Experiments have been performed in the spiral wake that surrounds the vortex shed from the tip of a rectangular NACA 0012 half wing. Both single-point and simultaneous two-point hot-wire measurements were made ten chord lengths downstream of the wing at a Reynolds number of 320,000. The structure of this flow consists of a small concentrated vortex core, surrounded by a circulating velocity field that winds the wake into a spiral about the core. Small amplitude wandering motions of the core were detected and quantitative estimates of the wandering amplitude and its contributions to the Reynolds stress fields were found. Outside of the core region the turbulence structure is dominated by this spiral wake. The maximum turbulence levels exist in the part of of the wake that begins to spiral about the core. The 3-D region is the region where the wake is wound about the vortex and the 2-D region is the nearly two-dimensional portion of the wake inboard of the wing-tip. The stresses in the 3-D region, when scaled on local length and velocity scales, increase significantly over those in the 2-D region. This increase is presumably a consequence of the additional rates of strain imposed on the wake by the vortex. Stretching intensifies turbulent structures aligned with the stretching direction. Two-point measurements were made in the 2-D and 3-D regions of the wake to reveal the spanwise extent of the instantaneous turbulent structures in the wake. A high correlation was found at the smallest probe separations. There are stronger correlations and coherence in the 3-D region than in the 2-D region. Correlation length scales and coherence were found to increase significantly from the 2-D region to the peak turbulence region. This reveals that the stretching and additional rates of strain imposed on the wake by the vortex are organizing the spanwise turbulent structures. / Master of Science

Rotary wing aircrafts in any flight conditions suffer from excessive vibration which makes the passengers feel uncomfortable and causes fatigue failure in the structure. The main sources of vibration are the rotor harmonic airloads which originate primarily from the rapid variation of flow around the blade due to the vortex wake. In this thesis, a mathematical model is developed for rotor blades to compute the harmonic airloads at rotor blades for two flight conditions vertical takeoff and landing, and forward flight. The sectional lift, drag, and pitching moment are computed at a radial blade station for both flight conditions. The lift at a particular radial station is computed considering trailing and shed vortices and summing over each blade. The results for airloads are obtained after considering zeroth, first, and second harmonics. The calculated results for airloads are compared to the experimental flight-test data.

Wakes of lifting bodies contain vortex sheets that roll up into strong streamwise vortices. The long time behavior of such vortices depends on the turbulence in the wake and the stability characteristics of the vortices themselves. In the near wake of a rectangular wing the flow field consists of a spiraling wake that winds around a pair of vortex cores. The study of the turbulence structure and life of wing tip vortices is of great importance to air traffic control in congested airports. In this dissertation a computer code is developed for the temporal as well as spatial simulations of trailing vortices. A sixth-order compact finite-difference method is used in the cross plane. The streamwise derivatives are represented either by a Fourier series for temporal simulations (periodic flow) or by a sixth-order compact scheme for spatial simulations. The time marching scheme is a third-order Runge-Kutta method. The code is used to study the nonlinear development of temporal helical instability waves in a trailing vortex. Contours of a passive scalar are used to study the entrainment process that redistributes angular and axial momenta between the core and its surroundings. Such a process leads to quenching of the instability waves in the vortex core. The code is also used to predict the spatial development of mean flow in the wake of a rectangular wing. New treatment of the outflow boundary condition on the pressure is formulated so that a strong streamwise vortex can exit the computational domain without distortion. Temporal large-eddy simulation (LES) is performed to study the development of large scale structures in the wake and their interaction with the tip vortex. A modified MacCormack scheme developed by Gottlieb and Turkel(1976) has been used to solve the LES equations. A model of the initial conditions in the near wake of a rectangular wing is devised to investigate mechanisms of turbulence production in the spiral wake around the core of a tip vortex. The model consists of a streamwise vortex sheet whose strength is found from Prandtl lifting line theory. A Gaussian streamwise velocity profile is superimposed on the field of the vortex sheet. This profile represents the spanwise vorticity. The integrated spanwise vorticity of this profile is zero. A novel feature of this study is that the mean flow contains both streamwise and spanwise vorticity. The model is then used to initialize the flow field for temporal LES of the instabilities of the spanwise vorticity during roll up. The results show that the sinuous mode prevails in the spiral wake around the core. The strength and streamwise length scale of the instability vary along the span because of the continuous variation of the wake thickness due to stretching by the tip vortex. The large scale structures produced by the instability of the spiral wake cause the formation of undulations on the core - consistent with the hypothesis of Devenport et al. (1996). / Ph. D.

An isolated wing-tip vortex from a square-tipped NACA 0012 wing at an angle of attack of 5 degrees was studied in a water tunnel at a chord based Reynolds number of approximately 24000. Measurements were taken using stereo particle image velocimetry at three measurement planes downstream of the wing under each of three freestream turbulence conditions. The amplitude of wandering of the vortex axis increased with increasing distance downstream of the wing and with increasing freestream turbulence intensity. The magnitude of the peak azimuthal velocity decreased with increasing distance from the wing as well as with increases in the freestream turbulence intensity. The streamwise velocity in the vortex core was less than the freestream velocity in all cases. Time resolved histories of the instantaneous waveform shape and location of the vortex axis were determined from sequences of images of fluorescent dye released from the wing.

An isolated wing-tip vortex from a square-tipped NACA 0012 wing at an angle of attack of 5 degrees was studied in a water tunnel at a chord based Reynolds number of approximately 24000. Measurements were taken using stereo particle image velocimetry at three measurement planes downstream of the wing under each of three freestream turbulence conditions. The amplitude of wandering of the vortex axis increased with increasing distance downstream of the wing and with increasing freestream turbulence intensity. The magnitude of the peak azimuthal velocity decreased with increasing distance from the wing as well as with increases in the freestream turbulence intensity. The streamwise velocity in the vortex core was less than the freestream velocity in all cases. Time resolved histories of the instantaneous waveform shape and location of the vortex axis were determined from sequences of images of fluorescent dye released from the wing.

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.