Although the leading-order motion of waves is periodic - in other words backwards and forwards - many types of waves including those driven by gravity induce a mean flow as a higher-order effect. It is the induced mean flow of three types of gravity waves that this thesis examines: surface (part I), internal (part II) and interfacial gravity waves (part III). In particular, this thesis examines wave groups. Because they transport energy, momentum and other tracers, wave-induced mean flows have important consequences for climate, environment, air traffic, fisheries, offshore oil and other industries. In this thesis perturbation methods are used to develop a simplified understanding of the physics of the induced mean flow for each of these three types of gravity wave groups. Leading-order estimates of different transport quantities are developed. For surface gravity wave groups (part I), the induced mean flow consists of two compo- nents: the Stokes drift dominant near the surface and the Eulerian return flow acting in the opposite direction and dominant at depth. By considering subsequent orders in a separation of scales expansion and by comparing to the Fourier-space solutions of Longuet-Higgins and Stewart (1962), this thesis shows that the effects of frequency dis- persion can be ignored for deep-water waves with realistic bandwidths. An approximate depth scale is developed and validated above which the Stokes drift is dominant and below which the return flow wins: the transition depth. Results are extended to include the effects of finite depth and directional spreading. Internal gravity wave groups (part II) do not display Stokes drift, but a quantity analogous to Stokes transport for surface gravity waves can still be developed, termed the “divergent- flux induced flow” herein. The divergent-flux induced flow it itself a divergent flow and induces a response. In a three-dimensional geometry, the divergent-flux induced flow and the return flow form a balanced circulation in the horizontal plane with the former transporting fluid through the centre of the group and the latter acting in the opposite direction around the group. In a two-dimensional geometry, stratification inhibits a balanced circulation and a second type of waves are generated that travel far ahead and in the lee of the wave group. The results in the seminal work of Bretherton (1969b) are thus validated, explicit expressions for the response and return flow are developed and compared to numerical simulations in the two-dimensional case. Finally, for interfacial wave groups (part III) the induced mean flow is shown to behave analogously to the surface wave problem of part I. Exploring both pure interfacial waves in a channel with a closed lid and interacting surface and interfacial waves, expressions for the Stokes drift and return flow are found for different configurations with the mean set-up or set-down of the interface playing an important role.

[pt] A ocorrência do escoamento slug em tubulações horizontais é de especial interesse para a indústria de petróleo devido aos riscos operacionais indesejados associados a esse padrão de escoamento. Portanto, nas últimas décadas um intenso esforço foi dedicado ao estudo e modelagem do escoamento slug. Ferramentas preditivas baseadas na estabilidade linear de Kelvin-Helmhotz foram amplamente desenvolvidas na literatura para prever a transição para esse regime de escoamento. Esses modelos são derivados da análise de estabilidade modal de perturbações bem definidas. No entanto, para escoamento em tubulação, um número bastante limitado de estudos experimentais dedicados para investigação da evolução de perturbações que originem o regime slug está disponível. Além disso, estudos a partir da introdução de perturbações bem definidas, que podem fornecer informações precisas para validação de modelos e simulações numéricas, foram encontrados. O presente trabalho abordou o problema da transição para o regime slug a partir da caracterização da evolução de ondas interfaciais. Essas perturbações controladas foram excitadas com um modo de geração na interface do escoamento estratificado utilizando uma placa oscilatória. O trabalho se concentra na caracterização de ondas interfaciais no regime linear, que corresponde ao regime de estudo da maioria dos modelos disponíveis na literatura. Portanto, um limiar de amplitude para ondas lineares foi estimado experimentalmente. O acionamento da placa oscilatória foi sincronizado com as aquisições de imagens, permitindo medições sincronizadas em fase. As medições do campo de velocidade foram realizadas usando a técnica de Velocimetria de Imagem de Partículas (PIV) e Iluminação de Fundo (Shadowgraphy). O perfil de velocidade e turbulência do escoamento foram medidos simultaneamente nas fases do liquido e do gás. A sincronização em fase permitiu a extração do perfil de flutuação de velocidade coerentes as ondas interfaciais. Os resultados obtidos são originais e mostraram, pela primeira vez na literatura, que os modos interfaciais em ambas as fases são quase independentes dos modos cisalhantes, dentro da faixa de parâmetros abordados neste trabalho. A caracterização de ondas não lineares foi brevemente investigada, indicando mudanças no perfil do escoamento médio. Além disso, foi obtida uma correlação para o fator de atrito das ondas interfaciais, levando a uma melhoria na estimativa da altura do líquido e da perda de carga do tubo quando combinadas nas relações de fechamento dos modelos 1-D. A metodologia experimental proposta neste trabalho é uma ferramenta valiosa para produzir informações precisas que podem ser usadas para validar e aprimorar modelos teóricos e simulações numéricas. O estudo pode contribuir para a compreensão dos mecanismos físicos envolvidos na transição do escoamento estratificado para slug. / [en] The occurrence of slug regime in horizontal pipelines is of special interest for the oil and gas industry due to the unwanted operational risks associated with this flow. Hence, an intense effort has been devoted to the study and to model this flow regime. Predictive tools based on linear Kelvin-Helmhotz stability have been widely applied in the literature for prediction of slug onset. These models are derived from stability analysis of well-defined disturbances. However, for pipe flows, a limited number of experimental studies devoted to investigate the evolution of disturbances that lead to the initiation of slugs is available. In addition, no studies are found using of well define disturbances, which could provide accurate information for validation of models and numerical simulations. The present work addresses the problem by the studying of the evolution of controlled waves excited at the liquid interface. To this end, an oscillating paddle was employed. The work focuses the characterization of interfacial waves within the linear regime, which correspond to the regime of most models available in the literature. The amplitude threshold for linear waves was experimentally estimated. The driving signal of the oscillating paddle was synchronized with image acquisitions, enabling phase locked measurements of the waves and hence the use of ensemble averaging techniques. Phase-locked measurements of the velocity field in the liquid and gas layers were performed using off-axis Particle Image Velocimetry (PIV) technique and Shadowgraph. Mean flow, streamwise and wall normal fluctuations were measured simultaneously in the liquid and gas phases. For a range of flow rates and exciting wave frequencies the combined techniques employed allowed the extraction from the measured velocity fields, the coherent part of flow fluctuations related with the exciting waves. The results obtained have shown, seemingly, for the first time, that interfacial modes in both phases are nearly independent of near wall disturbances within the range of parameters covered in this work. Characterization of nonlinear waves was briefly investigated indicating changes in the mean velocity. Moreover, a correlation for wave friction factor based on wave and flow parameters was obtained, leading to an improvement on the liquid heightand pipe head loss estimation when are combined into the closure relations used for the 1-D models. The experimental methodology proposed in this work is a valuable tool to produce accurate information that can be used to validate and improve theoretical models and numerical simulations. It can contribute to the understanding of the physical mechanisms involved in the transition from stratified to slug flows.

Liquid metal batteries are discussed today as an economic grid-scale energy storage, as required for the deployment of fluctuating renewable energies. These batteries consist of three stably stratified liquid layers: two liquid metal electrodes are separated by a thin molten salt electrolyte, this way forming an electrochemical concentration cell. The completely liquid interior, which is on the one hand very beneficial for the energy efficiency, also poses some major challenges on the other hand. Strong cell currents in combination with electromagnetic fields make liquid metal batteries highly susceptible to various kinds of magnetohydrodynamic instabilities. In particular, the so-called metal pad roll instability, which can drive uncontrollable wave motions in both interfaces, was identified as a key limiting factor for the operational safety. The metal pad roll instability is well known from conceptually similar aluminum reduction cells, but still poorly understood in the framework of liquid metal batteries. Mainly by developing analytical wave models, but also by employing numerical simulations and by setting up a newly designed wave experiment, the present thesis pursues the goal of providing a better understanding of interfacial wave dynamics and the manifestation of the metal pad roll instability in liquid metal batteries. As a main result, a three-layer formulation of standing gravity-capillary waves reveals that the pressure coupling between the two interfaces plays a crucial role in the cell stability. Three different coupling regimes, which partially involve novel types of interfacial wave instabilities, are identified and classified by two dimensionless parameters. Building on this theoretical work, the wave experiment is exploited to further investigate different metal pad roll-related wave properties. The crucial importance of the contact line dynamics is emphasized and viscous damping, which is important for the estimation of instability onsets, is discussed as a function of the layer heights. Finally, a hybrid interfacial sloshing model is formulated and equipped with recently derived two-layer damping rates to account for viscous dissipation. The model allows to study and interpret the forced wave mechanics in the wave experiment as a function of eight dimensionless parameters and can, as an additional application, be exploited to optimize mixing in orbitally shaken bioreactors. As a further key result, the sloshing model reveals the formation of novel spiral wave patterns under the effect of strong damping.

[pt] No presente trabalho estudou-se numericamente a instabilidade das ondas na interface do escoamento estratificado de água e óleo em um canal plano. Esse padrão de escoamento, associado ao estágio inicial da formação de golfada, é comum em aplicações industriais, de áreas como produção de petróleo, nuclear, química e muitas outras. Através da introdução de perturbações controladas na interface do escoamento estratificado, analisou-se a evolução dessas perturbações à luz das teorias de estabilidade hidrodinâmica. Os experimentos numéricos foram realizados utilizando o método de Volume of Fluid (VOF) do simulador comercial ANSYS Fluent versão 15.0. Analisou-se o comportamento do escoamento em dois regimes distintos com relação a amplitude das ondas interfaciais. No primeiro regime, empregaram-se ondas pequenas o suficiente para que efeitos não lineares fossem desprezíveis. Os resultados obtidos apresentaram boa concordância com as previsões fornecidas por um solver das equações de Orr-Sommerfeld, para escoamento bifásico estratificado em um canal, indicando que a ferramenta numérica foi capaz de reproduzir o comportamento das ondas interfaciais. Mostrou-se que existe uma faixa de amplitudes, em torno de 0,2 porcento da altura do canal, a partir da qual os efeitos não lineares se tornam relevantes. No regime não linear foram avaliados diferentes cenários de interação não linear entre ondas, os quais geralmente são associados a transição do regime do escoamento estratificado para golfadas. Identificou-se o cenário mais relevante, analisando-se,a eficiência de cada uma dessas interações isoladamente. Observou-se que interações não lineares entre ondas de comprimento parecido são as que crescem mais rapidamente. Esse mecanismo parece ser dominante também na presença de um grande número de ondas, como é o caso esperado em um evento natural. Utilizou-se um modelo fracamente não linear, baseado nas equações de Stuart-Landau, para modelar o comportamento das ondas no escoamento, obtendo-se excelente concordância com os resultados das simulações. Isso é interessante do ponto de vista prático, pois sugere que modelos não lineares simples, como é o caso da equação de Stuart-Landau, podem ser implementados para melhorar as ferramentas utilizadas para prever mudanças de regime em escoamentos bifásicos. / [en] In the present work, the instability of waves at the interface of the stratified flow of water and oil in a plane channel was numerically studied. This flow pattern, which is associated with the initial stages of slug formation, is common in industrial application in areas such as oil production, nuclear, chemical and many others. Through the introduction of controlled perturbations at the interface of a stratified flow, the evolution of the perturbations was analyzed based on hydrodynamics stability theories. Numerical experiments were performed using the Volume of Fluid (VOF) method of the ANSYS Fluent release 15.0 commercial simulator. The behavior of the flow in two different regimes with respect to the amplitude of the interfacial waves was analyzed. In the first regime, small enough waves were employed so that non-linear effects were negligible. The results obtained presented good agreement with the predictions provided by a solver of the Orr-Sommerfeld equations for stratified two-phase flow in a channel, indicating that the numerical tool was able to reproduce the behavior of the interfacial waves. It was shown that there is a range of amplitudes, around 0.2 per cent of the channel height, above which the non-linear effects become relevant. In the nonlinear regime, different scenarios of nonlinear interaction between waves, which are usually associated with transition from stratified flow pattern to slug flow, were evaluated. The most relevant scenario was identified, based on the efficiency of each independent interaction. It was observed that non-linear interactions between waves of similar length present the fastest growth. This mechanism seems to be dominant also in the presence of a large number of waves, as present in natural events. A weakly nonlinear model, based on the Stuart- Landau equations, was employed to model the wave behavior in the flow, obtaining an excellent agreement with the results of the simulations. This is interesting from a practical point of view, since it suggests that simple nonlinear models, such as the Stuart-Landau equation, can be implemented to improve the tools used to predict regime changes in two-phase flows.

Tesis por compendio / [ES] El flujo anular es uno de los regímenes de flujo bifásico más importantes y se caracteriza por que una fracción de líquido muy pequeña conocida como película de líquido que viaja cerca de la pared y un núcleo gaseoso. El flujo anular se puede observar durante la operación de plantas nucleares y en diferentes escenarios transitorios, aunque también en muchas otras aplicaciones industriales. La película de líquido es determinante en muchas de ellas ya que posee una alta capacidad de transferencia de masa, momento y energía. Parte de estas propiedades se deben a que la película presenta un comportamiento interfacial no linear con desarrollo de ondas interfaciales. Además, en determinadas instalaciones donde se la película de líquido actúa como refrigerante, es esencial conocer su comportamiento tanto por motivos de optimización como por razones de seguridad. Para estudiar los fundamentos del comportamiento de la película de líquido se han llevado a cabo una serie de experimentos en una instalación diseñada para generar flujo anular aire-agua en tubería circular vertical. En esta instalación se ha medido la evolución temporal del espesor de la película de líquido bajo diferentes condiciones y subrégimenes, como flujo en caída libre o flujo en cocorriente ascendente y descendente. El sistema de medida empleado se ha diseñado y construido para esta aplicación y consiste en sondas de conductancia de 3 electrodos rasantes a la pared y dispuestas en diferentes partes de la sección de test. Tanto el sistema electrónico como el dispositivo de calibración se diseñaron específicamente para trabajar con estas son-das de conductancia. La instalación cuenta con dos diámetros diferentes para poder comparar también el efecto del diámetro de la tubería así como aumentar el rango de medidas disponibles en bases de datos. Una de las características más particulares de la película de líquido son sus ondas interfaciales. Las principales ondas que se pueden diferenciar son las disturbance waves, ondas coherentes de gran calibre; y las ripple waves, ondas de pequeño tamaño, no coherentes que se generan constantemente antes de desaparecer al ser absorbidas por otras ondas. Las variables principales de la película de líquido que se han analizado en la instalación experimental son el espesor medio, la altura y frecuencia de las disturbance waves, la altura de las ripple waves y la altura de líquido no perturbado. Se han lleva-do a cabo diferentes estudios experimentales con objeto de añadir un valor adicional a las medidas. Para flujo anular descendente se ha estudiado el desarrollo de la película a través de diferentes zonas de medida y se han comparado las secciones de test de diferente diámetro. Además, múltiples correlaciones se han propuesto y los resultados se han comparado con estudios similares de otros autores. Para el análisis del flujo anular ascendente, se ha añadido un estudio del efecto de la tensión superficial en las variables de la película de líquido mediante la adición de pequeñas cantidades de 1-butanol. Es objeto de esta tesis también la modelación del flujo anular mediante análisis numérico. Los códigos de fluidodinámica computacional (CFD) son herramientas computacionales que permiten analizar el comportamiento de los fluidos. Han experimentado una fuerte evolución a lo largo de los últimos años gracias a los avances tecnológicos y los resultados que se obtienen de su correcta utilización son muy prometedores. No obstante, el flujo multifásico sigue siendo difícil de modelar y es necesario contrastar las predicciones de los códigos CFD con medidas experimentales. Por lo tanto, la fenomenología de flujo anular desarrollado se ha estudiado también mediante el código ANSYS CFX. Existe un importante vacío de conocimiento en la cuantificación de la incertidumbre (UQ) de dichos códigos CFD. Esta tesis también presenta los fundamentos del método UQ Polynomial Chaos Expansion (PCE) aplicado a dos casos prácticos. / [CA] El flux anular és un dels règims de flux bifàsic més importants i es caracteritza perquè la fracció de líquid és molt xicoteta coneguda com a pel·lícula de líquid. El flux anul·lar es pot observar durant l'operació de plantes nuclears i en diferents escenaris transitoris, encara que també en moltes altres aplicacions industrials. La pel·lícula de líquid és determinant en moltes d'elles ja que posseeix una alta capacitat de transferència de massa, moment i energia. Part d'aquestes propietats es deuen al fet que la pel·lícula presenta un comportament interfacial no linear amb desenvolupament d'ones interfacials. A més, en determinades instal·lacions on li la pel·lícula de líquid actua com a refrigerant, és essencial conéixer el seu comportament tant per motius d'optimització com per raons de seguretat. Per a estudiar els fonaments del comportament de la pel·lícula de líquid s'han dut a terme una sèrie d'experiments en una instal·lació dissenyada per a generar flux anular aïre-aigua en canonada circular vertical. En aquesta instal·lació s'ha mesurat l'evolució temporal de la grossària de la pel·lícula de líquid sota diferents condicions i subrégimenes, com a flux en caiguda lliure o flux en cocorriente ascendent i descendent. El sistema de mesura emprat s'ha dissenyat i construït per a aquesta aplicació i consisteix en sondes de conductància de 3 elèctrodes i disposades en diferents parts de la secció de test. Tant el sistema electrònic com el dispositiu de calibratge es van dissenyar específicament per a treballar amb aquestes sondes de conductància. La instal·lació compta amb dos diàmetres diferents per a poder comparar també l'efecte del diàmetre de la canonada així com augmentar el rang de mesures disponibles en bases de dades. Una de les característiques més particulars de la pel·lícula de líquid són les seues ones interfacials. Les principals ones que es poden diferenciar són les disturbance waves, ones coherents de gran calibre; i les ripple waves, ones de xicoteta grandària, no coherents que es generen constantment abans de desaparéixer en ser absorbides per altres ones. Les variables principals de la pel·lícula de líquid que s'han analitzat en la instal·lació experimental són la grossària mitjana, l'altura i freqüència de les disturbance waves, l'altura de les ripple waves i l'altura de líquid no pertorbat. S'han dut a terme diferents estudis experimentals a fi d'afegir un valor addicional a les mesures. Per a flux anul·lar descendent s'ha estudiat el desenvolupament de la pel·lícula a través de diferents zones de mesura i s'han comparat els diferents diàmetres. A més, múltiples correlacions s'han proposat i els resultats s'han comparat amb estudis similars d'altres autors. Per a l'anàlisi del flux anul·lar ascendent, s'ha afegit un estudi de l'efecte de la tensió superficial en les variables de la pel·lícula de líquid mitjançant l'addició de xicotetes quantitats de 1-butanol. És objecte d'aquesta tesi també el modelatge del flux anul·lar mitjançant anàlisi numèrica. Els codis de fluidodinámica computacional (CFD) són eines computacionals que permeten analitzar el comportament dels fluids. Han experimentat una forta evolució al llarg dels últims anys gràcies als avanços tecnològics i els resultats que s'obtenen de la seua correcta utilització són molt prometedors. No obstant això, el flux multifásico continua sent difícil de modelar i és necessari contrastar les prediccions dels codis CFD amb mesures experimentals. Per tant, la fenomenologia de flux anular desenvolupat s'ha estudiat també mitjançant el codi ANSYS CFX. Existeix un important buit de conei-xement en la quantificació de la incertesa d'aquests codis CFD. En aquesta tesi es mostren els fonaments del Polynomial Chaos Expansion (PCE) com a mètode per a calcular la incertesa dels resultats de simulació mitjançant propagació. El PCE per quadratura de Gauss-Hermite s'ha aplicat a les simulacions de dos experiments. / [EN] Annular flow is one of the most important two-phase flow regimes and is characterized by a very small liquid fraction known as a liquid film travelling close to the wall and a gas core. Annular flow can be observed during the operation of nuclear plants, in different transient scenarios, and many other industrial applications. The liquid film is decisive in many of them as it has a high mass, momentum and energy transfer capacity. Many of these properties are due to the film exhibiting nonlinear interfacial behavior with the generation of interfacial waves. In addition, in certain facilities where the liquid film acts as a coolant, it is essential to know its behavior both for optimization and safety reasons. In order to study the fundamentals of the liquid film, a series of experiments have been carried out in a facility designed to generate air-water annual flow in a vertical circular pipe. In this facility, the time evolution of the liquid film thickness has been measured under different conditions and sub-regimes, such as free-fall flow or upward and downward cocurrent flow. The measurement system used has been designed and built for this application and consists of 3-electrode conductance probes mounted flush to the wall and arranged at different distances from the entrance of the test section. Both the electronics and the calibration device were specifically designed to work with these conductance probes. The facility has two different diameters to compare the effect of the pipe diameter and increase the range of measurements available in databases. One of the main characteristics of the liquid film is its interfacial waves. The two primary types of waves that can be distinguished are the disturbance waves, which are large coherent waves, and the ripple waves, small, non-coherent waves that are constantly generated before disappearing when absorbed by other waves. The main variables of the liquid film analyzed in the experimental setup are the mean film thickness, the height and frequency of the disturbance waves, the height of the ripple waves and the height of the unperturbed liquid. Different experimental studies have been carried out to add additional value to the measurements. For downward annular flow, the development of the film through different measuring zones has been studied, and the different test section diameters have been compared. In addition, multiple correlations have been proposed, and the results have been compared with similar studies by other authors. To analyze the upward annular flow, a study of the effect of surface tension on the liquid film variables by adding small amounts of 1-butanol has been added. The modelling of annular flow by numerical analysis is also the subject of this thesis. Computational Fluid Dynamics (CFD) codes are computational tools that allow the analysis of fluid behavior. They have undergone a strong evolution over the last few years thanks to technological advances, and the results obtained from their correct use are very promising. However, multiphase flow remains challenging to model, and it is necessary to contrast the predictions of CFD codes with experimental measurements. Therefore, the developed annular flow phenomenology has also been studied using the ANSYS CFX code. There is a significant knowledge gap in the uncertainty quantification of CFD codes. Some methodologies are available, although many are in the early stages or have not been explored by researchers. All applications of CFD codes in nuclear safety require extensive knowledge of the uncertainty of the predictions, so developing these methodologies is crucial. This thesis shows the fundamentals of Polynomial Chaos Expansion (PCE) as a method to calculate the uncertainty of simulation results by propagation. The PCE by Gauss-Hermite quadrature has also been applied to the simulations of two experiments: the experimental setup of this thesis, and an international benchmark. / I would like to acknowledge the support provided by the Ministerio de Economía, Industria y Competitividad and the Agencia Nacional de Investigación under the FPI grant BES-2017-080031, which provided funding for my research. / Rivera Durán, Y. (2023). Experimental and Modelling Study of Interfacial Phenomena in Annular Flow with Uncertainty Quantification [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/194606 / Compendio