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Title:Lagrangian dynamics of turbulence: Applications with 3D particle tracking velocimetry
Author(s):Kim, Jin Tae
Director of Research:Chamorro, Leonardo P
Doctoral Committee Chair(s):Chamorro, Leonardo P
Doctoral Committee Member(s):Rogers, John A; Best, Jim; Feng, Jie
Department / Program:Mechanical Sci & Engineering
Discipline:Theoretical & Applied Mechans
Degree Granting Institution:University of Illinois at Urbana-Champaign
Lagrangian Dynamics
Jellyfish propulsion
Jet flows
Abstract:Lagrangian dynamics of turbulence allow for a distinct characterization of the motion of particles. It is particularly useful in the understanding of dispersion, mixing, and transport phenomena. Due to the complexity and difficulty in quantifying Lagrangian properties, experimental studies on turbulence-driven phenomena in the Lagrangian frame of reference are comparatively limited and mostly focused on homogeneous and isotropic turbulent flows. In this work, I optimized a customized three-dimensional Particle Tracking Velocimetry (3D-PTV) to explore the Lagrangian dynamics of selected turbulent problems. 3D-PTV is a quantitative flow measurement technique that aims to track the Lagrangian paths of a set of particles in three dimensions using stereoscopic imaging. This dissertation focused on four cases of inhomogeneous and anisotropic turbulent flows including jets from various nozzle geometries, the transient jet-like induced by a single jellyfish, and the dynamics of Rayleigh B\'{e}neard (RB) convection cell coupled with inertial particles. Turbulent jets from circular and semi-circular pipes were characterized with 3D-PTV in the intermediate and far fields. Probability density functions (PDF) of the velocity fluctuations show a departure from the Gaussian distribution away from the jet core. PDF of the Lagrangian acceleration exhibit heavy tails in both geometries; however, the curvature PDF revealed a distinct footprint of the pipe shape. In addition, a rich data-set of Lagrangian trajectories was used to study the structure of various acceleration components, vorticity, and strain. The Lagrangian acceleration is decomposed into three distinctive sets: (1) streamwise-radial; (2) tangential-normal; and (3) local-convective components. The PDF and the joint distributions of each set are characterized at various radial locations from the jet core within a streamwise band $16 \leq x/d_h\leq 17$, where $d_h$ is the diameter of the pipe. The acceleration components are described by two distinctive distributions: one of them exhibits symmetry and heavy tails, whereas the other is best fitted by a power-law type. The increase departure from the Gaussian distribution with the distance from the core is a result of the increasing turbulence levels promoted by the mean shear. The variation of the third and fourth moments between the streamwise-tangential and the radial-normal accelerations evidence the anisotropy of the jet. Lagrangian statistics and pair dispersion induced by a single pulse of a small jellyfish were quantified using 3D-PTV. The PDFs of the Lagrangian velocities exhibit more intense mixing in the radial direction and reveal three stages defined by flow acceleration, mixing, and dissipation. The time evolution of the Lagrangian acceleration variance confirms each phase. Also, the flow reveals characteristics of homogeneous isotropic turbulence during the mixing phase. We show that this biological flow may induce rich wake dynamics characterized by pair dispersion with a super-diffusive $t^3$ regime, followed by a coherent $t^2$-Batchelor scaling and then $t^1$-Brownian motions. Kolmogorov microscales during the fully mixed phase were computed with three distinct approaches, including Heisenberg-Yaglom relation, the fluctuating rate of the strain tensor in the Eulerian frame, and the Batchelor scaling in pair dispersion. Turbulent Rayleigh-B{\'e}nard (RB) convection at aspect ratios $\Gamma=1.2$ and 2 was investigated using 3D-PTV to uncover distinctive Lagrangian statistics of thermal plumes. A laterally extended investigation volume allowed for capturing dynamics of the high vertical motion. The PDFs of the vertical Lagrangian acceleration exhibit heavier tails than the lateral acceleration. The second-order PDFs indicate that the intense vortical motion promotes stronger vertical acceleration than the lateral counterpart. As the second part of Lagrangian dynamics in a RB convection, the dynamics of rising air bubbles in turbulent Rayleigh-B\'{e}nard (RB) convection is experimentally described for the first time using 3D-PTV. Streams of 1-mm bubbles were released at various locations from the bottom plate. Results show that $R^2(t)$ underwent a transition phase like the ballistic-to-diffusive ($t^2$-to-$t^1$) regime in the vicinity of the cell center; it approaches to a bulk behavior $t^{3/2}$ in the diffusive regime as increasing the distance from the cell center. $R^2(t)\propto t^1$ is shown in the diffusive regime with a lower magnitude than the quiescent case at small $r$, indicating that the convective turbulence reduced the amplitude of the bubble's path instability. $R^2(t)\propto t^2$ was observed at large initial separations, showing the effect of the roll structure.
Issue Date:2020-05-04
Rights Information:Copyright 2020 Jin Tae Kim
Date Available in IDEALS:2020-08-27
Date Deposited:2020-05

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