(PHD, 2023)

Abstract:

This PhD thesis focuses on the flows on granular materials, such as sand, glass beads, and powders, which are sheared at low speeds with gravity perpendicular to the flow direction. The study is conducted using a combination of experiments, simulations, and theory, with the goal of developing a unifying theory of granular materials that can be described by continuum models. The main objective is to understand how microscale physics propagate to macroscale phenomena and to address issues related to setting boundary conditions and predicting timescales from unsteady to steady states. This research primarily aims to investigate stress variations in granular materials as a function of shear rate, encompassing both steady and unsteady states. Additionally, the thesis examines the phenomena of wall force anomalies and vortex flows. In Couette cell experiments and vertical plane shear simulations, granular material demonstrates a downward flow near the vertical shearing wall and an upward flow adjacent to another static vertical wall. Interestingly, this vortex flow causes a change in the direction of vertical shear stress when wall shearing commences, contradicting the prevalent assumption that particles consistently apply a downward force on the vertical wall.

The study concludes with key findings, including the observation that normal and shear stresses on the shearing wall increase slowly after the initiation of shearing, and that steady-state values for these stresses are independent of the shearing speed within a certain range. The study also found that the height of particles near the shearing wall decreases gradually with the presence of vortex flow, and that the shear rate near the moving wall is initially high and decreases slowly to reach a steady state. Additionally, we used a non-local constitutive model and Boussinesq approximation to predict the downward flow that is driven by gravity and variations in the solid fraction near the shearing surface, as well as the decay profile of velocity in an infinitely wide box for the steady state.

Overall, this thesis contributes to our understanding of granular materials in the slow flow regime, providing insights into their behavior under shear. The non-local model accurately predicts the downward flow and velocity decay profile, indicating its potential as a valuable tool for future research.

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(PHD, 2022)

Abstract:

Liquid-solid flows with inertial and viscous effects are critical for many engineering and geophysical applications, such as the processing of biomass slurry and the control of debris flows. However, modeling the rheological behaviors of these complex flows remains a challenge. Prior investigations on the liquid-solid flows typically cover suspensions in which the particle Reynolds numbers (*Re*) based on the particle diameter and shear rate are less than 1. Limited prior study at Caltech focuses on particle Reynolds numbers above 10. This thesis focuses on rheological experiments for the moderate Reynolds number regime where both inertial and viscous effects are important, with particle Reynolds numbers from 0.5 to 800. The rheological experiments include torque measurements of *mm* scale-sized polystyrene and SAN particles with a range of solid fractions from 10% to 50%, considering both neutrally-buoyant and settling suspensions with density ratios of 1 and 1.05. This thesis discusses rheological measurements of three different fields: pure fluids, neutrally-buoyant suspensions, and non-neutrally-buoyant suspensions.

The pure fluids measurements determine the flow starts to transition to turbulent flow for gap Reynolds numbers above 6500 in the Caltech Couette flow device. For suspensions with matched particle and fluid densities and solid fractions less than 40%, we find that the effective viscosity only depends on the particle solid fraction until we observe the shear-thickening behaviors for *Re* of approximately 10. For the intermediate *Re* from 10 to 100 and lower solid fractions, the effective viscosity not only depends on the particle solid fraction, but also shows increased dependence on *Re*. For *Re* greater than 100, the liquid-solid flows transition to the turbulent regime, similar to what we see for the pure fluids. At the maximum solid fraction of 50%, the magnitude of the effective viscosity has increased by a factor of 20 as compared to the results of the 10% solid fraction, but the effective viscosity is nearly independent of *Re*. A particle Reynolds number (*Re’*) based on the maximum shear flow velocity and the particle diameter is introduced to examine the effective viscosity of the suspensions. Since the present studies use particles with different sizes, *Re’* is found to be a better way to correlate the effective viscosity than the traditional *Re*. For the analysis of liquid-solid flows with a density ratio of 1.05, the effective viscosity of the particulate flow increases with the Stokes number for loading fractions of 10% and 20%, while the dependence is reversed for higher solid fractions.

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(PHD, 2015)

Abstract: This thesis presents experimental measurements of the rheological behavior of liquid-solid mixtures at moderate Reynolds (defined by the shear rate and particle diameter) and Stokes numbers, ranging from 3 ≤ Re ≤ 1.6 × 10^{3} and 0.4 ≤ St ≤ 195. The experiments use a specifically designed Couette cylindrical rheometer that allows for probing the transition from transporting a pure liquid to transporting a dense suspension of particles. Measurements of the shear stress are presented for a wide range of particle concentration (10 to 60% in volume) and for particle to fluid density ratio between 1 and 1.05. The effective relative viscosity exhibits a strong dependence on the solid fraction for all density ratios tested. For density ratio of 1 the effective viscosity increases with Stokes number (St) for volume fractions (φ) lower than 40% and becomes constant for higher φ. When the particles are denser than the liquid, the effective viscosity shows a stronger dependance on St. An analysis of the particle resuspension for the case with a density ratio of 1.05 is presented and used to predict the local volume fraction where the shear stress measurements take place. When the local volume fraction is considered, the effective viscosity for settling and no settling particles is consistent, indicating that the effective viscosity is independent of differences in density between the solid and liquid phase. Shear stress measurements of pure fluids (no particles) were performed using the same rheometer, and a deviation from laminar behavior is observed for gap Reynolds numbers above 4× 10^{3}, indicating the presence of hydrodynamic instabilities associated with the rotation of the outer cylinder. The increase on the effective viscosity with Stokes numbers observed for mixtures with φ ≤ 30% appears to be affected by such hydrodynamic instabilities. The effective viscosity for the current experiments is considerably higher than the one reported in non-inertial suspensions.

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(PHD, 2010)

Abstract: When two solid bodies collide in a liquid environment, the collision process is influenced by viscous effects and the increased pressure in the interstitial liquid layer between the two solid boundaries. A normal collision process is investigated for a range of impact Stokes numbers using both experimental and numerical methods. Experiments of a steel sphere falling under gravity and colliding with a Zerodur wall with Stokes number ranging from 5 to 100 are performed, which complement previous investigations of immersed particle-wall collision processes. The incompressible Navier-Stokes equations are solved numerically to predict the coupled motion of the falling particle and the surrounding fluid as the particle impacts and rebounds from the planar wall. The numerical method is validated by comparing the numerical simulations of a settling sphere with experimental measurements of the sphere trajectory and the accompanying flow-field. A contact model of the liquid-solid and solid-solid interaction is developed that incorporates the elasticity of the solids to permit the rebound trajectory to be simulated accurately. The contact model is applied when the particle is sufficiently close to the wall that it becomes difficult to resolve the thin lubrication layer. The model is calibrated with measured particle trajectories and is found to represent well the observed coefficient of restitution over a range of impact Stokes numbers from 1 to 1000. In addition, the model is modified to simulate the normal collision of two spheres. The effective coefficient of restitution obtained from the simulation shows a strong dependence on the binary Stokes number accordant with other researcher’s experimental results. The unique behaviors of the two spheres at low binary Stokes number including target motion prior to contact and group motion after collision are simulated by the current work.

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(PHD, 2010)

Abstract:

“Booming” sand dunes are able to produce low-frequency sound that resembles a pure note from a music instrument. The sound has a dominant audible frequency (70-105 Hz) and several higher harmonics and may be heard from far distances away. A natural or induced avalanche from a slip face of the booming dune triggers the emission that may last for several minutes. There are various references in travel literature to the phenomenon, but to date no scientific explanation covered all field observations.

This thesis introduces a new physical model that describes the phenomenon of booming dunes. The waveguide model explains the selection of the booming frequency and the amplification of the sound in terms of constructive interference in a confined geometry. The frequency of the booming is a direct function of the dimensions and velocities in the waveguide. The higher harmonics are related to the higher modes of propagation in the waveguide.

The experimental validation includes quantitative field research at the booming dunes of the Mojave Desert and Death Valley National Park. Microphone and geophone recordings of the acoustic and seismic emission show a variation of booming frequency in space and time. The analysis of the sensor data quantifies wave propagation characteristics such as speed, dispersion, and nonlinear effects and allows the distinction between the source mechanism of the booming and the booming itself.

The migration of sand dunes results from a complicated interplay between dune building, wind regime, and precipitation. The morphological and morphodynamical characteristics of two field locations are analyzed with various geophysical techniques. Ground-penetrating radar images the subsurface structure of the dunes and reveal a natural, internal layering that is directly related to the history of dune migration. The seismic velocity increases abruptly with depth and gradually increases with downhill position due to compaction. Sand sampling shows local cementation of sand grains within the discrete layers that explains the increase in velocity and decrease in porosity. The subsurface layering may influence the speed of dune migration and therefore have important consequences on desertification.

The positive qualitative and quantitative correlation between the subsurface layering in the dune and the manifestation of the booming sound implies a close relation between environmental factors and the booming emission. In this thesis, the frequency of booming is correlated with the depth of the waveguide and the seismic velocities. The variability on location and season suggests that the waveguide theory successfully unravels the phenomenon of booming sand dunes.

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(PHD, 2009)

Abstract:

This thesis presents experimental measurements of the shear stresses of a fluid-particulate flow at high Reynolds numbers as a function of the volume fraction of solids. From the shear stress measurements an effective viscosity, where the fluid-particulate flow is treated as a single fluid, is determined. This viscosity varies from the fluid viscosity when no solids are present to several orders of magnitude greater than fluid viscosity when the particles near their maximum packing state. It is the primary goal of this thesis to determine how the effective viscosity varies with the volume fraction of solids.

A variety of particle sizes, shapes, and densities were obtained through the use of polystyrene, nylon, polyester, styrene acrylonitrile, and glass particles, used in configurations where the fluid density was matched and where the particles were non-neutrally buoyant. The particle sizes and shapes ranged from 3 mm round glass beads to 6.4 mm nylon to polystyrene elliptical cylinders. To properly characterize the effect of volume fraction on the effective viscosity, the random loose- and random close-packed volume fractions were experimentally determined using a counter-top container that mimicked the in situ (concentric cylinder Couette flow rheometer) conditions. These volume fractions depend on the shape of the particles and their size relative to the container.

The effective viscosity for neutrally buoyant particles increases exponentially with volume fraction at fractions less than the random loose-packing. Between the random loose- and random close-packed states, the effective viscosity increases more rapidly with volume fraction and asymptotes to very large values at the close-packed volume fraction. The effective viscosity does not depend on the size or shape of particles beyond the influence these parameters have on the random packing volume fractions.

For non-neutrally buoyant particles, the difference in particle buoyancy requires an additional correction. The volume fraction at the time of the force measurement was recorded for several different ratios of particle-to-fluid density. This volume fraction increases with the shear rate of the Couette flow and decreases with the Archimedes number in a way that when plotted against the Reynolds number over the Archimedes number, these curves collapse onto one master curve. When the local volume fraction is used, the effective viscosity for non-neutrally buoyant particles shows the same dependence on volume fraction as the neutrally buoyant cases.

Particle velocities were also measured for both neutrally buoyant and non-neutrally buoyant particles. These particle velocities near the stationary inner wall show evidence for a small region near the walls with few particles. This particle depletion layer was measured directly using the velocity data and indirectly using the difference between the measured effective viscosities for the smooth- and rough-wall configurations. The slip in the smooth wall experiments can significantly affect the measured viscosity, but this deficiency can be corrected using the thickness of the depletion layer to find the actual value for the effective viscosity.

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(PHD, 2008)

Abstract:

Multiphase flows are fairly complex and they are usually studied as a bulk. In this thesis, these flows are approached by looking at single particle interactions (particle-particle and particle-wall). This work presents experimental measurements of the approach and rebound of a particle colliding with a ``deformable’ surface in a viscous liquid. The complex interaction between the fluid and the solid phases is coupled through the dynamics of the flow as well as the deformation process. A simple pendulum experiment was used to produced single controlled collisions; steel particles were used to impact different aluminum alloy samples (Al-6061, Al-2024, and Al-7075) using different aqueous mixtures of glycerol and water as a viscous fluid. The velocity of the particle before and after the collision was estimated by post-processing the particle position recorded with a high speed camera. For the combination of materials proposed, the elastic limit is reached at relatively low velocities. The deformations produced by the collision were analyzed using an optical profilometer. The measurements showed that the size of the indentations is independent of the fluid media. It was found that the size of the indentations was the same for collisions in air than for the rest of the collisions using various viscous fluids. The results show that the plastic deformation is only a function of the impact velocity and the material properties. The normal coefficient of restitution and deformation parameters account for losses due to lubrication effect and inelasticity, identifying then, the dominant energy loss mechanism during the collision process.

According to the strain imposed in the samples due to the collision, the deformations were either elastic or elastic-plastic. The equivalent load due to the impact velocities used in this work did not reach the fully-plastic regime. For the collisions in air, different models were used to compare the experimental results showing that the elastic-plastic regime is not well characterized by only the material properties and the impact velocity. The time-resolved contact force was measured during the process of the indentation for the dry collision experiments using a quartz load transducer.

The experiments clearly show four different regimes depending on the impact Stokes number: lubrication effect and elastic deformation, lubrication effect and elastic-plastic deformation, elastic deformation with no hydrodynamic effects, and elastic-plastic deformation with negligible lubrication effect. An analysis of the erosion of ductile materials during immersed collisions is presented. The size of the crater formed by the impact of a single particle against a ductile target can be estimated from theory, and these estimates agree well with experimental measurements.

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(PHD, 2006)

Abstract:

This thesis addresses the problem of inter-particle collisions in a viscous liquid. Experimental measurements were made on normal and oblique collisions between identical and dissimilar pairs of solid spheres. The experimental evidence supports the hypothesis that the normal and the tangential component of motions are decoupled during a rapid collision.

The relative particle motion in the normal direction is crucial to an immersed collision process and can be characterized by an effective coefficient of restitution and a binary Stokes number. The effective coefficient of restitution monotonically decreases with a diminishing binary Stokes number, indicating a particle motion with less inertia and higher hindering fluid forces. The correlation between the two parameters exhibits a similar trend to what is observed in a sphere-wall collision, which motivates a theoretical modeling.

The collision model developed in the current work includes a flow model and a revised rebound scheme. The flow model considers the steady viscous drag, the added mass force, and the history force. How the presence of a second nearby solid boundary affects these forces is investigated. A flow model is proposed with wall-correction terms and is used to predict an immersed pendulum motion toward a solid wall. General agreement with the available experimental data validates the model. The rebound scheme considers the magnitude of the surface roughness and the minimum distance of approach resuling from an elastohydrodynamic contact.

The performance of the collision model in predicting the effective coefficient of restitution is evaluated through comparisons with experimental measurements and an existing elastohydrodynamic collision model that the current work is based on.

Based on the current experimental findings, the tangential component of motion can be described by a dry collision model, provided that the material parameters are properly modified for the interstitial liquid. Two pertinent parameters are the normal effective coefficient of restitution and an effective friction coefficient.

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(PHD, 2005)

Abstract:

Wave propagation is a fundamental property of all physical systems. The wave speed is directly related to the compressibility of the system and determines the rate at which local disturbances are propagated into the bulk of the material. The wave propagation characteristics of conventional forms of matter are well understood and well documented. In contrast, waves in granular materials are more complex due to the heterogeneous nature of these systems. The key element of the mechanics of a granular system is the force chain. It is along these preferentially stressed chains of particles that waves are transmitted. These nonlinear chains are heavily dependent on the geometry of the bed and are prone to rearrangement even by the slightest of forces.

Results from both experiments and simulations on wave propagation in granular materials are presented in the current study. The experiments measure the pressures at two points within the granular bed that result from the motion of a piston at one end of the bed. The simulations are a two-dimensional version of the experiments and use a discrete, soft-particle method to detect the wave at both the output of the simulated bed and at any point within it. In addition to examining wave propagation in a granular bed at rest, simulations and experiments are also performed for a granular bed undergoing agitation perpendicular to the direction of the wave input. Imposed agitation increases the granular temperature of the bed and allows for the exploration of the effect of granular state changes on the wave propagation characteristics. Such information may provide a means to diagnose the state of a flowing granular material.

Measurements of the wave speed and attenuation in the bed reveal the unique properties of waves in granular systems that result from the nonlinearity of the bed and the heterogeneity of the force chains. Sinusoidal waves demonstrate the nondispersive nature of a granular bed and show the transient effects of force chain rearrangement. Pulsed waves display a semi-permanent shape qualitatively similar to predictions from nonlinear wave theory. In an agitated granular bed, measurements of the wave characteristics were found to be possible even in the presence of significant agitation. The prevailing confining pressure, which changes throughout the agitation cycle, was determined to be the system parameter that correlates best with changes to the wave speed.

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(PHD, 2003)

Abstract:

This thesis presents experimental measurements of the approach and rebound of a particle colliding with a wall in a viscous fluid. Steel, glass, nylon, and Delrin particles were used, with diameters ranging from 3 to 12 mm. The experiments were performed using a thick Zerodur or Lucite wall with various mixtures of glycerol and water. Normal and tangential coefficients of restitution were defined from the ratios of the respective velocity components at the point of contact just prior to and after impact. These coefficients account for losses due to lubrication effects and inelasticity.

The experiments clearly show that the rebound velocity depends strongly on the impact Stokes number and weakly on the elastic properties of the materials. Below a Stokes number of approximately 10, no rebound of the particle occurs. Above a Stokes number of approximately 500, the normal coefficient of restitution asymptotically approaches the value for a dry collision. The data collapse onto a single curve of restitution coefficient as a function of Stokes number when normalized by the dry coefficient of restitution.

Oblique collisions in a fluid are qualitatively similar to oblique collisions in a dry system, with a lowered friction coefficient dependent on surface roughness. For smooth surfaces the friction coefficient is drastically reduced due to lubrication effects. Values for the friction coefficient are predicted based on elastohydrodynamic lubrication theory. The particle surface roughness was found to affect the repeatability of some measurements, especially for low impact velocities.

A significant retardation of a particle approaching a target at a low Stokes number was observed and quantified. The distance at which the particle’s trajectory varies due to the presence of the wall is dependent on the impact Stokes number. The observed slowdown can be predicted from hydrodynamic theory to a good approximation.

An analysis of the erosion of ductile materials during immersed collisions is presented. The size of the crater formed by the impact of a single particle against a ductile target can be estimated from theory, and these estimates agree well with experimental measurements.

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(PHD, 2000)

Abstract:

This thesis examines the behavior of a granular material sheared in a gap between two moving boundaries. In fluid mechanics, this type of flow is known as a Couette flow. Two different kinds of granular Couette flows were studied. First, gravity-free flow between two infinite plates moving in opposite directions was investigated using computer simulations. Second, flow between a stationary outer cylinder and an inner rotating cylinder was studied using both experiments and computer simulations.

Two-dimensional discrete element computer simulations of infinite planar Couette flows were used to study the rheology, energy dissipation, and other flow properties in flows of particles of uniform size for three different gap widths. The energy dissipation rate was measured and a thermal analysis was conducted to determine the thermodynamic temperature rise and heat flux of such flows. Given a constant wall velocity, all of the properties in flows of identical particles were found to depend on the value of the solid fraction at the walls, which in turn depended on both the average solid fraction and the gap width. When the average solid fraction reached a critical threshold, the amount of work done on the flow drastically increased, increasing the average strain rate, granular temperature, wall stresses, and energy dissipation in the flow. This solid fraction threshold occurred after the center region of the flow had reached a dense limit and any further increase in solid fraction necessarily occurred in the wall regions. Various results from computer simulations were found to compare reasonably well with past results derived using kinetic theory.

Mixing and other flow properties were also investigated in planar Couette flows of two different particle sizes, as functions of the size ratio and solid fraction ratio of the two species. Larger particles were found to migrate away from the regions of high fluctuation energy near the two moving boundaries in all cases. Mixture flows were found to behave very similarly to flows of mono-sized particles at high ratios of the solid fraction of small to large particles. As the solid fraction ratio decreased and the number of large particles increased, results deviated from the corresponding flow of identical particles. Flows with large size ratios of large to small particles deviated the most from the result of mono-sized particles, because stresses and energy dissipation rates are both mass-dependent.

The second type of Couette flow, between two concentric cylinders, was investigated in a horizontal orientation (with the axis of rotation perpendicular to the direction of gravity) and in a vertical orientation (with the axis parallel to the direction of gravity), using both experiments and computer simulations. In the horizontal geometry, high-speed imaging was used to calculate experimental mean and fluctuation velocity profiles that were compared to results from three-dimensional discrete element simulations. Segregation of binary particle mixtures was also investigated in this geometry. Segregation in this flow was driven by a percolation mechanism acting at the free surface, causing large particles to migrate to the top. Computer simulations compared well qualitatively with experiments, successfully predicting the velocity profiles and the segregation pattern at the surface. When compared quantitatively, however, fluctuation velocities in the simulations were considerably greater than those found in the experiment, and the radial segregation observed in experiments did not occur to the same extent in simulations.

The vertically-oriented cylindrical Couette flow experiment was used to measure the shear stress on the outer cylinder wall as a function of different variables. The shear stress was found to be independent of the inner cylinder rotation rate, because the material was unconfined and allowed to dilate. The measured stress showed a linear dependence on the height of material in the apparatus, indicating a hydrostatic variation of the normal stress. The shear stress also varied significantly with the ratio of the gap width to the particle diameter.

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(PHD, 1999)

Abstract:

This experimental study is motivated by the widespread loss of life and property due to accidental fires in high rise buildings, and investigates the progress of hot, toxic, products during such fires. The Stack Effect and Turbulent Mixing, two of the primary factors responsible for smoke movement within tall buildings are the focus of this study. The results of this investigation could be used for the development of fire modeling codes that simulate high-rise building fires.

The experiments involve a 2.6 m tall square shaft with various cross sections and openings. The shaft was situated above a large temperature controlled hot air reservoir, and the two chambers were initially separated by a partition. At the start of the experiment the partition was removed in a rapid horizontal motion and the hot and cold gases were allowed to mix. For the shafts with openings, the gases were withdrawn from the apertures at different rates with the Reynolds number varying between 600 and 7200. The temperature of the gas and wall, and the heat transfer to the wall were measured as functions of time at various locations in the shaft. Additionally, hot wire anemometry techniques were used to obtain velocity data in the channel. Some experiments involved monitoring a tracer gas in the vertical channel. Simple one-dimensional analytical modeling was performed to validate the experimental results.

The experiments indicated an initial transient period followed by a “pseudo steady state.” At each elevation measured the cross-section averaged gas temperature, reached and fluctuated about a steady state value soon after the initial front of hot gas arrived at that location. For the closed channel experiments, the front arrival time was a function of the initial density ratio, the shaft width, and the gravitational constant.

The tracer gas trials suggested that the molecular diffusion was insignificant in comparison to the turbulent mixing. For the closed channels the observed velocity fluctuations were the same order of magnitude as the mean velocities. The time averaged heat transfer coefficient was weakly dependent on the initial reservoir temperature.

The vented shaft experiments indicated that the front propagation times are significantly affected by openings in the shaft and that the effect is more pronounced the higher the vents are located. The venting caused a significant rise in the steady state temperatures, and a reduction in both the temperature and velocity fluctuations. The local Nusselt number was independent of the Reynolds number and a function only of the Rayleigh number, indicating that the heat transfer was dominated by free convection effects.

The predictions made by the one dimensional analytical model agreed reasonably well with the experiments, particularly in the case of the closed channel.
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(PHD, 1998)

Abstract:

Experimental measurements of the particle pressure were obtained for a liquid fluidized bed and for a vertical gravity driven liquid-solid flow. The particle, or granular, pressure is defined as the extra pressure generated by the action of particles in a particulate multi-phase flow. Using a high-frequency-response pressure transducer, individual collisions of particles were collected and measured to obtain a time-averaged particle pressure. Results were obtained for a number of different particles and for two different test section diameters. Results show that the particle pressure experiences a maximum at intermediate concentrations, and that its magnitude is scaled with the particle density and the square of the terminal velocity of the particles. The particle pressure was found to be composed of two main contributions: one from pressure pulses generated by direct collisions of particles against the containing walls (direct component), and a second one from pressure pulses due to collisions between individual particles that are transmitted through the liquid (radiated component). The direct component of the particle pressure was studied by an analysis of particle collisions submerged in a liquid. A simple pendulum experiment provides controlled impacts in which measurements are made of the particle trajectories for different particles immersed in water. The velocity of the approaching particle is measured using a high speed digital camera; the magnitude of the collision is quantified using a high frequency response pressure transducer at the colliding surface. The measurements show that most of the particle deceleration occurs at less than half a particle diameter away from the wall. The measured collision pressure appears to increase with the impact velocity. Comparisons are drawn between the measured pressures and the predictions by Hertzian theory. A simple control-volume model is proposed to account for the effects of fluid inertia and viscosity. The pressure profile is estimated, and then integrated over the surface of the particle to obtain a force. The model predicts a critical Reynolds number at which the particle reaches the wall with zero velocity. Comparisons between the proposed model and the experimental measurements show qualitative agreement. Experiments involving binary collisions of particles were performed to investigate the radiated component of the particle pressure. This component results from the pressure front generated by the impulsive motion of a fluid resulting from a collision of particles in a liquid. When the two particles come into contact, the impulsive acceleration due to the elastic rebound produces a pressure pulse, which is transmitted through the fluid. A simple dual pendulum experiment was set up to generate controlled collisions. Measurements were obtained for a range of impact velocities, angles of incidence, and distances away from the wall for different pairs of particles. The magnitude of the impulse pressure appears to scale with the particle impact velocity and the density of the fluid. Based on the impulse pressure theory, a prediction for pressure generated due to the collision can be obtained. The model appears to agree well with the experimental measurements. The fluctuating component of the solid fraction was studied, as one of the sources of the particle pressure. The instantaneous cross-sectional averaged solid fraction was measured using an impedance meter. The root-mean square fluctuation of the solid fraction signal was measured in a liquid fluidized bed and a vertical gravity-driven flow, for different particle sizes and densities. Two types of fluctuations were identified: low-frequency large-scale fluctuations which dominate at high concentrations, and high-frequency small-scale fluctuations which are dominant at intermediate solid fractions. The effect of each type was isolated by filtering. When the large-scale fluctuations were present, the magnitude of the rms fluctuation was found to scale with particle diameter, but when eliminated the mean fluctuation appeared to scale with the particle mass instead.

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(PHD, 1997)

Abstract:

NOTE: Text or symbols not renderable in plain ASCII are indicated by […]. Abstract is included in .pdf document. In many experiments, especially those investigating aspects of fluid flow, it is common to observe time series data exhibiting chaos. Chaos lies in the realm of nonlinear dynamics, and specialized methods are available for the analysis of nonlinear time series. One particular method, called time delay analysis, is particularly useful for extracting information from time series representing measurements at a single point in space. In this thesis, hot-wire anemometry is used to obtain velocity time series from experiments on isothermal Taylor-Couette flow. For R/R[subscript c]=1.6, a simple limit cycle is observed, yielding an attractor of dimension of 1. For R/R[subscript c]=11.1, the attractor dimension increases, and the reconstructed attractor exhibits features characteristic of a transition to turbulence. In addition, various other states and transitions of the Taylor-Couette system are studied as well. Direct numerical simulations (DNS) have also been performed to study the effects of the gravitational and the centrifugal potentials on the stability of heated, incompressible Taylor-Couette flow. The flow is confined between two differentially heated, concentric cylinders and the inner cylinder is allowed to rotate. The Navier-Stokes equations and the coupled energy equation are solved using a spectral method. To validate the code, comparisons are made with existing linear stability analysis and with experiments. The code is used to calculate the local and average heat transfer coefficients for a fixed Reynolds number (R=100) and a range of Grashof numbers. The variation of the local coefficients of heat transfer on the cylinder surface is investigated, and maps showing different stable states of the flow are presented. Calculations of the time and space averaged equivalent conductivity show that the heat transfer decreases with Grashof number in axisymmetric Taylor vortex flow regime and increases with Grashof number after the flow becomes non-axisymmetric. The numerical simulations also demonstrate the existence of a hysteresis loop in heated Taylor-Couette flow, obtained by slowly varying the Grashof number. Two different stable states with same heat transfer are found to exist at the same Grashof number. The validity of Colburn’s correlation is investigated as well; the Prandtl number dependence is found to be slightly different from Pr[…] for the range of Reynolds number investigated. Finally, a time delay analysis of the radial velocity and the local heat transfer coefficient time series obtained from the numerical simulation of the radially heated Taylor-Couette flow is performed. The two-dimensional projection of the reconstructed attractor shows a limit cycle for Gr[…]-1700. The limit cycle behavior disappears at Gr[…]-2100, and the reconstructed attractor becomes irregular. The attractor dimension increases to about 3.2 from a value of 1 for the limit cycle case.

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(PHD, 1997)

Abstract:

The term “granular material flow” is applied in the literature to particulate flows such as the flow of coal down an inclined chute, the discharge of grains from a hopper or the motion of debris in a landslide. In these flows, the material has an overall bulk motion; however, individual particles may collide, roll or slide against each other, and may interact with the bounding surfaces. Hence, the individual particle motions are composed of a mean velocity component and a fluctuating, or random, velocity component. An analogy is drawn between this random motion and the random motion of molecules. As a result, much of the theoretical analysis of these flows has developed from concepts derived from dense-gas kinetic theory. Although this random velocity component is a key property in analytical studies, there have been few attempts to measure its magnitude in experimental studies. In the current work, measurements were made of two components of the average and fluctuating velocities in the flow of granular material in a vertical chute for flows with different particle and boundary properties. The fluctuation velocities were highly anisotropic, with the streamwise components being 2 to 2.5 times the magnitude of the transverse components. Increasing the surface roughness of the particles reduced the fluctuation velocities significantly.

Another area of considerable industrial interest is particle mixing in monodisperse and polydisperse particle flows. Because of the random component of particle motion, the particles can exhibit a diffusive motion similar to that found in gases and liquids. In the second part of this work, local self diffusion coefficients were measured in the granular flow using image processing techniques to track individual particles. The influence of flow shear rates and fluctuation velocities on the self diffusion coefficients was investigated. The self-diffusion coeffecients were found to increase with the shear rate and the fluctuation velocity, with the coefficients in the streamwise direction being an order-of-magnitude higher than those for the transverse direction. The surface roughness of the particles led to a decrease in the self-diffusion coefficients.

The effect of shearing on the convective heat transfer from a heater immersed in a granular flow was investigated experimentally. Comparisons were made with previous experiments and with results obtained for unsheared plug flows. The results indicated that the medium density close to the wall played a critical role in determining the overall heat transfer.

Finally, theoretical solutions, based on a combination of the dense-gas kinetic theory and an empirical friction model, were generated to study and compare experimental and theoretical results for velocity profiles and heat transfer characteristics in vertical, fully developed granular flows. The results indicated good agreement between theoretical and experimentally measured mean velocity proflies but the fluctuation velocity magnitudes were usually underpredicted by the theoretical solutions. There was qualitative agreement between experimental and theoretical results for convective heat transfer.

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(PHD, 1997)

Abstract:

Previous experimental and analytical results have shown that discharge-to-suction leakage flows in the annulus of a shrouded centrifugal pump contribute substantially to the fluid induced rotordynamic forces (Adkins, 1988). Experiments conducted in the Rotor Force Test Facility (RFTF) at Caltech on an impeller undergoing a prescribed circular whirl have indicated that the leakage flow contribution to the normal and tangential forces can be as much as 70% and 30% of the total, respectively (Jery, 1986). Recent experiments at Caltech have examined the rotordynamic consequences of leakage flows and have shown that the rotordynamic forces are functions not only of the whirl ratio but also of the leakage flow rate and the impeller shroud to pump housing clearance. The forces were found to be inversely proportional to the clearance and a region of forward subsynchronous whirl was found for which the average tangential force was destabilizing. This region decreased with flow coefficient (Guinzburg, 1992).

The present research is a continuation of the previous experimental work and has been motivated by the rotordynamic stability problems with the recently developed Alternate Turbopump Design (ATD) of the Space Shuttle High Pressure Oxygen Turbopump. The present study investigates the influence of swirl brakes, installed in the annular leakage path, as a means of reducing the undesirable rotordynamic forces over a range of flow rates. Also, the present study evaluates the effect on the rotordynamic forces of tip leakage restrictions at discharge used by the ATD for establishing axial thrust balance. As a first step to understanding the flow field in the leakage annulus, the region is probed with a laser velocimeter to provide basic information on these unsteady turbulent three-dimensional leakage flows and to serve as a standard of comparison for approximate theoretical models as well as applications of computational fluid dynamics.

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(PHD, 1997)

Abstract:

NOTE: Text or symbols not renderable in plain ASCII are indicated by […]. Abstract is included in .pdf document.

This thesis examines the fundamental behavior of a granular material subject to external vibrations. Experiments were designed to investigate the phenomena that appear in a container filled with glass spheres subject to vertical, sinusoidal oscillations. In addition, a discrete element computer simulation code was written to supplement the experimental program.

Experiments and simulations reveal that the behavior of the particle bed can be classified into two regimes known as shallow and deep beds. For example, when a shallow bed consisting of less than six layers of glass spheres is subjected to oscillations with acceleration amplitudes greater than approximately 2.Og where g is the acceleration due to gravity, the particles in the container are fluidized and do not display coordinated movement. However, when more than six particle layers are used, the particles move coherently and the deep bed behaves as a single, completely inelastic mass.

In the shallow bed regime three distinct sub-states are observed that differ in the degree of coherency in the particle motions. Each appears depending upon the number of particle layers in the bed and on the acceleration amplitude of the oscillations. The transitions between the states are gradual and not well-defined.

The transition from the deep bed to the shallow bed state is characterized by a sudden expansion of the bed that occurs at a critical acceleration amplitude for a fixed bed depth and particle type. Simulations indicate that when the particle fluctuating kinetic energy is dissipated completely each oscillation cycle, the bed remains in the deep bed state. If the energy is not completely dissipated, a shallow bed state results. A simple model consisting of an inelastic ball bouncing on a sinusoidally oscillating table reproduces the sudden expansion.

In the deep bed regime, phenomena such as side wall convection, surface waves, kinks, and kink convection cells appear depending primarily on the acceleration amplitude of the oscillations and, to a lesser degree, the number of particle layers in the bed. Phase maps of when these behaviors occur were constructed using both experimental and simulation data.

When the acceleration amplitude is greater than approximately lg, side wall convection cells appear at the vertical wall boundaries of the container. Particles move down along the vertical walls of the container and up within the bulk of the bed. Simulations indicate that the convection cells are the result of the frictional contact between particles and the walls and the asymmetry of the particle/wall collision rate over an oscillation cycle. Using the simulations, the width of the boundary layer next to the walls, the height of the convection cell center from the container base, and the particle flux in the boundary layer were measured as functions of the vibration parameters and particle properties. The results from the simulation compare well with experimental measurements. The simulation indicates that the boundary layer width is proportional to the container width when the bed aspect ratio, defined as the bed depth to the bed width, is greater than approximately 0.2. For beds with aspect ratios less than 0.2, however, the boundary layer width remains constant. Simulation results also demonstrate that the convection cell height is proportional to the bed depth and that the flux of particles in the boundary layer increases with increasing particle/wall friction and decreases for coefficients of restitution near one.

At acceleration amplitudes between approximately 2.Og and 3.5g, standing waves appear on the top free surface of the bed. These waves form at half the forcing oscillation frequency and are referred to as […]/2 waves. A second set of standing waves appears when the acceleration amplitude is greater than approximately 5.Og and persist up to at least 7.0g. These waves form at one-quarter the forcing frequency and are known as […]/4 waves. Experimental measurements indicate that the wave amplitude expressed as a Froude number increases with increasing acceleration amplitude for the […]/2 waves but remains constant for the […]/4 waves. Additionally, measurements of the wavelength suggest that the waves have a dispersion relation similar to that for deep fluid gravity waves where the wavelength is proportional to the square of the inverse frequency.

Kinks and kink convection cells appear in the particle bed after a period doubling bifurcation occurs in the flight dynamics of the bed. The formation of kinks can be explained using a simple model consisting of a completely inelastic ball on a sinusoidally oscillating table. Experimental measurements indicate a minimum allowable distance between nodes that is a function of the bed depth and acceleration amplitude. The convection cells bracketing each kink are shown to be the result of the out-of-phase motion of the bed sections and the interaction between fluidized and solidified regions of the bed.

The effect of vertical, sinusoidal vibrations on a discharging wedge-shaped hopper was also investigated. When the hopper exit is closed, side wall convection cells appear with particles moving up at the inclined container boundaries and down at the centerline of the bed. The same mechanism that causes downward convection at vertical walls can also explain the upward motion at inclined walls. Experimental measurements also indicate that the discharge rate from the vibrating hopper scales with the oscillation velocity amplitude. At low velocity amplitudes, the discharge rate from the hopper is slightly greater than the non-vibrating hopper discharge rate. At high velocity amplitudes, however, the discharge rate decreases significantly. A simple model accounting for the change in the effective gravity acting on the particle bed throughout the oscillation cycle and the impact velocity of the bed with the hopper predicts the observed trend.

The experiments and simulations conducted in the present work suggest that the boundary conditions and the fluid- and solid-like nature of granular materials are significant factors affecting the response of a granular bed. Additionally, this work demonstrates the value of discrete element computer simulations as a tool for complementing experimental observations.
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(PHD, 1994)

Abstract:

The current work is an investigation of supersonic film cooling effectiveness including interactions with a two-dimensional shock wave. Air and helium, which are either heated or cooled, are injected at Mach numbers between 1.2 and 2.2 into a Mach 2.4 air freestream. The adiabatic wall temperature is measured directly. The injection velocity and mass flux are varied by changing the total temperature and Mach number while maintaining matched pressure conditions.

Heated injection, with the injectant to freestream velocity ratios greater than 1, exhibit a rise in wall temperature downstream of the slot yielding effectiveness values greater than one. The temperature rise, which also occurs for cooled injection, is attributed to the merging of the injectant boundary layer and the lip-wake. As a result comparisons between heated and cooled injection may not be valid. With the exception of heated helium runs, larger injection Mach numbers slightly increase the effective cooling length per mass injection rate. The results for helium injection indicate an increase in effectiveness as compared to that for air injection. The experimental results are compared with studies in the literature.

Flow profiles at several axial locations, up to 90 slot heights, indicate that for the same Mach number the helium injections induce a larger wake and a thicker boundary layer than air injection.

The influence of the shock impingement on the recovery temperature is not large if the flow remains attached. Once separation occurs the temperature changes drastically with downstream distance. The shock strength for incipient separation is smaller when helium is injected than when no film coolant is present. However, the converse is true with air injection even though, for the same Mach number, the momentum flux for the air injection is less than that for the helium injection. The induced separation in the case of helium is attributed to the reduced fullness of its momentum flux profile prior to interaction. This research demonstrates how the performance of supersonic film cooling for thermal control is undermined by the susceptibility to shock induced separation, and raises concerns about hydrogen film cooling for N.A.S.P.

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(PHD, 1994)

Abstract:

This experimental study investigates the effect of an isothermal or heated superimposed axial flow on a Taylor-Couette flow in an open, vertical annulus with the inner cylinder rotating. The tangential component of the velocity is measured using a hot-wire anemometer, and the velocity power spectra are calculated. The flows studied are for Taylor numbers ranging from 1.2 x 10[superscript 7] to 2.4 x 10 [superscript 7], and the axial Reynolds number from 0 to 2500. At a low axial Reynolds number, the power spectrum of the velocity measurements shows a single dominant frequency. The frequency is indicative of the uniformly-spaced vortices passing through the anemometer, and roughly corresponds with the axial velocity divided by the vortex spacing. As the rotational speed is increased at a fixed axial flow rate, the dominant frequency decreases, indicating a change in the size of the vortices. As the axial Reynolds number is increased at a fixed rotational speed, the power spectra first indicate a decrease in the dominant frequency, and then a subsequent increase in the other frequencies. For very large axial flow rates, the power spectra indicate a broad distribution in frequencies.

The experiment also include the measurements of the transient and the local fluid temperatures, and the corresponding temperature spectra are calculated. Heating of the axial flow also changes the characteristic of the velocity spectra, where peaks at higher frequencies emerge in the spectra. In heated flows, the peaks of the greatest spectral strength in the velocity and temperature spectra are different, possibly indicating that the largest temperature and velocity fluctuations occur in different directions. The average temperature measurements indicate that as the axial flow rate is increased, the mean temperature distribution curves shift upward. The temperature ratio, (T[subscript max] - T[subscript min])/(T[subscript in] - T[subscript out]), also increases with an increasing in the axial Reynolds numbers.

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(PHD, 1993)

Abstract:

A granular flow is a two-component flow with an assembly of discrete solid particles dispersed in a fluid. Because of the similarity between the random motion of particles in a granular flow and the motion of molecules in a gas, the dense-gas kinetic theory has been broadly employed to analyze granular flows. However, most research only discusses aspects of momentum transport; three issues have received less attention: the diffusion process, the heat transfer problem, and the behavior of binary mixtures. The current research emphasizes these aspects.

A granular flow diffusion experiment was conducted in a vertical channel to investigate the effects that result in mixing of the material. The mean velocities, the longitudinal fluctuating velocities, and the mixing-layer thickness were measured. A simple analysis based on the diffusion equation shows that the thickness of the mixing layer increases with the square-root of downstream distance and depends on the magnitude of the velocity fluctuations relative to the mean velocity. The experimental velocity profiles were also compared with profiles calculated from theoretical analysis based on kinetic theory.

The analytical relations were developed for the flow-induced particle diffusivity and the thermal conductivity based on dense-gas kinetic theory. The two coefficients were found to increase with the square-root of the granular temperature, a term that quantifies the specific kinetic energy of the flow. The theoretical particle diffusivity was used to compare with the current experimental measurements involving the granular flow mixing layer. The analytical expression for the effective thermal conductivity was also compared with experimental measurements. The differences between the predictions and the measurements suggest limitations in some of the underlying kinetic-theory assumptions.

The constitutive relations were presented for a binary-mixture of granular materials as derived from the revised Enskog theory. The current research focuses on the process of granular thermal diffusion - a diffusion process resulting from the granular temperature gradient. A granular flow of binary-mixtures in an oscillatory no-flow system, in a sheared system, and in a vertical channel were examined, and indicated a complete segregation when granular thermal diffusion effect was sufficiently large.
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(Engineer, 1993)

Abstract:

This experimental research investigates transverse particle segregation in a binary mixture of spherical particles in air. in a gravity driven. vertical channel flow. Glass beads with similar properties, except for size and color, are randomly mixed in an upper hopper at the entrance of a vertical channel. When roughened channel walls are employed. particles show segregation by size, with a preferred position of larger particles at the centerline and approximately 80% of the distance between the centerline and the side walls. The concentration of the particles is found based on grey-scale color distribution as recorded by an image processing system. The effects of variations in flow rate. wall surface conditions, mixture ratios and channel width on segregation are studied as a function of downstream distance.

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