The understanding of the physics of the Coherent Structures and their interaction with the remaining fluid motions is of paramount interest in Turbulence Research. Indeed, recently had been suggested that separating and understanding the the different physical behavior of Coherent Structures and "uncoherent" background might very well be the key to understand and predict Turbulence. Available understanding of Coherent Structures shows that their size is considerably larger than the turbulent macro-scale, making permissible the application of Large Eddy Simulation to their simulation and study, with the advantage to be able to study their behavior at higher Re and more complex geometry than a Direct Numerical Simulation would normally allow. Original purpose of the present work was therefore the validation of the use of Large Eddy Simulation for the study of Coherent Structures in Shear-Layer and the its application to different flow cases to study the effect of the flow topology on the Coherent Structures nature. However, during the investigation of the presence of Coherent Structures in numerically generated LES flow fields, the aging in house Large Eddy Simulation (LES) code of the Environmental & Applied Fluid Dynamics Department has shown a series of limitations and shortcomings that led to the decision of relegating it to the status of Legacy Code (from now on indicated as VKI LES legacy code and of discontinuing its development. A new natively parallel LES solver has then been developed in the VKI Environmental & Applied Fluid Dynamics Department, where all the shortcomings of the legacy code have been addressed and modern software technologies have been adopted both for the solver and the surrounding infrastructure, delivering a complete framework based exclusively on Free and Open Source Software (FOSS ) to maximize portability and avoid any dependency from commercial products. The new parallel LES solver retains some basic characteristics of the old legacy code to provide continuity with the past (Finite Differences, Staggered Grid arrangement, Multi Domain technique, grid conformity across domains), but improve in almost all the remaining aspects: the flow can now have all the three directions of inhomogeneity, against the only two of the past, the pressure equation can be solved using a three point stencil for improved accuracy, and the viscous terms and convective terms can be computed using the Computer Algebra System Maxima, to derive discretized formulas in an automatic way. For the convective terms, High Resolution Central Schemes have been adapted to the three-dimensional Staggered Grid Arrangement from a collocated bi-dimensional one, and a system of Master-Slave simulations has been developed to run in parallel a Slave simulation (on 1 Processing Element) for generating the inlet data for the Master simulation (n - 1 Processing Elements). The code can perform Automatic Run-Time Load Balancing, Domain Auto-Partitioning, has embedded documentation (doxygen), has a CVS repository (version managing) for ease of use of new and old developers. As part of the new Frame Work, a set of Visual Programs have been provided for IBM Open Data eXplorer (OpenDX), a powerful FOSS Flow visualization and analysis tool, aimed as a replacement for the commercial TecplotTM, and a bug tracking mechanism via Bugzilla and cooperative forum resources (phpBB) for developers and users alike. The new M.i.O.m.a. (MiOma) Solver is ready to be used again for Coherent Structures analysis in the near future.

The present study considers steady laminar two-dimensional incompressible flow over both in-line and staggered flat tube bundles used in heat exchanger applications. The effects of various independent parameters, such as Reynolds number (Re), Prandtl number (Pr), length ratio (L/Da), and height ratio (H/Da), on the pressure drop and heat transfer were studied. A finite volume based FORTRAN code was developed to solve the governing equations. The scalar and velocity variables were stored at staggered grid locations. Scalar variables (pressure and temperature) and all thermophysical properties were stored at the main grid location and velocities were stored at the control volume faces. The solution to a one-dimensional convection diffusion equation was represented by the power law. The locations of grid points were generated by the algebraic grid generation technique. The curvilinear velocity and pressure fields were linked by the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm. The line-by-line method, which is a combination of the Tri-Diagonal Matrix Algorithm (TDMA) and the Gauss-Seidel procedure, was used to solve the resulting set of discretization equations. The result of the study established that the flow is observed to attain a periodically fully developed profile downstream of the fourth module. The strength increases and the size of the recirculation gets larger as the Reynolds number increases. As the height ratio increases, the strength and size of the recirculation decreases because the flow has enough space to expand through the tube passages. The increase in length ratio does not significantly impact the strength and size of the recirculation. The non-dimesionalized pressure drop monotonically decreased with an increase in the Reynolds number. In general, the module average Nusselt number increases with an increase in the Reynolds number. The results at Pr = 7.0 indicate a significant increase in the computed module average Nusselt number when compared to those for Pr = 0.7. The overall performance of in-line configuration for lower height ratio (H/Da = 2) and higher length ratio (L/Da = 6) is preferable since it provides higher heat transfer rate for all Reynolds numbers except for the lowest Re value of 25. As expected the staggered configurations perform better than the in-line configuration from the heat transfer point of view.

The understanding of the physics of the Coherent Structures and their interaction with the remaining fluid motions is of paramount interest in Turbulence Research. <p>Indeed, recently had been suggested that separating and understanding the the different physical behavior of Coherent Structures and "uncoherent" background might very well be the key to understand and predict Turbulence. Available understanding of Coherent Structures shows that their size is considerably larger than the turbulent macro-scale, making permissible the application of Large Eddy Simulation to their simulation and study, with the advantage to be able to study their behavior at higher Re and more complex geometry than a Direct Numerical Simulation would normally allow. Original purpose of the present work was therefore the validation of the use of Large Eddy Simulation for the study of Coherent Structures in Shear-Layer and the its application to different flow cases to study the effect of the flow topology on the Coherent Structures nature.<p>However, during the investigation of the presence of Coherent Structures in numerically generated LES flow fields, the aging in house Large Eddy Simulation (LES) code of the Environmental & Applied Fluid Dynamics Department has shown a series of limitations and shortcomings that led to the decision of relegating it to the status of Legacy Code (from now on indicated as VKI LES legacy code and of discontinuing its development. A new natively parallel LES solver has then been developed in the VKI Environmental & Applied Fluid Dynamics Department, where all the shortcomings of the legacy code have been addressed and modern software technologies have been adopted both for the solver and the surrounding infrastructure, delivering a complete framework based exclusively on Free and Open Source Software (FOSS ) to maximize portability and avoid any dependency from commercial products. The new parallel LES solver retains some basic characteristics of the old legacy code to provide continuity with the past (Finite Differences, Staggered Grid arrangement, Multi Domain technique, grid conformity across domains), but improve in almost all the remaining aspects: the flow can now have all the three directions of inhomogeneity, against the only two of the past, the pressure equation can be solved using a three point stencil for improved accuracy, and the viscous terms and convective terms can be computed using the Computer Algebra System Maxima, to derive discretized formulas in an automatic way.<p>For the convective terms, High Resolution Central Schemes have been adapted to the three-dimensional Staggered Grid Arrangement from a collocated bi-dimensional one, and a system of Master-Slave simulations has been developed to run in parallel a Slave simulation (on 1 Processing Element) for generating the inlet data for the Master simulation (n - 1 Processing Elements). The code can perform Automatic Run-Time Load Balancing, Domain Auto-Partitioning, has embedded documentation (doxygen), has a CVS repository (version managing) for ease of use of new and old developers.<p>As part of the new Frame Work, a set of Visual Programs have been provided for IBM Open Data eXplorer (OpenDX), a powerful FOSS Flow visualization and analysis tool, aimed as a replacement for the commercial TecplotTM, and a bug tracking mechanism via Bugzilla and cooperative forum resources (phpBB) for developers and users alike. The new M.i.O.m.a. (MiOma) Solver is ready to be used again for Coherent Structures analysis in the near future. / Doctorat en sciences appliquées / info:eu-repo/semantics/nonPublished

A particulate model is developed to analyze the effects of steady state and transient seepage of water through a randomly-packed coarse-grained soil as an improvement to conventional seepage analysis based on continuum models. In the new model the soil skeleton and pore water are volumetrically coupled. In the first phase of the study, the concept of relative density has been used to define different compaction levels of the soil layers of a completely saturated pavement filter system and observe the seepage response to compaction. First, Monte-Carlo simulation is used to randomly pack discrete spherical particles from a specified Particle Size Distribution (PSD) to achieve a desired relative density based on the theoretical minimum and maximum void ratios. Then, a water pressure gradient is applied across one two-layer filter unit to trigger water seepage. The pore water motion is idealized using Navier Stokes (NS) equations which also incorporate drag forces acting between the water and soil particles. The NS equations are discretized using finite differences and applied to discrete elements in a staggered, structured grid. The model predicted hydraulic conductivities are validated using widely used equations. The critical water velocities, hydraulic gradients and flow within the xi saturated soil layers are identified under both steady state and transient conditions. Significantly critical transient conditions seem to develop. In the second phase of the study the model is extended to analyze the confined flow through a partly saturated pavement layer and unconfined flow from a retention pond into the surrounding saturated granular soil medium. In partly saturated soil, the water porosity changes resulting from water flow is updated using the Soil Water Characteristics Curve (SWCC) of the soil. The results show how complete saturation develops due to water flow following the water porosity Vs pressure trend defined by the SWCC. Finally, the model is used to predict the gradual reduction in the water level of a retention pond and the location of the free-surface. The free-surface is determined by differentiating the wet and dry zones based on the Heaviside step function modified NS equations.

This thesis addresses issues related to the simulation and optimization of the injection molding of short fiber-reinforced plastics (SFRPs). The injection molding process is modeled by a two phase flow problem. The simulation of the two phase flow is accompanied by the solution of the Folgar-Tucker equation (FTE) for the simulation of the moments of fiber orientation densities. The FTE requires the solution of the so called 'closure problem'', i.e. the representation of the 4th order moments in terms of the 2nd order moments. In the absence of fiber-fiber interactions and isotropic initial fiber density, the FTE admits an analytical solution in terms of elliptic integrals. From these elliptic integrals, the closure problem can be solved by a simple numerical inversion. Part of this work derives approximate inverses and analytical inverses for special cases of fiber orientation densities. Furthermore a method is presented to generate rational functions for the computation of arbitrary moments in terms of the 2nd order closure parameters. Another part of this work treats the determination of effective material properties for SFRPs by the use of FFT-based homogenization methods. For these methods a novel discretization scheme, the 'staggered grid'' method, was developed and successfully tested. Furthermore the so called 'composite voxel'' approach was extended to nonlinear elasticity, which improves the approximation of material properties at the interfaces and allows the reduction of the model order by several magnitudes compared to classical approaches. Related the homogenization we investigate optimal experimental designs to robustly determine effective elastic properties of SFRPs with the least number of computer simulations. Finally we deal with the topology optimization of injection molded parts, by extending classical SIMP-based topology optimization with an approximate model for the fiber orientations. Along with the compliance minimization by topology optimization we also present a simple shape optimization method for compensation of part warpage for an black-box production process.:Acknowledgments v Abstract vii Chapter 1. Introduction 1 1.1 Motivation 1 1.2 Nomenclature 3 Chapter 2. Numerical simulation of SFRP injection molding 5 2.1 Introduction 5 2.2 Injection molding technology 5 2.3 Process simulation 6 2.4 Governing equations 8 2.5 Numerical implementation 18 2.6 Numerical examples 25 2.7 Conclusions and outlook 27 Chapter 3. Numerical and analytical methods for the exact closure of the Folgar-Tucker equation 35 3.1 Introduction 35 3.2 The ACG as solution of Jeffery's equation 35 3.3 The exact closure 36 3.4 Carlson-type elliptic integrals 37 3.5 Inversion of R_D-system 40 3.6 Moment tensors of the angular central Gaussian distribution on the n-sphere 49 3.7 Experimental evidence for ACG distribution hypothesis 54 3.8 Conclusions and outlook 60 Chapter 4. Homogenization of SFRP materials 63 4.1 Introduction 63 4.2 Microscopic and macroscopic model of SFRP materials 63 4.3 Effective linear elastic properties 65 4.4 The staggered grid method 68 4.5 Model order reduction by composite voxels 80 4.6 Optimal experimental design for parameter identification 93 Chapter 5. Optimization of parts produced by SFRP injection molding 103 5.1 Topology optimization 103 5.2 Warpage compensation 110 Chapter 6. Conclusions and perspectives 115 Appendix A. Appendix 117 A.1 Evaluation of R_D in Python 117 A.2 Approximate inverse for R_D in Python 117 A.3 Inversion of R_D using Newton's/Halley's method in Python 117 A.4 Inversion of R_D using fixed point method in Python 119 A.5 Moment computation using SymPy 120 A.6 Fiber collision test 122 A.7 OED calculation of the weighting matrix 123 A.8 OED Jacobian of objective and constraints 123 Appendix B. Theses 125 Bibliography 127 / Diese Arbeit befasst sich mit Fragen der Simulation und Optimierung des Spritzgießens von kurzfaserverstärkten Kunststoffen (SFRPs). Der Spritzgussprozess wird durch ein Zweiphasen-Fließproblem modelliert. Die Simulation des Zweiphasenflusses wird von der Lösung der Folgar-Tucker-Gleichung (FTE) zur Simulation der Momente der Faserorientierungsdichten begleitet. Die FTE erfordert die Lösung des sogenannten 'Abschlussproblems'', d. h. die Darstellung der Momente 4. Ordnung in Form der Momente 2. Ordnung. In Abwesenheit von Faser-Faser-Wechselwirkungen und anfänglich isotroper Faserdichte lässt die FTE eine analytische Lösung durch elliptische Integrale zu. Aus diesen elliptischen Integralen kann das Abschlussproblem durch eine einfache numerische Inversion gelöst werden. Ein Teil dieser Arbeit leitet approximative Inverse und analytische Inverse für spezielle Fälle von Faserorientierungsdichten her. Weiterhin wird eine Methode vorgestellt, um rationale Funktionen für die Berechnung beliebiger Momente in Bezug auf die Abschlussparameter 2. Ordnung zu generieren. Ein weiterer Teil dieser Arbeit befasst sich mit der Bestimmung effektiver Materialeigenschaften für SFRPs durch FFT-basierte Homogenisierungsmethoden. Für diese Methoden wurde ein neuartiges Diskretisierungsschema 'staggerd grid'' entwickelt und erfolgreich getestet. Darüber hinaus wurde der sogenannte 'composite voxel''-Ansatz auf die nichtlineare Elastizität ausgedehnt, was die Approximation der Materialeigenschaften an den Grenzflächen verbessert und die Reduzierung der Modellordnung um mehrere Größenordnungen im Vergleich zu klassischen Ansätzen ermöglicht. Im Zusammenhang mit der Homogenisierung untersuchen wir optimale experimentelle Designs, um die effektiven elastischen Eigenschaften von SFRPs mit der geringsten Anzahl von Computersimulationen zuverlässig zu bestimmen. Schließlich beschäftigen wir uns mit der Topologieoptimierung von Spritzgussteilen, indem wir die klassische SIMP-basierte Topologieoptimierung um ein Näherungsmodell für die Faserorientierungen erweitern. Neben der Compliance-Minimierung durch Topologieoptimierung stellen wir eine einfache Formoptimierungsmethode zur Kompensation von Teileverzug für einen Black-Box-Produktionsprozess vor.:Acknowledgments v Abstract vii Chapter 1. Introduction 1 1.1 Motivation 1 1.2 Nomenclature 3 Chapter 2. Numerical simulation of SFRP injection molding 5 2.1 Introduction 5 2.2 Injection molding technology 5 2.3 Process simulation 6 2.4 Governing equations 8 2.5 Numerical implementation 18 2.6 Numerical examples 25 2.7 Conclusions and outlook 27 Chapter 3. Numerical and analytical methods for the exact closure of the Folgar-Tucker equation 35 3.1 Introduction 35 3.2 The ACG as solution of Jeffery's equation 35 3.3 The exact closure 36 3.4 Carlson-type elliptic integrals 37 3.5 Inversion of R_D-system 40 3.6 Moment tensors of the angular central Gaussian distribution on the n-sphere 49 3.7 Experimental evidence for ACG distribution hypothesis 54 3.8 Conclusions and outlook 60 Chapter 4. Homogenization of SFRP materials 63 4.1 Introduction 63 4.2 Microscopic and macroscopic model of SFRP materials 63 4.3 Effective linear elastic properties 65 4.4 The staggered grid method 68 4.5 Model order reduction by composite voxels 80 4.6 Optimal experimental design for parameter identification 93 Chapter 5. Optimization of parts produced by SFRP injection molding 103 5.1 Topology optimization 103 5.2 Warpage compensation 110 Chapter 6. Conclusions and perspectives 115 Appendix A. Appendix 117 A.1 Evaluation of R_D in Python 117 A.2 Approximate inverse for R_D in Python 117 A.3 Inversion of R_D using Newton's/Halley's method in Python 117 A.4 Inversion of R_D using fixed point method in Python 119 A.5 Moment computation using SymPy 120 A.6 Fiber collision test 122 A.7 OED calculation of the weighting matrix 123 A.8 OED Jacobian of objective and constraints 123 Appendix B. Theses 125 Bibliography 127