The studies of particles advected by tubulent flows is an active area of research across many streams of sciences and engineering, which include astrophysics, fluid mechanics, statistical physics, nonlinear dynamics, and also chemistry and biology. Advances in experimental techniques and high performance computing have made it possible to investigate the properties these particles advected by fluid flows at very high Reynolds numbers. The main focus of this thesis is to study the statistics of Lagrangian tracers and heavy inertial particles in hydrodynamic and magnetohydrodynamic (MHD) turbulent flows by using direct numerical simulations (DNSs). We also study the statistics of particles in model stochastic flows; and we compare our results for such models with those that we obtain from DNSs of hydrodynamic equations. We uncover some of aspects of the statistical properties of particle trajectories that have not been looked at so far. In the last part of the thesis we present some results that we have obtained by solving the three-dimensional Euler equation by using a new method based on the Cauchy-Lagrange formulation. This thesis is divided into 6 chapters. Chapter 1 contains an introduction to the background material that is required for this thesis; it also contains an outline of the problems we study in subsequent Chapters. Chapter 2 contains our study of “Persistence and first-passage time problems with particles in three-dimensional, homogeneous, and isotropic turbulence”. Chapter 3 is devoted to our study of “Universal Statistical Properties of Inertial-particle Trajectories in Three-dimensional, Homogeneous, Isotropic, Fluid Turbulence”. Chapter 4 deals with “Time irreversibility of Inertial-particle trajectories in Homogeneous, Isotropic, Fluid Turbulence”. Chapter 5 contains our study of the “Statistics of charged inertial particles in three-dimensional magnetohydrodynamic (MHD) turbulence”. Chapter 6 is devoted to our study of “The Cauchy-Lagrange method for the numerical integration of the threedimensional Euler equation”.

La stratégie de combustion par auto-inflammation d’une charge homogène en composition s’intègre dans une démarche de réduction des émissions de particules et de NOx, tout en conservant les rendements thermiques élevés des moteurs Diesel classiques. Pour contrôler ce nouveau mode de combustion, une compréhension fine des mécanismes de couplage entre l'aérodynamique et la thermochimie est nécessaire. Des simulations numériques directes d'un écoulement homogène, turbulent, réactif et subissant une compression, ont été effectués. Deux régimes d'auto-inflammation ont ainsi pu être définis. Le premier, dit quasi-homogène, est caractérisé par une auto-inflammation en masse d'un volume important du mélange réactif et s'accompagne de fortes ondes de pression. Dans le second régime, dit localisé, les noyaux s'initient de manière plus sporadique dans l'espace et dans le temps et aucune onde de pression significative n'est générée lors de l'auto-allumage. / Combustion by autoignition of a homogeneous charge aims at reducing particulate matter as well as NOx emissions, while maintaining higher thermal efficiency of conventional diesel engines. To control this new mode of combustion, a fine understanding of the mechanisms of coupling between aerodynamics and thermochemistry is required. Direct Numerical Simulations of a turbulent reactive flow, undergoing a compression, have been performed. This study led to identification of two regimes. The first, known as quasi-homogeneous, is characterized by volumetric autoignition of large zones of the reactive mixture and results in the generation of strong pressure waves, which are potentially dangerous for the structure of engines. In the second regime, called localized, hot spots are initiated more sporadically in space and time, and their topology is such that no significant pressure wave is generated.

Understanding flow and transport in porous media is critical as it plays a central role in many biological, natural, and industrial processes. Such processes are not limited to one length or time scale; they occur over a wide span of scales from micron to Kilometers and microseconds to years. While field-scale simulation relies on a continuum description of the flow and transport, one must take into account transport processes occurring on much smaller scales. In doing so, pore-scale modeling is a powerful tool for shedding light on processes at small length and time scales.<br><br>In this work, we look into the multi-phase flow and transport through porous media at two different scales, namely pore- and Darcy scales. First, using direct numerical simulations, we study pore-scale Eulerian and Lagrangian statistics. We study the evolution of Lagrangian velocities for uniform injection of particles and numerically verify their relationship with the Eulerian velocity field. We show that for three porous media velocity, probability distributions change over a range of porosities from an exponential distribution to a Gaussian distribution. We thus model this behavior by using a power-exponential function and show that it can accurately represent the velocity distributions. Finally, using fully resolved velocity field and pore-geometry, we show that despite the randomness in the flow and pore space distributions, their two-point correlation functions decay extremely similarly.<br><br>Next, we extend our previous study to investigate the effect of viscoelastic fluids on particle dispersion, velocity distributions, and flow resistance in porous media. We show that long-term particle dispersion could not be modulated by using viscoelastic fluids in random porous media. However, flow resistance compared to the Newtonian case goes through three distinct regions depending on the strength of fluid elasticity. We also show that when elastic effects are strong, flow thickens and strongly fluctuates even in the absence of inertial forces.<br><br>Next, we focused our attention on flow and transport at the Darcy scale. In particular, we study a tertiary improved oil recovery technique called surfactant-polymer flooding. In this work, which has been done in collaboration with Purdue enhanced oil recovery lab, we aim at modeling coreflood experiments using 1D numerical simulations. To do so, we propose a framework in which various experiments need to be done to quantity surfactant phase behavior, polymer rheology, polymer effects on rock permeability, dispersion, and etc. Then, via a sensitivity study, we further reduce the parameter space of the problem to facilitate the model calibration process. Finally, we propose a multi-stage calibration algorithm in which two critically important parameters, namely peak pressure drop, and cumulative oil recovery factor, are matched with experimental data. To show the predictive capabilities of our framework, we numerically simulate two additional coreflood experiments and show good agreement with experimental data for both of our quantities of interest.<br><br>Lastly, we study the unstable displacement of non-aqueous phase liquids (e.g., oil) via a finite-size injection of surfactant-polymer slug in a 2-D domain with homogeneous and heterogeneous permeability fields. Unstable displacement could be detrimental to surfactant-polymer flood and thus is critically important to design it in a way that a piston-like displacement is achieved for maximum recovery. We study the effects of mobility ratio, finite-size length of surfactant-polymer slug, and heterogeneity on the effectiveness of such process by looking into recovery rate and breakthrough and removal times.

<div>The growing need to improve the power density of compact thermal systems necessitates developing new techniques to modulate the convective heat transfer efficiently. In the present research, acoustic streaming is evaluated as a potential technology to achieve this objective. Numerical simulations using the linearized and fully non-linear Navier-Stokes equations are employed to characterize the physics underlying this process. The linearized Navier-Stokes equations accurately replicate the low-frequency flow unsteadiness, which is used to find the optimal control parameters. Local and global stability analysis tools were developed to identify the modes with a global and positive heat transfer effect.</div><div><br></div><div>High-fidelity numerical simulations are performed to evaluate the effect of the excitation at selected frequencies, directed by the linear stability analysis, on the heat and momentum transport in the flow. Results indicate that, under favorable conditions, superimposing an acoustic wave, traveling along with the flow, can <i>resonate</i> within the domain and lead to a significant heat transfer enhancement with minimal skin friction losses. Two main flow configurations are considered; at the fixed Reynolds number Re_b=3000, in the supersonic case, 10.1% heat transfer enhancement is achieved by an 8.4% skin friction increase; however, in the subsonic case, 10% enhancement in heat transfer only caused a 5.3% increase to the skin friction. The deviation between these two quantities suggests a violation of the Reynolds analogy. This study is extended to include a larger Reynolds number, namely Re_b=6000 at M_b=0.75 and a similar response is observed. The effect of excitation amplitude and frequency on the resonance, limit-cycle oscillations, heat transfer, and skin friction are also investigated here.</div><div><br></div><div>Applying acoustic waves normal to the flow in the spanwise direction disrupts the near-wall turbulent structures that are primarily responsible for heat and momentum transport near the solid boundary. Direct numerical simulations were employed to investigate this technique in a supersonic channel flow at M_b=1.5 and Re_b=3000. The external excitation is applied through a periodic body force in the spanwise direction, mimicking loudspeakers placed on both walls that are operating with a 180^o phase shift. By keeping the product of forcing amplitude A_f and pulsation period (<i>T</i>) constant, spanwise velocity perturbations are generated with a similar amplitude at different frequencies. Under this condition, spanwise pulsations at <i>T</i>=20 and <i>T</i>=10 show up to 8% reduction in Nusselt number as well as the skin friction coefficient. Excitation at higher or lower frequencies fails to achieve such high level of modulations in heat and momentum transport processes near the walls.<br> <br>In configurations involving a spatially-developing boundary layer, a computational setup that includes laminar, transitional, and turbulent regions inside the domain is considered and the impact of acoustic excitation on this flow configuration has been characterized. Large-eddy simulations with dynamic Smagorinsky sub-grid scale modeling has been implemented, due to the excessive computational cost of DNS calculations at high-Reynolds numbers. The optimal excitation frequency that resembles the mode chosen for the fully-developed case has been identified via global stability analysis. Fully non-linear simulations of the spatially-developing boundary layer subjected to the excitation at this frequency reveal an interaction between the <i>pulsations</i> and the perturbations originated from the tripping which creates a re-laminarization zone traveling downstream. Such technique can locally enhance or reduce the heat transfer along the walls.<br></div>

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

This dissertation introduces a general, predictive and cost-efficient reduced-order modeling (ROM) technique for characterization of flame response under acoustic modulation. The model is built upon the kinematic flame model–G-equation to describe the flame topology and dynamics, and the novelties of the ROM lie in i) a procedure to create the compatible base flow that can reproduce the correct flame geometry and ii) the use of a physically-consistent acoustic modulation field for the characterization of flame response. This ROM addresses the significant limitations of the classical kinematic model, which is only applicable to simple flame configurations and relies on ad-hoc models for the modulation field. The ROM is validated by considering the acoustically-excited premixed methane/air flames in conical and M-shape configurations. To test the model availability to practical burners, a confined flame configuration is also employed for model evaluation. Furthermore, to investigate the generality of the ROM to the burner flame, the performance of the ROM with respect to the V-shape and the swirled V-shape is investigated. The model accuracy is evaluated concerning flame geometrical features and flame describing function, and assessed by comparing the ROM results with both experimental measurements and direct- numerical-simulation results. It is found that the flame describing/transfer functions predicted by the ROM compare well with reference data, and are more accurate than those obtained from the conventional kinematic model built upon heuristically-presumed modulation fields.

This thesis deals with the instabilities of the incompressible boundary-layer flow that is induced by a disk rotating in otherwise still fluid. The results presented are mostly limited to linear instabilities derived from direct numerical simulations (DNS) but with the objective that further work will focus on the nonlinear regime, providing greater insights into the transition route to turbulence. The numerical code Nek5000 has been chosen for the DNS using a spectral-element method in an effort to reduce spurious effects from low-order discretizations. Large-scale parallel simulations have been used to obtain the present results. The known similarity solution of the Navier–Stokes equation for the rotating-disk flow, also called the von Karman flow, is investigated and can be reproduced with good accuracy by the DNS. With the addition of small roughnesses on the disk surface, convective instabilities appear and data from the DNS are analysed and compared with experimental and theoretical data. A theoretical analysis is also presented using a local linear-stability approach, where two stability solvers have been developedbased on earlier work. A good correspondence between DNS and theory is found and the DNS results are found to explain well the behaviour of the experimental boundary layer within the range of Reynolds numbers for small amplitude (linear) disturbances. The comparison between the DNS and experimental results, presented for the first time here, shows that the DNS allows (for large azimuthal domains) a range of unstable azimuthal wavenumbers β to exist simultaneously with the dominantβ varying, which is not accounted for in local theory, where β is usually fixed for each Reynolds number at which the stability analysis is applied. Furthermore, the linear impulse response of the rotating-disk boundary layer is investigated using DNS. The local response is known to be absolutely unstable. The global response is found to be stable if the edge of the disk is assumed to be at infinity, and unstable if the domain is finite and the edge of the domain is placed such that there is a large enough pocket region for the absolute instability to develop. The global frequency of the flow is found to be determined by the edge Reynolds number. / <p>QC 20140708</p>

Résumé : La mesure des profils transitoires et de la vitesse de solidification sont deux données importantes pour le contrôle de procédés industriels impliquant un changement de phase. Dans le cas de l’électrolyse de l’aluminium, ce processus de solidification assure la protection du système et influe sur la performance énergétique du procédé de fabrication. Malheureusement, ces données se révèlent, dans la plupart des cas, difficilement accessibles. Ce travail de thèse porte sur le développement de nouveaux outils permettant l’étude et la caractérisation de la solidification de matériaux à changement de phase et à haute température. L’objectif est de développer un système de mesure du front de solidification de matériaux à changement de phase non destructif et ne perturbant pas le milieu de mesure, tout en assurant une précision et une réponse suffisamment rapide pour exploiter de nouvelles stratégies de contrôle dans les cuves d’électrolyse. Ce travail couple une étude expérimentale fondamentale de la solidification de la cryolithe avec une modélisation numérique de phénomène de changement de phase solide-liquide dans des conditions proches du fonctionnement de cuves d’électrolyse. // Abstract : Measurement of transient solidification fronts and of solidification rate are two important data for controlling industrial processes involving a solid-liquid phase change. In the case of aluminium electrolysis, this solidification process protects the system and affects the energy performance of the manufacturing process. Unfortunately, these data are not easy to obtain in most cases. This thesis focuses on the development of new tools for the study and on the solidification characterization of phase change materials at high temperature. The goal is to develop a nondestructive solidification front measurement system for phase change materials without disturbing the measurement medium, while ensuring accuracy and a fast enough response time to exploit new control strategies in electrolysis cells. This work couples a fundamental experimental study of the cryolite solidification with numerical modeling of solid-liquid phase change phenomenon under conditions close to those during normal operation of electrolytic cells.

Les tourbillons hélicoïdaux générés derrière les rotors sont étudiés. Pour les générer, une méthode basée sur le couplage entre la technique de la ligne active et un solveur des équations de Navier-Stokes (ENS), incompressibles et tridimensionnelles, a été développée. Elle consiste à modéliser la pâle par son équivalent de forces volumiques. Les équations, écrites en coordonnées cylindriques, sont résolues par un schéma de différences finies, écrit en parallèle. La méthode est d'ordre deux en temps et en espace. Le solveur des ENS a été validé par la reproduction des taux de croissance d'un écoulement de jet, instable, trouvés par la théorie d'instabilité linéaire. La comparaison avec des données expérimentales a montré que la méthode prédit bien l'aérodynamique de la pâle. Ensuite, le tourbillon de bout de pâle a été, en particulier, caractérisé. La vorticité et la vitesse azimutale ont été trouvées auto-similaire et la taille du coeur suit asymptotiquement la loi de diffusion linéaire 2D. Un modèle simple du coeur du tourbillon a été proposé. La présence d'une vitesse axiale dans le coeur du tourbillon a été montrée et a été caractérisée en fonction du rapport de vitesse au bout de la pâle. Finalement, une étude de stabilité du tourbillon a été faite en utilisant une vitesse angulaire variable pour perturber l'écoulement. Les taux de croissances des modes les plus instables sont en bon accord avec celui de l'instabilité d'appariement 2D des tourbillons. Trois types de modes ont été identifiés en fonction de la fréquence des perturbations et ont été trouvés similaires aux modes décrits par la théorie et aussi trouvés, précédemment, par l'expérience. / This present work is aimed to study helical vortices encountered in the wakes of rotating elements. For this, the generation of a helical wake of a one-bladed-rotor in a laminar velocity field, is simulated by the actuator line method. This method is a coupling of a Navier-Stokes (NS) solver with the Actuator Line Method where the blade is replaced by the body forces. This method has been implemented in a finite difference code, that we have written in parallel to solve the 3D incompressible NS equations written in cylindrical coordinates. The order of accuracy of the method is two both in time and space. The NS solver was validated comparing growth rates of an unstable jet, found numerically, and those of linear instability theory. A good agreement was found. A good agreement was also found comparing numerical results to analytical formulations and experimental data. It was shown that the method predicts well the blade aerodynamics . Then, the helical tip vortex is characterized for different Reynolds numbers and Tip Speed Ratios. The vorticity and the azimuthal velocity were found self-similar and the vortex core follows asymptotically the linear 2D diffusion law. A simple model for the helical vortex core was proposed. The presence of an axial velocity inside the vortex core was highlighted. Then, a stability study of the helical tip vortex was done using an angular velocity dependent on time to perturb the flow. The largest growth rates were found in good agreement with those of the (2D) pairing instability. Three types of modes were identified based on the perturbation frequency. The results are similar to those found in previous analytical and experimental works.

In this thesis direct numerical simulations are used to investigate two phenomenain shear flows: laminar-turbulent transition over a flat plate and periodicvortex shedding induced by a jet in cross flow. The emphasis is on understanding and controlling the flow dynamics using tools from dynamical systems and control theory. In particular, the global behavior of complex flows is describedand low-dimensional models suitable for control design are developed; this isdone by decomposing the flow into global modes determined from spectral analysisof various linear operators associated with the Navier–Stokes equations.Two distinct self-sustained global oscillations, associated with the sheddingof vortices, are identified from direct numerical simulations of the jet incrossflow. The investigation is split into a linear stability analysis of the steadyflow and a nonlinear analysis of the unsteady flow. The eigenmodes of theNavier–Stokes equations, linearized about an unstable steady solution revealthe presence of elliptic, Kelvin-Helmholtz and von K´arm´an type instabilities.The unsteady nonlinear dynamics is decomposed into a sequence of Koopmanmodes, determined from the spectral analysis of the Koopman operator. Thesemodes represent spatial structures with periodic behavior in time. A shearlayermode and a wall mode are identified, corresponding to high-frequency andlow-frequency self-sustained oscillations in the jet in crossflow, respectively.The knowledge of global modes is also useful for transition control, wherethe objective is to reduce the growth of small-amplitude disturbances to delaythe transition to turbulence. Using a particular basis of global modes, knownas balanced modes, low-dimensional models that capture the behavior betweenactuator and sensor signals in a flat-plate boundary layer are constructed andused to design optimal feedback controllers. It is shown that by using controltheory in combination with sensing/actuation in small, localized, regionsnear the rigid wall, the energy of disturbances may be reduced by an order of magnitude.