Rozprawy doktorskie na temat „Bubble breakup”

A generalized model for bubble coalescence and breakup has been developed, which is based on a comprehensive survey of existing theories and models. One important feature of the model is that all important mechanisms leading to bubble coalescence and breakup in a turbulent gas-liquid flow are considered. The new model is tested extensively in a 1D Test Solver and a 3D CFD code ANSYS CFX for the case of vertical gas-liquid pipe flow under adiabatic conditions, respectively. Two kinds of extensions of the standard multi-fluid model, i.e. the discrete population model and the inhomogeneous MUSIG (multiple-size group) model, are available in the two solvers, respectively. These extensions with suitable closure models such as those for coalescence and breakup are able to predict the evolution of bubble size distribution in dispersed flows and to overcome the mono-dispersed flow limitation of the standard multi-fluid model. For the validation of the model the high quality database of the TOPFLOW L12 experiments for air-water flow in a vertical pipe was employed. A wide range of test points, which cover the bubbly flow, turbulent-churn flow as well as the transition regime, is involved in the simulations. The comparison between the simulated results such as bubble size distribution, gas velocity and volume fraction and the measured ones indicates a generally good agreement for all selected test points. As the superficial gas velocity increases, bubble size distribution evolves via coalescence dominant regimes first, then breakup-dominant regimes and finally turns into a bimodal distribution. The tendency of the evolution is well reproduced by the model. However, the tendency is almost always overestimated, i.e. too much coalescence in the coalescence dominant case while too much breakup in breakup dominant ones. The reason of this problem is discussed by studying the contribution of each coalescence and breakup mechanism at different test points. The redistribution of the gaseous phase from the injection position at the pipe wall to the whole cross section is overpredicted by the Test Solver especially for the test points with high superficial gas velocity. Besides the models for bubble forces, the simplification of the Test Solver to a 1D model has an influence on the redistribution process. Simulations performed using CFX show that a considerable improvement is achieved with comparison to the results delivered by the standard closure models. For the breakup-dominant cases, the breakup rate is again overestimated and the contribution of wake entrainment of large bubbles is underestimated. Furthermore, inlet conditions for the liquid phase, bubble forces as well as turbulence modeling are shown to have a noticeable influence, especially on the redistribution of the gaseous phase.

A generalized model for bubble coalescence and breakup has been developed, which is based on a comprehensive survey of existing theories and models. One important feature of the model is that all important mechanisms leading to bubble coalescence and breakup in a turbulent gas-liquid flow are considered. The new model is tested extensively in a 1D Test Solver and a 3D CFD code ANSYS CFX for the case of vertical gas-liquid pipe flow under adiabatic conditions, respectively. Two kinds of extensions of the standard multi-fluid model, i.e. the discrete population model and the inhomogeneous MUSIG (multiple-size group) model, are available in the two solvers, respectively. These extensions with suitable closure models such as those for coalescence and breakup are able to predict the evolution of bubble size distribution in dispersed flows and to overcome the mono-dispersed flow limitation of the standard multi-fluid model. For the validation of the model the high quality database of the TOPFLOW L12 experiments for air-water flow in a vertical pipe was employed. A wide range of test points, which cover the bubbly flow, turbulent-churn flow as well as the transition regime, is involved in the simulations. The comparison between the simulated results such as bubble size distribution, gas velocity and volume fraction and the measured ones indicates a generally good agreement for all selected test points. As the superficial gas velocity increases, bubble size distribution evolves via coalescence dominant regimes first, then breakup-dominant regimes and finally turns into a bimodal distribution. The tendency of the evolution is well reproduced by the model. However, the tendency is almost always overestimated, i.e. too much coalescence in the coalescence dominant case while too much breakup in breakup dominant ones. The reason of this problem is discussed by studying the contribution of each coalescence and breakup mechanism at different test points. The redistribution of the gaseous phase from the injection position at the pipe wall to the whole cross section is overpredicted by the Test Solver especially for the test points with high superficial gas velocity. Besides the models for bubble forces, the simplification of the Test Solver to a 1D model has an influence on the redistribution process. Simulations performed using CFX show that a considerable improvement is achieved with comparison to the results delivered by the standard closure models. For the breakup-dominant cases, the breakup rate is again overestimated and the contribution of wake entrainment of large bubbles is underestimated. Furthermore, inlet conditions for the liquid phase, bubble forces as well as turbulence modeling are shown to have a noticeable influence, especially on the redistribution of the gaseous phase.

There exist several different numerical models for predicting bubble coalescence and breakup using computational fluid dynamics (CFD). Various combinations of these models will be employed to model a bioreactor process in a stirred reactor tank. A mass transfer coefficient, Kla, has been calculated and compared to those found experimentally by Thermo-Fisher Scientific, to validate the accuracy of currently available mathematical models for population balance equations. These include various combinations of bubble breakup and coalescence models coupled with the calculation of mass transfer coefficients.

Many flow regimes in Nuclear Reactor Safety Research are characterized by multiphase flows, with one phase being a continuous liquid and the other phase consisting of gas or vapour of the liquid phase. In dependence on the void fraction of the gaseous phase the flow regimes e.g. in vertical pipes are varying from bubbly flows with low and higher volume fraction of bubbles to slug flow, churn turbulent flow, annular flow and finally to droplet flow. In the regime of bubbly and slug flow the multiphase flow shows a spectrum of different bubble sizes. While disperse bubbly flows with low gas volume fraction are mostly mono-disperse, an increase of the gas volume fraction leads to a broader bubble size distribution due to breakup and coalescence of bubbles. Bubbles of different sizes are subject to lateral migration due to forces acting in lateral direction different from the main drag force direction. The bubble lift force was found to change the sign dependent on the bubble size. Consequently this lateral migration leads to a de-mixing of small and large bubbles and to further coalescence of large bubbles migrating towards the pipe center into even larger Taylor bubbles or slugs. An adequate modeling has to consider all these phenomena. A Multi Bubble Size Class Test Solver has been developed to investigate these effects and test the influence of different model approaches. Basing on the results of these investigations a generalized inhomogeneous Multiple Size Group (MUSIG) Model based on the Eulerian modeling framework has been proposed and was finally implemented into the CFD code CFX. Within this model the dispersed gaseous phase is divided into N inhomogeneous velocity groups (phases) and each of these groups is subdivided into Mj bubble size classes. Bubble breakup and coalescence processes between all bubble size classes Mj are taken into account by appropriate models. The inhomogeneous MUSIG model has been validated against experimental data from the TOPFLOW test facility.

Many flow regimes in Nuclear Reactor Safety Research are characterized by multiphase flows, with one phase being a continuous liquid and the other phase consisting of gas or vapour of the liquid phase. In dependence on the void fraction of the gaseous phase the flow regimes e.g. in vertical pipes are varying from bubbly flows with low and higher volume fraction of bubbles to slug flow, churn turbulent flow, annular flow and finally to droplet flow. In the regime of bubbly and slug flow the multiphase flow shows a spectrum of different bubble sizes. While disperse bubbly flows with low gas volume fraction are mostly mono-disperse, an increase of the gas volume fraction leads to a broader bubble size distribution due to breakup and coalescence of bubbles. Bubbles of different sizes are subject to lateral migration due to forces acting in lateral direction different from the main drag force direction. The bubble lift force was found to change the sign dependent on the bubble size. Consequently this lateral migration leads to a de-mixing of small and large bubbles and to further coalescence of large bubbles migrating towards the pipe center into even larger Taylor bubbles or slugs. An adequate modeling has to consider all these phenomena. A Multi Bubble Size Class Test Solver has been developed to investigate these effects and test the influence of different model approaches. Basing on the results of these investigations a generalized inhomogeneous Multiple Size Group (MUSIG) Model based on the Eulerian modeling framework has been proposed and was finally implemented into the CFD code CFX. Within this model the dispersed gaseous phase is divided into N inhomogeneous velocity groups (phases) and each of these groups is subdivided into Mj bubble size classes. Bubble breakup and coalescence processes between all bubble size classes Mj are taken into account by appropriate models. The inhomogeneous MUSIG model has been validated against experimental data from the TOPFLOW test facility.

Ein neues, verallgemeinertes Modell für Blasenkoaleszenz und –zerfall wurde entwickelt. Es basiert auf physikalischen Überlegungen und berücksichtigt verschiedene Mechanismen, die zu Blasenkoaleszenz und –zerfall führen können. In einer ausführlichen Literaturrecherche wurden zunächst die verfügbaren Modelle zusammengestellt und analysiert. Es zeigte sich, dass viele widersprüchliche Modelle veröffentlicht wurden. Keins dieser Modelle erlaubt die Vorhersage der Entwicklung der Blasengrößenverteilungen entlang einer Rohrströmung für einen breiten Bereich an Kombinationen von Volumenströmen der Gas- und der Flüssigphase. Das neue Modell wurde ausführlich in einem vereinfachten Testsolver untersucht. Dieser erfasst zwar nicht alle Einzelheiten einer sich entlang des Rohres entwickelten Strömungen, erlaubt aber im Gegensatz zu den CFD-Simulationen eine Vielzahl von Variationsrechnungen zur Untersuchung des Einflusses einzelner Größen und Modelle. Koaleszenz und Zerfall kann nicht getrennt von anderen Phänomenen und Modellen, die diese widerspiegeln, betrachtet werden. Es bestehen enge Wechselwirkungen mit der Turbulenz der Flüssigphase und dem Impulsaustausch zwischen den Phasen. Da die Dissipationsrate der turbulenten kinetischen Energie ein direkter Eingangsparameter für das neue Modell ist, wurde die Turbulenzmodellierung besonders genau untersucht. Zur Validierung des Modells wurde eine TOPFLOW-Experimentalserie zur Luft-Wasser-Strömungen in einem 8 m langen DN200-Rohr genutzt. Die Daten zeichnen sich durch eine hohe Qualität aus und wurden im Rahmen des TOPFLOW-IIVorhabens mit dem Ziel eine Grundlage für die hier vorgestellten Arbeiten zu liefern, gewonnen. Die Vorhersage der Entwicklung der Blasengrößenverteilung entlang des Rohrs konnte im Vergleich zu den bisherigen Standardmodellen für Blasenkoaleszenz und -zerfall in CFX deutlich verbessert werden. Einige quantitative Abweichungen bleiben aber bestehen. Die vollständigen Modellgleichungen sowie eine Implementierung über „User-FORTRAN“ in CFX stehen zur Verfügung und können für weitere Arbeiten zur Simulation polydisperser Blasenströmungen genutzt werden.

Cette thèse a étudié de façon systématique les processus de la rupture et de la coalescence impliquant une interface liquide-liquide (gouttelettes) ou gaz-liquide (bulles) en présence ou pas d’un champ magnétique dans des dispositifs microfluidiques, à l’aide d’une caméra rapide. Les mécanismes de la rupture d’une interface ferrofluide sous différents champs magnétiques ont été étudiés et comparés. On a constaté que la structure morphologique et la vitesse d’amincissement du cou peuvent être contrôlées activement par la force magnétique. Ainsi, le volume et la fréquence de formation de gouttelettes de ferrofluide peuvent être pilotés aisément. La rupture de l'interface liquide-liquide a généralement conduit à la formation de gouttelettes satellites avec sa taille proportionnelle au nombre capillaire de la phase continue. La coalescence des gouttelettes ont aussi été étudiée avec l’analyse de l'évolution du cou reliant deux gouttelettes. Il a été constaté que la formation du pont ou du cou liquide pouvait se produire dans la gamme de l'ordre de dizaines de micromètres entre les bords d'attaque sous champ magnétique. L'inertie d’origine d'attraction magnétique sur des gouttelettes de ferrofluide devenait la force motrice pour la coalescence lors de la première étape au détriment de la force capillaire
This thesis systematically investigates the breakup and coalescence processes of the involved droplet (bubble) interface under magnetic field or not in two-phase microfluidic flow, by using a high speed digital camera. The whole breakup processes of ferrofluid interface under different magnetic fields were investigated and compared. It was found that the morphological structure and necking velocity of the interface can be actively controlled by the magnetic force. Thus the volumes and the formation frequencies of ferrofluid droplets can be actively adjusted. The breakup of Liquid-Liquid interface usually leads to the formation of satellite droplet with its size proportional to the capillary number of the continuous phase. The coalescences of droplets were investigated. The evolution of the neck connecting two droplets was analyzed. It was found that the formation of liquid bridge or neck could occurs with a visible gap in the order of tens of micrometers between the leading edges under magnetic field and the inertia of the ferrofluid originating from the magnetic attraction fields becomes the driving force at the initial stage of coalescence instead of capillary force

Experimente mit neuartigen Messverfahren lieferten Daten über die Struktur von transienten Flüssig-keits-Gas-Strömungen für die Entwicklung und Validierung von mikroskopischen, d.h. geometrieunabhängigen Konstitutivbeziehungen zur Beschreibung des Impulsaustauschs zwischen Flüssig-phase und Gasblasen sowie zur Quantifizierung der Häufigkeit von Blasenkoaleszenz und -zerfall. Hierzu wurde eine vertikale Testsektion der Zweiphasentestschleife MTLoop in Rossendorf genutzt, wobei erstmals Gittersensoren mit einer Auflösung von 2-3 mm bei einer Messfrequenz von bis zu 10 kHz angewandt wurden. Dabei wurde die Evolution von Gasgehalts-, Geschwindigkeits- und Bla-sengrößenverteilungen entlang des Strömungsweges und bei schnellen Übergangsprozessen aufge-nommen und so die für die Modellbildung erforderlichen Daten bereitgestellt. Für den Test der Mo-dellbeziehungen wurde ein vereinfachtes Verfahren zur Lösung der Strömungsgleichungen entlang des Strömungswegs erstellt. Es basiert auf der Betrachtung einer größeren Anzahl von Blasengrö-ßenklassen. Die erhaltenen numerische Lösungen haben erstmals gezeigt, dass der bei Erhöhung der Gasvolumenstromdichte stattfindende Übergang von einer Blasenströmung mit Randmaximum zu einem Profil mit Zentrumsmaximum und anschließend zu einer Pfropfenströmung ausgehend von einem einheitlichen Satz physikalisch begründeter und geometrieunabhängiger Konstitutivgleichun-gen modelliert werden kann. Die Modellbeziehungen haben sich in einem abgegrenzten Gebiet der Volumenstromdichten als generalisierungsfähig erwiesen und sind für den Einbau in CFD-Modelle geeignet. Weiterhin wurden Arbeiten zur Kondensation durchgeführt, die direkten Bezug zu den Kon-densationsmodellen haben, die in Thermohydraulik-Codes enthalten sind. Die Untersuchung liefert darüber hinaus experimentelle Daten für die Modellvalidierung hinsichtlich des Verhaltens und des Einflusses nichtkondensierbarer Gase. Hierfür wurden spezielle Sonden für die Bestimmung der Konzentration und für die Lokalisierung von Pfropfen nichtkondensierbarer Gase entwickelt und bei transienten Kondensationsversuchen in einem leicht geneigten Wärmeübertragerrohr eingesetzt.

Experimente mit neuartigen Messverfahren lieferten Daten über die Struktur von transienten Flüssig-keits-Gas-Strömungen für die Entwicklung und Validierung von mikroskopischen, d.h. geometrieunabhängigen Konstitutivbeziehungen zur Beschreibung des Impulsaustauschs zwischen Flüssig-phase und Gasblasen sowie zur Quantifizierung der Häufigkeit von Blasenkoaleszenz und -zerfall. Hierzu wurde eine vertikale Testsektion der Zweiphasentestschleife MTLoop in Rossendorf genutzt, wobei erstmals Gittersensoren mit einer Auflösung von 2-3 mm bei einer Messfrequenz von bis zu 10 kHz angewandt wurden. Dabei wurde die Evolution von Gasgehalts-, Geschwindigkeits- und Bla-sengrößenverteilungen entlang des Strömungsweges und bei schnellen Übergangsprozessen aufge-nommen und so die für die Modellbildung erforderlichen Daten bereitgestellt. Für den Test der Mo-dellbeziehungen wurde ein vereinfachtes Verfahren zur Lösung der Strömungsgleichungen entlang des Strömungswegs erstellt. Es basiert auf der Betrachtung einer größeren Anzahl von Blasengrö-ßenklassen. Die erhaltenen numerische Lösungen haben erstmals gezeigt, dass der bei Erhöhung der Gasvolumenstromdichte stattfindende Übergang von einer Blasenströmung mit Randmaximum zu einem Profil mit Zentrumsmaximum und anschließend zu einer Pfropfenströmung ausgehend von einem einheitlichen Satz physikalisch begründeter und geometrieunabhängiger Konstitutivgleichun-gen modelliert werden kann. Die Modellbeziehungen haben sich in einem abgegrenzten Gebiet der Volumenstromdichten als generalisierungsfähig erwiesen und sind für den Einbau in CFD-Modelle geeignet. Weiterhin wurden Arbeiten zur Kondensation durchgeführt, die direkten Bezug zu den Kon-densationsmodellen haben, die in Thermohydraulik-Codes enthalten sind. Die Untersuchung liefert darüber hinaus experimentelle Daten für die Modellvalidierung hinsichtlich des Verhaltens und des Einflusses nichtkondensierbarer Gase. Hierfür wurden spezielle Sonden für die Bestimmung der Konzentration und für die Lokalisierung von Pfropfen nichtkondensierbarer Gase entwickelt und bei transienten Kondensationsversuchen in einem leicht geneigten Wärmeübertragerrohr eingesetzt.

Fluid particle break-up and coalescence are important phenomena in a number of industrial processes.

A Lagrangian momentum balance model for the collision process between two fluid particles has been developed and tested favorably against experimental data. It is based on an earlier model developed in our department. Oscillations were introduced and the volume balances that are solved avoid earlier approximations. Film drainage was also implemented into the model based on a literature review given. It is believed this approach will lead to a more fundamental modeling of the coalescence process.

An improved break-up model has been developed. It is an extension of earlier work at the department and it introduces an additional criterion for break-up. This criterion gives a lower limit for the daughter fragment sizes in binary break-up, thus also limiting the break-up of smaller fluid particles, and is a more consistent model than the earlier one.

Two break-up models, original model by Luo (1993) and improved model, and a coalescence model have been implemented in a population balance as algebraic sink and source terms. This population balance is in turn included in an in-house CFD-code. The models have been tested against experimental data from a bubble column in our laboratory, and the improved break-up model compares favorably with the experimentally obtained accumulated mass distribution. Too few bubbles are predicted in the lower population classes, but it is shown that this may as well be a result of the coalescence model used as the improved break-up model.

Frothers are used in flotation to aid generation of small bubbles, but little is known about the mechanisms that take place in the flotation machine to produce such an effect. Coalescence prevention is the common explanation, although the exact mechanism is obscure and almost no attention has been paid to a frother effect on bubble break-up, the other possible mechanism. This thesis presents a technique to study the effect of frothers on bubble coalescence at the generation stage (at a capillary tube) and a technique to study the effect of frothers on bubble coalescence and break-up in a turbulent field. The first technique is based on the sound bubbles emit when they form and coalesce. The sound signal was linked to bubble formation and coalescence events using high-speed cinematography. The technique has a resolution capable of detecting coalescence events that occur within 1-2 ms. The second technique allows discriminating between coalescence and break-up and is based on the exposure of a mono-size distribution of bubbles to a turbulent field generated by a three-bladed axial flow impeller. Analysis of bubble size distributions after contact with the turbulent field gives the coalescence and break-up fraction. The results show frothers reduce coalescence and alter the bubble size distribution of bubbles generated by break-up.
In the course of high-speed imaging an effect of frother on bubble shape and motion after formation was detected. Analysis of this forms the third major component of the work. A dependence of velocity on bubble aspect ratio is shown, which is in line with recent literature.

[ES] El principal desafío en los motores turbina de gas empleados en aviación reside en aumentar la eficiencia del ciclo termodinámico manteniendo las emisiones contaminantes por debajo de las rigurosas restricciones. Ésto ha conllevado la necesidad de diseñar nuevas estrategias de inyección/combustión que operan en puntos de operación peligrosos por su cercanía al límite inferior de apagado de llama. En este contexto, el concepto Lean Direct Injection (LDI) ha emergido como una tecnología prometedora a la hora de reducir los óxidos de nitrógeno (NOx) emitidos por las plantas propulsoras de los aviones de nueva generación. En este contexto, la presente tesis tiene como objetivos contribuir al conocimiento de los mecanismos físicos que rigen el comportamiento de un quemador LDI y proporcionar herramientas de análisis para una profunda caracterización de las complejas estructuras de flujo de turbulento generadas en el interior de la cámara de combustión. Para ello, se ha desarrollado una metodología numérica basada en CFD capaz de modelar el flujo bifásico no reactivo en el interior de un quemador LDI académico mediante enfoques de turbulencia U-RANS y LES en un marco Euleriano-Lagrangiano. La resolución numérica de este problema multi-escala se aborda mediante la descripción completa del flujo a lo largo de todos los elementos que constituyen la maqueta experimental, incluyendo su paso por el swirler y entrada a la cámara de combustión. Ésto se lleva a cabo través de dos códigos CFD que involucran dos estrategias de mallado diferentes: una basada en algoritmos de generación y refinamiento automático de la malla (AMR) a través de CONVERGE y otra técnica de mallado estático más tradicional mediante OpenFOAM. Por un lado, se ha definido una metodología para obtener una estrategia de mallado óptima mediante el uso del AMR y se han explotado sus beneficios frente a los enfoques tradicionales de malla estática. De esta forma, se ha demostrado que la aplicabilidad de las herramientas de control de malla disponibles en CONVERGE como el refinamiento fijo (fixed embedding) y el AMR son una opción muy interesante para afrontar este tipo de problemas multi-escala. Los resultados destacan una optimización del uso de los recursos computacionales y una mayor precisión en las simulaciones realizadas con la metodología presentada. Por otro lado, el uso de herramientas CFD se ha combinado con la aplicación de técnicas de descomposición modal avanzadas (Proper Orthogonal Decomposition and Dynamic Mode Decomposition). La identificación numérica de los principales modos acústicos en la cámara de combustión ha demostrado el potencial de estas herramientas al permitir caracterizar las estructuras de flujo coherentes generadas como consecuencia de la rotura de los vórtices (VBB) y de los chorros fuertemente torbellinados presentes en el quemador LDI. Además, la implementación de estos procedimientos matemáticos ha permitido tanto recuperar información sobre las características de la dinámica de flujo como proporcionar un enfoque sistemático para identificar los principales mecanismos que sustentan las inestabilidades en la cámara de combustión. Finalmente, la metodología validada ha sido explotada a través de un Diseño de Experimentos (DoE) para cuantificar la influencia de los factores críticos de diseño en el flujo no reactivo. De esta manera, se ha evaluado la contribución individual de algunos parámetros funcionales (el número de palas del swirler, el ángulo de dichas palas, el ancho de la cámara de combustión y la posición axial del orificio del inyector) en los patrones del campo fluido, la distribución del tamaño de gotas del combustible líquido y la aparición de inestabilidades en la cámara de combustión a través de una matriz ortogonal L9 de Taguchi. Este estudio estadístico supone un punto de partida para posteriores estudios de inyección, atomización y combus
[CA] El principal desafiament als motors turbina de gas utilitzats a la aviació resideix en augmentar l'eficiència del cicle termodinàmic mantenint les emissions contaminants per davall de les rigoroses restriccions. Aquest fet comporta la necessitat de dissenyar noves estratègies d'injecció/combustió que radiquen en punts d'operació perillosos per la seva aproximació al límit inferior d'apagat de flama. En aquest context, el concepte Lean Direct Injection (LDI) sorgeix com a eina innovadora a l'hora de reduir els òxids de nitrogen (NOx) emesos per les plantes propulsores dels avions de nova generació. Sota aquest context, aquesta tesis té com a objectius contribuir al coneixement dels mecanismes físics que regeixen el comportament d'un cremador LDI i proporcionar ferramentes d'anàlisi per a una profunda caracterització de les complexes estructures de flux turbulent generades a l'interior de la càmera de combustió. Per tal de dur-ho a terme s'ha desenvolupat una metodología numèrica basada en CFD capaç de modelar el flux bifàsic no reactiu a l'interior d'un cremador LDI acadèmic mitjançant els enfocaments de turbulència U-RANS i LES en un marc Eulerià-Lagrangià. La resolució numèrica d'aquest problema multiescala s'aborda mitjançant la resolució completa del flux al llarg de tots els elements que constitueixen la maqueta experimental, incloent el seu pas pel swirler i l'entrada a la càmera de combustió. Açò es duu a terme a través de dos codis CFD que involucren estratègies de mallat diferents: una basada en la generación automàtica de la malla i en l'algoritme de refinament adaptatiu (AMR) amb CONVERGE i l'altra que es basa en una tècnica de mallat estàtic més tradicional amb OpenFOAM. D'una banda, s'ha definit una metodologia per tal d'obtindre una estrategia de mallat òptima mitjançant l'ús de l'AMR i s'han explotat els seus beneficis front als enfocaments tradicionals de malla estàtica. D'aquesta forma, s'ha demostrat que l'aplicabilitat de les ferramente de control de malla disponibles en CONVERGE com el refinament fixe (fixed embedding) i l'AMR són una opció molt interessant per tal d'afrontar aquest tipus de problemes multiescala. Els resultats destaquen una optimització de l'ús dels recursos computacionals i una major precisió en les simulacions realitzades amb la metodologia presentada. D'altra banda, l'ús d'eines CFD s'ha combinat amb l'aplicació de tècniques de descomposició modal avançades (Proper Orthogonal Decomposition and Dynamic Mode Decomposition). La identificació numèrica dels principals modes acústics a la càmera de combustió ha demostrat el potencial d'aquestes ferramentes al permetre caracteritzar les estructures de flux coherents generades com a conseqüència del trencament dels vòrtex (VBB) i dels raigs fortament arremolinats presents al cremador LDI. A més, la implantació d'estos procediments matemàtics ha permès recuperar informació sobre les característiques de la dinàmica del flux i proporcionar un enfocament sistemàtic per tal d'identificar els principals mecanismes que sustenten les inestabilitats a la càmera de combustió. Finalment, la metodologia validada ha sigut explotada a traves d'un Diseny d'Experiments (DoE) per tal de quantificar la influència dels factors crítics de disseny en el flux no reactiu. D'aquesta manera, s'ha avaluat la contribución individual d'alguns paràmetres funcionals (el nombre de pales del swirler, l'angle de les pales, l'amplada de la càmera de combustió i la posició axial de l'orifici de l'injector) en els patrons del camp fluid, la distribució de la mida de gotes del combustible líquid i l'aparició d'inestabilitats en la càmera de combustió mitjançant una matriu ortogonal L9 de Taguchi. Aquest estudi estadístic és un bon punt de partida per a futurs estudis de injecció, atomització i combustió en cremadors LDI.
[EN] Aeronautical gas turbine engines present the main challenge of increasing the efficiency of the cycle while keeping the pollutant emissions below stringent restrictions. This has led to the design of new injection-combustion strategies working on more risky and problematic operating points such as those close to the lean extinction limit. In this context, the Lean Direct Injection (LDI) concept has emerged as a promising technology to reduce oxides of nitrogen (NOx) for next-generation aircraft power plants In this context, this thesis aims at contributing to the knowledge of the governing physical mechanisms within an LDI burner and to provide analysis tools for a deep characterisation of such complex flows. In order to do so, a numerical CFD methodology capable of reliably modelling the 2-phase nonreacting flow in an academic LDI burner has been developed in an Eulerian-Lagrangian framework, using the U-RANS and LES turbulence approaches. The LDI combustor taken as a reference to carry out the investigation is the laboratory-scale swirled-stabilised CORIA Spray Burner. The multi-scale problem is addressed by solving the complete inlet flow path through the swirl vanes and the combustor through two different CFD codes involving two different meshing strategies: an automatic mesh generation with adaptive mesh refinement (AMR) algorithm through CONVERGE and a more traditional static meshing technique in OpenFOAM. On the one hand, a methodology to obtain an optimal mesh strategy using AMR has been defined, and its benefits against traditional fixed mesh approaches have been exploited. In this way, the applicability of grid control tools available in CONVERGE such as fixed embedding and AMR has been demonstrated to be an interesting option to face this type of multi-scale problem. The results highlight an optimisation of the use of the computational resources and better accuracy in the simulations carried out with the presented methodology. On the other hand, the use of CFD tools has been combined with the application of systematic advanced modal decomposition techniques (i.e., Proper Orthogonal Decomposition and Dynamic Mode Decomposition). The numerical identification of the main acoustic modes in the chamber have proved their potential when studying the characteristics of the most powerful coherent flow structures of strongly swirled jets in a LDI burner undergoing vortex breakdown (VBB). Besides, the implementation of these mathematical procedures has allowed both retrieving information about the flow dynamics features and providing a systematic approach to identify the main mechanisms that sustain instabilities in the combustor. Last, this analysis has also allowed identifying some key features of swirl spray systems such as the complex pulsating, intermittent and cyclical spatial patterns related to the Precessing Vortex Core (PVC). Finally, the validated methodology is exploited through a Design of Experiments (DoE) to quantify the influence of critical design factors on the non-reacting flow. In this way, the individual contribution of some functional parameters (namely the number of swirler vanes, the swirler vane angle, the combustion chamber width and the axial position of the nozzle tip) into both the flow field pattern, the spray size distribution and the occurrence of instabilities in the combustion chamber are evaluated throughout a Taguchi's orthogonal array L9. Such a statistical study has supposed a good starting point for subsequent studies of injection, atomisation and combustion on LDI burners.
Belmar Gil, M. (2020). Computational study on the non-reacting flow in Lean Direct Injection gas turbine combustors through Eulerian-Lagrangian Large-Eddy Simulations [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/159882
TESIS

電力用遮断器の油圧操作装置において，油圧回路内の気泡が操作装置の動作に及ぼす悪影響を解消するために，新しい油圧回路方式である常時高圧安定回路方式を提案し，油圧回路内の流れおよび可動部の定式化と解析および実測を行った．本方式の動作特性と動作安定性，ピストンの制動特性，複数の油圧操作装置の駆動特性について検討し，本方式が有効かつ安定的に機能することを確認した．以上により，油圧操作装置の動作時間安定化技術を開発することができた．
We proposed and studied a hydraulic operation stabilizing system for a hydraulic operating device of a circuit breaker to eliminate the influence of air bubbles created in hydraulic fluid. We formulated the flow of hydraulic circuit and the motion of moving parts, which were numerically simulated and experimentally confirmed. We confirmed that this stabilizing system functioned effectively and stably through the investigation: operation characteristics and stability of the stabilizing system, braking characteristics of a piston-dashpot system and operation characteristics of two hydraulic operating devices. Based on the results, we could perform an engineering development for stabilizing operation time of the hydraulic operating device.
博士(工学)
Doctor of Philosophy in Engineering
同志社大学
Doshisha University

The dynamics and breakup of a bubble in axisymmetric flow fields has been investigated using numerical and analytical techniques. In particular, the transient bubble deformation, oscillation, and overshoot effects are considered in conjunction with the existence of steady-state solutions.

To explore the dynamics of a bubble with a high degree of deformation, a numerical technique suitable for solving axisymmetric, unsteady free boundary problems in fluid mechanics has been developed. The technique is based on a finite-difference solution of the equations of motion on a moving orthogonal curvilinear coordinate system, which is constructed numerically and adjusted to fit the boundary at any time. For example, the steady and unsteady deformations of a bubble in uniaxial and biaxial straining flows are examined for wide ranges of the Reynolds number and the Weber number. The computations reveal that a bubble in a uniaxial straining flow extends indefinitely if the Weber number is larger than a critical value (W > W_c). Furthermore, it is shown that a bubble may not achieve a stable steady state even at subcritical values of the Weber number if the initial state is sufficiently different from the steady state. Potential flow solutions for uniaxial straining flow show that an initially deformed bubble undergoes oscillatory motion if W < W_c, with a frequency of oscillation that decreases as the Weber number increases and equals zero at the critical Weber number.

In contrast to the uniaxial straining flow problem, a bubble at a finite Reynolds number in a biaxial straining flow has a stable steady state even though the deformation is extremely large. However, it is found that a bubble in a biaxial straining flow in the potential flow limit has exactly the same steady-state shape as in a uniaxial straining flow and a critical Weber number for breakup exists. Comparison of the results for the cases of high Reynolds numbers with the potential flow results suggests that the potential flow solution does not provide a uniformly valid approximation to the real flow at a high Reynolds number in the biaxial straining flow.

As a complementary analytical study to the numerical analysis, the method of domain perturbations is used to investigate the problem of a nearly spherical bubble in an inviscid, axisymmetric straining flow. The steady-state solutions suggest the existence of a limit point at a critical value of the Weber number. Furthermore, the asymptotic analysis for oscillation has provided a formula of oscillation frequency for the principal mode such as ω² = ω²₀(1 - 0.31W), where ω₀ is the oscillation frequency of a bubble in a quiescent fluid.

To include the weak viscous effect on the oscillation, a general formula for viscous pressure correction for a spherical bubble in an arbitrary axisymmetric flow has been derived in terms of the vorticity distribution. This formula has been applied to obtain the drag coefficient C_D = 48/R by directly integrating the normal stress over the surface for a spherical bubble in a uniform streaming flow at a high Reynolds number, which has so far been possible only via indirect macroscopic balances. The direct method also reveals that the drag coefficient up to O(R)⁻¹ depends only on the O(1) vorticity distribution right on the bubble surface, and is independent of the vorticity distribution inside the fluid.

Finally, a voidage bubble in a fluidized bed is considered in the low Reynolds number limit. The problem has been formulated as a generalized drop problem with one additional parameter. The analysis shows that the steady and unsteady deformations in the creeping flow limit are exactly the same as the conventional drop problem even though the flow fields are different. The effect of the additional parameter on deformation first appears when inertial effects are considered.

Coupled shape oscillations and translational motion of an incompressible gas bubble in a liquid container in response to forced vibration is studied numerically. Bond number (Bo) and the ratio of the vibration amplitude to the bubble diameter (A/D) are found to be the governing non-dimensional numbers. Bubble response is studied in both 2D and 3D. Different schemes are used for 2D and 3D simulations. In 2D, the flow solver is coupled to a Volume of Fluid (VOF) algorithm to capture the interface between the two phases while in 3D the interface is captured using a level set algorithm. The oscillation outcome ranges from small amplitude and regular oscillations for small Bo and A/D to large amplitude, nonlinear, and chaotic oscillations for large Bo and A/D. Chaotic behavior occurs due to the coupling between the nonlinear shape oscillations and large amplitude oscillatory translational motion. By further increase of the forcing, the inertia of the liquid results in the formation of a liquid jet which penetrates within the bubble core and pierces the bubble and a toroidal bubble shape is formed. The toroidal bubble shape then goes through large amplitude shape oscillations and smaller bubbles are formed. A summary of the 3D simulations provides a map which shows the bubble oscillation outcome as a function of Bo and A/D. The interaction between two bubbles is studied in 2D as well and the effect of vibration amplitude, frequency and liquid to gas density ratio on the interaction force is investigated.

The hydrodynamic phenomena occurring inside the enclosed downcomer section of a plunging jet bubble column are described in the study. The gas entrainment rate for a plunging liquid jet was found to consist of two components, namely the gas trapped within the effective jet diameter at the point of impact, and the gas contained within the film between the jet and induction trumpet surface at the point of rupture. Entrainment within the effective jet diameter has been examined by McCarthy (1972). In this study, a model was supported by the experimental results, provided the film attained a region of constant thickness. When the induction trumpet was ruptured prior to a constant film thickness being reached, the measured rate of filmwise entrainment was higher than the prediction. Filmwise entrainment was found to be initiated once a critical velocity along the surface of the induction trumpet was reached. The critical velocity was a function only of the liquid physical properties and was independent of the jet conditions and downcomer diameter. The velocity of the free surface of the induction trumpet was obtained from the velocity profile for the recirculating eddy generated by the confined plunging liquid jet. The jet angle used to describe the expansion of the submerged jet inside the downcomer was predicted from the radial diffusion of jet momentum into the recirculation eddy. The model was able to predict the jet angle when it was assumed that the radial diffusion of jet momentum was a function of the Euler number based on the jet velocity and absolute pressure in the headspace at the top of the downcomer. The model was also developed to predict the maximum stable bubble diameter generated within the submerged jet volume, where the energy dissipation attributed to bubble breakup was given by the energy mixing loss derived for the throat section of a liquid-jet-gas-pump. Good agreement was found between the measured and predicted maximum bubble diameter values. The average experimental Sauter mean/maximum diameter ratio was found to be 0.61, which was similar to that for other bubble generation devices. It was found that for turbulent liquid conditions in the uniform two-phase flow region, a transition from bubble to churn-turbulent flow occurred at a gas void fraction of approximately 0.2 when the gas drift-flux was zero. Under laminar liquid flow, this transition took place at a gas void fraction above 0.3. For the bubbly flow regime the Distribution parameter Co used by Zuber and Findlay (1965) to describe the velocity and gas void fraction profile, was found to be a function of the liquid Reynolds number. For laminar liquid flow, values of Co greater than unity were obtained. As the liquid Reynolds number was increased it was found that Co decreased, until a constant value of unity was obtained for fully turbulent flow. For the churn-turbulent regime it was found that the gas void fraction measurements for all of the experimental runs could be collapsed onto a single curve when a modified gas void fraction was plotted against the gas-to-liquid volumetric flow ratio. The modified gas void fraction included a correction factor to account for the difference in the bubble slip velocity between the experimental runs. The experimental results also indicated that the value of the constant in the gas void fraction correction factor was different for laminar and turbulent flow. Prior to bubble coalescence, it was found that the experimental drift-flux curves could be predicted from the measured bubble diameter, using the separated flow model development by Ishii and Zuber (1979). After the onset of coalescence the drift flux measurements departed from the original drift-flux curves at a rate which increased linearly with increasing gas void fraction. It was found that the slope of the line fitted to the coalesced region of the drift-flux curves increased with increasing liquid Reynolds number and reached a constant value under fully turbulent flow conditions. The model developed, together with the implications of the experimental results, are discussed with regard to optimising the design of an industrial plunging jet bubble column.
PhD Doctorate

The hydrodynamic phenomena occurring inside the enclosed downcomer section of a plunging jet bubble column are described in the study. The gas entrainment rate for a plunging liquid jet was found to consist of two components, namely the gas trapped within the effective jet diameter at the point of impact, and the gas contained within the film between the jet and induction trumpet surface at the point of rupture. Entrainment within the effective jet diameter has been examined by McCarthy (1972). In this study, a model was supported by the experimental results, provided the film attained a region of constant thickness. When the induction trumpet was ruptured prior to a constant film thickness being reached, the measured rate of filmwise entrainment was higher than the prediction. Filmwise entrainment was found to be initiated once a critical velocity along the surface of the induction trumpet was reached. The critical velocity was a function only of the liquid physical properties and was independent of the jet conditions and downcomer diameter. The velocity of the free surface of the induction trumpet was obtained from the velocity profile for the recirculating eddy generated by the confined plunging liquid jet. The jet angle used to describe the expansion of the submerged jet inside the downcomer was predicted from the radial diffusion of jet momentum into the recirculation eddy. The model was able to predict the jet angle when it was assumed that the radial diffusion of jet momentum was a function of the Euler number based on the jet velocity and absolute pressure in the headspace at the top of the downcomer. The model was also developed to predict the maximum stable bubble diameter generated within the submerged jet volume, where the energy dissipation attributed to bubble breakup was given by the energy mixing loss derived for the throat section of a liquid-jet-gas-pump. Good agreement was found between the measured and predicted maximum bubble diameter values. The average experimental Sauter mean/maximum diameter ratio was found to be 0.61, which was similar to that for other bubble generation devices. It was found that for turbulent liquid conditions in the uniform two-phase flow region, a transition from bubble to churn-turbulent flow occurred at a gas void fraction of approximately 0.2 when the gas drift-flux was zero. Under laminar liquid flow, this transition took place at a gas void fraction above 0.3. For the bubbly flow regime the Distribution parameter Co used by Zuber and Findlay (1965) to describe the velocity and gas void fraction profile, was found to be a function of the liquid Reynolds number. For laminar liquid flow, values of Co greater than unity were obtained. As the liquid Reynolds number was increased it was found that Co decreased, until a constant value of unity was obtained for fully turbulent flow. For the churn-turbulent regime it was found that the gas void fraction measurements for all of the experimental runs could be collapsed onto a single curve when a modified gas void fraction was plotted against the gas-to-liquid volumetric flow ratio. The modified gas void fraction included a correction factor to account for the difference in the bubble slip velocity between the experimental runs. The experimental results also indicated that the value of the constant in the gas void fraction correction factor was different for laminar and turbulent flow. Prior to bubble coalescence, it was found that the experimental drift-flux curves could be predicted from the measured bubble diameter, using the separated flow model development by Ishii and Zuber (1979). After the onset of coalescence the drift flux measurements departed from the original drift-flux curves at a rate which increased linearly with increasing gas void fraction. It was found that the slope of the line fitted to the coalesced region of the drift-flux curves increased with increasing liquid Reynolds number and reached a constant value under fully turbulent flow conditions. The model developed, together with the implications of the experimental results, are discussed with regard to optimising the design of an industrial plunging jet bubble column.
PhD Doctorate

Drop impact is a canonical problem in fluid mechanics, with numerous applications in industrial as well as natural phenomena. The extremely simple initial configuration of the experiment can produce a very large variety of fast and complex dynamics. Scientific progress was made in parallel with major improvements in imaging and computational technologies. Most recently, high-speed imaging video cameras have opened the exploration of new phenomena occurring at the micro-second scale, and parallel computing allowed realistic direct numerical simulations of drop impacts. We combine these tools to bring a new understanding of two fundamental aspects of drop impacts: splashing and air entrapment. The early dynamics of a drop impacting on a liquid pool at high velocity produces an ejecta sheet, emerging horizontally in the neck between the drop and the pool. We show how the interaction of this thin liquid sheet with the air, the drop or the pool, can produce micro-droplets and bubble rings. Then we detail how the breakup of the air film stretched between the drop and the pool for lower impact velocities can produce a myriad of micro-bubbles.