The collisions frequency of dispersed phases (particles, droplets, bubbles) in a turbulent carrier phase is a fundamental quantity that is needed for modeling multiphase flows with applications to chemical processes, minerals flotation, food science, and many other industries. In this dissertation, numerical simulations are performed to determine collisions frequency of bi-dispersed particles (solid particles and bubbles) in homogeneous isotropic turbulence. Both direct numerical simulations (DNS) and Large Eddy simulations (LES) are conducted to determine velocity fluctuations of the carrier phase. The DNS results are used to validate existing theoretical models as well as the LES results. The dissertation also presents a CFD-based flotation model for predicting the pulp recovery rate in froth flotation machines. In the direct numerical simulations work, particles and bubbles suspended in homogeneous isotropic turbulence are tracked and their collisions frequency is determined as a function of particle Stokes number. The effects of the dispersed phases on the carrier phase are neglected. Particles and bubbles of sizes on the order of Kolmogorov length scale are treated as point masses. Equations of motion of dispersed phases are integrated simultaneously with the equations of the carrier phase using the same time stepping scheme. In addition to Stokes drag, the pressure gradient in the carrier phase and added-mass forces are also included. The collision model used here allows overlap of particles and bubbles. Collisions kernel, radial relative velocity, and radial distribution function found by DNS are compared to theoretical models over a range of particle Stokes number. In general, good agreement between DNS and recent theoretical models is obtained for radial relative velocity for both particle-particle and particle-bubble collisions. The DNS results show that around Stokes number of unity particles of the same group undergo expected preferential concentration while particles and bubbles are segregated. The segregation behavior of particles and bubbles leads to a radial distribution function that is less than one. Existing theoretical models do not account for effects of this segregation behavior of particles and bubbles on the radial distribution function. In the large-eddy simulations efforts, the dissertation addresses the importance of the subgrid fluctuations on the collisions frequency and investigates techniques for predicting those fluctuations. The cases studied are of particles-particles and particles-bubbles collisions at Reynolds number Re_λ = 96. A study is conducted first by neglecting the effects of subgrid velocity fluctuations on particles and bubbles motions. It is found that around Stokes number of unity solid particles of the same group undergo the well known preferential concentration as observed in the DNS. Effects of pressure gradient on the particles are negligible due to their small sizes. Bubbles as a low inertia particles are very sensitive to subgrid velocity and acceleration fields where the effects of pressure gradient in the carrier phase are dominant. However, particle-bubble radial distribution functions from LES are not as low as that from DNS. To account for the effects of subgrid field on the dispersion of particles and bubbles, a new multifractal methodology has been developed to construct a subgrid vorticity field from the resolved vorticity field in frame work of LES. A Poisson's solver is used to obtain the subgrid velocity field from the subgrid vorticity field. Accounting for the subgrid velocity fluctuations (but neglecting pressure gradient) produced minor changes in the radial distribution function for particle-particle and particle-bubble collisions. We conclude from this study that for accurate particle tracking in LES the subgrid velocity fluctuations must be dynamically realizable field (temporally and spatially correlated with the large scale motion). Adding random SGS velocity fluctuations is not enough to capture the correct radial distribution functions of dispersed phases especially for bubbles-particles collisions where the pressure gradient term ( or acceleration Du_f′/Dt) is responsible for particle-bubble segregation around particle Stokes number near one. A CFD-based model for minerals flotation machines has been developed in this dissertation. The objective of flotation models is to predict the recovery rate of minerals from a flotation cell. The developed model advances the state-of-the-art of pulp recovery rate prediction by incorporating validated theoretical collisions frequency models and detailed hydrodynamics from two-phase flow simulations. Spatial distributions of dissipation rate and air volume fraction are determined by the two-phase hydrodynamic simulations. Knowing these parameters throughout the machine is essential in understanding the effectiveness of different components of flotation machine (rotor, stator or disperser, jets) on the flotation efficiency. The developed model not only predicts the average pulp recovery rate but also it indicates regions of high/low recovery rates. The CFD-based flotation model presented here can be used to determine the dependence of recovery rate constant at any locality within the pulp based on particle diameter, particle specfic gravity, contact angle, and surface tension. / Ph. D.

This thesis describes several approaches for stabilizing POD-ROMs (that is, reduced order models based on basis functions derived from the proper orthogonal decomposition) for both the CDR (convection-diffusion-reaction) equation and the NSEs (Navier-Stokes equations). Stabilization is necessary because standard POD-ROMs of convection-dominated problems usually display numerical instabilities. The first stabilized ROM investigated is a streamline-upwind Petrov-Galerkin ROM (SUPG-ROM). I prove error estimates for the SUPG-ROM and derive optimal scalings for the stabilization parameter. I test the SUPG-ROM with the optimal parameter in the numerical simulation of a convection-dominated CDR problem. The SUPG-ROM yields more accurate results than the standard Galerkin ROM (G-ROM) by eliminating the inherent numerical artifacts (noise) in the data and dampening spurious oscillations. I next propose two regularized ROMs (Reg-ROMs) based on ideas from large eddy simulation and turbulence theory: the Leray ROM (L-ROM) and the evolve-then-filter ROM (EF-ROM). Both Reg-ROMs use explicit POD spatial filtering to regularize (smooth) some of the terms in the standard G-ROM. I propose two different POD spatial filters: one based on the POD projection and a novel POD differential filter. These two new Reg-ROMs and the two spatial filters are investigated in the numerical simulation of the three-dimensional flow past a circular cylinder problem at Re = 100. The numerical results show that EF-ROM-DF is the most accurate Reg-ROM and filter combination and the differential filter generally yields better results than the projection filter. The Reg-ROMs perform significantly better than the standard G-ROM and decrease the CPU time (compared against the direct numerical simulation) by orders of magnitude (from about four days to four minutes). / Ph. D.

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Efficient temporal resolution and spatial grids are important in simulation of the inflow turbulence for wind turbine loads analyses. There have not been many published studies that address optimal space-time resolution of generated inflow velocity fields in order to estimate accurate load statistics. This study investigates turbine extreme and fatigue load statistics for a utility-scale 5MW wind turbine with a hub-height of 90 m and a rotor diameter of 126 m. Load statistics, spectra, and time-frequency analysis representations are compared for various alternative space and time resolutions employed in inflow turbulence field simulation. Conclusions are drawn regarding adequate resolution in space of the inflow turbulence simulated on the rotor plane prior to extracting turbine load statistics. Similarly, conclusions are drawn with regard to what constitutes adequate temporal filtering to preserve turbine load statistics. This first study employs conventional Fourier-based spectral methods for stochastic simulation of velocity fields for a neutral atmospheric boundary layer. In the second part of this study, large-eddy simulation (LES) is employed with similar resolutions in space and time as in the earlier Fourier-based simulations to again establish turbine load statistics. A comparison of extreme and fatigue load statistics is presented for the two approaches used for inflow field generation. The use of LES-generated flows (enhanced in deficient high-frequency energy by the use of fractal interpolation) to establish turbine load statistics in this manner is computationally very expensive but the study is justified in order to evaluate the ability of LES to be used as an alternative to more common approaches. LES with fractal interpolation is shown to lead to accurate load statistics when compared with stochastic simulation. A more compelling reason for using LES in turbine load studies is the following: for stable boundary layers, it is not possible to generate realistic inflow velocity fields using stochastic simulation. The present study presents a demonstration that, despite the computational costs involved, LES-generated inflows can be used for loads analyses for utility-scale turbines. The study sets the stage for future computations in the stable boundary layer where low-level jets, large speed and direction shears across the rotor, etc. can possibly cause large turbine loads; then, LES will likely be the inflow turbulence generator of choice. / text

La modélisation par simulation des grandes échelles (Large-Eddy Simulation - LES) des processus physiques régissant la couche limite atmosphérique (CLA) demeure complexe de part la difficulté des modèles à capter l'évolution de la turbulence entre différentes conditions de stratification. De ce fait, l'étude LES du cycle diurne complet de la CLA comprenant des situations convectives la journée et des conditions stables la nuit est très peu documenté. La simulation de la couche limite stable où la turbulence est faible, intermittente et qui est caractérisée par des structures turbulentes de petite taille est tout particulièrement compliquée. En conséquence, la capacité de la LES à bien reproduire les conditions météorologiques de la CLA, notamment en situation stable, est étudiée à l'aide du code de mécanique des fluides développé par EDF R&D, Code_Saturne. Dans une première étude, le modèle LES est validé sur un cas de couche limite convective quasi stationnaire sur terrain homogène. L'influence des modèles sous-maille de Smagorinsky, Germano-Lilly, Wong-Lilly et WALE (Wall-Adapting Local Eddy-viscosity) ainsi que la sensibilité aux méthodes de paramétrisation sur les champs moyens, les flux et les variances est discutées. Dans une seconde étude le cycle diurne complet de la CLA pendant la campagne de mesure Wangara est modélisé. L'écart aux mesures étant faible le jour, ce travail se concentre sur les difficultés rencontrées la nuit à bien modéliser la couche limite stable. L'impact de différents modèles sous-maille ainsi que la sensibilité au coefficient de Smagorinsky ont été analysés. Par l'intermédiaire d'un couplage radiatif réalisé en LES, les répercussions du rayonnement infrarouge et solaire sur le jet de basse couche nocturne et le gradient thermique près de la surface sont exposées. De plus l'adaptation de la résolution du domaine à l'intensité de la turbulence et la forte stabilité atmosphérique durant l'expérience Wangara sont commentées. Enfin un examen des oscillations numériques inhérentes à Code_Saturne est réalisé afin d'en limiter les effets

This thesis focused on investigating flow, coherent structures, and mechanisms leading to scour around a series of three submerged groynes in a high curvature (radius of curvature (R)/channel width (B)=1.5) channel bend using a Large Eddy Simulation Numerical (LES) model. Flow was investigated during both an initial and a later stage of scour. The results showed that the groynes appeared effective in keeping the main core of high streamwise velocity away from the outer bank wall in the region where they were installed, although high potential still existed for local scour around the groynes. During the initial stage of scour, horseshoe vortices (HVs) showed the greatest propensity to induce scour immediately upstream of the groyne tips. During the later stage of scour, the HV in front of the first upstream groyne (G1) induced very high mean pressure fluctuations on the outer bank wall. Scour was also of very great concern around the tip of G1 due to severe mean bed pressure fluctuations. Downstream of the groyne field, the presence of a counter-rotating outer bank cell was capable of endangering the stability of the outer bank. The second focus of this thesis was to investigate flow in a 135° channel bend using both Reynolds Averaged Navier Stokes (RANS) and LES numerical models. The RANS study examined the effects of curvature ratio (R/B), and aspect ratio (B/H, where H is the inlet flow depth), on secondary circulation strength, and bed shear stresses. The study revealed that a decrease in R/B was associated with an increase in secondary circulation strength and peak bed shear stress. A change in B/H also substantially affected cross stream circulation strength. The LES study was conducted in a 135° (R/B = 1.5) bend flume with a fixed bed corresponding to near equilibrium scour conditions, and the results were compared to a similar high curvature 193° bend numerical study. Inner bank vortices and shear layers were present in both cases although their characteristics were substantially different. Distributions of boundary friction velocities, and turbulence were also quite different for each case.

La réduction des émissions de polluants et la diminution de la consommation sont deux challenges fortement liés auxquels les constructeurs automobiles doivent faire face tout en maintenant les performances des moteurs. Les nouvelles stratégies telle que la réduction de la cylindrée associée à une optimisation de la boucle d'air (forte suralimentation et recirculation de gaz brûlés) possèdent ce potentiel. Cependant elles affectent la stabilité du moteur en favorisant les variations cycle à cycle (VCC) qui correspondent à une fluctuation de la combustion d'un cycle sur l'autre. L'objectif de cette thèse est de développer une méthodologie s'appuyant sur la Simulation aux Grandes Echelles (SGE) capable de prédire les VCC d'un moteur à allumage commandé. Les prédictions sont validées grâce à une base de données expérimentale conçue à l'IFP qui leur est dédiée. Une approche graduelle est employée : l'outil numérique est tout d'abord évalué sur une configuration simplifiée de moteur à piston sans combustion, puis appliqué à un moteur à allumage commandé entraîné pour valider la prédiction de l'aérodynamique interne. Sur cette dernière configuration le couplage avec le modèle de combustion DTFLES est rajouté pour simuler deux points de fonctionnement réactifs. Chacune de ces simulations intègre un ou plusieurs points de modélisation (les tétraèdres en maillage mobile, les modèles de choc et d'allumage, et la cinétique chimique) au préalable testés sur des configurations académiques. Ce travail de recherche montre que l'approche SGE, dans un contexte de calcul massivement parallèle, est un outil prometteur dans l'étude des VCC d'un moteur à allumage commandé de conception récente. / A major challenge for the development of internal combustion engines is to improve fuel economy and to reduce pollutant emissions while maintaining or enhancing engine performances. New strategies using downsizing with high levels of exhaust gas recirculation have this potential, but can impact on the combustion stability and trigger high cycle-to-cycle variations (CCV). The objective of this thesis is to set a methodology based on Large Eddy Simulation (LES) to study CCV of a Spark-Ignition (SI) engine. A gradual approach is used : the numerical tool is first evaluated on a motored axisymmetric piston-cylinder assembly, and then applied on a motored SI engine to validate the in-cylinder aerodynamic predictions. On this last configuration, the coupling with the turbulent combustion model DTFLES is added to simulate two operating points of the indirect injection engine mode. Each of these simulations takes into account one or several modeling key points (tetrahedra with moving mesh, the modelings of shock and ignition, and chemical kinetics) previously tested in academic configurations. This research work shows that LES approach, in the context of massively parallel computing, can be used to study the CCV of a realistic SI engine.

Les turbines à gaz aéronautiques doivent satisfaire des normes d'émissions polluantes toujours en baisse. La formation de polluants est directement liée à la qualité du mélange d’air et de carburant en amont du front de flamme. Ainsi, leur réduction implique une meilleure prédiction de la formation du spray et de son interaction avec l'écoulement turbulent gazeux. La simulation aux grandes échelles (SGE) semble un outil numérique approprié pour étudier ces mécanismes. Le but de cette thèse est d’évaluer l'impact de modèles d'injection simplifiés sur la SGE de l'écoulement diphasique évaporant d’une configuration complexe. La configuration cible choisie est un brûleur aéronautique installé sur le banc expérimental MERCATO. Le banc expérimental est equipé d’un système d’injection d'air vrillé et d’un système d'injection liquide avec un atomiseur pressurisé swirlé représentatif de foyers aéronautiques réels. Dans un premier temps, un modèle d'injection simplifié pour atomiseurs pressurisés swirlés négligeant les effets de l'atomisation sur la dynamique du spray est présenté. L'objectif principal de ce modèle réside dans la reproduction de conditions d’injection similaires pour des traitements Eulériens et Lagrangiens de la phase particulaire. Dans un second temps, la composante Lagrangienne de ce modèle d'injection est combinée à un modèle d'atomisation secondaire de la litérature pour permettre une prise en compte partielle des phénomènes de pulvérisation liquide. Les SGE de l'écoulement diphasique évaporant de la configuration MERCATO présentées comportent deux aspects. Premièrement, différents modèles d’injection sont évalués pour quantifier leur impact sur la dynamique de la phase particulaire. Deuxièmement, une comparaison de simulations Euler-Euler et Euler-Lagrange reposant sur un modèle d'injection unifié est effectuée. / Aeroautical gas turbines need to satisfy growingly stringent demands on pollutant emission. Pollutant emissions are directly related to the quality of fuel air mixing prior to combustion. Therefore, their reduction relies on a more accurate prediction of spray formation and interaction of the spray with the gaseous turbulent flowfield. Large-Eddy Simulation (LES) seems an adequate numerical tool to predict these mechanisms. The objective of this thesis is to evaluate the impact of simplified injection methods on the LES of the evaporating two-phase flow inside a complex geometry. The chosen target configuration is an aeronautical combustor installed on the MERCATO test-rig. The experimental setup includes an air-swirler injection system and a pressureswirl atomizer typical of realistic aeronautic combustors. In a first step, a simplified injection model for pressure swirl atomizers neglecting the impact of liquid disintegration on spray dynamics is presented. The main objective of this model lies in the reproduction of similar injection conditions for Eulerian and Lagrangian representations of the dispersed phase. In a second step, the Lagrangian injection method is combined to a secondary breakup model of the literature to partly account for the liquid disintegration process. The presented LES’s of the evaporating two-phase flow inside the MERCATO geometry consider two different aspects. First, the impact of injection modeling on spray dynamics is assessed. Second, Euler-Euler and Euler-Lagrange simulations relying on the common simplified injection model are compared.

Une part importante du bruit généré par les moteurs d'avion est liée à la combustion. Afin de réduire cette source de bruit, une compréhension fine des phénomènes associés est nécessaire. Deux mécanismes générateurs de bruit, et ayant pour origine la combustion, ont été identifié dans les moteurs d'avions dans les années 1970: un premier mécanisme dit direct, qui est lié directement à un dégagement de chaleur instationnaire, et l'autre dit indirect qui est lié aux interactions entre les étages de turbine et les fluctuations de température en sortie de chambre, également produites par la combustion. Des méthodes analytiques et des simulations numériques sont utilisées ici à la fois pour montrer l'importance du bruit de combustion indirect par rapport au bruit direct, et pour donner des limites de validité des approches analytiques qui sont basées sur l'hypothèse de tuyère compacte. Trois configurations différentes sont étudiées dans un premier temps: une tuyère quasi-1-D, une tuyère axi-symétrique 2-D, ainsi qu'une aube de turbine 2-D. Finalement, un secteur de chambre de combustion 3-D réelle (SNECMA) est calculé à l'aide de la Simulation aux Grandes Echelles. Les fluctuations en sortie du brûleur sont utilisées pour évaluer le bruit total généré par la combustion (direct et indirect) à l'aide des approches analytiques précédemment étudiées. / An important part of the noise generated by aero-engines is caused by the combustion. To decrease this source of noise, a precise comprehension of the underlying phenomenon is required. Two different mechanisms generating noise in aero-engines because of the combustion have been identified in the 1970’s: the direct mechanism that is directly related to the unsteady heat release, and the indirect one that is caused by the interactions between the turbine stages and the temperature fluctuations also produced by the combustion. Analytical methods and numerical simulations are used here both to show the importance of the indirect combustion noise compared with the direct one, and to provide some validity limits of compact nozzles analytical approaches. Three different configurations dealing with indirect noise are investigated: quasi-1- D nozzle, axisymmetric 2-D nozzle and 2-D turbine blade. Finally, an actual 3-D combustion chamber sector (SNECMA) is addressed with Large-Eddy Simulation. Fluctuations at the outlet of the combustor are used to compute the overall noise caused by the combustion (direct and indirect), by means of the investigated analytical models.

Comme le groupe de symétries de Lie des équations aux dérivées partielles représentent les propriétés physiques intrinsèques contenues dans les équations, il offre un outil efficace pour étudier et modéliser les phénomènes physiques. Ainsi, dans cette thèse, on se propose d’appliquer la théorie du groupe de symétries de Lie à la modélisation des écoulements anisothermes.On calcule alors des lois de paroi, et, plus généralement des lois d’échelle, pour la vitesse et la température dans le cas d’un écoulement parallèle. En fait, ces lois d’échelle se révèlent être simplement des solutions auto-similaires des équations de Navier-Stokes moyennées par rapport aux symétries des équations.Ensuite, par l’approche de la théorie des groupes de Lie, on construit une classe de modèles de sous-maille qui sont invariants par les symétries des équations de Navier-Stokes anisothermes.Ces modèles ont l’avantage de respecter les propriétés physiques des équations qui sont contenues dans les symétries. De plus, par cette approche, le modèle de flux de chaleur apparaît naturellement,sans qu’on ait besoin de faire appel à la notion de nombre de Prandtl de sous-maille,ce qui augmente la portée de ces modèles par rapport à la plupart des modèles existants. Par ailleurs, le comportement proche de la paroi de certains des modèles proposés est étudié. Enfin,des tests numériques en convection naturelle et en convection mixtes sont effectués. / Since the Lie group of a given partial differential equation, represent the intrinsic physical propertiesof the equation, it gives a strong tool for modeling its physical phenomenas. The mainpurpose of this thesis, is to apply the Lie group theory, in modeling non-isothermal flows. Therefore,we calculate wall laws and more generally scaling laws for the velocity and the temperatureof a parallel flow. In fact, these scaling laws are simply self-similar solutions of the Navier-Stokesequations averaged with respect to their symmetry.The approach of the Lie group theory, leads to a class of sub-grade models which are invariantvia the symmetries of the non-isothermal Navier-Stokes equations. These models respectthe physical properties contained in these symmetries. Moreover, via this approach the heat flowmodel appears naturally in this class, without introducing the notion of the Prandlt number,which is not the case for any other existing model. From the other side, the behavior near thewall of particular models in this class, is studied. Finally, numerical tests are done in both casesof the natural convection and the mixed one.