In many engineering applications involving mixing of highly viscous fluids or mixing at micro-scales, efficient mixing must be accomplished in the absence of turbulence. Similarly in geophysical flows large-scale, deterministic flow structures can account for a considerable portion of global transport and mixing. For these types of problems, concepts from non-linear dynamical systems and the theory of chaotic advection provide the tools for understanding, quantifying, and optimizing transport and mixing processes. In this thesis chaotic advection is studied numerically in three, steady, experimentally realizable, three-dimensional flows: 1) steady vortex breakdown flow in a cylindrical container with bottom rotating lid, 2) flow in a cylindrical container with exactly counter rotating lids, and 3) flow in a new model stirred-tank with counter-rotating disks. For all cases the three-dimensional Navier-Stokes equations are solved numerically and the Lagrangian properties of the computed velocity fields are analyzed using a variety of computational and theoretical tools. For the flow in the interior of vortex breakdown bubbles it is shown that even though from the Eulerian viewpoint the simulated flow fields are steady and nearly axisymmetric the Lagrangian dynamics could be chaotic. Silnikovs mechanism is shown to play a critical role in breaking up the invariance of the bubble and giving rise to chaotic dynamics. The computations for the steady flow in a cylindrical container with two exactly counter-rotating lids confirm for the first time the findings of recent linear stability studies. Above a threshold Reynolds number the equatorial shear layer becomes unstable to azimuthal modes and an intricate web of radial (cats eyes) and axial, azimuthally-inclined vortices emerge in the flow paving the way for extremely complex chaotic dynamics. Using these fundamental insights, a new stirring tank device with exactly counter-rotating disks is proposed. Results show for the first time that counter rotation of the middle disk in a three-disk stirred tank can create a flow with large chaotic regions. The results of this thesis serve to demonstrate that fundamental studies of chaotic mixing are both important from a theoretical standpoint and can potentially lead to valuable technological breakthroughs.

A numerical study of flow of power law fluid in an elbow bend has been carried out. The motivation behind this study is to analyze the velocity profiles, especially the pattern of the secondary flow of power law fluid in a bend as there are several important technological applications to which such a problem has relevance. This problem especially finds applications in the polymer processing industries and food industries where the fluid needs to be pumped through bent pipes. Hence, it is very important to study the secondary flow to determine the amount of power required to pump the fluid. This problem also finds application in heat exchangers.

The flow field in an annular seal is simulated for synchronous circular whirl orbits with 60Hz whirl frequency and a clearance/radius ratio of 0.0154 using the Fluent Computational Fluid Dynamics (CFD) code. Fluent's Moving Reference Frame model (MRF) is used to render the flow quasi-steady by making transformations to a rotating frame. The computed flow fields for velocity, pressure and shear stress measurements are compared with the experimental data of Winslow, Thames and Cusano. The CFD predictions are found to be in good agreement with the experimental results. The present CFD methodology can be extended to other whirl frequencies and clearances. The dynamic wall pressure distributions in an annular seal for non-circular whirl orbits were obtained using CFD. The simulations were performed using a time dependant solver utilizing Fluent's Dynamic Mesh model and User Defined Functions (UDFs). The wall pressure distributions obtained from the simulations are compared with data of Cusano. The CFD simulations over predicted the pressure field when compared to experimental results however the general trends in pressure contours are similar. The flow fields for varying rotor eccentricities are also studied by performing coordinate transformations and rendering the flow quasi-steady at set eccentricities using Fluent's MRF model. The computed velocity and pressure fields are compared with the time dependant solution obtained using Fluent's Dynamic Mesh model and UDFs for the same eccentricity. Good agreement in the velocity fields is obtained; however the pressure fields require further investigation. 2D Labyrinth seal simulations were performed for comparisons with experimental LDA data from Johnson. The velocity fields match the experimental LDA data to a fair degree of extent; however, Fluent simulations under predicted the secondary recirculation zones in Labyrinth Backward Swirl (LBS) case.

Thesis (M.S.)--Missouri University of Science and Technology, 2010. / Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed Jan. 5, 2010). Includes bibliographical references (p. 52-53).

Thesis (Ph. D.)--Ohio State University, 2009. / Title from first page of PDF file. Includes bibliographical references (p. 239-251).

CFD simulations were used to study single phase and multiphase flows through structured packing. Simulations utilizing a high fidelity, digital copy of a packing element were validated against experimental results for both single phase and multiphase flows. Single phase simulations were carried out on a variety of periodic packing elements to examine the impact of packing channel geometry on pressure drop. Multiphase simulations on periodic elements were used to examine the effect of hydrodynamic properties and boundary conditions. Single-phase simulations of nitrogen flow through the high fidelity geometry produced via X-ray CT scans showed average deviations less than 15% when compared to experimental measurements. This error was reduced to 7% when a mesh utilizing prism layers to accurately resolve the boundary layer was used. With a validated model for single phase flow, the application of CFD to packing design was investigated on periodic geometries with varied packing parameters (e.g. channel corrugation angle and channel side length). It was found that current industrial packings have channel geometries maximizing pressure drop, indicating some degree of optimization around channel geometry is possible depending on separation needs. Multiphase simulations using the Volume of Fluid model examined the effects of liquid density, viscosity, surface tension, and contact angle on small-scale packing geometries. Contact angle had the most pronounced influence on predicted wetting, and simulations demonstrated that using experimentally determined static contact angles was not an appropriate choice for the simulation contact angle. The predicted influence of surface tension qualitatively matched experimental data for wetted area. Liquid viscosity and density also demonstrated qualitative agreement with semi-empirical models derived from experimental data. Experimental data collected via absorption of CO2 into 0.1 mol/L NaOH were compared to simulation predictions using a geometry generated via X-ray CT scans. Wetted area predictions matched experimental data best when a fully wetting static contact angle (0°) was used, yielding simulated results 3.4% lower than experimental data on average. Irrigated pressure drop and holdup predictions were significantly higher than experimental data. / text

published_or_final_version / Electrical and Electronic Engineering / Master / Master of Philosophy

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