Bubbly and Buoyant Particle-Laden Turbulent Flows

Fluid turbulence is commonly associated with stronger drag, greater heat transfer, and more efficient mixing than in laminar flows. In many natural and industrial settings, turbulent liquid flows contain suspensions of dispersed bubbles and light particles. Recently, much attention has been devoted to understanding the behavior and underlying physics of such flows by use of both experiments and high-resolution direct numerical simulations. This review summarizes our present understanding of various phenomenological aspects of bubbly and buoyant particle-laden turbulent flows. We begin by discussing different dynamical regimes, including those of crossing trajectories and wake-induced oscillations of rising particles, and regimes in which bubbles and particles preferentially accumulate near walls or within vortical structures. We then address how certain paradigmatic turbulent flows, such as homogeneous isotropic turbulence, channel flow, Taylor-Couette turbulence, and thermally driven turbulence, are modified by the presence of these dispersed bubbles and buoyant particles. We end with a list of summary points and future research questions.Comment: 29 pages, 14 figure

Microbubbly drag reduction in Taylor-Couette flow in the wavy vortex regime

We investigate the effect of microbubbles on Taylor-Couette flow by means of direct numerical simulations. We employ an Eulerian-Lagrangian approach with a gas-fluid coupling based on the point-force approximation. Added mass, drag, lift, and gravity are taken into account in the modeling of the motion of the individual bubble. We find that very dilute suspensions of small non-deformable bubbles (volume void fraction below 1%, zero Weber number and bubble Reynolds number <10) induce a robust statistically steady drag reduction (up to 20%) in the so called wavy vortex flow regime (Re = 600-2500). The Reynolds number dependence of the normalized torque (the so-called Torque Reduction Ratio (TRR) which corresponds to the drag reduction) is consistent with a recent series of experimental measurements performed by Murai et al. (J. Phys. 14, 143 (2005)). Our analysis suggests that the physical mechanism for the torque reduction in this regime is due to the local axial forcing, induced by rising bubbles, that is able to break the highly dissipative Taylor wavy vortices in the system. We finally show that the lift force acting on the bubble is crucial in this process. When neglecting it, the bubbles preferentially accumulate near the inner cylinder and the bulk flow is less efficiently modified.Comment: 21 pages, 13 figures, extended and revised versio

Direct Numerical Simulations of Flows with Phase Change

AbstractDirect Numerical Simulations (DNS) of multiphase flows, where every continuum length and time scale are fully resolved, currently allow us to simulate flows of considerable complexity, such as the motion of several hundred bubbles or drops in turbulent flows, for sufficiently long time so that meaningful statistical quantities can be obtained. Additional physical processes such as heat transfer and phase change have also been included, although only for relatively small systems so far. After reviewing briefly recent studies of bubbles in turbulent channel flows, we discuss simulations of flows with phase change, focusing on bubble generation by boiling. The addition of new physics often results in new length and time scales that are shorter and faster than the dominant flow scales. Similarly, very small features such as thin films, filaments, and drops can also arise during coalescence and breakup of fluid blobs. The geometry of these features is usually simple, since surface tension effects are strong and inertia effects are relatively small and in isolation these features are often well described by analytical or semi-analytical models. Recent efforts to embed analytical and semi-analytical models to capture such features, in combination with direct numerical simulations of the rest of the flow, are discussed. We conclude by a short discussion of the use of DNS data for closure laws for model equations for the large scale flow

Numerical Analysis and Modelling of Liquid Turbulence in Bubble Columns at Various Scales by Computational Fluid Dynamics

Diese Doktorarbeit beschäftigt sich mit der Entwicklung verbesserter statistischer Modelle für die Blasen-induzierte Turbulenz (Pseudo-Turbulenz). Es wird eine Skalen-übergreifende Herangehensweise gewählt, die sowohl Direkte Numerische Simulationen (DNS) als auch Euler Euler (E-E) Simulationen umfasst. Die dabei betrachteten Skalen umfassen Einzelblasen und Blasenschwärme sowie Blasensäulen im Labor- und Pilotmaßstab. Die Simulationsergebnisse werden jeweils anhand von Experimenten und Korrelationen verifiziert. Die Anwendbarkeit von Modellen für die ingenieurtechnische Berechnung von einem industriellen Blasensäulenreaktor auf Basis von numerischen Strömungssimulationen mit dem E-E Ansatz (Zwei-Fluid-Modell) wird nachgewiesen. Zur Modellentwicklung werden umfangreiche DNS Berechnungen für Blasen-schwärme durchgeführt. Hierfür wird das am KIT entwickelte Rechenprogramm TURBIT-VOF verwendet und ein Teilgebiet einer flachen Blasensäule betrachtet. Mittels der DNS-Daten wird die Transportgleichung der turbulenten kinetischen Energie (TKE) der Flüssigphase ($\textit{k}_{L}$) analysiert, die den Grundstein der ingenieurtechnischen Turbulenz-modellierung darstellt. Es zeigt sich, dass der dominierende Quellterm auf Grenzflächeneffekte zurückzuführen ist, während die Produktion aufgrund von Scherspannungen für die betrachteten Bedingungen gering ist. Produktions- und Dissipationsterm sind nicht im lokalen Gleichgewicht. Der Überschuss der Produktion von $\textit{k}_{L}$ in Bereichen mit hohem lokalem Gasgehalt wird durch Diffusion in Bereiche mit geringem Gasgehalt umverteilt. Für die zuverlässige Berechnung von Strömungen in Blasensäulen mit dem E-E Ansatz ist eine adäquate Modellierung des Grenzflächenterms in der $\textit{k}_{L}$-Gleichung daher von großer Bedeutung. Ansätze aus der Literatur zur Schließung dieses Terms werden durch Vergleich mit den DNS-Daten analysiert und zwei tragfähige Modelle ausgewählt. Mit dem $\textit{k}$-$\epsilon$ Zwei-Fluid-Modell in OpenFOAM® wird eine industrielle Blasensäule berechnet und der Einfluss des Grenzflächenterms in der $\textit{k}_{L}$-Gleichung untersucht. Das Turbulenzmodell hat bei Normaldruck nur einen sehr geringen, bei 18,5 bar Druck aber einen merklichen Einfluss auf den Gasgehalt und die Gas- und Flüssigkeitsgeschwindigkeit. Bei hohem Druck wird der gemessene Gasgehalt für ein Wassersystem in der Simulation deutlich überschätzt. Für ein organisches System liegen die numerischen und experimentellen Ergebnisse sehr nahe beieinander. Unter Verwendung des innerhalb dieser Arbeit implementierten Turbulenzmodells wird für das Wassersystem der Gasgehalt in Experimenten mit einer Abweichung von 9 – 13% berechnet. TKE-Profile werden für unterschiedliche Bedingungen analysiert und es wird eine lineare Beziehung zwischen TKE und lokalem Gasgehalt und mittlerer Gasgeschwindigkeit identifiziert. Die in dieser Arbeit verwendete skalenübergreifende Herangehensweise trägt zur verbesserten Turbulenzmodellierung in Blasenströmungen und damit zur Etablierung der numerischen Strömungssimulation für die Auslegung von industriellen Blasensäulen bei

Deformable ellipsoidal bubbles in Taylor-Couette flow with enhanced Euler-Lagrange tracking

In this work we present numerical simulations of $10^5$ sub-Kolmogorov deformable bubbles dispersed in Taylor-Couette flow (a wall-bounded shear system) with rotating inner cylinder and outer cylinder at rest. We study the effect of deformability of the bubbles on the overall drag induced by the carrier fluid in the two-phase system. We find that an increase in deformability of the bubbles results in enhanced drag reduction due to a more pronounced accumulation of the deformed bubbles near the driving inner wall. This preferential accumulation is induced by an increase in the resistance on the motion of the bubbles in the wall-normal direction. The increased resistance is linked to the strong deformation of the bubbles near the wall which makes them prolate (stretched along one axes) and orient along the stream-wise direction. A larger concentration of the bubbles near the driving wall implies that they are more effective in weakening the plume ejections which results in stronger drag reduction effects. These simulations which are practically impossible with fully resolved techniques are made possible by coupling a sub-grid deformation model with two-way coupled Euler-Lagrangian tracking of sub-Kolmogorov bubbles dispersed in a turbulent flow field which is solved through direct numerical simulations. The bubbles are considered to be ellipsoidal in shape and their deformation is governed by an evolution equation which depends on the local flow conditions and their surface tension

DNS of the wall effect on the motion of bubble swarms

This paper presents a numerical study of the gravity-driven motion of single bubbles and bubble swarms through a vertical channel, using High-Performance Computing (HPC) and Direct Numerical Simulation (DNS) of the Navier-Stokes equations. A systematic study of the wall effect on the motion of single deformable bubbles is carried out for confinement ratios CR = {2,4,6} in both circular and square channels, for a broad range of flow conditions. Then, the rising motion of a swarm of deformable bubbles in a vertical channel is researched, for void fractions a = {8.3%, 10.4%, 12.5%} and CR = {4, 6}. These simulations are carried out in the framework of a novel multiple marker interface capturing approach, where a conservative level-set function is used to represent each bubble. This method avoids the numerical and potentially unphysical coalescence of the bubbles, allowing for the collision of the fluid particles as well as long time simulations of bubbly flows. Present simulations are performed in a periodic vertical domain discretized by 2 × 106 control volumes (CVs) up to 16.6 × 106 CVs, distributed in 128 up to 2048 processors. The collective and individual behavior of the bubbles are analyzed in detail.Peer ReviewedPostprint (published version

Numerical simulation of bubbles and drops in complex geometries by using dynamic meshes

CFD techniques are important tools for the study of multiphase flows, because most of the physical phenomena of these flows often happen on space and time scales where experimental methodologies are impossible in practice. Notwithstanding, numerical approaches are limited by the computational power of the present computers. In this sense, small improvements in the efficiency of the simulations can make the difference between an approachable problem and an unapproachable one. The proposal of this doctoral thesis is focused on developing numerical algorithms to optimize the simulations of multiphase solvers based on single fluids formulations, applied on three-dimensional unstructured meshes, in the context of a finite-volume discretization. In particular, the methods developed in the context of this PhD thesis use a conservative level set technique to deal with the multiphase domain. The work has been organized in five chapters and four appendices. The first chapter constitutes an introduction to the multiphase flows and the different approaches used to study them. The core work of the of this PhD thesis is explained throughout chapters two, three, and four. In those chapters, the improvements performed on the multiphase DNS techniques are addressed in detail, providing results comparisons and discussions on the obtained outcomes. After developing the main ideas of the thesis, a final concluding chapter is presented, summarizing the main findings of this research, and pointing out some future work. Finally, the appendices includes some material that can be useful to understand in depth some specific parts of the thesis but, conversely, they are not essential to follow the main thread. As said before, the core work of this thesis is presented throughout chapters two, three and four. In chapter two, four domain optimization methods are formulated and tested. By using these techniques, small domains can be used in rising bubble simulations, thus saving computational resources. These methods have been implemented in a conservative level set framework. Some of these methods require the use of open boundaries. Therefore, a careful treatment of both inflow and outflow boundaries has been carried out. This includes the development of a new outflow boundary condition as a variation of the classical convective outflow. At this point, a study about the sizing of the computational domain has been conducted, paying special attention to the placement of the inflow and outflow boundaries. Additionally, once the methods are formulated, several validation cases are run to discuss the applicability and robustness of each method. The third chapter present a physical study of a challenging problem: the Taylor bubble. By using the most promising technique from those presented in the previous chapter (i.e. the moving mesh method), the problem of an elongated bubble rising in stagnant liquid is addressed here. A transient study on the velocity field of the problem is provided. Moreover, the study also includes sensitivity analyses with respect to the initial shape of the bubble, the initial volume of the bubble, the flow regime and the inclination of the channel. Chapter number four presents an extension of the developed method to simulate bubbles and drops evolving in complex geometries. The use of an immersed boundary method allows to deal with intricate geometries and to reproduce internal boundaries within an ALE framework. The resulting method is capable of dealing with full unstructured meshes. Different problems are studied here to assert the proposed formulation, both involving constricting and non-constricting geometries. In particular, the following problems are addressed: a 2D gravity-driven bubble interacting with a highly-inclined plane, a 2D gravity-driven Taylor bubble turning into a curved channel, the 3D passage of a drop through a periodically constricted channel, and the impingement of a 3D drop on a flat plate.La Mecánica de Fluidos Computacional (CFD) es una importante disciplina para el estudio de flujos multifase. Esto se debe a que, en este tipo de flujos, la mayor parte de los fenómenos físicos ocurren en escalas de tiempo y espacio imposibles de detectar mediante una metodología experimental. Sin embargo, los enfoques numéricos están limitados por la potencia de cálculo de los ordenadores actuales. En este sentido, pequeñas mejoras en la eficiencia de las simulaciones pueden marcar la diferencia entre un problema que puede resolverse mediante CFD o uno que no. En la presente tesis doctoral se propone el desarrollo de varios algoritmos numéricos para optimizar simulaciones de flujos multifase basadas en formulaciones "single fluids", aplicadas en mallas no estructuradas y tridimensionales, en el contexto de discretizaciones "finite-volume". El trabajo se ha organizado en cinco capítulos y cuatro apéndices. El primer capítulo constituye una introducción a los flujos multifase y a los distintos enfoques usados para estudiarlos. El trabajo nuclear de la presente tesis reside en los capítulos tres, cuatro y cinco. En dichos capítulos se presentan las mejoras realizadas en las técnicas de resolución de flujos multifase mediante una metodología "DNS", aportando comparaciones de resultados y discusiones críticas de los resultados obtenidos. Después de desarrollar las ideas centrales de la tesis, se presenta un capítulo final con las conclusiones destacadas de este trabajo, señalando posibles líneas de trabajo futuro. Finalmente, se incluyen varios apéndices con material complementario que puede ser útil para profundizar en algún aspecto concreto del desarrollo, pero que a su vez no es esencial para entender las ideas principales del texto. Como se explica anteriormente, el trabajo central de la tesis se ha desarrollado a lo largo de los capítulos dos, tres y cuatro. En el segundo capítulo se formulan y prueban cuatro métodos de optimización de dominios de cálculo. Mediante la utilización de estos métodos se hace posible usar dominios de cálculo pequeños en problemas de burbujas ascendentes, ahorrando así recursos computacionales. Algunos de estos métodos requieren el uso de fronteras abiertas, por lo que se propone un estudio detallado de las condiciones de contorno de entrada y salida. Esto incluye el desarrollo de una nueva condición tipo "outflow". A continuación se estudia en profundidad el dimensionamiento del dominio de cálculo, prestando una atención especial a la posición de las fronteras de entrada y de salida. Con todo esto, el capítulo se cierra con una comparativa del rendimiento de los distintos métodos propuestos en varios problemas de burbujas ascendentes. El tercer capítulo presenta un estudio físico de un problema clave: la burbuja de Taylor. Usando la técnica con mejor rendimiento del capítulo anterior (es decir, la técnica de malla móvil), se aborda el problema de una burbuja alargada moviéndose en un fluido en reposo. Se lleva a cabo un estudio transitorio de la velocidad del campo fluido. Además, se realizan varios estudios de sensibilidad con respecto a la forma inicial de la burbuja, su volumen inicial, el régimen de flujo y la inclinación del canal. Por último, en el cuarto capítulo se presenta una extensión del método desarrollado para simular gotas y burbujas evolucionando en geometrías complejas. El uso de un método "Immersed Boundary" permite tratar geometrías complejas y reproducir fronteras internas en métodos que utilicen mallas móviles. En este punto, se estudian diversos problemas para validar la formulación propuesta, tanto en geometrías constrictivas como en no constrictivas. En particular, se han resuelto los siguientes problemas: una burbuja 2D interaccionando con un plano inclinado, una burbuja de Taylor 2D girando en un tubo curvo, el ascenso de una gota 3D dentro de un canal corrugado, y el impacto de una gota 3D contra una plaformaPostprint (published version