Granular media continue to be among the most manipulated materials found in various industries. Particle interactions in granular flow has fundamental importance in analyzing the performance of a wide range of key engineering applications such as hoppers, tumblers, and mixers etc. In spite of such ubiquitous presence, till date, our understanding of the granular flow is very limited. This restricts our ability to design efficient and optimal granular processing equipment. Additionally, the existing design abilities are also constrained by the number of particles to be analyzed, where, a typical industrial application involves millions of particles. This motivated the current research where investigations on the above limitations are pursued from three different angles: experimental, theoretical, and simulation. More specifically, this work aims to study particle-wall interaction and developing a computationally efficient cellular automata simulation framework for industrial granular applications. Towards this end, the current research is divided into two part: (I) energy dissipation during particle-wall interaction (II) cellular automata modeling. In part I, detailed experiments are performed on various sphere-thin plate combinations to measure the coefficient of restitution (COR) which is a measure of energy dissipation and it is one of the most important input parameters in any granular simulation. Alternatively, the energy dissipation measure also used to evaluate the elastic impact performance of superelastic Nitinol 60 material. Explicit finite element simulations are performed to gain detail understanding of the contact process and underlying parameters such as contact forces, stress-strain fields, and energy dissipation modes. A parametric study reveals a critical value of plate thickness above which the effect of plate thickness on the energy dissipation can be eliminated in the equipment design. It is found that the existing analytical expressions has limited applicability in predicting the above experimental and numerical results. Therefore, a new theoretical model for the coefficient of restitution is proposed which combines the effect of plastic deformation and plate thickness (i.e. flexural vibrations). In part II, in order to advance the existing granular flow modeling capabilities for the industry (dry and slurry flows) a cellular automata (CA) modeling framework is developed which can supplement the physically rigorous but computationally demanding discrete element method (DEM). These include a three-dimensional model which takes into account particle friction and spin during collision processing, which provides the ability to handle flows beyond solely the kinetic regime, and a multiphase framework which combines computational fluid dynamics (CFD) with CA to model multi-million particle count applications such as particle-laden flows and slurry flows.

No description available.

This dissertation presents a series of studies related to the study and control of slurry flow, process temperature, and aggressive diamonds in Chemical Mechanical Planarization (CMP). The purpose of these studies is to better understand the fundamentals of CMP and to explore solutions to some of CMP’s greatest challenges. Within-wafer removal rate non-uniformity (WIWRRNU) is a critical parameter to determine film thickness planarity on a wafer-scale level and it grossly impacts yield. Resolving this issue continues to be an area of intense focus in the industry. The first study in this dissertation shows the feasibility of adopting a new method to improve WIWRRNU during copper CMP that is solely based on intentional local temperature manipulation of the pad. A pad surface thermal management system is developed to locally change pad surface temperature. This system consists of one or more thermal transfer modules contacting the pad surface. In this study, the system is employed to adjust the "center-fast" copper removal rate profile to illustrate its effect during the process. Results shows that, when two thermal transfer modules are employed, local removal rates in the wafer center region decrease significantly while maintaining the removal rates near the wafer edge thereby significantly improving WIWRRNU. Another contribution of this dissertation is the investigation of the effect of pad groove design on slurry injection scheme during interlayer dielectric CMP. A novel slurry injector with multiple slurry outlets is designed, which provides optional slurry injection schemes (i.e. one injection point scheme and multi-injection point scheme). These schemes are compared with the standard slurry application method on a concentrically grooved pad and an xy-groove pad, respectively. On the concentrically grooved pad, the one injection point scheme generates significantly higher oxide removal rates (ranging from 22 to 35 percent) compared to the standard slurry application method at different slurry flow rates. On the xy-groove pad, the one injection point scheme still results in higher removal rates (ranging from 3 to 9 percent), however, its removal rate enhancement is not as high as that of the concentrically grooved pad. In order to further improve slurry availability on the xy-groove pad, the multi-injection point scheme is tested. Results show that the multi-injection point scheme results in significantly higher removal rates (ranging from 17 to 20 percent) compared to the standard slurry application method. This work underscores the importance of optimum slurry injection schemes for accommodating particular groove designs. The last contribution of this dissertation involves a study regarding aggressive diamond characterization and wear analysis during CMP. A 3M A3700 diamond disk is used to condition a Cabot Microelectronics Corporation (CMC) D100 pad for 30 hours. The top 20 aggressive diamonds for two perpendicular disk orientations are identified before the polishing, as well as after 15- and 30-hour polishing. The furrow surface area generated by these top 20 aggressive diamonds and their evolution are analyzed and compared. Results show that the original top 20 aggressive diamonds identified before polishing are subjected to wear after the first 15-hour polishing as the furrow surface area that they generate decreases dramatically (by 47%). As these original aggressive diamonds are worn, seven new aggressive diamonds are "born" and join the new top 20 list for both disk orientations. After the second 15-hour wafer polishing, the furrow surface area of these new top 20 aggressive diamonds do not change significantly. The furrow surface area created by all the active diamonds exhibits the same trend as the top 20 aggressive diamonds, confirming that most pad conditioning work is performed by these aggressive diamonds and that the disk loses its aggressiveness in the first 15 hours of polishing and then maintains its aggressiveness during the second 15 hours, albeit to a lesser extent.

Heat transfer and flow characteristics of phase change material slurry flow in microchannels with constant heat flux at the base were investigated. The phase change process was included in the energy equation using the effective specific heat method. A parametric study was conducted numerically by varying the base fluid type, particle concentration, particle size, channel dimensions, inlet temperature, base heat flux and melting range of PCM. The particle distribution inside the microchannels was simulated using the diffusive flux model and its effect on the overall thermal performance of microchannels was investigated. Experimental investigation was conducted in microchannels of 101 [micro]m width and 533 [micro]m height with water as base fluid and n-Octadecane as PCM to validate the key conclusions of the numerical model. Since the flow is not fully developed in case of microchannels (specifically manifold microchannels, which are the key focus of the present study), thermal performance is not as obtained in conventional channels where the length of the channel is large (compared to length of microchannels). It was found that the thermal conductivity of the base fluid plays an important role in determining the thermal performance of slurry. The effect of particle distribution can be neglected in the numerical model under some cases. The performance of slurry depends on the heat flux, purity of PCM, inlet temperature of the fluid, and base fluid thermal conductivity. Hence, there is an application dependent optimum condition of these parameters that is required to obtain the maximum thermal performance of PCM slurry flows in microchannels.

O transporte de minério em tubos é feito em larga escala não somente em longas distâncias, (através de minerodutos); como também dentro da mina, seja no trajeto entre a mina e a usina, como no caso de minerais lavrados por desmonte hidráulico, ou entre as operações unitárias dentro da usina de beneficiamento. O projeto dos sistemas de bombeamento de polpas requer o conhecimento das variáveis de escoamento, a perda de carga (ΔP) e a velocidade de deposição (Vd). Discutem-se aqui alguns modelos de predição para tais variáveis. Apesar da irrefutável importância deste tipo de transporte, ainda não há consenso sobre a validade dos modelos existentes. Este trabalho teve como objetivo a análise comparativa dos modelos de velocidade de deposição propostos por Durand e Condolios (1952), Wasp et al. (1977) e Wilson et al. (2006), e os modelos de perda de carga propostos por Durand e Condolios (1952), Wasp et al. (1977) e Newitt et al. (1955) com os resultados de laboratório. A acurácia dos modelos, apesar das limitações de cada um, é crucial para que as variáveis de projeto do sistema de bombeamento sejam estabelecidas por meio do uso desses modelos. A comparação foi baseada em ensaios realizados em três test loops de diâmetros de 2\", 3\" e 4\" com minério de ferro, carbonatito e areia, em concentrações de sólidos de 15%, 30% e 50%. Trabalhando com minérios de diferentes granulometrias, densidades e polpas com concentrações diferentes pudemos analisar a interferência desses parâmetros no escoamento e no uso dos modelos propostos. Os modelos de Vd se mostraram bastante úteis, sendo que o modelo proposto por Durand e Condolios (1952) teve as melhores correlações para todos os materiais estudados. Já os modelos de perda de carga não mostraram correlações aceitáveis com os resultados de laboratório, endossando as indicações de alguns autores, como Chaves (2012) e Abulnaga (2002) que não recomendam o uso de modelos de predição de perda de carga nos cálculos de dimensionamento destes sistemas. Como alternativa, é possível utilizar plantas piloto e ensaios laboratoriais. / Ore transportation in pipes is carried out on a large scale not only at long distances, such as ore pipelines, but also within the mine, or in the path between the mine and the plant, as the case of minerals drawn by hydraulic dismantling, or between operations within the beneficiation plant. The design of the slurry pumping systems requires the knowledge of the flow variables, as the head loss (ΔP) and the deposition velocity (Vd). Some prediction models for such variables are discussed in this dissertation. Despite the irrefutable importance of this type of transportation, there is still no agreement on the validity of the existing models. Their limitations make unfeasible to use them, and much more is necessary to improve in this field. This work aimed to make a comparative analysis of the deposition velocity models proposed by Durand and Condolios (1952), Wasp et al. (1977) and Wilson et al. (2006), and the head loss models proposed by Durand and Condolios (1952), Wasp et al. (1977) and Newitt et al. (1955) with laboratory results. The accuracy of the models, despite the limitations of each one, is crucial if pumping system design variables are established using these models. The comparison was based on laboratory tests performed on three diameter test loops, 2 \", 3\" and 4 \" with iron ore, carbonatite and sand a concentrations of 15%, 30% and 50% in weight solids concentrations. Working with different ore grain sizes and densities ores and pulps with different concentrations we can analyze the interference of these parameters in the flow and in the models use. The Vd models were very useful, and the Durand and Condolios (1952) model showed the best correlations for all ores studied. However, the head loss models did not show acceptable correlations with the laboratory results, endorsing the indications of some authors, such as Chaves (2012) and Abulnaga (2002), who do not recommend the use of prediction models for head loss in these systems sizing. Alternatively, it is possible to use pilot plants and laboratory tests.

In this dissertation, an experimental and numerical study of dense coarse solids-liquid flows has been performed. The experimental work mainly involved pressure drop measurements in a vertical flow loop. A limited number of measurements of solids velocity profiles were also obtained in the upward flow section of the flow loop. The numerical work involved simulations of coarse particles-in-water flows in vertical and horizontal pipes. The vertical flow simulations were performed using the commercial CFD software, ANSYS CFX-4.4, while ANSYS CFX-10 was used to simulate the flows in the horizontal pipes. The simulations were performed to investigate the applicability of current physically-based models to very dense coarse-particle flows.<p> In the experimental study, measurements of pressure drop and local solids velocity profiles were obtained. The experiments were conducted in a 53 mm diameter vertical flow loop using glass beads of 0.5 mm and 2.0 mm diameter solids for concentration up to 45%. The liquid phase was water. The measured pressure drop exhibited the expected dependence on bulk velocity and solids mean concentration. The wall shear stress was determined by subtracting the gravitational contribution from the measured pressure drop. For flow with the 0.5 mm particles at high bulk velocities, the values of the wall shear stress were essentially similar for each concentration in the upward flow sections but more variation, indicating the effect of concentration, was noted in the downward flow section. At lower bulk velocities, the wall shear stresses with the 0.5 mm glass beads-water flow showed a dependence on concentration in both test sections. This was attributed to an increase in the slip velocity. For the large particle (2.0 mm glass beads), similar observations were made but the effect of concentration was much less in the upward test section. In the downward test section, the wall shear stress for the flow of the 2.0 mm glass beads increased by almost a constant value for the bulk velocities investigated. The solids velocity profiles showed that the solids velocity gradient is large close to the wall. In addition, the solids velocity profiles indicated that the slip velocity increased at lower velocities due to increase in the bulk concentration in the upward flow section.<p> For the vertical flow simulations, different physical models based on the kinetic theory of granular flows were programmed and implemented in ANSYS CFX-4.4. These models, referred to as the kf-ef-ks-es, kf-ef-ks-es-Ts and kf-ef-ks-kfs models, were investigated by focusing on the closure laws for the solids-phase stress. The treatment of the granular temperature Ts depends on whether small- or large-scale fluctuating motion of the particles is considered. The models were implemented via user-Fortran routines. The predicted results were compared with available experimental results. The predicted solids-phase velocity profiles matched the measured data quite well close to the pipe wall but over-predicted it in the core region. The solids concentration, on the other hand, was significantly under-predicted for concentrations higher than 10%. Variations in the predictions of the phasic turbulent kinetic energy and the eddy viscosity were noted; the effect of solids concentration on them was mixed. A general conclusion drawn from the work is that a more accurate model is required for accurate and consistent prediction of coarse particle flows at high concentrations (less than 10%). In a related study, attention was given to wall boundary conditions again focusing on the effect of the solids-phase models at the wall. Comparison between numerical predictions, using some of the existing wall boundary condition models for the solids phase in particulate flows, with experimental results indicated that the physical understanding of the influence of the fluid and solids-phase on each other and their effect on frictional head loss is far from complete. The models investigated failed to reproduce the experimental results. At high solids concentration, it was apparent from the present study that the no-slip and free-slip wall boundary conditions are not appropriate for liquid-solid flows.<p> For the horizontal flow case, three-dimensional simulations were performed with a focus on the velocity and concentration distributions. Medium and coarse sand-in-water flows in three pipe diameters were considered to investigate the default solids stress models in ANSYS CFX-10. Simulations were performed for three cases by considering: 1) no additional solids-phase stress, i.e. no model for Ts; 2) a zero equation, and 3) an algebraic equilibrium model for the granular temperature. The model predictions were compared to experimental results. The effect of particle size, solids-phase concentration, and pipe diameter was explored using the algebraic equilibrium model. All the cases for the models considered exhibited the characteristic features of horizontal coarse particle slurry flows. The zero equation and the algebraic equilibrium model for the granular temperature produced similar results that were not significantly different from the prediction obtained when no solids-phase stress was considered. The comparison with experimental results was mixed. Locally, the measured solids-phase velocity distributions were over-predicted, whereas the solids concentration was reasonably reproduced in the core of all the pipes. The concentration at the bottom and top walls were over-, and under-predicted, respectively. This was attributed to the inappropriate phasic wall boundary condition models available.

In this dissertation, an experimental and numerical study of dense coarse solids-liquid flows has been performed. The experimental work mainly involved pressure drop measurements in a vertical flow loop. A limited number of measurements of solids velocity profiles were also obtained in the upward flow section of the flow loop. The numerical work involved simulations of coarse particles-in-water flows in vertical and horizontal pipes. The vertical flow simulations were performed using the commercial CFD software, ANSYS CFX-4.4, while ANSYS CFX-10 was used to simulate the flows in the horizontal pipes. The simulations were performed to investigate the applicability of current physically-based models to very dense coarse-particle flows.<p> In the experimental study, measurements of pressure drop and local solids velocity profiles were obtained. The experiments were conducted in a 53 mm diameter vertical flow loop using glass beads of 0.5 mm and 2.0 mm diameter solids for concentration up to 45%. The liquid phase was water. The measured pressure drop exhibited the expected dependence on bulk velocity and solids mean concentration. The wall shear stress was determined by subtracting the gravitational contribution from the measured pressure drop. For flow with the 0.5 mm particles at high bulk velocities, the values of the wall shear stress were essentially similar for each concentration in the upward flow sections but more variation, indicating the effect of concentration, was noted in the downward flow section. At lower bulk velocities, the wall shear stresses with the 0.5 mm glass beads-water flow showed a dependence on concentration in both test sections. This was attributed to an increase in the slip velocity. For the large particle (2.0 mm glass beads), similar observations were made but the effect of concentration was much less in the upward test section. In the downward test section, the wall shear stress for the flow of the 2.0 mm glass beads increased by almost a constant value for the bulk velocities investigated. The solids velocity profiles showed that the solids velocity gradient is large close to the wall. In addition, the solids velocity profiles indicated that the slip velocity increased at lower velocities due to increase in the bulk concentration in the upward flow section.<p> For the vertical flow simulations, different physical models based on the kinetic theory of granular flows were programmed and implemented in ANSYS CFX-4.4. These models, referred to as the kf-ef-ks-es, kf-ef-ks-es-Ts and kf-ef-ks-kfs models, were investigated by focusing on the closure laws for the solids-phase stress. The treatment of the granular temperature Ts depends on whether small- or large-scale fluctuating motion of the particles is considered. The models were implemented via user-Fortran routines. The predicted results were compared with available experimental results. The predicted solids-phase velocity profiles matched the measured data quite well close to the pipe wall but over-predicted it in the core region. The solids concentration, on the other hand, was significantly under-predicted for concentrations higher than 10%. Variations in the predictions of the phasic turbulent kinetic energy and the eddy viscosity were noted; the effect of solids concentration on them was mixed. A general conclusion drawn from the work is that a more accurate model is required for accurate and consistent prediction of coarse particle flows at high concentrations (less than 10%). In a related study, attention was given to wall boundary conditions again focusing on the effect of the solids-phase models at the wall. Comparison between numerical predictions, using some of the existing wall boundary condition models for the solids phase in particulate flows, with experimental results indicated that the physical understanding of the influence of the fluid and solids-phase on each other and their effect on frictional head loss is far from complete. The models investigated failed to reproduce the experimental results. At high solids concentration, it was apparent from the present study that the no-slip and free-slip wall boundary conditions are not appropriate for liquid-solid flows.<p> For the horizontal flow case, three-dimensional simulations were performed with a focus on the velocity and concentration distributions. Medium and coarse sand-in-water flows in three pipe diameters were considered to investigate the default solids stress models in ANSYS CFX-10. Simulations were performed for three cases by considering: 1) no additional solids-phase stress, i.e. no model for Ts; 2) a zero equation, and 3) an algebraic equilibrium model for the granular temperature. The model predictions were compared to experimental results. The effect of particle size, solids-phase concentration, and pipe diameter was explored using the algebraic equilibrium model. All the cases for the models considered exhibited the characteristic features of horizontal coarse particle slurry flows. The zero equation and the algebraic equilibrium model for the granular temperature produced similar results that were not significantly different from the prediction obtained when no solids-phase stress was considered. The comparison with experimental results was mixed. Locally, the measured solids-phase velocity distributions were over-predicted, whereas the solids concentration was reasonably reproduced in the core of all the pipes. The concentration at the bottom and top walls were over-, and under-predicted, respectively. This was attributed to the inappropriate phasic wall boundary condition models available.

O transporte de minério em tubos é feito em larga escala não somente em longas distâncias, (através de minerodutos); como também dentro da mina, seja no trajeto entre a mina e a usina, como no caso de minerais lavrados por desmonte hidráulico, ou entre as operações unitárias dentro da usina de beneficiamento. O projeto dos sistemas de bombeamento de polpas requer o conhecimento das variáveis de escoamento, a perda de carga (&#916;P) e a velocidade de deposição (Vd). Discutem-se aqui alguns modelos de predição para tais variáveis. Apesar da irrefutável importância deste tipo de transporte, ainda não há consenso sobre a validade dos modelos existentes. Este trabalho teve como objetivo a análise comparativa dos modelos de velocidade de deposição propostos por Durand e Condolios (1952), Wasp et al. (1977) e Wilson et al. (2006), e os modelos de perda de carga propostos por Durand e Condolios (1952), Wasp et al. (1977) e Newitt et al. (1955) com os resultados de laboratório. A acurácia dos modelos, apesar das limitações de cada um, é crucial para que as variáveis de projeto do sistema de bombeamento sejam estabelecidas por meio do uso desses modelos. A comparação foi baseada em ensaios realizados em três test loops de diâmetros de 2\", 3\" e 4\" com minério de ferro, carbonatito e areia, em concentrações de sólidos de 15%, 30% e 50%. Trabalhando com minérios de diferentes granulometrias, densidades e polpas com concentrações diferentes pudemos analisar a interferência desses parâmetros no escoamento e no uso dos modelos propostos. Os modelos de Vd se mostraram bastante úteis, sendo que o modelo proposto por Durand e Condolios (1952) teve as melhores correlações para todos os materiais estudados. Já os modelos de perda de carga não mostraram correlações aceitáveis com os resultados de laboratório, endossando as indicações de alguns autores, como Chaves (2012) e Abulnaga (2002) que não recomendam o uso de modelos de predição de perda de carga nos cálculos de dimensionamento destes sistemas. Como alternativa, é possível utilizar plantas piloto e ensaios laboratoriais. / Ore transportation in pipes is carried out on a large scale not only at long distances, such as ore pipelines, but also within the mine, or in the path between the mine and the plant, as the case of minerals drawn by hydraulic dismantling, or between operations within the beneficiation plant. The design of the slurry pumping systems requires the knowledge of the flow variables, as the head loss (&#916;P) and the deposition velocity (Vd). Some prediction models for such variables are discussed in this dissertation. Despite the irrefutable importance of this type of transportation, there is still no agreement on the validity of the existing models. Their limitations make unfeasible to use them, and much more is necessary to improve in this field. This work aimed to make a comparative analysis of the deposition velocity models proposed by Durand and Condolios (1952), Wasp et al. (1977) and Wilson et al. (2006), and the head loss models proposed by Durand and Condolios (1952), Wasp et al. (1977) and Newitt et al. (1955) with laboratory results. The accuracy of the models, despite the limitations of each one, is crucial if pumping system design variables are established using these models. The comparison was based on laboratory tests performed on three diameter test loops, 2 \", 3\" and 4 \" with iron ore, carbonatite and sand a concentrations of 15%, 30% and 50% in weight solids concentrations. Working with different ore grain sizes and densities ores and pulps with different concentrations we can analyze the interference of these parameters in the flow and in the models use. The Vd models were very useful, and the Durand and Condolios (1952) model showed the best correlations for all ores studied. However, the head loss models did not show acceptable correlations with the laboratory results, endorsing the indications of some authors, such as Chaves (2012) and Abulnaga (2002), who do not recommend the use of prediction models for head loss in these systems sizing. Alternatively, it is possible to use pilot plants and laboratory tests.

Die vorliegende Arbeit beschäftigt sich mit der Thematik des hydraulischen Feststofftransports in Druckrohrleitungen zur Bestimmung der hydraulischen Energieverluste des Wasser-Feststoff-Gemisches und der wirtschaftlichen Gemischgeschwindigkeit (der s.g. kritischen Geschwindigkeit) vcrit. Zu diesem Zweck wurde der Transportvorgang in verschiedenen Rohrkonfigurationen (horizontal, schräg und z. T. vertikal) an einem physikalischen Modell im Hubert-Engels-Labor des Instituts für Wasserbau und Technische Hydromechanik der Technischen Universität Dresden untersucht. Dabei kamen drei Sandfraktionen zum Einsatz (0,1 - 0,5 mm; 0,71 - 1,25 mm und 1,4 - 2,2 mm). Die Partikel weisen eine Dichte von ρF=2650 kg/m³ auf. Ziel der Untersuchungen war, mithilfe der Messdaten eine Formel zur Berechnung des Verlustanteils der dispersen Phase an dem gesamten Energieverlust besonders für das heterogene und das quasi-homogene Transportregime in Abhängigkeit von den Einflussgrößen (Dichte, Konzentration, Partikeldurchmesser etc.) abzuleiten. Ein weiterer Schwerpunkt der Arbeit war, die kritische Gemischgeschwindigkeit genauer zu betrachten und einen entsprechenden Rechenansatz aufzustellen. Diese Geschwindigkeit stellt den Übergang von dem Transport mit beweglicher Sohle zum heterogenen Feststofftransport dar. Nach Abschluss der physikalischen Versuche wurde der Feststofftransport mit der Software ANSYS-Fluent numerisch untersucht. Im Fokus der Modellierung stand die Festsetzung der Wandrandbedingung für die disperse Phase, mit Hilfen derer die physikalisch gemessenen Energieverluste erreicht werden konnten. Die Simulationen wurden mit dem Euler-Granular-Modell durchgeführt. Hierbei wird der Feststoff als zweites Kontinuum betrachtet und seine rheologischen Eigenschaften wurden durch die Erweiterung der kinetischen Theorie der Gase auf die disperse Phase (eng. kinetic theory of granular flow KTGF) berechnet. Das angewendete zwei-Fluid-Modell (TFM) eignet sich sehr gut für alle möglichen vorkommenden Feststoffkonzentrationen und liefert gute Übereinstimmung mit den Messergebnissen im Gegensatz zu dem Euler-Lagrange-Modell (DPM), welches lediglich bei niedrigen Feststoffkonzentrationen Anwendung findet.:Inhaltsverzeichnis Abbildungsverzeichnis Tabellenverzeichnis Symbolverzeichnis Indexverzeichnis 1 Einleitung und Zielsetzung 2 Grundlagen des hydraulischen Feststofftransports in Rohrleitungen 2.1 Das Energiegesetz 2.2 Feststofftransport in Rohrleitungen 2.3 Partikeleigenschaften 2.4 Typisierung der Partikelbewegung mit der Strömung 2.5 Einfluss der Turbulenz auf die Partikelbewegung in horizontaler Rohrleitung 2.6 Transportzustände in horizontaler Rohrleitung 2.7 Transportzustände in vertikaler Rohrleitung 2.8 Stopfgrenze 2.9 Kräftebilanz an einem Feststoffpartikel 2.10 Dimensionsanalyse 2.10.1 Auflistung der Einflussgrößen 2.10.2 Anzahl der dimensionslosen π-Parameter 2.10.3 Auswahl der Hauptvariablen 2.10.4 Ermittlung der π-Parameter 2.10.5 Form des funktionellen Zusammenhangs 3 Bemessungsansätze des hydraulischen Transports 3.1 Stand des Wissens 3.1.1 Feststofftransport in horizontaler Rohrleitung 3.1.2 Feststofftransport in geneigter Rohrleitung 3.1.3 Feststofftransport in vertikaler Rohrleitung 3.1.4 Die kritische Gemischgeschwindigkeit in horizontaler Rohrleitung 3.1.5 Die kritische Gemischgeschwindigkeit in geneigter Rohrleitung 3.1.6 Weitere Rechenmodelle 3.2 Erweiterung des Energiegesetzes auf Gemischströmung 3.2.1 In horizontaler Rohrleitung 3.2.2 In geneigter Rohrleitung 3.2.3 In vertikaler Rohrleitung 4 Experimentelle Untersuchungen 4.1 Aufbau der ersten Versuchsanlage 4.2 Messtechnik 4.3 Umbau der Versuchsanlage 4.4 Untersuchungsmaterial 4.5 Experimentelles Verfahren 5 Numerische Simulationen mit ANSYS-Fluent 5.1 Grundlagen der Mehrphasenströmungen 5.2 Auswahl des numerischen Modells 5.3 Das Granular-Euler-Modell 5.3.1 Die Erhaltungsgleichung 5.3.2 Die kinetische Theorie der dispersen Phase 5.4 Modellvalidierung 6 Vorstellung der Untersuchungsergebnisse 6.1 Ergebnisse der experimentellen Untersuchungen in horizontaler Leitung 6.1.1 Experimentelle Untersuchungen zum Energieverlust 6.1.2 Experimentelle Untersuchung zu der kritischen Geschwindigkeit 6.2 Ergebnisse der hydronumerischen Untersuchungen in horizontaler Rohrleitung 6.2.1 Randbedingungen 6.2.2 Numerische Lösung und Konvergenz 6.2.3 Parameteranalyse anhand eigener Versuche 6.2.4 Numerische Untersuchungen zur Wechselwirkung zwischen den hydraulischen Kenngrößen 6.3 Ergebnisse der experimentellen Untersuchungen in vertikaler Leitung 6.4 Ergebnisse der experimentellen Untersuchungen in geneigter Rohrleitung 6.4.1 Experimentelle Untersuchungen zum Energieverlust 6.4.2 Experimentelle Untersuchung zu der kritischen Gemischgeschwindigkeit 6.5 Ergebnisse der numerischen Untersuchungen in geneigter Rohrleitung 7 Fehleranalyse und weitere Betrachtungen 7.1 Degradierung des Feststoffes 7.2 Die Abnutzung der Pumpe 7.3 Abrieb und Durchbruch der Rohrleitungen 7.4 Die Instabilität des Systems bei geringen Geschwindigkeiten 7.5 Messabweichung des Durchflussmessers 7.6 Fehlerquelle bei der Untersuchung der kritischen Gemischgeschwindigkeit 7.7 Fortbewegung der Feststoffe bei Geschwindigkeiten unterhalb vcrit 7.8 Einfluss der Transportkonzentration auf den Arbeitspunkt der Pumpe 8 Zusammenfassung Literaturverzeichnis Anhang / The present work deals with the hydraulic transport characteristics of sand-water mixtures in pipelines to determine hydraulic gradients and the deposition-limit velocity (critical velocity). For this purpose, the transport process in various pipe configurations (horizontal, inclined and vertical) was investigated on a physical model at the Hubert Engels Laboratory of the Institute of Hydraulic Engineering and Technical Hydromechanics of the Technical University of Dresden. Three sand fractions were used (0.1 - 0.5 mm, 0.71 - 1.25 mm and 1.4 - 2.2 mm) with particles density of ρF = 2650 kg/m³. The aim of the investigations was to develop a model for calculating the head loss percent-age of the disperse phase in terms of total energy loss, especially for the heterogeneous and quasi-homogeneous transport regime correlating to the influence quantities (density, concentration, particle diameter, etc.). Another important aspect for this work was to consider the critical velocity and to set up a corresponding calculation approach for this parameter. The deposition-limit velocity represents the transition from sliding Bed transport to heterogeneous transport. In the next step, the solids transport process was investigated numerical with ANSYS-Fluent. The focus of the modeling was the determination of the wall boundary condition for the disperse phase, with help of which the physically measured energy losses could be re-stored. The simulations were performed with the Euler Granular model. Here, the solid is considered to be the second continuum, and its rheological properties were calculated by expanding the kinetic theory of gases to disperse phase (KTGF).:Inhaltsverzeichnis Abbildungsverzeichnis Tabellenverzeichnis Symbolverzeichnis Indexverzeichnis 1 Einleitung und Zielsetzung 2 Grundlagen des hydraulischen Feststofftransports in Rohrleitungen 2.1 Das Energiegesetz 2.2 Feststofftransport in Rohrleitungen 2.3 Partikeleigenschaften 2.4 Typisierung der Partikelbewegung mit der Strömung 2.5 Einfluss der Turbulenz auf die Partikelbewegung in horizontaler Rohrleitung 2.6 Transportzustände in horizontaler Rohrleitung 2.7 Transportzustände in vertikaler Rohrleitung 2.8 Stopfgrenze 2.9 Kräftebilanz an einem Feststoffpartikel 2.10 Dimensionsanalyse 2.10.1 Auflistung der Einflussgrößen 2.10.2 Anzahl der dimensionslosen π-Parameter 2.10.3 Auswahl der Hauptvariablen 2.10.4 Ermittlung der π-Parameter 2.10.5 Form des funktionellen Zusammenhangs 3 Bemessungsansätze des hydraulischen Transports 3.1 Stand des Wissens 3.1.1 Feststofftransport in horizontaler Rohrleitung 3.1.2 Feststofftransport in geneigter Rohrleitung 3.1.3 Feststofftransport in vertikaler Rohrleitung 3.1.4 Die kritische Gemischgeschwindigkeit in horizontaler Rohrleitung 3.1.5 Die kritische Gemischgeschwindigkeit in geneigter Rohrleitung 3.1.6 Weitere Rechenmodelle 3.2 Erweiterung des Energiegesetzes auf Gemischströmung 3.2.1 In horizontaler Rohrleitung 3.2.2 In geneigter Rohrleitung 3.2.3 In vertikaler Rohrleitung 4 Experimentelle Untersuchungen 4.1 Aufbau der ersten Versuchsanlage 4.2 Messtechnik 4.3 Umbau der Versuchsanlage 4.4 Untersuchungsmaterial 4.5 Experimentelles Verfahren 5 Numerische Simulationen mit ANSYS-Fluent 5.1 Grundlagen der Mehrphasenströmungen 5.2 Auswahl des numerischen Modells 5.3 Das Granular-Euler-Modell 5.3.1 Die Erhaltungsgleichung 5.3.2 Die kinetische Theorie der dispersen Phase 5.4 Modellvalidierung 6 Vorstellung der Untersuchungsergebnisse 6.1 Ergebnisse der experimentellen Untersuchungen in horizontaler Leitung 6.1.1 Experimentelle Untersuchungen zum Energieverlust 6.1.2 Experimentelle Untersuchung zu der kritischen Geschwindigkeit 6.2 Ergebnisse der hydronumerischen Untersuchungen in horizontaler Rohrleitung 6.2.1 Randbedingungen 6.2.2 Numerische Lösung und Konvergenz 6.2.3 Parameteranalyse anhand eigener Versuche 6.2.4 Numerische Untersuchungen zur Wechselwirkung zwischen den hydraulischen Kenngrößen 6.3 Ergebnisse der experimentellen Untersuchungen in vertikaler Leitung 6.4 Ergebnisse der experimentellen Untersuchungen in geneigter Rohrleitung 6.4.1 Experimentelle Untersuchungen zum Energieverlust 6.4.2 Experimentelle Untersuchung zu der kritischen Gemischgeschwindigkeit 6.5 Ergebnisse der numerischen Untersuchungen in geneigter Rohrleitung 7 Fehleranalyse und weitere Betrachtungen 7.1 Degradierung des Feststoffes 7.2 Die Abnutzung der Pumpe 7.3 Abrieb und Durchbruch der Rohrleitungen 7.4 Die Instabilität des Systems bei geringen Geschwindigkeiten 7.5 Messabweichung des Durchflussmessers 7.6 Fehlerquelle bei der Untersuchung der kritischen Gemischgeschwindigkeit 7.7 Fortbewegung der Feststoffe bei Geschwindigkeiten unterhalb vcrit 7.8 Einfluss der Transportkonzentration auf den Arbeitspunkt der Pumpe 8 Zusammenfassung Literaturverzeichnis Anhang