Date

2018

Document Type

Dissertation

Degree

Doctor of Philosophy

Department

Mechanical Engineering

First Adviser

Rockwell, Donald O.

Abstract

The study of wingtip vortices and their evolution has been an important topic due to the wide range of applications where they occur. In the present investigation, the evolution of a vortex from an oscillating wing, as well as its subsequent interaction with a downstream (follower) flat plate (wing), is characterized using particle image velocimetry, which leads to patterns of velocity, vorticity, swirl ratio and streamlines on cross-flow planes along the undulating vortex formed from an isolated wing undergoing controlled oscillation. For the case where the undulating vortex impinges upon a downstream wing, similar crossflow representations are used to characterize the flow structure. Additionally, a reconstruction technique is utilized to provide volumetric, global patterns of the streamwise development of the unsteady vortex, as well as its interaction with, and distortion along a downstream plate.The evolution of the vortex from an oscillating wing undergoing small amplitude perturbations shows large fluctuations of axial velocity deficit and circulation during the oscillation cycle. Correspondingly, large variations of swirl ratio occur and the onset of pronounced azimuthal vorticity arises. At a given cross-section of the vortex, the pattern of azimuthal vorticity moves around its axis in an ordered fashion as both it and the pattern of velocity defect increase in magnitude and scale. When the swirl ratio attains its minimum value during the oscillation cycle, and this value lies below the theoretically-established critical threshold for amplification of azimuthal modes, the magnitude and scale of the pattern of azimuthal vorticity is maximized. Subsequent increase of the swirl ratio yields attenuation of the azimuthal vorticity. Onset of pronounced azimuthal vorticity when the swirl ratio decreases, involves rapid amplification, then disruption, of the axial vorticity fluctuation.The onset and development of orbital motion of a trailing vortex from an oscillating wing has also been characterized; its response is frequency dependent. At low Strouhal number, the amplitude of the unidirectional excursion of the vortex remains essentially constant with streamwise distance and has a magnitude of the order of the amplitude of the wing oscillation. At moderate Strouhal number, the initial region of the vortex motion is unidirectional, but at larger streamwise distance, excursions of the vortex occur orthogonal to its initial unidirectional motion, thereby giving rise to an elliptical orbital trajectory oriented in the opposite direction to the circulation of the vortex. At high Strouhal number, the amplitude of the vortex undulation increases by nearly an order of magnitude with streamwise distance, and pronounced orbital motion of the vortex has the same sense as the vortex circulation at all streamwise distances. The genesis of orbital motion is small amplitude lateral motion of the forming vortex at the trailing edge of the wing during its controlled vertical motion; moreover, the phase shift of the vortex development relative to the wing motion is altered with respect to that at lower values of Strouhal number. Irrespective of the value of either the Strouhal number of excitation or the streamwise location along the undulating vortex, generic physical mechanisms occur. Changes in curvature along the vortex are closely related to changes in the axial velocity deficit, axial vorticity and swirl ratio, as well as, the onset and attenuation of pronounced azimuthal vorticity.Additionally, large time-dependent variations of the flow structure of the perturbed trailing vortex that impinges upon and develops along a flat plate located downstream are evident, relative to a steady vortex-wing interaction. The nature of the vortex-wing interaction is influenced by the spanwise location of vortex impingement on the wing and the time-dependent variations of the structure and position of the incident vortex. When the incident vortex is aligned with the tip of the wing, the upwash of the incident vortex gives rise to separation at the tip of the wing and an opposite-signed tip vortex is induced, thereby forming a dipole with the incident vortex. Contrary to the mode of the steady vortex dipole interaction with the wing, the dipole structure rotates around the tip of the wing in an ordered manner. Variations in the upwash of the incident vortex alter the strength of the induced vortex. When the incident vortex impinges inboard of the tip of the wing, it induces a vortex of same sign vorticity at the wingtip due to the downwash of the incident vortex, which causes separation at the tip. At the leading edge of the wing the incident vortex bifurcates and an induced vortex at the tip of the wing is evident. Moreover, vorticity of opposite sign, relative to that of the incident vortex, is evident across the wing surface during this bifurcation. It is also evident when the incident vortex is positioned above the wing. This occurs as a result of the gradient of spanwise velocity in the vertical direction; in other words, the change in spanwise velocity extending over the vertical distance from the surface of the wing to the center of the incident vortex.

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