| Injection molding is one of the most important technologies for the manufacturing of polymer products, composed of filling, packing and cooling stages, etc. Due to the complex flow behaviors of polymer melts in the mold and complex shape of products, the traditional trial-and-error approach for the mold design is incapable of meeting the requirements of massive manufacture. The emergence and flourishing developments of simulation-based technologies, such as computer-aided engineering (CAE) for injection molding, have thoroughly changed the conception of mold design, remarkably enhanced design capacity, shortening the design period and reducing the design cost.The simulation based technologies for injection molding are constructed on the basis of the study of rheology and the development of relevant numerical methods, etc. To achieve it, it is significant to explore the nature of rheological behaviors of polymer melts and to develop robust and efficient numerical algorithms for non-Newtonian viscoelastic flows.With such a motivation, the researches of the present thesis are mainly focused on the stabilization methods in viscoelastic flow simulation and three-dimensional free surfaces tracking method by using Finite Element Method.Stabilization methods have been of critical importance for numerical simulation of viscoelastic flows. With mixed variables, i.e. velocity-pressure-stress, taken as independent variables to solve for the incompressible viscoleastic flow problems, the results provided by means of standard Galerkin method will suffer severe spurious numerical oscillations.This numerical instability is attributed to the following two causes. The first is the violation of the compatibility conditions that impose restrictions on the choice of interpolation spaces for mixed variables, resulting from the reducibility of the discretized form for the incompressible governing equations. The incompatible interpolations (e.g. equal lower-order interpolations) will lead to spurious spatial oscillations in the resulting pressure and stress fields. The second stems from the convective operator term in the differential constitutive equation. As Weissenberg number increases, the convection term will tend to dominate the constitutive equation, then spurious oscillations occur in the resulting stress field.In this thesis with the introduction of the Finite Incremental Calculus (FIC) in the framework of fractional step method, the so-called "FSA-DEVSS-FIC" fractional step algorithm is proposed to restrain and even eliminate the two sources resulting in the numerical instability, The restrictions imposed on the choise of interpolation spaces for the mixed variables of the reducible discrete mixed formuation are circumvented with the introduction of the FIC into the mass conservation equation for pressure stabilization, in combination with DEVSS method. Furthurmore, stabilization mechanism is also introduced into the constitutive equation by virtue of FIC process to effectively depress the numerical instability steming from the convection domination in the constitutive equation when Weissenberg number is increased. The detailed derivation of FSA-DEVSS-FIC algorithm and its numerical validation by means of cavity flow problem and planar4:1contraction flow benchmark problem are presented in chapter4.The loss of positive definiteness of conformation tensor due to accumulated numerical errors has been paid more attentions in recent years. In numerical simulation of viscoelastic flows, the loss of positive definiteness of conformation tensor implies the loss of intrinsic physcial character of polymer melts, and in general indicates the failure of numerical algorithms. However, with the advent of log-conformation formulation presented in2004, an efficient mechanism is provided to enusre the positive definiteness of conformation tensor preserved in the simulation process.In this thesis the LG-FSA-DEVSS-FIC algorithm is developed by integrating the log-conformation formulation into the proposed FSA-DEVSS-FIC algorithm, In the framework of fractional step algorithm, the primary variables are solved in the decoupled and sequential way, thus the difference approximation to the gradient of log-comformation tensor is avoided. Furthermore, the developed algorithm provides with high solution accuracy for stresses, as the exponential profiles of stress can be reproduced in an element even with the equal lower order interpolations for mixed variables of velocity-pressure-log conformation tensor. The detailed derivation of LG-FSA-DEVSS-FIC algorithm and its numerical validation by means of cavity flow problem and cylinder flow benchmark problem are presented in chapter5.Moving front surfaces tracking of molten polymer is of significant importance for injection molding flow simulation. According to the kinematics of computational mesh, free-surfaces tracking methods can be classified into three categories, i.e. Lagrangian description, Eulerian description, and Arbitrary-Lagrangian-Eulerian (ALE) description.In this thesis a three-dimensional self-adaptive free-surfaces tracking method and local mesh regeneration strategy are proposed based-on ALE description. The three dimensional moving free surfaces are tracked in a self-adaptive manner by virtue of the moving least square (MLS) surface fitting technique, and the Laplace smoothing method is adopted to improve the mesh quality. Under ALE description, it should be mentioned that there is no need to project primary variables from the old mesh to the new one when positions of mesh nodes are adjusted, thus the accumulated interpolation errors due to the projection between old and new meshes are avoided. By the proposed local mesh regeneration strategy, the mesh regeneration frequently required during injection filling flow is limited in the local region in the vicinity of the moving free surfaces and is implemented with the hierarchical triangulation strategy. The computational cost associated with mesh regeneration is reduced decisively, and the numerical errors due to frequent remeshing are reduced, too. Detailed description of the proposed free surfaces tracking method, the implementation of three dimensional injection molding flow simulation with generalized Newtionian law model, and the numerical examples are presented in chapter7.
|
PDF Full Text Request