Understanding the flow around wind turbines is a highly relevant research question due to the increased interest in harvesting energy from renewable sources. This thesis approaches the topic by means of numerical simulations using the actuator line method and the incompressible Navier–Stokes equations in the spectral element code Nek5000. The aim is to gain enhanced understanding of the wind turbine wake structure and wind turbine wake interaction. A verification study of the method and implementation is performed against the finite volume solver EllipSys3D using two types of turbines, an idealized constant circulation turbine and the Tjæreborg turbine. It is shown that Nek5000 requires significantly lower resolution to accurately compute the wake development, however, at the cost of a smaller time step.The constant circulation turbine is investigated further with the goal of establishing guidelines for the use of the actuator line method in spectral element codes, where the mesh is inherently non-equidistant and currently used guidelines of force distribution based on Gaussian kernels are difficult to apply. It is shown that Nek5000 requires a larger kernel width in the fixed frame of reference to remove numerical instabilities. Further, the impact of different Gaussian widths on the wake development is investigated in the rotating frame of reference, showing that the convection velocity and the breakdown of the spiral tip and root vortices are dependent on the Gaussian width. In the second part, the flow around single and multiple wind-turbine setups at different operating conditions is investigated and compared with experimental results. The focus is placed on comparing the power and thrust coefficients and the wake development based on the time-averaged streamwise velocity and turbulent stresses. Further the influence of the tower model is investigated both upstream and downstream of the turbine. The results show that the wake is captured accurately in most cases. The loading exhibits a significant dependence on the Reynolds number at which the airfoil data is extracted. When the helical tip vortices are stable the turbulent stresses at the tip vortices are underestimated in the numerical simulations. This is due to the finite resolution and the projection of the actuator line forces in the numerical domain using a prescribed Gaussian width, which leads to lower induced velocities in the helical vortices. / <p>QC 20170523</p>

In order to study three-dimensional unsteady turbulent flow fields such as the wakes of bluff bodies, a Digital Particle Image Velocimetry (DPIV) system was developed. This system allows non-intrusive two-dimensional and time varying velocity measurements. Software and hardware modifications necessary to enhance the capabilities of the system were preformed, resulting in increased frequency resolution. However, due to hardware limitations and limitations inherited from the implementation of the method, space resolution is reduced. Subsequently, digital image processing tools to improve the space resolutions were developed. The advantages and limitations of the method for the study of turbulent flows are presented in detail. The developed system is employed in the documentation of time-varying turbulent flow fields. Initially we study the spanwise variation of the near wake of a low-aspect ratio, surface-mounted, circular cylinder piercing a free surface. The asymmetry of the end conditions combined with the natural unsteadiness of the vortex shedding generates a very complex flow filed which is difficult to study with conventional methods. By employing the aforementioned system we are able to reveal a departure of the two-dimensional character of the flow in the form of oblique vortex shedding. The effect of free surface on the vortex formation length and on the vortex reconnection process is documented. Near the free surface the alternate mode of vortex shedding is suppressed, leading to simultaneous shedding of vortices in the wake. Indications of vortex dislocations and change of the vortex axis in order to reconnect to the free surface are observed. Finally, a novel approach of reconstructing the three-dimensional, time -varying volume of the flow field by obtaining simultaneous measurements of Laser Doppler Velocimetry and Particle Image Velocimetry planes is presented. The same field is investigated with focus on the streamwise structures. Three-dimensional streamwise vortical structures are known to exist due to instabilities of plane shear layers. Similar streamwise vortices, also known as braid vortices have been observed in the past in the wake of circular cylinders with symmetric boundary conditions. The present spatio-temporal analysis demonstrated coexistence of two types of streamwise vortices in the wake, bilge and braid type of vortices. These may be due to the three dimensionality introduced by the free surface. In addition, the sufficient time resolution allowed the detection of the primary Von-Karman vortex through a plane of interrogation normal to the free stream, thus revealing the spanwise variation of the vortex shedding and its evolution at different downstream stations. The combination of the effect of the asymmetric boundary conditions with a free surface is investigated by adding one more source of three-dimensionality in terms of inclination of the cylinder axis. Hydrogen-bubble and particle-flow visualizations are preformed in combination with Laser-Doppler Velocimetry measurements. From both qualitative and quantitative results the effects of inclination and Froude number are documented. It is proved that the vortex shedding is suppressed for high values of the Froude number, however the inclination counteracts the vortex suppression and favors the vortex shedding mechanism. In addition, in the region of the no-slip boundary condition the flow is dominated by the effect of the horseshoe vortex. The case of a three-dimensional separated flow over a surface-mounted prism is investigated using a modified version of the system. The character of the separated from the leading edge corner shear layer and the formed separation bubble are documented in space and time along the mid-plane of symmetry of the body. Three different flows corresponding to different Reynolds numbers are studied. The unsteadiness of the flow is presented indicating a pseudo-periodic character. Large-scale, low-frequency oscillations of the shear layer that have been observed in the past using point measurement methods are now confirmed by means of a whole field velocity measurement, technique allowing a holistic view of the flow. In addition, the unsteadiness of the point of reattachment is associated with the flapping of the shear layer and the shedding of vorticity in the wake. Finally, it is demonstrated that the apparent vortex shedding mechanism of such flows is dependent on the interaction of the primary vortex of the separation bubble with a secondary vortex formed by the separation of the reverse flow boundary layer. By performing measurements with such time and space resolution the inadequacy of time averaged or point measurement methods for the treatment of such complex and unsteady flow fields becomes evident. In final case we employ Particle-Image Velocimetry to show the effect of unsteady excitation on two-dimensional separated flow over a sharp edged airfoil. It is proved that such an approach can be used to effectively control and organize the character of the flow, potentially leading to lift increase and drug reduction of bluff bodies / Ph. D.

<p>This work is a five-article-based collection of published and to-be-published research articles that explore a novel combination of inlet conditions, wind turbine design, and non-flat topography by performing scaled-down experiments in a wind tunnel.</p>

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.

"Fluid-structure interaction arises in a wide array of technological applications including naval and marine hydrodynamics, civil and wind engineering and flight vehicle aerodynamics. When a fluid flows over a bluff body such as a circular cylinder, the periodic vortex shedding in the wake causes fluctuating lift and drag forces on the body. This phenomenon can lead to fatigue damage of the structure due to large amplitude vibration. It is widely believed that the wake structures behind the structure determine the hydrodynamic forces acting on the structure and control of wake structures can lead to vibration control of the structure. Modeling this complex non-linear interaction requires coupling of the dynamics of the fluid and the structure. In this thesis, however, the vibration of the flexible cylinder is prescribed, and the focus is on modeling the fluid dynamics in its wake. Low-dimensional iterative circle maps have been found to predict the universal dynamics of a two-oscillator system such as the rigid cylinder wake. Coupled map lattice (CML)models that combine a series of low-dimensional circle maps with a diffusion model have previously predicted qualitative features of wake patterns behind freely vibrating cables at low Reynolds number. However, the simple nature of the CML models implies that there will always be unmodelled wake dynamics if a detailed, quantitative comparison is made with laboratory or simulated wake flows. Motivated by a desire to develop an improved CML model, we incorporate self-learning features into a new CML that is trained to precisely estimate wake patterns from target numerical simulations and experimental wake flows. The eventual goal is to have the CML learn from a laboratory flow in real time. A real-time self-learning CML capable of estimating experimental wake patterns could serve as a wake model in a future anticipated feedback control system designed to produce desired wake patterns. A new convective-diffusive map that includes additional wake dynamics is developed. Two different self-learning CML models, each capable of precisely estimating complex wake patterns, have been developed by considering additional dynamics from the convective-diffusive map. The new self-learning CML models use adaptive estimation schemes which seek to precisely estimate target wake patterns from numerical simulations and experiments. In the first self-learning CML, the estimator scheme uses a multi-variable least-squares algorithm to adaptively vary the spanwise velocity distribution in order to minimize the state error (difference between modeled and target wake patterns). The second self-learning model uses radial basis function neural networks as online approximators of the unmodelled dynamics. Additional unmodelled dynamics not present in the first self-learning CML model are considered here. The estimator model uses a combination of a multi-variable normalized least squares scheme and a projection algorithm to adaptively vary the neural network weights. Studies of this approach are conducted using wake patterns from spectral element based NEKTAR simulations of freely vibrating cable wakes at low Reynolds numbers on the order of 100. It is shown that the self-learning models accurately and efficiently estimate the simulated wake patterns within several shedding cycles. Next, experimental wake patterns behind different configurations of rigid cylinders were obtained. The self-learning CML models were then used for off-line estimation of the stored wake patterns. With the eventual goal of incorporating low-order CML models into a wake pattern control system in mind, in a related study control terms were added to the simple CML model in order to drive the wake to the desired target pattern of shedding. Proportional, adaptive proportional and non-linear control techniques were developed and their control efficiencies compared."

Near wake is the region of wake flow just behind the trailing edge of the body where the flow is strongly influenced by the upstream flow conditions and also perhaps by the charac­teristics of the body. The present work is concerned with the study of the development of turbulent near wake behind an infinitely yawed flat plate. The turbulent near wake behind an infinitely yawed flat plate is the simplest of the three-dimensional turbulent near wake flows. The present study aims at providing a set of data on the turbulent near wake behind an infinitely yawed flat plate and also at understanding the development and structure of the near wake. Detailed measurements of mean and turbulent quantities have been made using 3-hole probe, X-wire and 3-wire hotwire probes. Further an asymptotic analysis of the two-dimensional turbulent near wake flow has been formulated for the near wake behind an infinitely yawed flat plate. The feature that the near wake which is dominated by mixing of the oncoming turbulent boundary layer retains, to a large extent, the memory of the turbulent structure of the boundary layer, has been exploited to develop this analysis. The analysis leads to three regions of the wake flow (the inner near wake, the outer near wake and the far wake) for which the governing equations are derived. The matching conditions among these regions lead to logarithmic variations in both normal and longitudinal directions in the overlapping regions surrounding the inner wake. These features are validated by the present results. A computational study involving seven well known turbulence models was also under­taken in order to assess the performance of the existing turbulence models in the prediction of the turbulent near wake behind an infinitely yawed flat plate. In this study all the seven models are implemented into a common flow solver code, thus eliminating the influence of grid size, initial conditions and different numerical schemes while making the comparison. This study shows that the K - e model performs better than other models in predicting the near wake behind an infinitely yawed flat plate.

The resolution of the complex physics of rotating configurations is critical for any engineering analysis that requires multiple frames of reference. Two well-known applications are in the rotorcraft and wind energy industries. Rotor wake impingement from rotor-fuselage and wind turbine-tower interactions impact structural and acoustic characteristics. Additionally, parasite drag resulting from rotorcraft hubs may result in severe limitations on forward flight vehicle performance. Complex turbulent wakes from rotors and hubs impinging on downstream empennage can create adverse aeroelastic behavior and can affect handling qualities. Numerical simulations of these flows require state-of-the-art Navier Stokes methods using dynamic overset grids. However, many current methods typically used in industry result in wakes that dissipate essential features. In order to address these concerns, two advancements are introduced in this thesis. Feature-based grid adaptation on dynamic overset grids has been developed and demonstrated with an unstructured Navier Stokes solver. The unique feature of the adaptation technique is that it is applied globally on the overset grid system except within the boundary layer. In concert with grid adaptation, an efficient parallelized search algorithm for solution interpolation over massively distributed systems has been created. This results in cost-effective interpolation that retains the numerical order of accuracy and has been verified in both space and time. The improvements have been demonstrated for rotor-fuselage interaction and a generic rotating hub. Detailed analysis of convergence of the methodology and sensitivity of the results to relevant parameters have also been included.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The present work is dedicated to perform the mathematical modeling and DNS and LES simulations of a three-dimensional, temporally evolving incompressible plane wake are performed, seeking to evidence differences in stability, transition and onset of both coherent and small scale structures, when the flow is subjected to random perturbations of different amplitudes. The perturbations are generated using the Random-Flow-Generator (RFG) technique, being imposed to the flow as initial conditions. The Navier-Stokes equations are solved in a prismatic domain, with periodic boundary conditions in all directions, using Fourier pseudospectral method. The invariants of the velocity gradient tensor, Q and R, are analyzed for random perturbations with magnitudes 10&#8722;3, 10&#8722;4 and 10&#8722;5, showing the onset of their characteristic teardrop correlation map. Moreover, maps of the second and third invariants of the rate-of-strain tensor, QS and RS, are shown, in order to evidence the differences in local flow strain and topological characteristics of the dissipation of kinetic energy. Isosurface plots of Q and QW, as well as vorticity contours are shown, allowing visual identification of the coherent structures and confirming patterns predicted by the invariant maps. / O presente trabalho se dedica a modelagem matemática e a simulações numéricas DNS e LES de uma esteira tridimensional, incompressível, em desenvolvimento temporal, buscando evidenciar diferenças na estabilidade, transição e no desenvolvimento de estruturas coerentes e de pequena escala, quando o escoamento é submetido a perturbações randômicas de diferentes amplitudes. As perturbações são geradas utilizando-se a técnica Random Flow Generator (RFG), sendo sobrepostas à condição inicial do escoamento. As equações de Navier-Stokes são resolvidas em um domínio prismático, com condições de contorno periódicas em todas as direções, utilizando-se o método pseudoespectral de Fourier. Os invariantes do tensor gradiente de velocidade, Q e R, são analisados para perturbações de magnitude 10&#8722;3, 10&#8722;4 and 10&#8722;5, mostrando a formação de uma correlação no formato de gota, característica da resolução das equações de Navier-Stokes. Além disso, são apresentados mapas do segundo e terceiro invariante do tensor taxa de deformação, QS e RS, a fim de evidenciar as diferenças locais no escoamento e as características topológicas na taxa de dissipação de energia cinética. Isosuperfícies de Q e QW, bem como contornos de vorticidade são apresentados, possibilitando a identificação visual das estruturas coerentes, e confirmando os padrões de estruturas previstos pelos mapas de invariância. / Mestre em Engenharia Mecânica

Two post processing methods for quantifying the shadow effect of the offshore wind farm Princes Amalia (PA) onto Egmond aan Zee (OWEZ) wind farm are analyzed and benchmarked. The first method is the author’s proposed shadow effect determination method (SEDM), which quantifies an offshore wind farm’s shadow effect based on mesoscale WRF (Weather Research Forecast) idealized modeling and the observed frequency of the analyzed site’s wind conditions. The Fitch turbine parametrization scheme and Mellor-Yamada-Nakanishi-Niino (MYNN) surface layer and planetary boundary layer (PBL) schemes were used to simulate the wind farm’s interactions, based on site conditions. The proposed physical downscaling method (SEDM) uses filtered simulated atmospheric stability and wind speed conditions, in order to calculate the percent wind speed deficit downstream of PA, with regard, first, to observed wind speed frequency and, secondly, to wind speed and corresponding atmospheric stability regimes. Then a statistical downscaling method, based on the established Analog Ensemble (AnEn) technique, developed by Luca Delle Monache et al. (2011) was employed to verify the results from the first method. This method runs a post processing algorithm using the weighted average of the observations that were verified when the 15 best analogs were valid. Observed wind speed data at 10 m and 50 m height was used as Numerical Weather Prediction (NWP) input data and fit to observed time series data. From this, wind speeds at 116 m were extrapolated, in order to estimate the reconstructed atmospheric stability. The two methods were benchmarked and shadow effects were quantified in the range of 7.53% - 22.92% for the SEDM and within an 80% confidence interval of 0.23% -1.83% for the statistical downscaling method. Given the physical method’s exceedance of this confidence interval, WRF idealized modeling proves itself as a consistent means of quantifying an offshore wind farm’s wake, as demonstrated by comparable studies, however inaccurate when benchmarked to statistical modelling methods that use observed wind speed data to recreate atmospheric conditions. / Wake Research Group

Tato numerická studie je zaměřená na axisymetrickou pulzní trysku při zachování relativně nízkých Reynoldsových čísel a její fyzikální podstatu, která dosud nebyla zcela vysvětlena. Hlavním cílem práce bylo prozkoumat a zhodnotit vliv přidání periodického komponentu rychlosti ke stacionární složce rychlosti. Nejdříve byl řešen stacionární případ, poté byla do simulace přidána pulzace a byla vytvořena nestacionární simulace. Numerické řešení stacionárního případu bylo ověřeno pomocí asymptotického řešení, které předložil Hermann Schlichting [44]. Přesnost tohoto analytické řešení byla opravena na základě experimentálních poznatků Andradeho a Tsiena [1]. Pomocí této korekce je zmenšena oblast singularity řešení v blízkosti počátku proudění. Z matematického pohledu se v podstatě jedná korekcí prvního řádu, což bylo dokázáno Revueltou a spol [36]. Samotné analytické řešení bylo vytvořeno v MATLABu zatímco pro numerické řešení byl použit software Ansys Fluent. Při numerické simulaci byly Navier-Stokesovi rovnice integrovány ve své plné formě za pomoci algoritmu založeném na tzv. rovnici korekce tlaku. Pulzační tryska byla poté řešena pro různé parametry tak, aby bylo možné zhodnotit vliv jednotlivých parametrů na evoluci takto modulovaného proudu. Nakonec byla posouzena možná aplikace pulzních trysek v průmyslu s ohledem na možnost snížení emisí v průběhu spalovacího procesu.