Dynamics of vortex shedding from slender cones
The dynamics of vortex shedding from bluff bodies has been investigated experimentally for many decades, with the simple geometric case for the investigation being a uniform circular cylinder aligned with its axis normal to the flow. Even though much information regarding the dynamics of the flow has been accumulated over the years, the actual understanding of the phenomenon has progressed slowly. The motivation for the present study comes from the fact that the vast majority of previous work has been concerned with the shedding of vortices from uniform cylinders with the flow normal to its axis. This classic arrangement is seen to produce vortices that are parallel to the axis of the cylinder, depending on the endconditions. Even this seemingly simple symmetric arrangement is seen to produce results characterised by large discrepancies and varied interpretations. The question that one could ask now is what would happen if there were a slight variation in the geometry of the cylinder. A linear variation of the diameter of the body along its span would raise additional problems, but on the other hand might provide new and useful insight to the problem of vortex shedding itself, since the cross-section would still be circular. In this work a comprehensive study of the effect of the introduction of a slight spanwise taper on the phenomenon of vortex shedding is presented. The study involved the extensive use of experimental data obtained using hot-wire anemometry and particle image velocimetry techniques. The effect of the taper on the onset of vortex shedding and the variation of vortex shedding along the span are two of the topics that are investigated in the present work. Even though the cross-section of these cones was circular the onset of vortex shedding was delayed, with the extent depending on the severity of taper. The results of the study of onset characteristics were also seen to be of importance in the investigation/prediction of transonic buffet onset on twodimensional airfoils. It is known that near the critical conditions for the onset of transonic buffet, there is flow separation followed by large scale lift oscillations. Global flow instability has been shown to be a source of this unsteadiness (Crouch et al., 2009). Crouch et al. (2007) considered a generalised approach to predicting the onset of flow unsteadiness based on the global-stability theory. In order to assess the generalised approach they studied the onset of vortex shedding about a cylinder cross-section as a limiting case in 2-D. A study of the onset of unsteadiness about more complex geometries such as cones using full 3-D unsteady Navier-Stokes simulations incorporating global stability analysis (Garbaruk et al., 2009) is seen to be more analogous to flows of practical interest, viz. flow about a tapered wing. The present work provided important data pertaining to the dynamics of vortex shedding from cones, with particular interest in the frequency of vortex shedding at the onset of unsteadiness. It is also shown that the taper ratio does have a major effect on the vortex shedding process, with the normal periodic shedding being replaced by a deeply modulated form. This non-linear amplitude modulation was found to be a global process controlling the vortex shedding all along the span of body, especially those with small taper ratios. Finally an attempt has been made to mathematically model the vortex shedding process in terms of non-linear oscillators, with a coupling that represents the interaction of the shed vortices along the span. It turns out that the modelling techniques using a series of spanwise oscillators with a simple coupling term, as seen in the literature, is not sufficient to fully represent the flow.
AuthorsJagadeesh, Chetan Sakaleshpur
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