Fluid-Structure Interaction in Viscous Dominated Flows Public Deposited

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  • March 19, 2019
Creator
  • Zhao, Longhua
    • Affiliation: College of Arts and Sciences, Department of Mathematics
Abstract
  • Theoretical, numerical and experimental studies for several flows in the Low Reynolds number regime are reported in this thesis. It includes the flow structure and blocking phenomena in linear shear or rotation flow past an embedded rigid body, and flows induced by a slender rod precessing a cone to imitate the motion of nodal cilia are studied with the singularity method. The first subject is to explore interesting phenomena emerging in the fundamental problem of shear flow past rigid obstacles. An analytical and computational study of Lagrangian trajectories for linear shear flow past a sphere or spheroid at low Reynolds numbers is presented. Using the exact solutions available for the fluid flow in this geometry, we explore and analyze blocking phenomena, local bifurcation structures and their influences on dynamical effects arising in the fluid particle paths. In particular, based on the work by Chwang and Wu who established a blocking phenomenon in two-dimensional flows, whereby a cylinder placed in a linear shear prevents an unbounded region of upstream fluid from passing the body, we show that a similar blocking exists in three-dimensional flows. For the special case when the sphere is centered on the zero-velocity plane of the background shear, the separatrix streamline surfaces which bound the blocked region are computable in closed form by quadrature. With such analytical results, we study the foliation of the physical material streamline surfaces, identify the separation in the flow, and measure the blocked flow. When the sphere's center is out of the zero-velocity plane of the background shear, closed form expressions appear unavailable due to the broken up-down mirror symmetry. In this case, computations provide evidences for the persistence of the blocking region. Furthermore, a complex bifurcation structure in the particle trajectories is documented. We compute analytically the emergence of different critical points in the flow and characterize the global streamline topology associated with these critical points, which includes the emergence of a three-dimensional bounded eddy. Additionally, we study the case of a sphere embedded at a generic position in a rotating background flow, with its own prescribed rotation including fixed and freely rotating. Exact closed form solutions for fluid particle trajectories, stagnation points on the sphere, and critical points in the interior of the flow are derived. We extend our results further to spheroids as well, where similar blocking results are documented. The broken symmetry offered by a tilted spheroid geometry induces new three-dimensional effects on the streamline deflection, which can be viewed as effective positive or negative suction in the horizontal direction orthogonal to the background flow depending on the tilt orientation. We close this study with results of a spheroid embedded in a rotating background flow, with its own prescribed tilt orientation. Net fluid transport is observed in this flow, where the direction of transport depends on the direction of the background rotation and the tilt orientation of the spheroid. The study in the second part of this thesis is motivated by the intriguing properties of airway surface liquids in ciliated tissues, and in particular we aim at detailed understanding and theoretical prediction of certain aspects of the fluid dynamics arising in developing embryos. The fluid motion induced by spinning cilia is fundamental to many living organisms. Under some circumstances it is appropriate to approximate cilia as slender rigid rods. We study the effects of shape and orientation of these idealized cilia upon flow structures in a Stokes fluid. In this topic, we model the cilia-induced flow with the slender body theory and imitate the rotary motion of an isolated cilium by spinning a slender rod in highly viscous fluids. By utilizing the slender body theory and the image method, an asymptotic solution is constructed for a slender body attached to a no-slip plane and rotating about its base to sweep out a cone. With fully 3D stereoscopic images for the table-top experiment, 3D experimental particle tracking is constructed. We explore the complex flow structures and present quantified comparisons with the theoretical predictions. Intriguing short, intermediate and long time phenomena of particle trajectories are documented, and the intricacies of their theoretical modeling reported.
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  • In Copyright
Advisor
  • McLaughlin, Richard
  • Superfine, Richard
  • Vicci, Leandra
  • Forest, M. Gregory
  • Miller, Laura
  • Camassa, Roberto
Degree
  • Doctor of Philosophy
Degree granting institution
  • University of North Carolina at Chapel Hill Graduate School
Graduation year
  • 2010
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