| The stress, pressure and temperature fields as well as the effect of chemical reaction in polymer processes not only affect the appearance, shape and quality of final products, but also have great influences on the structures of molecule chain, supermolecule, the texture structure and their evolutions. The flow-induced crystallization and its orientation in polymer processing may improve the mechanical and optical properties of products. On the other hand, the flow instabilities which often occur in polymer processing will result in the deterioration of finished products in their properties and appearance, such as the sharkskin, melt fracture, the interface instability observed in coextrusion flows, the tiger strips on the surface of injection molding products, etc. and become crucial issues to be solved in order to ensure the product qualities. The studies of polymeric flow in polymer processing are not only related to the optimizations of processing conditions, die or mould, extrusion channel, along with the structure design of screw of extruder or injection molding machine, but also play important roles in reducing the energy consuming and the cost of production, so as to improve the competition ability of production. In one word, it is of importance to perform numerical simulation and analysis of polymer viscoelastic flow in the polymer industrial practice.In general, polymer processes exhibit complex rheological behavior and strong nonlinear characteristics, they are often in three dimension non-isothermal cases and the materials undergo elongation and shear deformations in high strain and strain rate areas. It is noted that the sharp corner of die or mould can often induce stress singularity and lead to flow instabilities. In addition, to trace moving free surfaces or moving interfaces among different melted components in some polymer processes, for example the injection mould filling process, particularly for viscoelastic flows, will bring great challenges to the numerical simulations. The modeling of macromolecule rheological behavior in polymer processing will provide the scientific bases for deep understanding the dynamics of polymeric fluid flows, optimizing technological conditions and improving the qualities of the polymer products. Hence, it bridges among the structure of the polymer, processing and product quality, and establishes a sound foundation for high-performance polymer products based on micromechanically-based and multiscale numerical simulations.The pressure-stabilized iterative fractional step algorithm based on the finite increment calculus (FIC) procedure, and the discrete elastic viscous stress splitting (DEVSS) using the inconsistent streamline-upwind (SU) method are applied in the present investigation. The XPP, PTT-XPP, MDCPP models recently developed and widely used for modeling viscoelastic behaviors of polymer melts and the S-MDCPP (Single/Simplified Modified Double Convected Pom-Pom) model proposed by the author are adopted for constitutive modeling of the contraction viscoelastic flow and extrusion swell flow in the present work. In addition, the non-isothermal non-Newtonian fluid in mold filling process is investigated. The typical difficulties encountered in modeling these engineering projects are discussed and some schemes are put forward, so as to develop the efficient and robust algorithms. Furthermore, according to the numerical results, the extrusion swell flow instabilities are analyzed in order to provide the scientific bases to solve the problems of product quality.To accurately describe the complex rheological behavior of polymer melts during the processing, the constitutive models of the generalized Newtonian and viscoelastic fluids are summarized and investigated in the present work. Meanwhile, the shortcomings and limitations of these models are identified. Particularly, some new constitutive equations recently derived from the Pom-Pom molecular theory, such as the Pom-Pom model, XPP, modified XPP, PTT-XPP and DCPP models are introduced and investigated in detail. From the numerical and experimental results reported in the literature for these new models, one will find that they may reflect the actual topological structure of branched polymer and reproduce well the complex rheological behavior of realistic branched polymer melts. However, they still, more or less, suffer from the difficulties in the uniqueness and convergence of the numerical solution procedure and the defects in the correctly reproducing the rheological phenomena in the numerical simulation. Hence, a new constitutive model, S-MDCPP (Single/Simplified Modified Double Convected Pom-Pom) model, which is conveniently implemented in the framework of the existing computer codes used for the simulation is developed in this study. The S-MDCPP model eliminates some shortcomings of the existing XPP, modified XPP and DCPP models, such as the multi-solution problem, excessive shear-thinning behavior, and so forth. The capability of this model in the numerical prediction is also investigated by means of the benchmark test problem of the planar 4:1 contraction flow. It is noted that the present model demonstrates good numerical stability and is capable of capturing real rheological behaviors under both high shear and elongational rates while the XPP and PTT-XPP models can only well capture those rheological behaviors in high shear or elongational rates respectively. Additionally, the extrusion swell flow of branched polymer melts is numerically simulated by using the S-MDCPP model. It is found that the maximum shear stress and stretch of backbone occur at the places near the die exit. In addition, the extrusion instability is explained and discussed from the macromolecule slip and stress relaxation mechanisms points of view. The XPP model, which is recognized to be able to well describe the flow characters of the branched polymer melts, is adopted to numerically simulate the planar contraction flow often encountered in the polymer processing in the present study.The influences of Weissenberg number and the material parameters of the XPP model on the flow characters exhibited in the contraction flow are discussed, and the distributions of the backbone stretch of branched polymer with different end arms are visualized. Moreover, the extrusion swell behavior of the polymer melts modeled by the PTT constitutive equation is simulated and the obtained numerical results are in good agreement with the experimental ones reported in the literature. Thus, the reliability of the algorithms adopted in this investigation is validated. Furthermore, the causes of the flow instability occurred in the extrusion processing are explicated for better understanding to the mechanism of occurrence of abnormal extruded products.Finally, the linear low density polyethylene (LLDPE) melts are described by the modified Cross-Arrhenius model and the Moldflow second order model, respectively, and the non-isothermal injection mold filling flows are simulated. Additionally, the injection short shots are performed so as to verify the locations and shape of the melts front obtained by the arbitrary Lagrangian-Eulerian (ALE) finite element simulation for the non-isothermal filling process. It is shown that the predicted locations and shape of the melts front are in good agreement with the experiment, and the time spent to complete the filling and predicted by the ALE finite element method is consistent with the experimental result. Moreover, the distributions of the horizontal velocity, pressure and temperature at different filling stages as well as the distributions of the horizontal velocity and temperature at various cross sections are given, which agree well with the results reported in the literatures. The distribution of the horizontal velocity at the time when the melts front completely reaches the wall of the mould cavity, i.e. at the end of the filling, is also given. The numerical results validate the reliability, accuracy and robustness of the ALE-based finite element algorithm employed in the present work, particularly in tracing the moving free surface for the injection filling process, and provide a sound base for further development of the present work to the three dimension injection molding process.
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