及高魏森伯格数下的预测能力和数值稳定性。拟采用流变仪获取高分子熔体在不同流动状态下的实验数据，并与S-MDCPP模型、XPP和PTT-XPP模型预测的结果比较；同时建立复杂加工流场的有限元模型，采用有限增量微积分过程重构质量守恒方程，以获得速度－压力－应力等低阶线性插值时压力场的稳定；针对对流占优、几何和应力奇异问题，借助迭代稳定分步算法、离散的弹性黏性应力分裂和非一致的上风流线(DEVSS/SU)方法，求解动量方程和黏弹性本构方程，并与可视化的实验结果比较，以验证最新提出的S-MDCPP模型预测高分子熔体在复杂流场中流变行为的能力，为深入理解高分子熔体的黏弹性行为，解决挤出加工过程中不稳定的流动提供科学依据。

本课题针对描述支化高分子熔体复杂流变行为的本构模型(S-MDCPP，DCPP， XPP)进行了深入的研究，重点考察申请人提出的S-MDCPP模型对稳态拉伸、剪切流动、瞬态拉伸流动和复杂流场中黏弹性流变行为的预测能力，并与其他模型的预测结果进行了比较。采用压力稳定的迭代分步算法以及DEVSS/SU或DEVSS/SUPG计算方案，利用有限元法求解黏弹性流体在复杂流道中的流动(收缩流动、十字交叉流动、绕柱流动、收缩-膨胀流动、挤出胀大流动)，得到了这些拉伸和剪切流动共存复杂流场中支化高分子的流变特征，并考察了不同本构模型参数对这些复杂流场的影响，以及高Weissenberg数下数值方案的稳定性，还给出了一些流道中心线上的应力松弛曲线和指数型的衰减模型。针对高分子熔体的挤出胀大问题，从数值模拟角度考察了本构参数对挤出胀大比的影响，还借助毛细管流变仪考察了不同剪切速率对挤出物表观形貌的影响，并讨论了出现熔体断裂，鲨鱼皮，螺纹状的产生机理。此外，还设计加工了4:1收缩流道，并用自行搭建的流动双折射光学系统和PIV系统在线测试了收缩流场中的主应力差条纹和流场速度。研究表明，S-MDCPP模型具有较好地预测支化高分子熔体在复杂流场中的流变行为的能力，并且所采用的计算方案是稳定和可靠的，模型预测结果与实验结果吻合较好。这些结果对促进高分子熔体本构模型的进展、计算方法的改进和深入理解支化高分子的复杂流变行为有积极意义。