Despite the staggering volume of work in the open literature on primary and secondary atomization, there is nothing known that addresses the mechanisms for, and injector geometry implications for, primary atomization within a self-sustained pulsating transonic three-stream injector. Thus, a computational effort involving 86 simulations, including multiple validation exercises, has been executed in order to develop a numerical foundation and then study the effects of nozzle geometry, numerical methodology, grid resolution, modeled domain extent, feed rates, feed flow modulation, feed flow swirl, feed materials, and operating conditions. This is the first undertaking ever reported to disclose the intense details of transonic pulsating flows within the three-stream injector. Metrics for assessment of acoustics and temporal spray character were numerous. Frequency responses among those metrics implied a common pulsation-driving mechanism. It has been discovered that liquid bridging with the production of a liquid fountain and shocklet-like structures in the retracted (pre-filming) zone, along with localized gas-liquid normal pressure gradients, are responsible for bulk pulsations. These findings were never reported in the literature, thus represent an important contribution of this study. Unexpectedly, a new trend for temporal mean droplet size, when normalized by distance from the nozzle, versus distance from the nozzle has been found, which took a common form among all geometries and feed materials tested. Therefore, there is some value to simulate air-water flows, first, to scope general parameters and characteristics, before modeling more computationally challenging slurry flows. This represents an additional contribution of this work not previously reported in the literature. Newly unveiled strong interactions between feed materials, geometry, and feed rate were discovered. Various combinations of inner nozzle retraction and slurry annular thickness were shown to be advantageous, depending on the goals of the injection system. The importance of either geometry variable for three-stream injectors has not been quantified until now. The predictive power of various modeling frameworks has been assessed for the first time. Axi-symmetric (AS) simulations can successfully predict absolute acoustic details; remarkably and surprisingly, AS simulations can also be used for directional indicators of bulk droplet size. This is an especially powerful revelation given the massive reduction in computational requirements for AS models. Reduced order 3-D models are required for better droplet size estimates. A relatively simple eddy-viscosity turbulent model seems to be adequate for predicting droplet sizes for three-stream injectors, in which the primary energy source is bulk pulsations. For larger two-stream systems (atomization energy is sourced in local shear layer instability development), however, a state-of-the-art hybrid model (newly implemented for this effort) appeared to be necessary to capture the resulting droplet scales. Lastly, droplet size and characteristic flow length scale predictions for two open literature non-Newtonian liquid atomizers were made available. / Ph. D.

Multidisciplinary Design Optimization (MDO) studies show the Strut/Truss Braced Wing (SBW/TBW) concept has the potential to save a significant amount of fuel over conventional designs. For the SBW/TBW concept to achieve these reductions, the interference drag at the wing strut juncture must be small compared to other drag sources. Computational Fluid Dynamics (CFD) studies have concluded the interference drag is small enough for the TBW concept to be practical. However, the turbulence models used in these studies have not been validated for transonic, high Reynolds number, junction flows. This study intends to assess turbulence models by comparing drag and surface streamlines obtained from experiment and CFD. The test model is a NACA 0012 fin at Mach number of 0.75 and a Reynolds number of 6 million with varying angle of attack. The CFD analysis includes both the fin and tunnel test section. The main turbulence model tested is the k-w Shear Stress Transport model. The fin is tested at different Mach numbers and inlet conditions to account for experimental variations. The study shows the CFD over predicts separation. The reasons for this discrepancy is likely the turbulence models employed. / Master of Science

The transport of heat that results from turbulence is a major factor limiting the temperature gradient, and thus the performance, of fusion devices. We use nonlinear simulations to show that a toroidal equilibrium scale sheared flow can completely suppress the turbulence across a wide range of flow gradient and temperature gradient values. We demonstrate the existence of a bifurcation across this range whereby the plasma may transition from a low flow gradient and temperature gradient state to a higher flow gradient and temperature gradient state. We show further that the maximum temperature gradient that can be reached by such a transition is limited by the existence, at high flow gradient, of subcritical turbulence driven by the parallel velocity gradient (PVG). We use linear simulations and analytic calculations to examine the properties of the transiently growing modes which give rise to this subcritical turbulence, and conclude that there may be a critical value of the ratio of the PVG to the suppressing perpendicular gradient of the velocity (in a tokamak this ratio is equal to q/ε where q is the magnetic safety factor and ε the inverse aspect ra- tio) below which the PVG is unable to drive subcritical turbulence. In light of this, we use nonlinear simulations to calculate, as a function of three parameters (the perpendicular flow shear, q/ε and the temperature gradient), the surface within that parameter space which divides the regions where turbulence can and cannot be sustained: the zero- turbulence manifold. We are unable to conclude that there is in fact a critical value of q/ε below which PVG-driven turbulence is eliminated. Nevertheless, we demonstrate that at low values of q/ε, the maximum critical temperature gradient that can be reached without generating turbulence (and thus, we infer, the maximum temperature gradient that could be reached in the transport bifurcation) is dramatically increased. Thus, we anticipate that a fusion device for which, across a significant portion of the minor radius, the magnetic shear is low, the ratio q/ε is low and the toroidal flow shear is strong, will achieve high levels of energy confinement and thus high performance.

Pas de résumé / Axisymmetric turbulence is investigated using direct numerical simulations. A fully spectral method is implemented using Chandrasekhar-Kendall eigenfunctions of the curl-operator. The numerical domain is a periodic cylinder with no-penetration and partial slip conditions at the wall. Numerical simulations are first carried out for freely decaying axisymmetric turbulence, starting from a variety of initial conditions. The simulations indicate that the global angular momentum is the most robust invariant of the system. It is further observed that large-scale coherent structures emerge, as in 2D isotropic turbulence. Energy decays more slowly than helicity, and the toroidal kinetic energy decays faster than its poloidal part. In the case where the toroidal kinetic energy becomes negligible, a quasi-two dimensional turbulence in the poloidal plane is obtained, with a behavior compatible with predictions of statistical mechanics theories. Forced and decaying simulations are then carried out to assess the cascade-behavior of the different invariants. The existence of an inverse cascade is shown to explain the robustness of the angular momentum and the possible ‘spontaneous generation’ of this quantity and of circulation in the flow. In helical flows, the existence of a dual cascade is confirmed, with a scenario compatible with the existence of an inverse energy cascade towards the large scales, and a direct cascade of helicity towards the small scales. The inverse energy cascade seems to be mainly associated with the poloidal velocity field. Using a helical decomposition of the flow, it is shown that the direct cascade of helicity seems to subsist even in the absence of net helicity, when the ‘cascade’ of the helicity contained in oppositely polarized modes is considered individually. The scaling of the energy spectra associated with the energy cascade is compatible with elementary dimensional arguments, whereas the scaling of the inverse (presumably helicity) cascade yields an anomalously steep slope. It is shown that this slope adjusts to the value predicted by dimensional analysis when the spectra are computed from a filtered velocity field in which strong intermittent regions of velocity are not accounted for. Finally, a preliminary (but unfortunately unfruitful) attempt is presented to apply a variational principle to the description of turbulent scalar mixing in three-dimensional turbulence.

Direct Numerical Simulation of channel flow was utilized to study the evolution of various vortex configurations presented as flow initial conditions. Simulations of longitudinally, laterally and cross-flow oriented vortices suggested that the predominant form of turbulent structure was the half hairpin vortex. This vortical structure was dominant in the simulations seen in this as well as other investigations. In all cases hairpin vortices quickly degenerated to half hairpin or inclined vortical structures. It is hypothesized that these structures function as the predominant momentum transfer mechanism within the boundary layer, entraining fluid into the vortex cores like miniature tornados and transporting this fluid to the top of the boundary layer while simultaneously dragging fluid viscously around the inclined core of the vortex causing mixing of low-speed and high-speed flows.

Cette thèse s'intéresse à la turbulence dans l'hélium (4He) superfluide, à des températures comprises entre 1.15 K et la température de transition superfluide, Tlambda = 2.17 K, ce qui correspond à une fraction de superfluide rho_s/rho comprise entre 97.6% et 0%. Il s'agit d'un travail essentiellement expérimental dont le but est de comparer la turbulence classique et la turbulence quantique, à l'aide de mesures locales de fluctuations de vitesse et de vorticité. Ces mesures sont complétées par l'analyse de champs de vitesse issus de simulations numériques.Nous avons développé une instrumentation spécifique, adaptée aux écoulements cryogéniques: des tubes de Pitot miniatures, dont les dimensions effectives ont pu être rendues sub-millimétriques, et un capteur original, basé sur la déflection d'une micro-poutrelle (300 microns x 100 microns x 1 microns) mesurée à l'aide d'un micro-résonateur supraconducteur dans la gamme de fréquence du GHz. Un premier prototype de ce capteur, micro-fabriqué à partir d'une galette de silicium, a été réalisé en salle blanche puis validé dans une conduite cryogénique. La résolution spatiale obtenue est du même ordre que celle des meilleurs anémomètres en He II, et il devrait être possible de l'améliorer d'une décade.Les tubes de Pitot ont été placés dans les souffleries superfluides TSF et TOUPIE. La première, fruit d'une collaboration nationale, a fourni un écoulement stationnaire de grille (Rlambda= 250, 1.65 K < T < 2.6 K, rho_s/rho < 80%) et un sillage proche. La seconde soufflerie, refroidie pour la première fois dans le cadre de cette thèse, a fourni un écoulement de sillage lointain (Rlambda = 1100, 1.55 K < T < 4.2 K, rho_s/rho < 86%).Les mesures ont mis en évidence dans ces écoulements des similarités fortes avec les écoulements classiques, aux échelles inertielles: spectre de vitesse en k^{-5/3}, constante de Kolmogorov et taux de turbulence identiques aux écoulements classiques, loi des 4/5, exposants anormaux pour les fonctions de structures des incréments de vitesse (intermittence). À plus petite échelle, les simulations numériques (1.15 K < T < 2.1565 K) mettent en évidence un comportement exotique : l'énergie s'accumule et tend vers l'équipartition, ce qui se traduit par un spectre de vitesse simulé en k^2. Ce phénomène s'accentue à basse température. Enfin, des mesures locales de fluctuation de vorticité ont été réalisées à l'aide de pinces à second son sur une gamme de température comprise entre 1.69 K (rho_s/rho=77%) et 2.01 K (rho_s/rho = 42%). Nous avons observé un raidissement de la pente des spectres de vorticité lorsque la température diminue. Ce résultat peut être interprété comme une conséquence du phénomène d'équipartition mis en évidence dans les simulations numériques à petite échelle. / The focus of this thesis is the turbulence of superfluid 4He at temperatures between 1.15K and the superfluid transition temperature Tlambda = 2.17K, corresponding to a superfluid fraction rho_s/rho between 97.6% and 0%. This work is mostly experimental. We aim to compare classical and quantum turbulence, using local velocity and vorticity fluctuations measurements. These measurements are backed up by numerical simulations.We developed dedicated probes, designed for cryogenic flows: Pitot tubes with sub-millimeter effective size and a new cantilever-based probe (300 microns x 100 microns x 1 microns) whose deflection is measured with a superconducting micro-resonator in the GHz frequency range. A first prototype was micro-machined from a silicon wafer in cleanroom and validated in a superfluid wind tunnel. The resolution was found similar to the one of the best anemometers operating in He~II and will be further improved.The Pitot tubes have been inserted inside two superfluid wind tunnels, TSF and TOUPIE. The former, designed and operated within a national collaboration, provided a stationary grid flow (Rlambda = 250, 1.65 K < T < 2.6 K, rho_s/rho < 80%) and a near-wake flow. The latter (Rlambda = 1100, 1.55 K < T < 4.2 K, rho_s/rho < 86%), which was cooled down for the first time during this thesis, provided a far-wake flow.The measurements have highlighted strong similarities with classical flows at inertial scales: k^{-5/3} velocity spectra, Kolmogorov constant and turbulence intensity indistinguishable above and below the superfluid transition, 4/5-law, anomalous velocity structure functions exponents (intermittency). At smaller scales, the numerical simulations (1.15 K < T < 2.1565 K) exhibit exotic behavior: kinetic energy piles up and tends to equipartition, which makes the simulated velocity spectrum scale like k^2. This phenomenon is enhanced at low temperature. Finally, local vorticity fluctuations measurements have been achieved using second sound tweezers over a temperature range, between 1.69 K (rhos/rho=77%) and 2.01 K (rhos/rho = 42%). We observed that the spectrum scaling steepens as the temperature decreases. This can be interpreted as a consequence of the equipartitioned reservoir evidenced by numerical simulations at small scale.

L’objet de ce travail de thèse est l’étude en soufflerie du sillage lointain des éoliennes à axe horizontal. La complexité phénoménologique du sillage des éoliennes fait que les mécanismes le régissant sont généralement traités d’un point de vue stationnaire : les principaux paramètres (déficit de vitesse, production de turbulence...) sont alors moyennés dans le temps. Néanmoins, considérer les instationnarités du sillage d’une éolienne placée en écoulement atmosphérique permet d’observer un phénomène appelé meandering, traduisant un battement aléatoire du sillage. Ce travail est construit en deux grandes parties : la vision stationnaire et la vision instationnaire du sillage d’un modèle simplifié d’éolienne, basé sur le principe du disque de Froude, placé dans une couche limite atmosphérique (CLA) modélisée en soufflerie à l’échelle 1/400. La première partie est composée de plusieurs études paramétriques sur l’influence du point de fonctionnement d’une éolienne, sur sa hauteur de mât ou encore sur le type de CLA. Une éolienne en situation de dérapage fait également l’objet d’études paramétriques. Celles-ci visent à étudier le comportement du sillage dans différentes situations et il est alors montré les limites des lois empiriques présentes dans la littérature, concernant notamment l’influence de la turbulence ambiante. La seconde partie se focalise sur la vision instationnaire, jusqu’ici rarement considérée. En utilisant l’anémométrie par fil chaud, les résultats montrent le rôle des grandes échelles de la turbulence atmosphérique sur l’apparition du meandering. L’amplitude du battement et les dimensions du sillage instantané sont ensuite appréhendées de façon quantitative par mesures PIV, montrant l’influence du point de fonctionnement de l’éolienne et de l’intensité de turbulence ambiante. / The aim of this work was to study the far wake of horizontal axis wind turbines in wind tunnels. Aerodynamic phenomena within the wakes are very complex and, most of the time, they are studied from a steady point of view : the main parameters (wake deficit, production of turbulence...) are therefore time averaged. Nevertheless, studying the wake unsteadiness of a wind turbine located in the atmospheric boundary layer (ABL) enables the consideration of the meandering phenomenon, which describes random oscillations of the wake. The present work was constructed in two main parts : firstly the steady vision and secondly the unsteady vision of a wind turbine wake, modelled according to the actuator disk theory and placed in an ABL reproduced in a wind tunnel at a geometric scale of 1/400. Several parametric studies are presented in the first part : on the influence of the wind turbine’s operating point, of its mast height and also on the influence of the ABL characteristics. Wind turbines in yaw are also considered. The wake behaviour is then studied in different configurations and the limits of the empirical laws in the literature are highlighted, especially the lack of the ambiant turbulence intensity consideration. The second part focuses on the unsteady point of view, rarely considered until today. Using hot wire anemometry, the role of the atmospheric large turbulent scales on the meandering phenomenon is proven. The oscillation magnitude and the instantaneous wake dimensions are also investigated using PIV, which leads to quantitative results on the meandering characteristics.

Rapid distortion theory (RDT) is applied to compressible ideal-gas turbulence subjected to homogeneous shear flow. The study examines the linear or rapid processes present in turbulence evolution. Specific areas of investigation include:(i) characterization of the multi-stage flow behavior,(ii) changing role of pressure in the three-regime evolution and (iii) influence of thermodynamic fluctuations on the different regimes. Preliminary investigations utilizing the more accurate Favre-averaged RDT approach show promise however, this approach requires careful validation and testing. In this study the Favre-averaged RDT approach is validated against Direct Numerical Simulation (DNS) and Reynolds-averaged RDT results. The three-stage growth of the flow field statistics is first confirmed. The three regime evolution of turbulence is then examined in three different timescales and the physics associated with each regime is discussed in depth. The changing role of pressure in compressible turbulence evolution shows three distinct stages. The physics of each stage is clearly explained. Next, the influence of initial velocity and thermodynamic fluctuations on the flow field are investigated. The evolution of turbulence is shown to be strongly dependent on the initial gradient Mach number and initial temperature fluctuations which tend to delay the onset of the second regime of evolution. The initial turbulent Mach number, which quantifies velocity fluctuations in the flow, influences turbulence evolution only weakly. Comparison of Reynolds-averaged RDT against Favre-averaged RDT for simulations of nonzero initial flow field fluctuations shows the higher fidelity of the latter approach.

Turbulence in classical fluids has been the subject of scientific study for centuries, yet there is still no complete general theory of classical turbulence connecting microscopic physics to macroscopic fluid flows, and this remains one of the open problems in physics. In contrast, the phenomenon of quantum turbulence in superfluids has well-defined theoretical descriptions, based on first principles and microscopic physics, and represents a realm of physics that can connect the classical and quantum worlds. Studies of quantum turbulence may thus be viewed as a path for progress on the long-standing problem of turbulence.A dilute-gas Bose-Einstein condensate (BEC) is, in most cases, a superfluid that supports quantized vortices, the primary structural elements of quantum turbulence. BECs are particularly convenient systems for the study of vortices, as standard techniques allow the microscopic structure and dynamics of the vortices to be investigated. Vortices in BECs can be created and manipulated using a variety of techniques, hence BECs are potentially powerful systems for the microscopic study of quantum turbulence.This dissertation focuses on quantized vortices in BECs, specifically experimental and numerical studies of their formation, dynamics, and decay, in an effort to understand the microscopic nature of vortices as elements of quantum turbulence. Four main experiments were performed, and are described in the main chapters of this dissertation, after introductions to vortices, experimental methods, and turbulence are presented. These experiments were aimed at understanding various aspects of how vortices are created and behave in a superfluid system. They involved vortex dipole nucleation in the breakdown of superfluidity, persistent current generation from a turbulent state in the presence of energy dissipation, decay of angular momentum of a BEC due to trapping potential impurities, and exploration of the spontaneous formation of vortices during the BEC phase transition. These experiments represent progress towards enhanced understanding of the formation, dynamics, and decay of vortices in BECs and thus may be foundational to more general studies of quantum turbulence in superfluids.

In this thesis we will investigate the role of diapycnal mixing on the ocean general circulation. This thesis is divided into three main parts. In the first part we show that there exists an almost infinite number of pathways to turbulence in oceanic energetic shear zones at high Reynolds number. Such a large number of accessible routes to truly chaotic motion is not typical of most of the existing body of laboratory and numerical experiments of shear-induced diapycnal mixing, but is shown to be of relevance to diapycnal mixing in geophysical flows. A key finding is that the use of generally accepted empirical relations based on laboratory experiments for the quantification of diapycnal mixing leads to large inaccuracies. In the second part we perform high resolution numerical experiments of diapycnal mixing in the oceanographically relevant high Reynolds number parameter range. Through detailed analysis of the flow energetics and mixing properties of these flows, we show that the net buoyancy flux facilitated by turbulence, the efficiency of diapycnal mixing, and the resultant effective diffusivity, all depend in non-trivial ways on the specific route to turbulence for each individual mixing event. This has important implications for practical methods of estimating an effective diapycnal mixing diffusivity from observations as well as for parametrization of mixing in ocean general circulation models. We show quantitatively that such methods can be inaccurate to the extent that they will need to be completely revised or replaced. In the third and final part of the thesis we investigate the sensitivity of the meridional overturning circulation of the abyssal ocean to the intensity and spatial variations of diapycnal mixing. We show that changes in intensity of mixing by factors well within the errors associated with practical estimates (as discussed above) lead to significant changes in ocean circulation. We show that enhanced abyssal mixing, surface winds, and meso-scale eddies play leading roles in driving the abyssal ocean circulation and in setting the stratification. As an example of the application of our analysis we show that proper parametrization of enhanced abyssal mixing leads to realization of the important role of the (often neglected) geothermal heat flux in driving the Antarctic Bottom Water circulation.