Numerical models for the simulation of longitudinal and transverse Stokes flow in cylindrical periodic porous media are presented. The models, which are based on a finite-volume formulation in primitive variables, utilize digital image representations of the geometries to simulate, making them particularly well-suited for the rapid automated analysis of creeping flow in porous media with complex morphologies. Complete details of the model formulations are given, including extensive treatment of the pressure boundary conditions at the solid-liquid interface needed to guarantee convergence with all possible geometries. The convergence behavior of both models is tested, and the models are shown to be second-order accurate.The models are used to simulate flow over the whole range of volume fractions of liquid in several regular geometries. The longitudinal model is used to simulate flow in square arrays of circular and square ducts, and both models are used to simulate flow in square and hexagonal arrays of circular cylinders and square arrays of square cylinders rotated by varying amounts. For each of the geometries, accurate empirical expressions for the Darcy permeability as a function of volume fraction solid are presented. Where applicable, model predictions of permeability are compared to existing analytical results.Subsequently, the models are used to simulate Stokes flow in random domains over a wide range of fractions liquid. The sequential random packing algorithm is used to generate 1,000 random packings of circular cylinders at each of 14 fractions of liquid, and longitudinal and transverse flow simulations are performed for each geometry. Histograms and summary statistics are computed for the permeability for each fraction liquid, and empirical expressions for mean permeability as a function of fraction liquid are given. The autocorrelation structure of the geometry and of the fluid velocity is analyzed, and an analysis of the scaling of longitudinal permeability variance is presented. In transverse flow at high packing densities, it is found that lightning-like patterns emerge in the fluid velocity. It is also found that the details of flows in such geometries are strongly sensitive to the placement of individual solid obstacles.

This thesis describes an investigation of the velocity field in a fluid around a solid sphere undergoing transient motion parallel to, and midway between, two plane walls. Particle Image Velocimetry (PIV) was used to measure the velocity at many discrete locations in a plane that was perpendicular to the walls and included the centre of the sphere. The transient motion was achieved by releasing the sphere from rest and allowing it to accelerate to terminal velocity. <p>To avoid complex wake structures, the terminal Reynolds number was kept below 200. Using solutions of glycerol and water, two different fluids were tested. The first fluid was 100%wt glycerol, giving a terminal Reynolds number of 0.6 which represents creeping flow. The second solution was 80%wt glycerol yielding a terminal Reynolds number of 72. For each of these fluids, three wall spacings were examined giving wall spacing to sphere diameter ratios of h/d = 1.2, 1.5 and 6.0. Velocity field measurements were obtained at five locations along the transient in each case. Using Y to denote the distance the sphere has fallen from rest, velocity fields were obtained at Y/d = 0.105, 0.262, 0.524, 1.05, and 3.15. <p>It was observed that the proximity of the walls tends to retard the motion of the sphere. A simple empirical correlation was fit to the observed sphere velocities in each case. A wall correction factor was used on the quasi-steady drag term in order to make the predicted unbounded terminal velocity match the observed terminal velocity when the walls had an effect. While it has been previously established that the velocity of a sphere is retarded by the proximity of walls, the current research examined the link between the motion of the sphere and the dynamics of the fluid that surrounds it. By examining the velocity profile between the surface of the sphere at the equator and the wall, it was noticed that the shear stresses acting on the sphere increase throughout the transient, and also increase as the wall spacing decreases. This is due to the walls blocking the diffusion of vorticity away from the sphere as it accelerates leading to higher shear stresses. <p>In an unbounded fluid, the falling sphere will drag fluid along with it, and further from the sphere, fluid will move upward to compensate. It was found that there is a critical wall spacing that will completely prevent this recirculation in the gap between the sphere and the wall. In the 80%wt glycerol case, this critical wall spacing is between h/d = 1.2 and 1.5, and in the 100%wt glycerol case the critical wall spacing is between h/d = 1.5 and 6.0.

Porous media flows are encountered in many natural and man-made systems such as gas adsorption, filtration, heat exchangers, combustion, catalytic reactors and groundwater hydrology. This study experimentally investigates these flows as function of pore Reynolds number, Re[subscript pore]. The pore Reynolds number is based on the porous bed hydraulic diameter, D[subscript H] =φD[subscript Β]/(1−φ) where φ is bed porosity and D[subscript B] is solid phase bead diameter and average bed interstitial velocity, V[subscript int]= V[subscript Darcy]/φ, where VDarcy= Q/A[subscript bed], with Q being the volumetric flow rate and A[subscript bed] the bed cross section normal to the flow. The flow characteristics are studied through application of a particle displacement technique called particle image velocimetry, PIV. In the case of PIV, flow fields are estimated by seeding the flow with tracer particles and then evaluating their displacements. Application of quantitative imaging technique such as PIV to a complex flow domain like porous bed requires matching refractive index of liquid phase to that of the solid phase. Firstly, the effect of slight index mismatch, due to experimental uncertainties, on obtaining highly accurate PIV measurements as expressed as an experimental uncertainty was explored. Mismatch of refractive indices leads to error in estimation of particle positions and their displacements due to refraction at solid-liquid interfaces. Slight mismatch, in order of 10⁻³, in refractive indices also leads to reduction in particle density, particle signal peak intensity and degrade the particle image. These effects on velocity field estimation using PIV is studied experimentally and numerically. The numerical model, after validating against experimental results, is used to generate an expression for the error in PIV measurements as a function of refractive index mismatch for a range of bead diameters, bed widths, bed porosity, and optical magnification. After refractive index matching, planar PIV measurements were taken at discrete locations throughout a randomly packed bed with aspect ratio (bed width to bead diameter) of 4.67 for steady, low pore Reynolds number flows, Re[subscript pore] ~ 6, intermediate Re[subscript pore] of 54 and unsteady flow with high Re[subscript pore] ranging from 400-4000. Details of the measurement uncertainties as well as methods to determine local magnification and determination of the dynamic velocity range are presented. The data are analyzed using the PIV correlation averaging method for steady flows and multigrid and multipass correlation methods for unsteady turbulent flows with the largest velocity uncertainties arising from in plane image loss and out of plane motion. Results for low Re[subscript pore] flows show the correspondence of the geometric and velocity correlation functions across the bed, and that the centerline of the bed shows a random-like distribution of velocity with an integral length scale on the order of one hydraulic diameter (or 0.38 bead diameters based on the porosity for this bed). The velocity variance is shown to increase by a factor of 1.8 when comparing the center plane data versus using data across the entire bed. It is shown that the large velocity variance contributes strongly to increased dispersion estimates, and that based on the center plane data of the variance and integral length scales, the dispersion coefficient matches well with that measured in high aspect ratio beds using global data. For unsteady and turbulent flow, velocity data were used to determine the following turbulence measures: (i) turbulent kinetic energy components, (ii) turbulent shear production rate, (iii) integral Eulerian length and time scales, and (iv) energy spectra all for a range of pore Reynolds numbers, Re[subscript pore], from 418 to 3964. These measures, when scaled with the bed hydraulic diameter, DH, and average interstitial velocity, V[subscript int], all collapse for Re[subscript pore], beyond approximately 2800, except that the integral scales collapse at a lower value near 1300-1800. The results show that the pore turbulence characteristics are remarkably similar from pore to pore and that scaling based on bed averaged variables like D[subscript H] and V[subscript int] characterizes their magnitudes despite very different local mean flow conditions. In the case of high Re[subscript pore] flows, large scale structures such as stationary and convected vortices and structures resembling jets were also identified. These structures were analyzed in detail using decomposition techniques like Large Eddy Scale decomposition and critical point analysis like swirl strength analysis. Direct velocity measurements were used to estimate Lagrangian statistics through Eulerian measures and then estimate contribution of flow structures to turbulent mechanical dispersion. Results agree well with those in the literature obtained using global measurements in very high aspect ratio, long test beds. Stationary vortical or recirculation regions were seen to play a dominant role in contributing to overall dispersion in porous beds. / Graduation date: 2013

This thesis describes an investigation of the velocity field in a fluid around a solid sphere undergoing transient motion parallel to, and midway between, two plane walls. Particle Image Velocimetry (PIV) was used to measure the velocity at many discrete locations in a plane that was perpendicular to the walls and included the centre of the sphere. The transient motion was achieved by releasing the sphere from rest and allowing it to accelerate to terminal velocity. <p>To avoid complex wake structures, the terminal Reynolds number was kept below 200. Using solutions of glycerol and water, two different fluids were tested. The first fluid was 100%wt glycerol, giving a terminal Reynolds number of 0.6 which represents creeping flow. The second solution was 80%wt glycerol yielding a terminal Reynolds number of 72. For each of these fluids, three wall spacings were examined giving wall spacing to sphere diameter ratios of h/d = 1.2, 1.5 and 6.0. Velocity field measurements were obtained at five locations along the transient in each case. Using Y to denote the distance the sphere has fallen from rest, velocity fields were obtained at Y/d = 0.105, 0.262, 0.524, 1.05, and 3.15. <p>It was observed that the proximity of the walls tends to retard the motion of the sphere. A simple empirical correlation was fit to the observed sphere velocities in each case. A wall correction factor was used on the quasi-steady drag term in order to make the predicted unbounded terminal velocity match the observed terminal velocity when the walls had an effect. While it has been previously established that the velocity of a sphere is retarded by the proximity of walls, the current research examined the link between the motion of the sphere and the dynamics of the fluid that surrounds it. By examining the velocity profile between the surface of the sphere at the equator and the wall, it was noticed that the shear stresses acting on the sphere increase throughout the transient, and also increase as the wall spacing decreases. This is due to the walls blocking the diffusion of vorticity away from the sphere as it accelerates leading to higher shear stresses. <p>In an unbounded fluid, the falling sphere will drag fluid along with it, and further from the sphere, fluid will move upward to compensate. It was found that there is a critical wall spacing that will completely prevent this recirculation in the gap between the sphere and the wall. In the 80%wt glycerol case, this critical wall spacing is between h/d = 1.2 and 1.5, and in the 100%wt glycerol case the critical wall spacing is between h/d = 1.5 and 6.0.

No description available.

The highly optimized performance of nature’s creations and biological assemblies has inspired the development of their engineered counter parts that can potentially outperform conventional systems. In particular, bat wings are populated with air flow hair receptors which feedback the information about airflow over their surfaces for enhanced stability and maneuverability during their flight. The hairs in the bat wing membrane play a role in the maneuverability tasks, especially during low-speed flight. The developments of artificial hair sensors (AHS) are inspired by biological hair cells in aerodynamic feedback control designs. Current mathematical models for hair receptors are limited by strict simplifying assumptions of creeping flow hair Reynolds number on AHS fluid-structure interaction (FSI), which may be violated for hair structures integrated on small-scaled Unmanned Aerial Vehicles (UAVs). This study motivates by an outstanding need to understand the dynamic response of hair receptors in flow regimes relevant to bat-scaled UAVs. The dynamic response of the hair receptor within the creeping flow environment is investigated at distinct freestream velocities to extend the applicability of AHS to a wider range of low Reynolds number platforms. Therefore, a threedimensional FSI model coupled with a finite element model using the computational fluid dynamics (CFD) is developed for a hair-structure and multiple hair-structures in the airflow. The Navier-Stokes equations including continuity equation are solved numerically for the CFD model. The grid independence of the FSI solution is studied from the simulations of the hairstructure mesh and flow mesh around the hair sensor. To describe the dynamic response of the hair receptors, the natural frequencies and mode shapes of the hair receptors, computed from the finite element model, are compared with the excitation frequencies in vacuum. This model is described with both the boundary layer effects and effects of inertial forces due to fluid-structure xiv interaction of the hair receptors. For supporting the FSI model, the dynamic response of the hair receptor is also validated considering the Euler-Bernoulli beam theory including the steady and unsteady airflow.

This thesis reports on an experimental study of slow viscoelastic flow through models of fibrous porous media. The models were square arrays of parallel cylinders, with solid volume fractions or ‘solidities’ of 2.5%, 5.0%, and 10%. An initial study using a Newtonian fluid provided a baseline for comparison with results for two Boger fluids, so that the effects of fluid elasticity could be determined. Boger fluids are elastic fluids that have near constant viscosities and can be used in experiments without having to account for shear-thinning effects. The experimental approach involved measurements of pressure loss through the three arrays and interior velocity measurements using particle image velocimetry (PIV). For the Newtonian flows, pressure loss measurements were in good agreement with the analytical predictions of Sangani and Acrivos (1982). PIV measurements showed velocity profiles which were symmetrical and independent of flow rate. Pressure loss measurements for the Boger fluid flows revealed that the onset of elastic effects occurred at a Deborah number of approximately 0.5, for both fluids and the three arrays. Flow resistance data collapsed for the two Boger fluids, and increased with solidity. For all three models, the flow resistance increased monotonically with Deborah number, reaching values up to four times the Newtonian resistance for the 10% model. PIV measurements showed that the transverse velocity profiles for the Newtonian and Boger fluids were the same at Deborah numbers below the elastic onset. Above onset, the profiles became skewed. The skewness, like the flow resistance, was observed to increase with both Deborah number and solidity. In the wake regions between cylinders in a column, periodic flow structures formed in the spanwise direction. The structures were staggered from column to column, consistent with the skewing. As either Deborah number or solidity increased, the flow structures became increasingly three-dimensional, and the stagger became more symmetric. An analysis of fluid stresses reveals that the elastic flow resistance is attributed to additional normal stresses caused by shearing, and not by extension.

This thesis reports on an experimental study of slow viscoelastic flow through models of fibrous porous media. The models were square arrays of parallel cylinders, with solid volume fractions or ‘solidities’ of 2.5%, 5.0%, and 10%. An initial study using a Newtonian fluid provided a baseline for comparison with results for two Boger fluids, so that the effects of fluid elasticity could be determined. Boger fluids are elastic fluids that have near constant viscosities and can be used in experiments without having to account for shear-thinning effects. The experimental approach involved measurements of pressure loss through the three arrays and interior velocity measurements using particle image velocimetry (PIV). For the Newtonian flows, pressure loss measurements were in good agreement with the analytical predictions of Sangani and Acrivos (1982). PIV measurements showed velocity profiles which were symmetrical and independent of flow rate. Pressure loss measurements for the Boger fluid flows revealed that the onset of elastic effects occurred at a Deborah number of approximately 0.5, for both fluids and the three arrays. Flow resistance data collapsed for the two Boger fluids, and increased with solidity. For all three models, the flow resistance increased monotonically with Deborah number, reaching values up to four times the Newtonian resistance for the 10% model. PIV measurements showed that the transverse velocity profiles for the Newtonian and Boger fluids were the same at Deborah numbers below the elastic onset. Above onset, the profiles became skewed. The skewness, like the flow resistance, was observed to increase with both Deborah number and solidity. In the wake regions between cylinders in a column, periodic flow structures formed in the spanwise direction. The structures were staggered from column to column, consistent with the skewing. As either Deborah number or solidity increased, the flow structures became increasingly three-dimensional, and the stagger became more symmetric. An analysis of fluid stresses reveals that the elastic flow resistance is attributed to additional normal stresses caused by shearing, and not by extension.

No description available.

Ce travail de thèse concerne les écoulements de fluides à seuil de contrainte autour d‘un obstacle cylindrique en milieu confiné avec une configuration d‘écoulement de Poiseuille.Expérimentalement, un banc d‘essai permettant d‘obtenir un écoulement en continu dans un circuit fermé a été mis en place. Les régimes d‘écoulement rampant, recirculant et instationnaire périodique ont été étudiés. De nouveaux résultats ont été obtenus avec un fluide newtonien et des solutions de Carbopol, polymère permettant de réaliser des fluides à seuil modèles utilisés en recherche et développement et dans l‘industrie. Une caméra rapide et un éclairage plan laser a servi pour l‘établissement d‘images qui ont ensuite été traitées par PIV. Les champs de vitesses cinématiques, les morphologies d‘écoulement et les paramètres critiques de transitions de régimes ont été déterminés.Numériquement, un modèle viscoplastique basé sur la loi de Herschel-Bulkley régularisée a été utilisé. Des résultats comme les morphologies d‘écoulement, la localisation des zones rigides, les champs de vitesses ont été obtenus. Ceci a permis de comparer les différences entre les effets liés à la nature des gels de Carbopol et la modélisation viscoplastiques. Une étude spécifique sur le glissement à l‘interface fluide-structure a également été réalisée avec l‘utilisation d‘un modèle de lubrification élasto-hydrodynamique. / The flow of yield stress fluids around a circular cylinder in a confined geometry has been investigated with a Poiseuille flow configuration.Experimentally, a test set-up was built which provides a continuous flow in a closed loop. We studied creeping, recirculating and vortex shedding flow regimes. New results has been realised with a Newtonian fluid and Carbopol solutions, models for yield stress behaviour in laboratory experiments and in industry. A high speed camera and a laser sheet have been used to perform images which are treated by PIV. Kinematic fields, flow morphologies and critical transition parameters have been determined.Numerically, a viscoplastic model based on the regularised Herschel-Bulkley law has been used. Results as flow morphologies, rigid areas and local flow parameters fields have been performed. That allowed us to compare the intrinsic effects of Carbopol solutions and the viscoplastic numerical model. A specific study on the wall slip has also been considered with an elasto-hydrodynamic lubrication model.