Les courants de gravité, écoulements issus de la présence d’un contraste de densité dans un fluide ou de la présence de fluides de densités différentes, sont rencontrés dans de nombreuses situations naturelles ou industrielles. Quelques exemples de courants de gravité sont les avalanches, les marées noires et les courants de turbidité. Certains courants de gravité peuvent représenter un danger pour l’homme ou l’environnement, il est donc nécessaire de comprendre et de prédire leur dynamique. Cette thèse a pour objectif d’étudier l’évolution de courants de gravité de masse fixée, et notamment l’influence d’une forme initiale non-axisymétrique sur la dynamique, effet jusque-là peu abordé dans la littérature. Pour cela, une large gamme de paramètres est couverte, incluant le rapport de masse volumique entre le fluide ambiant et le fluide dans le courant, le rapport de forme initiale, la forme de la section horizontale de la colonne de fluide (circulaire, rectangulaire ou en forme de croix), le nombre de Reynolds (couvrant jusqu’à 4 ordres de grandeur) et la nature du fluide lourd (salin ou chargé en particules). Deux campagnes d’expériences ont été menées et complétées par des simulations numériques hautement résolues. Le résultat majeur est que la propagation du courant et le dépôt de particules (lorsque particules il y a) sont fortement influencés par la forme initiale de la colonne de fluide. Dans le cas de la colonne initialement rectangulaire le courant se propage plus vite et dépose plus de particules dans la direction initialement de plus courte dimension. Ce comportement non-axisymétrique est observé dans une large gamme des paramètres étudiés ici. Pourtant les modèles analytiques existants et notamment le modèle dit de boîte (box model) qui prédit avec succès le comportement des courants de gravité/turbidité dans les cas plan et axisymétrique ne sont pas capables de reproduire ce phénomène. C’est pourquoi une extension du box model a été développée ici, et est en mesure de décrire la dynamique de courants de gravité de masse fixée dont la forme initiale est arbitraire. Le cas plus général d'un courant de gravité évoluant sur un plan incliné a été abordé et une dynamique intéressante a été observée. / Gravity currents are buoyancy driven flows that appear in a variety of situations in nature as well as industrial applications. Typical examples include avalanches, oil spills, and turbidity currents. Most naturally occurring gravity currents are catastrophic in nature, and therefore there is a need to understand how these currents advance, the speeds they can attain, and the range they might cover. This dissertation will focus on the short and long term evolution of gravity currents initiated from a finite release. In particular, we will focus attention to hitherto unaddressed effect of the initial shape on the dynamics of gravity currents. A range of parameters is considered, which include the density ratio between the current and the ambient (heavy, light, and Boussinesq currents), the initial height aspect ratio (height/radius), different initial cross-sectional geometries (circular, rectangular, plus-shaped), a wide range of Reynolds numbers covering 4 orders of magnitude, as well as conservative scalar and non-conservative (particle-driven) currents. A large number of experiments have been conducted with the abovementioned parameters, some of these experiments were complemented with highly-resolved direct numerical simulations. The major outcome is that the shape of the spreading current, the speed of propagation, and the final deposition profile (for particle-driven currents) are significantly influenced by the initial geometry, displaying substantial azimuthal variation. Especially for the rectangular cases, the current propagates farther and deposits more particles along the initial minor axis of the rectangular cross section. This behavior pertaining to non-axisymmetric release is robust, in the sense that it is observed for the aforementioned range of parameters, but nonetheless cannot be predicted by current theoretical models such as the box model, which has been proven to work in the context of planar and axisymmetric releases. To that end, we put forth a simple analytical model (an extension to the classical box model), well suited for accurately capturing the evolution of finite volume gravity current releases with arbitrary initial shapes. We further investigate the dynamics of a gravity current resulting from a finite volume release on a sloping boundary where we observe some surprising features.

Sandstorms are frequently accompanied by intense electric fields and lightning. In a very narrow region close to the ground, sand particles undergo a charge exchange during which larger-sized sand grains become positively charged and smaller-sized sand grains become negatively charged and then all particles become suspended by the turbulent fluid motion. Although the association of intense electric fields with sandstorms has long been observed, the mechanism that causes these intense electric fields has not yet been described. Here, we hypothesize that differently sized sand particles are differentially transported by turbulence in the flow, resulting in a large-scale charge separation and a consequential large-scale electric field. To confirm our hypothesis, we combined a large-eddy simulation framework comprising a turbulent atmospheric boundary layer and movement of sand particles with an electrostatic Gauss law to investigate the physics of the electric fields in sandstorms. We varied the strength of the sandstorm from weak to strong as parametrized by the number density of the entrained sand particles. Our simulations reproduced observational measurements of both mean and root mean squared fluctuation values of the electric field. Our results allowed us to propose a law in which the electric field scales to two-thirds of the power of the concentration of the sand particles in weak-to-medium strength sandstorms. The underlying approach to simulate the solid particle-laden flow is Eulerian-Eulerian in which the particles are characterized by statistical descriptors. To explore the essential physics of the electric field generation in a sandstorm, we model the high-Reynolds-number atmospheric boundary-layer (ABL) using two different canonical turbulent flows: one model is that of a turbulent boundary-layer (TBL), and the second one is that of a turbulent half-channel flow. For the particle phase, the direct quadrature method of moments (DQMOM) is chosen in which the abscissas and weights of the quadrature method are tracked directly. The utilization of this framework is proposed to examine the transport of sand in sandstorms. Furthermore, the physical mechanisms necessary for production and sustenance of large-scale electric fields in sandstorms is investigated.

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.

Le contexte général de cette thèse s'inscrit dans le cadre de la modélisation eulérienne instationnaire des écoulements turbulents anisothermes gaz - particules. La modélisation de ces écoulements est cruciale pour de nombreuses applications industrielles et pour la prédiction de certains phénomènes naturels. Par exemple, la combustion diphasique dans les moteurs automobiles et aéronautiques est précédée par l'injection et la dispersion de carburant liquide dans la chambre de combustion. Les phénomènes mis en jeu exigent alors une prédiction locale tenant compte du caractère instationnaire de l'écoulement turbulent et de la présence de géométries complexes. De plus, de nombreuses études expérimentales et numériques récentes ont mis en évidence le rôle prépondérant de l'inertie des particules sur les mécanismes de dispersion et de concentration préférentielle en écoulement turbulent. Ceci rend donc indispensable la prise en compte de ces mécanismes dans la modélisation diphasique. Au cours de ce travail de thèse, une approche eulérienne locale et instantanée a été développée pour prédire les écoulements gaz-particules anisothermes et turbulents. Elle est basée sur l'approche statistique du Formalisme Eulérien Mésoscopique (MEF) introduite par Février et al. (JFM, 2005). Cette approche a été ici étendue aux variables thermiques pour la prise en compte du caractère anisotherme de l'écoulement. Cette approche a été ensuite utilisée dans le cadre de la méthode des moments (Kaufmann et al., JCP, 2008), et un système d'équations locales et instantanées pour la phase dispersée a été proposé. La modélisation au premier ordre exige la fermeture des moments de second ordre apparaissant dans les équations de la quantité de mouvement et de l'énergie. La proposition de telles relations constitutives fait l'objet d'une partie de la thèse. Afin de fournir une méthode capable de prédire le comportement local, instantané et anisotherme de la phase dispersée dans des configurations `a une échelle réaliste, les équations pour la phase dispersée ont été filtrées et une modélisation aux grandes échelles (LES) est effectuée. Cette modélisation étends, par la prise en compte des variables thermiques, le travail de Moreau et al. (FtaC, 2010) sur l'approche LES Euler-Euler en conditions isothermes. L'approche complète est enfin appliquée aux résultats de simulation numérique d'un jet plan turbulent gazeux froid, chargé en particules, dans une turbulence homogène isotrope chaude monophasique. / The aim of this thesis is to provide an Eulerian modeling for the dispersed phase interacting with unsteady non-isothermal turbulent flows. The modeling of these flows is crucial for several industrial applications and for predictions of natural events. Examples are the combustion chambers of areo engines where the combustion is preceded by the injection and dispersion of liquid fuel. The prediction of such phenomena involves a local modeling of the mixture for taking into account the unsteady behavior of the turbulent flow and the presence of complex geometries. Moreover, many experimental and numerical studies have recently highlighted the significant role of the particle inertia on the mechanisms of dispersion and preferential concentration. Accounting for such mechanisms is therefore essential for modeling the particle-laden turbulent flows. In this thesis, a local and instantaneous Eulerian approach able to describe and to predict the local behavior of inertial particles interacting with non-isothermal turbulent flows has been developed. It is based on the statistical approach known as Mesoscopic Eulerian formalism (MEF) introduced by Février et al. (JFM, 2005). The statistical approach has been extended to the thermal quantities in order to account for the non-isothermal conditions into the modeling. This formalism is then used in the framework of the moment approach (Kaufmann et al., JCP, 2008) and a system of local and instantaneous equations for the non-isothermal dispersed phase has been suggested. The first order modeling requires to close second-order moments appearing in momentum and energy equations. The proposal of such constitutive relations makes the object of a part of this study. In order to provide an Eulerian approach usable in real configurations at industrial scale, the equations of the dispersed phase are filtered and the approach developed in the framework of the Large-Eddy Simulations. From the work of Moreau et al. (FTaC, 2010), the Eulerian-Eulerian LES approach is then extended to non-isothermal conditions. The whole modeling is then a priori tested against numerical simulations of a cold planar turbulent particle-laden jet crossing a homogeneous isotropic decaying hot turbulence.

An experimental study on impaction of a single drop on solid surfaces was conducted to show the effects of particles on the impact process. The parameters were: volume fraction of particles (0 to 0.3), particle size (0.47 to 250 micron), and ratio of particle size to drop size (0.00017 to 0.074). The effect of particle volume fraction on the spreading process depended on impact speed and substrate. At low impact speed, particles had little effect on the spreading except for surfaces where the equilibrium contact angle was low. For high impact speed, the influence of particles on spreading can be described by the effective viscosity. The effect of particle size on the spreading process also depended on impact speed and substrate. At low impact speed, the drop did not have enough kinetic energy to overcome the energy barrier associated with the large particles. For particle-laden liquids, retraction was affected by particle parameters. When pure liquid drops retracted from the maximum spreading ratio, the retraction appeared to be symmetric around the point of impaction while retraction of the particle-laden drop was sometimes asymmetric. Rebounding on the Teflon film depended on impact speed, particle volume fraction, and particle size. The impact speed must reach a critical value for rebounding to occur. Bouncing results suggested that the probability of bouncing decreased as viscosity increased, impact speed increased, and surface tension decreased. The non-wetting behavior and bouncing probably involved an air layer between the surface and the drop. When a low-velocity liquid drop impacts on a surface, ejection of a secondary drop from the top of the impacting drop was sometimes observed. When Renardy et al.'s (2003) criterion for the range of velocities for existence of a capillary wave was applied to for a 3.2-mm water drop; the range was between 0.2 to 1.5 m/s. However, drop ejection was observed at lower impact speed. When apparent viscosity of the particle-laden liquid obtained from Krieger's equation (1972) was used in the pure liquid models for predicting the maximum spreading ratio, good agreement between model predictions and experimental results was obtained when Park et al's model (2003) was used.

Le but de cette thèse est d'étudier le transport et le dépôt de particules solides dans les écoulements à travers les fractures. Dans un premier temps, l'écoulement monophasique à travers les fractures est étudié afin d'évaluer la validité de la loi cubique locale comme modèle de l'écoulement. Des canaux à parois sinusoïdales à géométrie variable sont utilisés pour représenter différents types de fractures. Un premier développement analytique montre que l'ouverture hydraulique de la fracture diffère de son ouverture moyenne lorsque la rugosité des parois est élevée. La méthode des éléments finis est ensuite utilisée pour résoudre les équations de continuité et de Navier-Stokes et comparer les solutions numériques aux prédictions théoriques de la loi cubique locale sur une gamme relativement étendue de nombres de Reynolds Re. Pour de faibles Re, typiquement inférieurs à 15, la loi cubique locale décrit raisonnablement l'écoulement, surtout lorsque la rugosité et le déphasage entre les parois sont relativement faibles. Dans un deuxième temps, les écoulements chargés de particules sont étudiés. Une approche analytique est d'abord développée pour montrer comment des particules distribuées dans un écoulement stationnaire et laminaire à travers une fracture peuvent être transportées sur de longues distances ou au contraire se déposer à l'intérieur. Plus précisément, une équation simple décrivant la trajectoire d'une particule est établie. Sur la base de cette équation, il est démontré que, quand l'inertie des particules est négligeable, leur comportement dépend directement de la géométrie de la fracture et d'un nombre adimensionnel W qui relie la vitesse de sédimentation des particules à la vitesse moyenne de l'écoulement. L'équation proposée est vérifiée en comparant ses prédictions à des simulations numériques de suivi de particules prenant en compte l'inertie des particules et résolvent complètement les équations de Navier-Stokes. Il est montré que l'équation est valide lorsque l'inertie du fluide est faible. Des diagrammes de régimes, permettant de prévoir le comportement des particules à travers la fracture sont proposés. Enfin, un appareil expérimental conçu dans le but d'effectuer une évaluation pratique du modèle analytique est présenté et les résultats préliminaires sont discutés. Les résultats expérimentaux préliminaires tendent valider le modèle analytique. De façon plus générale, les résultats obtenus à travers ce travail de thèse font progresser nos connaissances du comportement des petites particules transportées dans les écoulements de fractures. Potentiellement, ce travail devrait permettre d'améliorer notre prévision de la pollution souterraine, et peut avoir des applications dans le développement de nouvelles techniques de filtration de l'eau et de séparation des minéraux / The aim of the present thesis is to study the transport and deposition of small solid particles in fracture flows. First, single-phase fracture ow is investigated in order to assess the validity of the local cubic law for modeling ow in corrugated fractures. Channels with sinusoidal walls having different geometrical properties are considered to represent different fracture geometries. It is analytically shown that the hydraulic aperture of the fracture clearly deviates from its mean aperture when the walls roughness is relatively high. The finite element method is then used to solve the continuity and the Navier-Stokes equations and to simulate fracture ow in order to compare with the theoretical predictions of the local cubic law for Reynolds numbers Re in the range 0.067-67. The results show that for low Re, typically less than 15, the local cubic law can properly describe the fracture ow, especially when the fracture walls have small corrugation amplitudes. For Re higher than 15, the local cubic law can still be valid under the conditions that the fracture presents a low aspect ratio, small corrugation amplitude, and moderate phase lag between its walls. Second, particle-laden flows are studied. An analytical approach has been developed to show how particles sparsely distributed in steady and laminar fracture flows can be transported for long distances or conversely deposited inside the channel. More precisely, a rather simple particle trajectory equation is established. Based on this equation, it is demonstrated that when particles' inertia is negligible, their behavior is characterized by the fracture geometry and by a dimensionless number W that relates the ratio of the particles sedimentation terminal velocity to the ow mean velocity. The proposed particle trajectory equation is verified by comparing its predictions to particle tracking numerical simulations taking into account particle inertia and resolving the full Navier-Stokes equations. The equation is shown to be valid under the conditions that ow inertial effects are limited. Based on this trajectory equation, regime diagrams that can predict the behavior of particles entering closed channel flows are built. These diagrams enable to forecast if the particles entering the channel will be either deposited or transported till the channel outlet. Finally, an experimental apparatus that was designed to have a practical assessment of the analytical model is presented. Preliminary experimental results tend to verify the analytical model. Overall, the work presented in this thesis give new insights on the behavior of small particles in fracture flows, which may improve our prediction and control of underground contamination, and may have applications in the development of new water filtration and mineral separation techniques

Les écoulements chargés en particules sont présents dans de nombreuses applications industrielles telles que le transport de boues ou l’industrie chimique en général. Dans des mélanges constitués de particules solides immergées dans un fluide visqueux, les interactions entre particules jouent un rôle essentiel dans la viscosité globale du mélange.Le phénomène de suspension est causé par des interactions hydrodynamiques à courte distance, connues sous le nom de lubrification. Les forces de lubrification sont généralement sous-estimées en raison de leur nature et de la discrétisation spatiale du problème.Dans cette thèse, nous proposons un modèle de lubrification qui estime les forces et couples hydrodynamiques non résolues par un solveur couplant la résolution des équations de Navier-Stokes incompressible par une méthode de volumes pénalisés, à la résolution de la dynamique des particules par une méthode aux éléments discrets. Les corrections des contraintes hydrodynamiques sont faites localement sur la surface des particules en interaction sans aucune hypothèse sur la forme générale des particules. La version finale du modèle de lubrification proposée peut être utilisée pour des suspensions de particules convexes sans aucune tabulation. La méthode numérique a été validée avec des particules sphériques et des ellipsoïdes, en comparant des simulations à des données expérimentales.Dans le cas de particules sphériques, le modèle de lubrification est aussi précis que les modèles de lubrification existants qui sont limités à ce type de géométrie. La compatibilité du modèle avec des particules convexes a été validée en comparant des simulations,utilisant des ellipsoïdes, à des mesures expérimentales que nous avons réalisées. / Particle-laden flows can be found in many industrial applications such as slurry transport or the chemical industry in general. In mixtures made of solid particles emerged in a viscous fluid, particle interactions play an essential role in the overall mixture viscosity. The suspension phenomenon is caused by short-range hydrodynamic interactions, known as lubrication. Lubrication forces are usually underestimated due to their singularities and the spatial discretization of the numerical schemes. In this thesis, we propose a lubrication model for a coupled volume penalization method and discrete element method solver that estimates the unresolved hydrodynamic forces and torques in incompressible Navier-Stokes flows. Corrections are made locally on the surfaces of the interacting particles without any assumption on the global particle shapes. The final version of the local lubrication model can be used for suspension of convex particles without any tabulations. The numerical method has been validated against experimental data with spherical and ellipsoidal particles. With spherical particles, the lubrication model performs as well as existing numerical models that are limited to this specific particle shape. The model compatibility with convex particles has been validated by comparing simulations using ellipsoids to experimental measurements we made.

Le transport de particules par des écoulements turbulents est un phénomène présent dans de nombreux écoulements naturels et industriels, tels que la dispersion de polluants dans l'atmosphère ou du phytoplancton et plastiques dans et à la surface des océans. Les modèles prédictifs classiques ne peuvent prévoir avec précision la formation de larges fluctuations de concentrations. La première partie de cette thèse concerne une étude de la dispersion turbulente de traceurs émis à partir d'une source ponctuelle et continue. Les fluctuations spatiales de masse sont déterminées en fonction de la distance à la source et à l'échelle d'observation. La combinaison de plusieurs phénomènes physiques à l'origine du mélange limite la validité d'une caractérisation de géométrie fractale. Une approche alternative est proposée, permettant d'interpréter les fluctuations massiques en terme des différents régimes de séparation de pair dans des écoulements turbulents. La seconde partie concerne des particules ayant une inertie finie, dont la dispersion dans l'espace des vitesses requiert de développer des techniques de modélisation adaptées. Une méthode numérique originale est proposée pour exprimer la distribution des particules dans l'espace position-vitesse. Cette méthode est ensuite utilisée pour décrire la modulation de la turbulence bi- dimensionnelle par des particules inertielles. A grand nombres de Stokes, l'effet montré est analogue à celui d'une friction effective à grande échelle. Aux petits Stokes, le spectre de l'énergie cinétique du fluide et les transferts non-linéaires sont modifiées d'une manière non triviale. / The transport of particles by turbulent flows is ubiquitous in nature and industry. It occurs in planet formation, plankton dynamics and combustion in engines. For the dispersion of atmospheric pollutants, traditional predictive models based on eddy diffusivity cannot accurately reproduce high concentration fluctuations, which are of primal importance for ecological and health issues. The first part of this thesis relates to the dispersion by turbulence of tracers continuously emitted from a point source. Mass fluctuations are characterized as a function of the distance from the source and of the observation scale. The combination of various physical mixing processes limits the use of fractal geometric tools. An alternative approach is proposed, allowing to interpret mass fluctuations in terms of the various regimes of pair separation in turbulent flows. The second part concerns particles with a finite and possibly large inertia, whose dispersion in velocity requires developing efficient modelling techniques. A novel numerical method is proposed to express inertial particles distribution in the position-velocity phase space. Its convergence is validated by comparison to Lagrangian measurements. This method is then used to describe the modulation of two-dimensional turbulence by large-Stokes-number heavy particles. At high inertia, the effect is found to be analogous to an effective large-scale friction. At small Stokes numbers, kinetic energy spectrum and nonlinear transfers are shown to be modified in a non-trivial way which relates to the development of instabilities at vortices boundaries.

This thesis deals with the stability of particle laden flows. Both modal and non-modal linear analyses have been performed on two-way coupled particleladen flows, where particles are considered spherical, solid and either heavy or light. When heavy particles are considered, only Stokes drag is used as interaction term. Light particles cannot be modeled with Stokes drag alone, therefore added mass and fluid acceleration are used as additional interaction forces. The modal analysis investigates the asymptotic behavior of disturbances on a base flow, in this thesis a pressure-driven plane channel flow. A critical Reynolds number is found for particle laden flows: heavy particles increase the critical Reynolds number compared to a clean fluid, when particles are not too small or too large. Neutrally buoyant particles, on the other hand, have no influence on the critical Reynolds number. Non-modal analysis investigates the transient growth of disturbances, before the subsequent exponential behavior takes over. We investigate the kinetic energy growth of a disturbance, which can grow two to three orders of magnitude for clean fluid channel flows. This transient growth is usually the phenomenon that causes transition to turbulence: the energy can grow such that secondary instabilities and turbulence occurs. The total kinetic energy of a flow increases when particles are added to the flow as a function of the particle mass fraction. But instead of only investigating the total energy growth, the non-modal analysis is expanded such that we can differentiate between fluid and particle energy growth. When only the fluid is considered in a particle-laden flow, the transient growth is equal to the transient growth of a clean fluid. Besides thes Stokes drag, added mass and fluid acceleration, this thesis also discusses the influence of the Basset history term. This term is often neglected in stability analyses due to its arguably weak effect, but also due to difficulties in implementation. To implement the term correctly, the history of the particle has to be known. To overcome this and obtain a tractable problem, the square root in the history term is approximated by an exponential. It is found that the history force as a small effect on the transient growth. Finally, Direct numerical simulations are performed for flows with heavy particles to investigate the influence of particles on secondary instabilities. The threshold energy for two routes to turbulence is considered to investigate whether the threshold energy changes when particles are included. We show that particles influence secondary instabilities and particles may delay transition. / QC 20111013

<p>This thesis is concerned with particle subgrid scale (SGS) modeling in large-eddy simulation (LES) of particle-laden turbulence. Although most particle-laden LES studies have neglected the effect of the subgrid scales on the particles, several particle SGS models have been proposed in the literature. In this research, the approximate deconvolution method (ADM), and the stochastic models of Fukagata et al. (2004), Shotorban and Mashayek (2006) and Berrouk et al. (2007) are analyzed. The particle SGS models are assessed by conducting both a priori and a posteriori tests of a periodic box of decaying, homogeneous and isotropic turbulence with an initial Reynolds number of Re=74. The model results are compared with particle statistics from a direct numerical simulation (DNS). Particles with a large range of Stokes numbers are tested using various filter sizes and stochastic model constant values. Simulations with and without gravity are performed to evaluate the ability of the models to account for the crossing trajectory and continuity effects. The results show that ADM improves results but is only capable of recovering a portion of the SGS turbulent kinetic energy. Conversely, the stochastic models are able to recover sufficient energy, but show a large range of results dependent on Stokes number and filter size. The stochastic models generally perform best at small Stokes numbers. Due to the random component, the stochastic models are unable to predict preferential concentration.</p> / Master of Applied Science (MASc)