| Summary: |
This proposal entails research at a fundamental level, with the introduction of leading-edge and recent mathematical concepts and techniques (such as PGD) into the realm of computational fluid dynamics, but it has nevertheless important potential implications within the Portuguese industry context. Plastic injection moulding industry is of extreme relevance in Portugal, one of the world's leading manufacturers of moulds, which exports 85% of its production (in 2013, total production and export were 639 and 543 million Euros, respectively [1]). Injection moulding is a cyclic process of forming plastic into a desired shape by forcing the material, in the liquid state, under pressure into a cavity, with the final shaping achieved by cooling rheological complex materials called thermoplastics or polymer melts. Computer simulation in design and manufacture of plastic parts still faces numerous challenges, arising from both the inherent complexity of the physical description of such processes, as well as from the high number of variables and parameters involved in the process. On one side, the complex thermal and rheological behaviour during the filing and moving front of two materials with different properties, the configurational changes in the post-filling phase, the reaction kinetics and the presence of viscoelastic instabilities (as the fountain flow) presents a computational challenge. On the other side, the optimal design of these flows will depend on a large number of variables and dimensions, making the direct simulation approach (or even intensive parametric simulations) very limiting.
One good alternative to direct computing approaches is the use of separated decomposition representation, such as the Proper Generalized Decomposition (PGD) [2], a new powerful a priori model reduction technique, in which the complexity of the solution of the governing equation scales linearly with the spacial dimensions of the physical models, instead of the exponentially-gro  |
Summary
This proposal entails research at a fundamental level, with the introduction of leading-edge and recent mathematical concepts and techniques (such as PGD) into the realm of computational fluid dynamics, but it has nevertheless important potential implications within the Portuguese industry context. Plastic injection moulding industry is of extreme relevance in Portugal, one of the world's leading manufacturers of moulds, which exports 85% of its production (in 2013, total production and export were 639 and 543 million Euros, respectively [1]). Injection moulding is a cyclic process of forming plastic into a desired shape by forcing the material, in the liquid state, under pressure into a cavity, with the final shaping achieved by cooling rheological complex materials called thermoplastics or polymer melts. Computer simulation in design and manufacture of plastic parts still faces numerous challenges, arising from both the inherent complexity of the physical description of such processes, as well as from the high number of variables and parameters involved in the process. On one side, the complex thermal and rheological behaviour during the filing and moving front of two materials with different properties, the configurational changes in the post-filling phase, the reaction kinetics and the presence of viscoelastic instabilities (as the fountain flow) presents a computational challenge. On the other side, the optimal design of these flows will depend on a large number of variables and dimensions, making the direct simulation approach (or even intensive parametric simulations) very limiting.
One good alternative to direct computing approaches is the use of separated decomposition representation, such as the Proper Generalized Decomposition (PGD) [2], a new powerful a priori model reduction technique, in which the complexity of the solution of the governing equation scales linearly with the spacial dimensions of the physical models, instead of the exponentially-growing complexity characteristic of other non-decomposed strategies. Other interesting feature of this dimensional reduction technique relies on its applicability to optimization and real time simulations, by extending the simple dimensional separation of independent and dependent parametric quantities into new extra-coordinates.
The ultimate objective of this research proposal is to develop stable, accurate and parallelized numerical methodologies for the prediction of single and two-phase flows of thermo-rheologically complex fluids using the PGD technique. For such endeavour, we propose to use and modify an in-house finite volume viscoelastic code [3]. The design of the additional packages is scheduled to follow four specific PGD functionalities, namely: (i) a non-incremental multi-phase separated decomposition functionality for thermo-rheological flow problems and (ii) a thermal and multiphase separated decomposition and (iii) a parametric optimization functionality. These modular packages will be designed in a parallel computing environment (using both CPU and GPU parellelization), due to the high computational demand of the specific industrial applications in mind, such as the study of complex thermo-rheological flows in injection moulding. At the end of this research project the code will possess a vast set of capabilities that will make it useful for complex industrial applications. |