Bubbly turbulent flows occur in a variety of industrial, naval and geophysical problems. In these flows, the bubbles in the flow interact with turbulence and/or vortical structures present in the continuous phase, resulting in bubble motion and deformation, and at the same time modifying the turbulence and/or vortical structures. Despite the fact that this has been a subject of interest for some time, mechanisms of bubble break-up due to turbulence and turbulence modulation due to bubbles are not well understood. To help understand this two-way coupled problem, we study in this thesis, the interaction of single and multiple bubbles with vortical structures; the thesis being broadly divided in to three parts. In the first part, we study the interaction of a single bubble with a single vortical structure, namely a vortex ring, formed in the continuous phase (water). This may be thought of as a simplified case of the interaction of bubbles with vortical structures in any turbulent flow. We then increase the complexity and study the interaction of a single bubble with naturally occurring vortical structures present in a fully developed turbulent channel flow, and then finally to the case of a large number of bubbles injected in to a fully developed turbulent channel. The bubble motions and deformations in all three cases are directly imaged using high speed visualizations, while the flow field information is obtained using time-resolved Particle-Image Velocimetry (PIV) in the first two cases, and from pressure drop measurements within the channel in the latter case. The interaction of a single vortex ring with a bubble has been studied for a large range of vortex ring strengths, represented in terms of a Weber number (We). We find that in all cases, the bubble is first captured by the low pressure within the core of the ring, then stretched azimuthally within the core, and gradually broken up in to a number of smaller bubbles. Along with these bubble deformations, the vorticity within the core of the ring is also modified significantly due to bubble capture. In particular, at low We, we find that the core of the ring fragments as a result of the interaction resulting in a large reduction in the enstrophy of the ring and its convection speed. In the second part of the thesis, interaction of a single bubble with naturally occurring vortical structures present in a fully developed turbulent channel is studied. In this case, single bubbles of different sizes are injected either from bottom or top wall into a channel at Reynolds number of about 60,000. We study the trajectories of the single bubble, and also investigate the effect that such bubbles have on the naturally occurring vortical structures present in these flows. The injected bubble is found to have three broadly different types of bubble paths when injected from the bottom wall, which are sliding along the wall, bouncing motions and vertical escape from the vicinity of the wall. Even at the same bubble diameter Db and channel flow Re, we find that different realizations show considerable variations, with all three bubble paths being possible. PIV measurements of a bubble captured by a naturally occurring vortical structure in the flow, shows a more rapid decrease in enstrophy compared to naturally occurring structures in the absence of bubbles, as seen in the interaction of a bubble with a vortex ring. We also find that the bubble can interact with multiple vortical structures, depending on their strength and spatial distribution in the flow, resulting in a complex bouncing bubble motion. In the third part of the study, a large number of bubbles are injected in to the channel through porous plates fixed at the top and bottom channel walls. The main parameters here are the channel Re, bubble void fraction (α) and the orientation of injection. In this case, in addition to bubble visualizations, the pressure drop through the channel is measured at different vertical locations. These measurements show large vertical variations in the measured pressure drop due to the presence of bubbles. The overall drag reduction in these cases is obtained from an integral of the pressure drop variation along the vertical direction. The visualizations show a number of bubble dynamics regimes depending on the parameters, with possibilities of both increased and decreased drag compared to the reference no bubble case. From simultaneous measurements, we relate the variations in drag reduction to the different bubble dynamics regimes. We find that at the same void fraction (α), the drag reduction obtained can be very different due to changes in bubble dynamics regimes caused by changes in other parameters. Top wall injection is observed to give good drag reductions over a wide range of flow Re and α, but is seen to saturate beyond a threshold α. In contrast, the bottom wall injection case shows that drag reduction continuously increases with αat high Re. The present study shows a maximum of about 60% increase and a similar 60% reduction in wall drag over the entire range of conditions investigated.

Doctor of Philosophy / Department of Mechanical and Nuclear Engineering / Zhongquan Zheng / In this study, a vortex particle method is used to simulate incompressible vortical flows, specifically aircraft wake vortices. This is particularly suitable for a wake vortex system that is slowly varying in the axial direction and has a high Reynolds number and low Mach number. The flow field, in the form of vorticity, is employed as the source in the far-field acoustic calculation using a vortex sound formula that enables computation of acoustic signals radiated from an approximated incompressible flow field. In a two-dimensional vortex system, the stretching effect in the axial direction is neglected. The purpose of this study is to focus on vortex core behaviors. A numerical simulation is performed in a more realistic wake consisting of a counter-rotating vortex pair with inviscid ground effects and shear flows. A Kirchhoff spinning-core vortex model is thus used as a starting point. In a vortex system with multiple vortices, such as a complicated aircraft vortex wake vortices, the sound emission frequency of the unsteady vortex core is subjected to change because of interactions between multiple vortices. The behaviors of the influence, indicated by the ratio between the core size and the distance of the vortices, are investigated as well as the underlining vortex core dynamic mechanisms. Cases of co-rotating vortices and a multiple-vortex system composed of two counter-rotating vortex pairs are studied for applications to aircraft wake vortex sound. In three-dimensional vortices, sinusoidal instabilities, which occur in the axial direction at various length scales, result in significant flow structure changes in these vortices, and thus influence their radiated acoustic signals. Cases of vortex rings and a pair of counter-rotating vortices are studied when they are undergoing both long-wave and short-wave instabilities. Both inviscid and viscous interactions are considered and the effects of turbulence are simulated using sub-grid-scale models. A higher peak frequency than the Kirchhoff frequency appears due to the straining field caused by mutual perturbation, under both long-wave and short-wave instabilities. Vortices with the initial core vorticity of the Gaussian distribution and the elliptic distribution are also studied.

Cette thèse est une étude expérimentale de la formation et de la maturation d’un anneau tourbillonnaire. Elle porte sur les écoulements faiblement inertiels (Reynolds : 5 à 500) en fluide newtonien puis non newtonien. Les anneaux sont générés par un système cylindre-piston. Ils sont analysés par visualisation et par vélocimétrie par images de particules (PIV). La dynamique en fluide newtonien à faible nombre de Reynolds se révèle plus complexe que celle à grands Reynolds avec l’apparition d’un anneau secondaire contrarotatif. Les résultats obtenus en fluide rhéofluidifiant montrent l’influence de l’indice de comportement ainsi que les zones de comportement rhéofluidifiant et newtonien. Les explorations en fluides viscoplastique et viscoélastique montrent la formation d’un ou plusieurs anneaux secondaires contrarotatifs, qui diffèrent dans leur formation et leur dynamique des anneaux observés en fluide newtonien et que l’on associe aux propriétés physiques intrinsèques du fluide. / The present work is an experimental study of the generation and the maturation of vortex rings, in order to characterize their structure and their global dynamics for small to moderate Reynolds numbers (between 5 and 500) in Newtonian and non-Newtonian fluids. The experimental set-up consists of a vertical cylindrical piston-tube system with the lower part immersed in a filled tank. Measurement campaigns have been carried out using dye visualization and Particle Image Velocimetry (PIV). A first part of the work is focussed on Newtonian fluid and allows the dynamics at low Reynolds numbers to be investigated qualitatively and quantitatively. This dynamics turns out to be more complex than the one classically observed at high Reynolds numbers, and is characterized by the production of a counter-rotating secondary vortex ring. The results obtained for shear thinning fluids show the influence of the power-law index on the development and the propagation of the ring. The computation of the shear rate field allows the results to be analyzed in terms of shear thinning and Newtonian regions. Finally a preliminary investigation for viscoplastic and viscoelastic fluids has been performed. In both cases, it is shown that one (for viscoplastic fluids) or several (for viscoelastic fluids) counter-rotating secondary vortex rings are generated, a phenomenon that can be associated with the intrinsic physical properties of the fluid. All these results provide several perspectives of study in the field of vortex rings dynamics in the weakly inertial regimes.

L’étude des vortex trouve sa justification dans le rôle que ces derniers jouent dans la turbulence quantique. L’équation de Gross-Pitaevskii ne peut pas nous permettre de modéliser convenablement l’Hélium superfluide, mais on peut l’utiliser pour obtenir le paramètre d'ordre d’un superfluide modèle, ayant le maximum de propriétés en commun avec l’Hélium, notamment une courbe de dispersion identique, par la modification du terme d’interactions.En supposant que le minimum roton influence l’essentiel de la physique, on détermine la forme du paramètre d’ordre loin de la perturbation créée par le vortex rectilinéaire axisymétrique par deux approches différentes - il apparaît alors que seuls deux paramètres sont nécessaires pour caractériser entièrement le profil.Le modèle proposé par Pomeau-Rica, qui offre la possibilité d’étudier le superfluide près de la cristallisation, met en lumière l’impact de la profondeur du minimum roton sur l’amplitude des oscillations. Par comparaison avec les résultats obtenus ab initio par Reatto, les résultats donnés par le modèle de Berloff-Roberts exhibent un déphasage marqué, qui semble être une conséquence non-physique de la forme du spectre d’excitation. Les calculs énergétiques laissent à penser que les oscillations portent une faible fraction de l’énergie du vortex, l'énergie cinétique dominant.Le calcul du paramètre d’ordre est effectué pour un anneau de grande taille par rapport à la distance interatomique, à vitesse nulle et à vitesse non-nulle. La détermination des énergies potentielle et cinétique permet d’accéder à la vitesse maximale atteinte par l’anneau en fonction de son rayon et de la comparer à la vitesse critique de Landau. / Vortices study's justification lays in the fact that those former play an important part in quantum turbulence. The Gross-Pitaevskii equation can't be a proper model for superfluid helium, but we can still use it to determine the order parameter of a theoretical superfluid, which has then the maximum amount of properties in common with liquid helium, and in particular, the same dispersion relation, thus gained by modifying the interaction terms.We then make the assumption that all the physical properties of the superfluid are triggered by the existence of the roton minimum, which allows us to calculate the order parameter far from the perturbation created by an axisymmetric rectilinear vortex, using two different methods. At that point, it appears that only two parameters are needed to fully characterize vortex profil.Pomeau-Rica's model offers the possibility to study the superfluid near crystallization and reveals the influence of the roton minimum's shape and depth on oscillations' amplitude. Results are subsequently compared to those given by Reatto's ab initio calculations. In Berloff-Roberts' model, profil displays a strong phase shift, which seems to be a non-physical consequence of the dispersion relation's shape at high frequencies. Energies reckoning leads us to think that oscillations carry a small fraction of the total vortex' energy, meaning that the kinetic energy is dominant.The order parameter for a vortex ring, whose radius is much larger than the interatomic distance, is calculated at zero and nonzero speed. Potential and kinetic energies are estimated and help us obtain the maximal speed reached by such a ring, depending on its radius and finally discussed this speed in regard to the Landau critical speed.

Ce travail de thèse porte sur les propriétés de stabilité des tourbillons hélicoïdaux, structures que l'on retrouve notamment dans le sillage des rotors d'hélicoptères et d'éoliennes.Dans une première partie, le développement spatio-temporel de l'instabilité d'appariement est caractérisé à l'aide d'un code numérique pseudo-spectral pour une allée infinie d'anneaux tourbillonnaires. On montre que ce modèle axisymétrique d'écoulement est en effet une bonne approximation du système hélicoïdal dans la limite des grands rayons et petits pas d’hélice. Dans ces conditions, et en utilisant un adimensionnement judicieux, on obtient également que le résultat théorique pour le taux de croissance spatio-temporel obtenu pour une double allée de tourbillons ponctuels s’avère être une bonne prédiction pour le cas hélicoïdal.Dans une seconde partie, on décrit comment un ou plusieurs tourbillons hélicoïdaux ont pu être générés de façon très peu perturbée à l’aide de modèles réduits de rotors dans le canal hydrodynamique du laboratoire. Grâce à l’introduction de perturbations d’amplitudes et de fréquences soigneusement contrôlées, le taux de croissance de l’instabilité d’appariement a pu être mesuré et comparé aux résultats théoriques. L’évolution non linéaire de ces perturbations ainsi que d’autres modes instables, à plus petites longueurs d’onde, ont également pu être observés expérimentalement pour la première fois.Enfin, ces résultats ont été appliqués au cas des rotors d’hélicoptères pour la prédiction du régime de Vortex Ring State (VRS) et à la transition vers la turbulence du sillage des éoliennes. / This thesis is devoted to the stability properties of helical vortices, which are of interest for applications such as helicopter and wind turbine wakes.In a first part, the spatio-temporal development of the pairing instability is characterised for an infinite array of vortex rings, using a pseudo-spectral numerical code. We show that this axisymmetric flow model is indeed a good approximation of the helical system in the limit of large helix radius and small pitch. Under these assumptions, and by using appropriate dimensionless variables, we also show that the theoretical result concerning the spatio-temporal growth rate for a double row of point vortices represents a good prediction for the helical case.In a second part, we describe how one or several helical vortices were generated in a carefully controlled way using small-scale rotor models in the water channel of the laboratory. Introducing perturbations with well-defined amplitudes and frequencies, the growth rate of the pairing instability could be measured experimentally and compared to theoretical predictions. The non-linear evolution of these perturbations, as well as other unstable modes of smaller wavelengths, were also observed experimentally for the first time.Finally, these results were applied to helicopter wakes for the prediction of the Vortex Ring State (VRS) regime and to the transition to turbulence in wind turbine wakes.