This thesis investigates vortex dynamics of a plunging airfoil by studying the vorticity transport mechanisms of two-dimensional direct numerical simulations. The simulations were used to study a simplified flat airfoil in a freestream that was subject to pure plunging motion. Quantitative and qualitative analyses were used the validate the two-dimensional simulations and gain insight into the effects of eliminating three-dimensional physics in a nominally two-dimensional flow. Additionally, a parametric study was conducted to analyze the effects of Reynolds and Strouhal numbers on the transport of vorticity.

Planar and stereo particle image velocimetry measurements were conducted of a wing-tip vortex decaying in free-stream turbulence in order to understand the evolution of a vortex and its decay mechanism. The vortex decayed faster in the presence of turbulence. The decay of the circulation was found to be almost entirely due to a decrease in circulation of the vortex core, caused by the relative decrease in peak tangential velocity without a corresponding increase in core radius. These events were found to be connected with the stripping of core fluid from the vortex core. The increased rate of decay of the vortex in turbulence coincided with the formation of secondary vortical structures which wrapped azimuthally around the primary vortex. It was also found that regardless of the free-stream condition, the core scaled by peak tangential velocity and core radius.

Elastic cylinder vibration due to different shear parameter in the water flow is investigated experimentally in this research. The water flow ranges from 0.4 m/s to 1.06 m/s. It is found from the experiment that shear parameter has a significant influence on the amplitude of the cylinder vibration. The greater the shear parameter becomes, the later the delaying phenomenon also becomes. The delaying phenomenon will bring about resonant procrastination. Additionally, the greater shear parameter lessens the cylinder¡¦s drag force, but the lift force will be augmented, and the vibration orbit will be asymmetric. At lower flow velocity, cylinder¡¦s displacement is greater. With the enhancement of the shear parameter or the reduced velocity, the flow type and the vortex street behind the cylinder will turn more and more impalpable, and eventually become chaotic.

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Mechanical and Aerospace Engineering." Includes bibliographical references (p. 111-115).

This thesis is concerned with three-dimensional vortex dynamics, in particular the modelling of vortex structures in an inviscid context. We are motivated by the open problem of regularity of the inviscid equations, i.e. whether or not these equations possess solutions. This problem is manifest in small scales, where vortex filaments are stretched and intensify as they are drawn into increasingly thin tendrils. This creates great difficulty in the investigation of such flows. Our only means of experimentation is to perform numerical simulations, which require exceptionally high resolution to capture the small scale vortex structures. A new numerical method to solve the inviscid Euler equations for three-dimensional, incompressible fluids is presented, with special emphasis on spatial adaptivity to resolve as broad a range of scales as possible in a completely self-similar fashion. We present a hybrid vortex method whereby we discretise the vorticity in Lagrangian filaments and perform and inversion to compute velocity on an arbitrary unstructured finite-volume grid. This allows for a two-fold adaptivity strategy. First, although naturally spatially adaptive by definition, the vorticity filaments undergo ‘renoding'. We redistribute nodes along the filament to concentrate their density in regions of high curvature. Secondly the Eulerian mesh is adapted to follow high strain by increasing resolution based on local filament dimensions. These features allow vortex stretching and folding to be resolved in a completely automatic and self-similar way. The method is validated via well known vortex rings and newly discovered helical vortex equilibria are also used to test the method. We begin by presenting this new class of three-dimensional vortex equilibria which possess helical symmetry. Such vortices are observed in propeller and wind turbine wakes, and their equilibria shapes have until now been unknown. These vortices are described by contours bounding regions of uniform axial vorticity. Material conservation of axial vorticity enables equilibria to be calculated simply by a restriction on the helical stream function. The states are parameterised by their mean radius and centroid position. In the case of a single vortex, the parameter space cannot be fully filled by our numerical approach. We conjecture that multiply connected contours will characterise equilibria where the algorithm fails. We also consider multiple vortices, evenly azimuthally spaced about the origin. In such cases instabilities often lead to a single helical vortex.

This dissertation addresses the creation of polarization vortex beams. Vortex retarders are components with uniform retardance but a fast axis which rotates around its center with can create polarization vortices. The goal was to develop a simple method for producing vortex retarders for visible wavelengths, with a continuous fast axis, and for multiple vortex modes.The approach was to use photo-aligned liquid crystal polymers (LCP). The target was a halfwave retardance for wavelengths in the range of 540~550nm. A photo-alignment layer was spin-coated onto a substrate, baked, and alignment was set through exposure to linear polarized UV (LPUV) light. The alignment layer was exposed through a narrow wedge shaped aperture located between the substrate and polarizer. Both the polarizer and substrate were continuously rotated during exposure process in order to create a continuous variation in photo-alignment orientation with respect to azimuthal locations on the substrate. The mode of the vortex retarder was determined by the relative rotation speeds. The LCP precursor was spin-coated and subsequently polymerized using a UV curing processes. Elements produced were analyzed by measuring the space variant Mueller Matrix of each component. Our measurements demonstrated that the vortex retarders were half wave plates with a continuous fast axis orientation. Measurement of the center region of the vortex retarders identifies a 100-200um region of disorientation. At 0.5mm resolution, a high depolarization index in the center of the vortex retarders was observed. The DOP was low in the center for a horizontal linear polarized input field but remained high for circular polarized input.The viability of these components was assessed by determining the point spread matrix (PSM) and the optical transfer matrix (OTM) and comparing these to theoretical calculations. The agreement between the measured and predicted PSM was excellent. The major difference was the non-zero response in the m03 and m30 elements indicating circular diattenuation. The OTM comparison between measured and predicted demonstrated an excellent quantitative match at lower spatial frequencies and a good qualitative match at higher spatial frequencies. Measured results confirm that vortex retarders produced using photo-aligned LCP produce near theoretical performance in an optical system.

Le but de la thèse est de comprendre l'influence dynamique des effets diabatiques, comme la convection humide, sur les instabilités des vortex atmosphériques terrestres et planétaires. Un modèle verticalement intégré, avec les paramétrisations type relaxation des transitions de phase et de dégagement de la chaleur latente, le modèle de St-Venant avec la convection humide, a été utilisé. La version précédente du modèle a été améliorée pour inclure l'eau précipitable, sa vaporisation et son entrainement. L'approche consiste en 1) analyse détaillée de stabilité des profils idéalisés, ou extraits des données, des vortex, 2) étude de saturation non-linéaire des instabilités à l'aide de schéma numérique de haute résolution aux volumes finis. Les résultats principaux de la thèse sont : 1. Démonstration et quantification d'une forte influence des effets humides sur les instabilités des vortex synoptiques, y compris asymétrie cyclone-anticyclone des vortex de faible intensité aux latitudes moyennes, et de l'intensification des vortex type cyclones tropicaux, avec formation des nuages caractéristiques. 2. Explication de l'origine dynamique de l'hexagone au pôle Nord de Saturne, et de l'absence de structure similaire au pôle Sud, en termes d'instabilité du système vortex polaire - jet circumpolaire, et sa saturation non-linéaire. 3. Explication de la structure observée du vortex polaire hivernal sur Mars en termes d'instabilité et sa saturation en présence de réchauffement /refroidissement radiatif et de déposition de CO2 (transition de phase gaz - solide). Une nouvelle paramétrisation simple a été proposée pour ce processus, incluant l'influence des noyaux de déposition. / The thesis is devoted to understanding dynamical influence of diabatic effects, like moist convection, on instabilities of vortices in Earth and planetary atmospheres. A vertically integrated atmospheric model with relaxational parameterisation of phase transitions and related heat release, and with convective fluxes included in mass and momentum equations, the moist-convective rotating shallow water model, was used for this purpose. The previous version of the model was improved to include precipitable water and its vaporisation and entrainment. The approach consists in 1)detailed stability analysis of idealised, or extracted from the data, vortex profiles, 2)study of nonlinear saturation of the instabilities with the help of finite-volume high-resolution numerical code. The main results of the thesis are: 1. Demonstration and quantification of strong influence of moist effects upon instabilities of synoptic vortices, including cyclone-anticyclone asymmetry of mid-latitude vortices of weak intensity, and intensification of tropical-cyclone like vortices with formation of typical cloud patterns. 2. Explanation of the dynamical origin of the Saturn's North Polar hexagon, and of the lack of similar structure at the South Pole, in terms of instability of the coupled polar vortex and circumpolar jet, and their nonlinear saturation.3. Explanation of the observed structure of Mars' winter polar vortex in terms of instability of the latter, and its saturation in the presence of radiative heating/cooling and CO2 deposition (gas-solid phase transition). A new simple parameterisation of the latter process, including the influence of deposition nuclei, was developed in the thesis.

The introduction of intermittent renewable energy sources, such as wind and solar power, to the power grid, demands some hydraulic turbines to operate at unfavorable operating conditions not initially designed for. Strong swirl develops at loads below the best efficiency point, (BEP) due to angle mismatch between the guide vanes and the fixed runner blades typical for Francis and Propeller turbines. A rotating vortex rope (RVR) is developed at part load (PL) operation as a consequence of the strong swirl exiting the runner for the aforementioned turbines. The RVR is associated with harmful pressure pulsations, decreasing turbine efficiency, and increasing maintenance time. Thus, it is of great interest to develop and investigate methods to mitigate the RVR. Methods to mitigate the adverse effect associated with the RVR at PL are studied in the presented research. An active mitigation method was numerically studied for a down-scaled propeller turbine, named "injection of pulsating momentum" (IPM). IPM aimed to locally disrupt the RVR by injecting pulsating momentum horizontally into a local part of the quasi-stagnant region in the draft tube. Numerical results indicate a significant reduction of the pressure pulsations associated with the RVR using approximately 5% of the runner flow. A passive mitigation method was also studied on a numerical model of the Porjus U9 Prototype using stationary rods radially protruded into the draft tube flow field. Solid rod protrusion aims to alter the mean flow properties in the draft tube cone, disrupting the formation of the RVR. Numerical results of stationary rod protruding to the RVR shear layer region indicates a complete reduction of the RVR plunging component and a significant reduction of the RVR rotating component due to an increased swirl at the draft tube center.

Coherent vortex-dominated structures in the wake are ubiquitous in natural and engineered flows. The well-known 'von Karman street', in which two rows of counter-rotating vortices develop on the leeward side of a solid body immersed in a fluid, is only one such vortex-based structure in the wake. Recent work on fluid-structure interaction has shown that several other types of vortex structures can arise in natural and engineered systems. The production of these vortex structures downstream often mark the onset of qualitative and/or quantitative changes in the forces exerted on the vortex-shedding body upstream, and can be used as diagnostic tools for engineering structures undergoing Vortex-Induced Vibrations. This dissertation presents a two-part study of vortex dynamics in the laminar wakes of bluff bodies. The first part consists of a series of experiments on a transversely oscillating circular cylinder in a uniform flow field at Re≲250. These experiments were carried out in a gravity-driven soap film channel, which provides a `two-dimensional laboratory' for hydrodynamics experiments under certain conditions. In these experiments, we generated a `map' of the vortex patterns that arise in the wake as a function of the (nondimensional) frequency and amplitude of the cylinder's motion. Our results show that the '2P mode' of vortex shedding can robustly occur in the two-dimensional wake of an oscillating cylinder, contrary to what has been reported in the literature. By making small changes to the meniscus region of the soap film, we have explored possible mechanisms that can explain why the `P+S mode' of vortex shedding is usually reported to be more prevalent than the '2P mode' at low Reynolds number, when the flow is two-dimensional. In doing so, we have found that small modifications to the cylinder on the order of the boundary layer thickness can make a significant difference to the vortex shedding process. In the second part, we develop a generalized form of von Karman's drag law for N-vortex streets: periodic wakes in which the vortices are arranged in regularly-repeating patterns with N>2 vortices per period. The original form of von Karman's drag law then reduces to a special case of this generalized form, which has the potential to model several kinds of vortex-dominated wakes that have been reported in the literature. In this work, we show how this generalized drag law can be used to model '2P' and 'P+S' wakes in both `drag' and `thrust' form. As a contribution to the study of three-dimensional wakes, we also studied a periodic array of vortex rings, which are often used to represent the wakes of marine organisms like jellyfish and squid. We described the problem mathematically using a newly-developed Green's function, and comprehensively examine the fluid physics of such an array of vortex rings as a function of the non-dimensional parameters that govern this phenomenon. In the process, we have discovered a new type of topology that arises in this flow, which may have connections with the `optimal vortex formation length' of vortex rings. / Doctor of Philosophy / The interaction of solid objects with fluids such as water and air, often termed Fluid-Structure Interaction (FSI), gives rise to a wide variety of natural phenomena. Understanding FSI is important as an avenue of scientific interest as well as for engineering applications. In this dissertation, we are interested in the subset of FSI phenomena known as wakes: the fluid flow that is left behind when a solid moves rapidly through quiescent fluid, or when water or air flows rapidly past a stationary obstacle. In such situations, the flow is often rapidly rotating, taking the form of vortices or eddies, i.e., concentrated regions of rotating fluid. These eddies, or vortices, can be described mathematically using simple differential equations, and are the subject of the field of vortex dynamics, which is a branch of fluid mechanics. In the first part of this thesis, we have made contributions to the experimental study of FSI and wakes by making use of an experimental technique known as a gravity-driven soap film channel. In these experiments, a 'soap film', i.e., the surface of a soap bubble, is stretched out over a longitudinal channel formed by nylon wires and held taut in a rectangular shape. This rectangular film of soap is only a few micrometers thick, and is continuously fed by soap solution from the top and drained at the bottom, resulting in a steadily-flowing 'channel' of two-dimensional flow. In this experimental setup, we introduce a circular acrylic cylinder to serve as the archetypal 'obstacle' to fluid flow and oscillate it at a range of frequencies and amplitudes while using a high-speed camera to visualize the flow. This gives rise to a fascinating set of qualitatively distinct vortex patterns in the wake, with the structure depending on the selected frequency and amplitude of cylinder oscillation. In the second part of this thesis, we have developed mathematical models of two-dimensional wakes using a system of point vortices and of three-dimensional wakes using a system of circular vortex rings. We show how these idealized mathematical models of rotating flow, i.e., point vortices and vortex rings, can be used as building blocks for physically-plausible models of actually-occurring wakes, including those which were observed in the first part of this work. For two-dimensional wakes, we use Newton's laws applied to a fluid to determine the forces being exerted on a solid body, immersed in a fluid, whose wake takes the form of regularly-repeating vortices known as 'vortex streets'. This allows us to give, for the first time, theoretical predictions of the drag or thrust force associated with vortex streets such as those observed in our experiments.

The unsteady interaction of a vortex core with a NACA 0015 airfoil is studied in two dimensions. A two-component, three-beam Helium-Neon laser-Doppler Velocimetry system is used to take data in a water tunnel. Ensemble-averaged velocity fields are obtained in the region of the leading edge of the airfoil. Finite-difference algorithms were written to obtain vorticity and pressure in the data field. Computer animation of the unsteady vorticity was accomplished first with a Fortran code written for an Apple Macintosh computer and later with a commercial software package for a SUN Microsystems graphics terminal. / Master of Science