Dynamics of longitudinal wake vortices

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Authors
Kliment, Linda K.
Issue Date
2009-07
Type
Dissertation
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en_US
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Abstract

In the present study, the mid-field vortex wake is investigated. For the most part, the results focus on the motion of a pair of co-rotating vortices prior to merger, both in and out of ground effect. However, in order to verify the experimental and computational methods, results for single vortices, counter-rotating pairs, and complex wakes are also presented. A method is presented which allows measurement of the time dependent motion of vortex filaments. This optical method interferes minimally with the wake and allows recording of vortex location and time-dependent motion. From the position and time information recorded, extraction of the amplitudes of motion, core motion, spiraling behavior, vortex strengths, and the principal planes of motion is possible. First, a single vortex is studied in order to establish a basis for comparison. The dye remains in the core and the motion of a single vortex is shown to exhibit a growth in amplitude with increasing downstream distance and strength. The core motion is shown to be minimal, remaining smaller that one core diameter. In addition, when the single vortex is forced to oscillate at a given frequency, the dye still remains in the core, even though the amplitudes of motion are large. The forcing frequency is identified easily against the background noise. Two four-vortex cases are then presented. The first case consists of filaments that spiral while in the second they scatter. These results are consistent with those shown in literature and show that the experimental method can be used for analyzing complex wakes. Pairs of unforced, co-rotating filaments are studied outside of ground effect. Many cases are presented, some for nearly equal strengths and others in which one vortex is much stronger than the other. As in the single-vortex case, the amplitudes of motion are shown to increase as the downstream distance becomes greater. The constant rate of spiraling is shown to increase as the vortex strength increases and vortex span decreases. Vortex span either remains constant or decreases with downstream distance depending on the vortex separation distance. The motion of the center of spiraling is shown to be minimal, similar to the motion of the vortex core in the single-vortex cases. The filaments are shown to sometimes oscillate along preferred directions, which is inconsistent with a theoretical model developed in 1975. A few cases are also presented in which the merger location is analyzed. However, these are visual investigations only, since it is not possible to obtain quantitative data for such cases with the experimental method available. The behavior of co-rotating vortices in the presence of forcing functions is then presented. The results are compared to the theoretical model developed in 1975 and those published after 2002. However, a direct comparison with analytical results is not possible due to the large scatter in the experimental data. Regardless, the experimental results show that the forced corotating vortices do have an unstable oscillatory motion with growing amplitude. The preferred direction of motion implies the presence of stationary waves. These results contradict those of the analytical model developed in 1975 but agree in nature with those published more recently. Ground effect is then considered for counter-rotating vortices, because there is a wealth of information on this topic in the literature. When counter-rotating vortices are near a ground plane, a lateral drift as well as a rebounding behavior is present. The counter-rotating vortices are shown to have a preferred direction of motion which tends to become parallel to the ground plane. The motion is also shown to have increasing amplitude, although this quantity is slightly reduced by the presence of the ground plane. In addition, ground roughness in the form of streamwise ridges has no affect on the vortex trajectories, within the range of downstream distances observable in these experiments. After comparing the results to those in literature, it is concluded that the experimental method is valid and can be used to study co-rotating vortices in ground effect. Literature lacks information on co-rotating vortices in ground effect. The results in this document show that co-rotating vortices in ground effect have a lateral drift as well as a rebound similar to those of counter-rotating pairs. The resulting motion is similar to that of leapfrogging vortex rings. Preferred directions of motion are present, although no trend can be established. In addition, the amplitudes of motion are reduced slightly by the presence of the ground, just as they are for the counter-rotating vortices. Due to the lack of information on co-rotating vortices in ground effect in the current literature, a comparison is impossible. Therefore, two simple computation efforts are undertaken in order to verify some of the flow features. Using a two-dimensional viscous analysis, limited to laminar flow, it is shown that when co-rotating vortices are placed near a stationary wall, a boundary layer forms on the surface and separates. The secondary vortex released by boundary layer separation leads to rebounding of the primary vortices. In addition to affecting the trajectory, the no-slip boundary also affects the time to vortex merger as well as leading to an elongation of the vorticity contours. Furthermore, this analysis demonstrates that making the strengths of the two vortices differ slightly does not affect the spiraling rate, surface boundary layer separation, or rebound. A second inviscid model is also used to study cases consisting of two vortices of unequal strengths. Having unequal strengths does affect the lateral drift of corotating vortices in ground effect. Also, the center of spiraling shifts towards the stronger vortex. However, the inviscid model shows that the vortex span is unaffected by difference in strengths.

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Thesis (Ph.D.)--Wichita State University, College of Engineering, Dept. of Aerospace Engineering
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Wichita State University
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