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.

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.

Orientadores: Amir Ordacgi Caldeira, Newton Cesário Frateschi / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-22T06:59:34Z (GMT). No. of bitstreams: 1 Santos_FelipeGustavodaSilva_M.pdf: 5201395 bytes, checksum: aa675cbe9765e61acda958aff38d1a42 (MD5) Previous issue date: 2013 / Resumo: Dispositivos baseados em junções Josephson tem desempenhado um papel importante tanto em ciências básicas quanto aplicadas. Neste trabalho, descrevemos a fabricação e caracterização DC de junções Josephson do tipo ScS (superconductor-constrição-supercondutor). Os dispositivos exibem uma característica VI que concorda com o bem conhecido modelo RSJ (resistência nula abaixo de uma corrente crítica mas constante e não nula acima dessa corrente) para temperaturas ~ 2 K. Para temperaturas um pouco maiores, observamos vários estados resistivos na curva VI, os quais são tipicamente atribuídos ao fluxo de vórtices de Abrikosov no interior da constrição. As medidas, porém, também sugerem que este pode não ser o caso nesses dispositivos devido à pequena magnitude do campo magnético autoinduzido na constrição, se comparado aos campos típicos que a levariam ao estado misto / Abstract: Josephson junction devices have played a role in fundamental and applied sciences. In this work, we report the fabrication and DC characterization of niobium Josephson junctions of the ScS (superconductor-constriction-superconductor) type. The devices exhibit a VI characteristic in accordance with the well known RSJ model (vanishing resistance below a critical current and constant nonzero resistance above it) for temperatures ~ 2 K. For slightly higher temperatures, we observe several resistive states in the VI curve which are usually attributed to the flow of Abrikosov vortices within the constriction. Our measurements, however, suggest that this might not be the case in these devices due to the smallness of the self-induced magnetic field in the constriction in comparison with the typical fields which drive it into the mixed state / Mestrado / Física / Mestre em Física

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.

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The later stages of separated shear layer transition within separation bubbles developing over a NACA0018 airfoil operating at a chord Reynolds number of 105 and at angles of attack of 0, 5, 8, and 10 degrees were investigated experimentally in a wind tunnel. Several experimental tools, including a rake of six boundary-layer hot-wire anemometers, were used to perform measurements over the model. Novel high-speed flow visualization performed with a smoke-wire placed within the separated shear layer showed that roll-up vortices are shed within separation bubbles forming on the suction side of the airfoil. The structures were found to convect downstream and eventually break down during laminar-to-turbulent transition. Top view visualizations revealed that, at angles of attack of 0, 5, and 8 degrees, roll-up vortices form coherently across the span and undergo significant spanwise deformations prior to breaking down. At angles of attack of 5 and 8 degrees, rows of streamwise-oriented structures were observed to form during vortex breakdown. Statistics regarding the formation and development of shear layer roll-up vortices were extracted from high-speed flow visualization sequences and compared to the results of boundary layer measurements. It was found that, on the average, roll-up vortices form following the initial exponential growth of unstable disturbances within the separated shear layer and initiate the later stages of transition. The onset of these nonlinear stages was found to occur when the amplitude of velocity disturbances reached approximately 10% of the free-stream velocity. The rate of vortex shedding was found to fall within the frequency band of the unstable disturbances and lie near the central frequency of this band. The formation of vortices has been linked to the generation of harmonics of these unstable disturbances in velocity signals acquired ahead of mean transition. Once shed, vortices were found to drift at speeds between 33% and 44% of the edge velocity. Vortex merging at an angle of attack of 5?? was investigated. It was found that the majority of roll-up vortices proceed to merge with either one or two other vortices. Vortex merging between two and three vortices was found to occur periodically in a process similar to vortex merging in plane mixing layers undergoing subharmonic forcing of the most amplified disturbance. The flapping motion of the separated shear layer was investigated by performing a cross-correlation analysis on the high-speed flow visualization sequences to extract vertical displacement signals of the smoke within the shear layer. The frequency of flapping was found to correspond to the unstable disturbance band. At an angle of attack of 5??, it was found that the separated shear layer has a low-frequency component of flapping that matches a strong peak in velocity and surface pressure spectra that lies outside the unstable disturbance frequency band. The spanwise development of disturbances was assessed in the aft portion of the separation bubbles by performing a cross-correlation analysis on signals acquired simultaneously across the span with the rake of hot-wires. The spanwise correlations between signals was found to be well-correlated ahead of shear layer roll-up, after which disturbances became rapidly uncorrelated ahead of mean reattachment. These results were found to be linked to the coherent roll-up and subsequent breakdown of roll-up vortices.

This thesis examines the structure, stability and interaction of geophysical vortices. We do so by restricting our attention to relative vortex equilibria, or states which appear stationary in a co-rotating frame of reference. We approach the problem from three different perspectives, namely by first studying the single-vortex, quasi-geostrophic shallow-water problem, next by generalising it to an (asymmetric) two-vortex problem, and finally by re-visiting the single-vortex problem, making use of the more realistic, although more complicated, shallow-water model. We find that in all of the systems studied, small vortices (compared to the Rossby deformation length) are more likely to be unstable than large ones. For the single-vortex problem, this means that large vortices can sustain much greater deformations before destabilising than small vortices, and for the two-vortex problem this means that vortices are able to come closer together before destabilising. Additionally, we find that for large vortices, the degree of asymmetry of a vortex pair does not affect its stability, although it does affect the underlying steady state into which an unstable state transitions. Lastly, by carefully defining the "equivalence" between cyclones and anticyclones which appear in the shallow-water system, we find that cyclones are more stable than anticyclones. This is contrary to what is generally reported in the literature.

The increased fatigue loads and decreased power output of a wind turbine placed in the wake of another turbine is a well-known problem when building new wind power farms. In order to better estimate the total power output of a wind power farm, knowledge about the development and stability of wind turbine wakes is crucial. In the present thesis, the wake behind a small-scale model turbine was investigated experimentally in a wind tunnel. The velocity in the wake was measured with hot-wire anemometry, for different free stream velocities and tip speed ratios. To characterize the behaviour of the model turbine, the power output, thrust force and rotational frequency of the model were also measured. These results were then compared to calculations using the Blade Element Momentum (BEM) method. New turbine blades for the model was constructed using the same method, in order to get an estimate of the distribution of the lift and drag forces along the blades. This information is needed for comparisons with certain numerical simulations, which however remains to be performed.By placing the turbine at different heights in a turbulent boundary layer, the effects of forest turbulence on wind turbine outputs (power and thrust) could also be investigated.The evolution of the tip vortices shed from the turbine blades was studied by performing velocity measurements around the location of the tip vortex breakdown. The vortices' receptivity to disturbances was then studied by introducing a disturbance in the form of two pulsed jets, located in the rear part of the nacelle. In order to introduce a well-defined disturbance and perform phase-locked measurements, a new experimental setup was constructed and successfully tested for two different disturbance frequencies. The mean streamwise velocity and the streamwise turbulence intensity was found to scale well with the free stream velocity and the spreading of the wake was found to be proportional to the square root of the downstream distance.  The comparison for power and thrust between measurements and BEM calculations showed good agreement in some cases but worse agreement when the pitch angle of the blades was small.The velocity measurements showed that the tip vortices can be susceptible to disturbances and an earlier breakdown could be detected. However, more measurements need to be made to fully investigate the dependance on disturbance frequency and amplitude. / QC 20120504

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No description available.