Flows of Complex Fluids in Porous Media with Applications to Composites Manufacturing

다국어 초록 (Multilingual Abstract)

A wide variety of environmental and technological processes involve problems of a fluid flow through porous media, such as spreading of contaminants in soil, the enhanced oil recovery in petroleum industry, the trickle bed reactor for catalyzed reaction, various filtration processes in chemical engineering and composites manufacturing. The thesis covers the most of all numerical, theoretical and experimental aspects on both Newtonian and non-Newtonian fluid flows through porous media. In the first topic, we present a new three-dimensional finite element technique to solve flows in a representative porous volume with fibrous microstructures. Through the extensive numerical simulations for various fiber and fabric architectures, we investigate the relationship between the permeability and fiber architectures in order to establish a reasonable approximation method in estimating the permeability of such complex 3D architectures. Specifically we discuss the applicability and the limitation of the macroscopic permeability averaging rule for those purposes, using the permeability of simple structural building blocks. In second topic, we studied flow behaviors of a non-Newtonian fluid in spherical microstructures by a direct numerical simulation. A shear-thinning (power-law) fluid through both regular and randomly packed spheres has been numerically investigated in a representative unit cell with the tri-periodic boundary condition. The flow mobility of regular packing structures, including simple cubic (SC), body-centered cubic (BCC), face-centered cubic (FCC), as well as randomly packed spheres, has been investigated quantitatively by considering the amount of shear-thinning, the pressure gradient and the porosity as parameters. Furthermore, the mechanism leading to the main flow path in a highly shear-thinning fluid through randomly packed spheres has been discussed. In the third topic, we derive the analytical solution of a power-law fluid through periodic arrays of square and hexagonal packing cylinders by the lubrication theory to characterize the mobility dependence on the pressure drop, the amount of shear-thinning and the fiber volume fraction. Based on the theoretical modeling and direct numerical simulations, we propose a simple geometrical scaling rule for the mobility by separating the fluid rheological contribution from the rheological contribution. This simple scaling rule will be employed to approximate the dependence of mobility on the pressure gradient for various packing structures, which facilitates simple and reliable prediction of the flow mobility for power-law fluids in porous media. In the fourth topic, we present numerical simulations for flow behaviors of viscoelastic fluid passing through the porous media. We employ the DEVSS/DG (Discrete Elastic-Viscous Splitting / Discontinuous Galerkin) finite element scheme combined with the mortar-element method for the bi-periodic boundary condition and the fictitious domain method for a proper representation of fibers in a fluid. The matrix logarithm has been incorporated to achieve stable solutions at high Weissenberg number. By employing an Oldroyd-B and Leonov models as constitutive equations, we discuss effects of elasticity on the flow resistance in typical porous microstructures of viscoelastic flows: square-, hexagonal-, as well as random-packing unidirectional fibers. The increase of flow resistance has been observed for the first time, as far as authors know, as the Weissenberg number exceeds a critical value by numerical simulation. The significant growth of the flow resistance has turned out to be related with the extensional stretching of polymers in viscoelastic flows in porous media and the energy dissipation of the viscoelastic flow in porous media has also been analyzed. The last topic is about the experimental work on the flow visualization for the the VARTM process. In this experimental study, an ultrasound visualization system has been set up for in-situ monitoring of the resin flow impregnating through opaque carbon fiber reinforcements. The flow front advancement through the carbon fabrics covered by a bagging film can be identified and visualized by the high frequency B (brightness) mode ultrasound imaging technique. The resin advancement in the opaque carbon fabrics has turned out to form a non-uniform plug flow along the pressure gradient direction and the potential void formation can be observed from the mesoscopic resin flow behavior: the inter-tow regions have been preferentially filled by the resin fluid and the fiber tow region behaves as a sink that probably remain as a void defect. The local unsaturated transient velocity of the resin flow has been also evaluated, which is particularly important in understanding saturation behaviors in dual scale fabrics and is hardly measurable by other means. In spite of the hardware limitations on the resolution, the proposed ultrasound visualization system can provide a less expensive and portable visualization tool to understand the microstructure of opaque reinforcements and monitor the resin flow behavior during the VARTM process in the industrial composite manufacturing environment.

목차 (Table of Contents)

• 1. Introduction 1
• 1.1. Backgrounds 1
• 1.1.1. Polymer matrix composite materials 1
• 1.1.2. Liquid composite molding process 2
• 1.1.3. Characterization of fluid flows in porous media 3
• 1.2. Objectives and thesis organization 4
• 1.2.1. Objective of this study 4
• 1.2.2. Thesis organization 5
• 1.3. Literature reviews 6
• 2. Permeability prediction of fibrous porous media with complex 3D architectures 11
• 2.1. Overview 11
• 2.2. Modeling 11
• 2.3. Numerical methods 13
• 2.4. Results and discussions 16
• 2.4.1. Regular packing fiber problems: verification 16
• 2.4.2. Permeability of multi-directional fibers 17
• 2.4.3. The macroscopic permeability averaging rule for the microscopic permeability 19
• 2.4.4. Permeability of 3D architectures with fiber tow geometries 22
• 2.4.5. Dependence of Kozeny constants on fibrous architecture and fiber fractions 25
• 2.5. Conclusions 26
• 3. Numerical simulation of a shear-thinning fluid through packed spheres 27
• 3.1. Overview 27
• 3.2. Modeling and numerical methods 27
• 3.2.1. Problem definition 28
• 3.2.2. Governing sets of equations 29
• 3.2.3. Numerical methods 29
• 3.3. Results 30
• 3.3.1. Comparison with literatures: regular packing spheres with a Newtonian fluid 30
• 3.3.2. Effects of the pressure gradient and the amount of shear-thinning on the flow mobility 33
• 3.3.3. Randomly packed spheres 37
• 3.4. Conclusions 40
• 4. A scaling rule for flow mobility of a power-law fluid through porous media 41
• 4.1. Overview 41
• 4.2. Theoretical derivation and numerical modeling 41
• 4.2.1. Perspectives of the scaling rule from a simple pressure-driven circular pipe flow 41
• 4.2.2. Theoretical modeling of power-law fluid through packing fibers 45
• 4.2.3. Numerical simulation of power-law fluid through packing fibers 49
• 4.3. Results and discussions 50
• 4.3.1. Verification 50
• 4.3.2. Approximations of the rheological function  for regular packing fibers 51
• 4.3.3. Random packing fibers and an universal scaling rule for various packing structures 55
• 4.4. Conclusions 57
• 5. Numerical simulation of viscoelastic flows through porous media 59
• 5.1. Overview 59
• 5.2. Modeling 59
• 5.2.1. Problem definition 59
• 5.2.2. Definition of Weissenberg number 60
• 5.2.3. Governing sets of equations 61
• 5.3. Numerical methods and implementations 62
• 5.3.1. Combined weak formulation with DEVSS/DG 62
• 5.3.2. Implementations 63
• 5.4. Results 64
• 5.4.1. Verifications 64
• 5.4.2. Flow resistance in regular packing fiber arrays 66
• 5.4.3. Flow resistance in random packing fiber arrays 67
• 5.4.4. Energy dissipation analysis of the viscoelastic flow in the porous media 71
• 5.5. Conclusions 72
• 6. Visualization of resin impregnation through opaque reinforcement textiles during the VARTM process using ultrasound 75
• 6.1. Overview 75
• 6.2. Materials and methods 75
• 6.2.1. Experimental setup 75
• 6.2.2. Ultrasound imaging system and post image processing 77
• 6.3. Results and discussions 79
• 6.3.1. Microstructures of the carbon fabric layers 79
• 6.3.2. Monitoring flow front during VARTM process 80
• 6.4. Conclusions 82
• 7. Conclusions 83
• Bibliography 87