Stirring tanks are very important equipments used for mixing, separating, chemical reaction, etc. A typical stirring tank is a cylindrical vessel with an agitator driving the fluid and generating turbulence to promote mixing. Flotation cells are widely used stirring tanks in phase separation where multiphase flow is involved. Flotation refers to the process in which air bubbles selectively pick up hydrophobic particles and separate them from hydrophilic solids. This technology is used throughout the mining industry as well as the chemical and petroleum industries. In this research, efforts were made to investigate the multi-phase flow hydrodynamic problems of some flotation cells at different geometrical scales. Pitot-static and five-hope probes were employed to lab- pilot- and commercial-scale tanks for velocity measurements. It was found that the tanks with different scales have similar flow patterns over a range of Reynolds numbers. Based on the velocity measurement results, flotation tanks' performance was evaluated by checking the active volume in the bulk. A fast-response five-hole probe was designed and fabricated to study the turbulence characteristics in flotation cells under single- and multi-phase flow conditions. The jet stream in the rotor-stator domain has much higher turbulence intensity compared with other locations. The turbulent dissipation rate (TDR) in the rotor-stator domain is around 20 times higher than that near tank's wall. The TDR could be used to calculate the bubble and particle slip velocities. An isokinetic sampling probe system was developed to obtain true samples inthe multi-phase flow and then measure the local void fraction. It was found that the air bubbles are carried out by the stream and dispersed to the whole bulk. However, some of the bubbles accumulate in the inactive regions, where higher void fractions were detected. The isokinetic sampling probe was then extended to be an isokinetic borescope system, which was used to detect the bubble-particle aggregates in the tank. Aggregates were found in the high-turbulence level zones. The isokinetic sampling probe and the isokinetic borescope provide new methods for flotation tank tests. An experiment was also set up to study the dynamics of bubble particle impact. Four different modes were found for the collision. The criterion is that if the fluid drainage time is less than the residence time, the attachment will occur, otherwise, the particle will bounce back. / Ph. D.

This study deals with fibre suspension flows through cylindrical pipes. Thepresent work aims at measurements of opaque flows, which are common inindustries. Nuclear magnetic resonance imaging (NMRI) and ultrasound velocimetryprofiling (UVP) were employed as non-invasive and optic-independenttools to measure the velocity profiles. As a first experiment, a paper-pulp suspensionflow through a sudden contraction and expansion was investigated.The results show the NMRI technique can be used to measure the stronglyunsteady flow such as separated regions though the MR signal is attenuateddue to the turbulence in the flow. The flow loop had however an insufficientinlet length which caused asymmetric profiles at the test section. As a secondexperiment, a flow loop which provided fully developed flows at the test sectionwas designed. After that, the velocity profiles of rayon-fibre and micro-spheresuspension flows were measured by the NMRI and the UVP independently.In principle, these two techniques measure the different velocities of the fibresuspensionflows, i.e. the velocity of the water and the fibre. In dilute suspensionflows, where the velocities of the two phases were assumed to be thesame, the velocity profiles were in good agreement. This shows the validityof the two measurement techniques. However, it should be pointed out thatthere is a limitation of the current UVP method for highly concentrated flows.The velocity profiles obtained by the UVP at high concentrations seems notto represent physics while the NMRI is not affected by the concentrations. Itis argued that the advances of the NMRI for the measurement of the highlyconcentrated flows.

The entrainment process in two-phase buoyant jets differs significantly from their singlephase counterparts, and is not well understood. Entrainment models developed for singlephase flow are often used in two-phase jetting simulations, albeit with limited success. In this work, Particle Image Velocimetry (PIV) and shadowgraph flow visualization experiments have been conducted on submerged round gas jets of varying speeds and nozzle diameters with the goal of improving our understanding of the entrainment process in a two-phase (gas-liquid) jet. The total entrainment estimated using the PIV measurements is higher than the respective values suggested by a common empirical model developed for singlephase buoyant jets. A two-phase theoretical entrainment model used for comparison shows an overestimation of entrainment, but predicts the increase in the rate of entrainment with axial distance from the jet nozzle seen in the PIV results. This thesis also presents advances in PIV processing methodology that were developed concurrently with the entrainment research. The novel Spectral Phase Correlation (SPC) allows for particle displacement to be determined directly from phase information in the Fourier domain. Some of the potential benefits of the SPC explored here include (1) avoidance of errors introduced by spatial peak-finding routines; (2) use of a modal analysis that can be used to provide information such as correlation quality; and (3) introduction of a means of incorporating information from multiple image windows. At low image noise levels, the method performs as well as an advanced CC-based method. However, difficulties unwrapping the aliased phase information cause the SPC's performance to degrade at high noise levels. / Master of Science

This dissertation investigates the flow physics, turbulence structure, and particle classification process in hydrocyclones using large-eddy simulations of turbulent multiphase flow. Two types of hydrocyclones are considered. The first is a classifying hydrocyclone, and the second is a mineral flotation hydrocyclone, also known as an air-sparged hydrocyclone (ASH). Large-eddy simulations (LES) are conducted for multi-phase flow (air, water, and sand particles) so that the complex anisotropic turbulence of a swirling flow is computed correctly. The effects of mesh refinements on the mean flow and turbulence stresses are investigated, and (LES) results are validated by comparisons with experimental data for classifying hydrocyclone. The two-phase flow in air-sparged hydrocyclone has not been analyzed before. ANSYS CFX software V17.2 has been used to conduct the simulations. Firstly, large-eddy simulations have been conducted for two-phase flow (water and air) in a conventional hydrocyclone using the Eulerian two-fluid (Eulerian-Eulerian) and Volume-of- Fluid (VOF) models. Subgrid stresses are modeled using a dynamic eddy–viscosity model, and results are compared to those using the Smagorinsky model. The effects of grid resolutions on the mean flow and turbulence statistics have been thoroughly investigated. Five block-structured grids of 0.72, 1.47, 2.4, 3.81, and 7.38 million elements have been used for the simulations of a typical conventional hydrocyclone designed and tested by Hsieh (75 mm hydrocyclone) [1]. Mean velocity profiles and normal Reynolds stresses have been compared with experimental data. The results of the Eulerian two-fluid model agree with those of the VOF model. A fine mesh in the axial and radial directions is necessary for capturing the turbulent vortical structures. Turbulence structures in the hydrocyclone are dominated by helical vortices around the air core. Energy spectra are analyzed at different points in the hydrocyclone, and regions of low turbulent kinetic energy are identified and attributed to stabilizing effects of the swirling velocity component. Turbulent energy spectra in the different regions of the hydrocyclone have been analyzed. The energy spectra are calculated at two points near the air-water interface. They show a short inertial subrange where energy decays as f−5/3, followed by viscous damping where energy drops as f−7, where f is frequency. However, for the points located near the boundary where high turbulent kinetic energy is found, the energy spectra exhibit f^(−4) decay. Secondly, the two-fluid (Eulerian two-fluid) model and large-eddy simulation are used to compute the turbulent two-phase flow of air and water in a cyclonic flotation device known as an Air-Sparged Hydrocyclone (ASH). In the operation of ASH, the air is injected through a porous cylindrical wall. The study considers a 48-mm diameter hydrocyclone and uses a block-structured fine mesh of 10.5 million hexahedral elements. The air-to-water injection ratio is 4, and a uniform air bubble diameter of 0.5 mm has been specified. The flow field in ASH has been investigated for the inlet flow rate of water of 30.6 L/min at different values of underflow exit pressure. The present simulations show that the value of static pressure imposed at the underflow section strongly affects the distribution of air volume fraction, water axial velocity, tangential velocity, and swirling layer thickness in ASH. The loci of zero-axial velocity surfaces have been determined for different exit pressures. The water split ratio through the overflow opening varies with underflow exit pressure as 6%, 8%, 16%, and 26% for 3, 4, 5, and 6 kPa, respectively. These results indicate that regulating the pressure at the underflow exit can be used to optimize ASH's performance. Turbulent energy spectra in different regions of the hydrocyclone have been analyzed. Small-scale turbulence spectra at near-wall points exhibit f^(−4) law, where f is frequency. Whereas for points at the air-column interface, the energy spectra show an inertial subrange f^(−5/3) followed by a dissipative range of f^(−7) law. Thirdly, large-eddy simulation (LES) has been used to investigate the flow separation in multi-phase flow (gas, liquid, and solid) in a classifying hydrocyclone using the multi-fluid (Eulerian multi-fluid) model. The results of the CFD simulation are compared with the Hsieh [1] experimental data. The water phase is considered a continuous phase, while air and solid particles are considered dispersed phases. Drag between water-air and water-sand is the only considered interfacial force. The Schiller-Naumann and Wen-Yu models are used to model the drag, and the Gidaspow model is used to calculate the solid pressure term. Various particle sizes are tested in the hydrocyclone to investigate the underflow recovery percentages. The results agree with the experimental data for the particles of a diameter smaller than 20 μm, while the results vary based on the model for the large particles. Therefore, using the Wen Yu and Schiller-Naumann model for the drag model and the Gidaspow model for the solid pressure in the three-fluid model could give acceptable results for the small particles underflow recovery and volume fraction distribution. However, the models failed for large particles. Finally, the large particle size separation needs more investigation. / Doctor of Philosophy / Hydrocyclones are widely used in mining and chemical industries. They can be used as separation devices to separate solid or fluid particles based on their size or/and weight. They can also be used as flotation devices to capture certain mineral particles from a slurry of water and solid particles. The flow field within a hydrocyclone is complex as it involves flow of different phases of matter (liquid, gas, and solid). It is also a turbulent flow in which the velocity and pressure fluctuate in time with many frequencies. The efficiency of the hydrocyclone depends on its geometry and distribution of the velocity. Computer simulations are very efficient tools to predict and study the flow field in hydrocyclones. This dissertation used a computer simulations to explain how turbulence could affect the particle separation from the slurry inside the hydrocyclones. The water's velocity fields, swirling flow, air behavior, pressure distribution and turbulence statistics are analysed. Understanding the turbulence structure and statistics in hydrocyclones is important for particle tracking and dispersion. Also, turbulent structure affects the motion of the air bubbles and solid particles in the flow field, which eventually will affect the hydrocyclone's performance. In short, a more comprehensive understanding of the behavior of turbulence of hydrocyclones represents an important tool that can guide the design of hydrocyclones according to their use goals and will help engineers who model these processes to develop a better model.

This thesis focuses on two problems lying within the field of soft condensed matter: the viscous fingering or Saffman-Taylor instability and nematic liquid crystals in confinement. Whenever a low viscosity fluid displaces a high viscosity fluid in a porous medium, for example water pushing oil out of oil reservoirs, the interface between the two fluids is rendered unstable. Viscous fingers develop, grow and compete until a single finger spans all the way from inlet to outlet. Here, using a free energy lattice Boltzmann algorithm, we examine the Saffman-Taylor instability for two different wetting situations: (a) when neither of the two fluids wet the walls of the channel and (b) when the displacing fluids completely wets the walls. We demonstrate that curvature effects in the third dimension, which arise because of the wetting boundary conditions, can lead to a novel suppression of the instability. Recent experiments in microchannels using colloid-polymer mixtures support our findings. In the second part of the thesis we examine nematic liquid crystals confined in wedge-structured geometries. In these systems the final stable configuration of the liquid crystal system is controlled by the complex interplay between confinement, elasticity and surface anchoring. Varying the wedge opening angle this competition leads to a splay to bend transition mediated by a defect in the bulk of the wedge. Using a hybrid lattice Boltzmann algorithm we study the splay-bend transition and compare to recent experiments on {em fd} virus particles in microchannels. Our numerical results, in quantitative agreement with the experiments, enable us to predict the position of the defect as a function of opening angle, and elucidate its role in the change of director structure. This has relevance to novel energy saving, liquid crystal devices which rely on defect motion and pinning to create bistable director configurations.

Master of Science / Department of Mechanical and Nuclear Engineering / Steven Eckels / Both cavitating and flashing flows are important phenomena in fluid flow. Cavitating flow, a common consideration in valves, orifices, and metering devices, is also a concern in loss of coolant accidents for liquid water in power plants when saturation pressures are below atmospheric pressure. Flashing flow is a common consideration for devices such as relief and expansion valves and fluid injectors as well as for loss of coolant accidents in which the coolant’s saturation pressure is above atmospheric. Of the two phenomena, flashing flow has received greater interest due to its applicability to safety concerns, though cavitating flow is perhaps of greater interest in terms of energy efficiency. It is possible for cavitating and flashing flow to actually become sonic. That is, the local velocity of a fluid can exceed the local speed of sound due to the unique properties of two-phase mixtures. When a flow becomes sonic, it is possible for the flow to accelerate and impose additional energy losses that would not otherwise occur. Models of this aspect of two-phase flow are not well developed, typically only being presented for the case of constant area ducts. In this paper two models for cavitating sonic flow are developed and described by applying the integral forms of the mass, momentum, and energy equations to a control volume of variable cross-sectional area. These models, based on the homogeneous equilibrium model (HEM) and separated flow model, are then applied to experimental data taken by the author with R-134a as the fluid of interest. Experimental data were taken with four instrumented converging-diverging nozzles of various geometries using a custom testing rig that allowed for precise control and measurement of flow parameters such as mass flow, temperature, and pressure. The resultant data from the models are then examined, focusing on the resultant velocities, Mach numbers, quality, and shear stresses.

A mild gasification method has been developed to provide an innovative clean coal technology. The objective of this study is to developed a numerical model to investigate the thermal-flow and gasification process inside a specially designed fluidized-bed mild gasifier using the commercial CFD solver ANSYS/FLUENT. Eulerain-Eulerian method is employed to calculate both the primary phase (air) and secondary phase (coal particles). The Navier-Stokes equations and seven species transport equations are solved with three heterogeneous (gas-solid), two homogeneous (gas-gas) global gasification reactions. Development of the model starts from simulating single-phase turbulent flow and heat transfer to understand the thermal-flow behavior followed by five global gasification reactions, progressively with adding one equation at a time. Finally, the particles are introduced with heterogeneous reactions. The simulation model has been successfully developed. The results are reasonable but require future experimental data for verification.

Non-Aqueous Phase Liquids (NAPLs) include commonly occurring organic contaminants such as gasoline, diesel fuel and chlorinated solvents. When released to subsurface environments their spreading is a complex process of multi-component, multi-phase flow. This work has strived to develop new models and methods to describe the spreading of NAPLs in heterogeneous geological media. For two-phase systems, infiltration and immobilisation of NAPL in stochastically heterogeneous, water-saturated media were investigated. First, a methodology to continuously measure NAPL saturations in space and time in a two-dimensional experiment setup, using multiple-energy x-ray-attenuation techniques, was developed. Second, a set of experiments on NAPL infiltration in carefully designed structures of well-known stochastic heterogeneity were conducted. Three detailed data-sets were generated and the importance of heterogeneity for both flow and the immobilised NAPL architecture was demonstrated. Third, the laboratory experiments were modelled with a continuum- and Darcy’s-law-based multi-phase flow model. Different models for the capillary pressure (Pc) – fluid saturation (S) – relative permeability (kr) constitutive relations were compared and tested against experimental observations. A method to account for NAPL immobility in dead-end pore-spaces during drainage was introduced and the importance of accounting for hysteresis and NAPL entrapment in the constitutive relations was demonstrated. NAPL migration in three-phase, water-NAPL-air systems was also studied. Different constitutive relations used in modelling of three-phase flow were analysed and compared to existing laboratory data. To improve model performance, a new formulation for the saturation dependence of tortuosity was introduced and different scaling options for the Pc-S relations were investigated. Finally, a method to model the spreading of multi-constituent contaminants using a single-component multi-phase model was developed. With the method, the migration behaviour of individual constituents in a mixture, e.g. benzene in gasoline, could be studied, which was demonstrated in a modelling study of a gasoline spill in connection with a transport accident. / Flerfasföroreningar innefattar vanligt förekommande organiska vätskor som bensin, dieselolja och klorerade lösningsmedel. Spridningen av dessa föroreningar i mark är komplicerad och styrs av det samtidiga flödet av organisk vätska, vatten och markluft samt utbytet av komponenter (föroreningar) mellan de olika faserna. Detta arbete syftade till att utveckla nya metoder och modeller för att studera spridningen av flerfasföroreningar i mark: (i) En metodik utvecklades för att i laboratorium noggrant och kontinuerligt mäta hur en organisk vätska är rumsligt fördelad i en tvådimensionell experimentuppställning. Metoden baserades på röntgenutsläckning för olika energinivåer. (ii) Infiltration av organisk vätska i vattenmättade medier studerades för olika konfigurationer av geologisk heterogenitet. I experimentuppställningen packades olika sandmaterial noggrant för att konstruera en välkänd, stokastiskt heterogen struktur. Spridningsprocessen dokumenterades i tre detaljerade mätserier och heterogenitetens påverkan på flöde och kvarhållning av den organiska vätskan påvisades. (iii) Experimenten simulerades med en numerisk modell. Olika modeller prövades för att beskriva de grundläggande relationerna mellan kapillärtryck (Pc) vätskehalt (S) och relativ permeabilitet (kr) för detta tvåfassystem av vatten och organisk vätska. En relation infördes för att beskriva partiell orörlighet hos den organiska vätskan i porer vars halsar tillfälligt blockeras av vatten då mediet avvattnas. Vikten av att i de grundläggande relationerna ta hänsyn till hysteresis och kvarhållning av organisk fas visades. (iv) Olika Pc-S-kr relationer för trefassystem av vatten, organisk vätska och markluft testades mot befintliga experimentella data. En ny relation för hur slingrigheten (eng. tortuosity) beror av vätskehalten infördes i kr-S relationen och olika möjligheter för att skala Pc-S relationen analyserades. (v) En modelleringsmetodik utvecklades för att studera spridningen av flerkomponentsföroreningar. Med metoden kunde spridningsbeteendet hos enskilda, särskilt skadliga komponenter som t.ex. bensen särskiljas då ett bensinutsläpp i samband med en transportolycka simulerades.

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A computational fluid dynamics model has been developed to examine the separation of an oil film from a spherical oil-coated particle falling through quiescent water due to gravity. Using this model, the separation process was studied as a function of the viscosity ratio of oil to water, R, and the ratio of viscous forces to surface tension, represented by the Capillary number Ca. The governing equations of this flow-induced motion are derived in a non-inertial spherical coordinate system, and discretized using a finite volume approach. The Volume-of-Fluid method is used to capture the oil/water interface. The model predicts two mechanisms for oil separation: at R less than 1, the shear difference between the particle/oil interface and the oil/water interface is not significant and Ca determines whether separation occurs or not; at R larger than 1, the shear difference is considerable, and the Ca effect becomes less dominant.