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Description

Title:Free response of a freely-rotatable eccentric linearly-sprung circular cylinder in or absent a cross-flow
Author(s):Ding, Ke
Director of Research:Pearlstein, Arne J
Doctoral Committee Chair(s):Pearlstein, Arne J
Doctoral Committee Member(s):Feng, Jie; Fischer, Paul F; Vanka, S. Pratap
Department / Program:Mechanical Sci & Engineering
Discipline:Mechanical Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Nonlinear Energy Sink, Vortex-Induced Vibration, Energy Transfer, Transient Chaos
Abstract:Suppression, or sometimes promotion, of vortex-induced vibration of a cylinder or other body is of interest in a number of applications, including design of marine structures, tall buildings, marine hydrokinetic energy systems, and operations involving mass transfer and chemical reaction. This has led to the development of a number of approaches to VIV control, with the circular cylinder being the prototypical body. In some of these applications (e.g., marine hydrokinetic energy harvesting), the cylinder can, in principle be allowed to rotate. For that class of systems, we propose a new approach, taking advantage of the fact that if the cylinder's center of mass does not lie on its axis of rotation, inertial coupling between cylinder rotation and rectilinear vibration of the cylinder will transfer energy between these two modes, in much the same way as in the earlier work of Tumkur et al. (J. Fluid Mech. 898, 196-235, 2017), Blanchard et al. (Phys. Rev. Fluids, 4, 054401, 2020), and Blanchard and Pearlstein (Phys. Rev. Fluids, 5, 023902, 2020) for a nonrotatable cylinder with an attached rotational "nonlinear energy sink". The key differences are that in the freely-rotatable case, no attached mass is required, and the cylinder rotation interacts directly with the flow through the no-slip boundary condition. Here, we report a computational investigation of a linearly-sprung rigid circular cylinder, allowed to oscillate transversely to a horizontal flow uniform far from the cylinder, and to rotate about the cylinder axis, which is taken to be vertical. The cylinder mass distribution is allowed to be "eccentric", in that the center of mass of the cylinder does not lie on the axis of rotation. This eccentricity leads to inertial coupling of rectilinear vibration to rotation, with the rotation being viscously damped due to friction with the shaft. Absent flow (i.e., the "dry" case), the equations of cylinder motion are identical to the case of a rotational nonlinear energy sink considered by Gendelman et al. (J. Appl. Mech. 79, 011012, 2012), in which a linearly-sprung primary mass undergoes rectilinear oscillation inertially coupled to the damped rotation of a point mass, leading to targeted energy transfer from the former to the latter. The body need not be a cylinder, and can have any shape and mass distribution, provided that its center of mass does not lie on the axis of rotation. The motion is governed by two dimensionless parameters (a rotational damping parameter, and an inertial coupling parameter), which have different interpretations in the point-mass case of Gendelman et al. than in our case. For two combinations of the parameters and an investigation of the motionless projection of the initial condition space (zero values of the rectilinear and rotational velocities), this work a) shows that all asymptotic solutions are either "zero-energy" (motionless) or "semi-trivial" (with no rotation, and purely harmonic rectilinear motion); b) uses a Floquet analysis to determine a multi-valued stability boundary separating orbitally stable semi-trivial solutions from unstable solutions, c) identifies within each range of orbitally stable solutions a single solution which has a large basin of attraction, d) identifies a region in the motionless initial condition space in which all initial potential energy is dissipated, and e) identifies and characterizes regions in the motionless initial condition space in which the asymptotic states are sensitive to initial conditions, giving rise to fractal and riddled basins of attraction. For the dry case, an approach is considered in which two barriers prevent rotation into a position where a semi-trivial solution exists, which necessarily requires that the asymptotic solution have zero energy. Previous work with a barrier considered has been restricted to the case in which the coefficient of restitution was less than unity, so that energy was dissipated each time impact with a rotational barrier occurs. Here, it is shown that inelastic impact is not required for complete dissipation of the initial energy, and that exclusion of the semi-trivial solutions is sufficient. Transition from regular oscillations to transient chaos is characterized in detail. In the "wet" case, in which a cross-flow interacts with a freely-rotatable, linearly-sprung circular cylinder having a not necessarily axisymmetric mass distribution, the stability boundary separating stable steady, symmetric motionless-cylinder (SSMC) solutions from unstable cases, including time-harmonic vortex-induced vibration (VIV) solutions and SSMC solutions that have undergone noninfinitesimal rotation from the initial orientation, is determined. Among other results, it is found that the steady flow past an eccentric, rotatable, linearly-sprung circular cylinder is stable over a range of Reynolds number and dimensionless spring constant for which flow past a nonrotatable sprung cylinder is unstable. This work provides an approach to completely suppress or excite VIV by removing or imposing rotational damping, depending on the phase at which the damping is removed or imposed. It thus demonstrates that a separate rotating element (which must be placed inside the cylinder, or beyond the spanwise extent of the cylinder) used Blanchard and Pearlstein (Phys. Rev. Fluids, 5, 023902, 2020), is not necessary, and that the "switching" demonstrated by those authors can be accomplished using a circular cylinder with an eccentric center of mass. The response when a pair of rotational barriers is added to restrict rotational motion is also investigated.
Issue Date:2021-10-12
Type:Thesis
URI:http://hdl.handle.net/2142/113790
Rights Information:Copyright 2021 Ke Ding
Date Available in IDEALS:2022-04-29
Date Deposited:2021-12


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