Дисертації з теми "Inertial particle dynamics"

La turbulence est connue pour sa capacité à disperser efficacement de la matière, que ce soit des polluantes dans les océans ou du carburant dans les moteurs à combustion. Deux considérations essentielles s’imposent lorsqu’on considère de telles situations. Primo, l’écoulement sous-jacente pourrait avoir une influence non-négligeable sur le comportement des particules. Secundo, la concentration locale de la matière pourrait empêcher le transport ou l’augmenter. Pour répondre à ces deux problématiques distinctes, deux dispositifs expérimentaux ont été étudiés au cours de cette thèse. Un premier dispositif a été mis en place pour étudier l’écoulement de von Kàrmàn, qui consiste en une enceinte fermé avec de l’eau forcé par deux disques en contra-rotation. Cette écoulement est connu pour être très turbulent, inhomogène, et anisotrope. Deux caméras rapides ont facilité le suivi Lagrangien des particules isodenses avec l’eau et petites par rapport aux échelles de la turbulence. Ceci a permis une étude du bilan d’énergie cinétique turbulente qui est directement relié aux propriétés de transport. Des particules plus lourdes que l’eau ont aussi été étudiées et montrent le rôle de l’anisotropie de l’écoulement dans la dispersion des particules inertielles. Un deuxième dispositif, un écoulement de soufflerie ensemencé avec des gouttelettes d’eau micrométriques a permis une étude de l’effet de la concentration locale de l’eau sur la vitesse de chute des gouttelettes grâce à une montage préexistant. Un modèle basé sur des méthodes théorique d'écoulements multiphasiques a été élaboré enfin de prendre en compte les effets collectifs de ces particules sedimentant dans un écoulement turbulent. Les résultats théoriques et expérimentaux mettent en évidence le rôle de la polydispersité et du couplage entre les deux phases dans l’augmentation de la sédimentation des gouttelettes<br>Turbulence is well known for its ability to efficiently disperse matter, whether it be atmospheric pollutants or gasoline in combustion motors. Two considerations are fundamental when considering such situations. First, the underlying flow may have a strong influence of the behavior of the dispersed particles. Second, the local concentration of particles may enhance or impede the transport properties of turbulence. This dissertation addresses these points separately through the experimental study of two different turbulent flows. The first experimental device used is the so-called von K\'arm\'an flow which consists of an enclosed vessel filled with water that is forced by two counter rotating disks creating a strongly inhomogeneous and anisotropic turbulence. Two high-speed cameras permitted the creation a trajectory data base particles that were both isodense and heavier than water but were smaller than the smallest turbulent scales. The trajectories of this data base permitted a study of the turbulent kinetic energy budget which was shown to directly related to the transport properties of the turbulent flow. The heavy particles illustrate the role of flow anisotropy in the dispersive dynamics of particles dominated by effects related to their inertia. The second flow studied was a wind tunnel seeded with micrometer sized water droplets which was used to study the effects of local concentration of the settling velocities of these particles. A model based on theoretical multi-phase methods was developed in order to take into account the role of collective effects on sedimentation in a turbulent flow. The theoretical results emphasize the role of coupling between the underlying flow and the dispersed phase

In this work we rst study the non-Newtonian effects on the inertial instabilities in shear flows and second the inertial suspensions of finite size rigid particles by means of numerical simulations. In the first part, both inelastic (Carreau) and elastic models (Oldroyd-B and FENE-P) have been employed to examine the main features of the non-Newtonian fluids in several congurations; flow past a circular cylinder, in a lid-driven cavity and in a channel. In the framework of the linear stability analysis, modal, non-modal, energy and sensitivity analysis are used to determine the instability mechanisms of the non-Newtonian flows. Signicant modifications/alterations in the instability of the different flows have been observed under the action of the non-Newtonian effects. In general, shear-thinning/shear-thickening effects destabilize/stabilize the flow around the cylinder and in a lid driven cavity. Viscoelastic effects both stabilize and destabilize the channel flow depending on the ratio between the viscoelastic and flow time scales. The instability mechanism is just slightly modied in the cylinder flow whereas new instability mechanisms arise in the lid-driven cavity flow. In the second part, we employ Direct Numerical Simulation together with an Immersed Boundary Method to simulate the inertial suspensions of rigid spherical neutrally buoyant particles in a channel. A wide range of the bulk Reynolds numbers, 500&lt;Re&lt;5000, and particle volume fractions, 0&lt;\Phi&lt;3, is studied while fixing the ratio between the channel height to particle diameter, 2h/d = 10. Three different inertial regimes are identied by studying the stress budget of two-phase flow. These regimes are laminar, turbulent and inertial shear-thickening where the contribution of the viscous, Reynolds and particle stress to transfer the momentum across the channel is the strongest respectively. In the inertial shear-thickening regime we observe a signicant enhancement in the wall shear stress attributed to an increment in particle stress and not the Reynolds stress. Examining the particle dynamics, particle distribution, dispersion, relative velocities and collision kernel, confirms the existence of the three regimes. We further study the transition and turbulence in the dilute regime of finite size particulate channel flow. We show that the turbulence can sustain in the domain at Reynolds numbers lower than the one of the unladen flow due to the disturbances induced by particles.<br><p>QC 20151127</p>

The self-similar evolution of a turbulent Rayleigh-Taylor (R-T) mix is investigated through experiments and numerical simulations. The experiments consisted of velocity and density measurements using thermocouples and Particle Image Velocimetry techniques. A novel experimental technique, termed PIV-S, to simultaneously measure both velocity and density fields was developed. These measurements provided data for turbulent correlations, power spectra, and energy balance analyses. The self-similarity of the flow is demonstrated through velocity profiles that collapse when normalized by an appropriate similarity variable and power spectra that evolve in a shape-preserving form. In the self-similar regime, vertical r.m.s. velocities dominate over the horizontal r.m.s. velocities with a ratio of 2:1. This anisotropy, also observed in the velocity spectra, extends to the Taylor scales. Buoyancy forcing does not alter the structure of the density spectra, which are seen to have an inertial range with a -5/3 slope. A scaling analysis was performed to explain this behavior. Centerline velocity fluctuations drive the growth of the flow, and can hence be used to deduce the growth constant. The question of universality of this flow was addressed through 3D numerical simulations with carefully designed initial conditions. With long wavelengths present in the initial conditions, the growth constant was found to depend logarithmically on the initial amplitudes. In the opposite limit, where long wavelengths are generated purely by the nonlinear interaction of shorter wavelengths, the growth constant assumed a universal lower bound value of

Particle suspensions occur in many situations in nature and industry. In this master’s thesis, the motion of a single rigid spheroidal particle immersed in Stokes flow is studied numerically using a boundary integral method and a new specialized quadrature method known as quadrature by expansion (QBX). This method allows the spheroid to be massless or inertial, and placed in any kind of underlying Stokesian flow.   A parameter study of the QBX method is presented, together with validation cases for spheroids in linear shear flow and quadratic flow. The QBX method is able to compute the force and torque on the spheroid as well as the resulting rigid body motion with small errors in a short time, typically less than one second per time step on a regular desktop computer. Novel results are presented for the motion of an inertial spheroid in quadratic flow, where in contrast to linear shear flow the shear rate is not constant. It is found that particle inertia induces a translational drift towards regions in the fluid with higher shear rate.<br>Partikelsuspensioner förekommer i många sammanhang i naturen och industrin. I denna masteruppsats studeras rörelsen hos en enstaka stel sfäroidisk partikel i Stokesflöde numeriskt med hjälp av en randintegralmetod och en ny specialiserad kvadraturmetod som kallas quadrature by expansion (QBX). Metoden fungerar för masslösa eller tröga sfäroider, som kan placeras i ett godtyckligt underliggande Stokesflöde.   En parameterstudie av QBX-metoden presenteras, tillsammans med valideringsfall för sfäroider i linjärt skjuvflöde och kvadratiskt flöde. QBX-metoden kan beräkna kraften och momentet på sfäroiden samt den resulterande stelkroppsrörelsen med små fel på kort tid, typiskt mindre än en sekund per tidssteg på en vanlig persondator. Nya resultat presenteras för rörelsen hos en trög sfäroid i kvadratiskt flöde, där skjuvningen till skillnad från linjärt skjuvflöde inte är konstant. Det visar sig att partikeltröghet medför en drift i sidled mot områden i fluiden med högre skjuvning.

Ce projet expérimental étudiera la dynamique des gouttelettes dans une interface turbulente / non turbulente, avec présence de cisaillement. Pour mener à bien cette recherche, nous utiliserons des installations et des techniques de mesure uniques, à savoir deux souffleries équipées de systèmes produisant de la turbulence qui peuvent être activés différentiellement pour générer une interface turbulente / non turbulente. Cette collaboration permettra de couvrir une large gamme de gradients d'intensité turbulente, de taux de cisaillement et de nombres de Reynolds pour l'étude de la dynamique des particules inertielles dans des conditions turbulentes / non turbulentes. L'étude produira des données sur les différentes tailles de gouttelettes qui couvrent la plage des nombres de Stokes, et qui caractérisent l'inertie des particules par rapport à l'échelle micrométrique de turbulence. Les domaines d'application peuvent être l'injection de carburant dans les systèmes de conversion d'énergie, le revêtement par pulvérisation industriel, la formation de pluie chaude dans les nuages ​​et les embruns des vagues déferlantes dans la zone de surf<br>This experimental project will investigate the dynamics of droplets at the interface between turbulent and non-turbulent regions, with shear. To conduct this research, we will utilize unique facilities and measurement techniques, namely two wind tunnels equipped with turbulence-generating systems that can be differentially activated to create a turbulent/non-turbulent interface. This collaboration will cover a wide range of turbulent intensity gradients, shear rates, and Reynolds numbers for studying the dynamics of inertial particles in turbulent/non-turbulent conditions. The study will produce data on various droplet sizes spanning the range of Stokes numbers, characterizing particle inertia relative to the micrometric scale of turbulence. Potential applications include fuel injection in energy conversion systems, industrial spray coating, warm rain formation in clouds, and sea spray in the surf zone

Les suspensions rencontrées dans diverses applications d’ingénierie (telles que l’extraction de pétrole brut, l’élaboration d’aliments, de béton ou de produits cosmétiques) peuvent présenter une dynamique riche lorsqu’elles sont soumises à un écoulement dans des géométries complexes. Il est important de savoir prédire la réponse de ces matériaux hétérogène sous écoulement compte tenu des applications. Pour construire des modèles prédictifs, il est indispensable de comprendre les phénomènes à différentes échelles, dans diverses configurations telles que l’écoulement d’une dispersion solide-liquide dans un coude ou dans un canal en forme de T, le mélange de cette dispersion par un agitateur, etc. Les écoulements de suspension normaux à un obstacle ont reçu peu d’attention (le fluide porteur étant liquide). Dans ce contexte, nous avons examiné la dynamique des particules dans l’écoulement de Hiemenz (un écoulement de type couche limite incident à une paroi), à l’aide de simulations numériques. Nous nous sommes concentrés essentiellement sur une ou deux particules de même densité que le fluide, et de taille finie comparée à l’épaisseur de couche limite (les particules ont une inertie finie près de la paroi car elles sont forcées de s’arrêter à la paroi). Nous avons utilisé des simulations numériques directes afin de mesurer le glissement des particules par rapport à l’écoulement local, la force d’interaction de nature hydrodynamique ainsi que la perte d’énergie. Toutes ces quantités ont été déterminées en tant que fonctions uniques du rapport entre la taille des particules et l’épaisseur de la couche limite visqueuse. Les simulations ont mis en évidence que l’approche d’une particule vers la paroi, suivant l’axe de symétrie de l’écoulement, subit une transition d’un régime de ralentissement dominé par les effets visqueux à un régime de type rebond, cette transition prenant place pour une taille de particule O. Nous avons établi un modèle pour la force hydrodynamique exercée sur la particule s’approchant de la paroi et pour le coefficient de restitution en écoulement normal à la paroi. Pour deux particules identiques sur l’axe, certaines séparations conduisent à une collision de particules avant que la particule inférieure (la plus proche de la paroi) ne touche la paroi; l’échange de quantité de mouvement qui en résulte conduit à une vitesse d’impact supérieure à celle d’une particule particule isolée. Les simulations révèlent que la dynamique de la paire inclut un rebond sans contact de la particule inférieure avec la paroi, en raison de la mise à l’abri par la particule supérieure contre la tranée, permettant à la force de pression de dominer<br>Two-phase suspensions encountered in various engineering applications(like crude oil extraction, elaboration of food, concrete or cosmetics), can exhibit rich dynamics when submitted to flow in complex geometries. Predicting the response of such heterogeneous material under flow is an important issue in view of applications. To build these predictive models, basic understanding of the dif- ferent scales is required for configurations such as pipe flow through an elbow or T-shape section, mixing a solid-liquid dispersion by a rotating impeller, etc. Suspension flows normal to an obstacle have seen limited attention with the carrier fluid being liquid phase. In this context, we examined particle dynamics in the well-known Hiemenz boundary-layer flow, with the aid of numerical simu- lations. We focused essentially on one or two neutrally buoyant particles, which are of finite size compared to the boundary layer thickness (particles have a finite inertia near the wall because they are forced to stop at the wall), and which are located at the symmetry axis of the flow. We used direct numerical simulations in order to measure the particle slip with respect to the local flow, the hydrodynamic force experienced by the particle and the energy loss during solvent-mediated particle-wall interaction. All these quantities were determined as unique functions of the ratio between the particle size and the thickness of the viscous boundary layer. When the particle size is increased, the simulations highlighted a transition of the particle dynamics from viscous damping to rebound, occurring for particle size O(). We established a model for the hydrodynamic force experienced by the incident particle, and for the restitution coefficient in wall-normal flow. For two identical particles on the axis, certain separations lead to particle collision before the lower (closer to wall) particle hits the wall; the resulting momentum exchange leads to larger impact velocity than for one particle. The simulations reveal that dynamics of the colliding pair includes unexpected rebound without contact with the wall for the lower of two particles, due to sheltering by the upper particle from drag allowing the pressure force to dominate

Cette thèse est consacrée au mécanisme conduisant à des taux de collisions importants dans les suspensions turbulentes de particules inertielles. Le travail a été effectué en suivant numériquement des particules, par simulations directes des équations de Navier-Stokes, et également par étude de modèles simplifiés. Les applications de ce domaine sont nombreuses aussi bien dans un contexte industriel que naturel (astrophysique, géophysique). L'approximation des collisions fantômes (ACF), souvent utilisée pour déterminer les taux de collision numériquement, consiste à compter dans une simulation, le nombre de fois que la distance entre les centres de deux particules devient plus faible qu'une distance seuil. Plusieurs arguments théoriques suggéreraient que cette approximation conduit à une surestimation du taux de collision. Cette thèse fournit non seulement une estimation quantitative de cette surestimation, mais également une compréhension détaillée des mécanismes des erreurs faites par l'ACF. Nous trouvons qu'une paire de particules peut subir des collisions répétées avec une grande probabilité. Ceci est relié à l'observation que, dans un écoulement turbulent, certaines paires de particules peuvent rester proches pendant très longtemps. Une deuxième classe de résultats obtenus dans cette thèse a permis une compréhension quantitative des très forts taux de collisions souvent observés. Nous montrons que lorsque l'inertie des particules n'est pas très petite, l'effet " fronde/caustiques ", à savoir, l'éjection de particules par des tourbillons intenses, est responsable du taux de collision élevé. En comparaison, la concentration préférentielle de particules dans certaines régions de l'espace joue un rôle mineur.

An understanding of the motion of soft capsules in microchannels is useful for a number applications. This knowledge can be used to develop devices to sort biological cells based on their size and stiffness. For example, cancer cells have a different stiffness from healthy cells and thus can be readily identified. Additionally, devices can be developed to detect flaws in synthetic particles. Using a 3D hybrid lattice Boltzmann and lattice spring method, the motion of rigid and soft capsules in a pressure-driven microfluidic flow was probed. The effect of inertial drift is evaluated in channels different Reynolds numbers. Other system parameters such as capsule elasticity and channel size are also varied to determine their effect. The equilibrium position of capsules in the channel is also obtained. The equilibrium position of rigid and soft capsules depends on the relative particle size. If the capsule is small, the equilibrium position is found to be closer to the channel wall. Conversely, for larger capsules, the equilibrium position is closer to the channel centerline. The capsule stiffness affects the magnitude of the cross-stream drift velocity. For a given Reynolds number, the equilibrium position of softer capsules is closer to the channel centerline. However, It is found that the equilibrium position of soft capsules is insensitive to the magnitude of the Reynolds number.

Thesis (Ph. D.)--Massachusetts Institute of Technology, School of Architecture and Planning, Program in Media Arts and Sciences, 2003.<br>Includes bibliographical references (leaves 69-70).<br>We describe theoretical and practical aspects of the particle trap as an inertial sensor. The insight motivating this approach is that a trapped particle acts like a mass on a spring, but the restoring forces are provided by electrostatic fields. Exquisitely machined physical mechanisms can be replaced by carefully tuned mechanical physics. Such inertial sensors could be simpler to build yet exhibit superior performance because their operating parameters can be dynamically controlled. Most currently available inertial sensors are inherently planar devices that obtain no more than two degrees of motional sensitivity from a given proof mass. The availability of an accurate, inexpensive, integrated six-degree-of-freedom inertial sensor would enable new applications of inertial sensing that are presently either infeasible or unconsidered. By adding inertial terms to the Paul trap dynamics we derive classical observables that depend on the local acceleration field. We also confirm that these observables appear in practice, in what we believe to be the first electrodynamic particle trap accelerometer. An important (and unusual) aspect of our accelerometer is its dynamic tunability: its effective spring constant depends on the trap drive parameters. Our roughly constructed trap also exhibits a large region of linear response to acceleration, and we present evidence suggesting that our accelerometer has performance comparable to commercially available sensors.<br>by Ernest Rehmatulla Post.<br>Ph.D.

This thesis focuses on ingestion of foreign objects into standard turboprop engine GE H80 situated in aircraft Let L-410 Turbolet. Aim of this study is to create methodology of numerical simulation of particle movement inside the engine, which could be used during design process of Inertial Particle Separator device. Thesis consists of backward-facing step benchmark study which validates used methodology. Second part describes flow field calculation and numerical setup. The last part is dedicated to particle tracking analysis. Simulated trajectories are visually investigated, and coordinates of particle impacts at 1st rotor of a compressor are correlated to position of real observed damage.

Les écoulements chargés de particules turbulentes sont répandus dans les applications industrielles et les phénomènes naturels. Au cours des dernières décennies, deux observations: la concentration préférentielle et la modification de la vitesse de sédimentation des particules se sont révélées être les conséquences les plus pertinentes de ces interactions particules - turbulence. Compte tenu de la complexité du problème, ce travail est composé de quatre lots de travaux.Le premier paquet implique une analyse des pièges de la méthode de pavage Vorono "{i}, qui est largement utilisée pour quantifier la concentration préférentielle. Nous avons trouvé quelques pièges qui compromettent les résultats de l'analyse en utilisant des enregistrements unidimensionnels. En outre, nous proposons une nouvelle méthode pour démêler les amas induits par la turbulence des fluctuations spatiales aléatoires, un problème commun signalé par d'autres chercheurs.Le deuxième ensemble comprend l'analyse de la turbulence en phase porteuse dans notre installation de soufflerie. À cet égard, nous conjecturons que les différents générateurs de turbulence (réseaux actifs, ouverts et passifs) modifient la cascade de turbulence et pourraient ainsi avoir un impact sur la concentration préférentielle des particules et le comportement de sédimentation. Dans ce but, nous avons analysé les flux générés par la grille active et constaté qu'une grille active laissée ouverte (avec un minimum de blocage) présente des échelles similaires à celles trouvées dans les grilles fractales. De plus, l'échelle de longueur intégrale n'a pas pu être facilement calculée pour les flux générés par la grille active en utilisant des protocoles triples aléatoires en raison du comportement de la fonction d'autocorrélation dans ces flux, qui ne franchit pas zéro. Nous proposons une nouvelle méthode pour résoudre ce problème qui pourrait être facilement appliquée dans une myriade de situations.Le troisième paquet consiste à estimer le taux de dissipation turbulente sur la phase porteuse due à la présence de particules. Au moyen d'une extension du théorème de Rice, qui relie l'échelle de longueur de Taylor à la distance moyenne entre les passages par zéro, nous avons proposé une méthode pour estimer la turbulence de la phase porteuse en présence de particules. Cette méthode utilise des ensembles de données de particules enregistrées par interférométrie doppler de phase. Nos résultats sont cohérents avec les expériences précédentes et les simulations numériques.Le quatrième paquet se réfère à la modification de sédimentation des particules. Nous avons trouvé que le nombre de Taylor Reynolds Re_lambda est le principal contributeur à la modification de la sédimentation des particules: à des valeurs croissantes de Re_lambda , la vitesse de sédimentation des particules est réduite. De plus, à des valeurs croissantes de Re_lambda , les frontières entre la modification positive et négative de la sédimentation se déplacent vers des valeurs plus petites du nombre de Rouse Ro = V_T / u<br>Turbulent particle laden flows are widespread in industrial applications, and natural phenomena. Over the last decades, two observations: preferential concentration, and particle settling velocity modification have stood out as the most relevant consequences of such particle - turbulence interactions. Given the complexity of the problem, this work is composed of four work packages.The first package involves a pitfall analysis of the Vorono"{i} tessellation method, which is widely used to quantify preferential concentration. We found some pitfalls that compromise the results of the analysis using uni-dimensional records. In addition, we propose a new method to disentangle turbulence driven clusters from random spatial fluctuations, a common problem reported by other researchers.The second package involve the analysis of the carrier phase turbulence in our wind tunnel facility. In this regard, we conjecture that the different turbulence generators (active, open, and passive grids) do change the turbulence cascade, and thereby, they could impact the particles preferential concentration and settling behavior. To this aim, we have analysed active grid generated flows, and found that an active grid left open (with minimum blockage) exhibits scalings similar to those found in fractal grids. Moreover, The integral length scale could not be easily computed for active grid generated flows using triple random protocols due to the behavior of the autocorrelation function in such flows, which does not cross zero. We propose a new method to tackle this problem which could be easily applied in a myriad of situations.The third package consist of estimating the turbulent dissipation rate on the carrier phase due to the particle presence. By means of an extension of the Rice theorem, which relates the Taylor length scale with the average distance between zero crossings, we have proposed a method to estimate the carrier phase turbulence in the presence of particles. This method uses particle datasets recorded by phase doppler interferometry. Our results are consistent with previous experiments, and numerical simulations.The fourth package refers to the particle settling modification. We found that the Taylor Reynolds number Re_lambda is the leading order contributor the particles settling modification: at increasing values of Re_lambda the settling velocity of the particles is reduced. Also, at increasing values of Re_lambda the boundaries between positive, and negative particle settling modification shifts to smaller values of the Rouse number Ro=V_T/u

Dispersed particle flows occur in many industrial, biological and geophysical applications. The knowledge of how these flow behave can for example lead to improved material processes, better predictions of vascular diseases or more accurate climate models. These particle flows have certain properties that depend on single particle motion in fluid flows and especially how they are distributed both in terms of spatial position and, if they are non-spherical, in terms of orientation. Much is already known about the motion of perfectly spherical particles. For non-spherical particles, apart from their translation, it is important to know the the rotational motion due to local velocity gradients. Such studies have usually been restricted by the assumption that particles are extremely small compared to fluid length scales. In this limit, both inertia of the particle and inertia of the fluid can be neglected for the particle motion. This thesis gives a complete picture of how a spheroidal particle (a particle described by a rotation of an ellipse around one of its principal axes) behave in a linear shear flow when including both fluid and particle inertia, using numerical simulations. It is observed that this very simple problem possess very interesting dynamical behavior with different stable rotational states appearing as a competition between the two types of inertia. The effect of particle inertia leads to a rotation where the mass of the particle is concentrated as far away from the rotational axis as possible, i.e.\ a rotation around the minor axis. Typically, the effect of fluid inertia is instead that it tries to force the particle in a rotation where the streamlines of the flow remain as straight as possible. The first effect of fluid inertia is thus the opposite of particle inertia and instead leads to a particle rotation around the major axis. Depending on rotational state, the particles also affect the apparent viscosity of the particle dispersion. The different transitions and bifurcations between rotational states are characterized in terms of non-linear dynamics, which reveal that the particle motion probably can be described by some reduced model. The results in this theses provides fundamental knowledge and is necessary to understand flows containing non-spherical particles.<br>Flöden med dispergerade partiklar påträffas i många industriella, biologiska och geofysiska tillämpningar. Kunskap om hur dessa flöden beter sig kan bl.a. leda till förbättrade materialprocesser, bättre förutsägelser om hjärt- och kärlsjukdomar eller mer noggranna väderprognoser. Dessa flödens egenskaper beror på hur enskilda partiklar rör sig i en fluid och speciellt hur de är fördelade både i termer av position och, om de är icke-sfäriska, i termer av orientering. Mycket är redan känt om rörelsen av perfekt sfäriska partiklar. För icke-sfäriska partiklar är det inte bara translationen som är av intresse utan det är även viktigt att veta hur partiklarna roterar till följd av lokala hastighetsgradienter. Sådana studier har tidigare varit begränsade av antagandet att partiklarna är extremt små jämfört med fluidens typiska längdskalor. I denna gräns kan både partikelns och fluidens tröghet antas försumbar. Den här avhandlingen ger en komplett bild av hur en sfäroidisk partikel (en partikel som beskrivs av en rotation av en ellips runt en av dess huvudaxlar) beter sig i ett linjärt skjuvflöde när tröghetseffekter inkluderas. Resultaten har erhållits genom numeriska simuleringar. Det visar sig att detta enkla problem är väldigt rikt på olika dynamiska beteenden med flera stabila rotationstillstånd som uppstår tilll följd av både partikel- och fluidtröghet. Inverkan av partikeltröghet leder till en rotation där massan av partikeln är koncentrerad så långt ifrån rotationsaxeln som möjligt, d.v.s. en rotation runt lillaxeln. Den typiska inverkan av fluidtröghet är istället att fluiden försöker påtvinga partikeln en rotation där strömlinjer förblir så raka som möjligt. Primärt leder detta till att partikeln istället roterar runt storaxeln. Beroende på rotationstillstånd, så har partikeln även olika inverkan på den märkbara viskositeten av partikeldispersionen. De olika övergångarna och bifurkationerna mellan rotationstillstånd är karaktäriserade i termer av icke-linjär dynamik, vilket visar på att partikelrörelserna förmodligen kan beskrivas med en reducerad modell. Resultaten i denna avhandling är därför fundamental kunskap och ett nödvändigt steg mot att förstå beteendet av flöden med dispergerade, icke-sfäriska partiklar.<br><p>QC 20140328</p>

Cette thèse étudie les phénomènes de concentration préférentielle et de sédimentation de particules inertielles transportées dans un écoulement turbulent. Pour cela, des expériences ont été menées en soufflerie dans une turbulence engendrée en aval d’une grille active et ensemencée avec des gouttelettes d'eau. La concentration préférentielle se manifeste par la ségrégation spatiale des particules qui bien qu’initialement ensemencée de façon homogène, tendent à se regrouper en amas, laissant en déplétion d’autres zones de l’écoulement. Un effort particulier a été consacré à séparer les mécanismes liés à l’inertie des particules, à la turbulence et aux effets collectifs impactant la formation des amas et modifiant la vitesse de sédimentation des particules. Quatre principaux paramètres non-dimensionnels ont été variés afin d’établir le rôle spécifique de chacun d’entre eux sur les processus de concentration préférentielle et de sédimentation : le nombre de Rouse $Ro $, représentant le rapport de la vitesse de sédimentation des particules à la vitesse fluctuante de l’écoulement; le nombre de Stokes $St$, quantifiant l'inertie des particules comme le rapport entre le temps de réponse des particules et le temps dissipatif de l’écoulement; le nombre de Reynolds $ RE_lambda$ représentant le degré de turbulence et enfin la fraction volumique de la phase dispersée $phi_v$.Deux techniques expérimentales (suivi Lagrangien des particules et interférométrie à phase Doppler) ont été utilisées pour l'acquisition des données et pour le diagnostic de la concentration préférentielle et de la sédimentation des gouttelettes dispersées. Le suivi Lagrangien de particules a été réalisé par visualisation à haute vitesse cadence des gouttelettes dispersées dans une nappe de laser. Cela donne accès aux statistiques simultanées de la distribution spatiale des particules et de leur vitesse. La niveau de clustering a été quantifié à l’aide de tessélation de Voronoï. Nous établissons des lois d’échelles quantitatives caractérisant la dépendance du degré de clustering et de la géométrie des amas en fonction des paramètres de l’étude ($St$, $Re_lambda$ et $ phi_v$. Ces lois d’échelles indiquent une forte influence de $Re_lambda$ et de $phi_v$, mais un faible effet de $St$. Ce résultat est cohérent avec un rôle dominant du mécanisme « sweep-stick » comme origine de la concentration préférentielle, tel que proposé par Vassilicos. En outre, l'analyse conditionnelle des vitesses de sédimentation des particules en fonction de leur appartenance ou non à des amas montre que les zones à fortes concentration tendent à sédimenter plus rapidement que les zones peu concentrées, suggérant un possible rôle des effets collectifs dans l’augmentation de la vitesse de chute. Les mesures par interférométrie de phase Doppler ont ensuite permis d’analyser plus en détail les statistiques de vitesse et de concentration de particules conditionnées à la taille des particules. Ces mesures montrent une augmentation de la vitesse de sédimentation pour les particules de petits diamètres, en accord avec des études précédentes. En revanche, la sédimentation est ralentie pour les particules de plus grand diamètre. Ceci indique une subtile intrication de plusieurs mécanismes possibles affectant la sédimentation turbulente de particules<br>This PhD thesis investigates the phenomena of preferential concentration and settling of sub-Kolmogorov inertial particles transported in a turbulent flow. To this end, experiments have been carried out in active-grid-generated turbulence in a wind-tunnel, seeded with water droplets. Preferential concentration manifests itself as the emergence of spatial segregation of the particles, which where initially homogeneously seeded in the carrier flow, leading to clusters and voids. A particular effort has been put in disentangling the roles of particles inertia, of turbulence and of collective effects on the emergence of clustering and the modification of settling velocity and in investigating the interplay between clustering and settling. Four main non-dimensional parameters have been varied to establish the role of each in the clustering process and on the settling of the particles: the Rouse number $Ro$, representing the ratio of the settling velocity of the particles to the fluctuating velocity of the fluid ; the Stokes number $St$ , quantifying particle inertia as the ratio of the particle response time to the flow dissipative time scale ; the Reynolds number $Re_lambda$ representing the degree of turbulence and the volume fraction $phi_v$ representing the concentration of the particles in the two-phase flow.Two experimental techniques (Lagrangian Particle Tracking and Phase Doppler Interferometry) are used to acquire data and diagnose the clustering and settling properties of the dispersed droplets.2D-Lagrangian Particle Tracking has been performed using high-speed visualization of the dispersed droplets in a laser sheet. This gives access to simultaneous statistics of particles spatial distribution and velocity. Clustering has been quantified using Voronoï tessellation and quantitative scalings on the dependency of clustering intensity and clusters dimensions on $St$, $Re_lambda$ and $phi_v$ are found. They show a strong influence of $Re_lambda$ and volume fraction $phi_v$ but a weak effect of $St$. This finding is consistent with a leading role of the “sweep-stick” mechanism in the clustering process, as proposed by Vassilicos. Furthermore, conditional analysis of the velocities of particles within clusters and voids has been performed showing that clusters tend to settle faster than voids, pointing to the role of collective effects in the enhancement of settling.Phase Doppler Interferometry has then been used to further analyse velocity statistics, and particle concentration field conditioned on particle diameter. Enhancement of the settling velocity for small diameters is observed, in agreement with previous studies. On the contrary, for larger particles settling velocity is found to be hindered. This indicates a subtle intrication of several possible mechanisms affecting the settling, including preferential sweeping, loitering and collective effects

Face à l'urgence climatique, l’efficacité énergétique et la réduction des émissions polluantes est devenue une priorité pour l'industrie aéronautique. La précision de la modélisation des phénomènes physicochimiques joue un rôle critique dans qualité de la prédiction des émissions de suie et des gaz à effet de serre par les chambres de combustion. Dans ce contexte, des méthodes d’apprentissage profond sont utilisées pour construire des modélisations avancées des émissions de particules. Une méthode automatisée de réduction et d’optimisation de la cinétique chimique d’un combustible aéronautique réel est dans un premier temps appliquée à la simulation aux grandes échelles pour la prédiction des émissions de monoxyde de carbone. Ensuite, des réseaux de neurones sont entraînés pour simuler le comportement dynamique des suies dans la chambre de combustion et prédire la distribution de taille des particules émises<br>With the climate change emergency, pollutant and fuel consumption reductions are now a priority for aircraft industries. In combustion chambers, the chemistry and soot modeling are critical to correctly quantify engines soot particles and greenhouse gases emissions. This thesis aimed at improving aircraft numerical pollutant tools, in terms of computational cost and prediction level, for engines high fidelity simulations. It was achieved by enhancing chemistry reduction tools, allowing to predict CO emissions of an aircraft engines at affordable cost for the industry. Next, a novel closure model for unresolved terms in the LES filtered transport equations is developed, based on neural networks (NN), to propose a better flame modeling. Then, an original soot model for engine high fidelity simulations is presented, also based on NN. This new model is applied to a one-dimensional premixed sooted flame, and finally to an industrial combustion chamber LES with measured soot comparison

La pollution de l'air, en particulier celle due aux particules fines et ultrafines, a des effets délétères considérables sur la santé humaine. Plusieurs études ont établi un lien direct entre l'exposition à la pollution particulaire et diverses maladies respiratoires et cardiovasculaires. À l'intérieur des véhicules, la menace est d'autant plus préoccupante en raison de concentrations importantes de polluants particulaires recensées. Par conséquent, l'amélioration de la qualité de l'air dans l'habitacle des véhicules est désormais une priorité majeure pour les constructeurs automobiles. Dans ce contexte, cette thèse vise à comprendre l'environnement intérieur des véhicules en caractérisant la distribution spatiale des polluants, en particulier des particules fines et ultrafines, en fonction de leur taille ainsi que de paramètres tels que la topologie de l'écoulement et le niveau de turbulence. Ces connaissances permettront notamment de cibler des solutions localisées de purification de l'air, d'optimiser l'emplacement des micro-capteurs qui équiperont de plus en plus les futurs véhicules, et de proposer des solutions pour une gestion efficace des systèmes de filtration en fonction de la répartition de ces particules et de leurs concentrations dans l'habitacle. Tout d'abord, une attention particulière a été accordée à la modélisation de l'écoulement monophasique. Deux approches de modélisation numérique ont été adoptées : l'approche RANS (Reynolds Averaged Navier-Stokes), basée sur la résolution des champs moyens des équations de Navier-Stokes, et l'approche de simulation à grande échelle LES (Large Eddy Simulation), qui consiste à résoudre les grandes structures contenant la majeure partie de l'énergie cinétique et à modéliser la contribution des plus petites échelles. Dans le cas de l'approche RANS, divers modèles de fermeture du premier et du second ordre ont été testés et comparés. En outre, une analyse de la structure de turbulence de l'écoulement dans l'habitacle a été réalisée à l'aide de la méthode du diagramme d'anisotropie de Lumely (Anisotropy Invariant Mapping). Enfin, pour valider les résultats des modèles numériques, une campagne de mesures du champ de vitesse, basée sur la technique de l'anémométrie à fil chaud, a été menée dans l'habitacle d'une voiture de type SUV. Ensuite, la dynamique des polluants particulaires dans l'habitacle de la voiture a été étudiée à l'aide du modèle DIM (Diffusion-Inertia Model). Ce modèle eulérien de diffusion inertielle des particules permet de prendre en compte différents mécanismes de transport, notamment le transport par le champ moyen, l'effet des forces volumiques (i.e. la gravité), la déviation des particules par rapport aux lignes de courant du fluide (effets centrifuges), la diffusion brownienne et turbulente, et la turbophorèse ou le transport par les gradients d'énergie cinétique turbulente. Le modèle a d'abord été validé sur des configurations standard telles que la dispersion dans des enceintes ventilées de petite échelle, le dépôt dans des coudes circulaires à 90°, ainsi que dans le cas du transport de particules dans un jet rond. Le modèle a ensuite été appliqué à la simulation du transport de particules à l'intérieur d'un véhicule à grande échelle. L'influence de la taille des particules sur les champs de concentration internes a d'abord été analysée. Ensuite, l'influence de la présence de passagers a été étudiée. Enfin, une campagne de mesures de la concentration de particules dans l'habitacle a été réalisée afin d'évaluer la pertinence du modèle diphasique. Cette étude a permis le développement d'un modèle complet de simulation de la dispersion des polluants particulaires dans un habitacle en fonction de conditions de ventilation et de caractéristiques des particules<br>Air pollution, especially that caused by fine and ultrafine particles, has significant deleterious effects on human health. Several studies have established a direct link between exposure to particulate pollution and various respiratory and cardiovascular diseases. Within vehicles, the threat is even more concerning due to the significant concentrations of particulate pollutants recorded. Therefore, improving air quality inside vehicle cabins is now a major priority for automotive manufacturers. In this context, this study aims to understand the interior environment of vehicles by characterizing the spatial distribution of pollutants, particularly fine and ultrafine particles, as a function of their size and parameters such as flow topology and turbulence level. This knowledge will be crucial for targeting localized air purification solutions, optimizing the placement of the micro-sensors that will equip future vehicles, and providing solutions for the more effective management of filtration systems as a function of the distribution and concentrations of these particles in the car cabin. First, special attention was devoted to modeling the single-phase flow. Two numerical modeling approaches have been adopted: the RANS (Reynolds Averaged Navier-Stokes) approach, based on solving the mean flow fields of the Navier-Stokes equations, and the LES (Large Eddy Simulation) approach, which involves solving the large structures containing the major part of the kinetic energy and modeling the contributions of the smaller scales. In the case of the RANS approach, various closure models, of first- and second-order, have been tested and compared. Furthermore, the turbulence structure of the flow inside the car cabin has been analyzed using Lumley's Anisotropy Invariant Mapping method (AIM). Finally, to validate the results of the numerical models, a velocity field measurement campaign, based on hot-wire anemometry technique, was conducted inside the cabin of an SUV-type car. Next, the dynamics of particulate pollutants in the car cabin was studied using the Diffusion-Inertia Model (DIM). This Eulerian model of inertial particle diffusion takes into account various transport mechanisms, including transport by the mean field, the effect of volume forces (i.e., gravity), particle deviation from fluid streamline (centrifugal effects), Brownian and turbulent diffusion, and turbophoresis or transport by turbulent kinetic energy gradients. The model was first validated on standard configurations such as dispersion in small-scale ventilated enclosures, deposition in 90° circular bends, and particle transport in a round jet flow. The model was then applied to simulate particle transport inside a large-scale vehicle. The influence of particle size on internal concentration fields was first analyzed. Then, the influence of passenger presence was studied. Finally, a particle concentration measurement campaign was conducted in the cabin to assess the relevance of the two-phase model. This study has led to the development of a complete model for simulating the dispersion of particulate pollutants inside a car cabin based on ventilation conditions and particle characteristics

Dispersed particle flows are encountered in many biological, geophysical but also in industrial situations, e.g. during processing of materials. In these flows, the particles usually are non-spherical and their angular dynamics play a crucial role for the final material properties. Generally, the angular dynamics of a particle is dependent on the local flow in the frame-of-reference of this particle. In this frame, the surrounding flow can be linearized and the linear velocity gradient will determine how the particle rotates. In this thesis, the main objective is to improve the fundamental knowledge of the angular dynamics of non-spherical particles related to two specific biobased material processes. Firstly, the flow of suspended cellulose fibers in a papermaking process is used as a motivation. In this process, strong shear rates close to walls and the size of the fibers motivates the study of inertial effects on a single particle in a simple shear flow. Through direct numerical simulations combined with a global stability analysis, this flow problem is approached and all stable rotational states are found for spheroidal particles with aspect ratios ranging from moderately slender fibers to thin disc-shaped particles. The second material process of interest is the production of strong cellulose filaments produced through hydrodynamic alignment and assembly of cellulose nanofibrils (CNF). The flow in the preparation process and the small size of the particles motivates the study of alignment and rotary diffusion of CNF in a strain flow. However, since the particles are smaller than the wavelength of visible light, the dynamics of CNF is not easily captured with standard optical techniques. With a new flow-stop experiment, rotary diffusion of CNF is measured using Polarized optical microscopy. This process is found to be quite complicated, where short-range interactions between fibrils seem to play an important role. New time-resolved X-ray characterization techniques were used to target the underlying mechanisms, but are found to be limited by the strong degradation of CNF due to the radiation. Although the results in this thesis have limited direct applicability, they provide important fundamental stepping stones towards the possibility to control fiber orientation in flows and can potentially lead to new tailor-made materials assembled from a nano-scale.<br><p>QC 20160929</p>

In many problems in dynamical systems one is interested in the identification of sets which have qualitatively different fates. The finite-time Lyapunov exponent (FTLE) method is a general and equation-free method that identifies codimension-one sets which have a locally high rate of stretching around which maximal exponential expansion of line elements occurs. These codimension-one sets thus act as transport barriers. This geometric framework of transport barriers is used to study various problems in phase space transport, specifically problems of separation in flows that can vary in scale from the micro to the geophysical. The first problem which we study is of the nontrivial motion of inertial particles in a two-dimensional fluid flow. We use the method of FTLE to identify transport barriers that produce segregation of inertial particles by size. The second problem we study is the long range advective transport of plant pathogen spores in the atmosphere. We compute the FTLE field for isobaric atmospheric flow and identify atmospheric transport barriers (ATBs). We find that rapid temporal changes in the spore concentrations at a sampling point occur due to the passage of these ATBs across the sampling point. We also investigate the theory behind the computation of the FTLE and devise a new method to compute the FTLE which does not rely on the tangent linearization. We do this using the 925 matrix of a probability density function. This method of computing the geometric quantities of stretching and FTLE also heuristically bridge the gap between the geometric and probabilistic methods of studying phase space transport. We show this with two examples.<br>Ph. D.

Les ondes gravito-inertielles jouent un rôle majeur dans les échanges d'énergie globaux sur la planète. Si la génération des ondes est bien connue dans l'atmosphère et l'océan, le devenir de ces ondes au cours de leur propagation n'est pas complètement défini aujourd'hui. Ces ondes peuvent interagir de façon non-linéaire avec elles-mêmes et créer des structures de plus petite échelle qui vont se dissiper plus facilement. Ainsi, le phénomène d'instabilité paramétrique sous-harmonique (PSI), a été étudié de façon expérimentale. Nous avons effectué la première mise en évidence expérimentale de l'interaction de trois ondes planes inertielles bi-dimensionnelles, sous la forme d'une triade résonnante. Cette étude améliore en outre la compréhension de la turbulence en rotation. Les ondes internes peuvent aussi créer, ou interagir avec des écoulements lents de grande échellequi peuvent modifier la biodiversité au fond des océans. Nous avons mis en évidence une situation expérimentale à l'origine d'un tel écoulement moyen induit par les ondes et, à l'aide d'un modèle théorique simplifié, nous avons expliqué la formation de ces écoulements. Enfin, on étudie également des tourbillons en fluide stratifié pour permettre de futures études sur l'interaction d'ondes gravito-inertielles avec des tourbillons.

While the theory of suspension flows and particle dynamics is well understood under Stokes flow conditions when viscous forces dominate, little is known at finite Reynolds number when the inertial forces of the suspending fluid are important. In the present study, expressions are derived that allow for dynamic calculations of particle, drop, and bubble motion at finite Reynolds number. The results show a significant change in the temporal behavior of the force/velocity relationship from that derived from the unsteady Stokes equations, particularly as a body approaches its steady state. At finite Reynolds number, when the convective inertial effects are included, the hydrodynamic force on a body has much weaker history dependence on the past motion of the body and it reaches its steady state faster than what would be predicted if only the unsteady inertial effects are accounted for. When compared with numerical solutions of the Navier-Stokes equations, the analytical force expressions perform well up to a Reynolds number of 0.5. A common theme to the derivations is the use of the reciprocal theorem which provides for an efficient and elegant means for computing inertial effects in suspension mechanics. Connections with past approaches are made in light of these new applications of the reciprocal theorem.

A computational fluid dynamics model has been developed to examine the separation of an oil film from a spherical oil-coated particle falling through quiescent water due to gravity. Using this model, the separation process was studied as a function of the viscosity ratio of oil to water, R, and the ratio of viscous forces to surface tension, represented by the Capillary number Ca. The governing equations of this flow-induced motion are derived in a non-inertial spherical coordinate system, and discretized using a finite volume approach. The Volume-of-Fluid method is used to capture the oil/water interface. The model predicts two mechanisms for oil separation: at R less than 1, the shear difference between the particle/oil interface and the oil/water interface is not significant and Ca determines whether separation occurs or not; at R larger than 1, the shear difference is considerable, and the Ca effect becomes less dominant.

Beams are ubiquitous in our everyday life and can be found in a variety of length scales, from large supports of buildings to carbon nanotubes. Similarly, bubbles can also span a variety of scales, ranging from tiny bubbles in a glass filled with champagne to the giant soap bubbles formed by artists to attract crowds. Yet, the behavior of beams and bubbles can often occur so fast that the dynamics go unnoticed. This dissertation aims to understand the mechanics of beams and bubbles in four different examples. We combine table-top experiments with mathematical models to predict how each system will behave when exposed to different extreme conditions. We start by examining the retraction of a rubber band once it has been stretched and released. This process is similar to plucking a string, where the dynamics are governed by tensile and inertial forces, resulting in a trapezoidal shape during retraction. However when a rubber band is stretched and released, a region of high-curvature develops. Our experiments and mathematical model highlight that bending forces can be significant and give rise to a curved self-similar shape to the retracting rubber band. The next example involves the competition of surface tension and twisting on a flexible rod. Most studies in the field of elasto-capillarity have focused on how surface tension can bend an elastic structure, leaving the possibility of twisting unexplored. Here we utilize particles with discrete wettabilities -- or Janus particles -- at liquid interfaces that can be used to twist a flexible cylinder. The third system is focused around the spreading behavior of bubbles on submerged surfaces coated with a layer of oil. These liquid-infused surfaces have remarkable applications due to their ability to minimize contact line pinning. However, this property has mostly been exploited using liquid drops. We here study the early spreading behavior of a bubble once it has made contact with the liquid-infused surface. The final chapter is centered around the collapse of bubbles resting on the surface of an ultra viscous liquid. When a bubble on such a surface is ruptured, the bubble film collapses vertically downwards, leading scientists to believe that gravity is driving the collapse. Yet, interfacial forces are dominant in highly curved liquid surfaces and exceed gravitational forces. By turning the setup upside-down, we show that surface tension is indeed responsible for the collapse and the subsequent wrinkling instability that develops.

In this thesis we study a variety of problems in fluid turbulence, principally in two dimensions. A summary of the main results of our studies is given below; we indicate the Chapters in which we present these. In Chapter 1, we provide an overview of several problems in turbulence with special emphasis on background material for the problems we study in this thesis. In particular, we give (a) natural and laboratory examples of fluid turbulence, (b) and introductory accounts of the equations of hydrodynamics, without and with polymer additives, Eulerian and Lagrangian frameworks, and the equations of motion of inertial particles in fluid flows. We end with a summary of the problems we study in subsequent Chapters of this thesis. In Chapter 2, we carry out the most extensive and high-resolution direct numerical simulation, attempted so far, of homogeneous, isotropic turbulence in two-dimensional fluid films with air-drag-induced friction and with polymer additives. Our study reveals that the polymers (a) reduce the total fluid energy, enstrophy, and palinstrophy, (b) modify the fluid energy spectrum both in inverse- and forward-cascade regimes, (c) reduce small-scale intermittency, (d) suppress regions of large vorticity and strain rate, and (e) stretch in strain-dominated regions. We compare our results with earlier experimental studies and propose new experiments. In Chapter 3, we perform a direct numerical simulation (DNS) of the forced, incompressible two-dimensional Navier-Stokes equation coupled with the FENE-P equations for the polymer- conformation tensor. The forcing is such that, without polymers and at low Reynolds numbers Re, the lm attains a steady state that is a square lattice of vortices and anti-vortices. We nd that, as we increase the Weissenberg number (Wi), this lattice undergoes a series of nonequilibrium phase transitions, first to spatially distorted, but temporally steady, crystals and then to a sequence of crystals that oscillate in time, periodically, at low Wi, and quasiperiodically, for slightly larger Wi. Finally, the system becomes disordered and displays spatiotepmoral chaos and elastic turbulence. We then obtain the nonequilibrium phase diagram for this system, in the Wi − Re plane, and show that (a) the boundary between the crystalline and turbulent phases has a complicated, fractal-type character and (b) the Okubo-Weiss parameter provides us with a natural measure for characterizing the phases and transitions in this diagram. In Chapter 4, our study is devoted to heavy, inertial particles in two-dimensional (2D) tur- bulent, but statistically steady, flows that are homogeneous and isotropic. The inertial particles are distributed uniformly in our simulation domain when St = 0; they start to cluster as St increases; this clustering tendency reaches a maximum at St 1 and decreases thereafter. We then obtain PDFs of and show that their left tails, which come from extensional regions, do not depend sensitively on St; in contrast, their right tails, from the vortical regions of the flow, are consistent with the exponential form ∼ exp ‰− + Ž; and we nd that the scale + decreases with St until St _0:1 and then saturates at a value _0:75. Our persistence-type studies yield the following results, when we consider forcing that leads to an energy spectrum that is dominated by a forward-cascade regime: In strain-dominated or extensional regions of the flow, wend that the cumulative PDF of the persistence time decays exponentially; this decay yields a time scale T−, which increases rapidly with St, at low values of St, but more slowly after St _0:75. By contrast, in vortical regions of the flow, this cumulative PDF displays a tail that has power-law and exponential parts; the power-law part yields the persistence exponent _ and the exponential tail gives a time scale T−; _ increases with St, whereas T− decreases with St; _ and T− reach saturation values as St increases. From the cumulative PDF of the particle mean-square displacement r2, we obtain the time scale Ttrans at which there is a crossover from ballistic to diffusive behavior; we _nd that Ttrans increases with St. The PDFs of v2, the square of the particle velocity, and v2 ejected, the square of the velocity of a particle just as it is ejected from a region with _ > 0 (vortical region) to one that has _ < 0 (extensional region), do not show a significant dependence on St; the tails of these PDFs are characterized by power-law decays with exponents _1 and _5~3, respectively. Our next set of results deal with statistical properties of special combinations of the acceleration a =dv~dt and the velocity v. For instance, the curvature of the trajectory is _ =aÙ~v2, where the subscript Ù denotes the component perpendicular to the particle trajectory; we obtain PDFs of _ and _nd there from that particles in regions of elongational flow have, on average, trajectories with a lower curvature than particles in vortical regions; this . We also determine how the number of number of points NI , at which a ×v changes sign along a particle trajectory, as time increases; we _nd that the increase of NI with time and decrease as St increases. Our ninth set of results show that the characteristic decay time T_ for decreases with St. In Chapter 5, we study the statistical properties of orientation and rotation dynamics of elliptical tracer particles in two-dimensional, homogeneous and isotropic turbulence by direct numerical simulations. We consider both the cases in which the turbulent flow is generated by forcing at large and intermediate length scales. We show that the two cases are qualitatively different. For the large-scale forcing, the spatial distribution of particle orientations forms large- scale structures, which are absent for the intermediate-scale forcing. The alignment with the local directions of the flow is much weaker in the latter case than in the former. For the intermediate- scale forcing, the statistics of rotation rates depends weakly on the Reynolds number and on the aspect ratio of particles. In contrast with what is observed in three-dimensional turbulence, in two dimensions the mean-square rotation rate decreases as the aspect ratio increases. In Chapter 6, we study the issue of intermittency in numerical solutions of the 3D Navier-Stokes equations on a periodic box [0; L]3. This is addressed through four sets of numerical simulations that calculate a new set of variables defined by Dm(t) = where All four simulations unexpectedly show that the Dm are ordered for m =1 ….,9 such that Dm+1 <Dm. Moreover, the Dm squeeze together such that Dm+1/Dm 1 as m increases. The values of D1 lie far above the values of the rest of the Dm, giving rise to a suggestion that a depletion of nonlinearity is occuring which could be the cause of Navier{Stokes regularity. The first simulation, by R. Kerr, is of very anisotropic decaying turbulence ; the second and third, which have been carried out by me, are of decaying isotropic turbulence from random initial conditions and forced isotropic turbulence at fixed Grashof number, respectively ; the fourth, by D. Donzis, is of very-high-Reynolds-number forced, stationary, isotropic turbulence at resolutions up to 40963 collocation points. For the sake of completeness and for a comparison of the data from all these four simulations, all the results are presented; however, in the Sections that deal with the simulations, I indicate who carried out the calculations reported there. I also present an extension of this work to two-dimensional fluid turbulence; this has not been submitted for publication so far. We hope our in silico studies of 2D and 3D turbulence will stimulate new experimental, numerical, and theoretical studies.

In this thesis we study a variety of problems in fluid turbulence, principally in two dimensions. A summary of the main results of our studies is given below; we indicate the Chapters in which we present these. In Chapter 1, we provide an overview of several problems in turbulence with special emphasis on background material for the problems we study in this thesis. In particular, we give (a) natural and laboratory examples of fluid turbulence, (b) and introductory accounts of the equations of hydrodynamics, without and with polymer additives, Eulerian and Lagrangian frameworks, and the equations of motion of inertial particles in fluid flows. We end with a summary of the problems we study in subsequent Chapters of this thesis. In Chapter 2, we carry out the most extensive and high-resolution direct numerical simulation, attempted so far, of homogeneous, isotropic turbulence in two-dimensional fluid films with air-drag-induced friction and with polymer additives. Our study reveals that the polymers (a) reduce the total fluid energy, enstrophy, and palinstrophy, (b) modify the fluid energy spectrum both in inverse- and forward-cascade regimes, (c) reduce small-scale intermittency, (d) suppress regions of large vorticity and strain rate, and (e) stretch in strain-dominated regions. We compare our results with earlier experimental studies and propose new experiments. In Chapter 3, we perform a direct numerical simulation (DNS) of the forced, incompressible two-dimensional Navier-Stokes equation coupled with the FENE-P equations for the polymer- conformation tensor. The forcing is such that, without polymers and at low Reynolds numbers Re, the lm attains a steady state that is a square lattice of vortices and anti-vortices. We nd that, as we increase the Weissenberg number (Wi), this lattice undergoes a series of nonequilibrium phase transitions, first to spatially distorted, but temporally steady, crystals and then to a sequence of crystals that oscillate in time, periodically, at low Wi, and quasiperiodically, for slightly larger Wi. Finally, the system becomes disordered and displays spatiotepmoral chaos and elastic turbulence. We then obtain the nonequilibrium phase diagram for this system, in the Wi − Re plane, and show that (a) the boundary between the crystalline and turbulent phases has a complicated, fractal-type character and (b) the Okubo-Weiss parameter provides us with a natural measure for characterizing the phases and transitions in this diagram. In Chapter 4, our study is devoted to heavy, inertial particles in two-dimensional (2D) tur- bulent, but statistically steady, flows that are homogeneous and isotropic. The inertial particles are distributed uniformly in our simulation domain when St = 0; they start to cluster as St increases; this clustering tendency reaches a maximum at St 1 and decreases thereafter. We then obtain PDFs of and show that their left tails, which come from extensional regions, do not depend sensitively on St; in contrast, their right tails, from the vortical regions of the flow, are consistent with the exponential form ∼ exp ‰− + Ž; and we nd that the scale + decreases with St until St _0:1 and then saturates at a value _0:75. Our persistence-type studies yield the following results, when we consider forcing that leads to an energy spectrum that is dominated by a forward-cascade regime: In strain-dominated or extensional regions of the flow, wend that the cumulative PDF of the persistence time decays exponentially; this decay yields a time scale T−, which increases rapidly with St, at low values of St, but more slowly after St _0:75. By contrast, in vortical regions of the flow, this cumulative PDF displays a tail that has power-law and exponential parts; the power-law part yields the persistence exponent _ and the exponential tail gives a time scale T−; _ increases with St, whereas T− decreases with St; _ and T− reach saturation values as St increases. From the cumulative PDF of the particle mean-square displacement r2, we obtain the time scale Ttrans at which there is a crossover from ballistic to diffusive behavior; we _nd that Ttrans increases with St. The PDFs of v2, the square of the particle velocity, and v2 ejected, the square of the velocity of a particle just as it is ejected from a region with _ > 0 (vortical region) to one that has _ < 0 (extensional region), do not show a significant dependence on St; the tails of these PDFs are characterized by power-law decays with exponents _1 and _5~3, respectively. Our next set of results deal with statistical properties of special combinations of the acceleration a =dv~dt and the velocity v. For instance, the curvature of the trajectory is _ =aÙ~v2, where the subscript Ù denotes the component perpendicular to the particle trajectory; we obtain PDFs of _ and _nd there from that particles in regions of elongational flow have, on average, trajectories with a lower curvature than particles in vortical regions; this . We also determine how the number of number of points NI , at which a ×v changes sign along a particle trajectory, as time increases; we _nd that the increase of NI with time and decrease as St increases. Our ninth set of results show that the characteristic decay time T_ for decreases with St. In Chapter 5, we study the statistical properties of orientation and rotation dynamics of elliptical tracer particles in two-dimensional, homogeneous and isotropic turbulence by direct numerical simulations. We consider both the cases in which the turbulent flow is generated by forcing at large and intermediate length scales. We show that the two cases are qualitatively different. For the large-scale forcing, the spatial distribution of particle orientations forms large- scale structures, which are absent for the intermediate-scale forcing. The alignment with the local directions of the flow is much weaker in the latter case than in the former. For the intermediate- scale forcing, the statistics of rotation rates depends weakly on the Reynolds number and on the aspect ratio of particles. In contrast with what is observed in three-dimensional turbulence, in two dimensions the mean-square rotation rate decreases as the aspect ratio increases. In Chapter 6, we study the issue of intermittency in numerical solutions of the 3D Navier-Stokes equations on a periodic box [0; L]3. This is addressed through four sets of numerical simulations that calculate a new set of variables defined by Dm(t) = where All four simulations unexpectedly show that the Dm are ordered for m =1 ….,9 such that Dm+1 <Dm. Moreover, the Dm squeeze together such that Dm+1/Dm 1 as m increases. The values of D1 lie far above the values of the rest of the Dm, giving rise to a suggestion that a depletion of nonlinearity is occuring which could be the cause of Navier{Stokes regularity. The first simulation, by R. Kerr, is of very anisotropic decaying turbulence ; the second and third, which have been carried out by me, are of decaying isotropic turbulence from random initial conditions and forced isotropic turbulence at fixed Grashof number, respectively ; the fourth, by D. Donzis, is of very-high-Reynolds-number forced, stationary, isotropic turbulence at resolutions up to 40963 collocation points. For the sake of completeness and for a comparison of the data from all these four simulations, all the results are presented; however, in the Sections that deal with the simulations, I indicate who carried out the calculations reported there. I also present an extension of this work to two-dimensional fluid turbulence; this has not been submitted for publication so far. We hope our in silico studies of 2D and 3D turbulence will stimulate new experimental, numerical, and theoretical studies.

Modelling highly non-linear, strongly temperature- and rate-dependent visco-plastic behaviour of poly-crystalline solids (e.g., metals and metallic alloys) is one of the most challenging topics of contemporary research interest, mainly owing to the increasing use of metallic structures in engineering applications. Numerous classical models have been developed to model the visco-plastic behaviour of poly-crystalline solids. However, limitations of classical visco-plasticity models have been realized mainly in two cases: in problems at the scale of mesoscopic length (typically in the range of a tenth of a micron to a few tens of micron) or lower, and in impact problems under high-strain loading with varying temperature. As a remedy of the first case, several length scale dependent non-local visco-plasticity models have been developed in the last few decades. Unfortunately, a rationally grounded continuum model with the capability of reproducing visco-plastic response in accord with the experimental observations under high strain-rates and varying temperatures remains elusive and attempts in this direction are often mired in controversies. With the understanding of metal visco-plasticity as a macroscopic manifestation of the underlying dislocation motion, there are attempts to develop phenomenological as well as physics-based continuum models that could be applied across different regimes of temperature and strain rate. Yet, none of these continuum visco-plasticity models accurately capture the experimentally observed oscillations in the stress-strain response of metals (e.g. molybdenum, tantalum etc.) under high strain rates and such phenomena are sometimes even dismissed as mere experimental artefacts. The question arises as to whether the existing models have consistently overlooked any important mechanism related to dislocation motion which could be very important at high strain-rate loading and possibly responsible for oscillations in the stress-strain response. In the search for an answer to this question, one observes that the existing macro-scale continuum visco-plasticity models do not account for the effects of dislocation inertia which is identified in this thesis as a dominating factor in the visco-plastic response under high strain rates. Incorporating the effect of dislocation inertia in the continuum response, a visco-plasticity model is developed. Here the ow rule is derived based on an additional balance law, the micro-force balance, for the forces arising from (and maintaining) the plastic flow. The micro-force balance together with the classical momentum balance equations thus describes the visco-plastic response of isotropic poly-crystalline materials. The model is thermodynamically consistent as the constitutive relations for the fluxes are determined on satisfying the laws of thermodynamics. The model includes consistent derivation of temperature evolution, thus replaces the empirical route. Partial differential equations (PDEs) describing the visco-plastic behaviour in the present model is highly non-linear and solving them requires the employment of numerical techniques. Had the interest been limited only to problems with nicely behaved continuous field variables, the finite element method (FEM) could have been a natural choice for solving the governing PDEs. Keeping in mind the limitations of the FEM in discretizing such large deformation problems and in handling discontinuities, a smooth particle hydrodynamics (SPH) formulation for the micro-inertia driven visco-plasticity model is undertaken in this thesis. The visco-plasticity model is then exploited to simulate ductile damage by suitably coupling the discretized SPH equations with an existing damage model. The current scheme does not necessitate the introduction of a yield or damage surface in evolving the plastic strain/ damage parameters and thus the numerical implementation avoids a computationally intensive return mapping. Our current approach therefore provides for an efficient numerical route to simulating impact dynamics problems. However, implementation of the SPH equations demands some additional terms such as artificial viscosity to arrive at a numerically stable solution. Using such stabilizing terms is however bereft of a rational or physical basis. The choice of artificial viscosity parameters is ad-hoc -an inappropriate choice leading to unphysical solutions. In order to circumvent this, the micro-inertia driven visco-plasticity model is reformulated using peri dynamics (PD), a more efficacious scheme to treat shock waves/discontinuities within a continuum model. Remarkably, the PD model naturally accounts for the localization residual terms in the local balances for internal energy and entropy, originally conceived of by Edelen and co-workers nearly half a century ago as a source of non-local interaction. Exploiting the present model, we also explore the determination of conservation laws based on a variational formulation for dissipative visco-plastic solids wherein the system variables are appropriately augmented with those describing the time-reversed dynamics. This in turn enables us to undertake symmetry analyses on the resulting Lagrangian to assess, for instance, material resistance to crack propagation. Specifically, our results confirm that materials with higher rate sensitivity tend to offer higher resistance to fracture. Moreover, it is found that the kinetic energy of the inertial forces contributes to increased plastic flow thereby reducing the available free energy for crack propagation. This part of the work potentially opens a model-based route to the design of micro-defect structures for optimal fracture resistance.