Analysis, stability and control of wake flows past a circular cylinder: A numerical and theoretical study.
Item
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Title
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Analysis, stability and control of wake flows past a circular cylinder: A numerical and theoretical study.
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Identifier
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AAI9808012
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identifier
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9808012
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Creator
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Tang, Shaojie.
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Contributor
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Adviser: Nadine Aubry
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Date
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1997
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Language
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English
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Publisher
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City University of New York.
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Subject
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Engineering, Mechanical | Engineering, Aerospace | Engineering, Civil
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Abstract
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Two-dimensional wake flows past a circular cylinder have been investigated from low to moderately high Reynolds numbers, focusing on the stability and the control by means of low dimensional models and numerical simulations.;In the first part of this work, the impulsively started flow past a cylinder is computed by a two-dimensional direct numerical simulation over the range of Reynolds numbers {dollar}20\le Re\le 1000.{dollar} At low Reynolds numbers, the flow consists of twin vortices which are images of one another by reflection through the centerline. This bubble of vortices first grows with time, before saturating to a steady solution. As Reynolds number is increased further, the flow keeps its symmetric bubble structure for a short time, undergoes a symmetry breaking instability and develops into a shedding vortex street. This symmetry breaking is naturally captured in our numerical simulation in the sense that the vortex shedding develops without the necessity of any external forcing or perturbation, as well as artificially captured by introducing a particular perturbation. The critical Reynolds number is predicted by our numerical simulations to be 47.5. This (natural) symmetry breaking is found to be responsible for a significant increase in drag. Our results before and after the symmetry breaking events are compared with others' numerical and experimental results.;In the second part of this work, we concentrate on understanding and modeling the symmetry breaking bifurcation observed at {dollar}Re\ge 47.5{dollar} in our numerical simulations. Foppl's vortex model is studied here as a low dimensional model for the symmetric bubble. The stability analysis of a fixed bubble in the model shows that there are two asymmetric eigenmodes, a stable mode and an unstable one. We show by direct numerical simulations of the impulsively started flow past a circular cylinder how the instability properties of the model mimic those of the real flow.;In the third part of this work, we show how the introduction of two additional weak potential vortices in the model is capable of (neutrally) stabilizing the flow by making the real part of all eigenvalues of the Jacobian matrix zero. We then control vortex shedding behind a circular cylinder in numerically simulated viscous flows by inserting two small vortex perturbations. The control has the effect of either suppressing vortex shedding, making the flow converge toward a stable, symmetric bubble, or altering vortex shedding by generating a reversed Karman vortex street.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
