This thesis presents the investigation of an Euler-Lagrange framework for modeling bubble coalescence in dispersed bubbly flows. The interaction between bubbles may be caused by several mechanisms. Among them, the random motion due to turbulent fluctuations is normally of major significance. One focus of this work is to apply a bubble dispersion model for modeling turbulence-induced coalescence, occurring in a certain percentage of collision events. Large bubbles appear due to coalescence, and their disturbance to the liquid phase is not negligible in most circumstances. However, the point-mass Euler-Lagrange method requires the bubble or particle size to be much smaller than the cell size when the interphase coupling is considered. Otherwise, numerical instabilities may arise. Therefore, interpolation methods between the Euler and the Lagrange phase for finite-size bubbles that are bigger than or of the same size as numerical cells are studied.
The Euler-Lagrange method describes the continuous phase on the Euler grid, and the dispersed phase is treated as Lagrange points in the simulation. Bubble motion is governed by an ordinary differential equation for the linear momentum considering different forces. The turbulent dispersion of the dispersed phase is reconstructed with the continuous random walk (CRW) model. Bubble-bubble collisions and coalescence are accounted for deterministically. The time-consuming search for potential collision partners in dense bubbly flows is accelerated by the sweep and prune algorithm, which can be utilized in arbitrary mesh types and sizes. If the interphase coupling is considered in the simulations, the spatially distributed coupling method is used for the Lagrange-to-Euler coupling. For the Euler-to-Lagrange coupling, a new approach is proposed.
To evaluate the dispersion and coalescence models, one-way coupled simulations of bubbly pipe flows at low Eötvös numbers are conducted. Validation against the experiments demonstrates that the one-way coupled EL-CRW dispersion model can well reproduce the bubble distribution in a typical dense bubbly pipe flow. Good agreement of the bubble size distribution at the pipe outlet between the simulation and the experiment is obtained.
Two-way coupled simulations are performed to validate the interpolation methods. A combination of coupling approaches is employed in a square bubble column reactor to examine the general validity for a large-scale bubbly flow. Combining the proposed interpolation scheme with the dispersion and bubble interaction models, the coalescence and breakage in bubbly flows are studied in a turbulent pipe flow. The predicted bubble size distribution shows a good match to the measurement. The results are independent of the mesh resolution in the studied range from point-mass simulations to finite-size situations.:Nomenclature
1 Introduction
1.1 Motivation and background for the thesis
1.2 Outline
2 Equations for modeling bubbly flows
2.1 Governing equations of the continuous phase
2.2 Governing equations of the dispersed phase
2.3 Modifications to the bubble force equations
2.3.1 One-way coupled simulations with RANS modeling
2.3.2 Two-way coupled simulations
2.4 Generation of fluctuations
2.4.1 Different approaches to dispersion modeling
2.4.2 Normalized continuous random walk model
2.4.3 Employing the mean velocity field to determine forces
3 Bubble collision, coalescence and breakup
3.1 Previous studies and requirement of the interaction modeling
3.2 Detection of collisions with the sweep and prune algorithm
3.3 Coalescence modeling
3.3.1 Condition of bubble coalescence
3.3.2 Model of Kamp et al. [2001]
3.3.3 Model of Hoppe and Breuer [2018]
3.3.4 Model of Schwarz et al. [2013]
3.3.5 Comparison of coalescence models
3.4 Breakup modeling
3.4.1 Turbulence induced breakups
3.4.2 Post-breakup treatment
4 Interpolation techniques for two-way coupled simulations
4.1 Lagrange-to-Euler coupling
4.1.1 Introduction to the spatially distributed coupling
4.1.2 Intersection plane method
4.1.3 Subcell method
4.1.4 Random points method
4.2 Euler-to-Lagrange coupling
4.2.1 Approaches for computing the undisturbed velocity
4.2.2 Coarser grid method
4.2.3 Averaging the fluid velocity in front of the bubble
4.2.4 Velocity from upstream disk
4.2.5 Gradient of the undisturbed liquid velocity
5 One-way coupled simulation of bubble dispersion and resulting interaction
5.1 Implementation and verification of the continuous random walk model
5.2 Bubble dispersion in turbulent channel flows
5.3 Bubble dispersion and interaction in turbulent pipe flows
5.3.1 Overview of studied cases
5.3.2 Results of the bubble dispersion
5.3.3 Results of the bubble coalescence
6 Two-way coupled simulation of finite-size bubbles
6.1 Flow solver and algorithm
6.2 Assessing the Lagrange-to-Euler coupling methods
6.2.1 Previous studies
6.2.2 Simulation setups for a single bubble in quiescent liquid
6.2.3 Results and discussion
6.3 Assessing the Euler-to-Lagrange coupling methods
6.3.1 Simulation of two bubbles rising inline
6.3.2 Simulation of a bubble rising in linear shear flows
6.4 Large-eddy simulation for a square bubble column
6.5 Bubble coalescence in a turbulent pipe flow
7 Conclusions and outlook
Appendices
A.1 Equations of turbulence models
A.2 Numerical implementation of the full CRW drift term
A.3 Results of bubble coalescence modeling for case B to case E
A.4 Search algorithm of the upstream disk method
Bibliography / Diese Arbeit stellt die Untersuchung eines Euler-Lagrange-Rahmens zur Modellierung der Blasenkoaleszenz in dispergierten Blasenströmungen vor. Die Interaktion zwischen Blasen kann durch mehrere Mechanismen verursacht werden. Unter ihnen sind die zufälligen Bewegungen aufgrund von turbulenten Fluktuationen von großer Bedeutung. Ein Schwerpunkt dieser Arbeit ist die Anwendung eines Blasendispersionsmodells zur Modellierung der turbulenzinduzierten Koaleszenz, die in einem bestimmten Prozentsatz der Kollisionsereignisse auftritt. Große Blasen entstehen durch Koaleszenz und ihre Störung der flüssigen Phase ist in den meisten Fällen nicht zu vernachlässigen. Die Punkt-Masse-Euler-Lagrange-Methode erfordert jedoch, dass die Blasengröße viel kleiner als die Zellgröße ist, wenn die Interphasenkopplung berücksichtigt wird. Andernfalls kann es zu numerischen Instabilitäten kommen. Daher werden Interpolationsmethoden zwischen den zwei Phasen untersucht.
Die kontinuierliche Phase wird auf dem Euler-Gitter beschrieben und die dispergierte Phase wird als Punkte behandelt. Die Blasenbewegung wird durch eine gewöhnliche Differentialgleichung unter Berücksichtigung verschiedener Kräfte bestimmt. Die turbulente Dispersion der Blasen wird mit dem CRW-Modell (continuous random walk) rekonstruiert. Blasen-Blasen-Kollisionen werden deterministisch berücksichtigt. Die Suche nach potentiellen Kollisionspartnern wird durch den Sweep- und Prune-Algorithmus beschleunigt, der in beliebigen Gittertypen und -größen eingesetzt werden kann. Wird die Interphasenkopplung berücksichtigt, so wird für die Lagrange-zu-Euler-Kopplung die spatially distributed coupling verwendet. Für die Euler-zu-Lagrange-Kopplung wird ein neuer Ansatz vorgeschlagen.
Um die Dispersions- und Koaleszenzmodelle zu bewerten, werden Einweg-gekoppelte Simulationen von blasenbeladenen Rohrströmungen bei niedriger Eötvös-Zahl durchgeführt. Die Validierung zeigt, dass das einseitig gekoppelte EL-CRW-Dispersionsmodell die Blasenverteilung in einer typischen dichten, blasenbeladenen Rohrströmung gut reproduzieren kann. Es wird eine gute Übereinstimmung der Blasengrößenverteilung am Rohrauslass zwischen der Simulation und dem Experiment erzielt.
Zur Validierung der Interpolationsmethoden werden Zweiweg-gekoppelte Simulationen durchgeführt. Eine Kombination von Kopplungsansätzen wird in einem Blasensäulenreaktor eingesetzt, um die allgemeine Gültigkeit zu untersuchen. Durch Kombination des vorgeschlagenen Interpolationsschemas mit den Dispersions- und Blasenwechselwirkungsmodellen werden die Koaleszenz und der Zerfall in einer turbulenten blasenbeladenen Rohrströmung untersucht. Die berechnete Blasengrößenverteilung zeigt eine gute Übereinstimmung mit der Messung und erweist sich als unabhängig von der Netzauflösung im untersuchten Bereich von PunktMasse-Simulationen bis zu Situationen mit Blasen endlicher Größe.:Nomenclature
1 Introduction
1.1 Motivation and background for the thesis
1.2 Outline
2 Equations for modeling bubbly flows
2.1 Governing equations of the continuous phase
2.2 Governing equations of the dispersed phase
2.3 Modifications to the bubble force equations
2.3.1 One-way coupled simulations with RANS modeling
2.3.2 Two-way coupled simulations
2.4 Generation of fluctuations
2.4.1 Different approaches to dispersion modeling
2.4.2 Normalized continuous random walk model
2.4.3 Employing the mean velocity field to determine forces
3 Bubble collision, coalescence and breakup
3.1 Previous studies and requirement of the interaction modeling
3.2 Detection of collisions with the sweep and prune algorithm
3.3 Coalescence modeling
3.3.1 Condition of bubble coalescence
3.3.2 Model of Kamp et al. [2001]
3.3.3 Model of Hoppe and Breuer [2018]
3.3.4 Model of Schwarz et al. [2013]
3.3.5 Comparison of coalescence models
3.4 Breakup modeling
3.4.1 Turbulence induced breakups
3.4.2 Post-breakup treatment
4 Interpolation techniques for two-way coupled simulations
4.1 Lagrange-to-Euler coupling
4.1.1 Introduction to the spatially distributed coupling
4.1.2 Intersection plane method
4.1.3 Subcell method
4.1.4 Random points method
4.2 Euler-to-Lagrange coupling
4.2.1 Approaches for computing the undisturbed velocity
4.2.2 Coarser grid method
4.2.3 Averaging the fluid velocity in front of the bubble
4.2.4 Velocity from upstream disk
4.2.5 Gradient of the undisturbed liquid velocity
5 One-way coupled simulation of bubble dispersion and resulting interaction
5.1 Implementation and verification of the continuous random walk model
5.2 Bubble dispersion in turbulent channel flows
5.3 Bubble dispersion and interaction in turbulent pipe flows
5.3.1 Overview of studied cases
5.3.2 Results of the bubble dispersion
5.3.3 Results of the bubble coalescence
6 Two-way coupled simulation of finite-size bubbles
6.1 Flow solver and algorithm
6.2 Assessing the Lagrange-to-Euler coupling methods
6.2.1 Previous studies
6.2.2 Simulation setups for a single bubble in quiescent liquid
6.2.3 Results and discussion
6.3 Assessing the Euler-to-Lagrange coupling methods
6.3.1 Simulation of two bubbles rising inline
6.3.2 Simulation of a bubble rising in linear shear flows
6.4 Large-eddy simulation for a square bubble column
6.5 Bubble coalescence in a turbulent pipe flow
7 Conclusions and outlook
Appendices
A.1 Equations of turbulence models
A.2 Numerical implementation of the full CRW drift term
A.3 Results of bubble coalescence modeling for case B to case E
A.4 Search algorithm of the upstream disk method
Bibliography
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:76508 |
| Date | 09 November 2021 |
| Creators | Yang, Xinghao |
| Contributors | Fröhlich, Jochen, Breuer, Michael, Technische Universität Dresden |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | 10.1016/j.ces.2021.116566, 10.1007/s42757-020-0082-2 |
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