A new rotor dynamic wake distortion model, which can be used to account for the rotor transient wake distortion effect on inflow across the rotor disk during helicopter maneuvering and transitional flight in both hover and forward flight conditions, is developed. The dynamic growths of the induced inflow perturbation across the rotor disk during different transient maneuvers, such as a step pitch or roll rate, a step climb rate and a step change of advance ratio are investigated by using a dynamic vortex tube analysis. Based on the vortex tube results, a rotor dynamic wake distortion model, which is expressed in terms of a set of ordinary differential equations, with rotor longitudinal and lateral wake curvatures, wake skew and wake spacing as states, is developed. Also, both the Pitt-Peters dynamic inflow model and the Peters-He finite state inflow model for axial or forward flight are augmented to account for rotor dynamic wake distortion effect during helicopter maneuvering flight. To model the aerodynamic interaction among main rotor, tail rotor and empennage caused by rotor wake curvature effect during helicopter maneuvering flight, a reduced order model based on a vortex tube analysis is developed. Both the augmented Pitt-Peters dynamic inflow model and the augmented Peters-He finite state inflow model, combined with the developed dynamic wake distortion model, together with the interaction model are implemented in a generic helicopter simulation program of UH-60 Black Hawk helicopter and the simulated vehicle control responses in both time domain and frequency domain are compared with flight test data of a UH-60 Black Hawk helicopter in both hover and low speed forward flight conditions.

Findings from a project involving rotating equipment defect detection using the Algorithm of Mode Isolation (AMI) are presented. The prototypical system evaluated is a rotating shaft, supported by hydrodynamic bearings at both ends, with one disk mounted to the shaft. Shaft cracks and bearing wear are the two equipment defects considered. An existing model of the prototypical system from the literature, termed the simplified model. is modified to simulate the presence of a transverse shaft crack at mid-span. This modified model is termed the standard model. Ritz series analysis, in conjunction with a previously published description of the compliance related to the presence of a transverse shaft crack, is used to describe the decrease in shaft stiffness associated with the crack. The directional frequency response function (dFRF) is shown in the literature to provide benefits over the standard frequency response function (FRF) in both system identification and shaft crack detection for rotating equipment. The existing version of AMI is modified to process dFRFs and termed Two-Sided AMI. The performance of Two-Sided AMI is verified through system identification work using both the simplified model and a rigid rotor model from the literature. The results confirm the benefits of using the dFRF for system identification of isotropic systems. AMI and Two-Sided AMI are experimental modal analysis (EMA) routines, which estimate modal properties based on a frequency domain expression of system response. Eigenvalues and associated modal residues are the modal properties considered in the present work. Three defect detection studies are fully described. In the first, the simplified model is used to investigate bearing wear detection. Various damage metrics related to the eigenvalue and the residue are evaluated. The results show that residue-based metrics are sensitive to bearing wear. Next, the standard model is used in an in-depth investigation of shaft crack detection. When a shaft crack is present, the standard model is time-varying in both the fixed and moving coordinate systems. Therefore, this analysis is also used to evaluate performing EMA on non-modal data. In addition to continuing the evaluation of various xiv damage metrics, the shaft crack study also investigates the effects of noise and coordinate system choice (fixed or moving) on shaft crack detection. Crack detection through EMA processing of noisy, non-modal data is found to be feasible. The eigenvalue-based damage metrics show promise. Finally, the standard model is used in a dual-defect study. The system is configured with both a shaft crack and a worn bearing. One defect is held constant while the magnitude of the other is increased. The results suggest that AMI is usable for defect detection of rotating machinery in the presence of multiple system defects, even though the response data is not that of a time-invariant system. The relative merits of both input data types, the FRF and the dFRF, are evaluated in each study.

Rotordynamics is an important area in mechanical engineering. Many machines contain rotating parts. It is well known that rotating components can develop large amplitude lateral vibrations near certain speeds called critical speeds. This large amplitude vibration is called rotor whirl. This thesis is about rotor whirl. Conventional treatments in rotordynamics use what are called gyroscopic terms and treat the rotor as a one-dimensional structure (Euler-Bernoulli or Timoshenko) with or without rigid masses added to them. Gyroscopic terms are macroscopic inertial terms that arise due to tilting of spinning cross-sections. This approach, while applicable to a large class of industrially important rotors, is not applicable to a general rotor geometry. In this thesis we develop a genuine continuum level three dimensional formulation for rotordynamics that can be used for many arbitrarily shaped rotors. The key insight that guides our formulation is that gyroscopic terms are macroscopic manifestations of the prestress induced due to spin of the rotor. Using this insight, we develop two modal projection techniques for calculating the critical speed of arbitrarily shaped rotors. These techniques along with our prestress based formulation are the primary contributions of the thesis. In addition, we also present two different nonlinear finite element based implementations of our formulation. One is a laborious load-stepping based calculation performed using ANSYS (a commercially available finite element package). The other uses our nonlinear finite element code. The latter two techniques are primarily developed to provide us with an accurate answer for comparison with the results obtained using the modal projection methods. Having developed our formulation and the subsequent modal projection approximations, we proceed to validation. First, we analytically study several examples whose solutions can be easily obtained using routine methods. Second, we consider the problem of a rotating cylinder under axial loads. We use a semi-analytical approach for this problem and offer some insights into the role played by the chosen kinematics for our virtual work calculations. The excellent match with known results obtained using Timoshenko theory validates the accuracy of our formulation. Third, we consider several rotors of arbitrary shape in numerical examples and show that our modal projection methods accurately estimate the critical speeds of these rotors. After validation, we consider efficiency. For axisymmetric rotor geometries, we implement our formulation using harmonic elements. This reduces the dimension of our problem from three to two and considerable savings in time are obtained. Finally, we apply our formulation to describe asynchronous whirl and internal viscous damping phenomena in rotors.

Die heutige und zukünftige Entwicklung beim Entwurf von Axialverdichtern für die Anwendung in Flugzeugtriebwerken ist immer stärker davon geprägt, ein möglichst großes Druckverhältnis mit möglichst wenigen Stufen zu erzeugen. Ziel ist es, möglichst viel Leistung mit möglichst geringem Gewicht umzusetzen, um die Effizienz der Maschine weiter zu verbessern. Um dies zu erreichen, muss eine Erhöhung der Stufendruckverhältnisse und damit eine Erhöhung der Stufenbelastung in Kauf genommen werden. Die höhere Belastung hat jedoch einen Anstieg der Verluste aufgrund der stärker werdenden Sekundärströmungen zur Folge, und wirkt sich zunächst negativ auf die Stabilität und den Wirkungsgrad der Maschine aus. Diese negativen Effekte können nur durch eine Weiterentwicklung der Schaufelgeometrie kompensiert werden. Hierbei stoßen die derzeit benutzten Entwurfsmethoden jedoch an ihre Grenzen. Aus diesem Grund wurde ein neues Verfahren für den dreidimensionalen Entwurf von Rotoren in Axialverdichtern entwickelt. In dieser Arbeit wird dessen Entwicklung präsentiert. Das Verfahren umfasst die systematische Anwendung von Pfeilung und V-Stellung, sowie die dreidimensionale inverse Berechnung der radialen Skelettlinienverteilung. Um damit eine Verbesserung des Rotorwirkungsgrades zu erreichen, müssen vor allem die kritischen wand- bzw. spaltnahen Bereiche optimal an die Strömungsumgebung angepasst werden. Die vorliegende Arbeit beschreibt ausführlich die theoretischen Grundlagen der Rotorströmung und des Rotorentwurfs. Basierend darauf werden für die Umsetzung eines vollständigen dreidimensionalen Schaufelentwurfs zwei Panelverfahren zur Berechnung der dreidimensionalen jedoch reibungslosen Strömung, zur Lösung der Nachrechen- bzw. der Entwurfsaufgabe, entwickelt. Die Panelverfahren werden angewandt, um eine Methodik für den effektiven Einsatz von Pfeilung, V-Stellung und inverser Skelettlinienberechnung für den dreidimensionalen Rotorentwurf festzulegen. Die gewonnenen Erkenntnisse werden anschließend für den Entwurf eines hochbelasteten Rotors in einem einstufigen Niedergeschwindigkeitsverdichter nach dieser neuen Entwurfsmethodik genutzt. Anhand von Ergebnissen aus Rechnungen und Messungen für diesen Rotor wird die Wirksamkeit des Verfahrens demonstriert. / The recent and future design of axial compressors for aero engines is strongly affected by the aim to generate a high pressure ratio with less stages to increase power and reduce weight to achieve an improved efficiency. This can only be achieved when the stage pressure ratio is raised which leads to increased stage loading. But the higher stage loading results in higher losses caused by stronger secondary flows. This has a negative effect on compressor stability and efficiency. To counteract the negative effects enhanced blade geometries are necessary. With the recently used design methods this is hardly to achieve. For that reason a new method for the three-dimensional design of rotors and stators in axial compressors has been developed. This report summarizes that work. The method accounts for the systematic application of sweep and dihedral as well as the three-dimensional inverse calculation of the camber-line distributions along blade height. To achieve improved efficiency the regions close to the end-walls and the tip and hub gap have to be adapted to the flow environment. The recent report described in detail the theoretical background of the compressor blade flow and compressor blade design. Based on that, two inviscid panel methods for the fully three-dimensional design of compressor blades are described. The panel methods are applied to define a methodology for the effective application of sweep, dihedral and inverse camber-line calculation in a three-dimensional blade design process. Afterwards the findings are used to design a highly-loaded single-stage low-speed research compressor rotor. The validity of the presented design method is proven with CFD and test results.

This thesis combines measurements with the development of simulation tools for vertical axis wind turbines (VAWT). Numerical models of aerodynamic blade forces are developed and validated against experiments. The studies were made on VAWTs which were operated at open sites. Significant progress within the modeling of aerodynamics of VAWTs has been achieved by the development of new simulation tools and by conducting experimental studies.         An existing dynamic stall model was investigated and further modified for the conditions of the VAWT operation. This model was coupled with a streamtube model and assessed against blade force measurements from a VAWT with curved blades, operated by Sandia National Laboratories. The comparison has shown that the accuracy of the streamtube model has been improved compared to its previous versions. The dynamic stall model was further modified by coupling it with a free vortex model. The new model has become less dependent on empirical constants and has shown an improved accuracy.     Unique blade force measurements on a 12 kW VAWT were conducted. The turbine was operated north of Uppsala. Load cells were used to measure the forces on the turbine. A comprehensive analysis of the measurement accuracy has been performed and the major error sources have been identified. The measured aerodynamic normal force has been presented and analyzed for a wide range of operational conditions including dynamic stall, nominal operation and the region of high flow expansion. The improved vortex model has been validated against the data from the new measurements. The model agrees quite well with the experiments for the regions of nominal operation and high flow expansion. Although it does not reproduce all measurements in great detail, it is suggested that the presented vortex model can be used for preliminary estimations of blade forces due to its high computational speed and reasonable accuracy.

In this thesis we employ various mean-field approaches to study the shortrange interaction effects in topological insulators. We start with the Kane-Mele model on the decorated honeycomb lattice and study the stability of topological insulator phase against different perturbations. We establish an adiabatic connection between a noninteracting topological insulator and a strongly interacting spin liquid in its Majorana fermion representation. We use the Hartree-Fock mean-field approach, slave-rotor approach and slave-boson approach to study correlation effects related to topological insulators. With the spontaneous symmetry breaking mechanism, we can have an interaction driven topological insulator with extended Hubbard models on the kagome lattice and decorated honeycomb lattice. For the interplay among spin-orbit coupling, distortion and correlation effect in transition metal oxides, we use the slave-rotor mean-field approach to study its phase transition. We identify regimes where a strong topological Mott insulator and a weak topological insulator reside due to the strong Coulomb interaction and distortion. This is relevant to experiments with the transition metal oxides as they hold promise to realize topological insulators. To study the doping effects and a possible spin liquid in Kane-Mele-Hubbard model on the honeycomb lattice, we employ the slave-boson mean-field approach which is appropriate for the intermediate interaction strength. We compare our results with those obtained from other methods. / text

This thesis describes the analysis, fabrication and testing of a rotor with extremely flexible blades, focusing on application to a micro-helicopter. The flexibility of the rotor blades is such that they can be rolled into a compact volume and stowed inside the rotor hub. Stiffening and stabilization of the rotor is enabled by centrifugal forces acting on a tip mass. Centrifugal effects such as bifilar and propeller moments are investigated and the torsional equation of motion for a blade with low torsional stiffness is derived. Criteria for the design of the tip mass are also derived and it is chosen that the center of gravity of each blade section must be located ahead of the aerodynamic center. This thesis presents the design of 18-inch diameter two-bladed rotors having untwisted circular arc airfoil profile with constant chord. A systematic experimental investigation of the effect of various blade parameters on the stability of the rotor is conducted in hover and forward flight. These parameters include blade flexibility in bending and torsion, blade planform and mass distribution. Accordingly, several sets of blades varying these parameters are constructed and tested. It is observed that rotational speed and collective pitch angles have a significant effect on rotor stability. In addition, forward flight velocity is found to increase the blade stability. Next, the performance of flexible rotors is measured. In particular, they are compared to the performance of a rotor with rigid blades having an identical planform and airfoil section. It is found that the flexible blades are highly twisted during operation, resulting in a decreased efficiency compared to the rigid rotor blades. This induced twist is attributed to an unfavorable combination of tip body design and the propeller moment acting on it. Consequently, the blade design is modified and three different approaches to passively tailor the spanwise twist distribution for improved efficiency are investigated. In a first approach, extension-torsion composite material coupling is analyzed and it is shown that the centrifugal force acting on the tip mass is not large enough to balance the nose-down twist due to the propeller moment. The second concept makes use of the propeller moment acting on the tip mass located at an index angle to produce an untwisted blade in hover. It is constructed and tested. The result is an untwisted 18-inch diameter rotor whose maximum Figure of Merit is equal to 0.51 at a blade loading of 0.14. Moreover, this rotor is found to be stable for any collective pitch angle greater than 11 degrees. Finally, in a third approach, addition of a trailing-edge flap at the tip of the flexible rotor blade is investigated. This design is found to have a lower maximum Figure of Merit than that of an identical flexible rotor without a flap. However, addition of this control surface resulted in a stable rotor for any value of collective pitch angle. Future plans for increasing the efficiency of the flexible rotor blades and for developing an analytical model are described. / text

An experimental study on the application of Digital Image Correlation (DIC) to measure the deformation and strain of rotating blades is described. Commercial DIC software was used to obtain measurements on three different types of rotors with diameter ranging from 18 to 39 and with varying flexibility to explore applicability of the technique over a breadth of scales. The image acquisition was synchronized with the frequency of rotation such that images could be obtained at the same phase and the consistency of measurements was observed. Bending and twist distributions were extracted from the data with deformation as high as 0.4 measured with a theoretical accuracy of 0.0038 and span-wise resolution of 0.066. The technique was demonstrated to have many advantages including full-field high resolution results, non-intrusive measurement, and good accuracy over a range of scales. The span-wise deformation profiles from the DIC technique are used in conjunction with Blade Element Momentum Theory to calculate the thrust and power consumed by the rotor with rigid vi blades; results are comparable to load cell measurements albeit thrust is somewhat under-predicted and power is over-predicted. Overall, the correlation between DIC calculated thrust and BEMT approximations for comparable blades with constant pitch were within 12% through the onset of stall. Measurement of flexible blade deformation that would not have been possible with other techniques demonstrated the utility of the DIC method and helped to confirm predictions of flexible blade behavior. / text

Ces dernières décennies de nombreux modèles de paliers à feuilles ont été développés. Aujourd'hui, la limite de ces modèles est apparente notamment au niveau de la compréhension des comportements non linéaire du système rotor palier et de la quantification de sa dissipation énergétique. Il est essentiel pour les développements futurs de maîtriser les instabilités liées au fonctionnement de ces paliers. Grâce à une approche variationnelle et la MEF, la structure flexible a été modélisée comme une structure mince soumise à la pression d'un fluide compressible, isotherme, laminaire puis turbulent. Nous tenons compte dans cette étude, des frottements secs internes en utilisant la loi de Coulomb et la méthode du Lagrangien augmenté. Le modèle de structure est couplé avec équations de Reynolds des films minces afin de déterminer le comportement du rotor à l'aide du principe fondamental de la dynamique. Nous avons montré la pertinence de l'approche choisie, notamment l'utilisation du modèle de structure mince sur le comportement dynamique du rotor et sur le champ de pression hénéré dans le palier. On démontre aussi l'intéraction entre les déflections des bumps et le frottement sec. L'action du flambage est doublement accentué par le phénomène de frottement présent entre les feuilles, modifiant ainsi la dissipation d'énergie dans le palier. Le second objectif a été d'identifier l'origine des phénomènes subsynchrones afin de développer des nouveaux paliers en se dédouanant des instabilités qu'elles engendrent.

Cette thèse propose différentes méthodologies de calcul du bruit à large bande générée par l'interaction rotor-stator d'une soufflante de turboréacteur et ce de la génération des sources acoustiques jusqu'au rayonnement en champ lointain. En premier lieu, le mécanisme d'interaction rotor-stator est étudié à travers une turbulence de grille homogène et isotrope (THI) impactant un profil isolé. Le cas de l'interaction rotor-stator en milieu guidé est ensuite traité et appliqué à une maquette de compresseur axial. Enfin, la dernière partie traite de la simulation du rayonnement aval en sortie de conduit. Dans chacune de ces parties, des approches analytiques et numériques sont proposées. Les méthodes analytiques permettentune prévision rapide du problème simplifié, et les méthodes numériques permettent de leverles hypothèses au prix d'un temps de calcul plus long.Le modèle d'Amiet est mis en œuvre pour simuler le bruit d'interaction THI-profil àtravers une expérience en soufflerie anéchoïque. Ce modèle simplifiant le profil en une plaque plane non portante, une approche numérique est également mise en place. La convection de perturbations de vitesse incidentes synthétisant une THI et impactant un profil isolé est simulée à l'aide d'un code CAA (Computational AeroAcoustics) résolvant les équations d'Euler en deux dimensions. Les différences de rayonnement entre une plaque plane et un profil cambré épais observées expérimentalement sont en partie retrouvées. Une simulation plus avancée d'un calcul LES (Large Eddy Simulation) 3D est également abordée.Dans la deuxième partie du mémoire, le modèle d'Amiet est étendu au problème de l'interaction rotor-stator en conduit. Différentes formulations sont proposées et discutées. Elles sont appliquées au cas d'un banc d'essai du DLR (centre de recherche aérospatiale allemand) avec des données d'entrée provenant d'un calcul RANS (Reynolds Averaged Navier-Stockes) ou bien directement de mesures. Les prévisions acoustiques ainsi obtenues sont satisfaisantes (+/-2 dB avec des données d'entrée expérimentales) compte tenu de la relative simplicité des modèles. Un calcul LES est exploité pour fournir directement les sources de bruit (fluctuations de pression pariétale). Les spectres obtenus montrent des tendances similaires à ceux issus du modèle d'Amiet malgré certains phénomènes non-physiques encore présents au niveau du calcul LES.Pour terminer, le rayonnement en champ libre est traité. Une manière simple et rapidede résoudre ce problème consiste à utiliser une intégrale de Kirchhoff, en supposant unécoulement moyen uniforme. Une comparaison avec une solution analytique (technique deWiener-Hopf) exacte pour les mêmes conditions montre que le rayonnement du bruit largebande est bien prévu par la méthode de Kirchhoff pour des angles de rayonnement inférieursà 90°. Cependant, pour prendre en compte la géométrie d'éjection de la nacelle et l'effet d'un écoulement hétérogène (cisaillement) sur le rayonnement en champ libre, une approche numérique est mise en place. Une technique permettant de simuler le caractère aléatoire des sources turbulentes ainsi que de satisfaire l'hypothèse de modes acoustiques incohérents est développée. Cette méthodologie est appliquée au cas simple du conduit semi-infini, puis à une tuyère réaliste. Les calculs sont validés à l'aide de solutions analytiques sur les configurations simplifiées. Une analyse critique des instabilités créées dans la couche de cisaillement et de leur influence sur les formulations intégrales couplées au calcul Euler pour obtenir le bruit en champ lointain complète ce dernier chapitre.