This work studies the effects of radial flow on the aerodynamic phenomena occurring on a retreating blade with a focus on dynamic stall and reverse flow as applied to both a helicopter rotor in forward flight and a wind turbine operating at a yaw angle. While great progress has been made in understanding the phenomenon of two-dimensional dynamic stall, the effect of rotation on the dynamic stall event is not well understood. Experiments were conducted on a rigid two bladed teetering rotor at high advance ratios in a low speed wind tunnel. Particle image velocimetry (PIV) measurements were used to quantify the flow field at several azimuthal angles on the rotating blade during the dynamic stall event. The effect of centrifugal forces induced ``pure'' radial velocity on the dynamic stall event at 270 degrees azimuth was studied in detail. Further investigation of the radial flow field suggested that the mean radial velocity attenuated on moving outboard due to an apparent shear layer instability and it was demonstrated to be of first order importance in the flow field. These radial flow results prompted an exploration of the flow over a rotating disk to establish similarities of the radial flow over rotating blade in separated flow to that over a rotating disk in separated flow. While a greater part of this work focused on aspects of dynamic stall on the retreating blade, the final parts focus on the exotic flow regime of reverse flow (characterized by flow from the trailing edge to the leading edge of the blade). Aerodynamic loads measurement and surface flow visualization via tufts are used to first quantify the behavior of a static yawed blade in reverse flow. PIV measurements are then used on a static yawed blade and a rotating blade in reverse flow conditions to ascertain the effects of rotation on reverse flow.

Dynamic behavior of flexural-torsional coupled vibration of rotating beams using the Rayleigh-Ritz method with orthogonal polynomials as basis functions is studied. The present work starts from a review of the development and analysis of four basic types of beam theories: the Euler-Bernoulli, Rayleigh, Shear and Timoshenko and goes over to a study of flexural-torsional coupled vibration analysis using basic beam theories. In obtaining natural frequencies, orthogonal polynomials used in the Rayleigh-Ritz method are studied as an efficient way of getting results. The study is also performed for both non-rotating and rotating beams. Orthogonal polynomials and functions studied in the present work are : Legendre, Chebyshev, integrated Legendre, modified Duncan polynomials, the eigenfunctions of a pinned-free uniform beam, and the special trigonometric functions used in conjunction with Hermite cubics. Studied cases are non-rotating and rotating Timoshenko beams, bending-torsion coupled beam with free-free boundary conditions, a cantilever beam, and a rotating cantilever beam. The obtained natural frequencies and mode shapes are compared to those available in various references and results for coupled flexural-torsional vibrations are compared to both previously available references and with those obtained using NASTRAN finite element package. / Master of Science

Rotating blades, which are the most critical components of any turbo-machinery, need to be designed to withstand forced vibrations due to accidental tip rub impact against inner surface of casing. These vibrations are typically dependent on operating conditions and geometric parameters. In the current study, a rotor test rig with a maximum tip speed capability of 144 km/hr has been developed for studying the dynamic behavior of representative jet engine compressor blades actuated by the closure of clearance between the tip of a given rotating blade and a sector of the inner lining of the casing. Ten different blade profiles are chosen in the present research. The blades are obtained by lofting NACA GOE123 airfoil cross-section along different stacking axes. Rotor test rigs which simulate transient dynamic events require high frequency data acquisition systems like slip ring arrangement or telemetric transmission. While slip rings introduce noise into the signal, the telemetric transmission works out to be rather expensive. To circumvent the stated shortcomings of data acquisition systems, a novel rotor-mounted data acquisition system has been implemented here which captures dynamic strains in vibrating blades during operation. The current data acquisition system can store data for duration of five seconds with a sampling rate of 35 kHz. It has been calibrated with four standard tests, and provides a simple and efficient mode of data capturing. Three blades with airfoil sections (a flat beam-type blade of uniform rectangular cross-section, a blade with twisted cross-sections stacked along a straight line, and a blade similar to the latter but with a curved stacking axis) are tested under controlled rub conditions at four different speeds. The maximum test speed is restricted to 800 rpm for reasons of safety although the set-up is designed to operate up to a maximum speed of 2000 rpm. For each of the rotor speeds, a blade is tested for three to four different stagger angles in the range of 0o-30o. By plotting the RMS values of measured dynamic responses with respect to stagger angle for a given rotor speed, it has been observed, perhaps for the first time in published literature, that a stagger angle of around 20o yields the maximum RMS value of strain response. A major objective of the current study has been to utilize the data generated in the tip rub impact tests for validating a predictive numerical model of the test set-up using explicit finite element analysis. To this end, a finite element model of the rotor rig inclusive of a rotor with two blades and the static frame structure is developed and analyzed using an explicit LS-DYNA solver. This model is calibrated with the test results of the three blade designs described above. In particular, it has been shown that the frequency contents of the measured dynamic strain responses agree quite well with frequencies obtained from the numerically computed responses. It has been found in the experimental responses that a given blade vibrates with two main frequencies: one corresponding to the first natural frequency of the rotor-blade system during the tip-rubbing phase (which lasts until the blade tip is in contact with the rub element which is a sector of the circular casing), and another corresponding to the first natural frequency of the blade when it vibrates freely without its tip being in contact with the rub-liner of the casing. A shortcoming of the current modeling approach is its inability to realistically represent the damping behaviors observed in the tests. For reasons of computational efficiency and consistent with the fact that there was no perceptible damage in the tested blades, an elastic constitutive behavior is specified for the blades, while the sacrificial PVC rub-liner is assumed to behave elasto-plastically. A limited study has also been carried out by assigning an elasto-plastic constitutive model to one of the blades previously represented with elastic properties only, and although incipient yielding is observed in a highly localized region at the tip of a blade (which can also be a numerical artifact), the responses under the two material behavior considerations (i.e. elastic and elasto-plastic) are found to be nearly same. Finally, this validated modeling approach is applied to the study of blades of ten distinct geometric profiles (including the three configurations already considered) at a speed of 800 rpm and the resonant speed of a given blade. Comparisons are made between the relevant responses (such as time-histories of root strain, shaft torque, blade axial displacement, bearing load and rub force) of nine blades with airfoil cross-sections (leaving aside the results for the first blade of rectangular cross-section which is only of academic interest). Based on this study, of all the blade designs, it has been found that the curve-stacked airfoils exhibit better ‘Rub-tolerant’ behavior. Both experimental and simulation results have predominantly proven the fact that adding curvature to a straight stacked blade through curve-stacked or bow result in reducing the rub induced vibration. While sweep and bow provide some aerodynamic advantages, they are not much helpful in containing the vibrations to a sustainable extent.

L’aérodynamique de l’hélicoptère est fortement impactée par les tourbillons générés aux extrémités de pales. La complexité des phénomènes en jeux et l’insuffisance de données expérimentales locales font du design d’extrémité un véritable défi. Cette étude propose une nouvelle approche dédiée à l’étude des extrémités en vol stationnaire. Une méthode numérique rapide et précise est mise au point afin d’étudier une extrémité de pale en rotation comme une extrémité d’aile fixe. Chaque étape de la construction de la méthode est validée par des comparaisons détaillées avec des données expérimentales publiées. Le code CFD elsA est dans un premier temps utilisé pour mettre en place une méthode de calcul basée sur la résolution des équations Reynolds-Averaged Navier-Stokes en stationnaire. La convergence de la solution et l’indépendance au maillage et aux paramètres numériques sont étudiées en détail en deux, puis en trois dimensions. La précision importante de la solution numérique permet d’analyser finement la physique de l’enroulement tourbillonnaire en extrémité. Des géométries tronquée et arrondie sont étudiées en détail, et révèlent la présence de systèmes tourbillonnaires complexes. Puis la nouvelle méthode d’adaptation pale en rotation / aile fixe est présentée. Une méthode de calcul hybride est mise au point entre le code de mécanique du vol HOST et le code elsA. En repère fixe, l’aérodynamique globale sur la pale et locale en extrémité est calculée fidèlement pour toutes les configurations étudiées. Comparée aux méthodes d’adaptation précédemment publiées, cette nouvelle stratégie offre une amélioration considérable concernant la simulation de l’aérodynamique de pale. / Helicopter aerodynamics is strongly influenced by the vortices generated from the rotor-blade tips. The design of efficient tip shapes is a challenging task because of the complexity of the aerodynamic phenomena involved and the lack of local blade-tip flow measurements. This work provides a contribution to the design of helicopter tips in hover. An efficient, relatively simple and quick numerical method is set up to study rotating blade tips in fixed-wing configurations. The accuracy of the method is shown at each step of the construction by comprehensive comparisons with reliable experimental data from the literature. First, an efficient steady Reynolds-Averaged Navier-Stokes method is constructed using ONERA's elsA code. Comprehensive studies of convergence, grid dependence and sensitivity to the numerical method are performed in two and three dimensions. The very good agreement of the solution with measurements and the accuracy of the numerical method allow a physical analysis with unprecedented detail of the vortex generation and roll-up near square and rounded wing tips. The new methodology of framework adaptation is then presented. An uncoupled hybrid strategy is set up using AIRBUS HELICOPTERS' Comprehensive Analysis code HOST and the Computational Fluid Dynamics solver elsA. Global and local performance calculations are validated for all investigated test cases. Comparison with previously published adaptation methods indicates considerable improvement in the prediction of the blade aerodynamics.