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 Title: On the dynamics of rigid and flexible structures under complex flows Author(s): Jin, Yaqing Director of Research: Chamorro, Leonardo P. Doctoral Committee Chair(s): Chamorro, Leonardo P. Doctoral Committee Member(s): Bentsman, Joseph; Ewoldt, Randy H.; Yan, Jinhui Department / Program: Mechanical Sci & Engineering Discipline: Mechanical Engineering Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): structure dynamics complex flows Abstract: Fluid-structure interaction (FSI) is a ubiquitous phenomenon of high relevance in engineering systems. During the past decades, substantial efforts have been placed on characterizing the dynamics of structures under a wide range of flow. However, associated phenomena under turbulence are poorly understood. Quantitative description of the non-linear, multiscale interaction between structure dynamics and flow remains as an outstanding open problem in science and engineering. Uncovering the dominant mechanisms modulating the dynamics of flow and structures would allow to significantly improve the design, reliability and life span of a wide range of engineering systems. This thesis aims to contribute in that direction by presenting experimental and theoretical results of selected FSI problems, which addressed the role of structure geometry, stiffness and flow. They include the oscillations of slung prisms, passive and active splitter pitching in the wake of cylinders, the effect of directional stiffness, and the unsteady dynamics of wall-mounted flexible plates, which are briefly summarized as follows. The pendulum-like oscillation and pitching patterns of cubic and rectangular slung prisms were inspected for two aspect ratios at various Reynolds numbers $Re$ under two freestream turbulence levels. The results show that the dynamics of the prisms can be characterized by two distinctive regions depending on the prism shape. Specifically, in the case of cubic prism the regions are defined by the growth rate of the pitching amplitude, whereas the dynamics of the rectangular prism is more sensitive to the angle of attack. In particular, when the large side initially faced the flow, the regions were defined by the synchronization between the vortex shedding and pure oscillations under very low turbulence. When the smaller side initially faced the flow, the regions were defined by the equilibrium pitching position. Regardless of the geometry of the prism and flow condition, the dominating oscillation frequency resulted close to the natural frequency of the small-amplitude pendulum-like oscillation. The distinctive pitching of hinged splitters in the trailing edge of elliptic cylinders was experimentally studied at various angles of attack ($AoA$) of the cylinder, Reynolds numbers and splitter lengths of the cylinder and freestream turbulence levels. Results show that the motions of the splitters contained dominating modes, $f_p$ and $f_v$, which were induced by the mean flow and wake dynamics. High background turbulence dampened the coherence of the regular vortex shedding leading to negligible $f_v$. For a sufficiently long splitter, namely twice the semimajor axis of the cylinder, dual vortex shedding mode occurred close to the leading and trailing edges of the splitter. In general, the splitters oscillated around an equilibrium position nearly parallel to the mean direction of the flow; however, a skewed equilibrium was also possible with a strong recirculation region. The flow and drag induced by active pitching of plates in the wake of a cylinder of diameter $d$ were experimentally studied for various plate lengths $L$ as well as pitching frequencies $f_p$ and amplitudes $A_0$. Results show the distinctive effect of the active pitching on these quantities. In particular, flow recovery was significantly modulated by $L$, $f_p$ or $A_0$. Specific pitching settings resulted in the wake with dominant meandering patterns and faster flow recovery. We defined a modified version of the amplitude-based Strouhal number of the system $St_S$ to account for the effect of the cylinder in the active pitching. It characterized the drag coefficient $C_d$ across all the cases studied, and revealed two regions intersecting at a critical value of $St_S\approx 0.2$. Below this value, the $C_d$ remained nearly constant; however, it exhibited a linear increase with increasing $St_S$ past this critical point. Inspection of the integral momentum equation showed the dominant role of the velocity fluctuations in modulating $C_d$ past the critical $St_S$. Flow-induced dynamics of flexible structures is, in general, significantly modulated by periodic vortex shedding. My work shows that for structures with directional stiffness, K$\acute{a}$rm$\acute{a}$n vortex shedding may dominate the wake of bodies governed by the natural frequency. This phenomenon can be a consequence of Kelvin-Helmholtz ($K-H$) instability, where the structural characteristics of the body dominate the oscillations. In addition to a single structure, the dynamics of two rectangular, flexible plates of low aspect ratio $h/b$ (height/width = 4) was experimentally investigated in tandem arrangements under uniform flows at various Cauchy numbers $Ca\in [15,\ 77]$, and spacing $s_x=\Delta x/h=0.5,\ 1$ and 2. Results show that the oscillations of the upstream plate were dominated by its natural frequency. However, the motions of the downstream plate were significantly modulated by the induced flow and coherent motions shed from the upstream structure. Despite that the intensity of the oscillations of the upstream plate increased monotonically with $Ca$, this was not the case for the downstream plate at $s_x=1$ and 2 due to flow fluctuations, vortex shedding and large structure deformation. As a result, it exhibited a local minimum. Supported with measurements, a mathematical model was derived to quantitatively explain this behavior. The unsteady dynamics of wall-mounted, flexible plates under inclined flows was fundamentally described using theoretical arguments and laboratory experiments under various Cauchy numbers $Ca=\rho_fbL^3U_0^2/(EI)\in[8,83]$ (where $\rho_f$ is the fluid density, $b$ and $L$ are the plate width and length, $U_0$ is the incoming velocity, $E$ is the Young's modulus and $I$ is the second moment of the area) and inclination angles $\alpha$. Three-dimensional particle tracking velocimetry and high-resolution force sensor were used to characterize the evolution of the plate dynamics and aerodynamic force. We show the existence of three distinctive, dominant modes of tip oscillations, which are modulated by the structure dynamic and flow instability. The first mode is characterized by small-amplitude, planar fluttering-like motions occurring under a critical Cauchy number, $Ca=Ca_c$. Past this condition, the motions were dominated by the second mode consisting on unsteady twisting superimposed to the fluttering patterns. The onset of this mode was characterized by a sharp increase of the force fluctuation intensity. At sufficiently high $Ca$ and $\alpha$, the plate may undergo a third mode given by large-scale tip orbits about the mean bending. Using the equation of motion and first-order approximations, we propose a formulation to estimate $Ca_c$ as a function of $\alpha$; it exhibits solid agreements with experiments. Issue Date: 2019-06-06 Type: Text URI: http://hdl.handle.net/2142/105594 Rights Information: Copyright 2019 Yaqing Jin Date Available in IDEALS: 2019-11-26 Date Deposited: 2019-08
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