Turbulence dispersion is a phenomenon of practical importance in many multiphase flow systems. It has a strong effect on the distribution of the dispersed phase. Physically, this phenomenon is a result of interactions between individual particles of the dispersed phase and the continuous phase turbulence eddies. In a Lagrangian simulation, a particle-eddy interaction sub-model can be introduced and the effect of turbulence dispersion is automatically accounted for during particle tracking. Nevertheless, tracking of particleturbulence interaction is extremely expensive for the small time steps required. For this reason, the Lagrangian method is restricted to small-scale dilute flow problems. In contrast, the Eulerian approach based on the continuum modeling of the dispersed phase is more efficient for densely laden flows. In the Eulerian frame, the effect of turbulence dispersion appears as a turbulent diffusion term in the scalar transport equations and the so-called turbulent dispersion force in the momentum equations. The former vanishes if the Favre (mass-weighted) averaged velocity is adopted for the transport equation system. The latter is actually the total account of the turbulence effect on the interfacial forces. In many cases, only the fluctuating effect of the drag force is important. Therefore, many models available in the literature only consider the drag contribution. A new, more general derivation of the FAD (Favre Averaged Drag) model in the multi-fluid modeling framework is presented and validated in this report.

The rise velocity of injected air phase from the injection point toward the vadose zone is a critical factor in in-situ air sparging operations. It has been reported in the literature that air injected into saturated gravel rises as discrete air bubbles in bubbly flow of air phase. The objective of this study is to develop a quantitative technique to estimate the rise velocity of an air bubble in coarse porous media. The model is based on the macroscopic balance equation for forces acting on a bubble rising in a porous medium. The governing equation incorporates inertial force, added mass force, buoyant force, surface tension and drag force that results from the momentum transfer between the phases. The momentum transfer terms take into account the viscous as well as the kinetic energy losses at high velocities. Analytical solutions are obtained for steady, quasi-steady, and accelerated bubble rise velocities. Results show that air bubbles moving up through a porous medium equilibrate after a short travel time and very iv short distances of rise. It is determined that the terminal rise velocity of a single air bubble in an otherwise water saturated porous medium cannot exceed 18.5 cm/sec. The theoretical model results compared favorably with the experimental data reported in the literature. A dimensional analysis conducted to study the effect of individual forces indicates that the buoyant force is largely balanced by the drag force for bubbles with an equivalent radius of 0.2-0.5 cm. With increasing bubble radius, the dimensionless number representing the effect of the surface tension force decreases rapidly. Since the total inertial force is quite small, the accelerated bubble rise velocity can be approximated by the terminal velocity.

In this study, the phenomenon of two-phase flow was investigated in a square channel. The experiment was performed with stagnant liquid conditions. The gas and liquid dynamics of the bubbly flow were observed in two regions far from the inlet. Air was inserted through a porous media at three superficial gas velocities: 4.6 mm/s, 2.5 mm/s, and 1.4 mm/s. Two techniques were applied in the experiment to measure the bubbly flow: an optical probe and an in-house developed tracking algorithm. Measurements of the bubble interface velocity, void fraction, bubble frequency, time of flight, and Sauter mean diameter were obtained by using the optical probe. The duration of the probe measurements for all three flow rates and both regions lasted approximately 33 hours. The tracking algorithm was used to analyze the experimental data for two visual methods: shadowgraphy and Particle Tracking Velocimetry (PTV). Shadowgraphy provided gas-phase measurements of the bubble centroid velocity and its fluctuations, void fraction, bubble size, and Reynolds stresses. Five data sets were acquired for each flow rate, resulting in a total of 327,540 shadowgraphy images. Liquid parameters such as the velocity, fluctuations in the velocity, and the Reynolds stresses were provided by PTV. Only one data set containing 10,918 images was obtained from liquid measurements for each flow rate. One data set was sufficient to provide reliable statistics since tracking two consecutive images lead to approximately 15,000 velocity vectors. The data obtained from this study was an effort to assist in the verification, validation, and improvement of two-phase flow simulations.

Les réacteurs chimiques impliquant une phase liquide et une phase gazeuse sont couramment utilisés dans l'industrie pétrochimique et biologique car les écoulements à bulles ont de très bonnes propriétés de transfert et de mélange. Cela permet de mêler intimement différents composés et d'optimiser les réactions chimiques. Néanmoins, les mécanismes et les phénomènes mis en jeu dans le mélange au sein d'un écoulement à bulles restent encore mal connus. Ce travail a donc consisté à identifier les différents mécanismes de mélange en écoulement à bulles pour réviser le modèle physique de transport des espèces chimiques. Afin de distinguer et séparer les différents mécanismes, le mélange d'un traceur passif a été étudié dans différentes configurations expérimentales. Premièrement, l'étude du mélange dans un écoulement à bulles fortement confiné dans une cellule de Hele-Shaw a permis de mettre en évidence le mélange par capture du traceur dans les sillages. Ce mécanisme de mélange, fortement intermittent et convectif, s'est révélé être incompatible avec un processus purement diffusif. Deuxièmement, l'étude du mélange dans un essaim de bulles homogène tridimensionnel a été entreprise. Au contraire du cas confiné, le mélange, qui est causé par l'agitation induite par les bulles dans le liquide, est bien de nature diffusive. Nous avons donc pu mesurer les coefficients de diffusion effectifs en fonction de la fraction volumique de gaz. Ces coefficients sont différents dans les directions verticale et horizontale, ce qui traduit le caractère anisotrope du mélange. De plus, ils deviennent constants au-delà d'une certaine valeur de fraction volumique. Pour finir, nous avons considéré le mélange dans un essaim inhomogène de bulles, où se développe une boucle de recirculation du liquide. Dans le cas d'une recirculation modérée, la dispersion du traceur peut être estimée en combinant le mélange résultant de l'agitation des bulles avec l'advection par le mouvement moyen du fluide. / Bubble columns are commonly used for chemical processes because of their good mixing and transfer capabilities. This work aims at understanding and modelling the mixing induced by bubbles. In order to distinguish the differents mixing mechanisms, the dispersion of a low-diffusive scalar has been investigated in various experimental configurations. The first one is a bubbly flow in a Hele-Shaw cell where the confinement prevents from the developpement of turbulence. In this case, the mixing is controlled by the capture and the transport by the bubble wakes. This mechanism, which cannot be described by an effective diffusivity, has been modelled by considering the intermittent transport of finite volumes of dye. The second configuration is a homogeneous swarm of rising bubbles where the mixing results from the dispersion by the bubble-induced turbulence. It can therefore be modelled by an anistropic effective diffusivity, which becomes independent of the gas volume fraction beyond a certain value. Finally, an inhomogenous bubbly flow, where a liquid recirculation loop is present, has been considered. In the case of a moderate inhomogeneity, shear induced-turbulence is not generated by the gradients of the mean flow and the mixing can be modelled by the sum of the bubble-induced dispersion and the advection by the mean flow.

This thesis presents two important contributions to the modeling of entrainment of air bubbles in water, with focus on ship hydrodynamics applications. The first contribution consists of a general framework for modeling turbulent air entrainment. The framework attempts to describe the evolution of bubbles from their formation at the free surface, size distribution changes due to breakup and coalescence, and rise due to buoyancy. This proposed framework describes the complex entrainment process as a series of simpler mechanisms which can be modeled independently. For each mechanism a simple but mechanistic model is developed to provide closure while leaving the door open for future improvements. These unique characteristics enable the entrainment model to be used in general problems while still producing results at least as good as the few other available models. The massive entrainment of air that takes place around a ship leads to very high void fractions and accumulation of bubbles against the hull, particularly underneath the flat regions of the hull and in low pressure regions near appendages. These processes also pose challenges for two phase solvers. As a second contribution in this thesis, numerical algorithms for two phase flows are developed to eliminate the numerical instabilities normally occurring at high void fractions or large void fraction gradients. A hybrid method to improve pressure-velocity coupling for collocated grids is introduced, which keeps advantages typical of staggered grids in mass conservation and face flux computations. A new two phase coupling strategy is developed to guarantee stability at high void fraction. The balanced force method is extended to general curvilinear grids to suppress spurious velocities. The overall methodology provides strong coupling among pressure, velocity and void fraction, while avoiding numerical instability, and works for free-surface flows on dynamic overset grids. The proposed numerical schemes are tested for 1D and 2D cases. It is shown that the two phase solver is stable and efficient, even under extreme cases. Good mass conservation properties for multigroup simulations are also demonstrated. The air entrainment model is tested for a 2D wave breaking case and compared with extensive experimental data. The results show good predictions for entrainment location and two-phase properties. Full scale simulations for Athena R/V are performed using the same modeling constants obtained for the 2D wave breaking case. A grid study is also carried out to evaluate grid convergence properties of the model. While the model can predict well experimental data at full scale for the ship, it also shows dramatic improvements respect to previous entrainment models by converging in grid and not needing to re-evaluate the model constants for each new application. The high-speed Kann boat is also simulated at full scale, showing encouraging results for a preliminary entrainment model for aeration due to impact. The proposed numerical schemes are proved stable and robust in high Reynolds number flows with complex relevant geometries. In addition, these full scale simulations also identify modeling and numerical issues for future improvements.

To simulate dispersed two-phase flows CFD tools for predicting the local particle number density and the size distribution are required. These quantities do not only have a significant effect on rates of mixing, heterogeneous chemical reaction rates or interfacial heat and mass transfers, but also a direct relevance to the hydrodynamics of the total system, such as the flow pattern and flow regime. The Multiple Size Group (MUSIG) model available in the commercial codes CFX-4 and CFX-5 was developed for this purpose. Mathematically, this model is based on the population balance method and the two-fluid modeling approach. The dispersed phase is divided into N size classes. In order to reduce the computational cost, all size groups are assumed to share the same velocity field. This model allows to use a sufficient number of particle size groups required for the coalescence and breakup calculation. Nevertheless, the assumption also restricts its applicability to homogeneous dispersed flows. We refer to the CFX MUSIG model mentioned above as the homogeneous model, which fails to predict the correct phase distribution when heterogeneous particle motion becomes important. In many flows the non-drag forces play an essential role with respect to the bubble motion. Especially, the lift force acting on large deformed bubbles, which is dominated by the asymmetrical wake, has a direction opposite to the shear induced lift force on a small bubble. This bubble separation cannot be predicted by the homogeneous MUSIG model. In order to overcome this shortcoming we developed an efficient inhomogeneous MUSIG model in cooperation with ANSYS CFX. A novel multiple velocity multiple size group model, which incorporates the population balance equation into the multi-fluid modeling framework, was proposed. The validation of this new model is discussed in this report.

Turbulence dispersion is a phenomenon of practical importance in many multiphase flow systems. It has a strong effect on the distribution of the dispersed phase. Physically, this phenomenon is a result of interactions between individual particles of the dispersed phase and the continuous phase turbulence eddies. In a Lagrangian simulation, a particle-eddy interaction sub-model can be introduced and the effect of turbulence dispersion is automatically accounted for during particle tracking. Nevertheless, tracking of particleturbulence interaction is extremely expensive for the small time steps required. For this reason, the Lagrangian method is restricted to small-scale dilute flow problems. In contrast, the Eulerian approach based on the continuum modeling of the dispersed phase is more efficient for densely laden flows. In the Eulerian frame, the effect of turbulence dispersion appears as a turbulent diffusion term in the scalar transport equations and the so-called turbulent dispersion force in the momentum equations. The former vanishes if the Favre (mass-weighted) averaged velocity is adopted for the transport equation system. The latter is actually the total account of the turbulence effect on the interfacial forces. In many cases, only the fluctuating effect of the drag force is important. Therefore, many models available in the literature only consider the drag contribution. A new, more general derivation of the FAD (Favre Averaged Drag) model in the multi-fluid modeling framework is presented and validated in this report.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第18590号 / 工博第3951号 / 新制||工||1607(附属図書館) / 31490 / 京都大学大学院工学研究科原子核工学専攻 / (主査)教授 功刀 資彰, 教授 中部 主敬, 准教授 横峯 健彦 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

An accurate measurement of bubbly flow has a significant value for understanding the bubble behavior, heat and energy transfer pattern in different engineering systems. It also helps to advance the theoretical model development in two-phase flow study. Due to the interaction between the gas and liquid phase, the flow patterns are complicated in recorded image data. The segmentation and reconstruction of overlapping bubbles in these images is a challenging task. This dissertation provides a complete set of image processing algorithms for bubbly flow measurement. The developed algorithm can deal with bubble overlapping issues and reconstruct bubble outline in 2D high speed images under a wide void fraction range. Key bubbly flow parameters such as void fraction, interfacial area concentration, bubble number density and velocity can be computed automatically after bubble segmentation. The time-averaged bubbly flow distributions are generated based on the extracted parameters for flow characteristic study. A 3D imaging system is developed for 3D bubble reconstruction. The proposed 3D reconstruction algorithm can restore the bubble shape in a time sequence for accurate flow visualization with minimum assumptions. The 3D reconstruction algorithm shows an error of less than 2% in volume measurement compared to the syringe reading. Finally, a new image synthesis framework called Bubble Generative Adversarial Networks (BubGAN) is proposed by combining the conventional image processing algorithm and deep learning technique. This framework aims to provide a generic benchmark tool for assessing the performance of the existed image processing algorithms with significant quality improvement in synthetic bubbly flow image generation. / Ph. D. / Bubbly flow phenomenon exists in a wide variety of systems, for example, nuclear reactor, heat exchanger, chemical bubble column and biological system. The accurate measurement of the bubble distribution can be helpful to understand the behaviors of these systems. Due to the complexity of the bubbly flow images, it is not practical to manually process and label these data for analysis. This dissertation developed a complete suite of image processing algorithms to process bubbly flow images. The proposed algorithms have the capability of segmenting 2D dense bubble images and reconstructing 3D bubble shape in coordinate with multiple camera systems. The bubbly flow patterns and characteristics are analyzed in this dissertation. Finally, a generic image processing benchmark tool called Bubble Generative Adversarial Networks (BubGAN) is proposed by combining the conventional image processing and deep learning techniques together. The BubGAN framework aims to bridge the gap between real bubbly images and synthetic images used for algorithm benchmark and algorithm.

En años recientes se han realizado esfuerzos para incrementar la compresión de los fenómenos asociados al flujo bifásico líquido - gas, para lo cual se han establecido modelos matemáticos que intentan reflejar el comprotamiento del flujo, como es el caso del modelo de los Dos Fluídos. Una causa de la complejidad que representa el modelado es la transferencia de masa, momento y energía entre fases debida a la interacción entre fases. Actualmente los modelos de cálculo empleados en CFD y en códigos termohidraúlicos confían en correlaciones experimentales altamente dependientes del régimen de flujo para determinar el área interfacial, sin embargo este procedimiento no refleja la naturaleza física y se presentan irregularidades en la zona de la interfase debidas a fenómenos de transporte no descritos por estos modelos. En este sentido se ha propuesto recientemente una teoría de transporte de area interfacial que parece ser una solución viable al problema de la obtención de ecuaciones constitutivas del area interfacial y con ella, el cierre del modelo. Esta ecuación consta de términos convectivos y temporales que pueden ser resueltos analíticamente, por otro lado contiene términos fuente y sumidero que representan la creación y destrucción de burbujas que aún no han sido completamente modelados; para la comprension de dichos términos es requerida información experimental, misma que este trabajo intenta generar mediante la obtención de una base de datos experimentales que aporten información útil para el modelado de sistemas bifásicos. Para la obtención de la base de datos fue necesario diseñar, construir e instrumentar una instalación experimental que permitiera la formación de flujos bifásicos agua-aire con velocidades superficiales de fase líquida y gas similares a las existentes en los actuales reactores nucleares. El sistema de formación de mezcla bifásica que se diseñó y construyó permite la obtención de varios regímenes de flujo, en su funcionamiento emplea medio / Méndez Díaz, S. (2008). Medida experimental de la concentración de área interfacial en flujos bifásicos finalmente dispersos y en transición [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/3301