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.

Una nueva aproximación euleriana-lagarangiana, en su forma de acople en dos vías, para la simulación de flujo de burbujas, agua-aire es presentada en la tesis, en la que se incluyen los efectos de las colisiones entre burbujas, así como las posibles roturas o coalescencia de burbujas. Esta aproximación utiliza el modelo Continuous Random Walk, CRW, para tener en cuenta las fluctuaciones de la velocidad. Esta aproximación se enmarca dentro de un modelo de turbulencia k-epsilon para la fase continua del líquido. En esta tesis se estudiarán los métodos para realizar el acople entre ambas aproximaciones, el efecto de la fuerza lift y de la dispersión turbulenta sobre la distribución de la fracción de huecos, así como los modelos de coalescencia y rotura de burbujas que puedan ser empleados en este tipo de aproximación. Se ha partido de un código euleriano para simular la parte continua, y sobre él se ha acoplado la aproximación lagrangiana. Para que ese acople afecte a la fase continua sobre su solver ser han añadido fuentes de momento y turbulencia. Además se ha modificado el volumen computacional de cada celda para que tenga en consideración el volumen ocupado por la fase dispersa. El acople en doble vía hace que los perfiles de velocidad y turbulencia de la fase continua se modifiquen notablemente y que se aproximen a los reales, lo que resulta básico para la correcta simulación de las fuerzas interfaciales. La colisión entre burbujas, y burbujas y pared se ha incluido. Este efecto es necesario como paso previo a incluir los procesos de rotura o coalescencia de burbujas, aunque la colisión en sí tenga efectos limitados en la distribución de la fracción de huecos. El proceso de coalescencia se basa en el modelo de Chester ( 1991 ) , el modelo compara el tiempo de colisión con el tiempo de drenaje de la película entre burbujas para determinar si existe o no coalescencia. El modelo de rotura se basa en el modelo de Martínez-Bazán. Uno de los principales hitos de / Ali Abd El Aziz Essa ., M. (2012). COUPLED LAGRANGE-EULER MODEL FOR SIMULATION OF BUBBLY FLOW IN VERTICAL PIPES CONSIDERING TURBULENT 3D RANDOM WALKS MODELS AND BUBBLES INTERACTION EFFECTS [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/18068 / Palancia

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.

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 no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/3301 / Palancia

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.

[EN] The present PhD thesis aims at the development of a one-dimensional solver capable of solving single- and two-phase flow fluid systems. The novelty of this project lies in the use of an open source CFD platform, called OpenFOAM, as a development framework for the new tool. For the new solver development, the conservation equations based on Navier- Stokes (three-dimensional system) have been analyzed and reduced to one dimension. For the two-phase simulations, the Two Fluid Model method was used as base. In addition, a series of empirical models have been selected as closing equations of the system. The final solver includes a series of requirements that reinforce their capabilities. Among them, the use of a second mesh that represents the solid and takes into account the heat transmitted to the fluid by conduction through a solid, stands out. On the other hand, the possible transfer of mass between phases in twophase fluids has been taken into account. Similarly, a subcooled boiling model has been implemented which takes into account the possible generation of vapor near the wall while the bulk is kept below saturation temperature. Finally, this paper presents the verification and validation of the solver. The verification has been carried out mainly with the system code TRACE, whose validation has been demonstrated in numerous works and its use is very extended in the scientific community. For the validation, we have the results of two experimental cases that allow us to demonstrate the physical validity of the new application developed. The use of this platform allows for a much more direct coupling between one- and three-dimensional domains, obtaining a better optimization of the calculation. / [ES] El presente trabajo de doctorado tiene por objetivo el desarrollo de un solver unidimensional capaz de resolver sistemas de fluidos monofásicos y bifásicos. La novedad de este proyecto reside en el uso de una plataforma CFD de código abierto, llamada OpenFOAM, como marco para el desarrollo de la nueva herramienta. Para el desarrollo del nuevo solver, se han analizado las ecuaciones de conservación basadas en Navier-Stokes (tridimensionales) y se han reducido a una dimensión. Para la parte bifásica del solver, se utiliza el método Two Fluid Model. Además, se han incluido todos los modelos empíricos necesarios como ecuaciones de cierre del sistema. El solver final incluye una serie de requerimientos que refuerzan sus capacidades. Entre ellas, destacan, por un lado, el uso de una segunda malla que represente el sólido y tenga en cuenta el calor transmitido al fluido por conducción a través de un sólido. Por otro lado, se ha tenido en cuenta la posible transferencia de masa entre fases en fluidos bifásicos. Igualmente, se ha implementado un modelo de ebullición subenfriada que tiene en cuenta la posible generación de vapor cerca de la pared mientras el centro del fluido se mantiene por debajo de la temperatura de saturación. Finalmente, este trabajo presenta la verificación y validación del solver. La verificación se ha realizado principalmente con el código de sistema TRACE. Para la validación, se cuenta con los resultados de dos casos experimentales que permiten demostrar la validez física de la nueva aplicación desarrollada. La implementación del nuevo solver en esta plataforma abierta permite un futuro acoplamiento mucho más directo entre mallas unidimensionales y tridimensionales, obteniendo una mayor optimización del cálculo. / [CA] El present treball de doctorat té per objectiu el desenvolupament d'un nou solver unidimensional capaç de solucionar sistemes amb fluids monofàsics i bifàsics. La novetat d'aquest projecte resideix en l'ús d'una plataforma CFD de codi obert, anomenada OpenFOAM com a marc de desenvolupament de la nova eina. Per al desenvolupament del nou solver, s'han analitzat les equacions de conservació basades en Navier-Stokes (tridimensionals) i s'han reduït a una dimensió. Per a la part bifàsica del solver s'utilitza el mètode Two Fluid Model. A més, s'han inclòs tots els models empírics necessaris com a equacions de tancament del sistema. El solver final inclou una sèrie de requeriments que reforcen les seues capacitats. Entre elles, destaquen, d'una banda, l'ús d'una segona malla que represente el sòlid i es tinga en compte la calor transmesa al fluid per conducció a través d'un sòlid. D'altra banda, s'ha tingut en compte la possible transferència de massa entre fases en fluids bifàsics. Igualment, s'ha implementat un model d'ebullició subrefredada que té en compte la possible generació de vapor prop de la paret mentre el centre del fluid es manté per davall de la temperatura de saturació. Finalment, aquest treball presenta la verificació i validació del solver. La verificació s'ha realitzat principalment amb el codi de sistema TRACE, la validació del qual s'ha demostrat en nombrosos treballs i el seu ús està molt estés en la comunitat científica. Per a la validació, es compta amb els resultats de dos casos experimentals que permeten demostrar la validesa física de la nova aplicació desenvolupada. L'ús d'esta plataforma permiteix un futur acoblament més directe, entre elements unidimensionals i tridimensionals, obtenint una major optimització del càlcul. / Gómez-Zarzuela Quel, C. (2020). Development and assessment of a one-dimensional CFD solver for boiling flows in bubbly regimes [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/148368 / TESIS