Subglacial processes that control the water pressure and flow determine the large-scale behavior of the overlying ice by regulating basal resistance. We implement a model in which a steady-state subglacial conduit system is surrounded by fully saturated porous media. We investigate branching in this system at fixed angles of 15 degrees, 30 degrees and 45 degrees to the direction of ice flow and further assess these systems by calculating the hydraulic potential gradient to determine conduit flow path. We solve our governing equations for porous media flow and allow ice infiltration of the pore space to occur at a critical effective stress N infiltration. For low values of N infiltration, ice infiltration of sediment allows these conduits to follow their original paths. Where insufficient ice infiltration occurs, the conduit path instead lies parallel to the direction of ice flow. Our results speak to the importance of incorporating small-scale processes into models of subglacial hydrologic networks.

The primary aim of this thesis is to investigate the transition between different flow regimes in porous media. The complete transition spectrum of single-phase flow, from creeping flow to inertial, unsteady laminar, and turbulent flow regimes, was examined in sphere packings. Further understanding of the fundamental fluid dynamics was derived based on the pore-scale flow visualisation using magnetic resonance velocimetry (MRV). Spiral imaging was selected as the ultrafast imaging protocol to probe the transient phenomena, and the acquisition was further accelerated by combining subsampling and compressed sensing reconstruction. In a random sphere packing column with column-to-diameter ratio of 3.44, the inertial effect and the onset of unsteady regime were examined with respect to the principal flow characteristics: the inertial core/channeling, backflow, and helical vortices. Helical vortices have been observed experimentally in a random packing for the first time, and the analogy between the swirling flow and helical vortices provides insight into the design and operation of packed bed reactors. Another new observation is that the transition to the unsteady regime is a highly heterogeneous process, where the evolution of the flow instability depends on the pore geometry. Moreover, pixelwise validation was achieved between the experimental and simulation results on three-dimensional velocity fields in the inertial regime; this is enabled by an image-based meshing pipeline, which reproduces the geometry of the random packing in MRV for the numerical simulation. The unsteady regimes were further investigated using a regular sphere packing, the simple cubic packing (SCP). The spectral analysis, in both the random and regular packing, revealed a route to chaos from the steady to periodic, quasi-periodic, and chaotic dynamics, which was only predicted numerically before. During the transition to turbulence, the coherent structures were extracted using proper orthogonal decomposition (POD), which yields a coherent picture regarding the turbulent dynamics, when combined with the skewness, flatness, and quadrant analysis. Furthermore, it was found that the macroscopic properties converged at lower Reynolds number than the microscopic features. In conclusion, the opportunity to measure flow fields at high spatial and temporal resolution will play an increasingly significant role in the advancement of fundamental fluid dynamics. In this thesis, MRV is used, which is particularly advantageous for non-invasive measurements in opaque systems. This thesis provides the experimental and analysis toolkits for such studies and has demonstrated the contribution to characterising and understanding different flow regimes in porous media.

In this dissertation we develop and analyze numerical method to solve general elliptic boundary value problems with many scales. The numerical method presented is intended to capture the small scales effect on the large scale solution without resolving the small scale details, which is done through the construction of a multiscale map. The multiscale method is more effective when the coarse element size is larger than the small scale length. To guarantee a numerical conservation, a finite volume element method is used to construct the global problem. Analysis of the multiscale method is separately done for cases of linear and nonlinear coefficients. For linear coefficients, the multiscale finite volume element method is viewed as a perturbation of multiscale finite element method. The analysis uses substantially the existing finite element results and techniques. The multiscale method for nonlinear coefficients will be analyzed in the finite element sense. A class of correctors corresponding to the multiscale method will be discussed. In turn, the analysis will rely on approximation properties of this correctors. Several numerical experiments verifying the theoretical results will be given. Finally we will present several applications of the multiscale method in the flow in porous media. Problems that we will consider are multiphase immiscible flow, multicomponent miscible flow, and soil infiltration in saturated/unsaturated flow.

In this dissertation we develop and analyze numerical method to solve general elliptic boundary value problems with many scales. The numerical method presented is intended to capture the small scales effect on the large scale solution without resolving the small scale details, which is done through the construction of a multiscale map. The multiscale method is more effective when the coarse element size is larger than the small scale length. To guarantee a numerical conservation, a finite volume element method is used to construct the global problem. Analysis of the multiscale method is separately done for cases of linear and nonlinear coefficients. For linear coefficients, the multiscale finite volume element method is viewed as a perturbation of multiscale finite element method. The analysis uses substantially the existing finite element results and techniques. The multiscale method for nonlinear coefficients will be analyzed in the finite element sense. A class of correctors corresponding to the multiscale method will be discussed. In turn, the analysis will rely on approximation properties of this correctors. Several numerical experiments verifying the theoretical results will be given. Finally we will present several applications of the multiscale method in the flow in porous media. Problems that we will consider are multiphase immiscible flow, multicomponent miscible flow, and soil infiltration in saturated/unsaturated flow.

Les joints à brosse sont des joints compliants utilisés dans les turbomachines. Ils sont constitués d'une brosse de fils très fins compactés entre deux plaques, de telle manière que l'ensemble comble l'écart séparant le stator du rotor. Les fils sont le plus souvent constitués d'un alliage à base de cobalt appelé Haynes 25 (d'autres matériaux peuvent être utilisés, tels que le Kevlar). Le comportement de ces joints présente un fort couplage entre l'écoulement du fluide et la déformation de la brosse. Ce type de joints peut être modélisé en considérant la brosse comme un milieu poreux. Cette méthode présente l'avantage de permettre un calcul relativement simple de l'écoulement, mais elle demande l'usage de données expérimentales afin de calibrer ses perméabilités (i.e. sa capacité à laisser un fluide s'écouler à travers lui). L'objectif de cette thèse est de proposer une modélisation par milieu poreux indépendante des données expérimentales. Une simulation itérative entre le calcul de la déformation des fils sous l'action des efforts de pression et la résolution de l'écoulement dans le milieu poreux formé par la brosse déformée a été mise au point. Elle repose sur le calcul numérique des perméabilités obtenues à partir de la perte de charge générée par un réseau de cylindres représentatifs de la brosse.Des joints de faible diamètre en Haynes 25 ont été testés avec de l'air afin de vérifier la validité des résultats donnés par la simulation. L'évolution du débit avec la différence de pression et avec l'interférence des joints avec le rotor a été étudiée. Les déplacements du rotor et la température des joints ont été suivis durant les essais. / Brush seals are compliant dynamic seals that are used in the turbomachines. They are made of a brush of fine bristles sandwiched between two plates, in such a way that the assembly fills the gap between the rotor and the stator. The bristles are usually made from a cobalt based alloy called Haynes 25 (other materials can be used, such as Kevlar). The behaviour of these seals shows a strong coupling between the fluid flow and the brush deformation.This kind of seal can be modelled by considering the brush as a porous medium. This method presents the benefit of a rather simple calculation of the flow, but it requires the use of experimental data in order to calibrate its permeabilities (i.e. its ability to let the fluid flow through it). The aim of this thesis is to propose a model using the porous medium approach but without the need of preliminary experimental data. An iterative simulation between the calculation of the bristles' deformation under the influence of the pressure forces and the solving of the flow in the porous medium formed by the deformed brush was developed. It relies on the numerical calculation of the permeabilities obtained from the pressure drop generated by an array of cylinders representative of the brush.Low diameter Haynes 25 seals were tested with air in order to verify the validity of the results given by the simulation. The evolution of the mass flow rate with the pressure difference and the interference between the seal and the rotor was studied. Displacements of the rotor and temperature of the seals were also monitored during the tests.

Permeable Friction Course (PFC) is a layer of porous asphalt pavement with a thickness of up to 50 millimeters overlain on a conventional impervious hot mix asphalt or Portland cement concrete roadway surface. PFC is used for its driver safety and improved stormwater quality benefits associated with its ability to drain rainfall runoff from the roadway surface. PFC has recently been approved as a stormwater best management practice in the State of Texas. The drainage properties of PFC are typically considered to be governed primarily by two hydraulic properties: porosity and hydraulic conductivity. Both of these hydraulic properties are expected to change over the life of the PFC layer due to clogging of the pore space by trapped sediment. Therefore, proper measurement of the hydraulic properties can be problematic. Laboratory and field tests are necessary for accurately determining the hydraulic conductivity of the PFC layer in order to ensure whether the driver safety and water quality benefits will persist in the future. During testing, PFC experiences a nonlinear flow relationship which can be modeled using the Forchheimer equation. Due to the two-dimensional flow patterns created during testing, the hydraulic conductivity cannot be directly measured. Therefore, numerical modeling of the two-dimensional nonlinear flow relationship is required to convert the measureable flow characteristics into the theoretical flow characteristics in order to properly determine the isotropic hydraulic conductivity. This numerical model utilizes a new scalar quantity, defined as the hydraulic conductivity ratio, to allow for proper modeling of nonlinear flow in two-dimensional cylindrical coordinates. PFC core specimens have been extracted from three different roadway locations around Austin, Texas for the past four years (2007 to 2010). Porosity values of the core specimens range from 12% to 23%, and the porosity data suggest a statistical decrease over time due to trapped sediment in the pore space. A series of constant head tests used in the laboratory and a falling head test used in the field are recommended for measurement of PFC hydraulic characteristics using a modified Forchheimer equation. Through numerical modeling, regressions equations are presented to estimate the hydraulic conductivity and nonlinear Forchheimer coefficient from the measureable hydraulic characteristics determined during experimental testing. Hydraulic conductivity values determined for laboratory core specimens range from 0.02 centimeters per second (cm/s) to nearly 3 cm/s. Field measurements of in-situ hydraulic conductivity vary over a range from 0.6 cm/s to 3.6 cm/s. The results of this research provide well-defined laboratory and field methods for measurement of the isotropic hydraulic conductivity of PFC experiencing two-dimensional nonlinear flow and characterized by the Forchheimer equation. This methodology utilizes a numerical model which presents a proper solution for nonlinear flow in two-dimensions. / text

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Subsurface processes are usually characterized by rare field experiments, sparse measurements,multi-resolution interpretations, stochastic description, related uncertainties and computational complexity. Over the last few decades, different computational techniques and strategies have become indispensable tools for flow and solute transport prediction in heterogeneous porousmedia. This thesis develops a multi-resolution approach based on Fup basis functions with compactsupport, enabling the use of an efficient and adaptive procedure, closely related to currentunderstood physical interpretation. All flow and transport variables, as well as intrinsic heterogeneity,are described in a multi-resolution representation, in the form of a linear combination ofFup basis functions. Each variable is represented on a particular adaptive grid with a prescribedaccuracy. The methodology is applied to solving problems with sharp fronts, and to solving flowand advective transport in highly heterogeneous porous media, under mean uniform flow conditions.The adaptive Fup collocation method, through the well known method of lines, efficientlytracks solutions with sharp fronts, resolving locations and frequencies at all spatial and/or temporalscales. The methodology yields continuous velocity fields and fluxes, enabling accurate andreliable transport analysis. Analysis of the advective transport proves the robustness of the firstordertheory for low and mild heterogeneity. Moreover, due to the accuracy of the improved Monte-Carlo methodology, this thesis presents the effects of high heterogeneity on ensembleflow and travel time statistics. The difference between Eulerian and Lagrangian velocity statisticsand the importance of higher travel time moments are indicative of high heterogeneity. The thirdtravel time moment mostly describes a peak and late arrivals, while higher moments are requiredfor early arrivals which are linked with the largest uncertainty. A particular finding is the linearityof all travel time moments, which implies that in the limit an advective transport in multi-Gaussian field becomes Fickian. By comparison, the transverse displacement pdf converges to aGaussian distribution around 20 integral scales after injection, even for high heterogeneity. Thecapabilities of the presented multi-resolution approach, and the quality of the obtained results,open new areas for further research. / Markprocesser karakteriseras ofta av fåtaliga fältexperiment, glesa mätningar, heterogenitet påolika skalor, slumpmässighet och relaterade osäkerheter, samt beräkningsmässiga svårigheter.Under de senaste årtiondena har olika beräkningstekniker och strategier blivit ovärderliga verktygför att förutspå vattenflöde och ämnestransport i heterogena porösa medier. Denna doktorsavhandling utvecklar ett angreppssätt med flerskaliga upplösningar baserat på Fup basis funktionermed kompakt stöd, som möjliggör en effektiv och anpassningsbar procedur, nära relaterad tillrådande fysiska tolkningar. Alla flödes- och transportvariabler, så väl som heterogeniteten, beskrivsav en flerskaligt upplöst representation, i form av linjära kombinationer av Fup basis funktioner.Varje variabel representeras på ett speciellt anpassningsbar gridnät med given noggrannhet.Metoden appliceras för att lösa problem med skarpa fronter, samt vattenflöde och advektivämnestransport i starkt heterogena porösa medier. Adaptive Fup collocation metoden tillsammansmed den välkända Method of lines, spårar effektivt lösningar med skarpa fronter och löserupp positioner och frekvenser på alla rums- och/eller tidsskalor. Metoden ger kontinuerliga hastighetsfältoch flöden, och möjliggör noggrann och tillförlitlig transportanalys. Analys av advektivtransport understöder stabiliteten i första-ordningens transport teori för låg och mild heterogenitet.Utöver detta, som resultat av noggrannheten i den förbättrade Monte-Carlo metodiken, visardenna avhandling effekten av hög heterogenitet på ensemble statistiken för flöden och transporttider.Skillnaden mellan Eulerisk och Lagrangian hastighetsstatistik och betydelsen av högrestatistiska moment för transporttider, indikerar hög heterogenitet. Det tredje transporttidsmomentetbeskriver huvudsakligen sannolikhetspiken och de långa transporttiderna, medan högremoment behövs för de korta transporttiderna, som har den största osäkerheten. En speciell upptäcktär linjäariteten i transporttidsmoment, som indikerar att advektiv transport i multi-Gaussiska fält blir Gaussisk i gränsen. Som jämförelse konvergerar sannolikhetsfunktioner förden transversella transportförflyttningen mot en Gaussisk fördelning vid runt 20 korrelationslängder efter injektion, även för hög heterogenitet. Förmågan i det presenterade angreppssättet med flerskalig upplösning, och resultatens noggrannhet, öppnar nya områden för fortsatt forskning. / QC 20100714

The manufacturing process for the core of an RIP bushing was studied. Simulations of a test model was performed, due to the non-linear nature of the fluid filling process. Varying of governing parameters in the model, that could realistically be varied, was carried out and their affect was observed. The model was then compared to real measurements to view its practical reliability. Proposals to optimize the filling speed of the process in order to avoid the creation of bubbles was discussed and conducting it would be the next step for further research of the subject.

<p dir="ltr">The kinetic-based lattice Boltzmann method (LBM) is a specialized computational fluid dynamics (CFD) technique that resolves intricate flow phenomena at the mesoscale level. The LBM is particularly suited for large-scale parallel computing on Graphic Processing Units (GPU) and simulating multi-phase flows. By incorporating a volume fraction parameter, LBM becomes a volumetric lattice Boltzmann method (VLBM), leading to advantages such as easy handling of complex geometries with/without movement. These capabilities render VLBM an effective tool for modeling various complex flows. In this study, we investigated the computational modeling of complex flows using VLBM, focusing particularly on pulsatile flows, the transition to turbulent flows, and pore-scale porous media flows. Furthermore, a new discrete dynamical system (DDS) is derived and validated for potential integration into large eddy simulations (LES) aimed at enhancing modeling for turbulent and pulsatile flows. Pulsatile flows are prevalent in nature, engineering, and the human body. Understanding these flows is crucial in research areas such as biomedical engineering and cardiovascular studies. However, the characteristics of oscillatory, variability in Reynolds number (Re), and shear stress bring difficulties in the numerical modeling of pulsatile flows. To analyze and understand the shear stress variability in pulsatile flows, we first developed a unique computational method using VLBM to quantify four-dimensional (4-D) wall stresses in image-based pulsatile flows. The method is validated against analytical solutions and experimental data, showing good agreement. Additionally, an application study is presented for the non-invasive quantification of 4-D hemodynamics in human carotid and vertebral arteries. Secondly, the transition to turbulent flows is studied as it plays an important role in the understanding of pulsatile flows since the flow can shift from laminar to transient and then to turbulent within a single flow cycle. We conducted direct numerical simulations (DNS) using VLBM in a three-dimensional (3-D) pipe and investigated the flow at Re ranging from 226 to 14066 in the Lagrangian description. Results demonstrate good agreement with analytical solutions for laminar flows and with open data for turbulent flows. Key observations include the disappearance of parabolic velocity profiles when Re>2300, the fluctuation of turbulent kinetic energy (TKE) between laminar and turbulent states within the range 2300</p>