An interaction by exchange with the conditional mean (IECM) micromixing model is coupled to a three-dimensional single-particle Lagrangian stochastic (LS) model to estimate concentration fluctuations in plumes of a passive (i.e., non-buoyant), non-reactive (i.e., no chemistry) tracer dispersing from a variety of source configurations in four neutrally stratified flows: a horizontally-homogeneous wall shear layer flow; a horizontally-homogeneous representation of the Tombstone canopy flow; a three-dimensional inhomogeneous representation of the Tombstone canopy flow; and a three-dimensional inhomogeneous representation of the Mock Urban Setting Trials (MUST) canopy flow. The IECM micromixing model incorporates the combined effects of turbulent and molecular mixing on particle concentration. This allows the numerical estimation of all moments of the scalar concentration field, which is a significant advance over traditional LS models given that concentration fluctuations are a ubiquitous feature of a dispersing plume. The single-particle implementation of the LS-IECM model is based upon a previously reported implementation that used simultaneously computed particle trajectories to estimate the conditional mean concentration field [Cassiani, M. A., Franzese, P. A. and Giostra, U. A.: 2005, A PDF micromixing model of dispersion for atmospheric flow. Part I: development of model, application to homogeneous turbulence and to a neutral boundary layer, Atmospheric Environment 39, 1457-1469]. The model used in this thesis pre-calculates the conditional mean concentration field with an LS model for use with the IECM model, which runs as a separate simulation. The principal advantage of this single-particle approach is the performance increase on parallel computer architecture, which scales directly with the number of processors. The simulations presented in this thesis go beyond those performed with the previous model by considering three-dimensional inhomogeneous flows, as well as one-dimensional horizontally-homogeneous flows. The accuracy of the LS-IECM model was good for the flows with horizontal-homogeneity, and comparable to the results of previous simulations from older models. Rogue velocities in the simulations utilising inhomogeneous flow statistics resulted in acceptable to poor accuracy in these simulations. Suggestions for improvements to the model are made.

No description available.

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.

In this thesis, wall-resolved and wall-modeled large-eddy simulation (LES) have been employed to investigate turbulent flow and dispersion around a single and a group of wall-mounted bluff bodies which are partially and fully submerged in developing boundary layers, respectively. The dispersion is caused by a continuous release of a passive scalar from a ground-level point source located within the matrix of obstacles. The results have been validated through comparisons against the available experimental measurement data. Thorough physical analysis including investigation of the spatial evolution and temporal cascades of the kinetic and scalar energies, flow structures and their influences on dispersion of the concentration plume in the context of highly disturbed flows, and study of turbulence statistics for the flow and concentration fields have been performed to provide deeper insights into turbulent flow and dispersion in domains with complex geometries. An in-house code based on FORTRAN programming language, parallelized with MPI libraries has been developed, modified and optimized for conducting the simulations. The simulations have been conducted on public-domain supercomputers ofWest-Grid, specifically Orcinus and Grex, and also the local 256-core cluster system of the CFD LAB at the University of Manitoba.

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.

A novel higher-order moment-closure method is applied for the Eulerian treatment of gas-particle multiphase flows characterized by a dilute polydisperse and polythermal particle phase. Based upon the polydisperse Gaussian-moment model (PGM) framework, the proposed model is derived by applying an entropy-maximization moment-closure formulation to the transport equation of the particle-number density function, which is equivalent to the Williams-Boltzmann equation for droplet sprays. The resulting set of first-order robustly-hyperbolic balance laws include a direct treatment for local higher-order statistics such as co-variances between particle distinguishable properties (i.e., diameter and temperature) and particle velocity. Leveraging the additional distinguishing variables, classical hydrodynamic droplet evaporation theory is considered to describe unsteady droplet vaporization. Further, studying turbulent multiphase flow theory, a first-order hyperbolicity maintaining approximation to turbulent flow diffusion-inertia effects is proposed. Investigations into the predictive capabilities of the model are evaluated relative to Lagrangian-based solutions for a range of flows, including aerosol dispersion and fuel-sprays. Further, the model is implemented in a massively parallel discontinuous-Galerkin framework. Validation of the proposed turbulence coupling model is subsequently performed against experimental data, and a qualitative analysis of the model is given for a qualitative liquid fuel-spray problem.

The advection-diffusion equation has been extensively used in air pollution models to simulate mean contaminant concentrations in the planetary boundary layer (PBL). Therefore, in a Eulerian framework, it is possible to theoretically model the dispersion from a continuous point source, given adequate boundary and initial conditions and the knowledge of the mean wind velocity and turbulent concentration fluxes. The choice of an appropriate parameterization for such fluxes plays an important role in the performance of air quality dispersion models based on the advection-diffusion equation. As a consequence, much of the turbulent dispersion research is associated with the specification of these fluxes. The most commonly used approximation for closing the advection-diffusion equation is to relate the turbulent concentration fluxes to mean concentration gradients through the use of eddy diffusivities, which carry within them the physical structure of the turbulent transport phenomenon. For a continuous point source the eddy diffusivities may vary spatially and temporally along the contaminant travel time. Taylor s statistical diffusion theory (1921) determines that the turbulent dispersion depends on the distance from a continuous point source. In the proximity of the source, the fluid particles tend to preserve the memory from their initial turbulent environment. For long travel times, this memory is lost, and the motion of the particles depends only on the local turbulence properties (BATCHELOR, 1949).The aim of the present study is to present a new formulation for the eddy diffusivities in terms of the distance from the source in an inhomogeneous, shear-generated turbulence. The proposition is based on expressions for the turbulent velocity spectra and the statistical diffusion theory. These eddy diffusivities, derived for neutral conditions are described by a complex integral formulation that must be numerically solved. An additional aim of this work is to obtain a simple algebraic expression for the eddy diffusivities in a neutral PBL as a function of the turbulence properties (inhomogeneous turbulence) and the distance from the source. Therefore, the hypothesis to be tested in this study is whether the complex integral formulation for eddy diffusivities can be expressed (substituted) by a simpler algebraic expression. Finally, to investigate the influence of the memory effect in the turbulent dispersion process, a vertical eddy diffusivity is evaluated as a function of the distance from the source against its asymptotic limit employing an Eulerian air pollution model and atmospheric dispersion experiments that were carried out in strong wind conditions. / A equação de difusão-advecção tem sido amplamente utilizada em modelos de poluição do ar para simular as concentrações médias de contaminantes na camada limite planetária (CLP). Portanto, seguindo uma formulação Euleriana, é possível construir um modelo teórico de dispersão de uma fonte pontual contínua a partir de um limite adequado, de condições iniciais e do conhecimento da velocidade média do vento e dos fluxos turbulentos de concentração. A escolha de uma parametrização apropriada para estes fluxos desempenha um papel importante em modelos de dispersão e de qualidade do ar que se baseiam na equação de difusão-advecção. Como consequência, muitas das pesquisas em dispersão turbulenta estão relacionadas com a especificação destes fluxos. A aproximação mais comumente usada para fechar a equação de difusão-advecção relaciona os fluxos turbulentos de concentração com os gradientes de concentração média através do uso de coeficientes de difusão. Estes carregam em si a estrutura física do fenômeno de transporte turbulento. Para uma fonte pontual contínua, tais coeficientes podem variar espacialmente e temporalmente ao longo da viagem dos contaminantes. A teoria de difusão estatística de Taylor (1921) determina que a dispersão turbulenta dependa da distancia de uma fonte pontual continua. Na proximidade da fonte, as partículas de fluído mantêm a memória do seu ambiente inicial turbulento. Para longos tempos de viagem, essa memória se perde, e o movimento das partículas segue apenas as propriedades locais de turbulência (BATCHELOR, 1949). O objetivo deste estudo é apresentar uma nova formulação para os coeficientes de difusão assintóticos e em função da distância da fonte para turbulência não-homogênea. A proposição se baseia em expressões dos espectros de energia cinética turbulenta e na teoria da difusão estatística. Estes coeficientes de difusão função da posição, derivados de condições neutras, são descritos por uma formulação complexa integral que deve ser resolvida numericamente. Um objetivo adicional neste trabalho é a derivação de uma expressão algébrica simples para os coeficientes de difusão, em função das propriedades da turbulência (turbulência não-homogênea) e da distância da fonte. A hipótese a ser testada neste estudo é se a formulação complexa integral para os coeficientes de difusão pode ser substituída por uma simples solução algébrica. Para investigar a influência do efeito de memória no processo de dispersão turbulenta, a difusividade vertical é avaliada em função da distância da fonte contra o seu limite assintótico. Para tanto, se utiliza um modelo Euleriano de poluição do ar cujos resultados são comparados com experimentos de dispersão atmosférica que foram realizados em condições de vento forte.

No description available.

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